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Bast RC Jr, Kufe DW, Pollock RE, et al., editors. Holland-Frei Cancer Medicine. 5th edition. Hamilton (ON): BC Decker; 2000.

Cover of Holland-Frei Cancer Medicine

Holland-Frei Cancer Medicine. 5th edition.

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Chapter 38Cytokinetics

, MD, , MD, , MD, and , MD.

Cytokinetics is the study of the kinetics of cellular growth, a fundamental attribute of all multi-cellular life. Because oncology is the study of malignant growth, it is rooted, in a very fundamental sense, in this discipline. All the cardinal features of a cancer—its proclivity to increase in size, to disseminate, and to destroy the function of normal organs—are dependent on the reproduction of its cells. For this reason, growth kinetic concepts pervade clinical thinking in both overt and obscure ways. As evidence, we need only refer to the everyday language of clinicians, which is replete with kinetic terms: indolent growth, rapid growth, slow or no regression (“refractory to therapy”), and brisk regression (“responsive to therapy”). The meanings of these descriptive terms seem intuitive. They are, however, more complex and profound than a superficial familiarity would reveal. Is indolent growth always slow, never to accelerate? Is rapid growth always virulent, never to decelerate? How does the quantification of cellular proliferation relate to macroscopic growth patterns? What are the connections between growth rate and other attributes of cancer? Do the presumed sites of action of anticancer drugs, the disruption of mitosis, associate growth pattern with response to therapy? Is there a difference in this regard between the impact of drugs on cancer cells and on such rapidly proliferating host tissues as hematopoietic progenitors and gastrointestinal mucosa? How do new markers of oncogene expression, themselves related to multiple growth-related processes, relate to prognosis, natural history, and response to therapy?

An exciting development in the past decade has been the asking of these various kinetic questions in experimental treatment protocols. Can prognosis be predicted by pretreatment cytokinetic measurements? Does drug resistance emerge rapidly between diagnosis and the first opportunity to initiate chemotherapy? Is prognosis improved by shrinking a tumor mass as rapidly as possible, even before surgical removal? What is the optimal scheduling of non–cross-resistant chemotherapies? What is the relationship between drug dose and the rate of tumor regression? Can we use oncogene markers to plan treatment? These and similar issues are important to both the scientist who studies cytokinetics in cells, tissues, and tumors and the clinician who treats and studies patients.

The field of cytokinetics actually comprises two intertwined disciplines. The first is the study of cell proliferation. This is of interest not primarily in the biologic sense of examining how cells divide (which is discussed elsewhere in this volume), but in the numeric sense of studying how fast they divide, how many are dividing, and how biologic measurements, such as DNA content per cell and gene expression, relate to these kinetic processes. The second aspect of cytokinetics is growth curve analysis, the description of rates of change of cell number over time in both the unperturbed and perturbed (therapeutic) situation. The two disciplines are closely related, in that the kinetics of cellular proliferation partially determine the kinetics of tumor growth. In addition, both cellular proliferation and tumor growth are now thought to relate to many biologic characteristics of a cancer, including its tendency to invade, metastasize, and respond to drug therapy. Hence, this chapter will consider both disciplines, their connections, and their clinical implications.

Cell Proliferation

Mitotic Cycle: Percentage of Labeled Mitoses Curves

Mitosis, or cell division, is the basic biologic process that results in an increase in somatic cell numbers over time. The term growth applies to the increasing volume of a cellular population and is measured in units of volume (e.g., cubic centimeters) or weight (e.g., milligrams). Growth is largely the consequence of increasing numbers of cells but also can be influenced by the increasing size of the individual cells, edema, changes in the context of the extracellular matrix, hemorrhage, and infiltration by host cells, such as leukocytes. The term proliferation specifically applies to an increase in the number of cells, which is measured as cell number as a function of time. Cells divide by progressing through a sequence of steps that are collectively called the mitotic cycle. Other names for the mitotic cycle are the proliferative cycle, the generation cycle, and the cell cycle.

Classic autoradiographic techniques were first used to divide the cell cycle into four phases.1,2 The terms for these phases, described below, are still used today, although the method of assessment is now often biochemical or biophysical, not biologic as in the original usage.

The two key events in mitosis are the synthesis of DNA, which occurs mostly in the S-phase or S (for synthesis), and the actual division of the parent cell into two daughters during the M-phase or M (for mitosis). The M-phase is typified micromorphologically by the metaphase plate. The time gap between cell division and DNA synthesis is gap number 1, or G1. The time gap between DNA synthesis and cell division is gap number 2, or G2. Although the term mitosis is often used to refer to the M-phase, the adjective mitotic properly refers to all cells that are engaged in any portion of the whole process of self-replication. This whole process includes the submicroscopic events (G1, S, G2) that precede the M-phase, as well as the M-phase itself. This usage has the advantage of distinguishing cells that provide evidence of their intention to divide, from those cells, called G0 cells, that do not express that intention.

Cell cycle phases are best understood in the context of their means of quantification. The venerable mitotic index, the counting of metaphase figures in histologic slides, is of real scientific value. However, this is very labor intensive, so it has, unfortunately, decreased in popularity.3 An important variant of the mitotic index, also infrequently applied, is the stathmokinetic technique, in which a mitotic poison is applied prior to counting.4

Of all the older techniques, however, the most important, by far, is the thymidine labeling index (TLI).5 Here viable cells are exposed briefly in vitro to a radiolabeled precursor of DNA. The most common thymidine label is tritium (3H), but carbon 14 (14C) has also been used. The percentage of tumor cells with autoradiographic grains over their nuclei estimates the fraction of cells that were in S-phase during the period of thymidine exposure. Newer variants use monoclonal antibodies directed against proteins expressed during proliferation (see below) to allow mitotic (i.e., cycling) cells to be identified visually.6–8 In all these techniques, the microanatomy of the specimen is preserved so that the microscopist can actually know that the cell being counted is one of interest.

The highest refinement of the TLI is the percentage of labeled mitoses (PLM) curve. This technique counts, as a function of time after exposure, the number of M-phases that contain radioactive label. This measures the cells currently in M-phase that had been in S-phase during the exposure to radioisotope. The PLM method formerly was used to study human disease, but this application has been prohibited because it requires whole-body exposure to a long-lived radioisotope. In spite of its limitations, the technique has been of fundamental importance in the field of cytokinetics because it directly estimates the durations of phases of the cell cycle. Its theory is illustrated schematically in Figure 38.1. In Figure 38.1A, tritiated thymidine is administered as a pulse to label cells in the S-phase. As time passes (Fig. 38.1B), the labeled cells move beyond S and transverse G2. At this moment, no M-phase cells contain label, so the PLM is zero. Over the next short interval of time (Fig. 38.1C) labeled cells enter the M-phase. The PLM goes from zero to 100%, as shown in the graph at the bottom of Figure 38.1. The time elapsed from the pulse labeling to the achievement of 100% PLM is equivalent to the sum of the durations of G2 and M. The time required for the PLM to drop again to zero is the same as the time required for all the cells labeled during the S-phase to pass through their M-phase. This is the same as the duration of S-phase (Fig. 38.1D). If we follow the population through a second generation, the PLM will again rise from 0 to 100% (Fig. 38.1E). Figures 38.1C and 38.1E are the same except for a translocation in time, which is equivalent to one full cell cycle.

Figure 38.1. The mitotic cycle and percent labeled mitoses curve.

Figure 38.1

The mitotic cycle and percent labeled mitoses curve.

Actual PLM curves would be as sharp and as precise as is this hypothetic example were cycle lengths homogeneous and invariable, but, unfortunately, they are neither. Another complication is that because of the pharmacokinetics of radioisotopes and other technical considerations, it is rare for label ever to be present in all M-phase cells. Thus, sophisticated mathematic methods must be used to estimate phase lengths by model fitting.9 In spite of these limitations, however, almost everything that we now know concerning cycle dynamics has been learned from the PLM method.

It has been observed in animal models that the labeling index (LI) decreases with increasing tumor size, whether measured in cubic millimeters or milligrams.10,11 This is the major cause of a slowing of growth as a tumor (or a normal tissue, for that matter) gets larger. The consequences of this phenomenon is discussed below. The rate of decrease is slower for malignant than benign tissues, as demonstrated by the maintenance of high labeling indexes in large and metastatic cancers, also discussed below. Curve fitting has shown that the logarithm of the LI is linear in the logarithm of the tumor size. This may be related to the histologic architecture of the cancer, which is lost to varying degrees, compared with the tissue of origin. Structure may be quantified as a fractal (or mass) dimension.12 Less structure (more anaplasia) means that the fractal dimension is close to 3. Total loss of structure (complete anaplasia) would mean that the fractal dimension equals 3. The rate of decline of the LI is directly related to the fractal dimension, with more anaplastic tissues showing a slower rate of decline than the highly structured normal tissues from which they originated. Total lack of structure (anaplasia), with its fractal dimension of 3, is associated with exponential growth, without a rate of decline in the LI. The link between fractal dimension and LI might be that the cell number (N) relates to the diameter of the tissue (L) raised to the fractal dimension (D) power, while the volume of the tissue (V) is related to L3. Hence, N/V is related to V raised to the (d-3)/3 power, which decreases as V gets larger. If LI were proportional to N/V, as would be the case were the probability of mitosis determined by the concentration of a soluble growth factor produced by the cells, the relationship between LI and tumor size would be explained.13

Cell Cycle Phases and DNA Content

At its birth, a normal mammalian somatic cell contains a diploid number of chromosomes, and hence diploid (2N) DNA content. Following a successful cell division, the new cell generally experiences a time gap before it begins to engage in measurable DNA synthesis. Some very primitive or embryonic cells enter DNA synthesis immediately, but these are exceptions to the usual pattern. We have termed this gap G1, but a new cell is properly called G1 only if it exhibits the biologic intention of entering the S-phase. Should the cell never actually progress to the point of starting DNA synthesis, it would properly be classified as G0. Since both G0 and G1 cells are diploid in DNA content, we avoid the presumption of prescience by considering the two phases together. In performing this grouping, we recognize that the lengths of the G0-G1 phases are highly variable, fitting a log-normal probability distribution that is skewed markedly to the right, that is, toward longer times. Since the cells on the far right end of the distribution will never divide within the life span of the host, they are the G0 cells.

This statistical distinction between G0 and G1 has biologic correlates. Between their M- and S-phases, cells prepare to enter the S-phase by progressing through defined stages that are dependent on protein synthesis.14 These stages are regulated enzymatically by processes partially sensitive to such extracellular influences as growth factors and the supply of nutrients. Cancer cells may be less dependent on these external signals and conditions than are normal cells, which may account for their ability to grow in suspension cultures without extracellular matrix. This ability may be related to the activity of oncogenes or to the deregulation of suppressor genes, such as p53 or the retinoblastoma gene. The potency of genes like simian virus 40 large T antigen (SV40LT) to transform cells is particularly relevant to this point.15,16 Recently, it has been observed that normal human cells can be transformed by the insertion of three genes—SV40LT, hTERT (which encodes the catalytic subunit of telomerase), and an oncogenic ras—all of which convey some element of growth factor autonomy.17

Cells in G1 have already progressed beyond several preliminary steps to prepare for the S-phase, whereas G0 cells need further time to complete early synthetic events so that they can enter the G1-phase. These differences can be exploited in the laboratory to discriminate G0 from G1 cells. G0 cells tend to be smaller,18 and have lower RNA and protein contents than do G1 cells, as well as specific, characteristic messenger RNAs (mRNAs) and proteins.19,20 For example, the Ki-67 antigen is present in all mitotic cells (G1, S, G2, M), but is not found in G0 cells.8 Also, G0 cells do not metabolize the cationic dye rhodamine, which is thought, but has not been proven,21 to reflect the cells’ relatively low mitochondrial activity.22 However, G0 cells, in spite of their distinctive biologic characteristics, can be stimulated by external influences to proceed through the sequence of events that leads them into the G1-phase and eventually into the S-phase. This phenomenon is called recruitment.

After the M-phase, but before DNA synthesis accelerates, the cell either commits to proliferate by entering the S-phase or stops dividing by differentiating into a nonmitotic cell. The ratio G1/(G0 1 G1) at any one time defines the proportion of cells entering their next S-phase. A particular restriction point at the G1:S interface, now called Start, may be regulated by the p34cdc2 protein, which may couple with different cyclin proteins (whose levels vary within the cell cycle) to permit, alternately, a cell’s entry into the S- or its entry into the M-phase.23 Normally, the M-phase cannot take place unless the S-phase has been completed, and the S-phase cannot take place unless the M-phase has been completed. Abnormalities in this system could result in an unblocking of the normal “block to re-replication” which prevents parts of the genome from being replicated more than once during a single S-phase.24 Such abnormalities are one possible etiology for aberrant levels of DNA per neoplastic cell (see below). Once the cell enters the S-phase, its progression through the rest of the cycle is largely self-regulated.25 This regulation involves direct controls, in which a step must be completed before the next step commences, as well as indirect feedback loops.26

The S-phase, lasting between 12 and 24 hours in mammalian cells, is generally much less variable than the G0-G1 phase. Specific regions of chromosomes replicate at specific times, clusters of replication units initiating synchronously, with the whole complex process transpiring in a highly orchestrated manner.27 During the S-phase, a cell’s DNA content should increase from 2N to 4N. A very small number of S0 cells may actually stop synthesizing DNA before completing the S-phase.28 Their ultimate fate is unclear, although it is likely that some can resume the S-phase, while others are prevented from proceeding by intrinsic blocks in their self-regulation. Cells completing the S-phase enter the second gap, marked by a dramatic diminution in the rate of DNA synthesis. G2 usually lasts for about 3 hours in mammalian cells, ending when the M phase begins. Rarely, a cell can rest in the G2-phase and not proceed into actual cell division.29

The initiation of the M-phase may depend on the same molecular trigger as Start, but in a complex interplay with different cyclins and other factors, which are beyond the scope of this chapter.30 The M-phase is composed of several parts. In prophase, the cell assumes the shape of a sphere.31 The microtubules and microfilaments of the cell’s cytoskeleton rearrange, the Golgi apparatus disperses into small vesicles, protein synthesis drops, and the dispersed chromosomes (duplicated during the S-phase) cease metabolic activity and then condense into transportable units.32 During prometaphase, these units orient themselves linearly toward opposite ends of the cell and move to the midplane to form the metaphase plate. In anaphase, spindle fibers attached to kinetochores on each chromosome guide them toward centrosomes in opposite ends of the cell. In telophase, the nuclei reform, the chromosomes de-condense, and the cell normally divides into two approximately equal halves, one new nucleus per daughter cell. The M-phase is the least variable in length, lasting about 1 hour in most mammalian cells.

The total duration of the cell cycle varies considerably, but the average in human cancer is between 2 and 4 days. This is in marked contrast with the cell cycle in Drosophila, which may take minutes, or with that of mammalian embryos, which may take hours. Some normal cells, such as some human neurons, may never divide at all. Cancer is not always a disease of rapid proliferation, but it is always one of persistent proliferation. If a large number of cancer cells are dividing, even if they are dividing with deliberate speed, they will produce many offspring, which, by continuing to divide, will inevitably lead to an abnormal accumulation over time. For a given tissue, malignant or benign, the length of the cell cycle in vivo is fairly constant in spite of variations in the number of cycling cells in that population. However, subtle changes in cycle kinetics have been seen in cancers in laboratory animals that are allowed to grow large33,34 and phase lengths can shift significantly as cells are cultured in vitro.35 This is in addition to changes in the LI as tumor growth, discussed above.

