A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors

Abstract

Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model‐based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model‐based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.

Tumor Growth Dynamic Modeling in Oncology Drug Development and Regulatory Approval: Past, Present, and Future Opportunities

“…Unfortunately, the publication and application of individual tumor lesion models in clinical development is very limited. 8,51 The COVID-19 pandemic presents unprecedented challenges to patients, health care providers, and health care systems, including treatment of patients with cancer, due to self-isolation, significant limitations, or complete restriction to outpatient visit, cross-contamination during clinical visits, travel restrictions, or other considerations, such as the patient with cancer is also infected with COVID-19. [52][53][54] The American Society of Clinical Oncology (ASCO) provided links for various oncology societies or organizations who developed guidance for treating patients with cancer with priority categories.…”

“…At the recent American Conference on Pharmacometrics (ACoP) Annual Meeting in 2018, a systematic presentation of TGD, including its history and utilities, 7 were discussed in a symposium, thus illustrating challenges and opportunities. Subsequently, several research articles were published, focusing on specific areas of TGD models, such as tumor resistance models, 8 and expansion of joint model with new lesions. 9 This review is to present the comprehensive view of TGD, from its origin, to advanced mathematical methodologies, to its applications in clinical development, and to regulatory authorization.…”

Epigenetic Instability May Alter Cell State Transitions and Anticancer Drug Resistance

“…Although the approach has appeal given the mechanistic justification, and has produced a plethora of drug combinations, these approaches ultimately fail since they do not consider intratumoral heterogeneity and innate differences in cell sensitivity to drugs, as well as cellular adaptation including the role of epigenetic reprogramming [21]. Both deterministic and stochastic mathematical models have been employed to study intratumoral heterogeneity and the emergence of drug resistance in cancer [22][23][24][25][26][27].…”

Opportunities for Quantitative Translational Modeling in Oncology

“…60 Despite some progress, longitudinal tumor size models tend to be agnostic of mechanism of action (MoA). 61,62 Careful review of the dynamic features of nonclinical data accompanied by MoA-based hypothesis generation and model-based hypothesis validation can help identify mechanistic model features in nonclinical data, which may be hard to establish in clinical data due to small subject numbers and limitations of clinical practice. To this end, in vitro data on pazopanib's anti-angiogenic and cytotoxic effects together with dynamic features in mouse in vivo data guided the development of a semimechanistic model, including both MoAs, which resulted in improved characterization of both in vivo and clinical tumor size data.…”