Wednesday, June 16 at 11:30am (PDT)
Wednesday, June 16 at 07:30pm (BST)
Thursday, June 17 03:30am (KST)


Understanding lung function and disease through mathematical modeling and experiment

Organized by: Uduak George (San Diego State University, United States), Mona Eskandari (University of California Riverside, United Staes)
Note: this minisymposia has multiple sessions. The second session is MS15-CBBS.

  • Hannah Pybus (School of Mathematical Sciences, University of Nottingham, United Kingdom)
    "Airway constriction in asthma - is it the chicken or the egg?"
  • Despite its prevalence in the population, the causes of asthma remain poorly understood. Airway hyperresponsiveness causes airway constriction at low doses of agonist which is thought to activate cytokines, such as Transforming Growth Factor β (TGF-β). TGF-β is thought to play a key role in promoting airway remodelling, which in turn could exaggerate hyperresponsiveness in a positive feedback loop; however, it is not clear what comes first. To begin to elucidate this, our research combines mathematical models of contracting airways with ex vivo precision-cut lung-slice (PCLS) stretching experiments to study stress-driven TGF-β activation in asthmatic airways. In this talk, we describe our mathematical model that couples subcellular mechanotransductive signalling pathways to nonlinear hyperelastic models of airway mechanics to predict the levels of TGF-β activation in different experimental conditions. We account for TGF-β-mediated contraction of the airway smooth muscle and the subsequent change in effective mechanical properties of the PCLS as TGF-β activation progresses. In agreement with the experimental results, we find that TGF-β activation increases as the airway deforms with imposed stretch. Our work shows that airway contraction, induced by active TGF-β signalling, in conjunction with airway wall stiffening generates stress differences across the airway wall and consequently initiates a positive feedback loop of TGF-β activation. Our work gives access to the highly complex stress distribution within the airway wall and surrounding parenchyma that can be used to investigate the effects of contractile heterogeneity and examine airway wall structure. This integrated study provides information that is of vital importance in interpreting PCLS experiments that seek to clarify the mechanochemical mechanisms underpinning TGF-β activation, a key aspect of the disease, that has only recently received attention.
  • Ashley Schwartz (Computational Science Research Center, San Diego State University, United States)
    "New metrics for quantifying the spatial inhomogeneity of abnormal fluid in MR images of cystic fibrosis lungs"
  • Cystic fibrosis (CF) is a genetic disease that can produce thick mucus accumulation in the lung, limiting a person’s ability to breathe. Treatment plans for CF are often determined from disease severity as determined by the spirometry metric percent predicted forced expiratory volume in 1 second (ppFEV1). Spirometry does not yield information about mucus accumulation behavior and location that imaging may provide. Magnetic resonance (MR) imaging is an imaging technique with no radiation effects that yields information about fluid density, or water content, within the lung from blood, lung tissues, and lung abnormalities such as excess mucus. In this talk, we will present an automated image processing algorithm that makes use of three-dimensional MR images to locate, segment, and describe the lung abnormalities in CF versus control lungs. The spatial location and behavior of lung abnormalities is categorized into three different spatial behaviors: (i) generalized, (ii) localized diffuse, and (iii) localized. Lungs with generalized behavior have little but sparse abnormal lung fluid. Localized lungs have a focality or concentration of abnormal lung fluid in a particular region of the lung and sparsity elsewhere, while localized diffuse lungs have a high concentration of abnormal lung fluid in multiple regions. Control patients mostly presented as generalized. CF patient’s abnormal fluid behavior did not directly correlate with severity level as determined by ppFEV1. This suggests CF disease is heterogeneous within severity levels and ppFEV1 may be missing additional information about disease behavior. The algorithm developed provides unique information about abnormal lung fluid behavior that may be used to distinguish differences in CF disease missed by traditional spirometry metrics.
  • Nourridine Siewe (Rochester Institute of Technology, United States)
    "A Mathematical Model of the Role of MIF in Severe Malarial Anemia: What Happens in TB"
  • Tuberculosis (TB) is the leading cause of death by infectious disease worldwide. The pathogen responsible for this infection is Mycobacterium tuberculosis (MtB). Due to the large number of people affected by TB daily, it remains a public health concern because of lack of treatment options, causing scarcity of resources, and the abundance of drug-resistant TB strains. To assist in the fight against this disease, we propose building a mathematical model of the interactions between the human immune system and MtB. This model will be described by a system of ordinary differential equations to capture the complex interactions between the variety of cells and proteins involved in this biological system. The model will include the effect of commonly used drugs to treat TB, namely isoniazid and rifampin, whose pathways contribute in decreasing the number of MtB in the host. This model will allow for the quick and easy analysis of experimental TB treatments, expediting the process of developing new treatment protocols.
  • Blessing Emerenini (Rochester Institute of Technology, United States)
    "Trends in the mathematical modeling of Bacteria-Phage combat in lung treatment"
  • Presence of pathogenic microorganisms in our environment entail enormous problems for humans and livestock. The problem of pathogenic microrganisms is even grievous when they reside in host vital organs such as the lung. Bacteria is one of such pathogenic microorganisms and they prefer to live in communities called Biofilms. Existence of Biofilm in any system is a huge problem because by its nature it is usually difficult to get rid of it by mere antibiotics. There are currently many ongoing studies that focus on how to do away with such pathogens from our systems. One of the medical approaches to treating inhost bacteria infection is by introducing bacteriophages (a.k.a phage therapy). In order to understand the different strategies of pathogenic infections and phage-bacteria interactions, pathogen-host infection dynamics helps us to derive better treatments to extenuate infectious diseases or develop vaccinations, thus preventing the occurrence of infections altogether. In this study we present a general review of methods and characterizations to facilitate right decision for understanding interdisciplinary modeling approaches.

Combining modeling and inference in cell biology

Organized by: Maria-Veronica Ciocanel (Duke University, United States), John Nardini (North Carolina State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS13-CDEV.

