Multiscale Modeling in Physiology and Biophysics Subgroup (MMPB)

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Sub-group minisymposia

Mathematical Modeling of Blood Clotting: From Surface-Mediated Coagulation to Fibrin Polymerization

Organized by: Karin Leiderman (Colorado School of Mines, United States), Anna Nelson (University of Utah, USA)
Note: this minisymposia has multiple sessions. The second session is MS07-MMPB.

  • Anna Nelson (University of Utah, USA)
    "Understanding the effect of fibrinogen interactions on fibrin gel structure"
  • Fibrin polymerization, an important component of blood clotting, involves the conversion of soluble fibrinogen molecules in the blood plasma to fibrin monomers. These monomers can then polymerize to form a gel that is a major structural component of a blood clot. Oligomers composed of both fibrinogen and fibrin have been observed experimentally and are thought to impact the kinetics of the fibrin gelation process. Fibrinogen plays a dual role in fibrin polymerization; it can occupy available binding sites by binding to fibrin, inhibiting gelation, and monomeric fibrinogen and fibrinogen contained in oligomers can be converted to fibrin. To study the effects of fibrin-fibrinogen interactions on fibrin polymerization and fibrin gel structure, we developed a kinetic polymerization model with two monomers, where the reaction sites on the different species of monomers can participate in different binding reactions. With the chosen framework, gelation can occur, which is defined to be the finite time blow-up of a particular second moment of the oligomer distribution. We characterize the conditions under which a gel forms and examine the impact of fibrin-fibrinogen binding and fibrinogen conversion to fibrin on the branch point density in a gel, if one forms.
  • Michael Kelley (Colorado School of Mines, USA)
    "Modeling the effects of bivalently bound thrombin on fibrin polymerization"
  • Thrombin is an enzyme generated during the blood coagulation process and is crucial to the formation of a stable blood clot. Thrombin cleaves fibrinogen into fibrin, which polymerizes to form a stabilizing gel matrix. Thrombin can also bind directly to fibrin and become sequestered for long periods of time. Experimental models support the dogma that this retention is due to the dynamic interplay of thrombin binding to both low- and high-affinity binding sites on fibrinogen and an alternative splice variant of fibrinogen, $gamma’$ that makes up about 15% of the total fibrinogen pool. Recent experimental studies have suggested that $gamma’$ decreases the rate of fibrin polymerization but there are conflicting results in the literature regarding its effects on other aspects of fibrin polymerization such as rates of fibrinopeptide release and clot morphology. The goal of this study was to use a mathematical modeling approach to help interpret some of the disparate results. We built on an existing model of fibrin polymerization and added our previous model of bivalent thrombin-fibrin binding to investigate how thrombin and fibrin interact dynamically during polymerization. Preliminary results show that during dynamic fibrin polymerization, a large fraction of thrombin can become trapped within fibers as they form. Additionally, we show that the $gamma’$ binding of thrombin to fibrin acts to increase fiber thickness, modulating the formation of and polymerization of fibrin.
  • Francesco Pancaldi (University of California Riverside, USA)
    "Modeling study of clot contraction"
  • Blood clots are one major cause of death and disability worldwide. Blood clot formation has been relatively well studied, however, little is known about the contraction or retraction of clots. Clot contraction is driven by activated platelets that pull on fibrin fibers, causing a reduction in clot volume. In this talk, we present a model to quantify platelet and fibrin-mediated blood clot contraction mechanisms. The model combines a fibrin network mechanical model and a sub-model accounting for the forces generated by activated platelets. We used experimental measurements to calibrate model parameters and model simulations were used to reveal contraction mechanisms. The contraction was shown to depend on how pulling forces, generated by platelets, change based on local fiber stiffness and the number of filopodia per platelet. In particular, the number of filopodia per platelet contributed to the formation of distinct numbers and length of contraction phases, as defined by peaks in the change of fibrin density. Our simulations show that the number of filopodia per platelet is important to obtain the correct number and length of contraction phases. Finally, the model reproduced experimentally observed clustering of platelets within the contracting clot and predicted more rapid clustering at the initial stages of contraction.
  • Sumith Yesudasan (Sam Houston State University, USA)
    "Coarse-grained Molecular Model for Fibrin Polymerization"
  • The study on the polymerization of fibrinogen molecules into fibrin monomers and eventually a stable, mechanically robust fibrin clot is a persistent and enduring topic in the field of thrombosis and hemostasis. Despite many research advances in fibrin polymerization, the change in the structure of fibrin clots and its influence on the formation of a fibrous protein network are still poorly understood. In this paper, we develop a new computational method to simulate fibrin clot polymerization using dissipative particle dynamics simulations. With an effective combination of reactive molecular dynamics formularies and many body dissipative particle dynamics principles, we constructed the reactive dissipative particle dynamics (RDPD) model to predict the complex network formation of fibrin clots and branching of the fibrin network. The 340 kDa fibrinogen molecule is converted into a spring-bead coarse-grain system with 11 beads using a topology representing network algorithm, and using RDPD, we simulated polymerization and formation of the fibrin clot. The final polymerized structure of the fibrin clot qualitatively agrees with experimental results from the literature, and to the best of our knowledge this is the first molecular-based study that simulates polymerization and structure of fibrin clots.

Complex Fluids and Flows in Mathematical Biology

Organized by: Calina Copos (University of North Carolina at Chapel Hill, USA), Tony Gao (Michigan State University, USA), On Shun Pak (Santa Clara University, USA), Yuan-nan Young (New Jersey Institute of Technology, USA)
Note: this minisymposia has multiple sessions. The second session is MS03-MMPB.

