Workshop 7: Stem Cells, Development, and Cancer

(April 13,2015 - April 17,2015 )

Organizers


Heiko Enderling
Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Thomas Hillen
Mathematical and Statistical Sciences, University of Alberta
John Lowengrub
Mathematics, University of California, Irvine

Most tissues are hierarchically organized into lineages. A lineage is a set of progenitor-progeny relationships within which progressive changes in cell character occur. Typically, lineages are traced back to a self-perpetuating stem cell (SC), and end with a postmitotic terminal cell. One of the most exciting recent developments in the field of cancer biology is the recognition that lineage progression continues to occur in tumors. In particular there is an increasing body of evidence that like normal tissues, tumor cells that have the potential for unlimited self-renewal give rise in large numbers to cells that lack this potential - the so-called cancer stem cell hypothesis. By focusing for so many years on the majority cell populations in tumors, and not on the rarer cancer stem cells (cancer initiating cells), scientists and clinicians may have missed out on opportunities to understand, diagnose and treat the processes in cancer that matter most. Further, there is increasing evidence that cell stemness may be a function of the local environment rather than being a predetermined property of a cell. What are the consequences of this plasticity in cell behavior? Other important open questions in the field include: What cell types within the normal tissues are capable of being the cells of origin for tumors? What is the relationship between normal tissue stem cells and tumor-initiating cells (e.g., cancer stem cells)? Which signaling and other regulatory networks are altered in tumors relative to the normal tissues, and how do they function within the tumor? Finally, there is growing evidence that therapies aimed at the major cell types in tumors may sometimes make things worse, by leading to an expansion in the fraction of cancer stem cells. How can this be avoided? This workshop will address these and other questions through discussions among mathematical and computational modelers and experimentalists. In particular, the strong connections between normal development, tumor growth and the use of novel treatment strategies will be discussed.

Accepted Speakers

David Axelrod
Department of Genetics and Cancer Institute of New Jersey, Rutgers University
Arianna Bianchi
Department of Mathematics, Heriot-Watt University
Helen Byrne
Centre for Collaborative Applied Mathematics, University of Oxford
Dirk Drasdo
Bioinformatics, Physical and Mathematical Biology, Institut National de Recherche en Informatique Automatique (INRIA)
Avner Friedman
Department of Mathematics, The Ohio State University
Leonid Hanin
Department of Mathematics, Idaho State University
Anita Hjelmeland
Cell, Developmental and Integrative Biology, University of Alabama at Birmingham
Sasha Jilkine
ACMS, University of Notre Dame
Yangjin Kim
Department of Mathematics, Konkuk University
Marek Kimmel
Department of Statistics, Rice University
Michael Lewis
Lester and Sue Smith Breast Center, Lester and Sue Smith Breast Center
Paul Macklin
Center for Applied Molecular Medicine, University of Southern California
Anna Marciniak-Czochra
Institute of Applied Mathematics, Heidelberg University
Alexander Pearson
Hematology and Medical Oncology, University of Michigan
Noemi Picco
Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Jan Poleszczuk
Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute
Lynne-Marie Postovit
Oncology, University of Alberta
Jeremy Rich
Stem Cell Biology and Regenerative Medicine, Cleveland Clinic
Ignacio Rodriguez-Brenes
Mathematics, University of California, Irvine
Christina Surulescu
Mathematics, Felix-Klein-Zentrum für Mathematik, TU Kaiserslautern
Jose Ignacio Tello
Department of Applied Mathematics, Universidad Complutense de Madrid
Benjamin Werner
Genomics and Modeling Group, The Institute of Cancer Research
Dominik Wodarz
University of California, Irvine
Monday, April 13, 2015
Time Session
07:45 AM

Shuttle to MBI

08:00 AM
08:30 AM

Breakfast

08:30 AM
08:45 AM

Introductions and MBI Information

08:45 AM
09:00 AM

Introduction to Workshop - Thomas Hillen

09:00 AM
10:00 AM
Lynne-Marie Postovit - How Cancer Cells Hijack Stem Cell Pathways

Tumours contain populations of cells with stem cell like properties, and it is believed that these cells are responsible for cancer progression, resistance to therapy and metastatic potential. Stem cell-like populations are regulated by their immediate surroundings (microenvironment) characterized by proteins, immune cells, and biophysical features such low oxygen tensions. A growing body of evidence suggests that cancer cells hijack normal stem cell-associated regulatory networks in order to behave like stem cells. We have discovered that an embryonic-associated protein called Nodal maintains stem cell phenotypes in cancer, and that it promotes classical hallmarks of cancer such as angiogenesis, and metastasis. We have also found that biophysical features of a growing tumour, in particular low oxygen, can turn regular cancer cells into cancer stem cells. This lecture will describe these findings and will introduce the audience to the biology of normal and cancer stem cells. New and exciting advancements linked to how we may be able to treat and even prevent metastatic cancers by targeting stem cell proteins like Nodal will also be revealed.

10:00 AM
10:30 AM

Break

10:30 AM
11:10 AM
Leonid Hanin - Cancer Stem Cells Discovered ... Mathematically

Cancer stem cells have a variety of biological characteristics, and categorizing cancer cells as stem cells depends on selection of defining properties. In this work we focus on metastatic potential of cancer cells and answer the following question: Can one characterize the size of the subpopulation of metastasis-producing cells in a solid tumor?

To answer this question, we used a very general mathematical model of cancer progression accounting for primary tumor origination and growth, shedding of metastases off the primary tumor, selection of viable metastases, dormancy of metastases and their inception in a secondary site, and growth of metastases in the site of interest. The model assumes that metastasis shedding off the primary tumor is governed by a Poisson process whose rate at time t is proportional to the number of metastasis-producing cells, N(t), which in turn is assumed proportional to some power of the size of the primary tumor: N(t) = kS^θ (t). The case θ = 0 (or close to 0) suggests the presence within a primary tumor of a relatively stable, and hence self-renewing, subpopulation of metastasis-producing cells.

The model produces an explicit formula for the distribution of the site-specific sizes of metastases at any given time. Fitting the model to clinical data allows one to estimate model parameters including θ. This parameter was estimated for three patients with renal cancer, non-small cell lung cancer and pancreatic cancer. In all these cases, the value of θ was found to be quite small, which serves as an indirect evidence for the existence of cancer stem cells with high metastatic potential.

11:10 AM
11:50 AM
Dominik Wodarz - Mathematical models of chronic lymphocytic leukemia (CLL)

Chronic lymphocytic leukemia (CLL) is a malignancy of B cells and is the most common leukemia in adults. Patients have typically been treated with a combination of chemo and immuno-therapies. These have resulted in relatively good responses except in high risk patients in which p53 has been inactivated. Recently, new, targeted treatment approaches have been developed which have so far shown great promise in the clinic. One such drug is the Bruton tyrosine kinase (BTK) inhibitor ibrutinib. Upon treatment initiation, a lymphocytosis phase is observed during which the number of CLL cells can show a pronounced rise in the blood. The number of cells eventually reaches a peak and declines during therapy. It is thought that the lymphocytosis phase represents the redistribution of cells from tissue where the majority of the disease burden lies (lymph nodes, spleen, bone marrow) into the blood. One question is whether upon treatment the majority of the tissue CLL cells redistributes to blood, or whether only a small fraction of the tumor cells redistributes while a large fraction of tissue cells dies. We used mathematical models, applied to clinical data, in order to kinetically characterize the treatment responses to ibrutinib, and to investigate this question. In addition, the measurements of all crucial CLL parameters allowed us to build evolutionary mathematical models in order to study the emergence of ibrutinib-resistant cells. An important aim of this work is the development of a predictive computational framework that can give personalized predictions for patients about the long-term outcome of ibrutinib therapy.

11:50 AM
02:15 PM

Lunch Break

02:15 PM
02:55 PM
David Axelrod - Stem Cell Dynamics in Normal Human Colon Crypts and the Initiation and Therapy of Colon Cancer

An agent-based model of stochastic cell dynamics in human colon crypts was developed in the application NetLogo, and calibrated by measurements of numbers of stem cells, proliferating cells, and differentiated cells in human biopsy specimens. It was assumed that each cell’s probability of proliferation and probability of death is determined by its position in two microenvironment gradients along the crypt axis, a divide gradient and in a die gradient. A cell’s type is not intrinsic, but rather is determined by its position in the divide gradient. Cell types are dynamic, plastic, and inter-convertible. Parameter values were determined for the shape of each of the gradients, and for a cell’s response to the gradients. This was done by parameter sweeps that indicated the values that reproduced the measured number and variation of each cell type, and produced quasi-stationary stochastic dynamics. The behavior of the model was verified by its ability to reproduce the experimentally observed monoclonal conversion by neutral drift, the formation of adenomas resulting from mutations either in stem cells, proliferating cells, or differentiated cells, and by the robust ability of crypts to recover from perturbation by cytotoxic agents due to resistant quiescent stem cells. An example of the use of the virtual crypt will be given, viz., the evaluation of different cancer chemotherapy protocols.

02:55 PM
03:10 PM

Break

03:10 PM
03:50 PM
Avner Friedman - Major Genes in Colorectal Cancer

Major genes are defined as those that are necessary and sufficient for disease causation, with important mutations of the gene as causal mechanism. It is commonly accepted that in colorectal cancer the principal major genes are APC, K-RAS, TGF-B, SMAD and p53. However, it may be important to know which gene is the first to undergo mutation. Patients with ulcerative colitis or Crohn’s disease are at risk of developing colorectal cancer. In the first part of this talk I will show, with a mathematical model that in colitis-associated colon cancer p53 is the first gene that is mutated. In the second part of the talk, I will show, again by a mathematical model (and rigorous mathematical analysis) that on mutation in major genes is not sufficient to cause colorectal cancer.

03:50 PM
04:00 PM

Break

04:00 PM
06:00 PM

Reception and Poster Session

06:00 PM

Shuttle pick-up from MBI

Tuesday, April 14, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:45 AM
Marek Kimmel - Analysis of mutations leading to the myelodysplastic syndrome (MDS) using modified Moran models

Abstract not submitted.