  • Keisha Cook (Tulane University, United States)
    "Single Particle Tracking with applications to lysosome transport"
  • Live cell imaging and single particle tracking techniques have become increasingly popular amongst the mathematical biology community. We study endocytosis, the cellular internalization and transport of bioparticles. This transport is carried out in membrane-bound vesicles through the use of motor proteins. Lysosomes, known for endocytosis, phagocytic destruction, and autophagy, move about the cell along microtubules. Single particle tracking methods utilize stochastic models to simulate intracellular transport and give rise to rigorous analysis of the resulting properties, specifically related to transitioning between inactive to active states. This confidence in the stochastic modeling of particle tracking is useful not only for particle-containing lysosomes, but also broad questions of cellular transport studied with single particle tracking.
  • Christopher Miles (New York University, United States)
    "Stochastic organization of the mitotic spindle from spatiotemporal trajectories"
  • For cells to divide, they must undergo mitosis: the process of spatially organizing their copied DNA (chromosomes) to precise locations in the cell. Stochastically driven, this task is accomplished with mysterious speed and accuracy. Our collaborators in the New York State Dept of Health have recently obtained 3D spatial trajectories of every chromosome in a cell during mitosis. Can these trajectories tell us anything about the mechanisms driving them? Fundamental goals of data science (e.g., classification, inference) are challenging here due to the structure and context of this cutting-edge data. I will discuss progress on developing analysis for this data and efforts to model the emerging phenomena.
  • Ruth Baker (University of Oxford, United Kingdom)
    "Quantifying the impact of electric fields on single-cell motility"
  • Electrotaxis is attracting much interest and development as a technique to control cell migration due to the precision of electric fields as actuation signals. However, precise control of electrotactic migration relies on an accurate model of how cell motility changes in response to applied electric fields. We present and calibrate a parametrised stochastic model that accurately replicates experimental single-cell data and enables the prediction of input–output behaviour while quantifying uncertainty and stochasticity. The model allows us to elucidate and quantify how electric fields perturb the motile behaviour of the cell, and to make predictions about cellular motility under different electric fields.
  • Carter Jameson (North Carolina State University, United States)
    "Parameterizing agent based models of collective cell migration using topological information"
  • Agent-based models (ABMs) are valuable tools for investigating how rules that govern individual cell behavior affect collective population level migration. ABMs have been used to determine many key features of cell interactions during collective cell migration experiments, including how cells migrate and proliferate and the effects of pushing and pulling between cells. However, to the best of our knowledge, there do not currently exist ABMs of mesenchymal cell migration that have been parameterized with data using rigorous statistical methodology. A primary main reason for the lack of validated models is that current approaches to ABM parameter inference are computationally burdensome or may lead to inaccurate estimates. We developed a novel framework for parameter estimation of ABMs using topological data analysis (TDA). To validate this new approach, we simulated point-cloud datasets using a stochastic variant of the agent-based D’Orsogna model of interactive particle motion. We compared this framework, which relies on least-squares inference and Nelder-Mead direct search optimization on summaries of the topology, to least-squares inference on the particle density. We found that it was feasible to recover model parameters from either deterministic and stochastic variants of the D’Orsogna model.

Numerical methods in biomedical sciences

Organized by: Yifan Wang (University of California, Irvine, USA), Pejman Sanaei (New York Institute of Technology, USA)
Note: this minisymposia has multiple sessions. The second session is MS13-DDMB.

  • Sudhir Pathak (, USA)
    "Computational Modeling of the human brain tissue, Estimation and Quantifying tissue type"
  • MR imaging is a versatile technique that is used to image the anatomical micro-architecture of biological tissue, clinically affected regions such as traumatic injury, blood clot, tumor lesion, and tissue degeneration. In particular, diffusion MR imaging of the human brain can provide the connectivity pattern of the brain regions. In this presentation, I am going to talk about the characterization of the human brain tissue using diffusion MRI. Diffusion MRI is a novel technique that can be used to characterize the diffusion pattern of the micro-environment of the tissue. From these diffusion patterns, one can characterize geometrical and micro-compartmental information of both healthy and pathological tissues. A volume element of diffusion MR images of human brain tissue contains diffusion signals from free, hindered, and restricted water pools. Using mathematical models and proper MR sequences, these water pools can be used to infer diseases and brain connectivity. In the talk, I will present four such mathematical models, DTI, CHARMED, NODDI, and SMT. I will present the assumptions, (dis)advantage, and feasibility of these mathematical models in a clinical setting. These models can be key to providing important information in clinical diagnosis, presurgical planning and possibly used in deciding treatment.
  • Yuchi Qiu (Michigan State University, USA)
    "Learning biomolecules in mutagenesis via topological and geometric modeling"
  • Mutagenesis is widely used to understand the structure and function of biomolecules. Relying on emerging large mutation datasets in recent years, machine learning methods provide economic approaches to examine function of new mutant biomolecules in silico. The high geometric dimensionality, which usually contains thousands of atoms for one protein, is the main challenge for machine learning models to learn the three-dimensional biomolecules data. Topological and geometric modeling provide informative geometric simplification and scalable representation of the 3D data. In this talk, we develop a multi-scale method utilizing Poincare-Hopf theorem and Morse theory to analyze protein structure. We apply this method to predict mutation induced protein stability changes and it outperforms other existing methods.
  • Yu (Andy) Huang (Memorial Sloan Kettering Cancer Center, USA)
    "Computational Models of Transcranial Electrical Stimulation: Methodology, Optimization and Validations"
  • Transcranial electrical stimulation (TES) has been shown as a promising neurological therapy for a number of diseases. Nowadays, design of electrode montages and interpretation of experimental results for TES heavily rely on computational models, which predict the current-flow distribution inside the head. In this talk I will show you methodological details in building individualized TES models from structural magnetic resonance images of human heads, including image segmentation, electrode placement, finite element modeling, and numerical optimization for targeted stimulation. Model validations using intracranial in vivo recordings will also be discussed. I will also briefly talk about translational efforts that convert TES models into neuromodulation software, either open-source or proprietary, that are used for clinical research on stroke recovery
  • Mac Hyman (Tulane University, USA)
    "A Bipartite Network Sexual Transmission Model to Inform Public Health Efforts for Controlling the Spread of Chlamydia Trachomatis"
  • Chlamydia trachomatis (Ct) is the most commonly reported sexually transmitted infection in the USA and causes important reproductive morbidity in women. We created an individual-based heterosexual network model to simulate a realistic chlamydia epidemic on sexual contact networks for a synthetic population. The model is calibrated to the ongoing routine screening among sexually active men and women in New Orleans. The Centers for Disease Control and Prevention recommend routine screening of sexually active women under age 25 but not among men. Despite three decades of screening women, chlamydia prevalence in women remains high. Untested and untreated men can serve as a reservoir of infection in women, and increased screening of both men and women can be an effective strategy to reduce infection in women. We assessed the impact of screening men on the Ct prevalence in women. We used sensitivity analysis to quantify the relative importance of each intervention component. The model suggested the importance of intervention components ranked from high to low as venue-based screening, expedited index treatment, expedited partner treatment, and rescreening. The findings indicated that male screening can substantially reduce the prevalence among women in high-prevalence communities. Joint research with Zhuolin Qu, Asma Azizi, and Patty Kissinger.