  • Calina Copos (University of North Carolina, Chapel Hill, USA)
    "Chimenying movement from the perspective of a cell"
  • Cell migration is critical for many important physiological processes, such as embryogenesis, tissue repair, and cancer metastasis. In experiments, some cells have been shown to migrate using round membrane protrusions called blebs while confined between two surfaces, such as a gel and a glass coverslip. These cells do not need to adhere to the channel walls in order to migrate under confinement, yet it is unclear how traction forces are coordinated in space and time to generate motion. A dynamic 2D computational model of a blebbing cell in a narrow channel is presented. The model includes the mechanics of the cortical actin and cell membrane, intracellular fluid flow, and evolution equations for the cortical actin for bleb formation and retraction. Several channel models are considered, including two rigid walls and the combination of a rigid and elastic wall. Model outputs include cell velocity, intracellular pressure, and traction forces on the channel walls. The contribution of confinement pressure to total intracellular pressure is quantified, and model simulations show adhesion to the substrate is necessary for migration when the channel is modeled by two rigid walls.
  • Jorn Dunkel (Massachusetts Institute of Technology, USA)
    "Altruistic fluid transport during fly egg development"
  • Fluid flow plays an important role during egg cell development. From insects to mice, oocytes mature by acquiring cytoplasm from sister germ cells, yet the biological and physical mechanisms underlying this transport process remain poorly understood. To study the dynamics of “nurse cell dumping” in fruit flies, we combined direct imaging with flow-network modeling and found that the intercellular pattern and time scale of transport are in accordance with a fundamental hydraulic pressure law. Changes in actomyosin contractility are observed only in the second phase of nurse cell dumping as surface waves that drive transport to completion. These results show that tandem physical and biological mechanisms are required for complete and directional cytoplasmic transport into the egg cell. (Imran Alsous et al., PNAS 118: e2019749118, 2021)
  • Sarah Olson (Worcester Polytechnic Institute, USA)
    "Centrosome movement during mitosis"
  • Proper formation and maintenance of the mitotic spindle is required for faithful cell division. While much work has been done to understand the roles of the key molecular components of the mitotic spindle, identifying the consequences of force perturbations in the spindle remains a challenge. We develop a computational framework to account for centrosome movement within the cytoplasm and utilize live cell imaging to inform and validate the model. Specifically, we investigate the role of cortical dynein on spindle pole length fluctuations.
  • Arezoo Ardekani (Purdue University, USA)
    "Swimming near a surfactant laden interface"
  • The interaction of motile microorganisms and surrounding fluids is of importance in a variety of biological and environmental phenomena including the development of biofilms, colonization of microbes in human and animal bodies, formation of marine algal blooms and bacterial bioremediation. Many microorganisms, especially bacteria, actively search for nutrients via a process called chemotaxis. The physical constraints posed by hydrodynamics in the locomotion of microorganisms can combine with their chemotactic ability to significantly affect functions like colonization of nutrient sources. Motivated by bacterial bio-remediation of hydrocarbons released during oil spills, I will discuss the role of hydrodynamics toward dictating distribution of microbes around interfaces and drops in the presence and absence of surfactant. We find that the presence of the surfactant significantly alters the dynamics of the swimmers specially by affecting their reorientation.

Complex Fluids and Flows in Mathematical Biology

Organized by: Calina Copos (University of North Carolina at Chapel Hill, USA), Tony Gao (Michigan State University, USA), On Shun Pak (Santa Clara University, USA), Yuan-nan Young (New Jersey Institute of Technology, USA)
Note: this minisymposia has multiple sessions. The second session is MS02-MMPB.

  • Tony Gao (Michigan State University, USA)
    "Q-tensor model for undulatory swimming in a liquid crystal"
  • Microorganisms may exhibit rich swimming behaviors in anisotropic fluids, such as liquid crystals, that have direction-dependent physical and rheological properties. Here we construct a two-dimensional computation model to study the undulatory swimming mechanisms of microswimmers in a solution of rigid, rodlike liquid-crystalline polymers. We describe the fluid phase using Doi's Q-tensor model, and treat the swimmer as a finite-length flexible fiber with imposed propagating traveling waves on the body curvature. The fluid-structure interactions are resolved via an Immersed Boundary method. Compared to the swimming dynamics in Newtonian fluids, we observe non-Newtonian behaviors that feature both enhanced and retarded swimming motions in lyotropic liquid-crystalline polymers. We reveal the propulsion mechanism by analyzing the near-body flow fields and polymeric force distributions, together with asymptotic analysis for an idealized model of Taylor's swimming sheet.
  • David Stein (Simons Foundation, USA)
    "The many behaviors of deformable active droplets"
  • Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motion. In some cases, these phenomena have been well characterized, and theory can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this talk, I will discuss the behavior of droplets of an active nematic fluid. Through a mix of linear stability analysis and nonlinear simulations, we identify parameter regimes where single modes dominate and droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zig-zaggers, washing machines, wanderers, and pulsators.
  • Herve Nganguia (Indiana University of Pennsylvania, USA)
    "Swimming in a fluid pocket enclosed by a porous medium"
  • This talk presents a minimal theoretical model to investigate how heterogeneity created by a swimmer affects its own locomotion. As a generic locomotion model, we consider the swimming of a spherical squirmer in a purely viscous fluid pocket (representing the liquified or degelled region) surrounded by a Brinkman porous medium (representing the mucus gel). We obtain analytical expressions for the swimming speed, flow field, and power dissipation of the swimmer. Depending on the details of surface velocities and fluid properties, our results reveal the existence of a minimum threshold size of mucus gel that a swimmer needs to liquify in order to gain any enhancement in swimming speed.
  • Anup Kanale (University of Southern California, USA)
    "Flow-mediated instabilities in ciliary carpets"
  • Motile cilia that densely cover epithelial tissues are known to coordinate their beating in metachronal waves to transport fluid. Although hydrodynamic coupling seems to drive this coordination, the exact mechanisms leading to the emergence of ciliary waves remain unclear. Here, we propose a minimal model in which each cilium is a rotating bead driven by a phase-dependent active force, and we accordingly construct a coarse-grained continuum model. Isotropic states are unstable relative equilibria. Perturbations to these equilibria lead, beyond the transient regime, to noisy wave-like patterns that propagate along the direction of the ciliary beating. These noisy patterns seem globally attracting for all initial conditions, and depend only on the nature of the forcing at the level of an individual cilium. We use the continuum model to analyze the linear stability of both the synchronized and isotropic states to perturbations of all wavelengths and show that both states are unstable with growth rates that are in good agreement with the discrete cilia simulations. Our findings demonstrate a set of minimal conditions necessary to create wave-like coordination in ciliary carpets.

How can mathematical modelling aid medical decision making?

