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Sub-group minisymposia

The 10th anniversary of MBI’s 2013 Workshop for Young Researchers in Mathematical Biology

Organized by: Rebecca Everett, Angela Peace
Note: this minisymposia has multiple sessions. The other session is MS02-OTHE-1.

  • Hayriye Gulbudak University of Louisiana at Lafayette (Mathematics)
    "A delay model for persistent viral infections in replicating cells"
  • Persistently infecting viruses remain within infected cells for a prolonged period of time without killing the cells and can reproduce via budding virus particles or passing on to daughter cells after division. The ability for populations of infected cells to be long-lived and replicate viral progeny through cell division may be critical for virus survival in examples such as HIV latent reservoirs, tumor oncolytic virotherapy, and non-virulent phages in microbial hosts. We consider a model for persistent viral infection within a replicating cell population with time delay in the eclipse stage prior to infected cell replicative form. We obtain reproduction numbers that provide criteria for the existence and stability of the equilibria of the system and provide bifurcation diagrams illustrating transcritical (backward and forward), saddle-node, and Hopf bifurcations, and provide evidence of homoclinic bifurcations and a Bogdanov–Takens bifurcation. We investigate the possibility of long term survival of the infection (represented by chronically infected cells and free virus) in the cell population by using the mathematical concept of robust uniform persistence. Using numerical continuation software with parameter values estimated from phage-microbe systems, we obtain two parameter bifurcation diagrams that divide parameter space into regions with different dynamical outcomes. We thus investigate how varying different parameters, including how the time spent in the eclipse phase, can influence whether or not the virus survives.
  • Amy Buchmann University of San Diego (Mathematics)
    "A decade of modeling microscale biofluids"
  • One area of research within mathematical biology is computational biofluids. This includes understanding the mechanics of biological fluid flow systems in the human body (the circulatory and respiratory systems), cells, and microorganism motility. I became interested in biofluids right around the time that I attended the Workshop for Young Researchers in Mathematical Biology in 2013, and have spent most of my career working in this area focusing on microscale biofluids. In this talk, I will discuss several of my collaborative projects that study microorganisms by modeling the interactions between elastic structures in a viscous fluid.
  • Reginald McGee College of the Holy Cross (Mathematics and Computer Science)
    "Towards A Modeling Framework For Pediatric Sickle Cell Pain"
  • Sickle cell pain presents in acute episodes in pediatric patients, as opposed to the chronic pain observed in adults. The episodic nature of pain events in pediatric patients necessitates a distinct approach from what has been used to mathematically model pain severity levels in adults. Statistical studies have examined interactions between sleep actigraphy measurements --- like sleep quality and sleep efficiency --- and pain levels in pediatric populations, and we propose a framework for modeling pediatric pain dynamics that incorporates the effects of sleep actigraphy and electronic survey data over varying time windows. We hypothesize that cumulative effects of these measurements will be more important than daily measurements in both replicating pain severity levels and determining markers of a pain episode. The ability to identify markers preceding the onset of a pain episode will be crucial in improving patient quality of life. We present work in progress towards developing this modeling framework.
  • Michael A. Robert Virginia Tech (Department of Mathematics)
    "Investigating impacts on malaria transmission of altered bioamine levels in Anopheles mosquitoes"
  • Malaria is caused by Plasmodium species that are transmitted to humans primarily by Anopheles mosquitoes. Currently, over half of the world’s population is at risk of malaria, and after decades of progress towards eradication led to declines in cases reported globally, cases have increased since 2020, with 247 million cases and 619,000 deaths reported in 2021. Malaria infection is known to influence levels of biogenic amines in human blood. Specifically, individuals with severe malaria may exhibit increased concentrations of histamine and/or decreased concentrations of serotonin. The altered amine levels may also impact the biology and behavior of Anopheles mosquitoes that ingest them in bloodmeals, but it remains to be seen what role these changes may have on mosquito population dynamics and malaria transmission. We developed a stage-structured discrete time mathematical model of mosquito population dynamics coupled with population-level malaria transmission dynamics to investigate how these altered amine levels may play a role in the malaria transmission cycle. We incorporated demographic, behavioral, and parasite reproduction data into the model and explored scenarios that consider different possible concentrations of histamine and serotonin in bloodmeals and different effects thereof by studying differences in mosquito population size and malaria incidence and prevalence. We explore different possible extensions of the model and discuss our findings in the context of malaria control as well as future experimental work.

Recent Studies on the Biomechanics and Fluid Dynamics of Living Systems: Locomotion and Fluid Transport

Organized by: Alexander Hoover, Matea Santiago
Note: this minisymposia has multiple sessions. The other session is MS02-OTHE-2.

