Multiscale models of cancer heterogeneity, with applications in drug development and precision medicine

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Harsh Jain (Mathematics, Florida state University), Samuel Handelman (Internal Medicine, University of Michigan)


Mathematical modeling in oncology has a proven track record of providing crucial medical and bio- logical insights, and a new generation of approaches promise to revolutionize cancer care. These novel approaches elucidate the response of cancer cells to therapeutic interventions and will improve treatment outcomes within individuals and across populations. This mini-symposium will bring together notewor- thy advances in multiscale modeling that explain how heterogeneity at both cellular and inter-individual levels provides a challenge and an opportunity in improving cancer care. We will highlight the challenges faced in bridging cellular, molecular, phenotypic and organismal scales with bioinformatics approaches, dynamical systems modeling, and hybrid models. We will explore specific applications in prostate cancer, hepatocellular cancer, and combination therapies.

Matthias Reuss

Stuttgart Research Center Systems Biology, University of Stuttgart
"Spatial-temporal multiscale modelling and simulation of vascular tumour growth - development of new multicellular simulators based on structural consistency between model and computer architecture"
Multiscale modelling and simulation in systems medicine is an emerging methodology and discipline to tackle the challenges posed by complex disease, including cancer. We will present applications of a 3D multiscale hybrid discrete-continuum model to simulate angiogenesis and vascular tumour growth. The model uses a cellular automaton approach and couples intracellular dynamics, active cell movement, cell- cell interaction, extracellular diffusion, and a dynamically evolving vascular network. The model accounts for the interplay between subcellular events and the macroscopic properties of the tumour. Simulation of larger tumours taking into account the structure of the tissue and blood supply consisting of millions of interacting cells, and the architectures of real tissues, e.g. liver lobules, or validation of theoretical findings with aid of imaging and simulations of therapies for larger patient communities, are both compu- tationally challenging. Therefore, we will introduce new hardware and software developments applicable to multiscale modeling based on structural consistency between the multiscale model and the architecture of the computer hardware. These efficiently solve the problems of interactions between subcellular and tissue levels. I will summarize multicellular simulators based on hybrid structures of parallelised graphic and central processors. I will present applications of these hybrid parallelised computer systems to integrate simulation of 3D-growth of larger vascularized tumours, dynamic models of intracellular metabolism of hepatocytes, and the the 3D architecture of liver lobules. The coupled modeling of blood perfusion between intravascular and interstitial spaces in the microvasculature permits the simulation of the perfusion CT to create model-based images which can be compared with clinical observations from radiology.

Holger Perfahl

Stuttgart Research Center Systems Biology, University of Stuttgart
"Hybrid Modelling of Transarterial Chemoembolisation Therapies (TACE) for Hepatocellular Carcinoma (HCC)"
We will present an agent-based multiscale model of vascular tumour growth and angiogenesis to describe transarterial chemoembolisation (TACE) therapies. The model describes tumour and normal cells nested in a vascular system that changes structure in response to tumour-related growth factors and also interacts with oxygen that influences cell viability. Within the extended model TACE is included as a two-step process. First, the purely mechanical influence of the embolisation therapy is modelled by a local occlusion of the tumour vasculature. We distinguish between partial and complete responders, where parts of the vascular system are occluded for the former and the whole tumour vasculature is destroyed for the latter. In the second part of the model, drug eluting beads release the chemotherapeutic drug doxorubicin at destroyed vascular locations. Simulation results are parameterised to qualitatively reproduce clinical observations. Our simulations reveal that directly after a TACE treatment an unstable tumour state can be observed, where regrowth and total tumour death are equally likely. This short time-window is favorable for another therapeutic intervention with a less radical therapy. This procedure produces a more favorable outcome. Simulation results with an oxygen therapy within the unstable time- window demonstrate a potentially positive manipulated outcome. Finally, we conclude that our TACE model motivates new therapeutic strategies and can help clinicians to understand intertwined relations and crosstalk in tumours.

Samuel Handelman

Internal Medicine, University of Michigan
"Incorporation of morphological features to inverse problems in high-content screening of anti-cancer therapies"
Cell-based assays are a mainstay of drug development, including especially for anti-cancer drugs and anti-cancer drug combinations. However, these assays generally use cell-death as an endpoint, which is more suited to simple cytotoxicity than to anti-cancer efficacy. This is especially a challenge in the context of combination therapies, where the correct linkage function in a statistical model of two co-administered cytotoxic compounds is not obvious. Therefore, we propose imaging-based and molecular markers of cancer cell phenotype, as an alternative efficacy endpoint in cancer drug screening. We will combine and compare results in combination therapy screens with different efficacy measures and a range of linkage functions corresponding to different assumptions on the nature of cancer drug synergy. These approaches have the added benefit of better addressing inter-cellular heterogeneity, which is evident even in clonal cell lines. Finally. we will review relevant biological background helpful to a quantitative audience in contextualizing the other talks in this session.

Harsh Jain

Mathematics, Florida state University
"A Standing Variation Model of Prostate Cancer Response to Live Cell Vaccination"
Making quantitative predictions with data-driven models, the core approach of applied mathematical biology, requires parameter estimation from imperfect measurements. Therefore, parameter identifiability and estimability become a major concern. In this talk, I will present a model of immunotherapy in the treatment of prostate cancer. I introduce our novel approach, standing variation modeling, which exploits practical unidentifiability in model parameters to capture individual heterogeneity. In particular, we use experimental data to infer distributions on parameters that are critical to tumor growth and to the resultant immune response of the body. Sampling model parameters from these distributions allows us to simulate heterogeneity, both, at the level of the tumor cells, and the individual being treated. Model simulations offer an explanation for the very limited success of this prostate cancer immunotherapy that has been observed in practice.

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