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Pittman RN. Regulation of Tissue Oxygenation. San Rafael (CA): Morgan & Claypool Life Sciences; 2011.

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Regulation of Tissue Oxygenation.

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Chapter 8Matching Oxygen Supply to Oxygen Demand

When the demand for oxygen by the cells in a tissue changes, it is important to be able to have a corresponding change in the oxygen supply so that there is an efficient distribution of oxygen within the organism. The overall regulation of tissue oxygenation starts with appropriate oxygen uptake in the lungs, transfer of that oxygen by diffusion to the blood and then delivery of the oxygenated blood to the various organs by the pumping action of the heart and bulk flow of oxygenated blood through the complicated branching networks of blood vessels. Once the blood has made its way to the microcirculation, transfer of oxygen to its final destination in the parenchymal cells takes place. Despite the overall importance of the major systems involved in oxygen transport to the tissues—the lungs, heart, blood and major vessels connected to the organs—the final steps in regulation of tissue oxygenation take place in the confined spaces occupied by the tissue cells and their associated network of tiny microvessels, the microcirculation.


Fick's principle was introduced in Chapter 6, and it can be used to advantage in the discussion surrounding the matching of oxygen supply to oxygen demand. Fick's principle, applied to an oxygen-consuming, blood-perfused tissue, can be quantified by the following equation:

Image e8-1.jpg(8.1)
where VO2 is oxygen consumption (or demand), Q is blood flow, [O2]in is inlet oxygen content or concentration and [O2]out is outlet oxygen content or concentration. [O2] is determined by O2 bound to the hemoglobin in RBCs (≈98% of total) since the dissolved oxygen in plasma and RBCs is negligible.

It is important to recognize that Fick's principle can be applied at the level of the whole organism, in which VO2 is whole body oxygen consumption, Q becomes cardiac output and [O2]in and [O2]out are arterial and venous oxygen contents, respectively. At the level of a single organ, VO2 is the oxygen consumption of the organ, Q is the blood flow through the organ and the oxygen contents are those of arterial and venous blood (recall the consequences of parallel vascular architecture of the circulatory system). Since it is not difficult to define the extent of the tissue involved in these two applications of Fick's principle (i.e., whole organism or single organ), the interpretation of data on oxygen transport from these perspectives is relatively straightforward. Application of Fick's principle to collections of microvascular networks, a single network or a single microvessel, requires careful consideration of the tissue volume supplied with oxygen by the network(s) or single vessel. However, when appropriate boundaries are defined to match the tissue volume to the microvessels supplying it with oxygen, Fick's principle must work since it is based on the fundamental principle of conservation of mass.


Rearranging Fick's principle, as was done in Chapter 6, leads to the following expression:

Image e8-2.jpg
The term Q [O2]in represents the oxygen delivery or supply and is the convective transport of oxygen determined mainly by arterioles. The term {[O2]in − [O2]out} / [O2]in represents oxygen extraction and is the diffusive transport determined mainly by capillaries. How does the cardiovascular system match oxygen supply to changes in oxygen demand? The convective component of oxygen transport can be modified by changing oxygen delivery or supply (Q [O2]in) through altered blood flow brought about by changes in arteriolar tone [37]. The diffusive component of oxygen transport can be modified by changing oxygen extraction ({[O2]in − [O2]out} / [O2]in) through altered oxygen extraction in capillaries [37] brought about by changes in the so-called functional capillary density or the surface area of capillaries in contact with RBCs.


The transition from rest to exercise is a classic example of an increase in oxygen demand by the tissue. The arterioles are involved since there is an immediate need for increased blood flow to provide the additional oxygen needed to satisfy the increased ATP hydrolysis and to prevent the accumulation of products of increased metabolism. The increased blood flow arises from the dilation of arterioles, the microvessels that control blood flow. The chemical signals responsible for arteriolar vasodilation are derived from several sources: increased production of vasodilators from the active muscle tissue; increased production of NO due to increased shear stress communicated to the endothelium; and spread of vasodilation to upstream sites due to the propagated response. The capillaries are involved because there is an immediate need to extract more oxygen from the incoming blood. In the past, recruitment of previously unperfused capillaries has been thought to play an important role; however, about 80% of the anatomically present capillaries are already perfused with RBCs [79]. The current view is that recruitment of more surface area for oxygen exchange in the capillaries is the key factor. There is a need to extract more oxygen from the incoming blood to the capillaries. Since most (≈98%) of the oxygen in blood is bound to the hemoglobin in RBCs, the surface area in contact with RBCs is important. It has been observed that the RBC content (hematocrit) in capillaries increases during muscle contraction, so that the capillary surface area in contact with RBCs increases. This is another way of saying that the functional capillary density (FCD) increases during exercise. Although a number of approaches have been used to quantify FCD, not all of them are aimed at quantifying the surface area in contact with RBCs.


It is instructive to consider the diffusion of oxygen from a small cylindrical volume element that extends along a capillary of length L from position x to x + dx [62,66]. Oxygen enters and exits the volume element by convection (i.e., bulk flow) and also diffuses between the blood and interstitial fluid (ISF) across the surface of the volume element. By considering the mass balance of oxygen entering and leaving the volume element, the following expression is obtained:

Image e8-3.jpg
where Q is blood flow, [O2] is oxygen content at the specified positions along the capillary, a is the solubility of oxygen, D is the diffusion coefficient for oxygen, 2πRx is the surface area per unit length of capillary divided by the capillary wall thickness and PO2 is the partial pressure of oxygen at the specified locations (position x along the capillary and the ISF). It is assumed here that PO2 in the ISF can be considered uniform. Note that the left-hand side of this equation is the difference in convective flow of oxygen into and out of the volume element, whereas by mass balance, the right-hand side is the rate at which oxygen diffuses between the blood and ISF (i.e., Fick's first law of diffusion).