  • Alexander P. Hoover Cleveland State University (Mathematics)
    "Interfacing in-Situ and in-Silico Experiments in Organismal Fluid Pumping"
  • Far from the surface, the ocean's midwater present a rich frontier of biodiversity that is not well understood. Part of this gap in our knowledge is the great expense involved in collecting data with remotely operated vehicles. In this presentation, we will discuss the pipeline of developing in-silico computational experiments in concert with in-situ experimental data. Using a combination of particle image velocimetry data, optical scans, and confocal microscopy, we will discuss the creation of fluid-structure interaction models for organismal pumping and fluid transport, with the goal of developing an intuition on the physical mechanisms that drive their success. Using a combination of simplified geometries and scanned body meshes, we will employ the immersed boundary/finite element (IB/FE) method to simulate chambered, valveless pumping mechanism generated by the pelagic tunicate known as a larvacean. Additionally, we will use the same modeling methodology to explore the metachronal motion and fluid transport of the parapodial paddles of the pelagic, midwater polychaete known as tomopterids. All motion described in these systems will not be prescribed and will emerge from the interaction of active muscular tension, passive elastic recoil, and the local fluid environment.
  • Silas Alben University of Michigan (Mathematics Department)
    "Efficient bending and lifting patterns in snake locomotion"
  • We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. With lifting, a few types of optimal motions prevail. We have an s-shaped body with alternating lifting of the middle and ends at small-to-moderate transverse friction. With large transverse friction, curling and sliding motions are typical at small viscous dissipation, replaced by large-amplitude bending at large viscous dissipation. With small viscous dissipation we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10-100% higher.
  • Matea Santiago University of Arizona (Mathematics)
    "The role of elasticity and tension in soft coral pulsing"
  • The pulsing behavior of Xeniid soft corals is characterized by active muscle contraction and passive expansion, similar to many other swimming marine invertebrates. However, soft corals are sessile animals and do not locomote. Previous experimental and computational studies have indicated that the pulsing behavior mixes the surrounding fluid and enhances the photosynthesis of their zooxanthellae. Symbiotic photosynthesis is hypothesized to be the coral’s main energy source. Past computational work directly prescribed motion to the coral tentacles. This work instead drives motion by modeling the muscle contraction as applied active tension and expansion through the passive elasticity of the coral body. The role of elasticity and muscle tension is explored in the coral’s kinematics and the resulting fluid flow using the immersed finite element-finite difference (IFED) method implementation in the software library IBAMR to simulate the elastic-structure fluid interaction of the tentacles and surrounding fluid. These results will provide insight into the underlying biomechanics of the pulsing behavior by observing the emergent behavior of the system. The results of this study contribute to cnidarian biomechanics knowledge and have implications in soft robotics design.

The 10th anniversary of MBI’s 2013 Workshop for Young Researchers in Mathematical Biology

Organized by: Rebecca Everett, Angela Peace
Note: this minisymposia has multiple sessions. The other session is MS01-OTHE-1.

  • Ashlee N. Ford Versypt University at Buffalo, The State University of New York (Department of Chemical and Biological Engineering)
    "Multiscale Modeling of Tissue Remodeling and Damage"
  • Dr. Ford Versypt leads the Systems Biomedicine and Pharmaceutics research lab, which develops and uses multiscale systems engineering approaches including mathematical modeling and computational simulation to enhance understanding of the mechanisms governing tissue remodeling and damage as a result of diseases and infections and to simulate the treatment of those conditions to improve human health. The lab specializes in (a) modeling mass transport of biochemicals through heterogeneous porous materials—primarily extracellular matrices—that change morphology dynamically due to the influence of chemical reactions and (b) modeling dynamic, multi-species biological systems involving chemical, physical, and biological interactions of diverse, heterogeneous cell populations with these materials and the chemical species in tissue microenvironments. In this presentation, Dr. Ford Versypt will reflect on the trajectory of her research program through the last decade starting from modeling protein transport through degradable biomaterials for drug delivery and pharmaceutical manufacturing to focusing on pathophysiology of tissue damage and disease progression and pharmacokinetics/pharmacodynamics of treatments. This work is currently supported by an NSF CAREER award and NIH R35 MIRA grant.
  • Angela Peace Texas Tech University (Department of Mathematics and Statistics)
    "Adaptive foraging behaviors in food web models"
  • Nutritional constraints are common as food resources are rarely optimally suited for grazing species. Elemental mismatches between trophic levels can influence population growth and foraging behaviors. Consumers utilize optimal foraging techniques, such as compensatory and complementary feeding strategies. Mathematical models developed under the framework of Ecological Stoichiometry can help shed light on population dynamics subject to stoichiometric constraints. I will give a brief overview of stoichiometric producer-grazer models and present some commonly used functional forms for incorporating stoichiometric constraints into trophic interactions. Model extensions explore adaptive grazer foraging behaviors in stoichiometrically explicit food webs.
  • Open Discussion
    "Open Discussion: Best Practices for Workshops for Young Researchers"
  • Topics for this discussion will be about how best to organize a workshop for young researchers in mathematical biology. For example, what activities would be included in a schedule, how would students be recruited, and how would one best assess the success of such a workshop.

Recent Studies on the Biomechanics and Fluid Dynamics of Living Systems: Locomotion and Fluid Transport

Organized by: Alexander Hoover, Matea Santiago
Note: this minisymposia has multiple sessions. The other session is MS01-OTHE-2.

  • Daisuke Takagi University of Hawaii at Manoa (Mathematics)
    "Larval fish counteract ram and suction to capture evasive prey"
  • Fish larvae are considered to be suction feeders that rely on suction flow to capture prey. However, recent observations of clownfish larvae revealed that they behave like ram feeders that accelerate towards copepod prey. Capturing copepods is challenging because they are highly evasive and sensitive to fluid deformation. To identify the strategies needed for successful capture, we developed a simple model based on potential flow theory. Our results show that fish larvae with weak ram and suction strengths can still capture copepods through hydrodynamic stealth. This suggests that suction by fish larvae is used primarily for stealth rather than capture.
  • Lisa J. Fauci Tulane University (Mathematics)
    "A closed-loop neuromechanical model of locomotion of lampreys with spinal injuries"
  • In some vertebrates such as lampreys, swimming function can be regained after spinal injuries, but the exact mechanism of this recovery is not well understood. One hypothesis is that amplified proprioceptive (body-sensing) feedback can allow an injured lamprey to regain functional swimming even if the descending signal is lost. Here we present a multiscale model of an undulatory swimmer whose neural signaling is driven by a phase oscillator model that is fully coupled to a viscous, incompressible fluid. We examine the effects of amplified feedback on swimming behavior, and show that in some cases, feedback amplification below a spinal lesion is sufficient to partially or entirely restore effective swimming behavior.

