There exists evidence that in early stages tumors progress along linear, tubular, or irregular surface structures. This seems to be the case for atypical adenomatous hyperplasia (AAH), a precursor of adenocarcinoma of the lung. We previously published a simplified model, which showed that early structures had a potential towards spontaneous invasive growth following a latency phase. The transition was facilitated by diffusion of a growth factor and nonlinear cell cycle regulation in cancer cells. The mechanism is analogous to that in Turing pattern formation, although the patterns are irregular and unstable. We introduce more biologically justifiable signaling, in which only the free growth factor molecules diffuse. Flexible nonlinearities in the model accommodate several growth patterns of cells as well as internal versus external production of the growth factor. We show that the reaction-diffusion setup results in complicated spike-like solutions. We discuss these results in the light of published data on the AAH.

Anna Marciniak-Czochra

Marek Kimmel

Dynamics of Growth and Signaling along Linear and Surface Structures in Very Early Tumors

In this paper, a model for the radiation treatment of cancer which includes the effects of the cell cycle is derived from first principles. A malignant cell population is divided into two compartments based on radiation sensitivities. The active compartment includes the four phases of the cell cycle, while the quiescent compartment consists of the G0 state. Analysis of this active-quiescent radiation model confirms the classical interpretation of the linear quadratic (LQ) model, which is that a larger α/β ratio corresponds to a fast cell cycle, while a smaller ratio corresponds to a slow cell cycle. Additionally, we find that a large α/β ratio indicates the existence of a significant quiescent phase. The active-quiescent model is extended as a nonlinear birth–death process in order to derive an explicit time dependent expression for the tumour control probability (TCP). This work extends the TCP formula from Zaider and Minerbo and it enables the TCP to be calculated for general time dependent treatment schedules.

A. Dawson

T. Hillen

Derivation of the Tumour Control Probability (TCP) from a Cell Cycle Model

Nicola Bellomo

Brian D. Sleeman

Preface

In this paper, we carry out an examination of four mechanisms that can potentially lead to changing morphologies in a growing tumor: variations in nutrient consumption rates, cellular adhesion, excessive consumption of nutrients by tumor cells and immune cell interactions with the tumor. We present numerical simulations using a hybrid PDE-cellular automata (CA) model demonstrating the effects of each mechanism before discussing hypotheses about the contribution of each mechanism to morphology change.

L. G. de Pillis

D. G. Mallet

A. E. Radunskaya

Spatial Tumor-Immune Modeling

Interleukin-11 (IL-11) is a pleiotropic thrombopoietic cytokine and immune modulator, clinically approved for alleviation of chemotherapy-induced thrombocytopenia in non-myeloid malignancies. IL-11 therapy exerts fluid accumulation-associated adverse effects, complicating its administration and limiting its use. Implementation of standard biomathematical techniques to assess these effects is not possible, due to incomplete knowledge of the underlying mechanisms. This study investigates IL-11-induced blood volume expansion (BVE) by a new mathematical modelling methodology. Alternative models for BVE following IL-11 therapy were constructed, calibrated with clinical information and simulated in a number of treatment scenarios. The models demonstrated high compliance and were equally capable of reliably predicting BVE in a wide range of treatments, provided sufficient data. Model simulations indicate that frequent and low dose IL-11 regimens are favored for ensuring minimal fluid retention, upon the current IL-11 therapy.

Yuri Kheifetz

Moran Elishmereni

Smadar Horowitz

Zvia Agur

Fluid-Retention Side-Effects of the Chemotherapy-Supportive Treatment Interleukin-11: Mathematical Modelling of Putative Underlying Mechanisms

Following the poor clinical results of antiangiogenic drugs, particularly when applied in isolation, tumour biologists and clinicians are now turning to combinations of therapies in order to obtain better results. One of these involves vessel normalisation strategies. In this paper, we investigate the effects on tumour growth of combinations of antiangiogenic and standard cytotoxic drugs, taking into account vessel normalisation. An existing multiscale framework is extended to include new elements such as tumour-induced vessel dematuration. Detailed simulations of our multiscale framework allow us to suggest one possible mechanism for the observed vessel normalisation-induced improvement in the efficacy of cytotoxic drugs: vessel dematuration produces extensive regions occupied by quiescent (oxygen-starved) cells which the cytotoxic drug fails to kill. Vessel normalisation reduces the size of these regions, thereby allowing the chemotherapeutic agent to act on a greater number of cells.

Tom&#xe1;s Alarc&#xf3;n

Markus R. Owen

Helen M. Byrne

Philip K. Maini

Multiscale Modelling of Tumour Growth and Therapy: The Influence of Vessel Normalisation on Chemotherapy

This paper deals with the application of the mathematical kinetic theory for active particles, with discrete activity states, to the modelling of the immune competition between immune and cancer cells. The first part of the paper deals with the assessment of the mathematical framework suitable for the derivation of the models. Two specific models are derived in the second part, while some simulations visualize the applicability of the model to the description of biological events characterizing the immune competition. A final critical outlines some research perspectives.

I. Brazzoli

A. Chauviere

On the Discrete Kinetic Theory for Active Particles. Modelling the Immune Competition

A vast array of mathematical models have been proposed for all stages of cancer formation across a wide range of spatio–temporal scales. Attention is now turning to coupling these models across scales and building models of “virtual tumours” for use in in silico testing of novel drugs and treatment regimes. This leads naturally to the requirement for detailed knowledge of the underlying geometry and physiological properties of individual tumours for use in: (i) multi-scale mathematical models of in vivo tumour growth and development; (ii) fusion of multi-scale, multimodal medical imaging techniques to improve the diagnosis and treatment of individual patients; and (iii) training of cancer specialists and surgeons.

Joe Pitt-Francis

Dan Chen

Mark Slaymaker

Andrew Simpson

Michael Brady

Ingeborg van Leeuwen

Fiona Reddington

Phil Quirke

Gina Brown

David Gavaghan

Multimodal Imaging Techniques for the Extraction of Detailed Geometrical and Physiological Information for Use in Multi-Scale Models of Colorectal Cancer and Treatment of Individual Patients

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