09:45 AM
10:15 AM

Break

10:15 AM
10:55 AM
Jeremy Rich - Target Identification in Glioma Initiating Cells

Gliomas display cellular hierarchies with tumor initiating cells (TICs) at the apex that are functionally defined by the ability to self renew and propagate tumors similar to the parental tumors from which they are derived. TICs remain controversial, but their clinical relevance has been supported by resistance to cytotoxic therapies (Bao et al. Nature 2006) and promotion of tumor angiogenesis (Bao et al. Cancer Research 2006). TICs reside in specific functional niches in perivascular and hypoxic niches (Li et al. Cancer Cell 2009) that may offer the ability to disrupt tumor maintenance and therapeutic resistance through targeting the niche. Investigating TICs has already yielded novel molecular targets and pathways that are amenable to therapeutic targeting (Kim et al. Genes Development 2012; Eyler et al. Cell 2011; Guryanova et al. Cancer Cell 2011). Using patient-derived tumor models, we have interrogated the regulation of the TIC phenotype by both cell intrinsic and microenvironmental influences present in tumors. TICs are enriched under low nutrient conditions due to the cooption of the high affinity GLUT3 transporter normally expressed by neurons (Flavahan et al. Nature Neuroscience 2013). We have now extended these findings to demonstrate that cellular metabolism is differentially regulated within the tumor hierarchy at several levels to provide resources for sustained self-renewal and proliferation (Xie et al. Nature Neuroscience 2015). We also recently found that TICs have basal genotoxic stress activating PARP permitting radiosensitization (Venere et al. Cell Death Differentiation 2014). To discover novel TIC targets, we are using several technologies, including aptamers (Kim et al. Cancer Research 2013), flow cytometry (Lathia et al. Cell Reports 2014), and phage display (Liu et al. Cell Death Diff. 2014), showing that TICs manifest nodes of fragility mediating cell survival and invasion (e.g. JAM-A, VAV3, and CD97). Combining TIC models from patients with non-neoplastic progenitors from epilepsy resections, we are interrogating additional molecular regulators of the cellular hierarchy that can be distinguished from normal stem cells to minimize toxicity. The conventional pyramidal unidirectional differentiation cascade with TICs at the apex has been called into question by studies demonstrating plasticity of the TIC phenotype (Cheng et al. Cell 2013), thus suggesting that targeting only TICs will likely fail to cure patients and require simultaneous targeting of TICs and the bulk tumor. Although the field of TIC biology is relatively young, continued elucidation of the tumor hierarchy holds promise for development of novel patient therapies.

10:55 AM
11:35 AM
Paul Macklin - New open source tools for simulating large 3-D multicellular systems on the desktop

In diversefields spanning developmental biology, tissue engineering, and cancer, dynamical interactions between large multicellular populations and the microenvironment shape the emergent behaviors of the larger systems, often in surprising ways. While mathematical models can help to understand these systems, 3-D simulation studies often require solving for the dynamics of 105 or more cells, along with several diffusing growth substrates and signaling factors. Such simulations are challenging, generally requiring either complex parallelization on supercomputers, or restriction to smaller systems of 103 or 104 cells in 2-D or very small 3-D domains. Moreover, largely incompatible data formats have impeded the development of robust tools for 3-D visualization and data analysis, further slowing systematic investigations. We will discuss our work to address these problems with parallelized open source codes designed for desktop computers or single HPC compute nodes. We will introduce PhysiCell: an agent-based model that simulates cell cycling, apoptosis, necrosis, volume changes, and biomechanics-based movement in 3-D systems of 105 to 106 cells. We will introduce BioFVM: a finite volume solver for diffusive transport in large 3-D tissues (5+ diffusing substrates on 106 or more voxels: 5-10 mm3 at 20 m resolution). We will discuss MultiCellDS: a draft data standard for cell phenotype and multicellular simulation data. And we will discuss our efforts to connect these tools to simulate breast cancer and colon cancer metastases in the liver. It is our hope that this work will help seed an ecosystem of compatible computational tools and experimental data. At the close of the talk, we will open the floor to discussion on how these tools can be adapted to meet the needs of the stem cell modeling community. See mbi2015.MathCancer.org for more information.

11:35 AM
01:35 PM

Lunch Break

01:35 PM
02:15 PM
Ignacio Rodriguez-Brenes - Replicative Senescence as a Tumor Suppressor Pathway

Abstract not submitted.

02:15 PM
02:55 PM
Anita Hjelmeland - Modeling Effects of the Tumor Microenvironment on Brain Tumor Stem Cell Phenotypes

Abstract not submitted.

02:55 PM
03:10 PM

Break

03:10 PM
03:50 PM
Yangjin Kim - Mathematical models of oncolytic virus therapy and characterization of the invasive and non-invasive glioma

In this talk, a mathematical model of Chase-ABC mediated oncolytic virus therapy targeting cancer stem cells and CSPG-driven glioma infiltration will be presented. Glioblastoma is the most aggressive type of brain cancer with the median survival time of one year. Oncolytic viruses are genetically engineered viruses that are designed to kill cancer cells while doing minimal damage to normal healthy tissue. After being injected into a tumor, they infect cancer cells, multiply inside them, and when a cancer cell is killed they move on to spread and infect other cancer cells. Chondroitinase ABC (Chase-ABC) is a bacterial enzyme that can remove a major glioma ECM component, chondroitin sulfate glycosoamino glycans (CSGG) from proteoglycans without any deleterious effects in vivo. It has been shown that Chase-ABC treatment is able to promote the spread of the viruses, increasing the efficacy of the viral treatment. We develop a mathematical model to investigate the effect of the Chase-ABC on the treatment of glioma by oncolytic viruses (OV). We show that the model’s predictions agree with experimental results for a spherical glioma. We then use the model to test various treatment options for both primary tumor and infiltrating tumor cells in the heterogeneous microenvironment of the brain. A new strategy of targeting cancer stem cells in a niche using transported oncolytic viruses will be also presented. The primary treatment option is surgery but invasive cells in brain tissue eventually regrow back even with chemo- and radio-therapy, generating poor clinical outcomes. Therefore, it is important to distinguish invasive glioma phenotypes from non-invasive cells. Experiments by Silver et al illustrated that concentrations of CSPG, one of major extracellular matrix component within a tumor, determine invasive and non-invasive phenotypes. We developed a mathematical model of CSPG-driven dynamics of a growing glioma, using a free boundary framework. We take into account the rich dynamics of astrocytes and microglia in brain tissue as illustrated in Silver et al. The simulation results are in good agreement with experimental data in Silver et al. We also show how oncolytic virus therapy can be used to eradicate tumor cells. There is a critical threshold value of CSPG levels for optimal killing of both invasive and non-invasive tumorcells.

04:15 PM

Shuttle pick-up from MBI

Wednesday, April 15, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:45 AM
Benjamin Werner - Reconstructing the in vivo dynamics of hematopoietic stem cells from telomere length distributions.

Most mammalian tissues are hierarchically organized. Few self renewing stem cells give rise to shorter-lived progeny.Here, we investigate the in vivo patterns of stem cell divisions in the human hematopoietic system throughout life. We analyze the shape of telomere length distributions underlying stem cell behavior within individuals. These distributions contain a fingerprint of the initial telomere length and progressive telomere loss. We test our predictions on telomere length data of 356 healthy individuals, including 47 cord blood and 28 bone marrow samples. We find an increasing stem cell pool during childhood and adolescence and an approximately maintained stem cell population in adults. Furthermore, our method is able to detect individual differences from a single tissue sample, i.e. a single snapshot. Prospectively, this allows us to compare cell proliferation between individuals and identify abnormal stem cell dynamics, which affects the risk of stem cell related diseases.

09:45 AM
10:15 AM

Break

10:15 AM
10:55 AM
Arianna Bianchi - Neoneurogenesis and tumor metastasis: myth or reality?

Primary tumors infrequently lead to the demise of cancer patients; rather, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs (metastasis). Malignant tumors release both lymph- and angio- genic factors, through two specific processes termed lymphangiogenesis and angiogenesis, respectively. In addition, recent experimental evidence shows that tumors initiate their own innervation by the release of neurotrophic factors (neoneurogenesis). The relationship between tumor progression and the nervous system is a complex and poorly understood part of cancer pathogenesis. It is likely that this process is regulated by a multitude of factors in the tumor/nerve microenvironment; these pathways are even further complicated by treatment and disease history as well as other genetic and socioeconomic factors. It is therefore important to study the interactions between the nervous system and tumor cells through mathematical/computational modelling: in this way we will take into account the most significant elements of the plethora of interacting pathways regulating this process. The present work is a first attempt to model the neurobiological aspect of cancer development through a system of differential equations.


NOTE: This is a joint work with Dr Georgios Lolas, TU Dresden (Germany).

10:55 AM
11:35 AM
Sasha Jilkine - Stochastic models of stem cell dedifferentiation in cancer

Recent evidence suggests that, like many normal tissues, many cancers are maintained by a small population of cancer stem cells that divide indefinitely to produce more differentiated cancerous cells.

Tissues, however, contain many more differentiated cells than stem cells, and mutations may cause such cells to "dedifferentiate" into a stem-like state.

We study the effects of dedifferentiation on the time to cancer onset and found that the effect of dedifferentiation depends critically on how stem cell numbers are controlled by the body. If homeostasis is very tight (due to all divisions being asymmetric), then dedifferentiation has little effect, but if homeostatic control is looser (allowing both symmetric and asymmetric divisions), then dedifferentiation can dramatically hasten cancer onset and lead to exponential growth of the cancer stem cell population. We also consider effects of various negative feedback loops from the progenitor population on regulation of homeostasis.

Our results suggest that dedifferentiation may be a very important factor in cancer and that more study of dedifferentiation and stem cell control is necessary to understand and prevent cancer onset.