Organized by: Jasmina Panovska-Griffiths (University of Oxford), Eduard Campillo-Funollet (University of Sussex)

  • Elizabeth Ford (Brighton and Sussex Medical School)
    "Can modelling of primary care patient records enable detection of dementia earlier than the treating physician?"
  • Timely diagnosis of dementia is a policy priority in the United Kingdom (UK). However, recent research shows that a third to a half of patients with dementia do not have a diagnosis recorded in their primary care patient record, and for those that get a diagnosis, it takes over three years for the diagnosis to be made. We explored using modelling to automate early detection of dementia using data from electronic health records (EHRs). We investigated: a) how early a machine-learning model could accurately identify dementia before the physician; b) if models could be tuned for dementia subtype; and c) what the best clinical features were for achieving detection. Using EHRs from Clinical Practice Research Datalink in a case-control design, we selected patients aged >65y with a diagnosis of dementia recorded 2000-2012 (cases) and matched them 1:1 to controls, giving a total of 95k patients. We trained random forest classifiers, and evaluated models using Area Under the Receiver Operating Characteristic Curve (AUC). We examined models by year prior to diagnosis, dementia subtype, and the most important features contributing to classification. Classification of dementia cases and controls was poor 2-5 years prior to physician-recorded diagnosis but good in the year before. Features indicating increasing cognitive and physical frailty dominated models 2-5 years before diagnosis; in the final year, initiation of the dementia diagnostic pathway (memory loss symptoms, screening and referral) explained the sudden increase in accuracy. This leads us to think that automated detection of dementia earlier than the treating physician may be problematic using only primary care data, and that linking multiple sources of healthcare data could improve model performance.
  • Robin Thompson (University of Warwick)
    "Can modelling be used to predict whether or not the novel coronavirus will spread in the UK?"
  • The most devastating infectious disease epidemics are those that have a wide geographical range, as opposed to being confined to a small region. Early in the COVID-19 epidemic, an important question was whether or not SARS-CoV-2 would spread elsewhere and cause local outbreaks outside of China. A vital factor was the probability of establishment whenever a pathogen arrives in a new location, since this is a key component of any pathogens pandemic potential. We assessed this in real-time during the COVID- 19 epidemic. In this talk, we show how the probability of sustained transmission in other locations can be estimated from data that are available during infectious disease outbreaks. We show how estimates can be extended to include features such as transmission from paucisymptomatic infectors (infectious individuals with few symptoms). If time allows, we will also show how estimates can be generated for other pathogens and other epidemiological settings.
  • Fred Vermolen (Delft University of Technology)
    "Can modelling aid the process of deep tissue healing without scarring?"
  • Deep tissue injury is often followed by contraction of the scar. This contraction is caused by the pulling forces exerted by myofibroblasts and fibroblasts, which are cells that are responsible for the regeneration of collagen. In this talk, we will review several mechanical frameworks, such as viscoelasticity and morpho- elasticity, in which the latter framework can be used to simulate plastic deformations. Furthermore, we will consider cell-based as well as continuum simulation frameworks and some remarks about our upscaling efforts will be given. These upscaling strategies currently incorporate the relation between the use of the immerse boundary method and smoothed particle approach. Since many input parameters are patient-dependent, we will also present some results from the quantification of uncertainty that we have carried out.
  • Jasmina Panovska-Griffiths (University of Oxford)
    "Can combining modelling and brain radiomics non- invasively stratify brain gliomas?"
  • Combining MRI techniques with modelling is rapidly gaining attention as a promising method for staging of brain gliomas. This study assesses the diagnostic value of such a framework applied to stratify- ing treatment-nave gliomas from a multi-center patients into WHO grades II-IV and across their isocitrate dehydrogenase (IDH) mutation status. 333 patients from 6 tertiary centres, diagnosed histologically and molecularly with primary gliomas were retrospectively identified. Shape, intensity distribution and tex- ture features over the tumour mask were extracted. A random-forest algorithm was employed (2-fold cross-validation, 250 repeats) to predict grades or mutation status using the extracted features. Shape, distribution and texture features showed significant differences across mutation status. WHO grade II-III differentiation was mostly driven by shape features while texture and intensity feature were more relevant for the III-IV separation. Increased number of features became significant when differentiating grades further apart from one another. Gliomas were correctly stratified by mutation status in 71% and by grade in 53% of the cases (87% of the gliomas grades predicted with distance less than 1). Combining brain radiomics with modelling presents a promising approach for non-invasive glioma molecular subtyping and grading.

Mathematical Modeling of Blood Clotting: From Surface-Mediated Coagulation to Fibrin Polymerization

Organized by: Karin Leiderman (Colorado School of Mines, United States), Anna Nelson (University of Utah, USA)
Note: this minisymposia has multiple sessions. The second session is MS01-MMPB.

  • Amandeep Kaur (University of California Merced, USA)
    "A new view of an old mechanism: mathematical modeling of TFPI inhibition in coagulation"
  • Blood coagulation is a complex network of biochemical reactions necessary to form a blood clot. The process occurs in three, overlapping stages: initiation, amplification, and propagation, with inhibitory mechanisms occurring at each stage to help avoid the system over clotting. Initiation in the tissue factor pathway begins when clotting factor VIIa (FVIIa) in the plasma binds its cofactor, tissue factor (TF), in the subendothelium and forms an active enzyme complex. Next, clotting factor X (FX) in the plasma can bind TF:VIIa, form an intermediate complex where it is enzymatically cleaved into activated FX (FXa). FXa is necessary for further events in coagulation. It has long been recognized that tissue factor pathway inhibitor (TFPI) is a strong inhibitor of TF:VIIa activity during initiation, with the primary mechanism of action reportedly being TFPI binding to FXa in the plasma, forming a complex, and then rebinding to TF:VIIa to form the newly inhibited, quaternary complex TF:VIIa:TFPI:Xa. However, previous mathematical models of this type of inhibition, for small injuries under flow, show that flow itself is a more important inhibitor of the system than TFPI. The goal of this study was to revisit previous experimental studies of TFPI where additional inhibitory reactions were suggested to be at play and use mathematical models and constrained optimization to fit these reactions schemes to multiple sets of data simultaneously. Our preliminary results suggest that the alternative reaction scheme for TFPI better describes the experimental data. Next, we highlight the ramifications of using one scheme versus the other when interpreting results from mathematical models of coagulation.
  • Jamie Madrigal (Colorado School of Mines, USA)
    "Estimating lipid-dependent reaction velocities"
  • Blood coagulation is a network of biochemical reactions whereby dozens of proteins act collectively to initiate a rapid clotting response. It is known that many of the coagulation reactions require a cellular (lipid) surface on which to occur and, in addition, the enzymatic rates are thought to be enhanced on lipid surfaces; surface diffusion and near-surface concentrations of substrates are thought to play important roles in this enhancement. Experimental data shows that at both low and high lipid concentration, rates of enzymatic reactions are low while there is some optimal intermediate lipid concentration where the rate is the fastest; this is known as the template effect. To our knowledge, this effect has never been accounted for in previous mathematical models of coagulation reactions and thus these models all result in enzyme generation that increases monotonically as lipid concentration increases. We have developed a mathematical model of lipid-mediated enzyme reactions in which the association rates between lipid-bound reactants are modified by an interaction probability. The interaction probability is derived by considering the fraction of the lipid surface that is occupied by any lipid-bound species. Preliminary model results agree with experiment ones and show the template effect. Next, for an enzymatic reaction where the experimentally measured reaction velocities are considerably different for varying lipid concentrations, we used the model with constrained optimization to estimate the intrinsic kinetic rate constants that can be fixed across lipid concentrations.
  • Anastasiia Mozokhina (Peoples Friendship University of Russia (RUDN University), Russia)
    "The influence of microthrombi in small vessels on the pulmonary blood flow"
  • Blood coagulation is an important physiological mechanism aimed to stop bleeding if the integrity of blood vessel walls is violated due to an injury. However, if the fragile balance between pro- and anticoagulant factors is not preserved, this can lead to different pathological states including thrombosis, possibly leading to heart attack, stroke, pulmonary embolism, or deep vein thrombosis. On the other side, various bleeding disorders including hemophilia can appear in the case of insufficient blood coagulation. During the ongoing COVID-19 epidemic, multiple microthrombi are observed in small pulmonary vessels leading to reduced pulmonary blood circulation and to decrease of oxygen saturation level, representing the main mortality cause of the coronavirus disease. In the current work, the model of thrombi growth is combined with the quasi-one-dimensional blood flow model of pulmonary circulation. The model is used to estimate the influence of blood vessel obstruction on the total blood flow through the lungs. The modelling results can be used as a first approximation for a non-invasive estimation of oxygen level during the coronavirus disease. The work is supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018)
  • Dmitry Nechipurenko (Lomonosov Moscow State University, Russia)
    "Initiation and confinement of coagulation reactions under the shear flow"
  • Under conditions of the high shear rate, formation of the hemostatic plug relies on platelet adhesion, activation and aggregation, and the platelet plug is additionally stabilized by fibrin mesh. It is generally considered, that coagulation reactions are significantly inhibited under flow conditions due to dilutional effects of the blood flow. However, in vitro experiments suggest that fibrin formation in platelet free plasma is possible even under arterial blood flow conditions and critically depends on the tissue factor density, the size of the “damaged” region with tissue factor and the shear rate itself. However, the exact mechanisms, which a) protect initial stages of coagulation reactions from dilution by arterial flow and b) further confine fibrin polymerization in space - are poorly understood. Here we describe both experimental and theoretical framework to address these questions. In vitro experiments were based on perfusion of recalcified platelet free plasma through microfluidic flow chambers combined with fluorescent microscopy and address the dynamics of fibrin propagation in 4D under controlled shear rate. In silico models are focused on the primary stages of coagulation process under defined shear rate and serve as important tool for elucidation and investigation of the possible mechanisms. Using in vitro model we have inferred the critical spatiotemporal parameters of fibrin polymerization process under arterial shear rate. In silico model was further used to study the kinetics of thrombin generation depending on critical internal parameters and correlated with experimental data. Our results suggest a novel mechanism, which might be important for the protection of the primary coagulation reactions from the blood flow. This work was supported by the Russian Foundation for Basic Research grant 19-51-15004 to F.A. and performed within the framework of the Development Program of the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University

