Wednesday, June 16 at 05:45pm (PDT)
Thursday, June 17 at 01:45am (BST)
Thursday, June 17 09:45am (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 MS14-CBBS.

  • Ariel Nikas (Emory University, School of Medicine, United States)
    "Using morphoelasticity to model early lung branching"
  • Morphoelasticity, an emerging area of continuum mechanics, can describe the large strains of organogenesis. We apply this framework modeling lung branching. Many previous models of lung branching morphogenesis were focused on the complex morphogen signaling systems and either omit explicit modeling of shape change, or model shape change by moving a surface normal to itself without explicit mechanics equations. Previous models have shown that morphogen flux distribution corresponds to the location of branching, and that this distribution is reliant on local geometry. We explicitly modeled both the morphogen signaling and the resulting growth dependent on the calculated morphogen flux distribution, in a novel application of morphoelastic shell modeling for lung growth. We concluded that local geometry affects the resulting shape change. Specifically, we observed tubule lengthening for all local geometries and shouldering for epithelium of elliptical cross-section. We also observed that the thickness of the epithelium affects the resulting shape change. This modeling approach of shell mechanics combined with morphoelasticity allowed us to test complex hypotheses on growth and can be generalized for many other organ systems.
  • Mona Eskandari (University of California at Riverside, United States)
    "Characterizing pulmonary mechanics using an experimental-computational framework"
  • COVID-19 has driven respiratory biomechanics to the forefront. Classified now as an endemic, investigative pulmonary research using computational biomechanical models is central to gaining predictive insights regarding fundamental lung physiology. The complex and hierarchical structure of the lung challenges advancements, given the bulk mechanical behavior representation is disconnected from its local tissue response. We address this knowledge gap by introducing the first structural inverse finite element model of the breathing lung using a reduced order surface representation. Using a custom-designed apparatus to imitate inflation and deflation in the ex-vivo lung, we interface the system with large deformation digital image correlation capabilities to ultimately link local strains to inflation volumes and pressures, compounding the role of the intricate bronchial network, parenchymal tissue, and visceral pleura behavior. An optimized heterogenous and hyperelastic continuum model employing adjoint methods accurately captures the experimentally observed topological lung surface strain distributions for varying pressure levels. This novel multiscale framework can facilitate in-silico explorations to improve ventilation strategies and examine how chronic disease endurance modifies the lung's load-bearing biomechanics.
  • Ramana Pidaparti (University Of Georgia Athens, United States)
    "Computational Models and Informatics for Lung Inflammation and Aging"
  • At Design Informatics and Computational Engineering (DICE) laboratory in the College of Engineering at UGA, quantitative analysis through airway lung models and informatics, computations and imaging data that correlates to inflammation, disease and aging is being conducted. A multi-scale model for cellular inflammation was developed for compliant lung geometry under mechanical ventilation by investigating respiratory mechanics at the organ, tissue and cellular levels. The cluster analysis of lung simulation data revealed that the clusters of airway strain data are correlated to airflow characteristics. The results from the inflammation model indicated that for the strain conditions considered, the model is capable of predicting the innate healing capacity of the tissue. Overall, the airway mechanical characteristics as well as lung function are compromised (about 40%-50%) due to aging. This talk provides an overview of the research at DICE lab in the College of Engineering at the University of Georgia.
  • Uduak George (San Diego State University, United States)
    "Mathematical modeling of fibroblast growth factor expression in developing lungs"
  • Fibroblast growth factor 10 (Fgf10) is a key regulator of lung development. Fgf10 is expressed at the sub-mesothelium, distal to the branching epithelial structures. Despite enormous progress in understanding the mechanisms that control lung development, the factors that determine the spatio-temporal expressions of Fgf10 are not well understood. In this study, we implemented a novel method to study Fgf10 expression at the lung mesothelium by using a system of surface reaction-diffusion equations. Numerical approximation of the equations was carried out by using the surface finite element method. Simulations of Fgf10 expression were done on murine lungs segmented from three-dimensional confocal microscopy images. Our simulation results reproduced some of the reported Fgf10 expression patterns from wet lab experiments available in the literature. The model identified the rate of reaction of Fgf10 and Fgf10 inhibitors as a possible key parameter in the regulation of Fgf10 expression. It also identified the size of the lung mesothelium, as a possible regulator of Fgf10 expression during murine lung morphogenesis.

Modeling of energy-utilizing biopolymers

Organized by: Holly Goodson (University of Notre dame, USA), Shant Mahserejian (Pacific Northwest National Laboratory, USA)