Preparing for the Next Pandemic: Modeling and Simulation in Drug Development

Organized by: Celeste Vallejo

  • Sriram Chandrasekaran University of Michigan (Biomedical Engineering)
    "Drug discovery and repurposing using hybrid machine learning and biochemical modeling"
  • By 2050, we may lose 10 million people a year to drug-resistant infections. Unfortunately, the pace of drug discovery has not kept up with the rapid emergence of these pathogens. Drug combinations have great potential to reduce the spread of drug-resistant bacteria. However, current drug-discovery approaches are unable to screen an astronomical number of drug combinations and do not account for pathogen heterogeneity or the complex in vivo environment. We have developed hybrid AI tools - INDIGO, MAGENTA, and CARAMeL, which predict the efficacy of drug regimens based on the properties of the drugs, the pathogen, and the immune and infection environment. Our hybrid AI methods combine engineering models with machine learning, which provides both predictive power and mechanistic insights. Using these methods, we have identified highly synergistic drugs to treat drug resistant infections including Tuberculosis, the world's deadliest bacterial infection. Our approach also accurately predicts the outcome of past clinical trials of drug regimens. Our ultimate goal is to create a personalized approach to treat infections using AI.
  • Amber Smith University of Tennessee Health Science Center (Department of Pediatrics)
    "PKPD modeling of Plasmodium falciparum ATP4 inhibitor SJ733 with the pharmacokinetic enhancer cobicistat"
  • SJ733 is a newly developed inhibitor of Plasmodium falciparum ATP4 with a favorable safety profile and rapid antiparasitic effect but insufficient duration to deliver a single-dose cure of malaria. To better understand the dynamics and predict cure regimens, we developed a PKPD model. The PK could be captured using a two-compartment model with enterohepatic recirculation. Pairing this with a mechanistic PD model suggested that efficacy was increased post-recirculation and that increasing exposure would be required for cure. This prompted us to measure PK profiles for multidose regimens with or without a pharmacoboost approach using cobicistat. Either approach could significantly increase exposure but with varying kinetics. Refitting the PK model and pairing it with the PD model predicted that an unboosted, multidose regimen would increase parasite clearance by ~3x compared to 5x in the cobicistat-boosted group. The simulations also showed that a reduction in parasite burden of 1e9 would require a minimum of 300 mg SJ733+cobicistat for 2 d or 600 mg SJ733 for 3 d or 200 mg for 4 d. These results provided candidate dosing approaches to move forward into Phase 2 trials against acute, uncomplicated malaria.
  • Celeste Vallejo Simulations Plus, Inc. (DILIsym Services)
    "Potential application of a mechanistic model of chronic lung disease to the treatment of post-COVID lung fibrosis and other respiratory pandemics"
  • Idiopathic pulmonary fibrosis (IPF) is a chronic condition in which the lungs become filled with scar tissue, reducing the amount of healthy lung tissue, thus making it difficult to breathe. There is no known cure for IPF, however some treatments have been shown to slow disease progression. IPFsym is a quantitative systems pharmacology (QSP) model for IPF developed to support drug development efforts. It mechanistically represents human pathophysiology including inflammation (e.g., neutrophils, macrophages, cytokines) and fibrosis (e.g., fibroblasts, extracellular matrix) based on human data. The integrated pathophysiology is linked to clinical outcomes like forced vital capacity (FVC). IPFsym includes simulated patients with disease progression comparable to real patients, and responses to approved treatments, pirfenidone and nintedanib, that align with clinical data. IPFsym has been applied to support clinical trial design for drugs in development. Because IPFsym includes many elements common to the fibrotic sequelae of infectious respiratory disease, there is tremendous opportunity to pivot towards pulmonary fibrotic diseases caused by respiratory pandemics (such as COVID-19). The process of model modifications and re-optimization involved in pivoting to a new indication (i.e., post-COVID-19 lung fibrosis) is illustrated through the successful conversion of IPFsym to a model of interstitial lung disease associated with systemic sclerosis (SSc-ILD).

Modeling sex differences in health and disease

Organized by: Melissa Stadt
Note: this minisymposia has multiple sessions. The other session is MS07-OTHE-1.