Flow Cytometry

The variation in cellular DNA content during the proliferative cycle can be exploited analytically by a collection of automated methods called flow cytometry. Visual procedures, such as mitotic index, TLI, and static Ki-67 staining, are slow, laborious, and subjective. These negative features may change with technologic advances in assessing cellularity on slides and in the automated counting of visually distinctive cells.36,37 At present, however, flow methods are the most rapid and quantitative.38 The major disadvantage of such techniques as flow cytometry, in which the cells being analyzed are not visualized, is that normal stromal cells, normal blood cells, and tumor cells of various types and degrees of oxygenation are all counted together. Another disadvantage is that reliable flow cytometry requires meticulous technique and hence constant attention to quality control. Nevertheless, flow cytometry has become the most widely applied method of cytokinetic assessment in the modern clinic. Hence, it has been the most productive in terms of accumulation of literature.

In fluorescence-activated cell sorting, a suspension of individual cells is automatically counted by being allocated into bins by DNA content, RNA content, cell size, antibody label, or combinations of such factors.39,40 This can be performed on fresh tissue—leukemias, tumor cells in effusions or ascites, enzymatically dispersed solid tumors—or on cells recovered from paraffin-embedded specimens.41 Enzymatic methods of dispersing fresh or fixed solid tumor specimens have been shown to produce high single-cell yields, representative of the tissue as a whole, with low degrees of contamination by cellular debris.42

Flow cytometry can be used to measure RNA per cell, which, as mentioned above, is helpful in distinguishing G0 from G1 cells. Various techniques of tagging cells for the purpose of sorting are being employed. For example, cells can be labeled by the Ki-67 antibody (conjugated to a fluorescent dye).8 Unfixed, viable cells can be exposed to bromodeoxyuridine, which is incorporated during the S-phase.43 These cells will then react with an antibromodeoxyuridine antibody tagged with a fluorescent dye, a method that has proven reliable in studies of solid tumors.44 Bromodeoxyuridine can also be administered intravenously (IV) to patients several hours prior to a biopsy. The tissue so recovered can then be examined for an S-phase label or can be exposed to tritiated thymidine to provide a double label, useful for examining phase durations, particularly in leukemia.45

The primary value of flow cytometry for cytokinetics is in its measurement of DNA content. DNA content is usually assessed by the use of intercalating or base-pair affinity dyes. The standard output of this technique is the DNA flow cytogram, also called a DNA histogram. Standardization of the G0-G1 peak for DNA histograms uses diploid cells from the same species as the tissue being studied.46 Human lymphocytes from normal donors are commonly used for many clinical applications. In the assessment of human breast cancer, for instance, lymphocytes are often obtained from normal lymph nodes removed at the time of primary surgery. The completed histogram graphs the relative proportions of cells with 2N DNA (i.e., diploid cells in the G0-G1-phase), 4N DNA (i.e., tetraploid cells in the G2-M-phase), and DNA content between 2N and 4N, called the S-phase fraction. Another cytometric term in common use is the proliferative index, the fraction of cells that are in the S-, G2-, or M-phase.

By measuring DNA content per cell, flow cytometry can also identify cells with abnormal amounts of DNA in the G0-G1 peak, termed aneuploid. Categories include near diploid (within 10% of 2N), hypodiploid (any value less than 2N), simple hyperdiploid (between 2N and 4N), tetraploid (4N), near-tetraploid (within 10% of 4N), hypertetraploid (greater than 4N), or combinations, called multiploid. Each aneuploid G0-G1 peak is expected to have a corresponding G2-M peak with twice as much DNA. The DNA index is the ratio between the fluorescence channel of the malignant G0-G1 peak and the normal diploid G0-G1-peak; < 0.9 or > 1.1 is often considered abnormal. The S-phase fraction may be impossible to measure in the presence of marked aneuploidy. This is especially true when a diploid G2-M peak overlaps with an aneuploid S peak. An overview of the literature suggests that ploidy can now be measured in more than 90% of solid tumors, and the S-phase fraction in about 80% of specimens. However, the classification of DNA histograms is not well standardized at present, so interpretations are highly variable, especially when paraffin-embedded, rather than fresh source material, is used.47

Mitotic Compartments

When a cell divides, the daughters either must remain in a mitotically quiescent state, enter the G1-phase, or die. There are no other possibilities. Entering the G1-phase means that the cell has positioned itself to divide again. Such a cell is thereby a member of the proliferative fraction, also called the growth fraction or the growth compartment.48 The second possibility is that the cell enters a prolonged G0-phase (or, rarely, an S0-phase or an arrested G2-phase), which means that the cell has joined the nonproliferative or quiescent fraction. Classically, the growth fraction is measured by dividing the LI by the ratio of the durations of the S-phase and the total cycle time.49

The S-phase fraction as measured by flow cytometry includes S0 cells in the quiescent fraction. For this and other technical reasons, the S-phase fraction is usually larger than the TLI. It correlates with, but is not equivalent to, the growth fraction.50 About 2 to 20% of cells in a typical cancer are in the S-phase at any point in time. Since the S-phase occupies one-quarter to one-half of the cell cycle, the growth fraction is usually 4 to 80%, with an average of less than 20%. Some normal tissues, such as bone marrow and alimentary mucosa, have larger growth fractions and shorter mitotic cycle times than many cancers, even cancers of those tissues.51,52

Nonproliferative cells fall into three categories. Some highly differentiated cells, such as many, if not all, neurons (this point is currently controversial), are permanently nonproliferative but may survive for the whole life of the organism. In distinction, most terminally differentiated cells, such as the polymorphonuclear leukocyte, have a finite life span. The third type of nonproliferative cell is in an unstable G0-phase, which means that it may be recruited into the G1-phase with the proper extracellular signal. Stem cells share with neurons the property of living as long as the organism. But, like unstable G0 cells, they can periodically, or on demand, produce viable progeny.53,54 Stem cells are also called clonogenic cells because of their capacity for unlimited proliferation. The signal for stem cell recruitment is often from physiologic changes in the environment, such as cell death or cell injury, or extracellular influences, such as by drugs or hormones. An operational definition of stem capacity is the ability to form colonies in soft agar.29,55 Cell culture experiments have found that from 1% to less than 0.1% of the cells in many common tumors have this property, but this may be an underestimate, since in vitro conditions may be more austere than those occurring naturally in vivo. Yet, even though malignant clonogenic cells are a minority population in a cancer, they are the prime targets of anticancer therapy since they constantly replenish the whole population. If chemotherapy preferentially kills mitotic cells, which is the mitotoxicity hypothesis, the ability of tumor stem cells to remain in the G0-phase for long periods may be one reason for failure of therapy.56

The third possible fate for a cell is death. Cells lost from any phase of the cell cycle are collectively called the cell loss fraction.57 Cell loss is important because the growth rate is the difference between cell production and cell loss. The common mechanism for cell death is apoptosis, which is under genetic control.58 Other mechanisms are desquamation and necrosis. Whatever the mechanism, a tumor with much cell loss may appear to be growing slowly, when, in fact, the rate of mitosis may be high. A well-known clinical example is basal cell epithelioma of the skin, which grows slowly in spite of showing a large number of metaphase figures.

The significance of apoptotic cell loss may be illustrated by a hypothetic numeric example. Let us imagine a tumor with a growth fraction of 100%, no cell loss, and a mitotic cycle time of 3 days. This tumor will double in size every 3 days. In this case, the generation time is equal to the doubling time, the time it takes the cell number to double in size. If, however, cells are lost from the tumor at one-half the rate of cell production, a cell loss fraction of 50%, the tumor will double in 6 days rather than in 3 days. The importance of cell loss goes well beyond the determination of growth rate. Each mitotic cycle carries with it a finite probability of mutation.59 A tumor with a higher cell loss rate takes more mitotic cycles to double in size than a tumor with a lower cell loss rate. Thus, the rate of cell loss, especially the rate of apoptotic, physiologic cell loss, relates directly to the rate of mutations toward biologic properties of clinical importance.

Cytokinetics and Biologic Diversity

Since 1980, more than 2,000 published studies have assayed the cytokinetics of clinical cancers. There have been major as well as minor applications. One use has been in the screening of cytologic specimens for malignant cells. This exercise exploits the observation that with few exceptions (noted below), normal cells are diploid, whereas about 70% of clinical cancers are aneuploid. Screening, however, has been of secondary interest. The major use of kinetic measurements has been for correlation with clinical course. The S-phase fraction, the TLI, and aneuploidy have all been evaluated as prognostic factors. The S-phase fraction may be no higher in neoplastic than in some normal tissues. However, within a given histologic type of cancer, both a high S-phase fraction and the presence of aneuploidy are frequently associated with a growth rate that is relatively more rapid, a malignant behavior that is relatively more aggressive, and a therapeutic response that is relatively poorer.

The reasons for the consistent association of aneuploidy with high S-phase fraction are conjectural. One possibility is that aneuploidy is caused by high S-phase activity because it is the consequence of errors in chromosomal construction. The reasoning in this regard is that a high S-phase fraction implies a large number of mitotic cycles per unit of time, which provides more opportunities for erroneous DNA replication. Against this argument is the observation that many normal tissues, such as bone marrow and epithelia, have high S-phase fractions but do not normally become aneuploid. This leaves another possibility: high S-phase fraction is not the cause of aneuploidy but rather the consequence of the chromosomal abnormalities reflected in the aneuploid state. Such abnormalities may be linked with oncogene activation or suppressor gene inactivation. Some clinically benign tumors are aneuploid, so chromosomal abnormalities do not always mean frank cancerous behavior. Yet aneuploidy is clearly a step in tumor progression: DNA errors lead to growth stimulation, high cell turnover results in more opportunities for error, and errors produce increasing genetic aberrancy. The question of how fast mutations accumulate by this process is clinically relevant and will be discussed in the context of growth curve models.

Regardless of the rate of mutations, however, the neoplastic process is so closely related to spontaneous genetic change that tumor progression toward increasing malignancy is regarded as an intrinsic property of cancer.45,60 The clonal origin of tumors has been described.61 It has been stated that over 80% of clinical cancers are monoclonal by glucose6-phosphate dehydrogenase (G6PD) isotype or cytogenetics.62 Yet clonal evolution as the tumors evolve leads to heterogeneity in morphology, metastatic behavior, biochemistry, ploidy, immunogenicity, steroid and growth factor receptors, and drug sensitivity.63 Metastases tend to grow faster than do the primary tumors from which they arise.64,65 There is ample evidence that cytokinetics either underlies or is a direct covariate of tumor progression, that is, the mechanism relating aneuploidy to S-phase fraction also relates tumor progression to S-phase fraction. This will be illustrated in the discussion of clinical correlates of cytokinetics and further below in the context of the doubling time and the Skipper-Schabel model.

As discussed theoretically above, the third determinant of growth rate, cell loss, is also relevant to the generation of genetic changes. High rates of cell turnover are implicated in carcinogenesis. Elevated levels of thyroid stimulating hormone predispose to thyroid cancer.66 Chronic thermal injury with compensatory hyperplasia67 and hyperplasia secondary to solar damage68 lead to skin cancer. Hyperproliferation of the bone marrow in dysmyelopoiesis69 and in chronic granulocytic leukemia70 can result in acute leukemia. Hyperproliferation of the epithelium, as of the colon in inflammatory bowel disease and polyps,71 and of the breast in murine models72 and clinical specimens,73,74 is also associated with neoplastic transformation. Indeed, chemical carcinogenesis requires a growth promoter.75 It is possible that the hyperproliferation of cancer cells as a compensatory response to chronic antineoplastic drug treatment may predispose to the development of drug resistance in Hodgkin’s lymphoma76 and gastrointestinal cancer.77

All the statistical associations among S-phase fraction, ploidy, cell loss fraction, and clinical behavior are of major scientific interest. It must be cautioned, however, that these associations are not always of practical importance, especially when kinetic parameters are highly correlated with more easily measured prognostic factors, such as tumor size. As is seen with any weak prognostic factor, small studies often have false-negative results. Conversely, false-positive reports may arise via data-driven subset analysis. For example, imagine that a population of patients is divisible into those with some arbitrary factor X and those without X, those with Y and those without Y, those with Z and those without Z, and so on. A small study may show that aneuploidy means poor prognosis for patients with Y but good prognosis for patients without Y, whereas both X and Z seem unrelated to ploidy and prognosis. Here the subset allocation (by Y) is chosen because ploidy seems to be useful within the subset, not because there is a biologic reason to suspect that ploidy and Y should be related. In fact, if ploidy carried no prognostic significance whatsoever, there is a real possibility that some other arbitrary division would distinguish the patients merely by chance. This other arbitrary division could be draped in the illusion of biologic tenability, but it would not prove reproducible in prospective confirmatory studies. Hence, purely statistical phenomena such as these should always be kept in mind when reading conflicting data concerning cytokinetics and clinical behavior.

Breast Cancer

Most invasive adenocarcinomas of the breast are of ductal origin. These have been studied extensively from a cytokinetic viewpoint. Ductal carcinoma in situ is thought to be a true neoplastic lesion that is not yet invasive but has a tendency to progress in that direction. There is some evidence that ploidy and proliferative activity can help identify lesions with greater potential for such progression.78 Regarding frank invasive ductal cancers, the TLIs of primary specimens have been shown to follow a log-normal probability distribution.79 This means that while the majority of TLIs are grouped about a median of 5 to 6%, some very large values are found in a few cases. Nuclear staining with the Ki-67 antigen correlates with TLI.80

As the phenotypic expression of genotypic abnormalities,81 TLI is a fairly stable property of a given breast cancer, that is, TLI values from primary specimens may correlate well with values determined from metastatic sites.82,83 High TLI predicts for the presence of necrosis in the tumor, low estrogen receptor content, anaplastic nuclear and histologic grade, and other predictors of poor clinical outcome. However, an analysis of more than 9,000 primary breast cancers failed to find an association between TLI and the most powerful predictors of prognosis: tumor size and lymph nodal involvement.84 Nevertheless, in locally advanced breast cancer, high TLI predicts high metastatic potential, short disease-free interval after intensive treatment, and short survival.85 Similarly, in node-positive breast cancer primarily treated with surgery and subsequently with adjuvant chemotherapy, a low TLI predicted for longer relapse-free and overall survival.86 In node-negative breast cancer patients not receiving adjuvant chemotherapy, a high TLI predicted for recurrence.87 Further evaluation of these 1,800 node-negative tumors found TLI to be of prognostic relevance for local and distant recurrence as well as survival.88 These data are highly controversial since another study with 8-year follow-up failed to show any association between TLI and survival.89 Nevertheless, Italian investigators are currently engaged in a clinical trial in which node-negative patients are assigned to receive adjuvant chemotherapy entirely on the basis of their cancers’ TLI measurements.90 They are also designing a trial for patients with 0 to 3 positive axillary lymph nodes where TLI and estrogen receptor status will determine the type of adjuvant therapy administered.83 A higher TLI has also been associated with a greater sensitivity to chemotherapy in metastatic breast cancer.91 The safest statement is that the value of TLI has not been fully established, but that indications are that important biologic information is contained therein, and that further investigation regarding both the prediction of prognosis and response to chemotherapy is justified.