Mathematical modeling of water resources

Organized by: Claudia Mazza Dias (UFFRJ - Universidade Federal Rural do Rio de Janeiro, Brazil), Anna Regina Corbo Costa (Cefet/RJ - Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Brazil), José Carlos Rubianes Silva (Cefet/RJ - Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Brazil), Kymie Karina S Saito (UFFRJ - Universidade Federal Rural do Rio de Janeiro, Brazil), Dayse Haime Pastore (CEFET-RJ)

  • Fernando Momo (Instituto de Ciencias. Universidad Nacional de General Sarmiento, Argentina)
    "How to convince policymakers that uncertainty exists: do mathematical models help or confuse?"
  • Policy makers have two problems when trying to make decisions about ecosystems, especially when these decisions involve aquatic resources: 1) They have problems to visualize the non-linear nature of ecological systems. This is important because the responses of aquatic ecosystems to exploitation or pollution can be abrupt and unpredictable. 2) They tend to think in terms of exact values and accurate predictions. This is serious because when we do not consider uncertainty and variability we do not adequately assess risks. I will show from two examples how these ideas can be corrected using mathematical models and how the results of those models should be adequately communicated to decision makers in order to clarify the concepts instead of confusing them even more.
  • João Frederico da Costa Azevedo Meyer (UNICAMP - Universidade Estadual de Campinas, Brazil)
    "Water quality and environmental and ecological risks"
  • My intention is that of presenting a situation which has been occurring in Brazil in recent years and which seriously affects water quality in hydrographic basins: tailings dams failures and their consequences both in immediate as well as long standing terms to the present and the future of nature and society. I will present the main results in terms of mathematically modeling aspects of dam failures and impact upon waterways undertaken by the Mathematical Engineering subgroup at the State University of Campinas the researching of which is part of a larger effort with two other subgroups: Society and Education, and Geophysical and Biotic Environments which form the Global Effort for Research and Action in Conflicts, Risks and Impacts associated to Tailings Dams (CRIAB).
  • Raquel Figueira (Hubz, Brazil)
    "Populacional Density Model of Limnoperna Fortunei for Três Irmãos Hydroelectric – São Paulo, Brasil"
  • The golden mussel is an invasive species in Brazil which causes great environmental and economic problems, including the displacement of native species, modification of natural habitats and damage to equipments in hydroelectric power plants and water treatment systems. The main objective of this research was to establish a method for the quick quantification of Golden Mussel populations in hydroelectric reservoirs in order to monitor the species and eventually employ control methods to combat this invasion. A hydrodynamic model of the area of the HPP Três Irmãos (São Paulo State) was created using Navier Stokes equations applied to a grid of triangular finite elements. The hydrodynamic model was then combined with a population growth model using a system of partial differential equations. The resulting map of population density clusters of the golden mussel matches field observations and shows the potential of this technique to control and monitor species in a large scale.
  • Renato Nascimento Elias (Civil Engineering Department at Federal University or Rio de Janeiro • PEC/COPPE/UFRJ, Brazil)
    "3D Numerical Modeling of Dambreak Problems using Finite Element Method"
  • Dams to store water, mud and mining sediments represent import civil engineering structures. Due to the scale of such large structures, any accident has severe social and ecconomical impacts in the surrouding areas. The simulation of dam break problems has emerged as an important tool to predict the impact of this kind of accidents. In this work, it is presented EdgeCFD: a numerical tool capable to simulate dam break problems. This tool employs a RB-VMS finite element formulation to simulate 3D incompressible fluid flow of Newtonian or non-Newtonian flows. In order to allows for high fidelity simulations, EdgeCFD is capable to run large scale parallel simulations using distributed and/or shared memory machines and state of art non-linear algorithms. Keywords: Navier-Stokes, Incompressible Fluid Flow, Dambreak, Volume-of-Fluid

Recent Perspectives on Mathematical Education

Organized by: Stacey Smith? (The University of Ottawa, Canada)
Note: this minisymposia has multiple sessions. The second session is MS13-EDUC.

  • Elissa Schwartz (Washington State University, USA)
    "Remedying the Leaky Pipeline"
  • Diversity is crucial for the success of mathematical biology education initiatives. Cultural and gender diversity among educators and researchers allows for the contribution of a wider range of ideas in mathematical biology education and research. Many trainees from historically underrepresented or disadvantaged backgrounds, however, disappear along their educational path. The loss of women scientists along the career path is common in academic systems around the world; this phenomenon has been described as the ‘Leaky Pipeline.’ It begins at early stages and continues throughout the career trajectory, gradually resulting in a small proportion of women researchers in STEM fields. To begin to remedy this issue, we conducted a virtual international workshop to connect women from underrepresented backgrounds to career advancement opportunities in STEM. In this project, we created a forum to uncover and break down barriers to progress along STEM careers experienced by women from underrepresented backgrounds. This professional development workshop contained 3 parts: a plenary talk and discussion, in which a guest speaker presented her inspirational story of her career journey; a discussion of challenges faced by participants that need to be overcome to take the next step in their STEM career development; and ‘mentoring pod’ small groups discussions (matching participant trainees with mentors in groups of 4-5 in breakout rooms) to target specific issues and facilitate development of participants’ mentoring networks. The event was attended by individuals from eleven countries: Afghanistan, Argentina, Australia, Canada, India, Nepal, Nigeria, Poland, Russia, Trinidad & Tobago, and the US. Data collected from this event (on challenges identified, solutions suggested, networks formed, and scholarship opportunities) will be used to identify which interventions actually work to mend the Leaky Pipeline, and to design similar programs in the future. Such efforts will be needed to improve retention rates in STEM, particularly among historically underrepresented groups.
  • Suzanne Lenhart (University of Tennessee at Knoxville, USA)
    "BioCalculus Assessment Tool"
  • The development and initial validity assessment of the BioCalculus Assessment (BCA) will be presented. This 20-question test was designed with the goal of comparing undergraduate life science students’ understanding of calculus concepts in different courses with alternative application emphases. The analysis of scores involved three populations (Calculus 1, Calculus 2 and Biocalculus) for which the Calculus 1 and 2 students were not exposed to applications in a life science setting while the Biocalculus students were presented concepts with a life science emphasis. Our findings show that the BCA provides a tool to assess the relative learning success and calculus comprehension of undergraduate biology majors from alternative methods of instruction.
  • Amanda Laubmeier ( Texas Tech University, USA)
    "Application-driven projects in differential equation and modelling courses"
  • Projects offer the flexibility for students to explore course material and their own understanding. Application-based projects can also reinforce connections between course material and students' interests. In this presentation, we discuss some attempts at short- and long-term projects for undergraduates. The projects are drawn from differential equations and modelling courses, and emphasis is placed on project design to encourage student creativity and exploration.
  • Stacey Smith? (The University of Ottawa, Canada)
    "Teaching While Trans"
  • Gender transitioning is on the rise among students, but it’s also happening among faculty too. This talk defines some transgender basics and highlights some of the challenges faced in mid-career academia as a result of transitioning from male to female. These include name changes and publications, university and online journal bureaucracies and interactions with students and colleagues. Finally, tips will be provided on how to be a good trans ally and small but helpful changes that can be made in the classroom to make the environment more inclusive.

