July 30-August 2, 2008
Society for Mathematical Biology Conference

hosted by the Centre for Mathematical Medicine, Fields Institute
held at University of Toronto, Medical Sciences Bldg


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5) Multiscale modeling of solid tumor growth and angiogenesis
Principal organiser: Professor John Lowengrub

Departments of Mathematics and Biomedical Engineering UC Irvine, Irvine CA 92697

Significance. Cancer is a fundamental scientific and societal problem, and in the past few decades, vast resources have been expended in an effort to understand the root causes of cancer, to elucidate the intricacies of cancer invasion, and to develop effective prevention and treatment strategies. Nevertheless, there are numerous examples of puzzling and seemingly inconsistent observations. Therefore, there is critical need for biologically
realistic mathematical modeling.

A key aspect of the complexity of cancer progression is the coupling of processes occurring across a wide range of length and time scales; this coupling must be addressed if key tumor dynamics are to be captured. While the biomathematics literature is replete with models that provide useful insight into cancer-related processes at particular time and length scales, considerably less effort has been devoted to coupling biological phenomena across various scales. One important example, which we will focus on in this minisymposium, is the nonlinear coupling between cancer invasion, the angiogenic response of the host and the implications of this coupling on potential treatment strategies.

In this minisymposium, we will focus on solid tumor growth. Tumors evolve through increasingly aggressive stages of development. After carcinogenesis, the next stage of development is the avascular growth phase whereby the cancer cells proliferate and form an in situ tumor. Since the tumor lacks a vasculature, nutrients and vital growth factors are received only by diffusion from the surrounding tissue. This may lead to hypoxia and acidosis. The following stage of tumor growth, angiogenesis, is characterized by the development of a tumor-induced neovasculature that grows from the main circulatory system toward the tumor in response to pro-angiogenic growth factors released by hypoxic tumor cells (or stressed host cells). After the recruitment and/or cooption of blood vessels, the vascularized tumor may invade the surrounding host tissue and metastasize to distant parts of the body. Sustained angiogenesis is a hallmark of cancer.

Here, the speakers will present multiscale mathematical models that are capable of describing all stages of tumor growth and in particular, the nonlinear coupling between the tumor progression and the angiogenic response of the host. State-of-the-art hybrid continuum-discrete models will be presented that will underscore the importance of the nonlinear coupling of biophysical processes across a range of scales and in particular coupling between the growing tumor and the development and remodeling of a tumorinduced neovascular network with blood flowing through it. The implications of treatment strategies on tumor progression will be discussed. While there are currently few such models of this highly complex and nonlinearly coupled system in the literature, this is an area of intense research activity because of its importance.

This minisymposium brings together ideas that have been explored very recently in the mathematical biology community and thus fits perfectly within the SMB conference. To our knowledge, this may be the first minisymposium that would specifically address the nonlinear modeling of the critical transition from avascular to vascular growth of solid tumors.

This minisymposium, and in particular the multiscale modeling aspect of the approach, should appeal to a wide range of mathematical modellers. The relevance of the problems to in vivo cancer progression and treatment should also attract experimentalists, clinicians and industry professionals.


1. Computational modeling identifies morphologic predictors of tumor invasion
Vittorio Cristini, School of Health Information Sciences
University of Texas MD Anderson Cancer Center
University Texas Health Science Center at Houston

Mathematical modeling based on first principles quantifies tumor growth's dependence on interactions between a set of variables-including genomic instability producing variations in sub-tumor clonal expansion and generating nutrient diffusion gradients-and demonstrates that these determinants of heterogeneity, and not angiogenesis per se, conspire to produce the typical morphologic patterns of infiltrative tumor boundaries in histopathology. We demonstrate that heterogeneity in sub-tumor clonal expansion and nutrient consumption drives migration and proliferation of the emerging more aggressive clones up a nutrient concentration gradient within and beyond the central tumor mass. This heterogeneity and loss of cell adhesion trigger a gross morphologic instability that leads to replacement of less aggressive clones and separation of tumor cell strands or clusters infiltrating into adjacent tissue. This model allows all variables that characterize the biophysics of tumor growth to be considered and could be applied to determine the probabilistic behavior of tumors given their pathologic appearance.