As described above, the most commonly measured cytokinetic parameter is now the S-phase fraction by flow cytometry (SPF). TLI and SPF show good correspondence.81,92 As for TLI, in many studies, high SPF in primary disease correlates with low estrogen and progesterone receptor content,92–96 high degree of nodal involvement, increasing nuclear anaplasia,97 and aneuploidy.98–101 The degree of axillary nodal involvement with cancer seems to correlate with high SPF in some studies,102 whereas in others, it appears to be independent of axillary nodal status, tumor size, and menopausal status.103 A few studies have reported a higher SPF in patients younger than 50 years of age, notably associated with a poorer prognosis.98,99,104 High SPF correlates, though weakly, with prognosis following local recurrence in a conserved breast.105

In node-negative breast cancer, the presence of either high SPF or aneuploidy has been correlated with a higher probability of relapse.106–108 This was only partially confirmed in a prospective series of node-negative breast cancer patients randomized to receive no postoperative adjuvant chemotherapy.102 In that large study, ploidy (measured in 79% of cases) had no prognostic value; SPF (measured in 73% of patients) did, with low SPF predicting longer disease-free survival. However, low SPF correlated so well with small tumor size that its value as an independent predictor remains to be established by further study, that is, both ploidy and SPF may convey prognostic information, but the clinical usefulness of the small magnitude of their impact, especially in light of more powerful covariates, must be considered controversial.109–111 Several studies with median follow-ups of at least 4 years have found that low SPF is an independent predictor of lower relapse rate or longer survival in node-negative disease.98,101,104,112–118 For example, one retrospective analysis of 195 patients with node-negative disease and tumors > 1 cm in diameter found that the relapse-free rate was 78% for cases with SPF less than 10%, but 52% for the others.113 A retrospective analysis by the National Surgical Adjuvant Breast and Bowel Project (NSABP) of over 4,000 patients with node-negative, estrogen receptor–positive breast cancer also found a significant correlation between SPF and disease-free and overall survivals.114 Similar data exist for node-positive cases. Yet, SPF does not consistently emerge as an independent factor in multivariate analyses.110,119 In addition, the value of SPF as a prognostic factor sometimes has been limited to subgroups.99,100,120–126 It is also of interest to note that for the patients treated by chemotherapy,102 treatment has a positive impact irrespective of the S-phase category. Hence, the data are not clear, and great caution regarding the clinical use of SPF must be exercised. In this regard, a consensus review of published data has concluded that SPF is associated with tumor grade, as well as the probability of relapse and survival in node-negative and node-positive disease, but that clinical applications remain indistinct.127 A recent review of 273 published studies found some conflicting results regarding the value of SPF. However, in general, most often there was a correlation of high SPF with poorer disease-free and overall survivals, positive axillary nodes, receptor-negative tumors, low tumor differentiation and increased tumor size.128 The authors cautioned that although SPF may be of clinical value, there is significant discordance among various laboratories and standardization of technical assays has not yet been achieved. The American Society of Clinical Oncology (ASCO) has not recommended the routine use of SPF to determine prognosis or therapeutic options.129

Ploidy, for all of its theoretic attractiveness, is now known not to be clinically useful. In the subset of stage II patients with estrogen receptor–negative tumors, diploidy has been reported to be a positive prognostic factor.130 Aneuploidy is indeed more common among more poorly differentiated tumors.95,96,131–133 For analysis of node-negative and node-positive disease, ploidy has been shown by some to be a prognostic marker,134–138 while others did not confirm it.96,97,120,121139140 One multi-subset analysis was in favor of ploidy but reported that SPF was a more powerful factor.122 Another subset analysis found prognostic significance of ploidy and estrogen receptor content.141 In node-positive patients, studies with a follow-up of at least 5 years have noted statistically significant differences in relapse-free survival119 and overall survival142 in favor of diploid versus aneuploid tumors. Other studies have reported no significant difference in relapse-free or overall survival on the basis of ploidy status.100,130 Several multivariate analyses found ploidy possibly to be an independent prognostic factor,143–145 whereas others did not confirm the findings.98,114,146 On the contrary, a consensus review of the usefulness of DNA index found that ploidy is a weak prognostic factor, which is not of independent value in multivariate analysis.127 As with SPF, the routine measurement of DNA content in breast cancer is not supported by the ASCO.129

Several studies have used less common techniques to evaluate the proliferation rate of breast cancers, including in vivo and in vitro labeling with the thymidine analogue 5-bromodeoxyuridine (BrdU) and in vitro staining with anti–Ki-67 antibodies. BrdU labeling seems to correlate well with TLI, large tumor size, poor differentiation, aneuploidy, and high SPF,147,148 but not estrogen receptor status.148,149 One study using in vivo BrdU labeling failed to find an association of the values in normal breast tissue and in cancer.150 However, the labeling of the normal cells in premenopausal women was higher than that in older women. Nuclear staining with Ki-67 antigen correlates with TLI80 and is abundant in cancers with poor estrogen receptor content, aneuploidy, high nuclear grade, and rapid relapse after primary surgery. The relationship between Ki-67 staining and tumor size or histologic grade has not been established,151 although a large study found estrogen receptor status, Ki-67 content, tumor size, and nodal status all to be independent prognostic factors.153 A retrospective analysis by the EORTC in node-negative disease also found Ki-67 to be of prognostic value.154 Comparison of in vivo BrdU labeling and in vitro Ki-67 staining in the same breast cancer patients found a strong correlation between these two factors as well as with other clinical markers.155 One study found a significant association between in vitro BrdU labeling and Ki-67. Both were of prognostic utility, although primarily in node-negative breast cancer.156

A correlation between Ki-67 and topoisomerase II alpha, another index of cell proliferation has also been reported.157

The breast cancer literature is filled with reports of putative prognostic factors that correlate, to various degrees, with proliferative measurements. These include c-erbB2 (HER-2/neu), epidermal growth factor receptor (EGFR, HER-1), mutant p53, cathepsin D and other proteases, nm-23,152,158 plasminogen activator inhibitor type-I (PAI-1),159 and other mutation suppressors. HER-2 is a proto-oncogene, located on chromosome 17q21-22, that is amplified in approximately 30% of primary breast cancers.160 It encodes a 185 kDa glycoprotein with tyrosine kinase activity that is involved in the transduction of signals for growth. Amplification and overexpression of c-erbB2 are observed at all stages of primary breast cancer and in lesions in all metastatic sites. Overexpression of c-erbB2 in node-positive patients correlates with high SPF and aneuploidy,161,162 but not with TLI.163,164 Moreover, c-erbB2 and SPF have been found in some studies to be independent prognostic factors for node-positive breast cancer,165,166 whereas other studies have not confirmed this observation.167,168 In ductal carcinoma in situ, c-erbB2 overexpression and high TLI appear to be associated.169 HER-1 is thought to be required to maintain normal breast epithelium, but it is overexpressed in 35 to 45% of breast cancers. Some have reported a correlation of HER-1 with SPF, ploidy, and Ki-67 staining, but this remains unclear.152,170 The p53 gene is one of the tumor suppressor genes involved by deletion or inactivation in the development of breast cancer. Wild-type p53 protein arrests cell division at the interface of G1 and S, binds DNA in a sequence-specific manner, and is a transcriptional activator.171 Mutations of p53 result in the production of an aberrant product with a long half-life and the absence of all of these functions. The p53 protein has been extensively evaluated in the context of kinetic assays.170,172–174 In particular, abnormal p53 expression may be of prognostic value in certain subsets of node-negative178 and node-positive disease.179 Expression of p53 may also be related to therapeutic benefit of radiation in node-negative breast cancer.180 Cathepsin D is an estrogen-related protein that acts as a peptide growth factor and may facilitate cancer cell migration and invasion.181 Its expression does not correlate with TLI or other proliferative factors.182,183 Evaluation of PAI-1 as a prognostic factor is also under investigation.159

More recently, several investigators have evaluated multiple potential prognostic markers in single studies. For example, patients receiving preoperative chemo-hormonal therapy underwent fine-needle aspirations before and after systemic therapy for analysis of receptor status, c-erbB2, p53, Ki-67, SPF, and ploidy.184,185 A “good clinical response” was of independent predictive value for survival. Lack of c-erbB2 expression and a reduction in Ki-67 staining after systemic therapy predicted for a clinical response. These results lend support to a possible role for these factors in this setting. A retrospective analysis of patients with node-negative tumors not treated with adjuvant systemic therapy found PAI-1, cathepsin D, and SPF to be of significant prognostic value for disease-free survival in a univariate analysis.186 Other markers, Ki-67, p53, HER-2/neu, and ploidy were also evaluated in this study. Similar analyses of multiple biologic factors have found different results, particularly among various patient populations.187,188

All these data signify that the growth fraction, as estimated by a large number of currently available techniques, is positively correlated with some aggressive manifestations of breast cancer, but not others, and never strongly or consistently. Hence, factors other than growth fraction alone must be important determinants of the malignant behavior of this disease. Numerous ongoing evaluations will aid in the identification of those factors of clinical significance.

Prostate Carcinoma

Numerous studies have assessed DNA content by flow cytometry in prostate cancer.189–197 The majority of these analyses indicate that ploidy provides prognostic information for localized prostate cancer. Aneuploid tumors recur more frequently than do diploid tumors.189–197 Aneuploidy tends to occur in more advanced stages of disease.198 Aneuploidy and SPF were shown to be significantly related to both large tumor size and a high Gleason score.199 SPF has been assessed by flow cytometry,200 in vivo bromodeoxyuridine labeling,201 and Ki-67 expression,201 but the clinical value of such assessments is uncertain. Currently, the study of cyclo-oxygenase-2 (COX-2) overexpression in prostate cancer is ongoing.202,203

Renal Cell Carcinoma

Conflicting data exist regarding the prognostic significance of DNA ploidy in renal cell carcinoma.204–213 DNA ploidy has been correlated significantly with both tumor grade and survival.211,212 In a univariate survival analysis, tumor stage and grade, Ki-67, silver-stained nucleolar organizer regions (AgNOR), and proliferating cell nuclear antigen (PCNA) are associated with significant survival.214 The predictive significance of cytokinetics regarding response to therapy can be resolved only by prospective studies.

Bladder Cancer

BrdU labeling has been used to assess the growth fraction in bladder cancer,215 but most studies have used DNA flow cytometry. A number of studies have noted an association between DNA ploidy, tumor grade, and aggressiveness of bladder cancer.216–220 Controversy exists over the significance of DNA ploidy. Some data show that DNA ploidy is not an independent prognostic factor,221,222 but another study shows that DNA image cytometry is correlated significantly with survival.223 Few studies have shown an association between c-erbB2 overexpression to tumor grade, stage, and survival.224,225

Testicular Carcinoma

It has been reported that a high DNA index in nonseminomatous germ cell tumors of the testes is associated with advanced disease at presentation.226 Aneuploidy, however, did not correlate with histology or vessel invasion. In seminoma, aneuploidy is associated with a shorter disease-free survival.227,228

Ovarian Cancer

Most studies have demonstrated that diploid tumors are associated with a better prognosis229–236 while other studies show no correlation between DNA ploidy and survival.237,238 A multivariate analysis has not identified that the aneuploidy population in ascitic fluid as an independently significant variable for predicting recurrence.239 Assessment of S-phase fraction by Ki-67 staining,240 flow cytometry, and thymidine labeling has produced variable results.241,242 Data are emerging on the significance of c-erbB2 over-expression in ovarian cancer.243,244

Uterine Cancer

In endometrial carcinoma, with few exceptions,245 aneuploidy has been associated with poorly differentiated tumors246,247 and decreased survival.246–250 A multivariate analysis has identified DNA ploidy, histologic subtype, p53 over-expression, and HER-2/neu overexpression as independent prognostic factors.251 However, other studies demonstrate that the significance of HER-2/neu is less clearly established.252,253 A recent study has demonstrated that tamoxifen therapy can increase the expression of progesterone and estrogen receptors in endometrial cancer. The effect is most pronounced in tumors with favorable clinicopathologic parameters.254

Cervical Carcinoma

DNA ploidy, S-phase fraction, and BrdU labeling have an unclear role as prognostic factors in cervical carcinoma.255–259 One study on 101 cases has suggested a correlation between SPF and BrdU labeling with survival.257,258 Yet, multivariate analyses have shown that SPF and DNA ploidy are not significant predictors of survival.256,259 One study has shown a correlation between the Ki-67 index and response to radiation therapy.260 The upregulation of the c-erbB2 oncoprotein has recently been shown to be associated with invasive cervical cancer and poor survival.261,262

Colorectal Carcinoma

Both retrospective and prospective data suggest that aneuploid colorectal carcinomas, particularly those in stages A, B, and C, have a worse prognosis.263–269 This is not a universal finding, however.270,271 A univariate analysis has shown that stage, nodal involvement, intestinal wall invasion, and poor tumor differentiation are all associated with worse survival, but no correlation is seen with DNA ploidy.271 The significance of p53 accumulation is unclear,272,273 as well as the role of K-ras mutations.274,275 Recent data have demonstrated the upregulation of COX-2 expression in colorectal cancer276,277 and that COX-2 overexpression is associated with advanced stage, larger size, and nodal involvement.278 A recent study has shown the regulation of COX-2 pathway in colorectal carcinogenesis by the HER-2/neu receptor.279 Additionally, several studies have demonstrated the correlation between HER-2/neu upregulation with advanced stage and worse survival.280–283

Carcinoma of the Pancreas

The cytokinetics of this disease has not been well studied. An analysis of 56 patients indicated that ploidy was an independent prognostic factor with a significant effect on survival.284 Another study on 36 patients showed a close correlation between DNA ploidy and the stage and grade of pancreatic cancers.285 A study on 64 patients showed that p53 and Ki-67 expressions did not relate to patient survival but bcl-2 expression did.286 There is controversy over the significance of HER-2/neu overexpression in pancreatic cancer.287,288

Hepatoma

There is conflicting information on the prognostic importance of DNA ploidy in hepatocellular carcinoma (HCC). Some retrospective multivariate analyses have shown a correlation between ploidy and survival,289,290 whereas another study does not.291 Ki-67 overexpression has been associated with a lower survival in HCC.292 The significance of p53 and HER-2/neu oncoprotein is unclear. One study has demonstrated an association between p53 accumulation and HER-2/neu overexpression with poor survival.293 The COX-2 enzyme has been found to be upregulated in HCC, the importance of which is also uncertain.294,295

Gastric and Esophageal Carcinomas

Previous data have shown cytometric analysis to be of prognostic significance in squamous cel carcinoma (SCC) of the esophagus.296 Patients with aneuploid tumors show more unfavorable prognosis than those with diploid tumors.297 Highly significant correlation has been shown between results of cytometric study and p53 overexpression.298 COX-2 upregulation has also been shown in well-differentiated regions of esophageal SCC,299 the clinical significance of which is unknown. There is controversy over the role of c-erbB2 overexpression in esophageal cancer as a prognostic factor.300–302

There has been conflicting data on the significance of tumor aneuploidy in gastric carcinoma. Some studies have supported that tumor aneuploidy is associated with decreased survival.303,304 However, another study does not show a correlation between DNA ploidy with prognosis.305 Multivariate analyses show that tumor stage remains to be the most important prognostic indicator.305 Controversy also exists concerning the importance of p53 accumulation. Once analysis reports that high p53 index is associated with poor survival,306 while another study shows that p53 overexpression is not an independent factor by multivariate survival analysis.307 COX-2 upregulation has been detected in gastric carcinoma308–310 and has also been correlated with lymph node involvement and stage.311 The c-erbB2 oncoprotein is also overexpressed in gastric cancer, but the significance of it is uncertain.312–314