Multiscale simulations of biological fluid dynamics

Organized by: Matea Santiago (University of California, Merced, United States), Shilpa Khatri (University of California, Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS09-MMPB.

  • Christiana Mavroyiakoumou (University of Michigan, United States)
    "Large amplitude flutter of membranes"
  • We study the dynamics of thin membranes---extensible sheets with negligible bending stiffness---initially aligned with a uniform inviscid background flow. This is a benchmark fluid-structure interaction that has previously been studied mainly in the small-deflection limit, where the flat state may be unstable. Related work includes the shape-morphing of airfoils and bat wings. We study the initial instability and large-amplitude dynamics with respect to three key parameters: membrane mass density, stretching rigidity, and pretension. When both membrane ends are fixed, the membranes become unstable by a divergence instability and converge to steady deflected shapes. With the leading edge fixed and trailing edge free, divergence and/or flutter occurs, and a variety of periodic and aperiodic oscillations are found. With both edges free, the membrane may also translate transverse to the flow, with steady, periodic, or aperiodic trajectories.
  • Alyssa Taylor (North Carolina State University, United States)
    "Fluid dynamics in hypoplastic left heart syndrome patients in supine and upright positions"
  • Patients with hypoplastic left heart syndrome (HLHS) have an underdeveloped left heart, leaving them with a single functioning ventricle. Their treatment involves a series of surgeries that create a univentricular (Fontan) circulation and includes a reconstructed aorta. While patients typically survive into adulthood, most experienced cardiovascular problems, including reduced cardiac output. Current clinical assessments are derived from 4D MRI images that quantify 3D flow patterns in the aorta. However, this data does not provide information about energy loss, wave intensity, or cerebral perfusion. This study uses a 1D arterial network model for the Fontan circulation to compute quantities of clinical interest in patients with HLHS. To investigate the effects of vascular reconstruction on perfusion, model predictions will be compared to a single ventricle control patient with a double outlet right ventricle (DORV) and native aorta. Outputs include pressure and flow predictions in vessels of the systemic system for patients at supine rest and upright exercise.
  • Christina Hamlet (Bucknell University, Department of Mathematics, United States)
    "Modeling the small-scale ballistics and fluid dynamics of nematocyst firing"
  • We model the fluid dynamics of nematocyst (stinging cell) firing to shed light on the importance of Reynolds number transitions due to ultrafast accelerations and boundary layer interactions in successful ballistic strategies on the microscale. Nematocyst firing is the fastest-known accelerating mechanism in the natural world and occurs on microscales. In this study, we combine mathematical modeling and computational fluid dynamics to simulate the fluid-structure interactions of an accelerating nematocyst stylus and its target prey coupled to viscous, incompressible fluid. 2D models of a fast-accelerating projectile and a passive target were modeled in an immersed boundary framework. In this presentation, results and insights into the effects of boundary layer interactions on predator-prey dynamics are analyzed and discussed.
  • Ebrahim Kolahdouz (University of North Carolina at Chapel Hill, United States)
    "Migration and trapping of deformable blood clots using a sharp interface Lagrangian"
  • Understanding the transport dynamics and fluid-structure interaction (FSI) of flexible blood clots in the venous vasculature is critical to predicting the performance of embolic protection devices like inferior vena cava (IVC) blood clot filters. IVC filters are metallic medical devices that are implanted in the IVC, a large vein in the abdomen through which blood returns to the heart from the lower extremities, to capture clots before they can migrate to the lungs and cause a potentially fatal pulmonary embolism. In this work, I introduce a FSI framework to simulate the migration and trapping of blood clots in the IVC, which is especially challenging due to the relatively large size of the clots that affects the local fluid dynamics, the large nonlinear deformations that are generated, and the occurrence of contact between the clots, the vein wall, and the implanted device. The proposed sharp interface immersed Lagrangian-Eulerian (ILE) method combines a partitioned approach to FSI with an immersed coupling strategy. Like other partitioned formulations, the ILE approach uses distinct momentum equations for the fluid and solid regions. Unlike body-fitted arbitrary Lagrangian-Eulerian methods, our approach uses a non-conforming discretization of the dynamic fluid-structure interface that is “immersed” in the surrounding fluid and does not require any grid regeneration or mesh morphing to treat large structural deformations. Blood is modeled as a Newtonian fluid and the blood clot is modeled with a non-linear finite element model and nearly incompressible hyperelastic material behavior. Fluid-structure interaction is mediated by a coupling approach that uses the immersed interface method that accounts for both dynamic and kinematic coupling conditions between the fluid and structure. A penalty approach is used to relax the kinematic constraint. Specifically, the penalty formulation uses two representations of the fluid structure interface, including a thin surface mesh and a bulk volumetric mesh, that are connected by forces that impose kinematic and dynamic interface conditions. The dynamics of the volumetric mesh are driven by the accurate exterior fluid traction obtained from the sharp interface approach. Simulation of clot transport and IVC filter trapping are presented. Verification and validation of the simulations is underway and will be performed by comparing with in vitro experimental measurements.