In order to solve the above equation and determine the longitudinal oxygen profile along the capillary, it is convenient to express [O2] in terms of PO2. Neglecting dissolved oxygen and using the quasi-linear portion of the oxygen dissociation curve (i.e., the central portion above and below P50), one can approximate [O2] as

Image e8-4.jpg
where β′ is the slope of the oxygen dissociation curve (dSO2/dPO2 in mm Hg−1) in the quasi-linear region, [Hb] is the blood hemoglobin concentration and CHb is the oxygen carrying capacity of the hemoglobin. Substituting for [O2] in the above mass balance Equation 8.3 yields:
Image e8-5.jpg
where we define β as βCHb and γ as 2πRx. Using the definition of the first derivative of PO2 allows rewriting Equation 8.5 as:
Image e8-6.jpg
and then as:
Image e8-7.jpg

Integrating both sides of Equation 8.7 along the capillary from x = 0 (inlet) to some intermediate point between the inlet and L (outlet) yields the longitudinal PO2 profile along the capillary:

Image e8-8.jpg
where Γ (= 2πR Γx) is the surface area of the capillary divided by its wall thickness. Finally, the PO2 at the outlet (x = L) is given by:
Image e8-9.jpg

These results allow one to express the Oxygen Extraction in terms of PO2. Since the oxygen extraction is {[O2]in − [O2]out} / [O2]in, by substituting [O2] ≈ β[Hb] PO2, we have

Image e8-10.jpg

What factors can change to increase oxygen extraction and hence elevate oxygen consumption? By examining the variables in the previous equation—PISFO2, α, D, Γ, Q, β and [Hb]—for a given value of inlet PO2, oxygen extraction will increase when PISFO2, Q, β or [Hb] decreases; or α, D, or Γ increases. Consider the case of exercise and ask what changes are known to take place in these variables. PISFO2 initially decreases due to the increase in VO2; Γ and [Hb] increase due to the increase of capillary surface area in contact with RBCs (the local hematocrit increases in capillaries during muscle contraction); Q increases due to arteriolar vasodilation to bring more oxygen and wash out metabolic products; and β decreases due to the decreased slope of the oxygen dissociation curve (elevated CO2 and H+ shift the dissociation curve to the right, the Bohr effect). Thus, the decreased PISFO2 and β will lead to increased oxygen extraction, while the increased Q will have the opposite effect on oxygen extraction. Since Γ and [Hb] are both proportional to hematocrit and thus their ratio will not change, to the approximation being used in this description, these variables will not have an effect on oxygen extraction during muscle contraction.

It is of interest to consider two extremes of oxygen transport in the context of the present description. Those extremes correspond to the ratio αDΓ/[Hb] used to characterize oxygen transport as being very large or very small. In the case where αDΓ/[Hb] « 1, Fick's principle takes the form:

Image e8-11.jpg
so that oxygen uptake is independent of blood flow and is proportional to αDΓ, a measure of oxygen diffusion. This limit is known as “diffusion-limited oxygen exchange” since more oxygen could be delivered to the tissue if only diffusion (higher αDΓ) could be increased. In the case where αDΓ/[Hb] » 1, Fick's principle takes the form:
Image e8-12.jpg
so that oxygen uptake is independent of diffusion (through αDΓ) and is proportional to [Hb], a measure of oxygen delivery to the capillaries. This limit is known as “flow-limited oxygen exchange” since more oxygen could be delivered to the tissue if only flow (higher Q) or [Hb] (more oxygen carriers) could be increased. Under physiological conditions, oxygen exchange in the peripheral tissues is typically considered to be flow-limited.


Most models of blood flow and convective oxygen delivery in tissues make the simplifying assumption that blood flow and the oxygen supply are uniform. Experimental observations of blood flow, however, have shown that it is a variable with considerable spatial heterogeneity, as well as temporal heterogeneity [64]. Ellsworth et al. [28] have demonstrated heterogeneity of blood flow and oxygen delivery in capillaries and used computational modeling to predict the consequences of such heterogeneity on tissue oxygenation. Not surprisingly, the greater the heterogeneity in oxygen supply, the greater the heterogeneity in tissue oxygenation. Piiper and Scheid [69] have compared homogeneous and heterogeneous models of oxygen supply and assessed the consequences of the diffusion limitation on tissue oxygenation. An interesting situation arises when one considers that both the oxygen supply by the circulatory system and the oxygen demand by the tissue are heterogeneous. Is local blood flow regulated in such a way as to match local oxygen supply and demand? Walley [111] has presented an analysis of this circumstance and suggested that the answer is in the affirmative. Alders et al. [1] have provided experimental evidence that in the heart, oxygen consumption is heterogeneously distributed in parallel to heterogeneous oxygen delivery. If such coordination of the convective oxygen supply to local oxygen demand occurs in general, then there would be a tendency for tissue oxygenation to remain constant and uniform, an appearance of regulation of tissue oxygenation.

Copyright © 2011 by Morgan & Claypool Life Sciences.
Bookshelf ID: NBK54115


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