Going backward in time with the coalescent and other ancestral structures

Organized by: Fernando Cordero (Bielefeld University, Germany), Sebastian Hummel (Bielefeld University, Germany)

  • Cornelia Pokalyuk (Goethe University Frankfurt, Institute for Mathematics, Germany)
    "Haldane’s formula in Cannings models with moderate selection"
  • A rule of thumb known as Haldane’s formula states that the probability of fixation for a single beneficial individual with small selective advantage s >0 and offspring variance v in a large population of N individuals is approximately equal to 2s/v. In my presentation I will report on a proof of this asymptotics in the regime of moderate selection, i.e. s_N∼ N^{−b} and b∈(0,1), for a class of Cannings models which allow for a paintbox construction. A forwards as well as a backwards point of view of the paintbox construction turns out to be suitable for the analysis. Via the backwards view we arrive at a time-discrete analogue of the ancestral selection process which is in sampling duality to the wildtype frequency process. In the regime of moderately weak selection (i.e. 1/2< b <1) and under conditions on the paintbox which ensure convergence of the neutral genealogy to Kingman’s coalescent, this sampling duality leads to a proof of Haldane’s formula (EJP 26(4), 2021). In the case of moderately strong selection (0< b <1/2) we make use of the forward construction and approximate the frequency process by Galton-Watson processes (arxiv:2008.02225). The results are joint work with Florin Boenkost, Adrián González Casanova and Anton Wakolbinger.
  • Maite Wilke Berenguer (Humboldt-Universität zu Berlin, Germany)
    "Can dormancy induce skewed offspring distributions?"
  • Dormancy naturally occurs in several forms. A classic example is seasonal dormancy: populations that switch into a dormant form during 'winter', only to wake up in 'spring' to resume reproduction. If single individuals wake up significantly earlier than the main population, the additional time for reproduction might be reflected in the offspring numbers at the end of summer, with the early birds' offspring constituting a positive fraction of the population in the following year. We give a simple model for the evolution of such a population and show that for some choices of model parameters the genealogy of the population will be described by a Lambda-coalescent. In particular, the Beta-coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all Lambda-coalescents that can arise in this framework.
  • Airam Blancas (Departamento de Estadística, ITAM, Mexico)
    "A coalescent model with recombination and population structure"
  • We introduce a Markov model to describe the backwards evolution of l-linked loci from p-structured populations. More precisely, we define a continuous time Markov chain with jumps at recombination, coalescence, and migration events. We delineate the space states in a way a that it is possible to keep track the ancestral populations at every locus as well as the population location of the lineages. We prove that the state space cardinality of the process is polynomial for admixture populations and provide an analytic expression for 3-loci lineages from without admixture populations.
  • Dario Spanò (University of Warwick, England)
    "Asymptotic genealogies for interacting particle systems"
  • We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman n-coalescent in the infinite system size limit in the sense of finite-dimensional distributions.Thus, the tractable n-coalescent can be used to predict the shape and size of SMC genealogies, as we illustrate by characterising the limiting mean and variance of the tree height. SMC genealogies are known to be connected to algorithm performance, so that our results are likely to have applications in the design of new methods as well.

Immunobiology and Infection Subgroup mini-symposium

Organized by: Stanca Ciupe (Virginia Tech, United States), Jessica Conway (Penn State University, USA), Amber Smith (University of Tennessee Health Science Center, USA), Jonathan Forde (Hobart and William Smith Colleges, USA)
Note: this minisymposia has multiple sessions. The second session is MS13-IMMU.

