Mathematical Challenges in the Analysis of Continuum Models for Cancer Growth, Evolution and Therapy (18w5115)
The Casa Matemática Oaxaca (CMO) will host the "Mathematical Challenges in the Analysis of Continuum Models for Cancer Growth, Evolution and Therapy" workshop from November 25th to November 30th, 2018. Mathematicians and other scientists are meeting at BIRS in a full-time brainstorming week to propose new avenues to comprehend and treat cancer. This one-week workshop gathers outstanding specialists in mathematics, evolutionary biology and cancer in the isolated environment provided by the BIRS research centre where they they will share knowledge, questions and relevant mathematical models, existing or to be designed, to meet the challenges of new conceptions about the nature of cancer. The idea of cancer as an evolutionary disease, not only due to genetic mutations, but also, and maybe mainly, due to adaptations to a radical changing tissue environment, may be taken into account by models of ‘adaptive dynamics’ that are amenable to theoretically optimised therapeutic strategies, intended to be ultimately transferred to the clinic. Among the viewpoints on cancer that can change its future and transform it to a chronic disease by designing new types of models directed towards rationally combined treatments are those of epigenetics (modifications of gene expression without mutations), and of the so-called ‘atavistic theory of cancer’, that considers cancer as a reversal of evolution from normal multicellularity in our organisms towards elementary, localised and selfish forms of cellular cooperation. These viewpoints will be debated in the workshop, with the aim to propose new theoretical models of cancer and new practical ways to circumvent it.
DOI (Serie): 10.5446/s_1390
11
2018
3
6 Stunden 46 Minuten
11 Ergebnisse
41:53
Plaza, Ramon G.2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
43:00
1Shen, ShensiAcquisition by cancer cells of a plethora of resistance-conferring genetic alterations greatly limits the clinical utility of most anti- cancer drugs. Therefore, there is a need to improve the effective- ness of treatment before mutational-acquired resistance prevails. Relapse is driven by a small subpopulation of residual or ‘‘drug-tolerant’’ cells, which are traditionally called ‘‘minimal residual disease’’ (MRD), that remain viable upon drug exposure. Recent in vitro findings have indicated that the emergence of these per- sisters is unlikely due to mutational mechanisms. A non-mutually exclusive scenario proposes that the drug-tolerant phenotype is transiently acquired by a small pro- portion of cancer cells through non-mutational mechanisms. To gain insights into the biology of MRD, we applied single-cell RNA sequencing to malignant melanoma BRAF mutated cells, and we identified a subpopulation of melanoma cells is tolerant to targeted therapy via metabolic reprogramming. Cancer cells were known to reprogram their metabolic profiles geared toward glycolysis, despite sufficient oxygen available to support oxidative phosphorylation (OXPHOS), a phenomenon known as the Warburg effect. We found that melanoma MRD can switch their metabolic program from glycolysis towards mitochondrial OXPHOS alimented by fatty acid oxidation (FAO), thereby renders the melanoma MRD highly sensitive to FAO inhibition in vitro and in mouse tumor models. This MRD-directed metabolic reprogramming suggests a more clever treatment combination regimen to fight against cancer resistance.
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
40:47
Sfakianakis, NikolaosThe lamellipodium is a thin, sheet-like structure that is found in the propagating front of fast moving cells like fibroblasts, keratocytes, cancer cells, and more. It is a dense network of linear biopolymers of the protein actin, termed actin-filaments. These actin-filaments are highly dynamic structures that participate in a plethora of processes such as polymerization, nucleation, capping, fragmentation, and more. These processes are important for the structure and functionality of the lamellipodium and the motility of the cell. They are, to a large extent, affected by the extracellular environment; for example, the chemical landscape in which the cell of resides and the local composition and architecture of the Extracellular Matrix (ECM), lead to biased motility responses of the cell. When in proximity to each other, they develop cell-cell adhesion via specialized transmembrane proteins of the \textit{cadherin} family. Collectively, they coagulate to clusters of cells that eventually merge to form cell monolayers. We model these phenomena using the Filament Based Lamellipodium Model (FBLM); an anisotropic, two-phase, two-dimensional, continuum model that describes the dynamics the lamellipodium at the level of actin-filaments and their interactions. The model distinguishes between two families (phases) of filaments and includes the interactions between them, as well as between the network of the filaments and the extracellular environment. The FBLM was first proposed in [1] and later extended in [2,4,5]. The FBLM is endowed with a problem specific Finite Element Method (FEM) that we have previously developed in [3]. In this talk we present the basic components of the FBLM and the FEM and focus on a series of simulations reproducing fundamental components of the motility of the cells, such us chemotaxis, haptotaxis, interaction with the environment [3, 4]. We also present our new findings with respect to cell-cell collision and adhesion, as well as the formation of clusters of cells and cell monolayers [5]. To confront the increased computational needs of the monolayer, we have developed a parallel version of our numerical method which we also address in this talk. Literature: [1] D. Oelz, C. Schmeiser. How do cells move? in Cell mechanics: from single scale-based models to multiscale modeling, Chapman and Hall, (2010). [2] A. Manhart, D. Oelz, C. Schmeiser, N. Sfakianakis, An extended Filament Based Lamellipodium: Model produces various moving cell shapes in the presence of chemotactic signals. J. Theor. Biol. (2015). [3] A. Manhart, D. Oelz, C. Schmeiser, N. Sfakianakis. Numerical treatment of the filament based lamellipodium model (FBLM) in Modelling Cellular Systems. (2016) [4] N. Sfakianakis, A. Brunk. Stability, convergence, and sensitivity analysis of the FBLM and the corresponding FEM, Bull. Math. Biol. (2018) [5] N. Sfakianakis, D. Peurichard, C. Schmeiser, and A. Brunk. The FBLM-FEM: from cell-cell adhesion to cluster formation, (in review).