Head and Neck Cancer

There is disagreement in the literature regarding the prognostic significance of DNA ploidy in squamous cell carcinoma of the head and neck.315–317 Some studies identified a more favorable prognosis for aneuploid tumors,318–320 whereas others found a better outcome for diploid tumors.317,321 One analysis found no significant association between DNA ploidy and response to chemotherapy.322 Several studies have reported increased radiosensitivity for aneuploid lesions.315 An evaluation of 110 patients with oral cavity lesions noted an increased likelihood of aneuploidy in poorly differentiated and larger tumors.323 Only limited studies with bromodeoxyuridine and thymidine have been performed.324,325 The overexpression of COX-2 is seen in both head and neck SCC (HNSCC) and adjacent normal appearing epithelium,326 the importance of which is unknown. The c-erbB2 oncoprotein is also upregulated in HNSCC, but more data are required to understand its significance.327–329

Lung Carcinoma

Numerous studies of non–small cell lung carcinoma (NSCLC) have found an association between aneuploidy and shorter survival times.330–337 However, other analyses have not confirmed this observation.338,339 Aneuploidy has also been correlated with phenotypic heterogeneity in NSCLC.340 Limited data are available concerning the prognostic significance of ploidy in small cell lung cancer.341 A multivariate analysis has shown that p53 overexpression is an independent factor with decreased survival.342 Emerging data on the upregulation of COX-2 enzyme and c-erbB2 oncoprotein in NSCLC seem to suggest a correlation with poor survival, but further analyses are needed.343–346

Brain Cancer

Determination of high growth fraction by BrdU labeling, Ki-67 staining, and mutant p53 expression (disinhibition of the normal G1-S blockade) was found to convey prognostic information in several studies of primary brain malignancies.347–351 A prospective study of 174 patients with intracranial gliomas found the BrdU labeling index to be an important predictor of survival for low-grade astrocytomas. This index, in conjunction with the patient’s age, was also predictive of survival for glioblastomas and malignant astrocytomas.349 Study of DNA content by flow cytometry and proliferation in various brain tumors has found a correlation between aneuploidy and high SPF in the more malignant tumors.352 Flow cytometry has been used to assess ploidy in meningiomas.353 Aneuploidy has been associated significantly with atypical, anaplastic, and recurrent meningiomas.354 In gliomas, aneuploidy has been associated with high histologic grade and poor outcome.348,352,355–357 The significance of c-erbB2 over-expression358,359 and COX-2 upregulation360 are being evaluated. In medulloblastoma, aneuploidy has been associated with poor prognosis,358,359 but aneuploid medulloblastomas may be more sensitive to treatment.360

Thyroid Cancer

Although aneuploidy has been noted in both malignant and benign thyroid lesions,361,362 a multivariate analysis has suggested that DNA ploidy is an independent prognostic factor for survival.363 Aneuploidy is also correlated with advanced thyroid cancer with spread to extrathyroid tissue.364 A multivariate analysis has also suggested that p53 overexpression is an independent prognostic factor for survival.363 Nuclear p53 immunoreactivity is associated with DNA aneuploidy365 in papillary thyroid cancer. In follicular thyroid neoplasia, carcinomas have a higher proliferation rate than adenomas, when assessed by SPF and PCNA.366 The percentage of Ki-67–positive fractions is found to be significantly higher in malignant than in benign thyroid tumors.367 Presently, the role of c-erbB2 is being evaluated in thyroid cancer.368

Thymomas

Aneuploidy has been associated with more advanced disease, increased tumor recurrence, and the existence of myasthenia gravis.369,370 In a multivariate analysis, aneuploidy and high proliferative activity, measured by AgNOR are associated with a shortened survival.371 The AgNOR counting is also correlated with the invasiveness and stage of thymomas as well as the presence of myasthenia gravis.372

Sarcomas

There is limited information on the role of DNA analysis for soft tissue and osteosarcomas. In soft tissue sarcoma, one study shows that aneuploidy is correlated with histologic grade373 but is not associated with survival.374 The presence of diploid or near-diploid tumors may be correlated with a more favorable prognosis for osteosarcomas and chondrosarcomas,375,376 although two studies have demonstrated that nondiploid tumors may be more sensitive to chemotherapy than diploid osteosarcomas.377,378 In synovial sarcoma, a multivariate analysis has shown that aneuploidy, high Ki-67 expression, and stage are associated with a shorter survival.379 One study reports that patients with steroid-induced Kaposi’s sarcoma (KS) have an aneuploidy pattern, and that most patients with classic KS have a diploid pattern.380 In peripheral primitive neuroectodermal tumor (PNET) and extraosseous Ewing’s sarcoma, one study shows that DNA ploidy and SPF are not found to have prognostic significance.381 The role of c-erbB2 is being studied.382

Pediatric Tumors

In neuroblastoma, several studies have noted an unfavorable prognosis for diploid neuroblastomas.383–388 Amplification of the N-myc oncogene has also been associated with these diploid tumors.388 Aneuploidy is more significantly associated with lower clinical stage, younger age at diagnosis, and without N-myc gene amplification.389 DNA content of neuroblastomas may also correlate with response to therapy.390 In Wilm’s tumors, there is controversy regarding DNA ploidy.388,391–393 One study reports that aneuploidy is associated with poor outcome,393 while another shows that ploidy status has no statistical correlation with survival.394 Most rhabdosarcomas are aneuploid. DNA content has been correlated with age394 and stage.395 A recent multivariate analysis confirms the importance of DNA ploidy status and SPF in predicting survival.396 In osseous and extraosseous tumors, one study suggests that aneuploidy may be an indicator of bad prognosis.397

Melanoma

Numerous analyses of patients with primary melanoma indicate a correlation between aneuploidy, more malignant melanoma, higher recurrence rates, and/or shorter survival.398–400 For metastatic melanoma, aneuploidy has been associated with a more favorable prognosis401 as well as a worse outcome.398 Evaluation of S-phase fraction by flow cytometry is also of prognostic significance for stage III399 and metastatic disease.401 In metastatic melanoma treated with chemotherapy, a multivariate survival analysis has shown that a high SPF measured in histologically verified metastases is associated with a higher response rate and a longer survival.402 For stage II melanoma, slow proliferation as measured by thymidine labeling indicates a significant advantage in relapse-free and overall survivals.403 In stage I cutaneous melanoma, there is a strong relationship between DNA ploidy and classic prognostic variables.404 The role of c-erbB2 in melanoma is being evaluated.405

Hodgkin’s Disease

The few studies of Hodgkin’s disease that have been reported have noted a low frequency of aneuploidy.406–408 This may be the result of the difficulty encountered in isolating malignant cells from a large population of benign cells of similar composition.409 A retrospective analysis of 137 patients with Hodgkin’s disease found no correlation between aneuploidy and other prognostic factors, or with survival.409 Although tumors with a high S-phase fraction had a less favorable outcome, this prognostic factor was not independent of others.409 A study has shown that high indices of PCNA, p53, and bcl-2 are associated with advanced disease and poor response to treatment, but the same is not seen with c-erbB2 overexpression.410

Non–Hodgkin’s Lymphoma

Non–Hodgkin’s lymphoma (NHL) is such a heterogeneous collection of diseases that it is not surprising that the role of DNA flow cytometry remains ill defined, with many conflicting data.411,412 Nevertheless, it is clear that aneuploidy is more common in lesions of high-grade or of B-cell lineage.409,413 As a prognostic factor, however, there is controversy regarding ploidy as a strong indicator of survival.415–417 In contrast, most studies418–421 have shown that S-phase fraction or other measures of proliferative activity422 are useful prognostically. S-phase fraction has been used to evaluate clinical course423 and to augment histologic classification.424 Few data are available regarding the cytokinetics of uncommon lymphomas, such as mycosis fungoides425 and nonendemic Burkitt’s lymphoma.426 In gastrointestinal lymphoma, a multivariate analysis on 37 cases has shown that stage and DNA ploidy patterns have a prognostic value in terms of survival.427 One study demonstrates the inverse relationship between bcl-2 overexpression and proliferation activity in intermediate- and high-grade NHLs, suggesting that bcl-2 inhibits apoptosis.428

Multiple Myeloma and Monoclonal Gammopathies

Aneuploidy is found in most cases of multiple myeloma, but it has also been found in benign monoclonal gammopathies.429–434 Several older studies have noted an association between aneuploidy and decreased survival,435–437 but more recent studies have not.431–434 In these studies, hyperdiploid status is associated with better survival. Labeling of bone marrow cells with bromodeoxyuridine and the monoclonal antibody Ki-67 can be used to determine proliferative activity in patients with multiple myeloma and monoclonal gammopathies.438,439 The BrdU labeling of plasma cells is a well-established independent prognostic factor in newly diagnosed multiple myeloma.439

Leukemias

Flow cytometric analysis of leukemias has been used primarily for immunophenotypic classification, cytogenetic studies, and the determination of gene rearrangements.440 Regarding the prognostic significance of DNA content, several studies of childhood acute lymphoblastic leukemia (ALL) have noted that the presence of hyperdiploid blasts conveys a more favorable outcome and a better response to therapy.441,442 Also, lower DNA content in the ALL blasts in children has been associated with a greater frequency of late relapses.443 However, in one trial the TLI of blasts before treatment was of no prognostic significance.444 Flow cytometry could be used to monitor residual disease in certain subgroups of ALL.445 Measurement of S-phase activity by bromodeoxyuridine has been employed to assess the sensitivity of ALL cells to cytosine arabinoside, and results have been mixed.446

In ALL in adults, aneuploidy has been associated with a worse outcome.447 However, another study shows that DNA index does not correlate with outcome or response to treatment.448 Although several studies have used a variety of techniques to assess the cell kinetics of acute myeloid leukemia (AML) and chronic myeloid leukemia (CML), the prognostic value of these measurements remains unclear.449–454 Some have found that aneuploidy predicts a more favorable prognosis, as it does in childhood ALL,447 but another study does not confirm this.455 Bromodeoxyuridine labeling of leukemic promyelocytes revealed a lower labeling index and longer cell cycle than in other types of AML.456 These results were thought to be secondary to the marked expression of transforming growth factor-beta (TGF-β). One analysis of AML found that a high proliferative activity, as measured by BrdU labeling and proliferative cell nuclear antigen staining, was a positive prognostic factor for those receiving S-phase–specific drugs prior to being given anthracyclines.458

Growth Curve Analysis

The correlations between cytokinetics and clinical behavior support the concept that cell proliferation is intimately associated with the generation of tumor heterogeneity. Cell proliferation is, in addition, the primary mechanism for tumor growth. Anticancer therapy is, of course, intended to reverse growth by killing or removing cancer cells. A type of mathematic function called a growth curve describes increases and decreases in the number of cells over time. These curves not only summarize clinical course, but they also relate to the rate of emergence of mutations toward clinically relevant cellular diversity. Through both these attributes, growth curves are proving to be useful in explaining human cancer and in indicating new directions for therapeutic research.

Skipper-Schabel-Wilcox Model

This model of tumor growth, formulated and popularized by investigators at the Southern Research Institute, is commonly called the log-kill model. It was the original, and is still the pre-eminent, model of tumor growth and therapeutic regression.457,458 The model is based on the observation that leukemia L1210 in BDF1 or DBA mice grows exponentially until it reaches a lethal tumor volume of 109 cells (1 cubic centimeter).460 Ninety percent of the leukemia cells divide every 12 to 13 hours. This percentage is the same for both a tiny tumor and a tumor close to the lethal volume. As a result, the doubling time is always constant: if it takes 11 hours for 100 cells to grow into 200 cells, it will take 11 hours for 107 cells to grow into 2 × 107 cells. This pattern generalizes for any constant fractional increase: if it takes 40 hours for 103 cells to grow into 104 cells (an increase by a factor of 10), it will take 40 hours for 107 cells to grow into 108 cells.

Exponential growth and its associated concept of the doubling time are clinically relevant.461 Different histologic types of cancer display a great variety of doubling times within the observable range of tumor sizes.462 The most therapeutically responsive human cancers, such as testicular cancer and choriocarcinoma, tend to have doubling times that are < 1 month long. Less responsive cancers, such as squamous cell cancer of the head and neck, seem to double in about 2 months. The relatively unresponsive cancers, such as colon adenocarcinoma, tend to double every 3 months. Clearly, this clinical observation may relate to the higher chemosensitivity of proliferating cells (see below), that is, if a tumor has a high fraction of dividing cells, it will tend to grow faster and will also tend to be more responsive to drugs that kill dividing cells. Alternatively, tumors with a higher rate of cell loss tend to have a relatively slower growth rate and also a higher rate of mutations toward drug resistance. A combination of factors may be relevant, in that slower growth due to fewer mitoses may impede therapeutic response because of kinetics, while slower growth due to a high rate of apoptosis may impede response due to drug resistance.

An unspoken assumption in these theoretic considerations is that the doubling time remains fixed and thereby accurately summarizes the proliferative behavior of a given tumor. This assumption may not be realistic, as will be examined in some detail below. Nevertheless, we may use exponential growth to illustrate some important properties, which are also relevant to more complex growth patterns.

Let us consider a hypothetical tumor that is growing exponentially and is also homogeneous in drug sensitivity. When such a tumor is treated with a specific chemotherapy regimen, the fraction of cells killed is always the same, regardless of the initial size of the malignant population. This has been demonstrated in experimental animal cancers that do indeed grow exponentially, L1210 being the major example. If a given dose of a given drug reduces 106 cells to 105, the same therapy applied against 104 cells will result in 103 survivors. These two cytoreductions are both examples of a one-log kill, which means a 90% decrease in cell number. It was shown quite early in the development of this field that for many drugs, the log kill increases with increasing dose.435,436 Hence, it requires higher drug dosages to eradicate larger inoculum sizes of transplanted tumors. In addition, if two or more drugs are used, the log kills are multiplicative, that is, imagine that a given dose of drug A kills 90% of a population of cells (a one log kill) when administered as a single agent. Imagine as well that were we to treat the same population of cells with a given dose of drug B as a single agent, we would also kill 90%. Then drug B added to therapy with drug A should kill 90% of the 10% of cells left after drug A alone, resulting in a kill of 99% of the cells (a two-log kill). In other words, two one-log kills equal one two-log kill. As a numeric example, if treatment A given alone leaves 105 cells out of 106, and if treatment B given alone would accomplish the same, the combination A + B (at full doses of each) should be able to reduce 106 cells to 104. If treatment C is also a one-log kill therapy, A + B + C against 106 cells should leave only 103 cells. If A + B + C is used to treat 103 cells, only 100, or one, cell should remain. Thus, if enough drugs at adequate doses were applied against a tumor of sufficiently small size, the number of cells left after treatment should be smaller than one, which means that the tumor is destroyed. This concept, the fundamental concept underlying combination chemotherapy, was first demonstrated to be of major value in the design of early curative approaches to childhood leukemia.465 Other applications will be discussed below.