  • Ivan Ramirez-Zuniga (University of Tennessee Health Science Center, USA)
    "A data-driven mathematical model of the role of energy in sepsis"
  • Mounting an adequate acute immune response against a pathogenic infection is energetically expensive. In an ideal scenario, this response may eradicate the infection but, in some cases, an imbalanced response may lead to sepsis. In this talk I will present a mathematical model that captures the dynamics of an immune response and its energy requirements to fight an infection. We calibrate our model with available animal data and identified key parameters for distinguishing between surviving and non-surviving subjects. On our analysis, we found that energy-related processes play a fundamental role in determining these outcomes. Moreover, we explore factors that modulate the inflammatory response across baseline and altered glucose conditions.
  • Sarah Minucci (Virginia Commonwealth University, USA)
    "Mathematical modeling of ventilator-induced lung inflammation"
  • Despite the benefits of mechanical ventilators, prolonged or misuse of ventilation may lead to ventilation-associated/ventilation-induced lung injury (VILI). Lung insults, such as respiratory infections and lung injuries, can damage the pulmonary epithelium, with the most severe cases needing mechanical ventilation for effective breathing and survival. Damaged epithelial cells within the alveoli trigger a local immune response. A key immune cell is the macrophage, which can differentiate into a spectrum of phenotypes ranging from pro- to anti-inflammatory. To gain a greater understanding of the mechanisms of the immune response to VILI and post-ventilation outcomes in the absence of evolving comorbidities, we mathematically modeled interactions between the immune system and site of damage while accounting for macrophage phenotype. We generated a collection of parameter sets with biologically feasible dynamics and used statistical methods and sensitivity analysis to hypothesize predictors of outcome and interventions for poor response to ventilation. Additionally, we analyzed macrophage phenotype using a system of ordinary differential equations and an agent-based model, both of which focused on the spectrum of macrophage activation on an individual cell level. Using both platforms, we tested different scenarios to examine macrophage response to damage.
  • Julia Arciero (Indiana University-Purdue University Indianapolis, USA)
    "Modeling novel immunoregulatory treatments for transplant patients"
  • Solid organ transplantation is a life-saving procedure that requires lifelong immunosuppression to prevent transplant rejection. Developing immunoregulatory treatments that minimize the need for chronic immunosuppression would be life-changing for transplant patients. Adoptive cell therapy with regulatory T cells (Treg) has emerged as a very promising approach, but there is limited understanding of the conditions that maximize Treg therapeutic effect. Mathematical modeling offers a unique and useful method for identifying cell therapy manipulations that would be most significant. This study introduces a mathematical model of transplant rejection that has been adapted to include adoptive transfer of Tregs with varied immunosuppression regimens. The model exhibits expected transplant behavior in the presence of immunosuppression, including graft acceptance with therapeutic levels of immunosuppression and graft rejection with subtherapeutic levels of immunosuppression. Preliminary results also indicate that combinatorial treatment strategies that incorporate adoptive transfer with subtherapeutic immunosuppression prolongs graft lifetime longer than either treatment in isolation. Ultimately, the model will be used to investigate optimal combinatorial dosing strategies that prevent graft rejection while minimizing immunosuppression. Modeling novel immunoregulatory treatments for transplant patients
  • Josua Aponte-Serrano (Indiana University, USA)
    "Integrating Validated Models of Viral Replication and Interferon Signaling into a Multi-Scale Spatial Framework to Identify Key Factors of Viral Infection Dynamics"
  • Multi-scale models are commonly used tools to address complex problems that span over multiple biological scales: from intracellular signaling and regulatory pathways to host-level systemic responses. We present a multi-scale spatial model of RNA viral replication and type-I interferon response in epithelial cells. The parameters of the models were identified using using both in vivo and in vitro data from Influenza A Virus (IAV). We show that, by following our cellularization workflow, we can integrate independently validated models into a multi-scale framework that reproduces the dynamics of each model subcomponent. By exploring the parameter space of this integrated model we identified factors that lead to viral plaque growth arrest such as modulation of the JAK-STAT pathway and differential propagation of the interferon signal and viral particles in the extracellular environment. Sensitivity analysis of the integrated model suggest that parameters associated with the interferon signaling pathways are identifiable under experimental conditions that inhibit virus growth. Finally, we should how this multi-scale model can be extended to incorporate additional aspects of the host-immune response to viral infection.

Celebrating Dr. Ngwa's 55th birthday with talks honoring his mathematical modeling work including malaria mosquitoes.

Organized by: Miranda Teboh-Ewungkem (Lehigh University, United States), Calistus N. Ngonghala, (University of Florida, Gainsville, FL, United States), Jude D. Kong (York University, Toronto, ON, Canada,, Canada)
Note: this minisymposia has multiple sessions. The second session is MS07-MEPI.

  • Ian Frigaard (University of British Columbia, Canada)
    "Yield stress fluids and G.A. Ngwa"
  • Yield stress fluids have broad applications in industrial and geophysical flows, ranging from food processing to industrial slurries and river-bed mud. They also come into play biologically in the lung pathways, in mammalian reproduction, in mucus barriers and in blood flow. Here we review key dynamical features of these fluids, difficulties in application and their biological relevance.
  • Abba B. Gumel (Arizona State University, School of Mathematical and Statistical Sciences, United States)
    "Mathematics of population biology of malaria mosquitoes and disease: a genetic-epidemiology modeling framework"
  • Malaria, a deadly infectious disease caused by the Plasmodium parasite transmitted to humans via the bite from infected adult female Anopheles mosquitoes, continues to exude significant public health and socio-economic burden globally (causing over 200 million cases and in excess of 400,000 deaths annually). In his pioneering work on modeling population abundance of mosquitoes, G. Ngwa noted, in the early 1990s, that deep understanding of the population dynamics of mosquitoes is very crucial to providing insight and understanding on the transmission dynamics and control of the diseases they cause. In line with the Ngwa ``follow the mosquito' philosophy, I will present mathematical models, mostly of the form of genetic-epidemiology, deterministic system of nonlinear differential equations, for understanding the population ecology and control of malaria mosquitoes and disease, using insecticide-based and biological interventions. We will explore the feasibility of achieving the concerted global effort to eradicate malaria by 2040 using currently available mosquito control and management strategies.
  • Gwendolyn B. Fru (University of Buea, Cameroon)
    "Mathematical modelling of the pharmacokinetics of antimalarial drugs under different treatment regimes"
  • Mathematical models are used to study how antimalarial drugs interact with the human body when administered through different modes. The developed models capture the parameters which identify with the way antimalarial drugs cure humans during treatment. Drug administration by intravenous infusion and oral therapy are considered, with the classification of antimalarial drugs into two categories; drugs which exhibit their antimalarial activity in their primary form and drugs which together with their metabolites exhibit antimalarial activity. The models also consider the drug concentration in the different compartments comprising the gut (solely in the case of oral administration of drug), plasma and red blood cells, with the considerations of drug diffusing out of the red blood cells solely as byproducts of metabolism and in another case, diffusing both as byproducts of metabolism and in their original form. Results display the variations in drug concentrations in the respective compartments when the drugs are administered. A simple within human host model for the Plasmodium parasite is developed and treatment is eventually added to the model giving a Drug Model. It is shown that both in the Drug - free and Drug Models, the disease free steady state always exists and is globally stable. The disease steady state of the Drug Model is parameterized as functions of drug concentration in the infected red blood cells, and it is shown that if drug concentration in the infected red blood cells exceed the minimum therapeutic level the densities of the infected red blood cells as well as the free floating parasites vanish. Thus curing of the infection has taken place.
  • Kristan Alexander Schneider (Hochschule Mittweida, University of Applied Sciences, Germany)
    "Modelling COVID-19 in Africa"
  • With the massive COVID-19 crisis in India, worries were raised that Africa could be affected similarly in the near future. More infectious SARS-CoV-2 variants that are more likely to cause symptomatic episodes in younger people and are emerging and spreading. This is particularly dangerous since some of the approved vaccines do not properly immunize against new variants. Hence, such mutations have potentially catastrophic effects for the African continent, characterized by a young population. Predictive SEIR models can be employed as decision support tools for COVID-19 management. Realistic models, applicable for the African continent, must take the age and spatial structures of the countries into account as well as the possibilities of different viral variants and available vaccines. Here, we introduce an age and spatially stratified COVID-19 model that explicitly takes the age-dependent contact behavior, different SARS-CoV-2 variants, and vaccination strategies into account.