11:35 AM
01:30 PM

Lunch Break

01:30 PM
02:15 PM
Heiko Enderling - Acute and Fractionated Irradiation Differentially Modulate Glioma Stem Cell Division Kinetics

Glioblastoma multiforme (GBM) is one of the most aggressive human malignancies with a poor patient prognosis. Ionizing radiation either alone or adjuvant after surgery is part of standard treatment for GBM but remains primarily noncurative. The mechanisms underlying tumor radioresistance are manifold and, in part, accredited to a special subpopulation of tumorigenic cells. The so-called glioma stem cells (GSC) are bestowed with the exclusive ability to self-renew and repopulate the tumor and have been reported to be less sensitive to radiation- induced damage through preferential activation of DNA damage checkpoint responses and increased capacity for DNA damage repair. During each fraction of radiation, non–stem cancer cells (CC) die and GSCs become enriched and potentially increase in number, which may lead to accelerated repopulation. We propose a cellular Potts model that simulates the kinetics of GSCs and CCs in glioblastoma growth and radiation response. We parameterize and validate this model with experimental data of the U87-MG human glioblastoma cell line. Simulations are conducted to estimate GSC symmetric and asymmetric division rates and explore potential mechanisms for increased GSC fractions after irradiation. Simulations reveal that in addition to their higher radioresistance, a shift from asymmetric to symmetric division or a fast cycle of GSCs following fractionated radiation treatment is required to yield results that match experimental observations. We hypothesize a constitutive activation of stem cell division kinetics signaling pathways during fractionated treatment, which contributes to the frequently observed accelerated repopulation after therapeutic irradiation.

02:15 PM
02:55 PM
Christina Surulescu - Mathematical models for anisotropic glioma invasion: a multiscale approach

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms. Since they are highly invasive they are hard to remove by surgery, as the tumor margin it most often not precisely enough identifiable. The understanding of glioma spread patterns is hence essential for both radiological therapy as well as surgical treatment. We propose a multiscale framework for glioma growth includinginteractions of the cells with the underlying tissue network, along with proliferative effects. Relying on experimental findings, we assume that cancer cells use neuronal fibre tracts as invasive pathways. Hence, the individual structure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide such information, thus opening the way for patient specific modeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale) cell dynamics, we deduce on the macroscale effective equations characterizing the evolution of the tumor cell population and perform numerical simulations based on DTI data. Particular attention is payed on the modeling of proliferation terms on the mesoscale level, in order to deduce the corresponding source terms on the macroscale.

02:55 PM
03:10 PM

Break

03:10 PM
03:50 PM
Helen Byrne - The Role of Wnt Signalling in Stem Cells and Early Colorectal Cancer

Wnt signalling plays a key regulatory role in many biological processes including cell proliferation, migration and cell fate specification. It is active during development and also during adulthood when it assists in the maintenance of homeostasis. Dysregulation of the Wnt signalling pathway is a hallmark of several developmental disorders, a number of degenerative diseases and a variety of different cancers.As such, it is an obvious target for therapeutic intervention. However, its complexity and cross talk with other subcellular and cellular processes make it difficult to understand the consequences of abnormal Wnt signalling and to predict (and compare) the impact of different therapeutic approaches.

Motivated in part by these considerations, a variety of mathematical models of the Wnt signalling pathway have now been developed. The models are typically formulated as systems of ordinary differential equations that describe how the subcellular concentrations of proteins such as -catenin, APC and Axin change over time and in response to Wnt stimulation. Recent models account for the localisation of these Wnt proteins in different subcellular compartments (e.g. the cytoplasm, nucleus and membrane), their transport between the various pools and, to a limited extent, their cross talk with the Delta-Notch and ERK signalling pathways.

In this talk I will review existing subcellular and multiscale models of Wnt signalling, with particular focus on the intestinal crypt, stem cells and the early stages of colorectal cancer.

04:15 PM

Shuttle pick-up from MBI

Thursday, April 16, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:45 AM
Dirk Drasdo - Parameterizing spatial-temporal models from image information

In this talk we will study in how far spatial-temporal tissue models can be largely parameterized from image information. The examples envisaged are liver regeneration after drug-induced damage, and growing multi-cellular spheroids of SK-MES-1. For regeneration in liver we will show how the iterative application of a pipeline consisting of confocal scanning microscopy, image analysis and modeling can be used to set up a quantitative spatial-temporal agent-based model of liver regeneration (Drasdo et. al., J. Hepat. 2014), that by simulated predictions successfully guided experiments on spatial tissue organization processes (Hoehme et. al, PNAS, 2010), liver metabolism (Schliess et. al., Hepatology, 2014), and the molecular control of cell proliferation towards new biological insight. We use our image modeling software TiQuant, integrated in an analysis pipeline of standardized imaging protocols for confocal laser scanning microcopy and image processing to infer 3D volume data sets (Hammad et. al., Arch. Toxicol., 2014), to quantify and thereby objectify image information (Friebel, in rev.). Spatial temporal simulations are either performed directly in the reconstructed 3D images, or in representative tissue samples obtained by sampling from statistical distributions over the parameters chosen to quantify the image information. For growing multi-cellular spheroids of SK-MES-1 cells, a model will be stepwise developed by stepwise including image data for different growth conditions.

09:45 AM
10:15 AM

Break

10:15 AM
10:55 AM
Alexander Pearson - Sampling of Single Ovarian Carcinoma Cell Data Predicts In-Vivo Treatment Response

Ovarian cancer is the seventh most common cancer worldwide, with more than 150,000 women dying annually from this disease. Cancer Stem-Like Cells (CSCs) have been characterized in ovarian cancer, and aldehyde dehydrogenase (ALDH) enzymatic activity is an excellent marker of ovarian CSCs in both SKOV3 (cell line) and primary patient samples. Our collaborators have developed single-cell microfluidics arrays which can isolate single cancer cells for observation under different treatment conditions. We developed a two-step, penalized sampling algorithm to predict the behavior of larger populations of cells based on microfluidics observations. Applying our sampling algorithm shows reasonable approximations of observed outcomes in larger, standard-culture in-vitro experiments. In order to assess the predictive accuracy of therapeutic intervention changes to the microfluidics culture, we applied Endothelial Growth Factor-Like Protein 6 (EGFL6), an ovarian tumor vascular factor. This resulted in an expansion of the majority low ALDH expressing cell population. These EGFL6-based population shifts are predicted in-vivo based on microfluidics data from single cells and use of our sampling algorithm. I propose that the combined use of microfluidics treatment experiments and our sampling algorithm could streamline novel drug development for interventions seeking to manipulate the CSC pool.

10:55 AM
11:35 AM
Noemi Picco - An in silico investigation of niche-driven cancer stem cell plasticity

Cancer stem cells are believed to be the sole initiator and driver of tumor growth, given their self-renewal and tissue restoration properties. Characterizing the behavior of this peculiar cell type will critically allow us to identify the dynamics that lead to the formation of solid tumors. A specialized microenvironment (the niche) is believed to be a key driver of stemness, offering a new, more plastic view of the stem phenotype, where the niche dictates the cell's ability to stay in a stem-like state. The idea that any cell can become a stem-like cell and also lose this phenotype and that this ability is purely context driven is quite novel.

An in silico investigation of the plasticity of stemness in early ductal carcinoma is presented, describing the dynamics at the single cell scale, result of the interaction between the phenotypically heterogeneous cancer cell population and environmental factors. A spectrum of in silico pathological tissues is obtained, which correspond to clinically observed scenarios.

11:35 AM
01:35 PM

Lunch Break

01:35 PM
02:15 PM
Michael Lewis - Data-Driven Mathematical Modeling of Mammary Ductal Elongation

The Terminal End Bud (TEB) at the growing tip of mammary ducts is one of the fastest growing structures in mammals. TEBs drive ductal elongation during puberty and regress once development of the ductal tree is complete. Because of similarities between TEB growth and breast cancer growth, successful modeling of this structure may yield insight into breast development as well as cancer progression. Previous mathematical models have focused on branching morphogenesis, but there are currently no models that address ductal elongation itself. Our model exploits the constrained geometry of the TEB in vivo which provided the framework for an initial mathematical model. Parameters in this model were then informed with measureable data (morphological characteristics, proliferation rate, cell cycle duration, and apoptosis). These data were then used to calculate a value representing the movement of cells from the TEB into the mature duct (termed the flux) and this calculated flux was then used to predict a linear elongation rate. The prediction was compared to an experimentally measured displacement within the mammary fat pad. Our initial measurements of proliferation, apoptosis, and cell sizes, predicted a linear elongation rate of 1.39 mm per day, which was significantly different from our experimentally measured displacement rate of 0.54mm per day. We then refined our model by incorporating changes in the direction of growth due to bifurcation, a cost function for bifurcation (which describes duplication of the TEB), as well as an additional flux term to account for a migration of cap cells into the body cell. Iteration of the revised mathematical model yielded an estimate significantly closer to the measured displacement rate, thus indicating that the most relevant biological parameters have been accounted for. In addition, our data overturned a long held belief that cap cells contribute to the body cell lineage. We are now poised for in silico experiments that may yield predictions consistent with cancer phenotypes, as well as predictions that recapitulate known mutation phenotypes.

02:15 PM
02:55 PM
Anna Marciniak-Czochra - Mathematical models of heterogeneity, clonal selection and therapy resistance in acute leukemias

Motivated by clonal selection observed in acute myeloid leukemia (AML), we propose mathematical models describing evolution of a multiclonal and hierarchical cell population. The models in a form of partial and integro-differential equations are applied to study the role of self-renewal properties and growth kinetics during disease development and relapse. Effects of different time and space scales are investigated. It is shown how resulting nonlinear and nonlocal terms may lead to a selection process and ultimately to therapy resistance. The results are compared to AML patient data. Model based interpretation of clinical data allows to assess parameters that cannot be measured directly. This might have clinical implications for future treatment and follow-up strategies.