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
42:02
Buttenschoen, AndreasIn both normal tissue and disease states, cells interact with one another, and other tissue components using cellular adhesion proteins. These interactions are fundamental in determining tissue fates, and the outcomes of normal development, wound healing and cancer metastasis. Traditionally continuum models (PDEs) of tissues are based on purely local interactions. However, these models ignore important nonlocal effects in tissues, such as long-ranged adhesion forces between cells. For this reason, a mathematical description of cell adhesion had remained a challenge until 2006, when Armstrong et. al. proposed the use of an integro-partial differential equation (iPDE) model. The initial success of the model was the replication of the cell-sorting experiments of Steinberg (1963). Since then this approach has proven popular in applications to embryogenesis (Armstrong et. al. 2009), zebrafish development (Painter et. al. 2015), and cancer modelling (e.g. Painter et. al. 2010, Domschke et. al. 2014, Bitsouni et. al. 2018). While popular, the mathematical properties of this non-local term are not yet well understood. I will begin this talk by outlining, the first systematic derivation of non-local (iPDE) models for adhesive cell motion. The derivation relies on a framework that allows the inclusion of cell motility and the cell polarization vector in s stochastic space-jump process. The derivation's significance is that, it allows the inclusion of cell-level properties such as cell-size, cell protrusion length or adhesion molecule densities into account. In the second part, I will present the results of our study of the steady-states of a non-local adhesion model on an interval with periodic boundary conditions. The significance of the steady-states is that these are observed in experiments (e.g. cell-sorting). Combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the mathematical properties of the non-local term, we obtain a global bifurcation result for the branches of non-trivial solutions. Using the equation’s symmetries the solutions of a branch are classified by the derivative’s number of zeros. We further show that the non-local operator’s properties determine whether a sub or super-critical pitchfork bifurcation occurs. Finally, I want to demonstrate how the equation's derivation from a stochastic random walk can be extended to derive different non-local adhesion operators describing cell-boundary adhesion interactions. The significance is that in the past, boundary conditions for non-local equations were avoided, because their construction is subtle. I will describe the three challenges we encountered, and their solutions.
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
26:54
Morales Bárcenas, José HéctorFor decades, elucidate the dynamics of the microenvironment of solid tumors has been considered a major research challenge. The fact is that different therapies have not succeeded to eliminate entirely cancer cells in tumors. This resistance feature to anticancer drugs is often attributed to genetic or even epigenetic causes. Another important, but less appreciated cause of this resistance -a possible manifestation of the former, is the geometrical and physical heterogeneity within the tumor microenvironment that leads to marked gradients in the rate of cell proliferation and to regions of hypoxia and acidity, all of which can influence the sensitivity of the tumor cells to drug treatment. There have been different approaches to overcome this resistance, mainly altering solid tumors' microenvironment, for instance, promoting angiogenesis to help the entrance of drugs. Radiation some times is not an option due to the hypoxia in the tumor deep tissue. On the other hand, these physical and geometrical factors have been identified to be responsible of the unsuccessful drug disperse in tumors in some specific time and spatial scales. In this direction, we present an update of our model of drug transport in solid tumors, that quantifies these factors in terms of space-dependent coefficients of the Fokker-Planck equation. The model follows experiments conducted in the Laboratory of Medical Physics and Molecular Imaging of the National Institute for Cancer (INCan) and the Institute of Physics (IFUNAM).
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
30:06
Rutter, EricaGlioblastoma Multiforme (GBM) is a malignant heterogenous cancer in the brain. We propose modeling GBM with heterogeneity in cell phenotypes using a random differential equation version of the reaction-diffusion equation, where the parameters describing diffusion (D) and proliferation (ρ) are random variables. We investigate the ability to perform the inverse problem to recover the probability distributions of D and ρ solely from spatiotemporal data, for a variety of probability distribution functions. We test the ability to perform the inverse problem for noisy synthetic data. We then examine the predicted effect of treatment, specifically, chemotherapy, when assuming such a heterogeneous population and compare with predictions from a homogeneous cell population model.