  • Lihong Zhao University of California, Merced (Department of Applied Mathematics)
    "Mathematical modeling of the menstrual cycle and hormonal contraception"
  • Developing a mechanistic understanding of the menstrual cycle is important to human health and wellness. Menstruation is driven by hormones. Hormonal imbalances can lead to issues with menstrual cycle that affect health, wellness, and quality of life. There is a high level of variability in hormone levels both between different individuals and from cycle to cycle within a single individual. In this talk, we will provide an overview of the current state-of-the-art in mathematical modeling of the menstrual cycle. We will show how we utilize a mechanistic mathematical model of the menstrual cycle to explore the qualitative effects of hormonal contraception on the menstrual cycle.
  • Erica Graham Bryn Mawr College (Mathematics)
    "Functional Variations in the Ovulatory Cycle: Insights from Modeling"
  • A normally functioning ovulatory cycle results from a tightly regulated system of crosstalk between the brain and the ovaries. Failure to regulate reproductive hormones may cause ovarian dysfunction and sometimes infertility. For example, polycystic ovary syndrome (PCOS) is a relatively common cause of such dysfunction, often accompanied by irregular glucose metabolism. Here we examine mechanisms of disruption and characterize ovulatory phenotypes through a new endocrine model and discuss the impact of metabolic abnormalities on the female endocrine system.
  • Carley V. Cook University at Buffalo (Department of Chemical and Biological Engineering)
    "Mathematical Modeling of Osteoporosis Due to Surgical Menopause"
  • Osteoporosis, characterized by decreased bone mass and structural deterioration, results from an imbalance in the bone tissue's metabolic processes. In the adult skeleton, bone is remodeled regularly due to dynamic interactions between several bone cell types: osteoclasts, osteoblasts, osteocytes, and their precursors. It is known that estrogens affect bone remodeling in both biological sexes. Specifically, postmenopausal bone loss results from estrogen deficiency in older women. Estrogen deficiency has a sudden onset when the ovaries are surgically removed, and osteoporosis risk is higher in these patients than for those experiencing natural menopause. We have developed a mathematical model for the bone cell dynamical responses to estrogen deficiency during the surgical menopausal transition using information about the key impacts observed in female mice and humans after ovary removal. We build upon an existing model for osteoporosis due to aging. Our new model considers the role of embedded osteocyte cells in regulating enhanced osteoclast formation, inducing enhanced bone resorption after surgical menopause. With two new adjustable parameters, the model fits clinical bone mineral density decreases. Other parts of the model results will be compared to various in vivo clinical and animal studies. The impacts of hormone replacement therapy on surgical menopause in silico scenarios will also be simulated and discussed.

Modeling sex differences in health and disease

Organized by: Melissa Stadt
Note: this minisymposia has multiple sessions. The other session is MS06-OTHE-1.

  • Melissa M. Stadt University of Waterloo (Applied Mathematics)
    "Maternal calcium homeostasis: A mathematical analysis of the differential impacts of pregnancy and lactation"
  • Calcium plays an essential role in many physiological functions such as skeletal mineralization, muscle contractions, blood clotting, and cell signaling. While extracellular calcium makes up less than 1% of total body calcium, it is tightly regulated since too high or too low calcium levels can have dangerous effects on the body. During pregnancy and lactation, there is excess demand on the maternal body due to the needs of the fetus or milk, therefore major adaptations must occur. Despite having a similar additional calcium demand, maternal adaptations in pregnancy and lactation differ. During pregnancy, intestinal absorption of calcium is massively increased in the mother’s body to meet the needs of the developing fetus. However, during lactation, calcium is resorbed from the bones to meet the needs of milk production. The goal of this project is to develop the first pregnancy- and lactation-specific mathematical models of calcium regulation. Model analysis reveals how both differential adaptations support the calcium demands of the fetus or milk while maintaining normal calcium ranges in the maternal body. 
  • Karin Leiderman University of North Carolina at Chapel Hill (Mathematics, Computational Medicine)
    "Mathematical modeling to understand the effects of estrogen on platelet activation"
  • Activated platelets are essential for hemostasis and blood clotting. The activation process is a coordinated sequence of events that begins at the platelet membrane where ligands bind receptors and initiate internal signaling pathways. Estrogen has been observed to both reduce and enhance platelet responsiveness in the literature, with varying estrogen concentrations having potentially different effects. It is not yet known if these observed changes are due to estrogen receptor signaling only, or if there are other mechanisms also at play. One idea is that estrogen could induce changes in membrane properties that alter the signaling pathways leading to platelet activation. It is known that signal transduction is partially regulated by membrane properties like fluidity and lipid rafts, and that steroid hormones directly affect these types of membrane properties. We developed a mathematical model that considers both possibilities. First, it considers the downstream signaling effects that estrogen binding to estrogen receptors have on platelet activation. Second, we also assume that high levels of estrogen alter the fluidity of platelet membranes, which affects the binding dynamics of the collagen receptor, glycoprotein VI, and ultimately platelet activation. Our model qualitatively captures flow cytometry data showing similar dose response curves for platelet activation due to collagen related peptides and similar biphasic responses whereby platelet activation increases with low levels of estrogen but then decreases sharply with high estrogen levels.
  • Tony Humphries McGill University (Mathematics and Statistics)
    "Sex Specific Mathematical Modelling of Erythropoiesis"
  • The human body produces more than 10^{11} blood cells per day, in a very dynamic process which can be affected by many factors including infection, hypoxia, blood loss and donation, and exogeneous drug administration. Blood cell production takes place in the bone marrow and is difficult to observe directly, while circulating concentrations of mature blood cells are easily measured. This makes hematopoiesis an interesting target for mathematical modelling which was already recognised in the 1970s, and there has been a wealth of mathematical modelling in the last 50 years. However, this modelling almost exclusively ignores sex-specific differences. In this talk we will describe the development of a sex-specific model of erythropoiesis. As well as the need to obtain parameter values for both sexes, the sex specific modelling provides the opportunity to explore some aspects of erythropoiesis which are less well understood, including the affects of male and female sex hormones. We apply our mathematical model to several situations including modelling blood donations for both sexes, while also incorporating the menstrual cycle in the female model. This collaboration started as a project at the 2023 Modelling Sex Differences in Physiology Workshop at the Banff International Research Station.