  • Jared Scripture (University of Notre Dame, USA)
    "Quantification of Microtubule Stutters: Dynamic Instability Behaviors that are Strongly Associated with Catastrophe"
  • Microtubules (MTs) are cytoskeletal fibers that undergo dynamic instability (DI), a remarkable process involving phases of growth and shortening separated by stochastic transitions called catastrophe and rescue. Dissecting dynamic instability mechanism(s) requires first characterizing and quantifying these dynamics, a subjective process that often ignores complexity in MT behavior. We present a Statistical Tool for Automated Dynamic Instability Analysis (STADIA), which identifies and quantifies not only growth and shortening, but also a category of intermediate behaviors that we term ‘stutters.’ During stutters, the rate of MT length change tends to be smaller in magnitude than during typical growth or shortening phases. Quantifying stutters and other behaviors with STADIA demonstrates that stutters precede most catastrophes in our dimer-scale MT simulations and in vitro experiments, suggesting that stutters are mechanistically involved in catastrophes. Related to this idea, we show that the anti-catastrophe factor CLASP2γ works by promoting the return of stuttering MTs to growth. STADIA enables more comprehensive and data-driven analysis of MT dynamics compared to previous methods. The treatment of stutters as distinct and quantifiable DI behaviors provides new opportunities for analyzing mechanisms of MT dynamics and their regulation by binding proteins.
  • Diana White (Clarkson University, USA)
    "Modelling microtubule dynamic instability: microtubule growth, shortening and pausing"
  • Microtubules (MTs) are protein polymers which help form the cytoskeleton of all eukaryotic cells. They are crucial for normal cell development, providing structural support for cells, aiding in cell polarization, as well as aiding in cell motility and division. In order to perform these functions, MTs take on different organizations, in addition to being very dynamic. In particular, MTs go through random periods of relatively slow polymerization (growth) followed by very fast depolymerization (shrinkage), a unique type of dynamics called dynamic instability. The onset of a MT shrinking event is called a catastrophe, while the event at which a MT starts to grow again is called a rescue. Although MT dynamic instability has traditionally been described solely in terms of growth and shortening, MTs have also been shown to pause for extended periods of time. Here, we present a novel mathematical model to describe dynamic instability of MTs in terms of growth, shortening and pausing. Our model is a coupled PDE model, that describes length variations in polymerized tubulin (those growing, shrinking, and pausing), with an ODE model to describe the temporal dynamics of free tubulin. Here, we explore how MT dynamics, and in particular MT catastrophe frequency, is altered in the presence of a pausing/quiescent phase, and compare these results with experimental findings.
  • Kimberly Weirich (Clemson University, USA)
    "Self-organization and shape change in active biopolymer droplets"
  • Complex mixtures of macromolecules self-organize to form the soft and active biological materials that structure the cellular cytoplasm. Ordered assemblies of cytoskeletal filaments, such as stress fibers and mitotic spindles, orchestrate the complex mechanical behavior of cells. Key to understanding these exquisite mechanics is elucidating the physical principles of self-organization in these systems. We recently reported dense condensates of cytoskeletal filaments that form liquid crystal condensed phases, where structure arises from the anisotropy of the filaments. Here, we discuss emergent self-organization and shape changes that result from forming composites of these liquid crystals with biological polymers of different rigidities and activity. Our results highlight the role of anisotropy in the self-organization of biological materials and suggest physical mechanisms of controlling shape change in bio-inspired, soft materials.
  • Sidney Shaw (Indiana University, USA)
    "Extracting local polymer dynamics for global cellular models."
  • Eukaryotic cells create dynamic polymer systems that affect a wide variety of critical cellular functions. The microtubule polymers in plant cells, for example, form patterns at the cell cortex that template the deposition of cellulose into the nascent primary wall with subsequent effects on the wall material properties that govern cell expansion. A key factor in creating and maintaining the patterned microtubule array is the persistent addition of tubulin subunits to the microtubule ‘plus’ end, with concurrent loss of subunits from the ‘minus’ end, affecting a form of polymer treadmilling that is critical to microtubule array patterning in this system. Prior simulations of this microtubule system coming to a steady-state with a fixed subunit number and cell volume indicated that the frequency of stochastic switching between states of plus-end growth and shortening, termed catastrophe, should critically impact all facets of the steady state polymer system. To further investigate the nature and conditions under which catastrophe occurs, we developed high temporal/spatial in vivo microscopy methods for examining the dynamic properties of cortical microtubules in super-resolved detail. Using model- based tracking algorithms, we observe that polymer growth shows a spectrum of intermediate growth states with transitions from growth to shortening being preceded by a bona fide pause state. Using high temporal resolution data, we find that the decision to resume growth or to catastrophe into depolymerization is temporally consistent with the conversion of GTP-tubulin at the microtubule plus end to GDP-tubulin through stochastic hydrolysis. In cells lacking expression of a known microtubule binding protein, we find evidence that the rate of GTP hydrolysis for tubulin subunits binding to the microtubule plus end differs significantly from wild type. Using computational modeling approaches to compare these systems, we provide evidence that plant cells modulate the tubulin GTPase rate constant in order to control the persistence of plus end growth and the frequency of microtubule catastrophe in this treadmilling system. These data are now being used to revise our cellular scale models for understanding how these microtubule achieve and maintain a steady-state microtubule array.

Modelling and Methods in Mathematical Biology

Organized by: Anthony Kearsley (National Institute of Standards and Technology, USA)

