Mathematical models of tumor cell proliferation: A review of the literature

Abstract

Introduction: A defining hallmark of cancer is aberrant cell proliferation. Efforts to understand the generative properties of cancer cells span all biological scales: from genetic deviations and alterations of metabolic pathways, to physical stresses due to overcrowding, as well as the effects of therapeutics and the immune system. While these factors have long been studied in the laboratory, mathematical and computational techniques are being increasingly applied to help understand and forecast tumor growth and treatment response. Advantages of mathematical modeling of proliferation include the ability to simulate and predict the spatiotemporal development of tumors across multiple experimental scales. Central to proliferation modeling is the incorporation of available biological data and validation with experimental data. Areas Covered: We present an overview of past and current mathematical strategies directed at understanding tumor cell proliferation. We identify areas for mathematical development as motivated by available experimental and clinical evidence, with a particular emphasis on emerging, non-invasive imaging technologies. Expert Commentary: The data required to legitimize mathematical models are often difficult or (currently) impossible to obtain. We suggest areas for further investigation to establish mathematical models that more effectively utilize available data to make informed predictions on tumor cell proliferation.

Transmembrane and Ubiquitin-Like Domain Containing 1 Protein (TMUB1) Negatively Regulates Hepatocellular Carcinoma Proliferation via Regulating Signal Transducer and Activator of Transcription 1 (STAT1)

“…The signaling molecules inside and outside the cells initiate a proliferation-related signaling pathway and tightly regulate cell proliferation under the action of various positive and negative regulatory factors. When there exists an imbalance in this regulation, abnormal cell proliferation can manifest, which may cause tumorigenesis and development [39,40].…”

Integrating multimodal data sets into a mathematical framework to describe and predict therapeutic resistance in cancer

“…These genomic and transcriptomic data sets can direct the choice of specific cancer drugs and illuminate novel resistance pathways, as well as provide a prognostic marker for patients who receive it. Simultaneously, the role of mathematical modeling in oncology has been widely recognized (35) and utilized to improve both our understanding of the dynamic mechanisms of drug response (12,36,37) as well as to develop approaches to guide the design of adaptive patient-specific treatment plans (14,19,20,38,39). However, connecting the wealth of "omics" data at the molecular level with temporal dynamics used to calibrate mathematical models for adaptive therapies remains a major challenge in the field.…”

Leveraging Mathematical Modeling to Quantify Pharmacokinetic and Pharmacodynamic Pathways: Equivalent Dose Metric

“…where k p and k d are the proliferation and dose-specific death rates, respectively, D is the delivered dose [defined to be the bound concentration of drug, C B , calculated with Equations (1–3)], r is a dose-specific constant describing the rate at which treatment induces an effect, θ is the dose-specific carrying capacity describing the maximum number of cells that can be observed in the experimental system, and N TC ( t ) is the number of cells at time t . Logistic growth models have traditionally been used to describe growth of a variety of biological species whose total size is limited (Gerlee, 2013; Jarrett et al, 2018). This equation accurately describes our experimental system (described in section Doxorubicin Treatment Response Imaging), in which cell population is limited by the surface area of the experimental platform.…”