02:55 PM
03:10 PM

Break

03:10 PM
03:50 PM
Jan Poleszczuk - Evolution and phenotypic selection of cancer stem cells

Cells of different organs at different ages have an intrinsic set of kinetics that dictates their behavior. Transformation into cancer cells will inherit these kinetics that determine initial cell and tumor population progression dynamics. Subject to genetic mutation and epigenetic alterations, cancer cell kinetics can change and favorable alterations that increase cellular fitness will manifest themselves and accelerate tumor progression. We set out to investigate the emerging intratumoral heterogeneity and to determine the evolutionary trajectories of the combination of cell-intrinsic kinetics that yield aggressive tumor growth. We develop a cellular automaton model that tracks the temporal evolution of the malignant subpopulation of so-called cancer stem cell, as these cells are exclusively able to initiate and sustain tumors. We explore orthogonal cell traits including cell migration to facilitate invasion, spontaneous cell death due to genetic drift after accumulation of irreversible deleterious mutations, symmetric cancer stem cell division that increases the cancer stem cell pool, and telomere length and erosion as a mitotic counter for inherited non-stem cancer cell proliferation potential. Our study suggests that cell proliferation potential is the strongest modulator of tumor growth. Early increase in proliferation potential yields larger populations of CC that compete with CSC and thus inhibit CSC division while a reduction in proliferation potential loosens such inhibition and facilitates frequent CSC division. The subpopulation of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from long-term dormancy to aggressive progression. Our study suggests that the clonal diversity that is captured in single tumor biopsy samples represents only a small proportion of the total number of phenotypes.

04:30 PM

Shuttle pick-up from MBI

05:30 PM
06:00 PM

Cash Bar - Crowne Plaza

06:00 PM
07:30 PM

Banquet at Crowne Plaza

Friday, April 17, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
08:45 AM

Breakfast

08:45 AM
09:30 AM
Mohammad Kohandel - Mathematical modeling of phenotypic switching in cancer

According to the cancer stem cell (CSC) hypothesis, in addition to their self-renewal, CSCs can undergo symmetric or asymmetric "unidirectional" divisions to generate daughter cells with low tumorigenic potential (non-CSCs). However, growing evidence supports violation of unidirectionality for the traditional stem cell based tissue hierarchy, suggesting a new model in which a significant degree of plasticity exists between the non-CSC and CSC compartments. This talk will survey our mathematical approaches to investigate the CSC hypothesis and the dynamic phenotypic switching between these populations, as well as therapeutic implications.

09:30 AM
10:00 AM

Break

10:00 AM
10:40 AM
Jose Ignacio Tello - On a mathematical model of cancer stem cells with non-local terms

Abstract not submitted.

10:40 AM
11:20 AM
Thomas Hillen - Mathematical Modelling of the Tumor Growth Paradox and more...

The tumor growth paradox describes the effect that a tumor after incomplete treatment grows larger than it was before treatment. A possible explanation is the presence of cancer stem cells (CSC). CSC are less sensitive to treatments and can repopulate the tumour. On my poster I present a basic CSC model to explain the tumor growth paradox. If combined with immune interactions we find that the immune system selects for CSC. Since CSC are known to be less sensitive to treatments such as chemotherapy and radiation therapy, we investigate the benefit gained by a differentiation promoter combined with radiation. We find that a differentiation promoter can have a drastic effect, allowing us to reduce the radiation dosage. Ongoing work relates to a non-local PDE version of the model to investigate spatial CSC distributions and invasions.

11:20 AM

Shuttle pick-up from MBI (One to airport and one back to hotel)

Name Email Affiliation
Alvarado, Cesar calvarad@unm.edu Mathematics and Statistics, University of New Mexico
Axelrod, David axelrod@biology.rutgers.edu Department of Genetics and Cancer Institute of New Jersey, Rutgers University
Bar, Eli eeb49@case.edu Neurological Surgery, Case Western Reserve University
Bawa, Usman bawa.usman@yahoo.com Biology Education, Federal college of education Technical potiskum
Bianchi, Arianna ab584@hw.ac.uk Department of Mathematics, Heriot-Watt University
Buttenschoen, Andreas andreas.buttenschoen@ualberta.ca Department of Mathematical and Statistical Sciences, University of Alberta
Butuci, Melina butuci@usc.edu Molecular and Computational Biology, USC
Byrne, Helen byrneh@maths.ox.ac.uk Centre for Collaborative Applied Mathematics, University of Oxford
Cannataro, Vincent vcannataro@ufl.edu Biology, University of Florida
Curtin, Lee pmxlc1@exmail.nottingham.ac.uk School of Mathematical Sciences, University of Nottingham
de Vries, Gerda gerda.devries@ualberta.ca Department of Mathematical & Statistical Sciences, University of Alberta
Drasdo, Dirk dirk.dras@gmail.com Bioinformatics, Physical and Mathematical Biology, Institut National de Recherche en Informatique Automatique (INRIA)
Durrett, Rick rtd@math.duke.edu Department of Mathematics, Duke University
Enderling, Heiko heiko.enderling@moffitt.org Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Espey, Michael espeym@mail.nih.gov Division of Cancer Biology, National Cancer Institute
Fessel, Kimberly fessel.6@mbi.osu.edu Mathematical Biosceinces Institute, The Ohio State University
Friedman, Avner afriedman@math.ohio-state.edu Department of Mathematics, The Ohio State University
Friedman, Samuel samuelf@usc.edu Medicine, University of Southern California
Govinder, Kesh govinder@ukzn.ac.za Mathematics, Statistics and Computer Science, University of KwaZulu-Natal
Hamilton, Ian hamilton.598@osu.edu EEOB/Mathematics, The Ohio State University
Hanin, Leonid hanin@isu.edu Department of Mathematics, Idaho State University
Hillen, Thomas thillen@ualberta.ca Mathematical and Statistical Sciences, University of Alberta
Hjelmeland, Anita hjelmea@uab.edu Cell, Developmental and Integrative Biology, University of Alabama at Birmingham
Jilkine, Alexandra ajilkine@nd.edu ACMS, University of Notre Dame
Kang, Hye-Won hwkang@umbc.edu Department of Mathematics and Statistics, University of Maryland, Baltimore County
Kim, Yangjin ahyouhappy@konkuk.ac.kr Department of Mathematics, Konkuk University
Kimmel, Marek kimmel@rice.edu Department of Statistics, Rice University
Knutsdottir, Hildur hildur@math.ubc.ca Mathematics, University of British Columbia
Kohandel, Mohammad kohandel@uwaterloo.ca Applied Mathematics, University of Waterloo
Komarova, Natalia komarova@uci.edu Department of Mathematics, University of California, Irvine
Konstorum, Anna akonstor@uci.edu Mathematics, University of California, Irvine
Kroos, Julia julia_kroos@web.de Mathematical Modeling in Biosciences, Basque Center for Applied Mathematics
Kumar, Sanjeev skumar@dbrau.ac.in Mathematics, Dr. B.R. Ambedkar University, Agra
Lewis, Michael mtlewis@bcm.edu Lester and Sue Smith Breast Center, Lester and Sue Smith Breast Center
Lowengrub, John lowengrb@math.uci.edu Mathematics, University of California, Irvine
Macklin, Paul Paul.Macklin@usc.edu Center for Applied Molecular Medicine, University of Southern California
Manem, Venkata vsmanem@math.uwaterloo.ca Radiation Oncology, Massachusetts General Hospital and Harvard Medical School
Marciniak-Czochra, Anna Anna.Marciniak@iwr.uni-heidelberg.de Institute of Applied Mathematics, Heidelberg University
Mohr, Marcel marcel.mohr@bioquant.uni-heidelberg.de Institute of Applied Mathematics, University of Heidelberg
Ogundipe, Olanrewaju loludipe@yahoo.com Drug design, Biochemistry and Cancer Research, University of Salford, UK
Olobatuyi, Oluwole olobatuy@ualberta.ca Mathematical and Statistical Sciences, University of Alberta
Paine, Ingrid runquist@bcm.edu Molecular and Cellular Biology, Baylor College of Medicine
Pearson, Alexander pearsona@med.umich.edu Hematology and Medical Oncology, University of Michigan
Picco, Noemi Noemi.Picco@moffitt.org Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Poleszczuk, Jan j.poleszczuk@mimuw.edu.pl Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute
Postovit, Lynne-Marie postovit@ualberta.ca Oncology, University of Alberta
Rich, Jeremy richj@ccf.org Stem Cell Biology and Regenerative Medicine, Cleveland Clinic
Rodriguez-Brenes, Ignacio iarodrig@uci.edu Mathematics, University of California, Irvine
Roh, Soyeon haezyrohs@gmail.com Department of Mathematics, University of Michigan-Ann Arbor
Sishc, Brock Brock.sishc@utsouthwestern.edu Radiation Oncology, UT Southwestern Medical Center
Sontag, Eduardo eduardo.sontag@gmail.com Department of Mathematics and BioMaPS Institute for Quantitative Biology, Rutgers University at New Brunswick
Stocks, Theresa theresa.stocks@gmx.de Department of Mathematics, Stockholm University
Surnov, Alexey alexsurnov88@gmail.com Institute of Physiological Chemistry, Dresden University of Technology
Surulescu, Christina surulescu@mathematik.uni-kl.de Mathematics, Felix-Klein-Zentrum für Mathematik, TU Kaiserslautern
Swan, Amanda acswan@ualberta.ca Mathematical and Statistical Sciences, University of Alberta
Taylor-King, Jake jake.taylor-king@dtc.ox.ac.uk Mathematical Institute, The University of Oxford
Tello, Jose Ignacio jtello@eui.upm.es Department of Applied Mathematics, Universidad Complutense de Madrid
Volpert, Vitaly volpert@math.univ-lyon1.fr Mathematics and applications, CNRS
Wang, Jin jin.d.wang@gmail.com Chemistry and Physics, Stony Brook University
Weekes, Suzanne sweekes@wpi.edu Mathematical Sciences Department, Worcester Polytechnic Institute
Werner, Benjamin benjamin.werner@icr.ac.uk Genomics and Modeling Group, The Institute of Cancer Research
Wodarz, Dominik dwodarz@uci.edu University of California, Irvine
Wyatt, Asia aawyatt@math.umd.edu Applied Mathematics and Scientific Computation, University of Maryland
Yusuf, Tunde Tajudeen ttyusuf@yahoo.com Department of Mathematics, Federal University of Technology
Ziebell, Frederik f.ziebell@dkfz-heidelberg.de Applied Mathematics, University of Heidelberg
Stem Cell Dynamics in Normal Human Colon Crypts and the Initiation and Therapy of Colon Cancer