  • Julia Seilert (Department of Food Process Engineering, Technische Universität Berlin, Germany)
    "Revisiting a model to predict pure triglyceride thermodynamic properties: parameter optimization and performance"
  • Understanding the thermodynamic properties of triglycerides and their mixtures is of major importance for food applications. Extensive experimental studies and mathematical modeling are needed to predict thermodynamic properties, namely melting temperature and enthalpy of fusion. To date, the most comprehensive work towards modeling triglyceride pure component properties was conducted by Wesdorp in “Liquid-multiple solid phase equilibria in fats: theory and experiments” (1990) building a semi-empirical model with a large set of parameters. The model generally performs well but is known to make thermodynamically inconsistent predictions for certain test cases. In this study, the underlying parameter set is improved in order to deliver more physically consistent predictions without deterioration of the primary model quality to describe the available experimental data. Thermodynamic constraints as well as bound constraints on variables are discussed regarding an interrelation of the model setup conditions.
  • Adarsh Kumbhari (School of Mathematics and Statistics, University of Sydney, Australia)
    " Modeling PD-L1 inside the tumor microenvironment"
  • The protein PD-1 and its ligand PD-L1 are upregulated on cancerous and immune cells within tumors, and blocking this pathway may induce anti-tumor immunity. The extent to which PD-L1 expression reflects immune activity, however, is poorly understood. Using mathematical modeling, we show that high PD-L1 expression can reflect both tumor escape and clearance. We also identify several T-cell populations that may better reflect dynamic changes to the tumor microenvironment. These findings suggest that moving beyond measuring PD-L1 expression could lead to better ways to predict patient responses to PD-L1 blockade.
  • Danielle Brager (National Institute of Standards and Technology, USA)
    "Mathematically Investigating Retinitis Pigmentosa"
  • Retinitis Pigmentosa (RP) is a collection of clinically and genetically heterogeneous degenerative retinal diseases. Patients with RP experience a loss of night vision that progresses to day-light blindness due to the sequential degeneration of rod and cone photoreceptors. While known genetic mutations associated with RP affect the rods, the degeneration of cones inevitably follows in a manner independent of those genetic mutations. Investigation of this secondary death of cone photoreceptors led to the discovery of the rod-derived cone viability factor (RdCVF), a protein secreted by the rods that preserves the cones by accelerating the flow of glucose into cone cells stimulating aerobic glycolysis. In this work, we formulate a predator-prey style system of nonlinear ordinary differential equations to mathematically model photoreceptor interactions in the presence of RP while accounting for the new understanding of RdCVF's role in enhancing cone survival. We utilize the mathematical model and subsequent analysis to examine the underlying processes and mechanisms (defined by the model parameters) that affect cone photoreceptor vitality as RP progresses. The physiologically relevant equilibrium points are interpreted as different stages of retinal degeneration. We determine conditions necessary for the local asymptotic stability of these equilibrium points and use the results as criteria needed to remain in a stage in the progression of retinal degeneration. Experimental data is used for parameter estimation. Pathways to blindness are uncovered via bifurcations and narrows our focus to four of the model equilibria. We perform a sensitivity analysis to determine mechanisms that have a significant effect on the cones at four stages of RP. We derive a non-dimensional form of the mathematical model and perform a numerical bifurcation analysis using MATCONT to explore the existence of stable limit cycles because a stable limit cycle is a stable mode, other than an equilibrium point, where the rods and cones coexist. In our analyses, a set of key parameters involved in photoreceptor outer segment shedding, renewal, and nutrient supply were shown to govern the dynamics of the system. Our findings illustrate the benefit of using mathematical models to uncover mechanisms driving the progression of RP and opens the possibility to use in silico experiments to test treatment options in the absence of rods.
  • Anca Radulescu (State University of New York at New Paltz, USA)
    "Estimating glutamate transporter surface density in mouse hippocampal astrocytes"
  • One of the main functions of astrocytes is to remove glutamate from the extracellular space, a task that is accomplished through the activity of glutamate transporters expressed in abundance in the plasma membrane. This property allows astrocytes to limit glutamate diffusion out of the synaptic cleft, to limit extrasynaptic receptor activation and preserve the spatial specificity of synaptic transmission. The distribution of glutamate transporters on is known to be heterogeneous, as these molecules are enriched in astrocyte tip processes as opposed to the rest of the membrane. We investigate in depth the effect of this non-uniform distribution, while also evaluating how local crowding effects can limit the transporter expression in small astrocytic processes. We first obtain an experimental estimate of the glutamate transporter surface expression in different sub-cellular compartments of mouse hippocampal astrocytes. We then generate a geometric model of astrocytes that capture statistically the main structural features of real astrocytes, to determine the proportion of the astrocyte cell membrane in different cellular compartments. We found stark differences in the density of expression of transporter molecules in different compartments, indicating that the extent to which astrocytes limit extrasynaptic glutamate diffusion depends not only on the level of astrocytic coverage, but also on the identity of the compartment in contact with the synapse. Together, these findings provide information on the spatial distribution of glutamate transporters in the mouse hippocampus, with potentially long-range implications for the fields of synaptic plasticity and astrocyte physiology.

Modeling and Simulation of Hydrodynamics in Cell Biology

Organized by: Thomas Fai (Brandeis University, USA), Ying Zhang (Brandeis University, USA)

