Format

Send to

Choose Destination
PLoS Comput Biol. 2014 Aug 28;10(8):e1003800. doi: 10.1371/journal.pcbi.1003800. eCollection 2014 Aug.

Classical mathematical models for description and prediction of experimental tumor growth.

Author information

1
Inria Bordeaux Sud-Ouest, Institut de Mathématiques de Bordeaux, Bordeaux, France; Center of Cancer Systems Biology, GRI, Tufts University School of Medicine, Boston, Massachusetts, United States of America.
2
Center of Cancer Systems Biology, GRI, Tufts University School of Medicine, Boston, Massachusetts, United States of America.
3
Department of Medicine, Roswell Park Cancer Institute, Buffalo, New York, United States of America.

Abstract

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

PMID:
25167199
PMCID:
PMC4148196
DOI:
10.1371/journal.pcbi.1003800
[Indexed for MEDLINE]
Free PMC Article

Supplemental Content

Full text links

Icon for Public Library of Science Icon for PubMed Central
Loading ...
Support Center