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Mathematical Oncology 2013

Part of the Modeling and Simulation in Science, Engineering and Technology Book Series

Editors: d'Onofrio, Alberto; Gandolfi, Alberto

DOI: 10.1007/978-1-4939-0458-7

ISBN: 978-1-4939-0457-0

Publisher: Springer New York - Springer Journals

Sep 23, 2014

1 - 10 of 10 Chapters

Available

Modeling Spatial Effects in Carcinogenesis: Stochastic and Deterministic Reaction-Diffusion

Bertolusso, Roberto; Kimmel, Marek

Pages: 3 –25

[This paper is a review including some original elements of a family of reaction-diffusion models of carcinogenesis exhibiting diffusion-driven (Turing) instability (DDI), but consisting of a single reaction-diffusion equation coupled with a system of ordinary differential equations (ODE). Such...
Available

Conservation Laws in Cancer Modeling

Fasano, Antonio; Bertuzzi, Alessandro; Sinisgalli, Carmela

Pages: 27 –61

[We review mathematical models of tumor growth based on conservation laws in the full system of cells and interstitial liquid. First we deal with tumor cords evolving in axisymmetric geometry, where cells motion is simply passive and compatible with the saturation condition. The model is...
Available

Avascular Tumor Growth Modelling: Physical Insights to Skin Cancer

Amar, Martina Ben

Pages: 63 –105

[In this chapter I present the state-of-the-art theoretical models for avascular tumor growth which are well established nowadays. I focus on models able to treat morphologic instabilities and phase segregation, two typical features of skin cancer for example melanoma. Contrary to experiments...
Available

A Cell Population Model Structured by Cell Age Incorporating Cell–Cell Adhesion

Dyson, Janet; Webb, Glenn F.

Pages: 109 –149

[An analysis is given of a continuum model of a proliferating cell population, which incorporates cell movement in space and cell progression through the cell cycle. The model consists of a nonlinear partial differential equation for the cell density in the spatial position and the cell age...
Available

A General Framework for Multiscale Modeling of Tumor–Immune System Interactions

Dolfin, Marina; Lachowicz, Mirosław; Szymańska, Zuzanna

Pages: 151 –180

[In this paper we review methods that allow the construction of a consistent set of models that may describe the interactions between a tumor and the immune system on microscopic, mesoscopic, and macroscopic scales. The presented structures may be a basis for a description on the sub–cellular,...
Available

The Power of the Tumor Microenvironment: A Systemic Approach for a Systemic Disease

Kareva, Irina; Wilkie, Kathleen P.; Hahnfeldt, Philip

Pages: 181 –196

[Cancer is increasingly recognized as not solely a disease of the genes and chromosomes but as a systemic disease that affects numerous components of the host including blood vessel formation, immune cell function, and nutrient recycling. This review summarizes a variety of time-dependent...
Available

Modeling Immune-Mediated Tumor Growth and Treatment

de Pillis, Lisette; Radunskaya, Ami

Pages: 199 –235

[The immune response is an important factor in the progression of cancer, and this response has been harnessed in a variety of treatments for a range of cancers. In this chapter we develop mathematical models that describe the immune response to the presence of a tumor. We then use these models...
Available

A Hybrid Multiscale Approach in Cancer Modelling and Treatment Prediction

Powathil, Gibin; Chaplain, Mark A. J.

Pages: 237 –263

[Cancer is a complex multiscale disease involving inter-related processes across a wide range of temporal and spatial scales. Multiscale mathematical models can help in studying cancer progression and serve as an in silico test base for comparing and optimizing various multi-modality anticancer...
Available

Deterministic Mathematical Modelling for Cancer Chronotherapeutics: Cell Population Dynamics and Treatment Optimization

Clairambault, Jean

Pages: 265 –294

[In this short review paper, I will present the mathematical models that have been designed in the frame of continuous deterministic cell population dynamics that aim at optimization of cancer treatments using chronotherapeutics. Many authors have dealt with chronobiology of cancer, less with...
Available

Tumor Microenvironment and Anticancer Therapies: An Optimal Control Approach

Ledzewicz, Urszula; Schättler, Heinz

Pages: 295 –334

[In this paper, results about the structure of cancer treatment protocols that can be inferred from an analysis of mathematical models with the methods and tools of optimal control are reviewed. For homogeneous tumor populations of chemotherapeutically sensitive cells, optimal controls are...

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