  • Paul Atzberger (UC Santa Barbara, USA)
    "Surface Fluctuating Hydrodynamics Approaches for Proteins Kinetics and Transport within Curved Lipid Bilayer Membranes"
  • We introduce surface fluctuating hydrodynamics approaches for investigating transport and fluid-structure interactions arising in cell mechanics within curved lipid bilayer membranes. We focus particularly on drift-diffusion dynamics of interacting proteins and microstructures. We show how a mesoscale stochastic description of the mechanics can be formulated (SPDEs) accounting for geometric contributions, hydrodynamic coupling, and thermal fluctuations. The underlying stochastic equations (SPDEs) pose practical challenges for use in simulations, including, (i) a need for accurate and stable discretizations of geometric terms and differential operators on curved geometries, (ii) techniques for hydrodynamics handling surface incompressibility constraints, and (iii) stiffness from rapid time-scales introduced by the thermal fluctuations. We show how practical spectral methods and meshfree computational approaches can be developed for simulations over long spatial-temporal scales. We then present results for protein and microstructure interactions within membranes and the roles played by hydrodynamic coupling and geometry.
  • Luoding Zhu (Indiana U-Purdue U Indianapolis, USA)
    "Modeling and simulation of fluid flow over osteocyte"
  • Bone’s structure, development, and remodeling are highly complex. Bone is permeated by an intricate system of interconnected canals (lacuno-canalicular network) that are filled with interstitial fluid and connect mechanosensing osteocytes. These networks multiply macroscale strains that occur during normal motion (e.g. walking or running) approximately tenfold by the time they reach the osteocytes. The amplification mechanism is still not well characterized. Due to the extreme complexity of the osteocyte-fluid-lacuno-canalicular system and the hard bone that encases the system, in-vivo laboratory experiments are challenging to conduct. Mathematical modeling, however, can provide a viable approach for shedding insights into the force amplification that occurs in the system. We introduce two mathematical models for modeling and simulation of fluid- osteocyte interaction. The first models fluid-osteocyte interactions in a lacuna- canalicular network in two dimensions by using the lattice Boltzmann approach. The model considers the influence of the number and geometry of the canaliculi on the wall shear and wall normal stress on the osteocyte. The second models an osteocyte exposed to viscous shear flow in three dimensions by using the immersed boundary approach. The osteocyte is represented by a network of fibers constructed based on images taken during experiments. The model considers how force is distributed throughout the osteocyte when external forcing is applied to the cell. These studies are ongoing and we will report our current progress on these efforts.
  • Nicholas Chisholm (Worcester Polytechnic Institute, USA)
    "Novel Regularized Stokeslets for Biological Fluid Flow Problems"
  • The method of regularized Stokeslets is well suited for simulating micro-scale biological fluid dynamics. Over the past two decades, it has proven very useful for describing the locomotion of microorganisms and the fluid-structure interactions of propulsive organelles such as cilia and flagella. However, there are many possible choices for regularizing the (singular) fundamental solution to the Stokes equations (the 'Stokeslet'), and this choice often requires tailoring to the specific problem at hand for best results. In this talk, we generate regularized Stokeslets using their associated biharmonic and vector potentials. These regularized Stokeslets are automatically divergence free, and they may be chosen to be equivalent (or arbitrarily close) to the singular Stokeslet outside a small region surrounding the point of forcing. Regularized Stokeslets having this latter property may be especially useful with known image systems for, e.g., the flow inside of a spherical cavity because boundary conditions at the cavity boundary may be satisfied exactly. We validate the usefulness of these regularized Stokeslets by quantifying their behavior for well-known problems such as flow due to the motion of a rigid cylinder/sphere and of thin, flexible filaments (e.g., cilia). We anticipate that our method will be useful for simulating intracellular forces and fluid flows during active cellular processes such as mitosis.
  • Thomas Fai (Brandeis University, USA)
    "Hydrodynamics of cell suspensions near walls"
  • Many real-world examples of fluid-structure interaction, such as the motion of red blood cells through blood vessels, involve the near-contact of elastic structures with boundaries. We use the immersed boundary method to simulate the interactions of deformable objects with walls. In practice, the near-contact with the wall and resulting lubrication layer are often under-resolved, and we show how certain formulations of the boundary conditions lead to spurious behaviors. We show how the lubricated immersed boundary method can be used to increase the accuracy of simulations in the case of dense cell suspensions, in which near-contact occurs through cell-wall, cell-cell, and intracellular interactions.

Modelling the combination of vaccination and Non-pharmaceutical interventions strategies to control COVID-19 propagation

Organized by: Jacques Bélair (Université de Montréal, Canada) & Elena Aruffo (York University, Canada)

  • Matthew Betti (Mount Allison University)
    "Combining data forecasting with scenario-based modeling for insights into a rapidly changing outbreak situation"
  • We present a simple, modified SIR model with the intended use of bridging the gap betweeen data-fitted forecasts and modeled scenario-based forecasting. Using a combination of data-driven forecasting, simple model structures, and ensemble fitting we are able to determine mid-range predictions for rapidly changing situations. Using results over the past year on COVID-19 we will highlight the strengths of such an approach when it comes to forecasting trajectories and how this can be used to help policy and decision making.
  • Marina Mancuso (Arizona State University)
    "Will Cross-Immunity Protect the Community Against COVID-19 Variants ?"
  • Several effective vaccines are currently being deployed to combat the COVID-19 pandemic (caused by SARS-CoV-2) around the world, resulting in significant reduction in the burden of the pandemic in places with high enough coverage. The effectiveness of COVID-19 vaccination programs is, however, significantly threatened by the emergence of new SARS-COV-2 variants that, in addition to being more transmissible and potentially more virulent than the resident strains, may at least partially evade existing vaccines. This talk is based on the use of a new multigroup and multi-strain mechanistic mathematical model for assessing the impact of the vaccine-induced cross-protective efficacy on the spread of the COVID-19 pandemic in the United States. In addition to estimating the vaccine-derived herd immunity threshold for the US, I will discuss conditions for which a new SARS-CoV-2 variant can fail to, or have the potential to, cause a significant surge in the US.
  • Elena Aruffo (York University)
    "Vaccination rollout and relaxation of non-pharmaceutical interventions: a combined approach"
  • After months of implementation of non-pharmaceutical interventions to control the spread of SARS-CoV-2 infection, in December 2020 many countries began COVID-19 vaccination campaigns. Over the past few months, the vaccination coverage in Toronto, Canada increased visibly, leading to high immunization levels among certain age groups. In collaboration with Toronto Public Health, the Canadian Centre for Disease Modeling modeling group employed a deterministic structured compartmental model to investigate the current immunization status in Toronto and explore potential strategies for safe reopening, given various degrees of vaccine coverage by age group, in order to maximize reductions in cases, hospitalizations and deaths. We further examined the impact of different time intervals between the first and second vaccine dose on the aforementioned outcomes.
  • Nicola Perra (University of Greenwich)
    "Modelling the COVID-19 pandemic at different spatio-temporal scales"
  • In the talk, I will provide an overview of different approaches I have applied to model the unfolding of the COVID-19 pandemic and its effects. In doing so, I will discuss the insights obtained by studying the initial phases of the pandemic, the first wave, and the vaccine rollout in the USA, Europe as well as Latin America. I will also discuss the key role of non-pharmaceutical interventions.