Multiscale simulations of biological fluid dynamics

Organized by: Matea Santiago (University of California, Merced, United States), Shilpa Khatri (University of California, Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-MMPB.

  • Lindsay Waldrop (Assistant professor, Chapman University, United States)
    "The effects of circulatory resistivity on performance of transport by systems with tubular, peristaltic hearts"
  • During individual development and evolutionary history, the chambered hearts of vertebrate animals begin as contracting, tubular hearts that pump peristaltically. This system has been extensively studied in computational models, but typically with a simple, racetrack circulatory system. The circulatory systems of animals are often resistive, including the closed systems of vertebrates consisting of capillary beds at its smallest diameters and the semi-closed systems of tunicates which have a connected bed of very small vessels in the pharyngeal basket. We used an immersed boundary model of peristaltic pumping attached to different circulatory systems that are more resistive: a branch that divides the top of the tube into two smaller tubes, a tube that widens and contain round, fixed obstacles, and a branched system with obstacles. We varied the Womersley number, compression ratio, and compress frequency of the pumping heart for each circulatory system and analyzed the system using uncertainty quantification with generalized polynomial chaos scheme and by calculating Sobol indices to quantify global sensitivity. We found that more resistive circulatory systems resulted in a 50% drop in average flow speed and a 33% drop in average volume flow rate within the circulatory systems of greater resistivity compared to the racetrack system. The pressure differential generated by the heart increased by 4.5 times in the system with the greatest resistivity. However, the cost of transport and work of pumping did not significantly increase, and the pattern of parameter sensitivity did not change with different circulatory systems. Results suggest that heart performance (cost of transport and flow) can be maximized by operating at lower pumping frequencies and higher Womersley numbers and that the relationship between performance and parameters do not change with the addition of resistive circulatory systems.
  • Laura Miller (Departments of Mathematics and Biomedical Engineering, University of Arizona, United States)
    "Slow and fast airflow past Saguaro and other cacti"
  • The cacti of the Sonoran desert in the southwest United States must deal with temperatures on the order of 120 degrees Farenheit and monsoons with wind speeds upwards of 100 miles per hour. It has been speculated that the ridges and spines of these cacti help dissipate heat in light wings, in addition to providing protection. It is also possible that the ridges and spines reduce drag acting on the cacti during strong winds. In this presentation, we use computational fluid dynamics to quantify the airflow around Saguaro and prickly pear cacti in both light and strong winds. The effects of the ridges and spines are systematically studied by smoothing the trunk and leaves. The resulting flow structures will be discussed in the context of drag reduction and heat dissipation.
  • Shilpa Kharti (Department of Applied Mathematics, University of California, Merced, United States)
    "Pulsing Soft Corals"
  • Soft corals of the family Xeniidae have a pulsing motion, a behavior not observed in many other sessile organisms. We are studying how this behavior may give these corals a competitive advantage, especially by allowing their symbiotic algae to photosynthesize to a greater extent. We will present computational simulations of the pulsations of the coral. Direct numerical simulations of the pulsing corals and the resulting fluid flow by solving the Navier-Stokes equations coupled with the immersed boundary method will be discussed. We will present results of how the fluid flow created by the corals is modified as we vary parameters of the fluid and the pulsing motion.
  • Matea Santiago (Department of Applied Mathematics, University of California, Merced, United States)
    "Soft Corals: Pulsing, Mixing, and Photosynthesis"
  • Some species of octocorals in the family Xeniidae actively pulse their tentacles. It is hypothesized that the pulsing mixes the fluid which enhances the photosynthesis of their symbiotic algae. We will present mathematical models and numerical methods for the tentacle motion and fluid flow coupled with the photosynthesis. The numerical simulations are analyzed to understand the benefit of pulsing for mixing and photosynthesis in different parameter regimes. The fluid flow is used to build Poincaré maps, a common tool in dynamical systems, used to understand fluid transport in periodic flows. This tool is coupled with the photosynthesis simulations to understand the enhancement of photosynthesis due to the flow.

Models and Computations for Studying Biofluid Applications

Organized by: Zhiliang Xu (Univeristy of Notre Dame, USA), Giordano Tierra (University of North Texas, USA), Shixin Xu (Duke Kunshan University)
Note: this minisymposia has multiple sessions. The second session is MS16-MMPB.