An agent-based model of stochastic cell dynamics in human colon crypts was developed in the application NetLogo, and calibrated by measurements of numbers of stem cells, proliferating cells, and differentiated cells in human biopsy specimens. It was assumed that each cell’s probability of proliferation and probability of death is determined by its position in two microenvironment gradients along the crypt axis, a divide gradient and in a die gradient. A cell’s type is not intrinsic, but rather is determined by its position in the divide gradient. Cell types are dynamic, plastic, and inter-convertible. Parameter values were determined for the shape of each of the gradients, and for a cell’s response to the gradients. This was done by parameter sweeps that indicated the values that reproduced the measured number and variation of each cell type, and produced quasi-stationary stochastic dynamics. The behavior of the model was verified by its ability to reproduce the experimentally observed monoclonal conversion by neutral drift, the formation of adenomas resulting from mutations either in stem cells, proliferating cells, or differentiated cells, and by the robust ability of crypts to recover from perturbation by cytotoxic agents due to resistant quiescent stem cells. An example of the use of the virtual crypt will be given, viz., the evaluation of different cancer chemotherapy protocols.

AD1 Promotes Astroglial Differentiation and Depletes Glioblastoma Stem Cells

Glioblastoma are among the least curable cancers in man, at least in part because of stem-like cellular subpopulations (herein referred to as glioma stem cells, GSC) refractory to current therapies. The cancer stem cell hypothesis suggests that tumor cells are organized in a pyramidal unidirectional differentiation cascade with GSC at the top and functionally defined by the ability to self-renew and initiate tumors identical to the original tumors from which they are derived. GSCs are maintained by both cell intrinsic and micro-environmental factors and conditions. In this study we focused on identifying small molecules which target tumor heterogeneity by promoting differentiation of GSC into less aggressive, more differentiated subpopulations. To this end, we have developed reporter models for astroglial and neuronal differentiation in HSR-GBM1, HSR040622 and HSR040821 tumor-derived, GSC-enriched, neurospheres lines, using lineage-specific reporter constructs. We employed these reporter lines to screen a library of over 700 bioactive small molecules for potential inducers of GSC differentiation. We identified several molecules which significantly induce astroglial differentiation in multiple GSC-enriched lines. In this report, we focus on one of these agents, (AD1 = (Astroglial Differentiation-1), which induces astroglial differentiation by up to 30-fold as compared with DMSO control. As differentiation should result in reduced self-renewal capacity, we next determined the effect of AD1 on clonogenicity in vitro using the extreme limited dilution assay (ELDA). We found that 48h treatment with AD1 significantly reduced clonogenic capacity of HSR-GBM1, HSR040622 and HSR040821 reporter lines by over 90%. To test this in vivo we examined the effect of AD1 on tumor initiation in an intracranial transplantation model. We found that ex vivo treatment with AD1 resulted in a significant increase in the survival of animals as 5 (of 6) animals transplanted with DMSO-treated cells exhibited massively infiltrating tumors while 2 (of 6) of the animals implanted with AD1 treated cells developed tumors, and those began to appear several weeks later. Importantly, the effects of AD1 are likely to be irreversible as cells extracted from tumors maintained reporter expression even after six passages in vitro.

Neoneurogenesis and tumor metastasis: myth or reality?

Primary tumors infrequently lead to the demise of cancer patients; rather, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs (metastasis). Malignant tumors release both lymph- and angio- genic factors, through two specific processes termed lymphangiogenesis and angiogenesis, respectively. In addition, recent experimental evidence shows that tumors initiate their own innervation by the release of neurotrophic factors (neoneurogenesis). The relationship between tumor progression and the nervous system is a complex and poorly understood part of cancer pathogenesis. It is likely that this process is regulated by a multitude of factors in the tumor/nerve microenvironment; these pathways are even further complicated by treatment and disease history as well as other genetic and socioeconomic factors. It is therefore important to study the interactions between the nervous system and tumor cells through mathematical/computational modelling: in this way we will take into account the most significant elements of the plethora of interacting pathways regulating this process. The present work is a first attempt to model the neurobiological aspect of cancer development through a system of differential equations.


NOTE: This is a joint work with Dr Georgios Lolas, TU Dresden (Germany).

A Mathematical Model for Lymphangiogenesis in Wound Healing

Few attempts have been made to mathematically model the lymphatic system, and those mostly concern its mechanical behaviour. Here we present a model whose aim is to describe the dynamics of lymphangiogenesis (i.e. the formation of lymphatic capillaries) after wound healing.

The model consists of five ordinary differential equations, which describe the concentrations of active TFG-beta and VEGF and the densities of macrophages, lymphatic endothelial cells and capillaries. Simulations are run in order to picture the time-course of these quantities in both normal and diabetic case. Finally, we include a representation of a treatment in the diabetic case to see how this affects the model.

The Role of Wnt Signalling in Stem Cells and Early Colorectal Cancer

Wnt signalling plays a key regulatory role in many biological processes including cell proliferation, migration and cell fate specification. It is active during development and also during adulthood when it assists in the maintenance of homeostasis. Dysregulation of the Wnt signalling pathway is a hallmark of several developmental disorders, a number of degenerative diseases and a variety of different cancers.As such, it is an obvious target for therapeutic intervention. However, its complexity and cross talk with other subcellular and cellular processes make it difficult to understand the consequences of abnormal Wnt signalling and to predict (and compare) the impact of different therapeutic approaches.

Motivated in part by these considerations, a variety of mathematical models of the Wnt signalling pathway have now been developed. The models are typically formulated as systems of ordinary differential equations that describe how the subcellular concentrations of proteins such as -catenin, APC and Axin change over time and in response to Wnt stimulation. Recent models account for the localisation of these Wnt proteins in different subcellular compartments (e.g. the cytoplasm, nucleus and membrane), their transport between the various pools and, to a limited extent, their cross talk with the Delta-Notch and ERK signalling pathways.

In this talk I will review existing subcellular and multiscale models of Wnt signalling, with particular focus on the intestinal crypt, stem cells and the early stages of colorectal cancer.

The Implications of Small Stem Cell Niche Sizes and Distributions of Mutational Effects in Tumorigenesis and Aging

Stem cells within the epithelial tissues of many animals are continually dividing to maintain tissue integrity and, as a byproduct of division, accumulating mutations. New mutations may affect this division rate along a continuous range of effects, known as the Distribution of Fitness Effects (DFE). The DFE within somatic stem cells is not known, however, understanding this DFE would allow us to predict the evolutionary trajectory of tissues within multicellular organisms as they age. We introduce a novel model of intestinal crypt homeostasis based off of recent empirical evidence and explore the implications of a full spectrum of both deleterious and beneficial mutational fitness effects. Given known mutations of large effect associated with tumorigenesis, we test the implications of a heavy tailed distribution, as well as the commonly assumed exponential distribution, of beneficial cellular fitness effects on tumorigenesis incidence. We find that, due to the compounded effects of small population sizes, i.e. genetic drift, many crypts are likely to accumulate cell lineages with mutations that have a deleterious effect to their division rate, resulting in a reduced capability to maintain tissue integrity (deemed aging). Beneficial effects to cellular division rate, although rare, can also accumulate, and may result in scenarios in which there is a net increase in stem cell number (deemed tumorigenesis). We test if empirically derived DFE from ``whole organisms" can account for known tumor incidence within somatic tissue. We also perform least squares fitting along a range of parameter space to find DFE and mutation parameters that best fit known tumor incidence. We find that despite the focus in the literature on mutations of large effect, DFE based on empirical measures in whole organisms results in a better fit to known incidence of tumorigenesis.

Parameterizing spatial-temporal models from image information

In this talk we will study in how far spatial-temporal tissue models can be largely parameterized from image information. The examples envisaged are liver regeneration after drug-induced damage, and growing multi-cellular spheroids of SK-MES-1. For regeneration in liver we will show how the iterative application of a pipeline consisting of confocal scanning microscopy, image analysis and modeling can be used to set up a quantitative spatial-temporal agent-based model of liver regeneration (Drasdo et. al., J. Hepat. 2014), that by simulated predictions successfully guided experiments on spatial tissue organization processes (Hoehme et. al, PNAS, 2010), liver metabolism (Schliess et. al., Hepatology, 2014), and the molecular control of cell proliferation towards new biological insight. We use our image modeling software TiQuant, integrated in an analysis pipeline of standardized imaging protocols for confocal laser scanning microcopy and image processing to infer 3D volume data sets (Hammad et. al., Arch. Toxicol., 2014), to quantify and thereby objectify image information (Friebel, in rev.). Spatial temporal simulations are either performed directly in the reconstructed 3D images, or in representative tissue samples obtained by sampling from statistical distributions over the parameters chosen to quantify the image information. For growing multi-cellular spheroids of SK-MES-1 cells, a model will be stepwise developed by stepwise including image data for different growth conditions.