Modeling containment and mitigation of COVID-19: experiences from different countries worldwide

Organized by: Andrei Akhmetzhanov (National Taiwan University College of Public Health, Taiwan), Natalie Linton (Hokkaido University, Japan)
Note: this minisymposia has multiple sessions. The second session is MS12-MEPI.

  • Jonathan Dushoff (McMaster University, Canada)
    "Defining, estimating and applying transmission-interval distributions"
  • The spread of epidemics is structured by delay distributions, including the now-famous “serial interval” between the symptom-onset times of an infector and an infectee (often conflated with the “generation interval” between infection times). Defining these time distributions clearly, and describing how they relate to each other, and to key parameters of disease spread, poses interesting theoretical and practical questions, some of which are still open. I will discuss how transmission intervals link the “speed” and “strength” of epidemics, issues in their estimation, and their role in helping monitor changes in the parameters underlying the spread of COVID-19 disease.
  • Sarah Kada (Centers for Disease Control and Prevention (CDC), U.S.A.)
    "Early assessment of SARS-CoV-2 controllability with contribution of asymptomatic and pre-symptomatic individuals"
  • Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the infectious agent responsible for coronavirus disease 2019 (COVID-19), is readily transmitted person to person. Optimal control of COVID-19 depends on directing resources and health messaging to mitigation efforts that are most likely to prevent transmission. We used an analytical model to assess the proportion of SARS-CoV-2 transmissions in the community that likely occur from persons without symptoms. This model assessed the relative amount of transmission from pre-symptomatic, asymptomatic, and symptomatic individuals across a range of scenarios in which the proportion of transmission from people who never develop symptoms (i.e., remain asymptomatic) and the infectious period were varied according to published best estimates. We used multiple scenarios of proportions of asymptomatic individuals with COVID-19 and infectious periods to estimate that transmission from asymptomatic individuals most likely accounted for more than half of all transmissions. In addition to identification and isolation of persons with symptomatic COVID-19, effective control of spread therefore require reducing the risk of transmission from people with infection who do not have symptoms. These findings suggested that measures such as wearing masks, hand hygiene, social distancing, and strategic testing of people who are not ill would be foundational to slowing the spread of COVID-19 until safe and effective vaccines are available and widely used.
  • Hao-Yuan Cheng (Epidemic Intelligence Center, Taiwan CDC, Taiwan)
    "Experience of COVID-19 elimination in Taiwan"
  • In my presentation I will review prevention and control measures against COVID-19 spread in Taiwan that have been centered on stringent border control, obligatory quarantine of all incoming travelers, and intensified contact tracing.
  • Ta-Chou Ng (National Taiwan University, Taiwan)
    "Comparison of Estimated Effectiveness of Case-Based and Population-Based Interventions on COVID-19 Containment in Taiwan"
  • Taiwan is one of the few countries with initial success in COVID-19 control without strict lockdown or school closure, yet reasons remain to be fully elucidated. This comparative effectiveness study evaluated the effectiveness of case-based (including contact tracing and quarantine) and population-based (including social distancing and facial masking) interventions for COVID-19 in Taiwan. We used a stochastic branching process model using COVID-19 epidemic data from Taiwan for model development and calibration. Effective reproduction number of COVID-19 cases and the probability of outbreak extinction were used to evaluate the effectiveness of each combination of interventions. Case detection, contact tracing, and 14-day quarantine of close contacts (regardless of symptoms) was estimated to decrease the reproduction number from the counterfactual value of 2.50 to 1.53 (95% CrI 1.50-1.57), which would not be sufficient for epidemic control, which requires a value of less than 1. In our estimated analysis, voluntary population-based interventions, if used alone, were estimated to have reduced the reproduction number to 1.30 (95% CrI 1.03-1.58). Combined case-based and population-based interventions were estimated to reduce the reproduction number to below unity (0.85; 95% CrI 0.78-0.89). Results were similar for additional analyses with influenza data and sensitivity analyses. We showed that only the combination of case-based and population-based interventions (with wide adherence) may explain the success of COVID-19 control in Taiwan in 2020. Either category of interventions alone would have been insufficient, even in a country with an effective public health system and comprehensive contact tracing program. Mitigating the COVID-19 pandemic requires the collaborative effort of public health professionals and the general public. Full article is available at:

Emergent behavior across scales: locomotion, mixing, and collective motion in active swimmers

Organized by: Robert Guy (University of California Davis, United States), Arvind Gopinath (University of California Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS09-MFBM.