  • Qi Wang (U of South Carolina, USA)
    "A Phase Field Embedding Method for Flow-Active Particle Interactions"
  • We present a novel computational framework to numerically investigate fluid structure interaction using the phase field embedding. Each solid structure or soft matter structure immersed in the fluid, grossly referred to as the particle in this paper, is represented by a volume preserving phase field. The motion of the active particle is driven by the surrounding fluid velocity and its self-propelling velocity. A repulsive force exists between each pair of particles and between a particle and the boundary. The particle also exerts a drag force to the fluid. When the particle is solid, its state is described by a zero velocity gradient tensor and a phase field that defines its profile. A thermodynamically consistent hydrodynamic model is then derived for the fluid-particle ensemble by the generalized Onsager principle. Structure-preserving numerical algorithms are developed for the thermodynamically consistent model. Numerical tests are carried out to verify the rate of convergence and some numerical examples are given to demonstrate the usefulness of the computational framework for simulating fluid-structure interactions for self-propelling active particles.
  • Jia Zhao (Utah State University, USA)
    "Partial demixing of RNA-protein complexes leads to intra-droplet patterning in phase-separated biological condensates"
  • An emerging mechanism for intracellular organization is liquid-liquid phase separation (LLPS). Found in both the nucleus and the cytoplasm, liquid-like droplets condense to create compartments that are thought to promote and inhibit specific biochemistry. In this work, a multiphase, Cahn-Hilliard diffuse interface model is used to examine RNA-protein interactions driving LLPS. We create a bivalent system that allows for two different species of protein-RNA complexes and model the competition that arises for a shared binding partner, free protein. With this system we demonstrate that the binding and unbinding of distinct RNA-protein complexes leads to diverse spatial pattern formation and dynamics within droplets. Both the initial formation and transient behavior of spatial patterning are subject to the exchange of free proteins between RNA-protein complexes. This study illustrates that spatiotemporal heterogeneity can emerge within phase-separated biological condensates with simple binding reactions and competition. Intra-droplet patterning may influence droplet composition and, subsequently, cellular organization on a larger scale.
  • Xinfeng Liu (Department of Mathematics, University of South Carolina, USA)
    "Mathematical modeling and computational investigation of heterogeneity in breast cancer cells"
  • Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are a highly tumorigenic cell type found in developmentally diverse tumors that are believed to be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence. Thus understanding the tumor growth kinetics is critical for development of novel strategies for cancer treatment. For this talk, I shall introduce mathematical modeling to study Her2 signaling for the dynamical interaction between cancer stem cells (CSCs) and non-stem cancer cells, and our findings reveal that two negative feedback loops are critical in controlling the balance between the population of CSCs and that of non-stem cancer cells. Furthermore, the model with negative feedback suggests that over-expression of the oncogene HER2 leads to an increase of CSCs by regulating the division mode or proliferation rate of CSCs.
  • Isaac Klapper (Temple University, USA)
    "Modeling Metabolism in Microbial Biofilms"
  • 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, physical, chemical, and biological constraints must be accomodated. Here techniques to model this organization will be discussed. In particular, the importance of coupling microscale metabolic information to community scale transport processes will be emphasized.

Dynamics of hematopoiesis in health and disease - from governing principles to clinical implications

Organized by: Peter Ashcroft (ETH Zurich, Switzerland), Tony Humphries (McGill University, Canada), Morten Andersen (Roskilde University, Denmark)
Note: this minisymposia has multiple sessions. The second session is MS13-MMPB.

  • Nathaniel Mon Père (Queen Mary University of London and Barts Cancer Institute, UK)
    "Somatic evolution in healthy hematopoietic stem cells"
  • The production of blood cells is known to be driven by a relatively small group of hematopoietic stem cells (HSCs) which both self-renew and provide lineage progenitors throughout the entirety of an individual’s lifetime. However, many properties of these dynamics are still debated or unknown, in part due to the difficulty of studying HSC behaviour in vivo. Because the stem cell pool self-renews it acquires somatic mutations which are subject to evolutionary pressures and stochastic drift. We show that information on the underlying dynamics is encoded in observations of this mutational landscape, which in turn can be obtained by modern sequencing methods. In particular we use observations of the distribution of mutational burdens and the variant allele frequency spectrum to estimate fundamental quantities such as the per division mutation rate, the size of the HSC pool, and the proportion of asymmetric divisions.
  • Gladys Poon (University of Cambridge, UK)
    "Synonymous mutations reveal genome-wide levels of positive selection in healthy tissues"
  • Genetic alterations under positive selection in ostensibly healthy tissues have implications for cancer risk. However, total levels of positive selection across the genome remain unknown. How much positive selection elsewhere in the genome is missed by gene-focused sequencing panels? Synonymous passenger mutations that hitchhike to high variant allele frequency are influenced by any driver mutation, regardless of type or location in the genome, and can therefore be used to estimate total levels of positive selection in healthy tissues. By comparing observed numbers of synonymous passengers to the numbers expected due to driver mutations in canonical cancer genes, we show that it is possible to quantify missing selection left to be explained by unobserved drivers elsewhere in the genome. Here we analyse the variant allele frequency spectrum of synonymous mutations from physiologically healthy blood and oesophagus to quantify levels of missing positive selection. In blood we find that only 20% of synonymous passengers can be explained by SNVs in canonical driver genes, suggesting high levels of positive selection for other mutations elsewhere in the genome. In contrast, approximately half of all synonymous passengers in the oesophagus can be explained by just the two driver genes NOTCH1 and TP53, suggesting little positive selection elsewhere. In tissues with high levels of ‘missing’ selection, we show that our framework can be used to guide targeted driver mutation discovery.
  • Thomas Stiehl (RWTH Aachen University, Germany)
    "Relating competition in the stem cell niche to biomarkers of acute myeloid leukemia progression - Insights from mathematical modeling"
  • Acute myeloid leukemia (AML) is one of the most aggressive cancers of the blood forming (hematopoietic) system. The disease is driven by a small population of leukemic stem cells (LSC). LSC give rise to the malignant cell bulk and out-compete hematopoietic stem cells (HSC) which are required to maintain healthy blood cell formation. HSC depend on a specific supportive micro-environment, the so-called stem cell niche, to fulfil their function. Based on recent experimental evidence we propose a mathematical model to quantitatively describe the competition of HSC and LSC for spaces in the stem cell niche. We calibrate the model to patient data and provide insights in the following questions: • Why and how can we use HSC counts as a prognostic biomarker in AML? • What can HSC counts at the time of diagnosis tell us about disease dynamics of individual patients? • Can measurements of HSC counts reveal information about LSC properties? • How can we use the mathematical model as a tool for risk-stratification and which additional information does it provide compared to clinical approaches? • For which subsets of AML patients is the model-based risk-stratification superior to the clinically established approach? • How can we simplify the model-based approach to render it more accessible to practitioners?
  • Johnny T. Ottesen (Roskilde University, Denmark)
    "Dynamics of Hematological Cancer-Infection Comorbidities – an in silico study"
  • Background: The immune system attacks threats like an emerging cancer or infections like COVID-19. Malignant cells may be in a dormant state or escape the immune system resulting in uncontrolled growth and cancer progression. If the immune system is busy fighting a cancer, a sudden severe infection may compromise the immunoediting and the comorbidity may be too taxing to control. Method: A novel mechanism based computational model coupling a cancer-infection development to the adaptive immune system is presented and analyzed. We used the model to investigate outcomes of two immunotherapies, interferon-alpha and CAR T-cell therapy as mono therapies as well as in combination with antibiotics. The model maps the outcome to the underlying physiological mechanisms and agree with numerous evidence based medical observations. Results and Conclusions: Progression of a cancer and the effect of treatments depend on the cancer size, the level of infection, and on the efficiency of the adaptive immune system. The model exhibits bi-stability, i.e. virtual patient trajectories gravitate towards one of the two stable steady states: a dormant state or a full-blown cancer-infection disease state. An infectious threshold curve exists and if infection exceed this separatrix for sufficiently long time cancer escapes and progresses. Thus, early treatment is vital for remission and severe infections may instigate cancer escape. Immunotherapy may sufficiently control cancer progression back into a dormant state but the therapy gains efficiency in combination with antibiotics.

