Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Mathematical biomedicine and modeling avascular tumor growth

In this chapter we review existing continuum models of avascular tumor growth, explaining howthey are inter related and the biophysical insight that they provide. The models range in complexity and include one-dimensional studies of radiallysymmetric growth, and two-dimensional models of tumor invasion in which the tumor is assumed to comprise a single population of cells. We also present more detailed, multiphase models that allow for tumor heterogeneity. The chapter concludes with a summary of the different continuum approaches and a discussion of the theoretical challenges that lie ahead

Modeling Three-dimensional Invasive Solid Tumor Growth in Heterogeneous Microenvironment under Chemotherapy

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and the drug-tumor interaction on individual cell level. We employ the hybrid model to investigate the evolution and growth dynamics of avascular invasive solid tumors under different chemotherapy strategies. Our simulations reproduce the well-established observation that constant dosing is generally more effective in suppressing primary tumor growth than periodic dosing, due to the resulting continuous high drug concentration. In highly heterogeneous microenvironment, the malignancy of the tumor is significantly enhanced, leading to inefficiency of chemotherapies. The effects of geometrically-confined microenvironment and non-uniform drug dosing are also investigated. Our computational model, when supplemented with sufficient clinical data, could eventually lead to the development of efficient in silico tools for prognosis and treatment strategy optimization.Comment: 41 pages, 8 figure

Targeting Cellular DNA Damage Responses in Cancer: An In Vitro-Calibrated Agent-Based Model Simulating Monolayer and Spheroid Treatment Responses to ATR-Inhibiting Drugs

We combine a systems pharmacology approach with an agent-based modelling approach to simulate LoVo cells subjected to AZD6738, an ATR (ataxia–telangiectasia-mutated and rad3-related kinase) inhibiting anti-cancer drug that can hinder tumour proliferation by targeting cellular DNA damage responses. The agent-based model used in this study is governed by a set of empirically observable rules. By adjusting only the rules when moving between monolayer and multi-cellular tumour spheroid simulations, whilst keeping the fundamental mathematical model and parameters intact, the agent-based model is first parameterised by monolayer in vitro data and is thereafter used to simulate treatment responses in in vitro tumour spheroids subjected to dynamic drug delivery. Spheroid simulations are subsequently compared to in vivo data from xenografts in mice. The spheroid simulations are able to capture the dynamics of in vivo tumour growth and regression for approximately 8 days post-tumour injection. Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and in this article, we exemplify how data-driven, agent-based models can be used to bridge the gap between in vitro and in vivo research. We further highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development

Unraveling Heterogeneity in Epithelial Cell Fates of the Mammary Gland and Breast Cancer.

Fluidity in cell fate or heterogeneity in cell identity is an interesting cell biological phenomenon, which at the same time poses a significant obstacle for cancer therapy. The mammary gland seems a relatively straightforward organ with stromal cells and basal- and luminal- epithelial cell types. In reality, the epithelial cell fates are much more complex and heterogeneous, which is the topic of this review. Part of the complexity comes from the dynamic nature of this organ: the primitive epithelial tree undergoes extensively remodeling and expansion during puberty, pregnancy, and lactation and, unlike most other organs, the bulk of mammary gland development occurs late, during puberty. An active cell biological debate has focused on lineage commitment to basal- and luminal- epithelial cell fates by epithelial progenitor and stem cells; processes that are also relevant to cancer biology. In this review, we discuss the current understanding of heterogeneity in mammary gland and recent insights obtained through lineage tracing, signaling assays, and organoid cultures. Lastly, we relate these insights to cancer and ongoing efforts to resolve heterogeneity in breast cancer with single-cell RNAseq approaches

Developing Droplet Based 3D Cell Culture Methods to Enable Investigations of the Chemical Tumor Microenvironment

Adaptation of cancer cells to changes in the biochemical microenvironment in an expanding tumor mass is a crucial aspect of malignant progression, tumor metabolism, and drug efficacy. In vitro, it is challenging to mimic the evolution of biochemical gradients and the cellular heterogeneity that characterizes cancer tissues found in vivo. It is well accepted that more realistic and controllable in vitro 3D model systems are required to improve the overall cancer research paradigm and thus improve on the translation of results, but multidisciplinary approaches are needed for these advances. This work develops such approaches and demonstrates that new droplet-based cell-encapsulation techniques have the ability to encapsulate cancer cells in droplets for standardized and more realistic 3D cell culture and cancer biology applications. Three individual droplet generating platforms have been designed and optimized for droplet-based cell encapsulation. Each has its own advancements and challenges. Together, however, these technologies accomplish medium to high-throughput generation (10 droplets/second to 25,000 droplets/second) of biomaterial droplets for encapsulation of a range of cell occupancies (5 cells/droplet to 400 cells/droplet). The data presented also demonstrates the controlled generation of cell-sized small droplets for biomolecule compartmentalization, droplets with diameters ranging between 100-400 μm depending on device parameters, and the generation of instant spheroids. Standardized assays for analyzing cells grown within these new 3D environments include proliferation assays of cells grown in mono- and co-cultures, the generation of large and uniform populations of scaffold supported multicellular spheroids, and a new system for culturing encapsulated cells in altered environmental conditions