  • Maxime Theillard (University of California Merced, United States)
    "Multi-scale multi-species modeling of emergent flows and active mixing in confined bacterial swarms"
  • Autonomous collective motion of disparate agents in nonequilibrium is fundamental to many biological and engineering systems. An example from biology is bacterial swarms, that are prototypical dense multi-phase active fluids. Here we present a new method for modeling such fluids under confinement. We use a continuum multiscale mean-field approach to represent each specie by its first three orientational moments, and couple their evolution with those of the suspending fluid. The resulting coupled system is solved using parallel hybrid level-set based discretization on adaptive cartesian grids for high computational efficiency and maximal flexibility in the confinement geometry. Motivated by recent experimental work, we employ our method to study emergent flows in bacterial swarms. Our computational exploration demonstrate that we can reproduce the observed emergent collective patterns including active dissolution. This work lays the foundation for a systematic characterization of natural and synthetic systems such as bacterial colonies, bird flocks, fish schools, colloidal swimmers, or programmable active matter.
  • Paulo Arratia (University of Pennsylvania, United States)
    "Bacteria hinder stretching and large-scale transport in time-periodic flows"
  • In this talk, I will show recent experiments on the mixing of a passive scalar (dye) in dilute suspensions of swimming textit{Escherichia coli} in time-periodic flows. Results show that the presence of bacteria hinders large scale transport and reduce overall mixing rate. Stretching fields, calculated from experimentally measured velocity fields, show that bacterial activity attenuates fluid stretching and lowers flow chaoticity. Simulations suggest that this attenuation may be attributed to a transient accumulation of bacteria along regions of high stretching. Spatial power spectra and correlation functions of dye concentration fields show that the transport of scalar variance across scales is also hindered by bacterial activity, resulting in an increase in average size and lifetime of structures. On the other hand, at small scales, activity seems to enhance local mixing. One piece of evidence is that the probability distribution of the spatial concentration gradients is nearly symmetric with a vanishing skewness. Overall, our results show that the coupling between activity and flow can lead to nontrivial effects on mixing and transport.
  • Bin Liu (University of California Merced, United States)
    "Anomalous size-dependent active transport in structured environments"
  • Variations of transport efficiency in structured environments between distinct individuals in actively self-propelled systems is both hard to study and poorly understood. Here, we study the transport of a non-tumbling Escherichia coli strain, an active-matter archetype with intrinsic size variation but fairly uniform speed, through a periodic pillar array. We show that long-term transport switches from a trapping dominated state for shorter cells to a much more dispersive state for longer cells above a critical bacterial size set by the pillar array geometry. Using a combination of experiments and modeling, we show that this anomalous size-dependence arises from an enhancement of the escape rate from trapping for longer cells caused by nearby pillars. Our results show that geometric effects can lead to size being a sensitive tuning knob for transport in structured environments, with implications in general for active matter systems and, in particular, for the morphological adaptation of bacteria to structured habitats, spatial structuring of communities and for anti-biofouling materials design.
  • Nick Cogan (Florida State University, United States)
    "Modeling the Origin of Life Reaction in Microfluidic Chambers"
  • The origins of life are rooted in the organization from small molecules to larger molecules into self-assemblies. This organization requires energetic input that appears to have been driven by temperature and pressure differentials near hydrothermic vents. It has been hypothesized that the building blocks of life originated at the crossroads of high temperature water exacting into the oceans via these vents. Many different chemical reactions have been proposed to study the dynamics of self assemblies across steep chemical gradients. In our study, we focus on the development of a solid membrane via a simplified chemical precipitate reaction. The aims are to understand the physical interaction between the precipitating solid and the fluid dynamics as the membrane barrier is formed. Mathematically, we use a multiphase framework that is highly customizable and addresses the transitions between solids and liquids in a variety of settings. We introduce a slight change in the standard formulation and show that this model is compatible with Darcys’ law and standard porous media equations in different limits. We also provide numerical and linearized results indicating the affect of a developing solid within a flowing liquid.

Fluid dynamics of swimming organisms

Organized by: Laura Miller (University of Arizona, U.S.A.), Arvind Santhanakrishnan (Oklahoma State University, U.S.A.)