Data-driven methods for biological modeling in industry

Organized by: Kevin Flores (North Carolina State University, USA)
Note: this minisymposia has multiple sessions. The second session is MS13-MFBM.

  • Richard Allen (Quantitative Systems Pharmacology, Early Clinical Development, Pfizer Worldwide Research Development and Medical, USA)
    "Analyzing and Predicting Clinical Trial Data with Systems Modeling"
  • Systems modeling approaches have found increasing utility in supporting the discovery and development of novel therapeutics. By capturing key biological interactions and incorporating a wide range of data to inform the model, a systems model can be a powerful tool to design, predict, and analyze clinical trials. However, typical clinical trials show a highly variable response – such that fitting a model to the mean at best might be losing some information, and at worse fully mischaracterizing the response. Conversely, mathematical representations of complex biology lead to large models and associated uncertainty in parameter estimation. In this talk I will introduce how systems modeling is being used in drug discovery and development, and the challenges of such an approach. In particular, I will discuss how we generate virtual patients and populations to explore parameter uncertainty in a model while constraining the response using the observed clinical variability. Furthermore, I will show – by example - how analysis of a virtual population can lead to physiological insights.
  • Florencio Serrano Castillo (Clinical Pharmacology, Modelling and Simulations, Amgen Inc., USA)
    "Dosing guidance optimization, leveraging real world heterogeneity to forecast clinical biomarker response"
  • Understanding the dynamic and variability of a drug’s pharmacokinetic (its concentration in the body) and pharmacodynamic (its effect on the body) profiles is of critical importance for the design and success of any clinical study. However, the development, implementation and validation of system-level models that explicitly relate the complex biological mechanisms ruling the relationships between dose, exposure, clinical response and safety of a drug while simultaneously describing clinical variability is often unfeasible due to both technical and logistic limitations. Population pharmacokinetic and pharmacodynamic models (popPK/PD) are a powerful tool to circumvent this limitations. popPK/PD models leverage the inherent nosiness of clinical/biological data to inform statistical models embedded into their core dynamic structure to describe both intrinsic and extrinsic sources of variability representative of the clinical setting. This hierarchical structure can then be leveraged to perform clinical trial simulations that predict the impact of various design options and thus inform strategic decisions throughout the development and life cycle management of a therapeutic. This talk will provide a general example of how to leverage a pseudo-mechanistic popPKPD to identify complex patterns between highly heterogeneous clinical dose and biomarker data in order to provide guidance regarding the feasibility and uncertainty associated with various proposed clinical scenarios. Furthermore, it will also describe methodologies on how to address typical challenges with this process, such as the validation of a previously developed model for a different patient population, the generation and implementation of appropriate clinical trial simulation schemes to address possible population and strategy characteristics, and the collation and interpretation of model-derived outputs in order to inform development strategies.
  • Zackary Kenz (DILIsym Services, a Simulations Plus Company, USA)
    "Quantitative Systems Pharmacology Modeling of Fibrotic Diseases"
  • Fibrotic diseases occur in multiple organs, characterized by escalating fibrosis affecting organ function. For example, in idiopathic pulmonary fibrosis (IPF), normal lung is progressively replaced by fibrotic architecture resulting in compromised movement and gas exchange. Similarly, in non-alcoholic steatohepatitis (NASH), normal liver cells are replaced with fibrotic matrix resulting in compromised liver clearance mechanisms. In both cases, there are no cures and few treatment options. These fibrotic diseases represent areas of unmet clinical need, where improved understanding of pathophysiology and treatment interventions could impact the drug development pipeline and patient care. To accelerate the clinical development of treatments in IPF and NASH, DILIsym Services has developed QSP models of each disease state. These models contain mechanistic representations of ongoing injury, inflammation, and accumulation of extracellular matrix, each of which represent potential targets for treatment intervention which can be quantitatively assessed within the model. Further, mechanisms are dynamically linked with clinical outcomes, providing insight across multiple scales from molecular intervention to cellular response to tissue response. Selected portions of the model development and validation will be discussed, along with example treatments. These QSP platforms are available and actively in use to support ongoing development of effective treatments for IPF and NASH patients.
  • Anna Neely (TigerRisk Partners, USA)
    "Estimating the growing risk of severe thunderstorms"
  • 'Severe weather is one of the biggest drivers of insured catastrophe losses in the US.  Catastrophe models are used to estimate risk of severe weather conditions - are they aiming at a moving target?  Losses to the insurance industry have increased at a rate of 9% annually since 2000.  Far outpacing expectations.  In this talk we'll dive into some of the drivers of this increase and de-mystify some insurance industry folklore.'

Deterministic and stochastic models for complex cardiovascular phenomena

Organized by: Martina Bukac (University of Notre Dame, United States), Daniele Schiavazzi (University of Notre Dame, United States)
Note: this minisymposia has multiple sessions. The second session is MS20-MMPB.