Acute and Fractionated Irradiation Differentially Modulate Glioma Stem Cell Division Kinetics

Glioblastoma multiforme (GBM) is one of the most aggressive human malignancies with a poor patient prognosis. Ionizing radiation either alone or adjuvant after surgery is part of standard treatment for GBM but remains primarily noncurative. The mechanisms underlying tumor radioresistance are manifold and, in part, accredited to a special subpopulation of tumorigenic cells. The so-called glioma stem cells (GSC) are bestowed with the exclusive ability to self-renew and repopulate the tumor and have been reported to be less sensitive to radiation- induced damage through preferential activation of DNA damage checkpoint responses and increased capacity for DNA damage repair. During each fraction of radiation, non–stem cancer cells (CC) die and GSCs become enriched and potentially increase in number, which may lead to accelerated repopulation. We propose a cellular Potts model that simulates the kinetics of GSCs and CCs in glioblastoma growth and radiation response. We parameterize and validate this model with experimental data of the U87-MG human glioblastoma cell line. Simulations are conducted to estimate GSC symmetric and asymmetric division rates and explore potential mechanisms for increased GSC fractions after irradiation. Simulations reveal that in addition to their higher radioresistance, a shift from asymmetric to symmetric division or a fast cycle of GSCs following fractionated radiation treatment is required to yield results that match experimental observations. We hypothesize a constitutive activation of stem cell division kinetics signaling pathways during fractionated treatment, which contributes to the frequently observed accelerated repopulation after therapeutic irradiation.

Major Genes in Colorectal Cancer

Major genes are defined as those that are necessary and sufficient for disease causation, with important mutations of the gene as causal mechanism. It is commonly accepted that in colorectal cancer the principal major genes are APC, K-RAS, TGF-B, SMAD and p53. However, it may be important to know which gene is the first to undergo mutation. Patients with ulcerative colitis or Crohn’s disease are at risk of developing colorectal cancer. In the first part of this talk I will show, with a mathematical model that in colitis-associated colon cancer p53 is the first gene that is mutated. In the second part of the talk, I will show, again by a mathematical model (and rigorous mathematical analysis) that on mutation in major genes is not sufficient to cause colorectal cancer.

Cancer Stem Cells Discovered ... Mathematically

Cancer stem cells have a variety of biological characteristics, and categorizing cancer cells as stem cells depends on selection of defining properties. In this work we focus on metastatic potential of cancer cells and answer the following question: Can one characterize the size of the subpopulation of metastasis-producing cells in a solid tumor?

To answer this question, we used a very general mathematical model of cancer progression accounting for primary tumor origination and growth, shedding of metastases off the primary tumor, selection of viable metastases, dormancy of metastases and their inception in a secondary site, and growth of metastases in the site of interest. The model assumes that metastasis shedding off the primary tumor is governed by a Poisson process whose rate at time t is proportional to the number of metastasis-producing cells, N(t), which in turn is assumed proportional to some power of the size of the primary tumor: N(t) = kS^θ (t). The case θ = 0 (or close to 0) suggests the presence within a primary tumor of a relatively stable, and hence self-renewing, subpopulation of metastasis-producing cells.

The model produces an explicit formula for the distribution of the site-specific sizes of metastases at any given time. Fitting the model to clinical data allows one to estimate model parameters including θ. This parameter was estimated for three patients with renal cancer, non-small cell lung cancer and pancreatic cancer. In all these cases, the value of θ was found to be quite small, which serves as an indirect evidence for the existence of cancer stem cells with high metastatic potential.

Mathematical Modelling of the Tumor Growth Paradox and more...

The tumor growth paradox describes the effect that a tumor after incomplete treatment grows larger than it was before treatment. A possible explanation is the presence of cancer stem cells (CSC). CSC are less sensitive to treatments and can repopulate the tumour. On my poster I present a basic CSC model to explain the tumor growth paradox. If combined with immune interactions we find that the immune system selects for CSC. Since CSC are known to be less sensitive to treatments such as chemotherapy and radiation therapy, we investigate the benefit gained by a differentiation promoter combined with radiation. We find that a differentiation promoter can have a drastic effect, allowing us to reduce the radiation dosage. Ongoing work relates to a non-local PDE version of the model to investigate spatial CSC distributions and invasions.

Modeling Effects of the Tumor Microenvironment on Brain Tumor Stem Cell Phenotypes

Abstract not submitted.

Stochastic models of stem cell dedifferentiation in cancer

Recent evidence suggests that, like many normal tissues, many cancers are maintained by a small population of cancer stem cells that divide indefinitely to produce more differentiated cancerous cells.

Tissues, however, contain many more differentiated cells than stem cells, and mutations may cause such cells to "dedifferentiate" into a stem-like state.

We study the effects of dedifferentiation on the time to cancer onset and found that the effect of dedifferentiation depends critically on how stem cell numbers are controlled by the body. If homeostasis is very tight (due to all divisions being asymmetric), then dedifferentiation has little effect, but if homeostatic control is looser (allowing both symmetric and asymmetric divisions), then dedifferentiation can dramatically hasten cancer onset and lead to exponential growth of the cancer stem cell population. We also consider effects of various negative feedback loops from the progenitor population on regulation of homeostasis.

Our results suggest that dedifferentiation may be a very important factor in cancer and that more study of dedifferentiation and stem cell control is necessary to understand and prevent cancer onset.

Mathematical models of oncolytic virus therapy and characterization of the invasive and non-invasive glioma

In this talk, a mathematical model of Chase-ABC mediated oncolytic virus therapy targeting cancer stem cells and CSPG-driven glioma infiltration will be presented. Glioblastoma is the most aggressive type of brain cancer with the median survival time of one year. Oncolytic viruses are genetically engineered viruses that are designed to kill cancer cells while doing minimal damage to normal healthy tissue. After being injected into a tumor, they infect cancer cells, multiply inside them, and when a cancer cell is killed they move on to spread and infect other cancer cells. Chondroitinase ABC (Chase-ABC) is a bacterial enzyme that can remove a major glioma ECM component, chondroitin sulfate glycosoamino glycans (CSGG) from proteoglycans without any deleterious effects in vivo. It has been shown that Chase-ABC treatment is able to promote the spread of the viruses, increasing the efficacy of the viral treatment. We develop a mathematical model to investigate the effect of the Chase-ABC on the treatment of glioma by oncolytic viruses (OV). We show that the model’s predictions agree with experimental results for a spherical glioma. We then use the model to test various treatment options for both primary tumor and infiltrating tumor cells in the heterogeneous microenvironment of the brain. A new strategy of targeting cancer stem cells in a niche using transported oncolytic viruses will be also presented. The primary treatment option is surgery but invasive cells in brain tissue eventually regrow back even with chemo- and radio-therapy, generating poor clinical outcomes. Therefore, it is important to distinguish invasive glioma phenotypes from non-invasive cells. Experiments by Silver et al illustrated that concentrations of CSPG, one of major extracellular matrix component within a tumor, determine invasive and non-invasive phenotypes. We developed a mathematical model of CSPG-driven dynamics of a growing glioma, using a free boundary framework. We take into account the rich dynamics of astrocytes and microglia in brain tissue as illustrated in Silver et al. The simulation results are in good agreement with experimental data in Silver et al. We also show how oncolytic virus therapy can be used to eradicate tumor cells. There is a critical threshold value of CSPG levels for optimal killing of both invasive and non-invasive tumorcells.

Analysis of mutations leading to the myelodysplastic syndrome (MDS) using modified Moran models

Abstract not submitted.

The role of adhesion in collective cell migration of cancer cells

Understanding collective cell migration can greatly aid in treatment of metastatic cancer since certain cancer cell lines migrate collectively as sheets or clusters. These sheets or clusters have three distinct properties, (1) cells remain connected, (2) multicellular polarity is maintained and (3) the cell cluster structurally modifies the tissue and migration path. In experiments with 2-D sheets of certain cancer cell lines, the invasion front has been shown to have a finger-like morphology. At the leading edge of a migrating sheet or cluster of cells there are a few leader cells that have distinct properties from the rest of the cells. The leader cells align collagen fibres which form a path of least mechanical resistance for the following cells. The emergence of leader cells remains unclear and understanding their appearance is the focus of my collaboration with Calvin Roskelly’s laboratory at UBC. I utilize a discrete model to understand the role of cell-cell and cell-ECM adhesions in leader cell emergence and in the finger like morphology of a leading edge.

Mathematical modeling of phenotypic switching in cancer

According to the cancer stem cell (CSC) hypothesis, in addition to their self-renewal, CSCs can undergo symmetric or asymmetric "unidirectional" divisions to generate daughter cells with low tumorigenic potential (non-CSCs). However, growing evidence supports violation of unidirectionality for the traditional stem cell based tissue hierarchy, suggesting a new model in which a significant degree of plasticity exists between the non-CSC and CSC compartments. This talk will survey our mathematical approaches to investigate the CSC hypothesis and the dynamic phenotypic switching between these populations, as well as therapeutic implications.

Incorporation of the HGF/c-Met axis into a multispecies model of solid tumor growth.

The tumor microenvironment consists of vascular endothelial cells, pericytes, immune inflammatory cells, and cancer associated fibroblasts (CAFs), all which contribute to the hallmarks of cancer. CAF-derived Hepatocyte Growth Factor (HGF) has been shown to be an important trigger for invasive and metastatic tumor behavior. HGF contributes to a pro-tumorigenic environment by activating its cognate receptor, c-Met, on tumor cells. Tumor cells, in turn, secrete growth factors that upregulate HGF production in CAFs, thereby establishing a dynamic tumor-host signaling program. Using a spatiotemporal multispecies model of tumor growth, we investigate how the development and spread of a tumor is impacted by the initiation of a dynamic interaction between tumor-derived growth factors and CAF-derived HGF. We show that establishment of such a dynamic results in increased tumor growth and morphological instability, the latter due in part to increased cell species heterogeneity at the tumor-host boundary. Invasive behavior is further increased if the tumor lowers responsiveness to paracrine pro-differentiation signals, which is a hallmark of neoplastic development. By modeling anti-HGF and anti-c-Met therapy, we show how disruption of the HGF/c-Met axis can lower tumor invasiveness and growth, thereby providing theoretical evidence that targeting tumor-microenvironment dynamics is a promising avenue for therapeutic development.