  • Silas Alben (University of Michigan, U.S.A.)
    "Collective locomotion of two-dimensional lattices of flapping plates"
  • We study the propulsive properties of rectangular and rhombic lattices of flapping plates at O(10--100) Reynolds numbers in incompressible flow. We vary five parameters: flapping amplitude, frequency (or Reynolds number), horizontal and vertical spacings between plates, and oncoming fluid stream velocity. Lattices that are closely spaced in the streamwise direction produce intense vortex dipoles between adjacent plates. The lattices transition sharply from drag- to thrust-producing as these dipoles switch from upstream to downstream orientations at critical flow speeds. The flows assume a variety of periodic and nonperiodic states, with and without up-down symmetry, and multiple stable self-propelled speeds can occur. With small lateral spacing, rectangular lattices yield net drag, while rhombic lattices may generate net thrust efficiently. As lateral spacing increases, rectangular lattices eventually achieve higher efficiencies than rhombic lattices, and the two types of lattice flows converge. At Re = 70, the maximum Froude efficiencies of time-periodic lattice flows are about twice those of an isolated plate. At lower Re, the lattices' efficiency advantage increases until the isolated flapping plate no longer generates thrust.
  • Anand Oza (Department of Mathematical Sciences, New Jersey Institute of Technology, U.S.A)
    "Coarse-grained models for schooling swimmers"
  • The beautiful displays exhibited by fish schools and bird flocks have long fascinated scientists, but the role of their complex behavior remains largely unknown. In particular, the influence of hydrodynamic interactions on schooling and flocking has been the subject of intense debate in the scientific literature. I will present a model for flapping wings in orderly formations, with the goal of identifying the formations for which swimmers optimally benefit from hydrodynamic interactions. I will then outline a framework for finding exact solutions to the evolution equations and for assessing their stability, giving physical insight into the preference for certain observed 'schooling states.' The model predictions agree well with experimental data on freely-translating, flapping wings in a water tank. The model is then used to develop a one-dimensional continuum theory for a dense flock, which exhibits traveling wave solutions. Generally, our results indicate how hydrodynamics may mediate schooling and flocking behavior in biological contexts.
  • Arvind Santhanakrishnan (Oklahoma State University, U.S.A.)
    "Hydrodynamics of multi-appendage metachronal swimming"
  • A large number of aquatic invertebrates use metachronal paddling for locomotion, where multiple appendages are oscillated sequentially starting from the back to the front of an animal. The broad diversity of body and appendage morphologies of metachronal swimmers make it difficult to generalize how specific morphological and kinematic parameters impact swimming performance. Modeling approaches can be particularly useful in this context to synthesize physical design principles underlying this successful locomotion strategy. We summarize our studies using robotic models to address how appendage spacing and stroke kinematics affect metachronal swimming performance. We will also present the development of a simplified mathematical model approximating the swimming appendages as pairs of two-dimensional hinged oscillating plates following simple harmonic trajectories. The model accounts for forces on the paddles and on the body to predict the general planar motion in the sagittal plane. Propulsive forces on each paddling appendage are calculated using drag-coefficient models. A comparison of the swimming speed predicted by the model to that of a robotic model will be presented.
  • Alexander Hoover (The University of Akron, U.S.A.)
    "Emergent metachronal asymmetries in a tension-driven, fluid-structure interaction model of tomopterid parapodia"
  • Metachronal waves are ubiquitous in propulsive and fluid transport systems across many different scales and morphologies in the biological world. Tomopterids are a soft-bodied, holopelagic polychaete that use metachrony with their flexible, gelatinous parapodia to deftly navigate the midwater ocean column that they inhabit. In the following study, we develop a three-dimensional, fluid-structure interaction model of a tomopterid parapodium to explore the emergent metachronal waves formed from the interplay of passive body elasticity, active muscular tension, and hydrodynamic forces. After introducing our model, we examine the effects that varying material properties have on the stroke of an individual parapodium. We then explore the temporal dynamics when multiple parapodia are placed sequentially and how differences in the phase can alter the collective kinematics and resulting flow field.

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 MS14-NEUR.

  • Anmar Khadra (McGill University, Canada)
    "Characterizing the spatiotemporal patterns produced by an excitable fish keratocyte model"
  • The spatiotemporal dynamics of self-organizing lamellipodium in crawling keratocytes have been previously studied using a partial differential equation model to understand the three main patterns of activity observed in such cells, including stalling, waving and smooth motility. The model consisted of three key variables: the density of barbed actin filaments, nascent adhesions (NAs) and VASP, an anti-capping protein that gets sequestered by NAs during maturation. Using parameter sweeping, the distinct regimes of behaviour associated with the three activity patterns were identified. By converting the PDE model into an ODE model, we successfully examined the excitability properties of this system and determined all of its patterns of activity. Our results revealed that there are two additional regimes not previously identified: bistability and type IV excitability. We found that these regimes are also present in the PDE model. Applying slow-fast analysis on the ODE model as well as machine-learning based image analysis showed that the ODE model exhibits a canard explosion through a folded-saddle and that rough motility seen in keratocytes is likely due to noise-dependent motility governed by dynamics at the interface of bistability and type IV excitability. The two parameter bifurcation suggested that the increase in the proportion of rough motion is due to a shift in activity towards the bistable and type IV excitable regimes induced by a decrease in NA maturation rate. In this talk, I will provide a summary of these findings.
  • Theodore Vo (Monash University, Australia)
    "Big Ducks in the Heart"
  • Early afterdepolarizations (EADs) are voltage oscillations observed during the repolarization phase of the cardiac action potential, and are a potentially lethal source of cardiac arrhyth- mia. Experiments have shown that the production of EADs can depend on the complex interplay between cellular ion channel properties, the extrinsic chemical environment, and the rate of sinoa- trial pacing. However, the mechanisms by which alterations in these qualities induce EADs are not well understood. In this work, we analyse a canonical model of the electrical activity in a cardiac cell using geometric singular perturbation techniques. We demonstrate that the EADs are canard-induced mixed-mode oscillations, and explain the essential role that canards play in producing the rich set of model EAD behaviours, some of which have also been observed in experiments. This dynamical viewpoint gives predictive power that is beyond that of the bio- physical explanation alone while also uncovering a common mechanism for phenomena observed in experiments on both atrial and ventricular cardiac cells.
  • Sushmita John (University of Pittsburgh, USA)
    "Transitions in neuronal bursting types"
  • Bursting patterns that fall into an intermediate category between square-wave (fold-homoclinic burst) and pseudo-plateau bursting (fold-subcritical Hopf. burst) have been observed in the voltage recordings of many bursting neurons. Existing research shows that certain mathematical models for these neurons exhibit a transition between square-wave and pseudo-plateau bursting patterns with small parameter changes. However, this transition may be dysfunctional for neurons that necessarily need to spike during the burst. In this work, we study in detail the transition from square-wave to pseudo-plateau bursting patterns seen in neuronal models. We explore properties and parameters of different models to identify the features of currents that affect this transition. The analysis is done using numerical simulations and dynamical systems methods such as fast/slow analysis, bifurcation theory and phase-plane analysis. This approach also helps us to fully characterize intermediate bursting patterns and compare them to the activity seen in bursting neuron types such as respiratory neurons. This is joint work with Dr. Jonathan Rubin.
  • André Longtin (University of Ottawa, Canada)
    "Multi-delay control, communication and complexity"
  • Physiological control is inherently slow with delays that can easily exceed the overall response time of a system’ components to time-varying inputs. It is also the case that control may encompass many subunits that act in concert, and that this involves multiple delays that can span milliseconds to seconds. It is generally assumed that the combination of nonlinearity and delays can lead to oscillatory and even more complex behaviour such as chaos or hyperchaos. But there is a point when multiple delays are present where one starts to think in terms of distributions of delays, and of their simplifying action on network dynamics via the integro-differential formulation of the dynamics. This talk will discuss this transition, and show how complexity collapses when there is a low density of delays. We will also discuss these results in the context of understanding the response properties of such multi-delay systems.