When the concept of fractional kill was first applied to the postoperative adjuvant treatment of micrometastases, say from breast cancer, it engendered enormous optimism.466,467 After all, micrometastases are very small collections of cancer cells. Indeed, very small solid tumors in the laboratory contain a higher percentage of actively dividing cells than do their larger counterparts.33,34 It is thought, as mentioned above, that most chemotherapeutic agents preferentially damage mitotic cells. Hence, the fraction of cells killed in a small tumor should actually be even greater than the fraction of cells killed in a histologically identical tumor of larger size. As a consequence, according to the Skipper-Schabel-Wilcox model, if the log-kill estimate is wrong, the error should be in the direction of underestimating the impact of therapy against micrometastases. Putting this all together, tumors of small volume should be easily cured by aggressive combination chemotherapy, even more readily than would be predicted by the model.

Clinical trails, unfortunately, have not entirely confirmed these optimistic predictions. An illustration is the postoperative adjuvant chemotherapy of early-stage breast cancer. After quality surgery very few cells should be left, largely disseminated in multiple micrometastatic sites. By Skipper’s model, these should be easily reduced to below the volume of a single cell by appropriate drug therapy.468,469 The adjuvant chemotherapy of breast cancer with active agents at conventional doses does indeed reduce the probability of patients developing stage IV disease and does result in improved survival. However, in composite, this effect is relatively modest.470,471 Is this because the duration of the therapy is not long enough? Assume that a given drug combination causes a one-log kill with each application. Six cycles of that combination should cure tumors of fewer than 106 cells. For tumors of exactly 106 cells, the six cycles would leave just one cell to regrow. If this were the case, then merely extending the duration of treatment beyond six cycles should kill the remaining cell and thereby increase the cure rate. From a modeling perspective, this same argument generalizes for higher degrees of cell kill and higher tumor cell burdens. Yet, durations of exposure to the same chemotherapeutic regimen longer than 4 to 6 months have not improved results in adjuvant chemotherapy.471 Hence, the predictions of the model—that cure in this setting should be easy and that duration of therapy should increase that likelihood—do not match actual observations.

What is wrong? If we accept the basic tenets of the Skipper-SchabelWilcox model, the failure of adjuvant chemotherapy to cure all cases of early breast cancer can only be due to cellular biochemical drug resistance. Skipper and colleagues were aware of the divergence between their theory and actual experience and, for this reason, hypothesized that some cells in the tumor must be refractory to the drugs used at the dose levels employed.

When we explore the implications of other models, we will see that it is not always necessary to hypothesize the existence of absolutely refractory cells. Nevertheless, the inclusion of the concept of absolutely resistant cells in the Skipper-Schabel-Wilcox model can account for many observations. According to this reasoning, once all the cells that are sensitive are eliminated by a certain length of treatment, continuing the same therapy for a longer duration will not give better results. The reason is that all the cells left after that initial course are drug resistant and therefore cannot be killed by further use of the same drugs. It is further assumed that such resistance is acquired during a cancer’s growth history (by the occurrence of mutations, a phenomenon called tumor progression). If that were the case, the only way to guarantee the absence of resistant cells is to initiate therapy at so small a tumor size that no recalcitrant mutants are as yet present. In L1210, the transplantable mouse leukemia that was used to formulate the Skipper model, drug-resistant cells are rarely found in small aliquots, which would seem to support the above reasoning. If this same reasoning were to apply to human cancer, it would mean that such drug-resistant cells would have to arise spontaneously between the time of the carcinogenic event and the time of the appearance of diagnostically large amounts of tumor.472 This concept leads to the conclusion that the development of a curative strategy depends entirely on the answers to two questions: when in the course of growth does resistance develop? Can tumors be diagnosed early enough so that we can start treatment when the (small) tumor is still curable?473

Delbruck-Luria Model

To try to answer these two questions, theoreticians have turned to quantitative models of the emergence of drug resistance. Indeed, the development of such models was one of the first major activities in the field of growth curve analysis. That is because drug resistance, by then as yet unknown biochemical mechanisms, was recognized quite early to be important in cancer therapeutics.474 The original work, however, was not based on the study of cancer cells, but rather some pioneering experiments in bacteriology. In 1943, Luria and Delbruck found that different bacterial cultures developed resistance to bacteriophage infection at random (and hence different) times in their growth histories. In fact, resistance often developed long before exposure to the viruses.475 Later, when the cultures were exposed to the viruses, the survival of the resistant bacteria could be assessed, thereby measuring the percentage of cells that had randomly acquired resistance. Luria and Delbruck reasoned that those cultures that had experienced a mutation earlier in their histories had more time to develop a high percentage of resistant bacteria. If a bacterium mutates toward property X with probability x at each mitosis, the probability of the cell not developing property X in one mitosis is 1 – x. In y mitoses, the probability of no mutations occurring is (1 – x)y. If each mitosis produces two viable cells (no cell loss), it takes N – 1 mitoses (over log2 N generation times) for one cell to grow into N cells, that is, one mitosis produces two cells, each of these two cells undergoes mitosis (for a cumulative total of three mitoses) to produce four cells, each of these four divides (for a cumulative total of seven mitoses) to produce eight cells, and so on. Hence, the probability of not finding any bacteria with property X in N cells is exp[(N – 1) * ln(1 – x)], which is approximately exp[–x(N – 1)], since x is small. (A numeric example of the application of this formula is given below.)

Within a decade of Delbruck and Luria’s original observation regarding bacteria, the same pattern was found by Law to apply to the emergence of methotrexate resistance in L1210 cells.476 Thus, antimetabolite resistance was reasoned to be a trait acquired spontaneously at random times in the pretreatment growth of this cancer.

The more modern view of cancer biology has not diminished enthusiasm for the concept of acquired mutations. Abnormalities of the process regulating the entry of G1 cells into S could disinhibit replication, producing aberrant levels of DNA per neoplastic cell at each cell division.477–480 By this mechanism, aneuploidy as well as drug resistance should be a function of the number of mitoses. Cell loss would actually increase the probability of mutations per given cell number, since more cell divisions would be required to produce that cell number than if no cell loss had occurred.

Goldie-Coldman Model

In a qualitative sense, the kinetic observations of Delbruck, Luria, Law, and others were highly influential in the genesis and development of the concept of combination chemotherapy.481 If tumor cells could acquire resistance to a drug prior to exposure to that drug, then the therapist could be faced with a disease heterogeneous in drug sensitivity even at the time of first diagnosis. Since it is numerically unlikely that any one cell could spontaneously become resistant to many different drugs (particularly if the drugs have different biochemical sites of action), only with combinations of drugs could one hope to eradicate all cells.482 Because of its influence on the development of combination chemotherapy this concept has been formative of modern medical oncology.

In a quantitative sense, the Delbruck-Luria model was re-applied to human cancer in 1979 by the work of Goldie and Coldman.483,484 These authors later refined their original model to include multiple sublines with double or higher orders of drug resistance and also the presence of cell loss.485 Their analysis contended that there is a high probability that mutations arise over a two-log (100-fold) increase in tumor size. This can be shown by the following calculation. Let us take a tenable mutation rate x of 1026.486 Using the expression exp[–x(N – 1)] that we derived above, the probability of no mutants in 105 cells is exp[–1026(105 – 1)], which equals 0.905. Similarly, the probability of no mutants in 107 cells is 0.000045, that is, it is unlikely that 105 cells have a least one drug-resistant mutant, but extremely likely that 107 cells have at least one such cell.

In this regard, it should be noted that while Goldie and Coldman focused on the property of drug resistance, an even clearer illustration of their concept might be found in the acquisition of metastatic ability. The capacity to metastasize is now established to be a reflection of genetic lability.487 The approximate volume of 107 packed cells is 0.01 cubic centimeter. If tumor cells are mixed with benign host tissue (including stromal cells, fibrosis, extracellular secretions, blood and lymphatic vessels, cellular infiltrate, and fluid-filled space) at a packing ratio of 1:10, 107 cancer cells will occupy a volume of 0.1 cubic centimeter. At a packing ratio of 1:100, which is often more realistic, 107 cancer cells would be found in a tumor volume of about 1.0 cubic centimeter. This example of scaling relates directly to clinical data. In primary breast cancer, the best predictor of axillary metastases is tumor size. Only 17% of invasive ductal lesions < 1 cm in diameter are metastatic to the axilla, contrasted with 41% of lesions of 2 cm in diameter and 68% of tumors of 5 to 10 cm.488 For primary breast cancer that does not involve axillary lymph nodes, the probability of eventual metastatic spread increases sharply when the mass in the breast is > 1 cm in diameter.489 Hence, metastatic ability is conspicuously more common in tumors larger than this critical size. A 1-cm spherical tumor contains a volume of slightly over 0.5 cubic centimeter, which is right in the middle of the range of 0.1 to 1.0 cubic centimeter described above as likely harboring between 105 and 107 cancer cells.

These calculations fit the model with reassuring precision. However, they cannot be regarded as proof of the model, since other explanations are possible (see Mitotoxicity Hypothesis below). Moreover, some very specific predictions of the Goldie-Coldman model have not been confirmed in the clinic, as discussed immediately below. This illustrates the complexity of the biology underlying common tumor growth curves and illustrates that all models are useful, only in that they summarize empiric observations and motivate experiments. Models never explain phenomena: they merely describe phenomena in mathematic language.

The specific, testable predictions of the Goldie-Coldman model regard drug sensitivity. Using the calculations above, the model predicts that a cancer arising from a single, drug-sensitive malignant cell has a 90% chance of being curable at 105 cells. Yet, if it has a 90% chance of being curable at that size, it will almost certainly become incurable by the time it grows to 107 cells. Thus, tumors larger than 0.1 to 1.0 cubic centimeter should always be incurable with any single agent. This line of reasoning led these authors to conclude that the best chemotherapeutic strategy is to treat as small a tumor as possible as early as possible. The earliest possible treatment might be perioperative or even preoperative. They also concluded that once treatment is started, as many effective drugs as possible should be applied as soon as possible. This strategy, according to the model, is needed to prevent cells that are already resistant to one drug from mutating to resist others.

These recommendations are intuitive, conforming to established empiric principles of combination chemotherapy.490 They differ from classic principles, only in that they concentrate on the emergence of resistance during treatment, as contrasted with the other possibility that resistance is already present at the start of treatment. Most uniquely, these recommendations imply that if several drugs cannot be used simultaneously at good therapeutic levels (because of overlapping toxicity or competitive interference), they should be used in a strict alternating sequence.

The recommendation for strict alternation is based on several assumptions. All are based on the principle of symmetry. Imagine that a tumor has two types of cells, type A and type B. The A-cells are sensitive only to therapy A, while the B-cells are sensitive only to therapy B. Symmetry means that A-cells are as sensitive to therapy A as B-cells are sensitive to therapy B. The second assumption is that the rate of mutation toward biochemical resistance is also symmetrical. This means that the A-cells mutate toward resistance to A at the same rate as the B-cells mutate to resistance to B. The third assumption is that the growth patterns and growth rates of the two types of cells are equivalent.491 Critical appraisal of the various assumptions and conclusions of the Goldie-Coldman model has raised several interesting points. It would be informative to examine these in some detail, not only to illuminate this one hypothesis but also to show the relevance of growth curve analysis to clinical problems.

The first, and most basic, assumption that we must question concerns the notion that all chemotherapeutic failure is rooted in absolute drug resistance. This is a widely held assumption, but it is not above criticism. In fact, evidence to the contrary is found easily in clinical experience. For example, lymphomas and acute leukemias frequently respond to chemotherapy when they relapse from a complete remission induced by the same chemotherapy. Patients with Hodgkin’s disease who achieve complete remission with combination chemotherapy and who relapse ≥ 18 months later have an excellent chance of attaining complete remission again when the same chemotherapy is re-applied.492 A similar situation is found in the treatment of breast adenocarcinoma. Stage IV (recurrent, metastatic disease) frequently responds to chemotherapy that had worked previously but failed to work subsequently. Various illustrations of this phenomenon have been documented in the literature. For example, the Cancer and Leukemia Group B (CALGB) treated patients with advanced breast cancer with cyclophosphamide, Adriamycin (doxorubicin), and 5-fluorouracil (CAF), with or without tamoxifen.493 Although none of these patients had prior chemotherapy for their advanced disease, some had had prior adjuvant chemotherapy. All parameters of disease sensitivity to treatment—the response rate, response duration, and overall survival—were unaffected by patients’ past histories of adjuvant chemotherapy. Similarly, patients on trials at the National Cancer Institute in Milan who developed stage IV breast cancer after adjuvant cyclophosphamide, methotrexate, and 5-fluorouracil (CMF) responded as well to CMF for advanced disease as those who previously had been randomized to be treated with radical mastectomy alone.494 From these observations we may safely conclude that breast cancers that regrow after exposure to adjuvant CMF are not universally resistant to CMF.495 We are now observing that patients experiencing recurrence of stage IV disease after the failure of high-dose chemotherapy (autologous bone marrow transplantation [ABMT]) can benefit in terms of tumor response to the re-application of conventional doses of chemotherapy drugs. Hence, all chemotherapeutic failure cannot be attributed to permanent drug resistance. It is possible that some cancers escape cure because a temporary absolute drug resistance develops that then reverses over time. It is also possible, however, that at least some cancers can escape cure by the use of drugs, even though some of their cells are not absolutely resistant to these drugs. This important possibility will be developed further as we consider growth models other than simple, symmetric exponential growth.

Another prediction from the Goldie-Coldman model that is interesting to examine is that tumors > 1.0 cubic centimeter (107 cells at a packing ratio of 1:100, 109 cells at maximum density packing) cannot be cured with single drugs. Two rapidly growing cancers, gestational choriocarcinoma and Burkitt’s lymphoma, both with dense packing of their cancer cells, have been cured with single drugs.496 Cures are achieved even when therapy is initiated at tumor sizes much larger than 1.0 cubic centimeter. Childhood acute lymphoblastic leukemias, other pediatric cancers, adult lymphomas, and germ cell tumors of greater than 1010 cells are frequently cured with two-drug and three-drug regimens. Hence, contradicting the model, the size of 107 cells does not always mean incurability.

For the purposes of planning chemotherapy schedules, the Goldie-Coldman model speculates that mutations develop rapidly during the treatable portion of a cancer’s growth history. This may seem tenable, since in our previous discussion of cell proliferation, we established that genetic lability is a key attribute of neoplasia. Yet, clinical observations hint at a deeper level of complexity.

As a starting example, let us examine metastatic ability as a measure of the rate of mutations. A primary breast cancer left untreated to grow in the breast, as was standard practice in the 19th century, always became metastatic.497 Yet at 30 years of follow-up after radical mastectomy (with no adjuvant chemotherapy), more than 30% of patients are alive and free of disease.498,499 The mortality rate drops gradually from about 10% per year in the first year to about 2% per year by year 25,500 but a plateau is reached after 30 years, with a rate of mortality indistinguishable from that of the general population.501,502 Hence, while most, if not all, breast cancers can become metastatic if left alone long enough, and many have already done so by the time of initial presentation, some have not. This speaks against the universal, rapid development of mutations.

Let us consider another situation, the case of a primary cancer that is diagnosed in the breast before it has developed metastatic ability. If the cancer cells in the breast are not completely removed or destroyed, will the residual cells mutate rapidly to produce metastatic clones? A protocol of the NSABP considered this question.503 Some patients with primary disease were treated by lumpectomy without radiotherapy. The local relapse rate was significant, indicating that residual tumor was left unchecked. Yet, such patients did not have a higher metastatic rate (measured by the survival rate) than patients treated adequately de novo by lumpectomy plus immediate radiotherapy or by mastectomy.