2. Three dimensional multiscale modeling of solid tumor growth
John Lowengrub
: Organizer University of California, Irvine

We present and investigate models for solid tumor growth that incorporate features of the tumor microenvironment including tumor-induced angiogenesis. Using analysis and nonlinear numerical simulations, we explore the effects of the interaction between the genetic characteristics of the tumor and the tumor microenvironment on the resulting tumor progression and morphology. We account for variable cell-cell/cell-matrix adhesion in response to microenvironmental conditions (e.g. hypoxia) and to the presence of multiple tumor cell species. We focus on glioblastoma and quantify the interdependence of the tumor mass on the microenvironment and on the cellular phenotypes. The model provides resolution at various tissue physical scales, including the microvasculature, and quantifies functional links of molecular factors to phenotype that for the most part can only be tentatively established through laboratory or clinical observation. This allows observable properties of a tumor (e.g. morphology) to be used to both understand the underlying cellular physiology and to predict subsequent growth or treatment outcome, thereby providing a bridge between observable, morphologic properties of the tumor and its prognosis.

3. Multiphase modelling of tissue growth in dynamic culture conditions
Sarah Waters,
Department of Mathematics, Oxford
Co-authors: O’Dea, R., Byrne, H.M., El-Haj, A

The growth of biological tissue is a complex process, resulting from the interaction of numerous processes on disparate spatio-temporal scales. Much research has been concentrated on the study of cartilage and bone tissue re-generation, motivated by the notorious incapacity of the former to self-repair and the response of the latter to its mechanical environment. Advances in the understanding of tissue growth processes promise to improve the viability and suitability of the resulting tissue constructs; the clinical applications are evident. Mechanical force is an important factor affecting the behaviour of a variety of different cell types; however, it remains unclear how this stimulus is inte-grated into the cellular response. Employing a macroscale multiphase model, the influence of (i) cell-cell and cell-scaffold interactions, and (ii) the mechanical environment, on tissue growth is investigated. The approach taken enables a macroscale model to be obtained that does not contain the precise details of the material at the microscale, but whose terms are shown to arise from appropriate microscopic considerations. The model equations are solved using asymptotic and numerical methods and the implications of these results are discussed.

4. An Alternate Approach to Predictive Oncology: Computer Modeling of Drug Pharmacokinetics and Effect in Vascularized Tumors
Sandeep Sanga (U.Texas Health Science Center, Houston TX): replacement for Paul Macklin
Co-authors: John P. Sinek, Sandeep Sanga, Xiaoming Zheng, Hermann B. Frieboes, Mauro Ferrari, Vittorio Cristini
The field of predictive oncology conventionally applies methodologies such as microarrays and immunohistochemical staining for comprehensively profiling gene expression and protein activities of genes in cancer tissue, and identifying biomarkers and signatures that are either prognostic and/or predictive of chemotherapy response. However, the complex nature of cancer has made it difficult to identify unique molecular and pathophysiological signatures for each disease variant, consequently hindering the ability to predict the performance of therapies in individual patients. Here, we take an alternate approach; we investigate the pharmacokinetics and pharmacodynamics of doxorubicin and cisplatin in vascularized tumors and show that microenvironmental considerations such as lesion-scale drug and nutrient distributions may significantly hamper therapeutic efficacy and should be considered as carefully as genetic and proteomic determinants. Our model takes into account tumor vascularity and morphology as well as cellular and lesion-scale pharmacokinetics determinants such as p-glycoprotein efflux and cell density. Drug transport is encapsulated using a multi-compartment model calibrated from published experimental data; this model tracks drug as it extravasates from the blood stream into the tumor interstitial space, diffuses through the lesion, enters cells and eventually reaches its intended target: DNA. Cell inhibition is modeled as a function of this DNA-bound drug. Unlike a truly in vivo situation, our in silico model provides the means to quantify expected in vivo IC50 under varying drug, oxygen, nutrient , and drug transporter conditions. The nonlinear interaction among various determinants representing cell and lesion phenotype as well as therapeutic strategies is a unifying theme of our results. Our results suggest that macroscopic environmental conditions, notably drug and nutrient distributions, give rise to considerable variation in tumor response to chemotherapy, hence clinical resistance. Moreover, the synergy or antagonism of combined therapeutic strategies depends heavily upon this environment.

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