Recent development in mathematical oncology in Asia and Australia

Organized by: Yangjin Kim (Konkuk University, Korea, Republic of), Eunjung Kim (Korea Institute of Science and Technology, Korea)
Note: this minisymposia has multiple sessions. The second session is MS09-ONCO.

  • Dumitru Trucu (Division of Mathematics, University of Dundee, DD1 4HN, Dundee, United Kingdom)
    "Multiscale 3D Glioblastoma Modelling: Bulk and Leading Edge Dynamics within the Fibrous Brain Tissue"
  • Glioblastoma multiform is one of the most aggressive types of brain cancer, and the understanding of its progression remains one of the greatest challenges. In this talk we propose a multi-scale moving boundary approach for the glioblastoma cell population invasion within the brain fibrous environment. This will account on both the proteolytic dynamics at the tumour interface and on the interaction with brain fibres and the emerging collagen fibres at the site of the tumour. These interactions will be explored in their natural 3D setting by accounting on their genuinely multiscale character both in terms of the peritumoural proteolytic activity of the matrix degrading enzymes, and the cell-brain fibres interactions. Our 3D computational exportation suggests that although current imaging technologies provide valuable details of the brain’s underlying structure, in order to provide meaningful predictions for tumour growth and to test new hypotheses, we may need to use this information in a different, novel ways when we model glioblastoma mathematically.
  • Peter Kim (University of Sydney, Australia)
    "How do viruses move? Modelling diffusion of oncolytic virus in collagen-dense tumours"
  • Solid tumours develop much like a fortress, acquiring characteristics that protect them against invasion. A common trait observed in solid tumours is the synthesis of excess collagen which traps therapeutic agents, resulting in a lack of dispersion of treatment within the tumour mass. In most tumours this results in only a localised treatment. Often the tumour quickly recovers and continues to invade surrounding regions. Anti-tumour viral therapy, although consisting of nano-sized particles, is no exception to this rule. Experimental results show collagen density affects viral diffusion. More specifically, when injected, viruses will move to regions of low collagen concentration; therefore, accurately modelling viral diffusion is an important aspect of modelling virotherapy. To understand the underlying dynamics that impede viral diffusion in collagen, we derive, from first principles, a novel non-Fickian diffusion term and show that this diffusion term can accurately capture experimental observations. Then, using a system of partial differential equations we explore how treatment under this diffusion term differs from the standard Fickian diffusion, commonly used in virotherapy models. The disparity between results highlights a significant gap in our understanding of virotherapy modelling and could mean estimates based on Fickian diffusion need to be reassessed for their biological impact.
  • Da Zhou (School of Mathematical Sciences, Xiamen University, China)
    "Cancer suppression: ingredients utilized by cellular hierarchy"
  • Many fast renewing tissues are characterized by a hierarchical cellular architecture, with tissue specific stem cells at the root of the cellular hierarchy, differentiating into a whole range of specialized cells. Growing evidence shows that the hierarchical cellular architecture has a profound effect on cancer suppression. In this talk, we will show some cancer-suppression mechanisms possibly utilized by cellular hierarchy using mathematical models. Specifically, we are concerned about cell competition, different modes of cell division and their effects on cancer suppression.
  • Junho Lee (Department of Mathematics, Konkuk University, Korea)
    "Role of neutrophil extracellular traps in regulation of lung cancer invasion : a computational model"
  • Lung cancer is one of the leading causes of cancer-related deaths worldwide and is characterized by hijacking immune system for active growth and aggressive metastasis. Neutrophils, which require establishing immune activity against tumors as the first line of defense, are damaged by tumor cells, which in many ways promote tumor invasion. The mutual interaction between a tumor and neutrophils from bone marrow or in blood induces the critical transition of the naive form, called the N1 type, to the more aggressive phenotype, called the N2 tumor-associated neutrophils (TANs), which then promotes tumor invasion. In this study, we investigate the mutual interactions between the tumor cells and the neutrophils that facilitate tumor invasion by developing a mathematical model that involves taxis-reaction-diffusion equations for the critical components in the interaction. These include the densities of tumor and neutrophils, and the concentrations of signaling molecules (TGFbeta-CXCL8-MMP) and structure such as neutrophil extracellular traps (NETs). We apply the mathematical model to a Boyden invasion assay used in the experiments to demonstrate that the N2 TANs can enhance tumor cell invasion by secreting the neutrophil elastase. We show (i) that the model can reproduce the major experimental observation on NET-mediated cancer invasion, (ii) how stimulated neutrophils with different N1 and N2 landscapes shape the metastatic potential of the lung cancers and (iii) that the efficacy of anti-tumor and anti-invasion drugs depend on N1  N2 landscapes of stimulated neutrophils. The mathematical model tests several hypotheses to guide future experiments with the goal of the development of new anti-tumor strategies.