Mathematical Approaches to Support Women’s Health

Organized by: Ashlee N. Ford Versypt

  • Ying Zhang Brandeis University (Mathematics)
    "Studying the Effects of Oral Contraceptives on Coagulation Using a Mathematical Modeling Approach"
  • The use of oral contraceptives (OCs) is known to increase the risk of thrombosis, but the mechanisms underlying this risk and the determinants of the tests that assess this risk are not fully understood. In this study, we used a mathematical model to study the effects of the OC levonorgestrel (lev) on blood clotting. Lev is reported to change the plasma levels of blood clotting factors. The model simulates coagulation reactions in a small injury under flow, takes clotting factors as inputs and outputs time courses of the coagulation enzyme thrombin. We created a virtual patient population with factor levels before and after lev use that were based on published patient data. After analyzing the simulated thrombin, we found that changes in factor levels due to lev increased the amount and speed of thrombin generation for all virtual patients. This suggested that the factor level changes alone can heighten the prothrombotic state of the model system. We extended the model to include generation of the inhibitor APC so we could test the effects of lev on the systems’ sensitivity to APC. In line with literature reports, the use of lev decreased the APC sensitivity, which correlates with increased thrombosis risk.
  • Susan Rogowski, Alejandra D. Herrera-Reyes, and Yena Kim Florida State University (Mathematics)
    "Parameter Estimation for COVID-19 SVIRD Model Using Predictor-Corrector Algorithm"
  • Stable parameter estimation is an ongoing challenge within biomathematics, especially in epidemiology. Oftentimes epidemiological models are composed of large numbers of equations and parameters. High dimensionality makes classic parameter estimation approaches, such as least square fitting, computationally expensive, and the presence of observational noise and reporting errors that accompany real-time data can make these parameter estimation problems ill-posed and unstable. The recent COVID-19 pandemic highlighted the need for efficient parameter estimation tools. In this paper, we develop a modified version of a regularized predictor-corrector algorithm aimed at stable low-cost reconstruction of infectious disease parameters. This method is applied to a new compartmental model describing COVID-19 dynamics, which accounts for vaccination and immunity loss (from vaccinated and recovered populations). Numerical simulations are carried out with synthetic and real data for COVID-19 pandemic. Based on the reconstructed disease transmission rates (and known mitigation measures), observations on historical trends of COVID-19 in the states of Georgia and California are presented. Such observations can be used to provide insights into future COVID policies.
  • Yeona Kang Howard University (Mathematics)
    "Extended-release Pre-Exposure Prophylaxis and Drug Resistant HIV"
  • The pharmacologic tail of long acting cabotegravir (CAB-LA, injectable PrEP) allows months-long intervals between injections, but it might encourage the growth of drug-resistant HIV strains during the acute infection stage. We present a within-host, mechanistic Ordinary Differential Equation model of the HIV latency and infection cycle in CD4+ T-cells to investigate. We develop a pharmacokinetic/pharmacodynamic model for long acting cabotegravir (CAB-LA, injectable PrEP) to relate the inhibitory drug response to the drug concentration in plasma as well as rectal, cervical, and vaginal fluids and tissue. After validating our model against experimental results, we build in-silico trials. First, we separately administer CAB-LA to the in-silico macaque and human patients prior to and post-SHIV/HIV exposure, to observe SHIV and HIV infectivity dynamics, respectively. The model does not include a mechanism for CAB-LA to generate drug-resistant HIV mutations, but we observe the result when mutations arise naturally. We find CAB-LA may encourage the drug-resistant strain to grow and to outcompete the wild-type in the acute stage. The in-silico trials show that the level of drug resistance, the effectiveness of CAB-LA against the mutations, and the degree of fitness for the mutant strain of virions to infect T-cells determine the course of the drug-resistant strain.
  • Rayanne Luke Johns Hopkins University (Applied Mathematics and Statistics)
    "Towards a mathematical understanding of ventilator-induced lung injury in preterm rat pups"
  • Approximately 1 % of infants are born extremely preterm and are prone to respiratory distress. Typical treatments are less effective for this group and invasive mechanical ventilation applied as a last resort causes trauma, leading to ventilator-induced lung injury (VILI). Further, maternal infection can cause prenatal and neonatal lung infection, inflammation, and often very preterm birth. Inflammation is expected to stiffen the lungs, but exceptions occur, and a complete picture of the mechanisms of stiffening remains unknown. To better understand these mechanisms, we present an application of parameter estimation to a compartment model of pressure-volume lung dynamics along with newly designed image analysis metrics. We also apply optimization to data from a neonatal rat model and identify key parameter differences between healthy and unhealthy groups that may suggest the mechanisms of VILI in infected respiratory systems. Finally, combined analyses of our strategies identify correlations between inflammatory markers and model parameters with no analog in the data, suggesting that mathematical approaches provide an important path towards understanding VILI and infection.