Data-Driven Mathematical Modeling of Mammary Ductal Elongation

The Terminal End Bud (TEB) at the growing tip of mammary ducts is one of the fastest growing structures in mammals. TEBs drive ductal elongation during puberty and regress once development of the ductal tree is complete. Because of similarities between TEB growth and breast cancer growth, successful modeling of this structure may yield insight into breast development as well as cancer progression. Previous mathematical models have focused on branching morphogenesis, but there are currently no models that address ductal elongation itself. Our model exploits the constrained geometry of the TEB in vivo which provided the framework for an initial mathematical model. Parameters in this model were then informed with measureable data (morphological characteristics, proliferation rate, cell cycle duration, and apoptosis). These data were then used to calculate a value representing the movement of cells from the TEB into the mature duct (termed the flux) and this calculated flux was then used to predict a linear elongation rate. The prediction was compared to an experimentally measured displacement within the mammary fat pad. Our initial measurements of proliferation, apoptosis, and cell sizes, predicted a linear elongation rate of 1.39 mm per day, which was significantly different from our experimentally measured displacement rate of 0.54mm per day. We then refined our model by incorporating changes in the direction of growth due to bifurcation, a cost function for bifurcation (which describes duplication of the TEB), as well as an additional flux term to account for a migration of cap cells into the body cell. Iteration of the revised mathematical model yielded an estimate significantly closer to the measured displacement rate, thus indicating that the most relevant biological parameters have been accounted for. In addition, our data overturned a long held belief that cap cells contribute to the body cell lineage. We are now poised for in silico experiments that may yield predictions consistent with cancer phenotypes, as well as predictions that recapitulate known mutation phenotypes.

TBD

Abstract not submitted.

New open source tools for simulating large 3-D multicellular systems on the desktop

In diversefields spanning developmental biology, tissue engineering, and cancer, dynamical interactions between large multicellular populations and the microenvironment shape the emergent behaviors of the larger systems, often in surprising ways. While mathematical models can help to understand these systems, 3-D simulation studies often require solving for the dynamics of 105 or more cells, along with several diffusing growth substrates and signaling factors. Such simulations are challenging, generally requiring either complex parallelization on supercomputers, or restriction to smaller systems of 103 or 104 cells in 2-D or very small 3-D domains. Moreover, largely incompatible data formats have impeded the development of robust tools for 3-D visualization and data analysis, further slowing systematic investigations. We will discuss our work to address these problems with parallelized open source codes designed for desktop computers or single HPC compute nodes. We will introduce PhysiCell: an agent-based model that simulates cell cycling, apoptosis, necrosis, volume changes, and biomechanics-based movement in 3-D systems of 105 to 106 cells. We will introduce BioFVM: a finite volume solver for diffusive transport in large 3-D tissues (5+ diffusing substrates on 106 or more voxels: 5-10 mm3 at 20 µm resolution). We will discuss MultiCellDS: a draft data standard for cell phenotype and multicellular simulation data. And we will discuss our efforts to connect these tools to simulate breast cancer and colon cancer metastases in the liver. It is our hope that this work will help seed an ecosystem of compatible computational tools and experimental data. At the close of the talk, we will open the floor to discussion on how these tools can be adapted to meet the needs of the stem cell modeling community. See mbi2015.MathCancer.org for more information.

Mathematical models of heterogeneity, clonal selection and therapy resistance in acute leukemias

Motivated by clonal selection observed in acute myeloid leukemia (AML), we propose mathematical models describing evolution of a multiclonal and hierarchical cell population. The models in a form of partial and integro-differential equations are applied to study the role of self-renewal properties and growth kinetics during disease development and relapse. Effects of different time and space scales are investigated. It is shown how resulting nonlinear and nonlocal terms may lead to a selection process and ultimately to therapy resistance. The results are compared to AML patient data. Model based interpretation of clinical data allows to assess parameters that cannot be measured directly. This might have clinical implications for future treatment and follow-up strategies.

Dynamics of Radiation - Induced Bystander Signals

It has been observed that unirradiated cells located in the neighborhood of a region irradiated at low irradiation dosage undergo the same order of radiation-induced effects as those cells that are directly irradiated. These effects are called radiation-induced bystander effects (RIBE). These RIBE are due to some diffusive proteins which are capable of reacting with the DNA of nearby cells, and thereby triggering these so-called bystander effects. These diffusive proteins are generally referred to as radiation-induced bystander signals. RIBE have implications for radiation therapy and radiation protection, and unfortunately, the dynamics/kinetics of the signals responsible for these RIBEs are still largely unknown. In particular, we are interested in the signal's lifespan and factors that can affect its longevity. In this poster, I will present a partial differential equation models that investigates the lifespan of this signal and factors that may affect its longevity. I also use this model to study its dynamics under a standard fractionated radiation treatments and examine its impact at subsequent fractions of radiation. Lastly, I will examine the contribution of this signal to the observed hypersensitivity region at low dose of radiation in the traditional surviving fraction curves.

A Geometrically-constrained Mathematical Model of Terminal End Bud Biology Predicts Mammary Ductal Elongation Rate

The Terminal End Bud (TEB) at the growing tip of mammary ducts is one of the fastest growing structures in mammals. TEBs drive ductal elongation during puberty and regress once development of the ductal tree is complete. Successful modeling of this structure may yield insight into breast development as well as cancer progression. Previous mathematical models have focused on branching morphogenesis, but there are currently no models that address ductal elongation itself. Our model exploits the constrained geometry of the TEB in vivo which provided the framework for an initial mathematical model. Parameters in this model were then informed with measureable data (morphological characteristics, proliferation rate, cell cycle duration, and apoptosis). These data were then used to calculate a value representing the movement of cells from the TEB into the mature duct (termed the flux) and this calculated flux was then used to predict a linear elongation rate. The prediction was compared to an experimentally measured displacement rate. Our initial measurements of proliferation, apoptosis, and cell sizes, predicted two separate elongation rates; one for the basal layer (1.24mm per day) and one for the luminal layer (0.78 mm per day). In order to reconcile these rates we investigated the possibility of an additional flux between the two layers. Indeed, when the migration of cap cells into the body cell layer is accounted for, the model predicts both layers to elongate at the same rate of ~0.8 mm per day. We then refined our model by incorporating changes in the direction of growth due to bifurcation, which would affect the straight line measurement. Iteration of the revised mathematical model yielded an estimate significantly closer to the measured displacement rate, thus indicating that the most relevant biological parameters have been accounted for. In addition, our data overturned a long held belief that cap cells contribute to the body cell lineage and expose the traditional outgrowth measurement as deceiving.

Sampling of Single Ovarian Carcinoma Cell Data Predicts In-Vivo Treatment Response

Ovarian cancer is the seventh most common cancer worldwide, with more than 150,000 women dying annually from this disease. Cancer Stem-Like Cells (CSCs) have been characterized in ovarian cancer, and aldehyde dehydrogenase (ALDH) enzymatic activity is an excellent marker of ovarian CSCs in both SKOV3 (cell line) and primary patient samples. Our collaborators have developed single-cell microfluidics arrays which can isolate single cancer cells for observation under different treatment conditions. We developed a two-step, penalized sampling algorithm to predict the behavior of larger populations of cells based on microfluidics observations. Applying our sampling algorithm shows reasonable approximations of observed outcomes in larger, standard-culture in-vitro experiments. In order to assess the predictive accuracy of therapeutic intervention changes to the microfluidics culture, we applied Endothelial Growth Factor-Like Protein 6 (EGFL6), an ovarian tumor vascular factor. This resulted in an expansion of the majority low ALDH expressing cell population. These EGFL6-based population shifts are predicted in-vivo based on microfluidics data from single cells and use of our sampling algorithm. I propose that the combined use of microfluidics treatment experiments and our sampling algorithm could streamline novel drug development for interventions seeking to manipulate the CSC pool.

Head and Neck Cancer Patient Derived Xenografts Change Growth Rate over Time

Patient derived xenograft models (PDX) are emerging as the preferred platform for evaluating antineoplastic therapies. PDX models are created by surgically implanting tumor tissue directly from human patients into an immune suppressed mouse. PDX models are preferred for drug development because they more closely resemble original human tumors compared to other models. To maintain the model, the PDX is serially passed into new mice as the physical size of the tumor increases. No mechanism has previously existed to monitor PDX tumor growth rates across different passages. Here we develop a simple mechanism to merge tumor size data over multiple passages. Evaluation of the merged data reveals increasing growth rates over time, even as PDX models display genotypic and expression profile stability.

An in silico investigation of niche-driven cancer stem cell plasticity

Cancer stem cells are believed to be the sole initiator and driver of tumor growth, given their self-renewal and tissue restoration properties. Characterizing the behavior of this peculiar cell type will critically allow us to identify the dynamics that lead to the formation of solid tumors. A specialized microenvironment (the niche) is believed to be a key driver of stemness, offering a new, more plastic view of the stem phenotype, where the niche dictates the cell's ability to stay in a stem-like state. The idea that any cell can become a stem-like cell and also lose this phenotype and that this ability is purely context driven is quite novel.

An in silico investigation of the plasticity of stemness in early ductal carcinoma is presented, describing the dynamics at the single cell scale, result of the interaction between the phenotypically heterogeneous cancer cell population and environmental factors. A spectrum of in silico pathological tissues is obtained, which correspond to clinically observed scenarios.

Evolution and phenotypic selection of cancer stem cells

Cells of different organs at different ages have an intrinsic set of kinetics that dictates their behavior. Transformation into cancer cells will inherit these kinetics that determine initial cell and tumor population progression dynamics. Subject to genetic mutation and epigenetic alterations, cancer cell kinetics can change and favorable alterations that increase cellular fitness will manifest themselves and accelerate tumor progression. We set out to investigate the emerging intratumoral heterogeneity and to determine the evolutionary trajectories of the combination of cell-intrinsic kinetics that yield aggressive tumor growth. We develop a cellular automaton model that tracks the temporal evolution of the malignant subpopulation of so-called cancer stem cell, as these cells are exclusively able to initiate and sustain tumors. We explore orthogonal cell traits including cell migration to facilitate invasion, spontaneous cell death due to genetic drift after accumulation of irreversible deleterious mutations, symmetric cancer stem cell division that increases the cancer stem cell pool, and telomere length and erosion as a mitotic counter for inherited non-stem cancer cell proliferation potential. Our study suggests that cell proliferation potential is the strongest modulator of tumor growth. Early increase in proliferation potential yields larger populations of CC that compete with CSC and thus inhibit CSC division while a reduction in proliferation potential loosens such inhibition and facilitates frequent CSC division. The subpopulation of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from long-term dormancy to aggressive progression. Our study suggests that the clonal diversity that is captured in single tumor biopsy samples represents only a small proportion of the total number of phenotypes.