  • Suncica Canic (University of California, Berkeley, United States)
    "Computational design of a bioartificial pancreas"
  • This talk will address the design of a first implantable bioartificial pancreas without the need for immunosuppressant therapy. The design is based on transplanting the healthy (donor) pancreatic cells into a poroelastic medium (alginate hydrogel, or agarose gel) and encapsulating the cell-containing medium between two nanopore semi-permeable membranes. The nanopore membranes are manufactured to block the immune cells while allowing passage of nutrients and oxygen to keep the transplanted cells viable as long as possible. The key challenge is maintaining the survival of transplanted pancreatic cells for an extended period of time of which oxygen is the main limiting factor. This challenge is addressed via our nonlinear, multi-scale, multi-physics mathematical and computational model. At the micro scale we use particle-based simulations to study the nano-scale structure of the poroelastic medium containing the cells, and combine the results with Convolution Neural Networks approaches to recover the macro-scale parameters, such as hydraulic conductivity of the poroelastic get matrix. The macro-scale parameters are used to study fluid-structure interaction between blood flow at the multi-layered poroelastic medium containing the cells. The output of the FSI simulations is then used in the advection-reaction-diffusion models to study oxygen supply to the seeded pancreatic cell. The results of the numerical simulations have aided optimal design of the first implantable bioartificial pancreas without the need for immunosuppressant therapy.
  • Philipp Milović (University of Zagreb, Croatia)
    "A block-coupled finite volume solver for analysis of large strain in incompressible hyperelastic materials"
  • Efficient solution procedures for fluid-structure interaction simulations of vascular flows require adequate solid phase solvers. Existing finite volume based solvers exhibit convergence and stability issues for problems of incompressible finite strain and unstructured meshes which commonly occur when modelling arterial tissue. In this work a block-coupled finite volume solution methodology employing a mixed displacement-pressure formulation for problems of incompressible finite strain in hyperelastic materials is developed. The solution strategy is based on integral momentum and mass conservation equations wherein pressure is used as an additional variable to improve numerical stability. The domain is discretized by cell-centred finite volumes of arbitrary polyhedral shape and a coupled solution procedure is used to improve convergence. Performance of the solution procedure is evaluated for several test cases and compared with analytical and finite element solutions.
  • Paolo Zunino (Politecnico di Milano, Italy)
    "A meso-scale computational model for micro-vascular oxygen transfer"
  • We address a mathematical model for oxygen transfer in the microcirculation. The model includes blood flow and hematocrit transport coupled with the interstitial flow, oxygen transport in the blood and the tissue, including capillary-tissue exchange effects. Moreover, the model is suited to handle arbitrarily complex vascular geometries. The purpose of this study is the validation of the model with respect to classical solutions and the further demonstration of its adequacy to describe the heterogeneities of oxygenation in the tissue micro-environment. Finally, we discuss the importance of these effects in the treatment of cancer using radiotherapy.
  • Rana Zakerzadeh (Duquesne University, United States)
    "The Role of Intraluminal Thrombus on the Vessel Wall Oxygen Starvation"
  • In this presentation, the biomechanical role of intraluminal thrombus (ILT) in an abdominal aortic aneurysm (AAA) is investigated. It is hypothesized that different ILT geometries can enhance wall strength while also inhibiting oxygen transport and inducing arterial wall degradation. The objective of this work is to simulate AAAs with variable ILT dimensions and analyze how ILT thickness and size influence AAA rupture. A comparison between different ILT morphologies was performed. Geometric variations studied include the thickness, length, and degree of asymmetry of the ILT. Nine two-bulged, symmetrical AAAs were modeled with varying ILT thicknesses (0.1 cm, 0.2 cm, or 0.4 cm) and lengths (4cm, 6cm, or 8cm) using CAD software. A finite element method simulation of the Fluid-Solid Interactions (FSI) between arterial wall, ILT and blood was solved to assess the influence ILT geometry has on wall stress and oxygen concentration Results are presented for wall stress and deformation patterns, lumen pressure and velocity fields, and oxygen concentration within the ILT and arterial wall. While ILT geometries were found to reduce wall stress, our simulations demonstrated that thicker and longer ILTs reduced oxygen transport, leading to wall degradation.

Multi-scale Physiological Systems

Organized by: Saeed Farjami (University of Surrey, United Kingdom), Anmar Khadra (McGill University, Canada)
Note: this minisymposia has multiple sessions. The second session is MS15-NEUR.

  • Saeed Farjami (University of Surrey, United Kingdom)
    "Non-sequential Spike Adding in Cerebellar Stellate Cells"
  • Cerebellar Stellate Cells are spontaneously spiking. Recently, our colleagues have recorded bursting activities in these cells by applying pharmacological agents known for blocking certain ion currents. Such activities are usually modelled in the form of systems with different time scales. When the slow variables are treated as parameters, the fast subsystem can provide good insights into the dynamics of the full model. Using slow-fast analysis, we explain the underlying mechanisms responsible for generating types of bursting emerging in the model. Also, a bifurcation analysis of the full model reveals the effect of different doses of the pharmacological agents on the system dynamics. Moreover, our investigations show that the number of spikes in an active phase of bursting changes when parameters of the system fluctuate. However, in contrast to former studies, adding new spikes does not happen sequentially. In this talk, we will discuss such phenomena and try to shed light on their underlying dynamics.
  • Michael Forrester (University of Nottingham, United Kingdom)
    "Using a multiscale next-generation neural-mass model to fit neuroimaging data"
  • Owing to their formulation as exact mean-field representations of neural oscillators, next-generation neural mass models are natural candidates to explore neurological phenomena related to local, and non-local, synchronisation in the brain, such as beta-rebound/beta-burst effects and large-scale functional connectivity. Here, we demonstrate applications of one such model over varying spatial scales and highlight its usefulness in exploring the importance of features of the underlying neuron model, such as gap-junction coupling and synaptic reversal potentials, in emergent large-scale population dynamics.
  • Victoria Booth (University of Michigan, USA)
    "Dynamics and bifurcations of sleep-wake behavior"
  • While transitions between sleep and wake states happen quickly, the timing of these transitions are modulated by the slower processes of the 24 h circadian rhythm and the homeostatic sleep drive, the irresistible urge for sleep after being awake. We are developing and analyzing mathematical models of neuronal sleep-wake regulatory networks to understand how the interaction of fast and slow processes dictate the timing and durations of sleep and wake episodes. In this talk, I will discuss recent analyses of solutions of these models based on construction of circle maps that have allowed identification of the bifurcations underlying the transitions of sleep-wake behavior over human development and across species.
  • Sue Ann Campbell (University of Waterloo, Canada)
    "Time delays may enhance or impede synchronization in brain networks"
  • We study the effect of time-delays in a neural field model for a brain network. The model considered is a network of Wilson-Cowan nodes with inhibitory weights dynamically modified to represent homeostatic regulation. Without time delay, the system has been shown to exhibit rich dynamics including oscillations, mixed-mode oscillations, and chaos. Synchronization of the nodes depends on the connectivity structure of the network. Using the Master Stability formalism, we show that time delays in the connections between the nodes 1) may stabilize brain dynamics by temporarily preventing the onset to oscillatory and pathologically synchronized dynamics, and 2) may enhance or diminish synchronization depending on the underlying eigenvalue spectrum of the connectivity matrix.