Dynamics of hematopoiesis in health and disease - from governing principles to clinical implications

Organized by: Peter Ashcroft (ETH Zurich, Switzerland), Tony Humphries (McGill University, Canada), Morten Andersen (Roskilde University, Denmark)
Note: this minisymposia has multiple sessions. The second session is MS12-MMPB.

  • Lora Bailey (Grand Valley State University, USA)
    "The resilience of hematopoietic feedback networks against mutations"
  • In hematopoietic systems, cell fate decisions such as stem cell differentiation or differentiated cell death may be controlled by cell populations through cell-to-cell signaling to keep the system in a state of homeostasis. By examining different feedback networks mathematically, we can determine not only which feedback networks are possible, but which have greater resilience against mutations. While networks with exactly one feedback loop are sufficient for maintaining homeostasis, they are all equally vulnerable to dangerous mutations that alter the present feedback and can lead to unlimited growth of cancerous populations. Therefore, a network with multiple, redundant feedback loops appears evolutionarily advantageous. We discovered that these redundant networks have varying degrees of resilience against mutations. For some redundant networks, any mutation that weakens or eliminates one of the existing feedback loops results in the growth of the cancerous stem cell population, while for other redundant networks this same type of alteration can lead to a depletion of the cancerous stem cell population and may slow down further unwanted evolution.
  • Mia Brunetti (Université de Montréal, Centre de recherche du CHU Sainte-Justine, Canada)
    "Mathematical modelling of the pre-leukemic phase of AML to evaluate clonal reduction therapeutic strategies"
  • Acute myeloid leukemia (AML) is an aggressive blood cancer subtype characterized by the uncontrolled proliferation of myeloblasts in the bone marrow and the blood. While rare, this disease has one of the highest mortality rates of any leukemias. The inefficiency of standard therapies, which target leukemic cells directly, highlights the need for a new approach to treating AML. Previous studies identified a premalignant phase preceding the onset of AML orchestrated by pre-leukemic stem cells (pre-LSCs). Pre-LSCs outcompete healthy hematopoietic stem cells and allow for AML to develop through their clonal expansion and the acquisition of secondary mutations. More recently, studies have suggested that different approved medications target pre-LSCs. These clonal reduction strategies could completely prevent the evolution of AML; however a better understanding of their impact on hematopoiesis is required. In response, we developed a Moran model of hematopoietic stem cells dynamics in the pre-leukemic phase. To this model, we integrated population pharmacokinetic-pharmacodynamics (PK-PD) models to investigate the clonal reduction potential of several candidate drugs. Our results suggest that three cardiac glycosides (proscillaridin A, digoxin and ouabain) reduce the expansion of premalignant stem cells through a decrease in pre-LSC viability, underlining the prospect of these treatments for AML.
  • Derek Park (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, USA)
    "Deep Reinforcement Learning of Optimal Chemotherapy Scheduling Demonstrates a Robustness vs. Performance Tradeoff in Patient Outcomes"
  • Hematopoietic and immune dynamics are a complex system that often underpins success or failure for cancer chemotherapy. While multiple mathematical models exist for simulating cancer treatment and response, there remains a significant deficit in regards to optimization and getting cohesive, generalizable strategies. Here, we present a deep reinforcement learning framework to optimize previously established models of hematopoietic and immune dynamics during chemotherapy. By testing differing reward mechanisms and training on biased cohorts, we demonstrate a robustness-performance trade-off when it comes to treating aggressive versus less-aggressive tumors. Finally, we present how this framework can be generalized to other hematopoietic models in cancer treatment settings.
  • John Higgins (Department of Systems Biology, Harvard Medical School; Department of Pathology, Massachusetts General Hospital, USA)
    "Population dynamics of circulating blood cells in the pathogenesis and diagnosis of some common diseases"
  • Circulating populations of red (RBC) and white blood cells and platelets in humans are tightly regulated, and rates of production, maturation, and turnover are modulated in response to disease. Anemia or low red blood cell count is a common early finding in diseases ranging from infection to cancer to malnutrition, and persistence of anemia is associated with poor patient outcomes. The age distribution of the circulating cell populations provides a history of disease-induced perturbations and homeostatic responses, but it is not currently feasible to measure these distributions. Standard clinical blood counts (CBCs) report only a handful of blood cell population statistics, but CBCs usually involve thousands of single-cell measurements. Building on existing theory and analysis, we have developed models of the RBC age distribution that use these and other routine clinical data sets to enable inferences about the RBC age distribution and how it is altered in common disease states. These models suggest for instance that the healthy response to blood loss often entails not only the recognized compensatory increase in production of new cells but also an unappreciated decrease in turnover of old cells, a response which would also serve to mitigate the effects of the loss.

Deterministic and stochastic models for complex cardiovascular phenomena

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

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

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.

Models and Computations for Studying Biofluid Applications

Organized by: Zhiliang Xu (Univeristy of Notre Dame, USA), Giordano Tierra (University of North Texas, USA), Shixin Xu (Duke Kunshan University)
Note: this minisymposia has multiple sessions. The second session is MS10-MMPB.