How Cancer Cells Hijack Stem Cell Pathways

Tumours contain populations of cells with stem cell like properties, and it is believed that these cells are responsible for cancer progression, resistance to therapy and metastatic potential. Stem cell-like populations are regulated by their immediate surroundings (microenvironment) characterized by proteins, immune cells, and biophysical features such low oxygen tensions. A growing body of evidence suggests that cancer cells hijack normal stem cell-associated regulatory networks in order to behave like stem cells. We have discovered that an embryonic-associated protein called Nodal maintains stem cell phenotypes in cancer, and that it promotes classical hallmarks of cancer such as angiogenesis, and metastasis. We have also found that biophysical features of a growing tumour, in particular low oxygen, can turn regular cancer cells into cancer stem cells. This lecture will describe these findings and will introduce the audience to the biology of normal and cancer stem cells. New and exciting advancements linked to how we may be able to treat and even prevent metastatic cancers by targeting stem cell proteins like Nodal will also be revealed.

Target Identification in Glioma Initiating Cells

Gliomas display cellular hierarchies with tumor initiating cells (TICs) at the apex that are functionally defined by the ability to self renew and propagate tumors similar to the parental tumors from which they are derived. TICs remain controversial, but their clinical relevance has been supported by resistance to cytotoxic therapies (Bao et al. Nature 2006) and promotion of tumor angiogenesis (Bao et al. Cancer Research 2006). TICs reside in specific functional niches in perivascular and hypoxic niches (Li et al. Cancer Cell 2009) that may offer the ability to disrupt tumor maintenance and therapeutic resistance through targeting the niche. Investigating TICs has already yielded novel molecular targets and pathways that are amenable to therapeutic targeting (Kim et al. Genes Development 2012; Eyler et al. Cell 2011; Guryanova et al. Cancer Cell 2011). Using patient-derived tumor models, we have interrogated the regulation of the TIC phenotype by both cell intrinsic and microenvironmental influences present in tumors. TICs are enriched under low nutrient conditions due to the cooption of the high affinity GLUT3 transporter normally expressed by neurons (Flavahan et al. Nature Neuroscience 2013). We have now extended these findings to demonstrate that cellular metabolism is differentially regulated within the tumor hierarchy at several levels to provide resources for sustained self-renewal and proliferation (Xie et al. Nature Neuroscience 2015). We also recently found that TICs have basal genotoxic stress activating PARP permitting radiosensitization (Venere et al. Cell Death Differentiation 2014). To discover novel TIC targets, we are using several technologies, including aptamers (Kim et al. Cancer Research 2013), flow cytometry (Lathia et al. Cell Reports 2014), and phage display (Liu et al. Cell Death Diff. 2014), showing that TICs manifest nodes of fragility mediating cell survival and invasion (e.g. JAM-A, VAV3, and CD97). Combining TIC models from patients with non-neoplastic progenitors from epilepsy resections, we are interrogating additional molecular regulators of the cellular hierarchy that can be distinguished from normal stem cells to minimize toxicity. The conventional pyramidal unidirectional differentiation cascade with TICs at the apex has been called into question by studies demonstrating plasticity of the TIC phenotype (Cheng et al. Cell 2013), thus suggesting that targeting only TICs will likely fail to cure patients and require simultaneous targeting of TICs and the bulk tumor. Although the field of TIC biology is relatively young, continued elucidation of the tumor hierarchy holds promise for development of novel patient therapies.

Replicative Senescence as a Tumor Suppressor Pathway

Abstract not submitted.

A mathematical model for the miR-451-AMPK- control system and proliferation and migration in glioblastoma.

Authors: Yangjin Kim (Konkuk University), Soyeon Roh (Konkuk University), Sean Lawler (Harvard Univ & BWH), and Avner Friedman (Ohio State University)

A mathematical model for the miR-451-AMPK- control system and proliferation and migration in glioblastoma.

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A Stochastic Model for the Normal Tissue Complication Probability (NTCP)

The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth death process to define an organ specific and patient specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework allows for a direct use of the NTCP model in clinical practice. We formulate, but do not solve, related optimization problems.

Mathematical models for anisotropic glioma invasion: a multiscale approach

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms. Since they are highly invasive they are hard to remove by surgery, as the tumor margin it most often not precisely enough identifiable. The understanding of glioma spread patterns is hence essential for both radiological therapy as well as surgical treatment. We propose a multiscale framework for glioma growth includinginteractions of the cells with the underlying tissue network, along with proliferative effects. Relying on experimental findings, we assume that cancer cells use neuronal fibre tracts as invasive pathways. Hence, the individual structure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide such information, thus opening the way for patient specific modeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale) cell dynamics, we deduce on the macroscale effective equations characterizing the evolution of the tumor cell population and perform numerical simulations based on DTI data. Particular attention is payed on the modeling of proliferation terms on the mesoscale level, in order to deduce the corresponding source terms on the macroscale.

Modelling glioma spread using anisotropic diffusion

In this poster, we present a model for glioma, or brain tumour spread. These tumours pose an interesting modelling problem, as the cells prefer to spread along the white matter tracts of the brain. This behaviour leads to irregular shapes that cannot be captured using traditional isotropic diffusion. To remedy this, an anisotropic diffusion model is used that includes directional information from the brain's white matter tracts. This allows us to advise our model using the geometry of the brain of an individual patient. We present some simulations for this anisotropic diffusion model using real patient data, and compare the results to a well-established glioma model.

On a mathematical model of cancer stem cells with non-local terms

Abstract not submitted.

Reconstructing the in vivo dynamics of hematopoietic stem cells from telomere length distributions.

Most mammalian tissues are hierarchically organized. Few self renewing stem cells give rise to shorter-lived progeny.Here, we investigate the in vivo patterns of stem cell divisions in the human hematopoietic system throughout life. We analyze the shape of telomere length distributions underlying stem cell behavior within individuals. These distributions contain a fingerprint of the initial telomere length and progressive telomere loss. We test our predictions on telomere length data of 356 healthy individuals, including 47 cord blood and 28 bone marrow samples. We find an increasing stem cell pool during childhood and adolescence and an approximately maintained stem cell population in adults. Furthermore, our method is able to detect individual differences from a single tissue sample, i.e. a single snapshot. Prospectively, this allows us to compare cell proliferation between individuals and identify abnormal stem cell dynamics, which affects the risk of stem cell related diseases.

Mathematical models of chronic lymphocytic leukemia (CLL)

Chronic lymphocytic leukemia (CLL) is a malignancy of B cells and is the most common leukemia in adults. Patients have typically been treated with a combination of chemo and immuno-therapies. These have resulted in relatively good responses except in high risk patients in which p53 has been inactivated. Recently, new, targeted treatment approaches have been developed which have so far shown great promise in the clinic. One such drug is the Bruton tyrosine kinase (BTK) inhibitor ibrutinib. Upon treatment initiation, a lymphocytosis phase is observed during which the number of CLL cells can show a pronounced rise in the blood. The number of cells eventually reaches a peak and declines during therapy. It is thought that the lymphocytosis phase represents the redistribution of cells from tissue where the majority of the disease burden lies (lymph nodes, spleen, bone marrow) into the blood. One question is whether upon treatment the majority of the tissue CLL cells redistributes to blood, or whether only a small fraction of the tumor cells redistributes while a large fraction of tissue cells dies. We used mathematical models, applied to clinical data, in order to kinetically characterize the treatment responses to ibrutinib, and to investigate this question. In addition, the measurements of all crucial CLL parameters allowed us to build evolutionary mathematical models in order to study the emergence of ibrutinib-resistant cells. An important aim of this work is the development of a predictive computational framework that can give personalized predictions for patients about the long-term outcome of ibrutinib therapy.

Mathematical Modeling of Neural Stem Cell Dynamics in the Adult Hippocampus

The dentate gyrus of the hippocampus harbours a niche of stem cells, capable of generating new neurons throughout adulthood. Although multiple studies have been conducted in the past to identify qualitative stem cell features such as multipotency or the age-related decline of the stem cell pool, a quantitative understanding of the dynamics of adult neurogenesis is still missing. This lack of quantification is mainly due to sparse data and diverse labelling approaches used by different studies in order to observe neural stem cells. Accordingly, different hypotheses about their dynamics have been formulated.

The two landmark studies on neural stem cell dynamcis have been conducted by Bonaguidi et al. (2011) and Encinas et al. (2011). While the former performed clonal analysis and concluded that stem cells can get activated multiple times from their quiescence in order to produce offspring, Encinas et al. (2011) carried out population level analysis and reasoned that neural stem cells get activated only once, enter a series of asymmetric divisions and vanish by differentiating into astrocytes.

In this study, we investigate both hypotheses by formulating them as mathematical models of ordinary differential equations. Moreover, we perform a quantification of stem cell dynamics by estimating model parameters from the data published in both studies. We find that the Bonaguidi model explains a wider range of published data than the one of Encinas, provided that it subscribes to Encinas' theory of stem cell depletion. Additionally, we make experimentally testable predictions in order to differentiate between the two models.

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Neoneurogenesis and tumor metastasis: myth or reality?
Arianna Bianchi

Primary tumors infrequently lead to the demise of cancer patients; rather, mortality and a significant degree of morbidity result from the growth of secondary tumors in distant organs (metastasis). Malignant tumors release both lymph- and an