The 2019 mathematical oncology roadmap

RC Rockne, A Hawkins-Daarud, KR Swanson… - Physical …, 2019 - iopscience.iop.org
Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology,
Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is …

Multiscale cancer modeling

TS Deisboeck, Z Wang, P Macklin… - Annual review of …, 2011 - annualreviews.org
Simulating cancer behavior across multiple biological scales in space and time, ie,
multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine …

[LIBRO][B] The mathematics and mechanics of biological growth

A Goriely - 2017 - books.google.com
This monograph presents a general mathematical theory for biological growth. It provides
both a conceptual and a technical foundation for the understanding and analysis of …

Classical mathematical models for description and prediction of experimental tumor growth

S Benzekry, C Lamont, A Beheshti… - PLoS computational …, 2014 - journals.plos.org
Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be
expressed as mathematical models. To explore this further, quantitative analysis of the most …

Mathematical models of cancer: when to predict novel therapies, and when not to

R Brady, H Enderling - Bulletin of mathematical biology, 2019 - Springer
The number of publications on mathematical modeling of cancer is growing at an
exponential rate, according to PubMed records, provided by the US National Library of …

Nonlinear modelling of cancer: bridging the gap between cells and tumours

JS Lowengrub, HB Frieboes, F **, YL Chuang, X Li… - …, 2009 - iopscience.iop.org
Despite major scientific, medical and technological advances over the last few decades, a
cure for cancer remains elusive. The disease initiation is complex, and including initiation …

Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment

ARA Anderson, AM Weaver, PT Cummings… - Cell, 2006 - cell.com
Emergence of invasive behavior in cancer is life-threatening, yet ill-defined due to its
multifactorial nature. We present a multiscale mathematical model of cancer invasion, which …

Interactions between the immune system and cancer: a brief review of non-spatial mathematical models

R Eftimie, JL Bramson, DJD Earn - Bulletin of mathematical biology, 2011 - Springer
We briefly review spatially homogeneous mechanistic mathematical models describing the
interactions between a malignant tumor and the immune system. We begin with the simplest …

Dissecting cancer through mathematics: from the cell to the animal model

HM Byrne - Nature Reviews Cancer, 2010 - nature.com
This Timeline article charts progress in mathematical modelling of cancer over the past 50
years, highlighting the different theoretical approaches that have been used to dissect the …

Mathematical models of avascular tumor growth

T Roose, SJ Chapman, PK Maini - SIAM review, 2007 - SIAM
This review will outline a number of illustrative mathematical models describing the growth
of avascular tumors. The aim of the review is to provide a relatively comprehensive list of …