Sub-group contributed talks

OTHE Subgroup Contributed Talks

  • Caleb Mayer University of Michigan
    "Mathematical Modeling of Circadian Rhythms Across Populations with Consumer-Grade Wearable Data"
  • With the rise of wearable technology in recent years, large-scale collections of physiological and behavioral data have become readily available for analysis. Mathematical models can effectively process these increasingly accessible signals, such as heart rate and activity, into information about the circadian rhythm of an individual. One subset of these models predicts circadian phase (often via a limit-cycle oscillator framework) based on the light and/or activity pattern of an individual, while another recently developed method extracts heart rate phase and other information by accounting for circadian variation, the impact of activity, and effects due to other physiological processes. In this talk, we adapt these modeling approaches to examine circadian features across populations, including students, cancer patients, and individuals with COVID-19. We discuss large-scale differences across populations and implications of the models for reducing fatigue and tracking disease progression, using a combination of synthetic and real data in order to test algorithm performance. We develop a real-time anomaly detection framework for identifying abnormal changes such as fever in oscillatory physiological signals. Finally, we explore parameter differences across populations and the effects of parameter perturbations on the models.
  • Edward J Hancock The University of Sydney
    "Modelling the Synchronization of the Membrane and Calcium Clocks in Lymphatic Muscle Cells"
  • Lymphoedema is a common dysfunction of the lymphatic system that results in fluid accumulating between cells. Fluid return through the lymphatic system is primarily provided by contractions of muscle cells in the walls of lymphatic vessels, driven by oscillations in the cell’s membrane potential (M-clock) and calcium ion concentration (C-clock). However, there is an incomplete understanding of the mechanisms involved in these oscillations, restricting the development of pharmacological treatments for dysfunction. Previously, we proposed a minimal model where self-driven oscillations in M-clock drove passive oscillations in the C-clock. Here, we extend this model to the case where the M-clock and the C-clock oscillators are both self-driven and coupled together. The synchronized behaviour enables the model to match experimental M-clock waveforms for both wild-type and knock-out data, resolving issues with previous models. We also use phase-plane analysis to explain the dual-clock coupling. The model has the potential to help determine mechanisms and find targets for pharmacological treatment of lymphoedema.
  • Haniyeh Fattahpour Georgia State University
    "Mathematical modeling of cell growth in a tissue engineering scaffold pore"
  • A tissue engineering scaffold is composed of pores lined with cells that allow nutrient-rich culture medium to pass through, thereby encouraging the proliferation of cells. Growth of the tissue is affected by a number of factors, including the flow rate and concentration of nutrients in the feed, the elasticity of the scaffold, and the properties of the cells. Many studies have examined these factors separately, but in this project, we aim to examine all of them together. In this work, we (i) develop a mathematical model that describes the dynamics and concentration of nutrients, scaffold elasticity, and cell proliferation; (ii) solve the model and simulate the cell proliferation process; (iii) develop a reverse algorithm that determines the initial scaffold pore configuration based on the desired geometry of the final tissue.
  • Yue Wu Stanford University
    "Classify dynamic responses to food through time-series glucose data"
  • Monitoring of health status is complex, and the common approach focuses on one-time measurement of clinical markers during a visit with a healthcare professional. This is not ideal as the physiological states are proven to change dynamically in response to daily activities (e.g., eating and exercise). For type 2 diabetes and prediabetes patients, continuous glucose monitoring (CGM), as well as monitoring of physical activities and sleep provide important information for individualized intervention suggestions. Here, we incorporated the novel and noisy real-life CGM measurements to evaluate the personal responses to 7 different types of carbohydrates and 3 different nutrients (fat, protein, and fiber) that tend to mitigate glucose spikes individually in 43 participants. We built a computational workflow to clean the data, removed errors from manual records and time zone shifts in traveling, and provided quality control for future data. We then viewed the data through smoothing, dimensionality reduction, and clustering. We discovered consistent separating patterns from common carbohydrates, with rice and beans being the two extremes. We discovered interesting individual responses to the additional mitigators, which indicate the importance of personalized intervention in diabetes.

