Abstract
BackgroundSimeoni and colleagues introduced a compartmental model for tumor growth that has proved quite successful in modeling experimental therapeutic regimens in oncology. The model is based on a system of ordinary differential equations (ODEs), and accommodates a lag in therapeutic action through delay compartments. There is some ambiguity in the appropriate number of delay compartments, which we examine in this note.MethodsWe devised an explicit delay differential equation model that reflects the main features of the Simeoni ODE model. We evaluated the original Simeoni model and this adaptation with a sample data set of mammary tumor growth in the FVB/N-Tg(MMTVneu)202Mul/J mouse model.ResultsThe experimental data evinced tumor growth heterogeneity and inter-individual diversity in response, which could be accommodated statistically through mixed models. We found little difference in goodness of fit between the original Simeoni model and the delay differential equation model relative to the sample data set.ConclusionsOne should exercise caution if asserting a particular mathematical model uniquely characterizes tumor growth curve data. The Simeoni ODE model of tumor growth is not unique in that alternative models can provide equivalent representations of tumor growth.
Highlights
Simeoni and colleagues introduced a compartmental model for tumor growth that has proved quite successful in modeling experimental therapeutic regimens in oncology
We propose an alternative mathematical formulation of the Simeoni model using delay differential equations, without recourse to a series of delay compartments
The model incorporating a delay differential equation is conceptually similar to the Simeoni model, the only difference being that the compartments Z2, Z3, and Z4 are replaced by a single compartment that incorporates a delay in elimination (Fig. 2)
Summary
Simeoni and colleagues introduced a compartmental model for tumor growth that has proved quite successful in modeling experimental therapeutic regimens in oncology. A distinguishing characteristic of the Simeoni tumor growth model is that under chemotherapy, a drug’s action is not instantaneous: rather, tumor cells pass through progressive stages of damage because of the drug’s mechanism of action. This delay in drug action is modeled through a series of delay compartments through which the cells transit before elimination. We conclude that one should be cautious if asserting that a particular tumor growth model uniquely characterizes experimental data
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