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
35:53
Rhodes, AdamMetastasis — the spread of cancer from a primary to a distant secondary location — is implicated in over 90% of all cancer related deaths. Despite its importance in patient outcome, a full understanding of the metastatic process remains elusive, largely because of the difficulty in studying the phenomenon experimentally. Recent experimental evidence — including the discovery of the so-called ‘pre-metastatic niche’ — has suggested that metastasis may be a more precisely controlled process than previously thought. In particular, it has been suggested that a developing tumor may be able to corrupt, or ‘educate’, infiltrating immune cells and have them switch from cytotoxic to tumor-promoting roles. Such ‘tumor educated’ immune cells can then travel to distant sites and establish favorable conditions for the settlement and growth of circulating tumor cells. In order to investigate the consequences of tumor-mediated immune education on metastatic spread and growth, we have developed an ordinary differential equation model for tumor-immune dynamics in the metastatic context. The model is studied analytically and numerically, with an examination of the effects of tumor education of immune cells on metastatic dormancy and metastatic blow-up.
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
29:23
Benzekry, SebastienIn the majority of cancers, secondary tumors (metastases) and associated complications are the main cause of death. To design the best therapy for a given patient, one of the major current challenge is to estimate, at diagnosis, the burden of invisible metastases and the future time of emergence of these, as well as their growth speed. In this talk, I will present the current state of our research efforts towards the establishment of a predictive computational tool for this aim. I will first shortly present the model used, which is based on a physiologically-structured partial differential equation for the time dynamics of the population of metastases, combined to a nonlinear mixed-effects model for statistical representation of the parameters’ distribution in the population. Then, I will show results about the descriptive power of the model on data from clinically relevant ortho-surgical animal models of metastasis (breast and kidney tumors). The main part of my talk will further be devoted to the translation of this modeling approach toward the clinical reality. Using clinical imaging data of brain metastasis from non-small cell lung cancer, several biological processes will be investigated to establish a minimal and biologically realistic model able to describe the data. Integration of this model into a biostatistical approach for individualized prediction of the model’s parameters from data only available at diagnosis will also be discussed. Together, these results represent a step forward towards the integration of mathematical modeling as a predictive tool for personalized medicine in oncology.
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
33:55
Stéphanou, AngéliquePharmacokinetics-pharmacodynamics (PK-PD) models are standardly used to assess the availability and effects of a drug. However those models expressed with ordinary differential equations (ODEs) only describe the evolution of the drug concentration with time assuming that all cells receive the same amount and are targetted homogeneously in the same way. In a tumour case however, the cells states and the local cell environment – in terms of oxygenation and acidity – vary depending on the cells location in the tumour (periphery versus core). As a consequence it might prove useful to integrate spatiality in the models in order to get a more accurate evaluation of the drug uptake by the cells. In this presentation, we show how the effects of temozolomide – a pH-dependent drug directed against brain tumours – can be over-evaluated by the standard PK approach. The integration of the spatial component also shows how the healthy tissue might also be affected by the drug and gives a mean to evaluate collateral effects. The model is thus very helpful to highlight the weaknesses of this therapy and to suggest some new means to significantly improve it.
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
44:33
Badoual, MathildeDiffuse low-grade gliomas are slowly growing tumors. After tens of years, they transform inexorably into more aggressive forms, jeopardizing the patient’s life. Mathematical modeling could help clinicians to have a better understanding of the natural history of these tumors and their response to treatments. We present here different models of these tumors: the first one is discrete and describes the appearance of the first glioma cells and the genesis of a tumor. The second model is continuous and consists in a PDE that describes the evolution of the cell density. This model can describe the natural evolution of gliomas, their response to treatments such as radiotherapy and the changes in their dynamics in pregnant women. The discrete and the continuous models are designed to be close to the biological reality. The results are quantitatively compared with either biological data or clinical data, at the cellular level (histological samples) and at the tissue level (MRI scans).
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery
38:23
2Martínez González, AliciaGlioblastoma (GBM) is the most frequent and lethal malignant brain tumor in adults due to its invasive capability and resistance to conventional therapies. GBM typically shows an heterogenous microenviron- ment including necrotic and hypoxic areas, abnormal vasculature and different tumor cell phenotypes. We will focus on mathematical models based on PDE that try to reproduce this complex system in order to understand it and better predict the tumor behaviour [1, 2]. In addition, we will discuss in-silico simu- lations based on a mathematical model for brain tumor response to the combination of antithrombotic, antioxidants and radiation therapies [3]. Our mathematical results predict a synergistic decrease in tumor volume when both, cytotoxic therapies and antioxidants were applied. In vitro and in vivo results have confirmed this benefit not only in terms of tumor reduction but also in terms of toxicity reduction. Combined mathematical simulations and on-chip validation of malignant cellular structures formation in GBM have confirmed their usability to better understand the tumor behaviour [4, 5]. Considering the promising results, a clinical trial is being designed.
2018Banff International Research Station (BIRS) for Mathematical Innovation and Discovery