OTHE Subgroup Contributed Talks

  • Chengyue Wu University of Texas at Austin
    "Optimization of a longitudinal imaging protocol to monitor the response of breast cancer to neoadjuvant therapy via Bayesian-based data assimilation"
  • Introduction: Neoadjuvant therapy (NAT) is considered the standard-of-care for locally advanced breast cancer. Recent studies indicated that magnetic resonance imaging (MRI) data acquired after the first 1-3 cycles of NAT can provide early prediction of breast cancer patient response. However, it remains to be determined when the best times are to collect the longitudinal images to maximize both predictive accuracy and patient convenience. In this study, we seek to establish an in silico framework to address this unmet need by integrating mechanism-based mathematical modeling with Bayesian-based data assimilation. Methods: A TNBC cohort (n = 139) from the ARTEMIS trial was used for this study. For each patient, longitudinal MRIs were collected before (MRI1), during (MRI2), and after (MRI3) the Adriamycin/Cyclophosphamide (A/C) NAT regimen. We have developed a mechanism-based mathematical model to make patient-specific predictions of TNBC response to the A/C therapy. In particular, the model is a reaction-diffusion equation describing the spatiotemporal change in tumor cellularity due to cell migration, proliferation, and treatment-induced death. We implemented the model with a Bayesian-based scheme: Using MRI1 for initialization and MRI2 for calculating the posterior distributions of model parameters, then making predictions at the end of A/C. The standard derivation (SD) of the predicted tumor volume was defined as the uncertainty. The difference between the mean of the predicted tumor volume and the MRI3 measurement was defined as the error. We then optimized to find the optimal day for collecting MRI2 that reduced the uncertainty and error of the model prediction at the completion of A/C. In particular, we generated synthetic data at candidate time points (termed MRI2*; i.e., time points at which we may want to collect additional MRI data) by fitting the model to all collected MRIs, recalibrated the model with the synthetic data MRI2* to make prediction at the completion of A/C, and then evaluated the corresponding prediction uncertainty and error. The date for MRI2* that minimized the prediction uncertainty and error is determined to be the optimal time point for the second imaging session. Results: Preliminary implementation and tests were performed on one patient with tumor volumes derived from the imaging data. The Bayesian-based scheme calibrated the model using the clinically measured MRI1 and MRI2 (i.e., MRI2 at day 30). Comparing the model prediction of the residual tumor volume to the measurement of MRI3, the prediction uncertainty and error were 24.72% and 32.64%, respectively. The identified optimal time point for the mid-treatment imaging session, MRI2* at day 38, provided a minimal prediction uncertainty and error of 13.02% and 7.55%, respectively. Thus, the optimized date for the second MRI resulted in a 47.33% decrease in uncertainty and a 76.87% decrease in error for predicting the residual tumor volume at the end of A/C. Conclusion: These preliminary results demonstrate that our approach has the potential to identify the optimal time point for the second MRI scan of a longitudinal MRI protocol to improve the precision and accuracy of early prediction of TNBC patient response to NAT. Ongoing efforts include extending the implementation to 3D and applying it to more patients. Acknowledgments: NCI U01CA142565, U01CA174706, U24CA226110. CPRIT RR160005. Clinical trial NCT02276443. MDACC Moon Shot Program. MDACC-TACC-Oden Institute Consortium Pilot Project.
  • Cole Butler North Carolina State University
    "Partially functional resistance in gene drive control"
  • Gene drives (GDs) allow scientists to spread a genetic cargo into a target population, even if the cargo is harmful to the carrier organism. GD technology has immense promise in everything from conservation efforts to the control of mosquito-borne diseases. To spread, GDs exploit DNA repair mechanisms to duplicate themselves at the expense of a target gene. However, repair does not always occur as intended, and can produce alleles that are resistant to the GD. Resistance is one of the greatest threats to GD use in the wild and is difficult to study at appropriate scales within laboratory experiments. Current approaches to studying resistance have predominantly relied on a binary paradigm: resistant alleles are either functional or non-functional. Neither resistant allele can be targeted by the GD construct but only the former restores proper genetic functioning to the organism. In this study, we consider the contribution of resistant alleles that are partially functional, and therefore fall outside this paradigm. Partially functional resistance occurs when a resistant allele restores some—but not all—genetic functioning to the organism. Organisms carrying such alleles do not spread the GD as efficiently but may still incur heavy fitness costs. Using a coupled genetic population dynamics model, we study GD performance in a target population with partially functional resistance. In addition to extending the current theoretical framework used to study resistance, we also study the roles played by certain DNA repair mechanisms, making our work generalizable to many target organisms. We pay particular attention to GD performance in certain mosquito species of interest, such as the malaria mosquito Anopheles gambiae, and the dengue mosquito Aedes aegypti. This work provides a key next step in understanding how the mechanisms behind resistance can help or hinder GD success. Furthermore, our work can inform the development of GDs going forward so as to mitigate the risk of control failure due to resistance arising in target populations.
  • Daniel Cooney University of Pennsylvania
    "A PDE Model for Protocell Evolution and the Origin of Chromosomes via Multilevel Selection"
  • The origin of chromosomes was a major transition in the evolution of complex cellular life. In this talk, we model the origin of chromosomes by considering a simple protocell composed of two types of genes: a “fast gene' with an advantage for gene-level self-replication and a “slow gene' that replicates more slowly at the gene level, but which confers an advantage for protocell-level reproduction. Using a PDE to describe the effects of within-cell and between-cell competition, we find that the gene-level advantage of fast replicators casts a long shadow on the multilevel dynamics of protocell evolution: no level of between-protocell competition can produce coexistence of the fast and slow replicators when the two genes are equally needed for protocell-level reproduction. We find that introducing a “dimer replicator', a linked pair of the slow and fast genes, can allow for long-time coexistence under multilevel competition between fast, slow, and dimer replicators. Our results suggest that the formation of a simple chromosome-like dimer replicator can help to overcome the shadow of lower-level selection and work in concert with multilevel selection to promote coexistence of genes that compete under gene-level replication but are synergistic at a higher level of selection.
  • Hayden Fennell Indiana University Bloomington
    "Computational Apprenticeship: A Constructivist Approach for Teaching Modeling and Simulation"
  • Over the past two decades, there has been growing recognition of the need for discipline-situated computational modeling and simulation pedagogy in post-secondary STEM curricula. However, current research in this area remains largely definitional and aspirational in nature, as there are limited empirical studies on how to best support the development of computational expertise in undergraduate students. Outside of computer science programs, a student's exposure to computing education often remains siloed within introductory programming courses that lack meaningful integration with disciplinary content. Furthermore, current practice in early undergraduate computational education in engineering programs tends to focus heavily on the procedural and technical aspects of programming knowledge rather than on the application of computation to problem-solving and design. Because the field of discipline-based computation is under-theorized, traditional instructional approaches have typically defaulted to teaching the cognitive aspects of computation. To build transferable skills and expertise, however, instructors can draw upon constructivist traditions by situating computation within disciplinary contexts. This talk presents computational apprenticeship (an application of the cognitive apprenticeship framework) as a constructivist research and practice framework for developing transferable computational expertise in the undergraduate STEM curriculum. Aspects of the computational apprenticeship model in practice are illustrated using examples from computational biology.

Sub-group poster presentations

OTHE Posters

Carolin Malsch University of Greifswald
Poster ID: OTHE-01 (Session: PS01)
"Performance Analysis for Parameter Estimators in Pharmacokinetics"

Classical compartment models of pharmacokinetics are represented by deterministic kinetic equations and embedded in a probability theoretical context in terms of residence time random variables. Several parameter estimation and test methods are available to estimate related model parameters. The aim of this study is to examine the performance of these methods in the context of individual and population pharmacokinetics. A simulation study for four standard compartment models for individual and population pharmacokinetics is conducted assessing the performance of the parameter estimation methods (a) minimum least squares, (b) maximum likelihood, and (c) minimum chi-squared estimation, as well as for the Chi-squared goodness of fit test. Performance measures include bias and standard error for the parameter estimators, and error probabilities for the Chi-squared test. In the simpler compartment models and given an appropriate choice of measurement time points, all three estimators show satisfying results with regard to bias and standard error. Parameter estimates are asymptotically normal distributed. Further, distribution of the Chi-squared test statistic approaches the Chi-squared distribution asymptotically. In case of non-optimal choice of measurement time points, performance is poor for all estimation methods. Maximum likelihood method appears to be most robust for parameter estimation, but subsequent Chi-squared test statistic fails to asymptotically approach the Chi-squared distribution. In the more complex compartment models, minimum Chi-squared estimation appears to be most robust with regard to test errors of subsequent Chi-squared goodness of fit test. For minimum least squares and maximum likelihood parameter estimation, subsequent Chi-squared test statistic shows severely distorted error probabilities, suggesting that the asymptotic distribution of the Chi-squared test statistic is not the Chi-squared distribution. Performance depends on the underlying model and the measurement time points in relation to the speed of elimination and dosage of the pharmakon. A simulation study can help to decide upon which method is most suitable in the application case.