This latter result is surprising, since some metastases from residual cancer should be expected even if that residual disease did not progress in its ability to release metastatic clones. Longer follow-up of this trial might eventually reveal a higher rate of distant metastases. However, the absence at 12 years of a major negative survival impact of local recurrence indicates that tumor can remain in a breast, grow in the breast, and yet not develop metastatic cells at a very high rate. If metastases develop, therefore, the odds are high that they have already done so before the time of first clinical presentation.

Since this view was first expounded in the first edition of this textbook, more recent evidence concerning radiotherapy to the chest wall after mastectomy has become available. These data may be regarded as confirmatory. Several papers have shown that for patients with a high probability of local recurrence the use of such radiotherapy decreases the chances of local and (the key point) distant recurrence.504–506 Yet the differences are small, and are not apparent for many years after primary therapy. At high rates of mutations the local residual disease would be expected to produce metastatic clones universally: hence, the rate of mutations cannot be very high. For further discussion of the practical and natural philosophical implications of these results, the reader is referred to a recent paper by Hellman.507

In a similar vein, the Goldie-Coldman model concludes that for chemotherapy to be effective it must be started as soon as possible after diagnosis. To restate the rationale: the hypothesized rapid mutation rates would otherwise produce cells that would be resistant to all treatments. Here as well, however, contradictory evidence is well known. For example, in a pioneering trial in the treatment of acute leukemia, the response to an antimetabolite (A) was the same whether that drug was used first or sequentially after the use of a different antimetabolite (B).508 Had mutations toward the drug A occurred rapidly during treatment with drug B, we should not have expected these results. Another two examples are found in the treatment of breast cancer. In a randomized trial, the International (Ludwig) Breast Cancer Study Group found that it was equally effective to give node-positive breast cancer patients either 7 months of chemotherapy starting within 36 hours of surgery or 6 months of chemotherapy starting about 4 weeks later.509 Again, rapid mutation rates should have impeded response after the delay, but this did not occur. A very important result, unfortunately as yet published only in abstract, was obtained in a trial of high-dose chemotherapy (with autologous hematopoietic stem cell rescue, ABMT) for metastatic breast cancer.510 Here patients in complete remission from conventionally-dosed chemotherapy were randomized to receive ABMT immediately or were followed in an unmaintained remission. Those 90% who relapsed from the unmaintained remission were treated with ABMT. The duration of disease control and survival from the time of ABMT was the same in both arms of the trial. (Incidentally, this translated to an overall improved median duration of disease control and survival for the patients receiving delayed ABMT. This is partially because the 10% of patients who remained disease free for more than 5 years from the conventional therapy without ABMT raised the whole curve. It is also because the delayed ABMT patients had an overall duration of disease control that was the sum of that which they experienced from the conventional therapy and from the ABMT.) Had mutations toward resistance to chemotherapy occurred rapidly during the unmaintained remission, the delayed-ABMT arm should have done worse. A trial in stage B nonseminomatous testicular cancer provides yet another example.511 This trial randomized patients after retroperitoneal lymph node dissection either to two cycles of cisplatin combination chemotherapy or to observation. At a median follow-up of 4 years, 6% of patients randomized to adjuvant chemotherapy relapsed, compared with 49% of patients randomized to observation. Yet, because the response of relapsing cases to subsequent chemotherapy was excellent, there was no significant survival difference between the two approaches. Hence, this is evidence that most testicular carcinomas retained their chemosensitivity in spite of a prolonged period of unperturbed growth. We may conclude, therefore, that leukemia cells, and breast and testicular cancer cells that are residual after surgery, can grow unperturbed and yet not develop drug-resistant mutants at a fast rate.

Other controversial implications challenge the validity of the Goldie-Coldman model. The model concludes that adjuvant treatment must be instituted as early as possible in the growth history of a cancer to be effective. Yet several pilot studies and one major multiinstitutional trial failed to find an advantage to preoperative chemotherapy for primary breast cancer.512,513 The model also concludes that if drugs are used postoperatively, they have to be used as soon as possible after surgery to be effective. Hence, Goldie-Coldman recommends that all drugs in an adjuvant regimen be introduced immediately, lest their biologic impact be dampened by mutations toward drug resistance. This hypothesis was questioned in a trial by the CALGB that gave node-positive primary breast cancer patients 8 months of an adjuvant CMF (plus vincristine and prednisone) regimen.514,515 The CMFVP was followed by either more CMFVP or by 6 months of vinblastine, Adriamycin, thiotepa, and halotestin (VATH). Patients receiving the cross-over therapy had a significantly improved disease-free survival, especially those with four or more involved axillary nodes. In a similar vein, it is of note that a trial in Milan found no advantage to Adriamycin following CMF for patients with one to three involved nodes,516 that is, the cross-over effect was not seen in patients with lower risk of relapse. This differs from the results of a pivotal trial using paclitaxel in the adjuvant setting, which is discussed below. The point is that for many patients, dominant resistance to VATH did not develop during the 8 months of CMFVP treatment in those cells escaping CMFVP. This result, therefore, does not confirm the Goldie-Coldman hypothesis. The implications of the CALGB’s results in patients with higher degrees of nodal involvement, including the issues of simultaneous versus sequential therapies, dose scheduling, and optimal duration, are discussed in more detail below.

The assertion most singularly identified with the Goldie-Coldman model is the recommendation for alternating chemotherapy sequences. To repeat; they say that it is so important to give drugs as early as possible that if one cannot deliver a true simultaneous combination using all the drugs, one should alternate sequences rather than use the drugs in sequential blocks. Has this strategy demonstrated unequivocal advantages? Numerous attempts to improve the prognosis of patients with SCLC by alternating chemotherapy sequences have resulted in little or no benefit.517 Another relevant trial concerns the treatment of diffuse aggressive non–Hodgkin’s lymphoma. The National Cancer Institute (NCI) found no advantage to a ProMACE-MOPP hybrid, which delivered eight drugs during each monthly cycle, over a treatment plan delivering a full course of ProMACE (prednisone, methotrexate, Adriamycin, cyclophosphamide, etoposide), which was then followed by MOPP (mechlorethamine, vincristine, procarbazine, prednisone).518

The Goldie-Coldman principle was also examined in the context of advanced Hodgkin’s disease, where MOPP was compared with MOPP alternating with Adriamycin, bleomycin, vinblastine, and dacarbazine (ABVD). ABVD is an effective first-line therapy for Hodgkin’s disease and is also an effective salvage regimen for patients who are refractory to MOPP.519,520 Among chemotherapy-naive patients, MOPP-ABVD was found to be superior to MOPP, with regard to complete remission rate, freedom from progression, and survival.521,522 These results suggested that their might be some advantage to the “all drugs early” idea. However, the CALGB found that the complete remission rate and failure-free survival with MOPP-ABVD, although better than with MOPP alone, was not different from that with ABVD alone.523 Indeed, the superiority of MOPP-ABVD and ABVD over MOPP may have been due to differences in dose received, since only about 40% of MOPP patients received full doses of the cytotoxic agents by the third cycle, whereas these percentages were greater than 70% on ABVD and on MOPP-ABVD. At comparable levels of received dose, there were no clear advantages to the alternation of MOPP and ABVD over ABVD alone. Similarly, the NCI found no advantage to MOPP alternating with lomustine, Adriamycin, bleomycin, and streptozocin over MOPP alone.524 An American intergroup trial has found that a hybrid of MOPP-ABVD was superior in complete remission duration, failure-free survival, and overall survival to MOPP followed by ABVD.525 As with MOPP-ABVD in the CALGB trial, however, it is possible that this result may be explained by dose differences, that is, patients treated with the hybrid regimen received higher doses because of the necessity to modify for toxicity the doses of MOPP in the regimen that delivered MOPP followed by ABVD. It is also possible that the earlier introduction of Adriamycin in the hybrid might have been advantageous because such an approach could diminish the adverse impact of the emergence of multi-drug resistance. These points are discussed below in the context of the NortonSimon model.

Lessons learned in the treatment of the lymphomas have extended to the treatment of breast cancer, that is, alternating cycles that have not resulted in a dosage difference have not proved advantageous. For example, the VATH regimen is active against tumors relapsing from or failing to respond to CMF, and thereby meets the non–cross-resistance requirements of the Goldie-Coldman model.526 Yet, in patients with advanced disease, the CALGB found no advantage to CMFVP alternating with VATH over CAF or VATH alone.527 A direct comparison of alternating and sequential chemotherapy in the adjuvant chemotherapy of breast cancer was conducted in Milan. This group had previously generated historically controlled data that suggested a benefit from a sequential approach,528 the rationale for which is discussed below.529 In the more recent study, female patients with stage II breast cancer involving four or more axillary lymph nodes were randomized between two arms.530 Arm I prescribed four 3-week courses of Adriamycin (A), followed by eight 3-week courses of intravenous CMF (C), symbolized as AAAACCCCCCCC. Arm II stipulated the use of two courses of intravenous CMF alternated with one course of Adriamycin four times for a total of 12 courses, symbolized as CCACCACCACCA. The total amounts of Adriamycin and CMF in both arms were equal. Yet the patients who received arm I had a higher diseasefree survival and a higher overall survival than those on arm II. With total dose controlled, alternating courses of chemotherapy were found to be inferior to a cross-over therapy plan. These preliminary results have been confirmed by long-term follow-up analysis.531

The sequential application of drugs has proved to be a useful strategy in the treatment of leukemias. In adult acute myelogenous leukemia, a high rate of complete remission is obtained with cytarabine plus anthracyclines, but the duration of the responses is short. Postremission maintenance therapy has been shown by the CALGB to be relatively ineffective when given at low doses.532 Moreover, a trial showed that 32 months of postremission therapy were not superior to 8 months of the same therapy,533 similar to the failure of longer courses of adjuvant chemotherapy to improve results achieved by 4 to 6 months of such treatment in breast cancer.471 A randomized trial was recently reported that studied 596 patients out of 1,088 who had achieved complete remission with induction chemotherapy.534 This trial was designed to question the effectiveness of intensive postremission chemotherapy, exploiting the steep dose-response curve for cytarabine.535 The study found that the high-dose regimen was the best of three different dose schedules of cytarabine. Indeed, the best results were comparable with those reported in similar patients undergoing allogeneic BMT during first remission.534,536 The Children’s Cancer Group (CCG) has reported that intensive induction, followed sequentially by intensive consolidation and later intensification, was superior to other strategies in the treatment of childhood acute lymphoblastic leukemia.537 These observations have major practical and theoretic implications, as they suggest that strategies other than those advocated by the Goldie-Coldman hypothesis may have significant clinical impact.

The foregoing detailed examination of the Goldie-Coldman model was provided not only to provide discussion points regarding this particular concept but also to illustrate the relevance of growth curve analysis to treatment design. The Goldie-Coldman model is mathematically sensible and may well be applicable to some aspects of cancer biology. The model is also of major historic importance, in that its publication rekindled interest in the quantitative development of drug resistance. These two points are valid even though several of the model’s major predictions have not been sustained by clinical data. Yet, we are left with an enigma: how can a model that is so reasonable and seemingly so well grounded in kinetic dogma (log-kill) fail to generate a successful clinical strategy? One reason for a discrepancy between tenable theory and empiric results is the invalidity of underlying assumptions. An assumption of particular consequence in this regard, one that merits re-evaluation in face of the negative data reviewed above, concerns the concept of absolute drug resistance.

Implications of Relative Drug Resistance

The Goldie-Coldman model is very concerned with absolute drug resistance. Yet, it is now well established that much drug resistance is relative rather than absolute.538 A cell that is absolutely resistant cannot be killed with any pharmacologic dose level of the agent. Relative drug resistance, on the other hand, depends on the dose level employed. In terms of the SkipperSchabel-Wilcox model, one tumor may experience a log kill of two (99% reduction in cell number) when it is exposed to a certain dose and duration of treatment. Another, more resistant, tumor may experience a log kill of one (90% shrinkage) when it is treated with exactly the same therapy. However, if the dose intensity of chemotherapy against the relatively resistant tumor is increased, the log kill can increase as well.539,540

Clinically, even two-fold increases in dose level can have profound effects on the curative impact of chemotherapy.538 Yet, this is not always seen with all drugs, nor in all diseases.541 In retrospective analyses of the adjuvant chemotherapy of operable breast cancer542,543 and of the chemotherapy of advanced lymphoma,544 a high dose seems to be a key beneficial variable. Yet, even here, the validity of conclusions based on retrospective data has been questioned.545,546 In randomized trials in childhood acute lymphoblastic leukemia,547 adult germ cell tumors,548 advanced breast cancer,549 and breast cancer in the adjuvant setting,550 the higher-dose regimen has proven superior. Yet, results do not indicate a strictly rising dose-response relationship. For example, doses of cyclophosphamide over 600 mg/m2 do not improve results in the adjuvant chemotherapy of breast cancer,551 nor do doses of doxorubicin over 60 mg/m2.552

How do we explain this complicated relationship between dose and effect? From a kinetic viewpoint, the importance of dose is defensible. In many animal experiments, the log kill will be greater for the regimen with a higher dose intensity.553 One problem is that the concept of dose intensity requires definition. It is not just the total amount of drug received, nor is it just the amount of drug received per unit of time; rather, it is a mathematic combination of both. Dose intensity is actually a combination of dose escalation (raising the dose level) and dose density (increasing the amount of drug per unit of time, usually by shortening the total duration of treatment, while keeping the total amount of drug constant). If regimen I gives X amount of drug over Y days, and if regimen II gives 2X amount of drug over Y days, then regimen II is clearly more dose intensive. Regimen III, giving X amount of drug over Y/2 days, is also more intensive than regimen I. Although the dose rate of drug delivery of regimen III (2X/Y drug per day) is equivalent to regimen II, regimen II delivers more total drug and thus may be superior to regimen III in clinical efficacy. Hence, dose intensity alone may not account for clinical superiority. Yet, sometimes, once a certain minimal total dose is achieved, further increases in total dose are unimportant. For example, a number of trials have shown that durations of adjuvant chemotherapy longer than 4 to 6 months do not improve clinical results in operable breast cancer.554–557 Therefore, once the minimal total dose is determined empirically and adhered to, dose intensity should be an important determinant of cell kill.

The shape of the relationship between cell-killing capacity and dose is not totally clear for any drug, but for some agents, some data suggest a strictly proportional relationship up to a point. We may use as an example the randomized trial by the CALGB that treated node-positive patients by one of three plans of CAF adjuvant treatment (cyclophosphamide, doxorubicin, 5-fluorouracil).550 (Further studies on dose levels greater than those employed in this trial are discussed in the next section.) Let Z equal a certain total cumulative dose of chemotherapy: the three regimens gave either 2Z over 4 months (plan I), 2Z over 6 months (plan II), or Z over 4 months (plan III). Plan I was superior to plan III in reducing the rate of recurrence, but no difference between plan I and plan II has as yet been reported, except for a subset of patients.558 Hence, the total anticancer influence of each of these regimens seems to be strictly proportional to the total dose administered. For plan I, it was 2Z, the sum of 2Z over the first 4 months plus zero for the 2 additional months. Plan II also gave 2Z but over the entire 6 months. Plan III delivered half as much total anticancer influence, the sum of Z over the first 4 months, then zero for the remaining 2 months. A proportional dose-response relationship would predict that plan III should be inferior to both plan I and plan II, which was observed. One qualifier in this argument is that if CAF chemotherapy cures some patients, then plan I might eventually prove to be superior to plan II. This is because the cancer cell killing accomplished at 4 months from 2Z given over 4 months should be greater than the cell killing measured at 4 or at 6 months from 2Z given over 6 months. For some patients given 2Z over 4 months, the log kill might be enough to preclude disease regrowth. This might explain the superiority of plan I in patients with HER-2–overexpressing tumors.558 That such tumors may be especially sensitive to higher dose levels of doxorubicin is now suggested by the results of several corroborating studies.559,560

The global conclusion of this analysis is that clinical treatment failure may be the consequence of insufficient dose intensity (i.e., 2Z over 6 months when it could have been given over 4 months). A tumor may relapse because some of its cells, relatively but not absolutely insensitive to the agents applied, are not exposed to enough drug to be eradicated. This is analogous to a bacterial infection relapsing because an insufficient dose intensity of an antibiotic is applied, even though the microorganisms are sensitive in vitro. In both infection and neoplasia, however, prolonged or repeated episodes of low-dose therapy can give rise to absolute resistance by the selection of biochemically resistant cells.

