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Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth.

ABSTRACT: Interactions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition, and proliferation inhibition) have been proposed, but precise determinants of the phenomenon remain poorly understood. Here, we formalized these theories into mathematical models and performed biological experiments to test them with empirical data. In syngeneic mice bearing two simultaneously implanted tumors, growth of only one of the tumors was significantly suppressed (61% size reduction at day 15, P < 0.05). The competition model had to be rejected, whereas the angiogenesis inhibition and proliferation inhibition models were able to describe the data. Additional models including a theory based on distant cytotoxic log-kill effects were unable to fit the data. The proliferation inhibition model was identifiable and minimal (four parameters), and its descriptive power was validated against the data, including consistency in predictions of single tumor growth when no secondary tumor was present. This theory may also shed new light on single cancer growth insofar as it offers a biologically translatable picture of how local and global action may combine to control local tumor growth and, in particular, the role of tumor-tumor inhibition. This model offers a depiction of concomitant resistance that provides an improved theoretical basis for tumor growth control and may also find utility in therapeutic planning to avoid postsurgery metastatic acceleration. Cancer Res; 77(18); 5183-93. ©2017 AACR.

SUBMITTER: Benzekry S

PROVIDER: S-EPMC5600871 | biostudies-literature | 2017 Sep

REPOSITORIES: biostudies-literature

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Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth.

Benzekry Sebastien S Lamont Clare C Barbolosi Dominique D Hlatky Lynn L Hahnfeldt Philip P

Cancer research 20170720 18

Interactions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition, and proliferation inhibition) have been proposed, but precise determinants of the phenomenon remain poorly understood. Here, we formalized these theories into mathematical models and performed biological experiments to test them with empirical data. In syngeneic mice bea ...[more]

PMID: 28729417

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Project description:Oncology drug efficacy is evaluated in mouse models by continuously monitoring tumor volumes, which can be mathematically described by growth kinetic models. Although past studies have investigated various growth models, their reliance on small datasets raises concerns about whether their findings are truly representative of tumor growth in diverse mouse models under different vehicle or drug treatments. In this study, we systematically evaluated six parametric models (exponential, exponential quadratic, monomolecular, logistic, Gompertz, and von Bertalanffy) and the semiparametric generalized additive model (GAM) on fitting tumor volume data from more than 30,000 mice in 930 experiments conducted in patient-derived xenografts, cell line-derived xenografts, and syngeneic models. We found that the exponential quadratic model is the best parametric model and can adequately model 87% studies, higher than other models including von Bertalanffy (82%) and Gompertz (80%) models; the latter is often considered the standard growth model. At the mouse group level, 7.5% of growth data could not be fit by any parametric model and were fitted by GAM. We show that endpoint gain integrated in time, a GAM-derived efficacy metric, is equivalent to exponential growth rate, a metric we previously proposed and conveniently calculated by simple algebra. Using five studies on paclitaxel, anti-PD1 antibody, cetuximab, irinotecan, and sorafenib, we showed that exponential and exponential quadratic models achieve similar performance in uncovering drug mechanism and biomarkers. We also compared exponential growth rate-based association analysis and exponential modeling approach in biomarker discovery and found that they complement each other. Modeling methods herein are implemented in an open-source R package freely available at https://github.com/hjzhou988/TuGroMix.SignificanceWe present a general strategy for mathematically modeling tumor growth in mouse models using data from 30,000 mice and show that modeling and nonmodeling approaches are complementary in biomarker discovery and drug mechanism studies.

Dataset Information

Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth.

Publications

Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth.

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