Isaac Klapper Temple University
Poster ID: OTHE-02 (Session: PS01)
"Coupling Metabolic and Community Scale Models for Microbial Communities"

Outside of laboratories, microbial communities (biofilms and other types) often exist in relatively stable environments where, on average, resource quality and quantity are predictable. Under such conditions, these communities are able to organize into tuned chemical factories, efficiently turning resources into biomass and waste byproducts. To do so, community scale physical, chemical, and biological constraints must be accommodated. At the cell scale, extensive omics data has enabled detailed, genome scale (GEM) modeling of metabolic response to chemical conditions. These two scale are coupled of course. Techniques to connect GEMs to community scale transport processes will be presented.

Laura Wadkin Newcastle University
Poster ID: OTHE-03 (Session: PS01)
"Exploring the lived experiences of female-identifying mathematics PhD students"

Women and other gender minorities are still under-represented in academic mathematics, with only 20% non-cis-male PhD students and 6% non-cis-male professors in the UK (London Mathematical Society’s Good Practice Report). Here we will present the results from a study at Newcastle University UK which explored the lived experiences of female-identifying mathematics PhD students through a series of one-to-one interviews. We seek to understand the extent to which the participants feel their gender has impacted their experiences as mathematics PhD students, including their relationships with supervisors, their view of role models, their identity as a mathematician, and their post-PhD choices.

Richard Foster Virginia Commonwealth University
Poster ID: OTHE-04 (Session: PS01)
"Thoracoabdominal asynchrony in a virtual preterm infant: computational modeling and analysis"

Thoracoabdominal asynchrony (TAA), the asynchronous volume changes between the rib cage and abdomen during breathing, is associated with respiratory distress, progressive lung volume loss, and chronic lung disease in the newborn infant. Preterm infants are prone to TAA risk factors such as weak intercostal muscles, surfactant deficiency, and a flaccid chest wall. The causes of TAA in this fragile population are not fully understood and, to date, the assessment of TAA has not included a mechanistic modeling framework to explore the role these risk factors play in breathing dynamics and how TAA can be resolved. We present a dynamic compartmental model of pulmonary mechanics that simulates TAA in the preterm infant under various adverse clinical conditions, including high chest wall compliance, applied inspiratory resistive loads, bronchopulmonary dysplasia, anesthesia-induced intercostal muscle deactivation, weakened costal diaphragm, impaired lung compliance, and upper airway obstruction. Sensitivity analyses performed to screen and rank model parameter influence on model TAA and respiratory volume outputs show that risk factors are additive so that maximal TAA occurs in a virtual preterm infant with multiple adverse conditions, and addressing risk factors individually causes incremental changes in TAA. An abruptly obstructed upper airway caused immediate nearly paradoxical breathing and tidal volume reduction despite greater effort. In most simulations, increased TAA occurred together with decreased tidal volume. Simulated indices of TAA are consistent with published experimental studies and clinically-observed pathophysiology, motivating further investigation into the use of computational modeling for assessing and managing TAA.

Steve Manns Ohio State University
Poster ID: OTHE-05 (Session: PS01)
"Patterns of Homeostasis in Input-Output Networks"

Homeostasis is a regulatory mechanism by which a distinguished output variable remains approximately constant as an external input parameter varies over an interval. When perceived from a mathematical perspective, a natural interpretation of this phenomenon is that the derivative of the output variable with respect to the external input parameter vanishes. In the recent literature, this interpretation of homeostasis has been called 'infinitesimal homeostasis' and has the advantage that it allows one to apply results from singularity theory. While there are a variety of interesting questions one can try to answer using this theory, the question taken up in this project is: 'What can one say about which variables in a given network exhibit infinitesimal homeostasis along with the output variable?' Such questions relate to patterns of homeostasis in input-output networks, and our goal is to provide an answer based on rigorous mathematics.

Organizing committee
  • Laura Kubatko, chair
  • Adriana Dawes
  • Mary Ann Horn
  • Janet Best
  • Adrian Lam
  • Grzegorz Rempala
  • Will Gehring
Scientific organizing committee
  • Adriana Dawes
  • Mary Ann Horn
  • Jane Heffernan
  • Hayriye Gulbudak
  • Jeffrey West
SMB 2023 is being held on the campus of The Ohio State University. As visitors to campus, all SMB participants must follow The Ohio State University Policy on Non-Discrimination, Harassment, and Sexual Misconduct.

Organizing committee
  • Laura Kubatko, chair
  • Adriana Dawes
  • Mary Ann Horn
  • Janet Best
  • Adrian Lam
  • Grzegorz Rempala
  • Will Gehring
Scientific organizing committee
  • Adriana Dawes
  • Mary Ann Horn
  • Jane Heffernan
  • Hayriye Gulbudak

  • Jeffrey West

SMB 2023 is being held on the campus of The Ohio State University. As visitors to campus, all SMB participants must follow The Ohio State University Policy on Non-Discrimination, Harassment, and Sexual Misconduct.