Integrating quantitative imaging and mechanistic modeling to characterize tumor growth and therapeutic response

Organized by: Guillermo Lorenzo (University of Pavia, Italy), David Hormuth (The University of Texas at Austin, US), Angela Jarrett (The University of Texas at Austin, US), Thomas Yankeelov (The University of Texas at Austin, US)
Note: this minisymposia has multiple sessions. The second session is MS20-ONCO.

  • Andrea Gardner (The University of Texas at Austin, US)
    "Quantification of interactions between epithelial-like and mesenchymal-like subpopulations in a triple-negative breast cancer cell line ecosystem"
  • Many cancer cell lines once thought to be relatively homogeneous are composed of distinct subpopulations. Informed by single-cell RNA sequencing of the triple-negative breast cancer cell line MDA-MB-231, we discovered a surface marker which effectively separates epithelial-like (EL) cells from mesenchymal-like (ML) cells from this population. Growth characteristics of EL and ML subpopulations were determined in monoculture and in co-culture and under varying environmental conditions. We find that while the ML cells are neutral to the presence of EL cells, the growth rate of the already faster EL cells is further boosted in the presence of ML cells. One would expect this phenomenon to lead to the extinction of the ML cells, however, these cells co-exist over many generations in vitro. To investigate this paradox, experimental data from live-cell imaging was integrated with an extended Lotka-Volterra competition model to quantify the intrinsic properties and interactions of these two-subpopulations and we present our findings here.
  • Haley Bowers (Wake Forest School of Medicine, US)
    "Image Data-Driven Biophysical Mathematical Model Based Characterization of Multicellular Tumor Spheroids"
  • Multicellular tumor spheroid (MCTS) systems provide an in vitro cell culture model system which replicates many of the complexities of an in vivo solid tumor and its tumor microenvironment. MCTS systems are often used to study cancer cell growth and drug efficacy. In this work, we present a coupled experimental-computational framework to estimate phenotypic growth and biophysical tumor microenvironment properties. This novel framework utilizes standard microscopy imaging of MCTS systems to drive a biophysical mathematical model of MCTS growth and mechanical interactions. This work is an extension of our previous in vivo mechanically-coupled reaction-diffusion modeling framework we developed a microscopy image processing framework capable of mechanistic characterization of MCTS systems. Using fluorescently labeled MDA-MB-231 breast cancer MCTS, we estimated biophysical parameters of cellular diffusion, rate of cellular proliferation, and cellular tractions forces. We found significant differences in between untreated and treated MCTS systems using these model-based biophysical parameters throughout the treatment time course, whereas traditional morphometric parameters were inconclusive. This experimental-computational framework estimates mechanistic MCTS growth and invasion parameters with significant potential to assist in better and more precise assessment of in vitro drug efficacy through the development of computational analysis methodologies for three-dimensional cell culture systems to improve the development and evaluation of antineoplastic drugs.
  • Anum Kazerouni (University of Washington, US)
    "Characterizing tumor heterogeneity using quantitative MRI habitats in breast cancer in vivo"
  • Within a tumor exists a dynamic interplay of spatially-varying cell populations and tissue microenvironments that both contributes to tumor progression and influences therapeutic response. For example, the uneven distribution of vasculature across a tumor can yield nonuniform drug delivery. Additionally, phenotypic diversity across cancer cells can result in variable response to treatment. These aspects of tumor heterogeneity provide a major challenge in the clinical treatment of breast cancer and result in significant diversity of outcomes across a patient population, emphasizing the need for personalized approaches to cancer treatment. Methods to characterize the spatiotemporal evolution of an individual tumor and its resulting heterogeneity can lend improved understanding of a patient’s tumor pathology and their potential response to therapy. Quantitative magnetic resonance imaging (MRI) is noninvasive and can, therefore, longitudinally detect changes in physiological characteristics across a tumor volume. In particular, diffusion-weighted (DW-) MRI and dynamic contrast-enhanced (DCE-) MRI provide quantitative assessment of tissue cellularity and vascularity, respectively—key tumor attributes that are affected by therapy. Accordingly, quantitative MRI measures have demonstrated promise as biomarkers of breast cancer treatment response in both preclinical and clinical settings. Recent work has investigated methods to spatially resolve intratumoral heterogeneity using quantitative MRI through an approach known as habitat imaging6. With this technique, physiologically distinct tumors subregions (i.e., habitats) are identified by clustering multiparametric image data, thus facilitating quantitative characterization of microenvironmental heterogeneity for individual tumors. In this presentation, we will describe how DW- and DCE-MRI data can be leveraged to spatially resolve physiologically distinct tumor habitats in vivo with biological validation ex vivo. Using preclinical models of breast cancer, we will demonstrate how this approach can be used to measure longitudinal alterations in the tumor microenvironment in response to treatment and identify tumor imaging phenotypes with differing therapeutic sensitivities. Additionally, we will describe the translation of this approach to the clinical setting and its promise in identifying breast cancer patients with increased likelihood of neoadjuvant therapy response based on tumor habitat composition. These tumor-specific characterizations of microenvironmental heterogeneity could provide a means to more accurately guide individualized patient treatment strategies.
  • David Hormuth (The University of Texas at Austin, US)
    "Image-driven modeling of radiation therapy response in gliomas"
  • Radiotherapy is a fundamental component of the treatment and management of high-grade gliomas. The efficacy of radiotherapy can vary from tumor to tumor due to spatial and temporal heterogeneity in (for example) cellularity, blood volume, and perfusion. A rigorous understanding of the dynamics of tumor heterogeneity could enable the personalization of radiotherapy for individual tumors. Quantitative imaging techniques such as diffusion weighted (DW-) magnetic resonance imaging (MRI) and dynamic contrast-enhanced (DCE-) MRI provide an opportunity to longitudinally, and non-invasively, observe the dynamics of tumor heterogeneity in 3D. We have developed an experimental and computational framework to integrate these longitudinal measurements of tumor heterogeneity into mathematical models of tumor growth and response. Seven animals implanted intra-cranially with the U87 glioblastoma cell line were imaged before, during, and after the delivery of radiotherapy. We then initialized and calibrated a family of 18 models of response to radiotherapy for each animal using DW-MRI and DCE-MRI. Using the calibrated model parameters we assessed the error in response predictions at the local and global levels. At the global level, we observed less than 16.2% error in tumor volume predictions while at the local level we observed a Pearson correlation coefficient of greater than 0.87 for each animal. This effort demonstrates the strength of using longitudinal MRI data for personalization of models predicting the response of brain tumors to radiotherapy.