If insufficient dose intensity is a major cause of failure to cure, then it is possible that increased dose intensity itself can improve clinical results.561,562 This statement is phrased as a possibility rather than as a certainty because it is highly dependent on the host tolerance to the chemotherapy and also on the shape (degree of steepness and nonlinearity) of the dose-response curve for each agent for each disease. It also depends on the shape of the curve of tumor volume regression, which is considered in the next section.

Gompertzian Model

The log-kill model originated from, and is expressed in terms of, exponential growth. How realistic is this pattern of growth for human cancer? Only some tumors in some special situations seem to follow this pattern. Nodular pulmonary metastases and, much less commonly, measurable lesions in other sites do seem to follow exponential growth during periods of observation that are short in relation to the total life histories of the tumors.563–565 Doubling times, ranging from 1 week to 1 year, with a median of 1 to 3 months, correlate with histologic type, growth fraction, and cell loss fraction. Yet, many, if not all, human cancers do not grow exponentially because they do not have constant doubling times.566–568

In 1825, Benjamin Gompertz described the nonexponential growth pattern that has received the most attention by cytokineticists.569 It differs from exponential growth in several important ways. In exponential growth, the fixed doubling time means that the growth rate relative to tumor size always remains constant. In Gompertzian growth, however, the doubling time increases steadily as the tumor grows larger. Figure 38.2 illustrates a typical breast cancer (the specifics of this tumor’s Gompertzian growth are detailed below). Between 102 cells and clinical appreciation at 1010 cells, the shape of the growth curve on the semilogarithmic plot deflects downward. An exponential curve would appear as a straight line. The progressive respective slowing of Gompertzian growth may be more the result of decreased cell production than of increased cell loss in larger tumors,33,34 that is, the fraction of dividing cells seems to decrease as the tumor gets larger, possibly in proportion to the ratio of tumor cells over total tumor volume, which decreases as volume increases as a consequence of fractal geometry.570 Failure to appreciate the existence of Gompertzian growth can lead to certain errors. For example, the false assumption of exponential growth would suggest that the tumor’s doubling time when below the level of clinical appreciation is the same as that which is clinically observed. That doubling time would be unrealistically slow.571 The assumption of exponentiality has led to some unrealistic estimates of the time from carcinogenesis to the appearance of clinical disease, that is, estimates that are too long.

Figure 38.2. Gompertzian model of breast cancer growth.

Figure 38.2

Gompertzian model of breast cancer growth.

The biologic basis for Gompertzian growth is still unclear. An old, now unpopular, concept is that a solid tumor “outgrows” its supply of nutrients and so cannot sustain unimpeded exponential growth. This has been challenged by evidence that large tumors, with relatively slow growth rates, usually have adequate vascularity. Indeed, that may be why they are large tumors: they can induce the blood vessels (neovascularization) that allow them to grow to large size.572 A new concept concerns the relation between the cancer cell and its local environment, which includes itself.579 Most cancers are composed of repeating elements—such as branching tree patterns or multiple nodules—that are self-similar over various scales of size. Such patterns are called fractals. The dimension of a fractal is called its mass dimension: a mass dimension of 3 means that the structure is solid and regular (like a brick); a mass dimension of 2 means that the cells are arranged in a sheet. The average mean mass dimension for a normal tissue is about 2.7.573–578 A fractal geometric pattern means that the number of cells is proportional to the tumor volume raised to a power ≤ 1, that power being a function of the mass dimension. Smaller mass dimensions produce lower power constants and, therefore, low ratios of number of cells per volume of tumor. Such tumors, with relatively few cells per microscopic field, tend to be more benign, whereas cancers with higher mass dimensions (more cancer cells and little intervening stroma) tend to be more malignant. It has been shown that masses growing in a manner that preserves the power relationship between cell number and volume follow a Gompertzian curve. The rate of deviation from exponentiality is functionally related to the power constant: values close to 1 give more aggressive growth, and smaller values give Gompertzian curves that plateau at a benign size, as in ductal carcinoma in situ of the breast.579 An interesting aspect of this thesis is that a precancerous mass can suddenly become recognizable as malignant with just a small additional increment in the power constant over a certain threshold. Since the power constant reflects the mass dimension, tissues with widely varying mass dimensions can be benign, but once the power constant is close to a critical degree (about 2.85/3.00), a further small change toward increased mass dimension could result in malignant transformation. The molecular bases of the power constants that define Gompertzian growth are an active topic of study, but current hypotheses concern autocrine and paracrine growth factor loops, which might also determine invasion and metastases,579 that is, if the cells are responding to a concentration of growth factors and if that concentration is proportional to the number of cells divided by their total volume, this would be enough to explain Gompertzian growth.

Some of the important characteristics and implications of Gompertzian growth will be illustrated below.580

Speer-Retsky Model

In the 19th century, breast cancer was often managed from diagnosis to death without surgery or any other effective treatment.497 Speer, Retsky, and colleagues used survival histories for such patients, plus the growth histories of mammographic shadows,581 and data for disease-free survival following mastectomy,582 to fit a model in which tumors grow in randomly increasing steps of Gompertzian plateaus.583 This work is interesting because it demonstrates that growth curves that deviate far from exponentiality can fit clinical data. However, the validity of the model has been challenged on several counts. First, it is questionable whether the temporary plateaus that are predicted by the model are ever actually observed.545 Second, the Speer-Retsky model predicts that to maximize the efficacy of postsurgical adjuvant chemotherapy, it should be applied intermittently over a prolonged duration so as to coincide with the presumed growth spurts. This approach, however, proved ineffective in a clinical trial.584 Third, the same clinical data as used by Speer and Retsky can be fitted more parsimoniously, and with greater accuracy, by a family of simple Gompertzian curves.580 A family of exponential curves could also be fitted to these data; however, the model that would result could not account for both disease-free survival and overall survival because the time from relapse to death would be too short. The curve used in Figure 38.2 is the median curve from the family of simple Gompertzian curves mentioned above.580 Note that it takes just 3 months for the tumor to increase by two logs from 102 to 104. Yet, it takes 5 months for 109 cells to grow just one log to 1010. This is a relevant example of increasing doubling time with increasing tumor volume.

Norton-Simon Model

The Skipper-Schabel-Wilcox model is so meaningful because it conceptualizes both tumor growth (exponential) and tumor regression (log-kill) in response to chemotherapy. We have already discussed the profound implications of the positive association between the rate of tumor regression and the dose intensity of chemotherapy. Experimental and clinical data also indicate that the rate of tumor regression is positively related to the growth rate of the unperturbed tumor just prior to treatment.585,586 This important observation is corroborated by experimental data: the logarithm of the surviving fraction of an experimental neoplasm is negatively correlated with the logarithm of the tumor size at the time of treatment.587

This log-log relationship extends the Skipper-Schabel-Wilcox model. In exponential growth, the growth rate is always proportional to tumor size. If a tumor at size X is growing at rate Y, the same tumor at size 2X would grow at rate 2Y. On a logarithmic scale, these growth rates would appear to be the same since the rate of growth per tumor size (Y/X) is the same in both cases. A rate of regression proportional to growth rate is, therefore, also proportional to tumor size, which results in a constant proportional (or “log”) kill, that is, imagine that a tumor at size X shrinks at rate Z to achieve a size X/2 in 1 week (a change in size by the proportion of one half). The same tumor at size 2X, if treated with the same chemotherapy, would shrink at rate 2Z to achieve size X in 1 week (also a change by the proportion of one-half). The absolute volume shrinkage would be X/2 in the first case and X in the second case, but the proportional change would be one-half in both cases (X to X/2; 2X to X). The distinction between the Skipper-Schabel-Wilcox model and the Norton-Simon model is that in Gompertzian growth, unlike exponential growth, the growth rate of the unperturbed tumor is always changing, that is, if a tumor at size X grows at rate Y, the same tumor at size 2X would grow at a rate less than 2Y.

In Figure 38.2 a realistic numeric example illustrates the implications of Gompertzian regression. In Figure 38.2A the tumor is observed to grow to clinical diagnosis at 1010 cells (about 10 cubic centimeters of packed tumor cells or about 100 cubic centimeters at a packing ratio of 1:10). Let us assume for the purposes of this illustration that 90% of the tumor is in the breast and axillary lymph nodes, and about 10% of the cells are scattered in various micrometastatic sites. The mass in the breast itself would be about 5 cm in diameter. If this mass and the axillary contents are removed completely (or destroyed completely with radiotherapy), the total body’s burden of tumor is reduced to the 109 metastatic cells. Since the 109 cancer cells are spread throughout the body, they are invisible to our diagnostic tests. No adjuvant therapy is given. The tumor grows for 13.5 months until it reaches about 1011 cells in total number, which is large enough for detection as metastases. At this time, chemotherapy is employed, reducing the total cell number to about 109 (a two-log kill). A period of remission is experienced but the tumor eventually relapses, leading to death at 1012 cells.

Figure 38.2B graphs the same tumor, but here the same chemotherapy is applied in the adjuvant setting at a total tumor size of 109 cells. The relative rate of growth (the slope of the curve on this semilogarithmic plot) is faster for the tumor at 109 cells than it would be for the same tumor at 1011 cells. This is clear from inspection of Figure 38.2A. According to the Norton-Simon model, the relative rate of regression of the 109-cell tumor will be faster as well, even though the dose and schedule of chemotherapy are identical. Figure 38.2B shows that the chemotherapy that had caused a two-log kill of 1011 cells causes instead a five-log kill of 109 cells. The 104 cells that result regrow to relapse as stage IV disease at 1011 cells and to kill the patient at 1012 cells. Comparison of Figures 38.2A and 38.2B demonstrates a remarkable result. The time from surgery to stage IV is clearly longer when adjuvant chemotherapy is applied. However, the time from surgery to death is identical! The greater fractional kill in the adjuvant setting is counterbalanced by a faster fractional regrowth. This may explain why the adjuvant chemotherapy of breast cancer has less impact on overall survival (a function of eventual tumor body burden) than on disease-free survival. It may also explain why the survival duration of patients with stage IV breast cancer has remained fairly stable in recent decades in spite of more aggressive approaches to management.588–590

What if another chemotherapy plan, more aggressive but still subcurative, is used in the adjuvant setting against the 109 cells? This is illustrated in Figure 38.2C. If 102 cells are left instead of 104, it will take only 3.5 months longer for the tumor to reach 1012, since the growth from 102 cells to 104 cells is very rapid. Hence, adjuvant therapies can differ greatly in log kill, with only a slight impact on eventual clinical results measured years later. This slight impact could easily be lost in the “noise” caused by random fluctuations, especially in clinical data sets of small size.

The pessimistic side of this observation is that much more aggressive chemotherapy may produce little real clinical benefit. Short-course very-high-dose chemotherapy with hematopoietic stem cell rescue has been employed in an effort to eradicate all breast cancer cells in the adjuvant setting. The results of randomized trials in this regard are mixed or preliminary. At the most recent meeting of the ASCO, several studies were presented, only one of which—chaired by Bezwoda in South Africa—was clearly in favor of the very-high-dose approach.591–594 The largest American trial—coordinated for the Intergroup by the CALGB—was not yet positive.592 But this study will require longer follow-up for definitive evaluation (about the years 2001 to 2002). The optimistic side of this analysis is that if the model holds, current adjuvant chemotherapies for breast cancer are actually bringing us much closer to total cellular eradication than we might otherwise be led to suspect. Indeed, the one positive study employed two cycles of high-dose treatment, which might be enough to bring some patients beyond the threshold of disease eradication.591,595 Even with drug-sensitive diseases, such as bacterial infections responsive to antibiotics, more than one cycle is almost always necessary for cure. Further evaluation of this regimen and other multi-cycle high-dose regimens is currently planned or in progress.

The basic concept is that survival can be improved to a significant degree only when tumor cell populations are actually eradicated or when their regrowth is otherwise meaningfully impeded. In our previous discussion of cellular proliferation, we concluded that heterogeneity in drug sensitivity is a characteristic of neoplasia. How can tumor cell eradication be accomplished in a heterogeneous cancer? The answer may lie in the application of kinetic principles. Gompertzian regression means that slower-growing collections of tumor cells will tend to regress more slowly in response to a given therapy than will the faster-growing tumor cells treated at the same time.596 In a heterogeneous cancer, therefore, the slower-growing clones are also the most kinetically resistant. These slower-growing cells should be in the minority by the time of diagnosis because, by then, they should have been overgrown by the faster-growing cells. The existence of a population of slow-growing cells may also be the consequence of the hypothetic ability of chemotherapy to differentiate cells that are not killed.597

The best way to treat a heterogeneous population is to treat the dominant, faster-growing populations as efficiently as possible and then to treat the numerically inferior, slower-growing populations as efficiently as possible.529 As in the Skipper-Schabel-Wilcox model, the most efficient therapy is the most dose-dense therapy, giving as much drug as possible over as short a period as possible. This pattern of therapy is accomplished much better by sequential treatment than by strict alternation. For example, in the adjuvant breast cancer trial from Milan described above, the alternating plan, CCACCACCACCA, gave eight cycles of CMF over 30 weeks and four cycles of Adriamycin over 33 weeks.531 The cross-over, sequential plan, AAAACCCCCCCC, gave eight cycles of CMF over 33 weeks and four cycles of Adriamycin over 9 weeks. The dose density of the CMF was almost the same, but for Adriamycin the cross-over significantly improved the density. This could, by itself, account for the superiority of the AAAACCCCCCCC treatment. A similar result has also been seen in the adjuvant chemotherapy of resected osteosarcoma: Adriamycin alone was superior to Adriamycin alternating with high-dose methotrexate, presumably because the dose density of the superior agent (Adriamycin) was diluted by the alternation.598 The results of trials in acute leukemia in adults and children537 described above are also consistent with the concept of dose-dense sequential treatment plus dose escalation as a means of increasing dose intensity and thereby inproving clinical benefit.

In the breast cancer trial from Milan,531 the use of Adriamycin initially might have caused greater cell kill by avoiding the expression of the multi-drug resistance gene, which tends to progress over time, independent of treatment.599,600 Conversely, the delayed use of Adriamycin might have compromised the efficacy of two other regimens described previously: ABVD following prolonged MOPP for advanced Hodgkin’s disease525 and Adriamycin following 6 months of CMF for primary breast cancer with low degrees of nodal involvement.516

Although the invention and interpretation of clinical trials intended to test cytokinetic principles are fraught with subtleties and complexities, dose-dense sequential therapy has been successful in the laboratory. The only way to cure 108 L1210 cells is by induction with cytosine arabinoside plus 6-thioguanine for two or three courses, followed by one course of high doses of cyclophosphamide and carmustine (BCNU) given simultaneously.602 In the treatment of BDF1 mice bearing the M5076 tumor, the addition of one dose of l-phenylalanine mustard (l-PAM) (a drug that by itself is only weakly active) after four doses of methyl-lomustine (CCNU) doubles the complete remission rate and the median survival.603 The presumed mechanism for this latter effect is that the few cells left after methyl-CCNU induction are l-PAM sensitive, whereas in the untreated situation, most cells are methyl-CCNU sensitive, and l-PAM resistant. In general, alkylating agents seem particularly helpful as the cross-over therapy.

Goldie and Coldman’s prediction of the superiority of alternating chemotherapy assumed stringent conditions of symmetrical tumor cell numbers, growth rates, and mutation rates. Day has performed computer simulations of mutation to drug resistance under asymmetrical conditions.604 He came to a conclusion similar to the Norton-Simon model regarding the expected superiority of a cross-over, sequential plan.605 By his worst drug rule, in a coordinated two-regimen plan, the therapy with a lower cell kill per treatment (the worst drug) should be used either first or, if it is used second, for a longer duration. However, the Norton-Simon model qualifies this to specify that the induction therapy must be sufficiently cytoreductive for the residual tumor cell burden to be low. This is another possible reason for the inferiority of ABVD following dose-reduced (and, hence, less cytotoxic) MOPP, compared with a hybrid MOPP/ABV, which could be delivered at fuller dosages.525 Theory therefore supports an efficient induction followed in sequence by one or more aggressive chemotherapeutic cross-overs. Indeed, in the treatment of acute lymphocytic leukemia in children, a classic trial demonstrated that induction by vincristine plus prednisone facilitates the anticancer activity of sequential methotrexate.606 The Children’s Cancer Study Group (CCSG) trial in childhood leukemia that gave intensive induction, consolidation, and intensification also demonstrated the importance of an efficient initial cytoreduction.537

The concept of dose-dense sequential therapy has been applied in several important clinical trials. A pilot study in breast cancer used Adriamycin following just 16 weeks of CMFVP for patients with node-positive primary disease.601 A major adjuvant trial in node-positive breast cancer gave doxorubicin plus cyclophosphamide with one of three dose levels of cyclophosphamide, followed by four cycles of paclitaxel or not. The justification of cross-over to paclitaxel (rather than forcing a simultaneous combination that would certainly have increased toxicity) was the concept of dose density. Although escalating the dose of doxorubicin did not improve results, the use of paclitaxel reduced the rate of recurrence by 22% and of death by 26%, which is comparable with the effects of CMF adjuvant chemotherapy over no therapy in the Worldwide (Oxford) Overview.470,551 This trial, coordinated by the CALGB for the Intergroup, led to the U.S. Food and Drug Administration (FDA) approval of paclitaxel for adjuvant use. The NSABP has completed accrual to a trial of similar design, and results are anticipated by the year 2001. The Eastern Cooperative Oncology Group (ECOG) is now coordinating an Intergroup trial of doxorubicin plus cyclophosphamide followed either by paclitaxel or docetaxel each four doses for 3 weeks, or 12 weekly administrations of each of these two taxanes. (The weekly administration is another method of increasing dose density.) The North-Central Cancer Treatment Group is coordinating a trial of doxorubicin plus cyclophosphamide followed by weekly paclitaxel with or without trastuzumab, the anti–HER-2 monoclonal antibody.607 The CALGB is conducting a 2 × 2 × 2 factorial study of stage III breast cancer that is also based on the dose-dense sequential use of doxorubicin plus cyclophosphamide, followed by weekly paclitaxel with or without trastuzumab. Other treatment plans exploit the ability of hematopoietic growth factors, such as granulocyte colony–stimulating factor (G-CSF) and granulocyte-macrophage (GM)-CSF608 to increase dose density and other means of hematopoietic reconstitution609,610 to permit dose escalation. In the adjuvant chemotherapy of breast cancer, the Intergroup has completed accrual to a Southwest Oncology Group (SWOG)-coordinated study of doxorubicin followed by G-CSF–supported high-dose cyclophosphamide versus a more conventional, simultaneous doxorubicin plus cyclophosphamide combination.611 Investigators at the Memorial SloanKettering Cancer Center have published data about a regimen called ATC that gives dose-dense doxorubicin followed by dose-dense paclitaxel followed by dose-dense cyclophosphamide.611 On the basis of results that hint at considerable efficacy, this regimen is now being compared with dose-escalated ABMT-supported treatment of women with stage II breast cancer and four to nine involved axillary lymph nodes. (The Intergroup is considering extending this study to include patients with 10 or more involved lymph nodes.) The CALGB has completed accrual to a 2 × 2 factorial trial that also applied several types of dose density. This trial is comparing doxorubicin plus cyclophosphamide followed by paclitaxel with all drugs given every 3 weeks or every 2 weeks as facilitated by the use of G-CSF. Another two arms use ATC (modified to use dose level comparable with the first two arms) with administrations every 3 or every 2 weeks.

For diffuse large cell lymphoma, an induction regimen with Adriamycin, vincristine, and prednisone has been followed by sequential high-dose cyclophosphamide, then methotrexate (plus vincristine), then etoposide, then l-PAM (plus total body irradiation), all with GM-CSF support. In a randomized comparison against a standard aggressive combination, the induction intensification plan proved superior in complete remission rate, failure from relapse, failure from progression, and event-free survival.612

These cytokinetic considerations may be as applicable to radiation therapy as to chemotherapy. The Gompertzian phenomenon of rapid repopulation of clonogenic cells after cytoreductive treatment is well documented in radiobiology. Moreover, clinical data suggest an acceleration of growth of the remaining viable tumor during the second part of protracted “split-course” radiation therapy.613,614 In the treatment of head and neck cancer, split-course treatment has been used to allow normal tissues to recuperate from radiation damage. In this treatment plan, it has been observed that an additional radiation dose is needed to overcome tumor regrowth during the rest interval between the split courses. The alternative hypothesis, that the higher radiation dose in split-course treatment could be needed because of increased radio-resistance of the tumor following the first part of the split course, is felt to be implausible.615 In fact, the tumor is actually more completely oxygenated during the second course of treatment, which should render it more radiosensitive.616 Hence, we are left with the likelihood of rapid regrowth between courses, more rapid than could be explained by exponential growth. The mechanism of such rapid regrowth relates to the three parameters that determine Gompertzian growth: mitotic cycle time, growth fraction, and cell loss (apoptotic) fraction. Cell cycle times of 2 to 4 days are commonly measured in head and neck cancers in the unperturbed state and after radiation therapy.617 Nevertheless, the doubling time can decrease from 60 to 4 days because of a persistence of the clonogenic cells (i.e., high growth fraction) resulting from a decrease in their tendency to differentiate or die by apoptosis (i.e., low cell loss fraction). It is important to note that this increase in proliferative parameters is occurring at a time of volume regression induced by the radiotherapy, that is, the observer may see cancer shrinkage, while the cells may be experiencing growth acceleration as a means of compensating for the effects of therapy. The same kinetic principles applicable to chemotherapy may be needed to overcome this potential cause of treatment failure. In this regard, a review of studies of head and neck radiotherapy has calculated the dose of irradiation needed to achieve local control in half the cases.616 This standard benchmark is consistently greater when the treatment is given over a 6-week interval than over a 4-week period,616 which is entirely consistent with the principle of dose density.

Mitotoxicity Hypothesis

Both the Skipper-Schabel-Wilcox and Norton-Simon models are based on the observation that the rate of tumor regression is positively related to the rate of unperturbed growth. The most obvious explanation for this observation is the mitotoxicity hypothesis: tumors regress most rapidly when they are growing most rapidly because more of their cells are then synthesizing DNA and other macromolecules in preparation for mitosis. Such metabolically active cells are thereby at particular risk for cytotoxicity by drugs that interfere with such synthetic processes.618 The intuitive notion is that poisoning the S-phase renders cells incapable of progressing successfully through the M-phase. This is a dominant idea in cytokinetic thinking, and it undoubtedly has considerable merit. Growth-stimulating substances (i.e., estradiol, epidermal growth factor) increase both cell proliferation and cell kill from Adriamycin in MCF-7 cells in vitro.619 Pharmacologic concentrations of estradiol enhance the cytotoxicity of the chemotherapeutic agent melphalan in hormone-responsive cell lines.620 These observations have been applied clinically, and hormone recruitment schemes have indeed resulted in high local response rates in locally advanced breast cancer.621,622 However, such treatments have proved only slightly better or no better than chemotherapy alone in metastatic breast cancer, except in data-driven subsets.623,624 Even when benefits were seen, methodologic issues have cast doubts on the analyzability of results.625

We must be cautious, moreover, in interpreting laboratory data that suggest an enhancement of chemotherapeutic cytotoxicity by manipulations that increase the S-phase fraction. Tamoxifen, which can cause a G1-S arrest in sensitive cell lines, does antagonize the cytotoxicity of melphalan and 5-fluorouracil, but it does so at dose schedules that do not affect cell proliferation.620 Tamoxifen actually enhances the cytotoxicity of Adriamycin and the alkylating agent 4-hydroxycyclophosphamide in this system. In fact, a broad acceptance of the mitotoxicity hypothesis leaves several cytokinetic enigmas unresolved. For example, only about 5% of the cells in an average tumor in breast cancer are in the S-phase. Thus, even if we use drugs that kill G1 and G2 cells, only about 15 to 20% of the tumor mass could possibly be killed by a single exposure to mitotoxic therapy. To get a one-log kill (90% regression) would require more than 10 such exposures (because [1 – 0.2]11 < 0.1). Yet regressions greater than one log are frequently seen after just a single exposure to high-dose chemotherapy.610 Even conventional chemotherapy, such as eight exposures to intravenous CMF, are simulated in Figure 38.2B to result in a five-log kill. It may, therefore, be implausible that such significant cytoreductions are due to mitotoxicity alone. Indeed, cytokinetic analysis of MCF-7 cells exposed to low levels of Adriamycin does not show an immediate S-phase reduction.626 There is an accumulation of cells in late S, G2, and M, but also a block of the G1 to S transition starting 2 days after treatment.

Another puzzle concerns the effect of chemotherapy on normal host tissues. Chemotherapy is certainly toxic to rapidly dividing bone marrow, alimentary mucosa, and hair follicles. Yet, these tissues usually recover from the impact of chemotherapy. Some cancers, however, that are growing no more rapidly than these normal tissues may experience cytoreductions from which they never recover, that is, acute leukemias, malignant lymphomas, choriocarcinomas, and germ cell cancers may be cured by chemotherapy regimens that do not eradicate the patient’s normal tissues that have comparable growth kinetics.

There is, at present, no established alternative to the mitotoxicity hypothesis that successfully relates cytokinetics to therapeutic cytotoxicity. One possibility is that chemotherapy could damage G0 cells that later exhibit their lethal injuries as they are recruited into cycle. Another, perhaps related, possibility is suggested by the thought that the hormonal therapy of responsive cancers works by growth factor perturbation, not by mitotoxicity.627 Could chemotherapy share with hormone therapy this mode of action? Long-term data on the probability of breast cancer relapse after adjuvant tamoxifen628 and CMF557 show similar qualitative changes. Breast cancer is a particularly relevant example because it is modulated by endogenous growth factors secreted by a subset of tumor cells in an individual cancer.629 The concept, however, may be generalizable since growth factors are important in many cancers. In the very genesis of cancer, malignant transformation frequently alters gene expression for growth factors, their receptors, and intracellular signal transduction proteins.630 Leukemogenic drugs, such as alkylating agents, are known to cause cytogenetic abnormalities, frequently at loci coding for products related to growth factors.631 It is even possible that the relation between tumor size and metastatic behavior, described in the context of the Goldie-Coldman model, is a consequence of the dependence of tumor cells on growth factors produced by the supporting stroma or the cells themselves.632

This discussion raises the possibility that chemotherapy, in addition to a gross mitotoxicity, might share with hormonal therapy an influence on growth factor loops.633 When hematopoietic cells are deprived of essential growth factors, they die by apoptosis.634,635 It has been well established that almost all chemotherapeutic drugs, as well as other lethal cytotoxins, also cause apoptosis.636 The existence of chemotherapy-induced apoptosis by growth factor disruption could clarify several mysteries. It could explain why the histologic analysis of breast cancers regressing after chemotherapy does not always reveal a high degree of necrosis.637 It could explain why the TLI of breast cancer appeared not to predict chemosensitivity in locally advanced disease and in the adjuvant setting.638 By implicating host-tumor paracrine interactions, the growth factor hypothesis might explain how tumor resistance to alkylating agents could be operant in vivo but not in vitro.639 The theory would not, moreover, be incompatible with mitotoxicity itself: rapidly growing cells that are dependent on growth factors would be expected to regress most rapidly when their growth support system is perturbed.

In the laboratory, chemotherapy can influence growth factor pathways. Doxorubicin, for example, may upregulate EGFR in HeLa and 3T3 cells.640 Activation of protein kinase C (an intracellular signal of growth factor ligand-receptor interaction) enhances the cytotoxicity of cisplatin without increasing drug uptake.641 In the treatment of human cancer xenografts, antibodies to EGFR, which can by themselves inhibit growth,642 synergize with cisplatin.643 Such antibodies also synergize with Adriamycin in the treatment of A431 cells in athymic mice.644 A major multi-institutional clinical trial has established that trastuzumab, which inactivates HER-2, increases response rate, duration, and survival in combination with doxorubicin plus cyclophosphamide or in combination with paclitaxel.607

A consideration of the impact of anticancer therapy on growth factor mechanisms must eventually encompass the diversity of cytokinetic features present in most clinical cancers. For example, clonogenic cells are those cells capable of inexhaustible proliferation. These are understood to have cytokinetic parameters that are markedly different from other cancer cells with more limited proliferative capacity. While the clonogenic stem cells are overshadowed numerically by the majority of cells in the tumor, these minority cells are the most important to eliminate in order to prevent tumor recurrence from unstable remission. Malignant clonogenic cells may cycle more quickly than nonclonogenic cells, but this is usually mitigated by a high cell loss fraction. Cell loss from the clonogenic pool is accomplished by multiple mechanisms: differentiation, apoptosis, necrosis, exfoliation, and transportation away from the tumor in blood and lymph. Clearly, these cells differ biologically and cytokinetically from other cancer cells, as determined by genotypic differences that must be exploited to effect a cancer cure. It is, therefore, encouraging that the cytotoxic effects of chemotherapy might extend well beyond crude mitotoxicity. In this regard, cytokinetic analysis may play a key role in unraveling the relationships between cytotoxicity and molecular growth control. It is worthwhile to note that both aspects of cytokinetics, the study of cell proliferation, and the analysis of growth curves, are relevant to this field of inquiry.

Conclusion

Cytokinetics is the fundamental physiology of cancer medicine. Its scope is so broad that this chapter merely introduces its basic concepts, laboratory foundations, theoretic underpinnings, clinical relevance, and prospects for future development. This is a rapidly evolving field, both conceptually and technically, that touches all aspects of experimental and practical oncology.

Acknowledgment

The authors are deeply indebted to Stephanie Miranda for her expertise in preparing the manuscript.

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