  • Rolf Ryham (Fordham University, USA)
    "Collective hydrodynamics of amphiphilic particles assembled as small unilamellar vesicles"
  • In this talk we study the collective hydrodynamic behavior of amphiphilic Janus particles assembled as small unilamellar vesicles (sUVs). The simulations use a hybrid approach that is shown to capture the formation of bilayers in a solvent (SIAM J Multiscale Model. Simul., vol 18, pp. 79-103). In this hybrid formulation, the non-local interactions between the coarse-grained lipid molecules are described by a hydrophobicity functional, giving rise to forces and torques (between lipid particles) that dictate the motion of both particles and the fluid flow in the viscous solvent. Both the hydrophobic and hydrodynamic interactions between the coarse-grained amphiphilic particles are formulated into integral equations, which allow for accurate and efficient numerical simulations in both two- and three-dimensions. We validate our hybrid coarse-grained model by reproducing various physical properties of a lipid bilayer membrane, and use this simulation tool to examine how a small unilamellar vesicle behaves under a planar shear flow, and investigate the collective dynamics of sUVs under a shear flow. Finally we also examine the possibility of membrane rupture by extreme flowing conditions.
  • Wenrui Hao (Penn State University, USA)
    "Computational models of cardiovascular disease"
  • In this talk, I will introduce several computational models of cardiovascular disease including both atherosclerosis and aortic aneurysm growth to quantitatively predict the long-term cardiovascular risk. These models integrate both the multi-layered structure of the arterial wall and the aneurysm pathophysiology together. The heterogeneous multiscale method is employed to tackle different time scales while the finite element method is adopted to the deformation of the hyperelastic arterial wall all the time. A three-dimensional realistic cardiovascular FSI problem with an aortic aneurysm growth based upon the patients' CT scan data is simulated to validate a medically reasonable long-term prediction.
  • Yiwei Wang (Illinois Institute of Technology, USA)
    "An energetic variational approach for wormlike micelle solutions: Coarse graining and dynamic stability"
  • Wormlike micelles are self-assemblies of polymer chains that can break and recombine reversibly. In this talk, we present a thermodynamically consistent two-species micro-macro model of wormlike micellar solutions by employing an energetic variational approach. The model incorporates a break- age and combination process of polymer chains into the classical micro-macro dumbbell model of polymeric fluids in a unified variational framework. The modeling approach can be applied to other reactive or active complex fluids. Different maximum entropy closure approximations to the new model will be discussed. By imposing a proper dissipation in the coarse-grained level, the closure model, obtained by “closure-then-variation”, preserves the thermo- dynamical structure of both mechanical and chemical parts of the original system. The same modeling approach can be applied to many active or reactive systems found in biology.
  • Giordano Tierra (University of North Texas, USA)
    "Energy-stable numerical schemes for fluid vesicles with internal nematic order"
  • Models of flows containing vesicles membranes with liquid crystalline phases have been widely studied in recent times due to its connection with biological applications. During the presentation I will present the main ideas to derive a new model to represent the interaction between flows and vesicle membranes with internal nematic order and preferential orientation of their molecules in the membrane. In fact, the dynamics of this system is determined by the dissipation of an energy that regulates the competition between different effects, through the kinetic, bending, elastic and anchoring energies. Moreover, I will introduce a new unconditionally energy-stable numerical scheme to approximate the model, and I will present several numerical results in order to show the well behavior of the proposed scheme and the dynamics of this type of vesicle membranes.

Aggregation - Growth - Fragmentation Phenomena arising in biology

Organized by: Magali Tournus (Ecole Centrale Marseille, France), Marie Doumic (INRIA Paris, France), Miguel Escobedo (Universidad del País Vasco, Spain)

  • Thomas C T Michaels (Department of Physics and Astronomy, University College London, UK)
    "Spatiotemporal control of filamentous protein aggregation"
  • Liquid cellular compartments form in the cyto- or nucleoplasm and can regulate aberrant filamentous protein aggregation. Yet, the mechanisms by which these compartments affect protein aggregation remain unknown. Here, we combine kinetic theory of protein aggregation and liquid-liquid phase separation to study the spatial control of irreversible protein aggregation in the presence of liquid compartments. We find that even for weak interactions aggregates strongly partition into the liquid compartment. Aggregate partitioning is caused by a positive feedback mechanism of aggregate nucleation and growth driven by a flux maintaining the phase equilibrium between the compartment and its surrounding. Our model establishes a link between specific aggregating systems and the physical conditions maximizing aggregate partitioning into the compartment. The underlying mechanism of aggregate partitioning could be used to confine cytotoxic protein aggregates inside droplet-like compartments but may also represent a common mechanism to spatially control irreversible chemical reactions in general.
  • Alex Watson (University College London, UK)
    "Growth-fragmentation and quasi-stationary methods"
  • A growth-fragmentation is a stochastic process representing cells with continuously growing mass and sudden fragmentation. Growth-fragmentations are used to model cell division and protein polymerisation in biophysics. A topic of wide interest is whether or not these models settle into an equilibrium, in which the number of cells is growing exponentially and the distribution of cell sizes approaches some fixed asymptotic profile. In this work, we present a new spine-based approach to this question, in which a cell lineage is singled out according to a suitable selection of offspring at each generation, with death of the spine occurring at size-dependent rate. The quasi-stationary behaviour of this spine process translates to the equilibrium behaviour, on average, of the growth-fragmentation. We present some Foster-Lyapunov-type conditions for this to hold.
  • Wei-Feng Xue (School of Biosciences, University of Kent, UK)
    "The division of amyloid fibrils – Experimental analysis and future challenges"
  • The division of amyloid protein fibrils is required for the propagation of the amyloid state, and is an important contributor to their stability, pathogenicity and normal function. Here, I will present our experimental work on resolving amyloid division and biological impact of their size distributions. By applying new theoretical results emerging from collaboration with mathematicians, these experiments to profile the dynamical stability towards breakage for different amyloid types using AFM imaging reveal particular differences in the division properties of disease- and non-disease related amyloid. Here, the disease associated amyloid formed from alpha-synuclein show lowered intrinsic stability towards breakage and increased likelihood of shedding smaller particles compared with non-disease related amyloid models. Our results enable the comparison of protein filaments’ intrinsic dynamic stabilities, and suggest mapping stability differences of polymorphic amyloid structures as an important challenge to resolve in unravelling their toxic and infectious potentials.
  • Magali Tournus (Ecole Centrale Marseille, France)
    " Recovering the parameters of the fragmentation equation"
  • We consider a suspension of particles that undergo fragmentation. We address the question of estimating the fragmentation parameters – i.e. the division rate B(x) and the fragmentation kernel k(y,x) – from measurements of the size particles distribution at various times. This is a natural question for any application where the sizes of the particles are measured experimentally whereas the fragmentation rates are unknown. The application that drives our work is the study of mechanical properties of amyloid fibrils that undergo fragmentation (are the mechanical properties related to toxicity?). In this talk, I will present the biological questions that motivate our work and the new experiments performed by Wei-Feng Xue team at Canterbury, then I will explain why the inverse problem is well posed under reasonable assumptions, and I will focus on how we can recover the fragmentation rate and kernel in practice.

Mathematics of Microswimming

Organized by: Qixuan Wang (UC Riverside, United States), Bhargav Rallabandi (UC Riverside, United States), Mykhailo Potomkin (UC Riverside, United States)
Note: this minisymposia has multiple sessions. The second session is MS19-MMPB.

  • Chaouqi Misbah (CNRS and Univ. Grenoble, France)
    "Swimming of Cells and Artificial Particles Driven by Shape Changes and Chemical Activity"
  • Locomotion is essential for living cells. It enables bacteria and algae to explore space for food, cancer to spread, and immune system to fight infections. Amoeboid swimming will be first discussed exhibiting variety of behaviors (like navigation, asymmetric motion in a channel, etc.). Then we discuss generic trajectories obtained for active particles driven by a chemical activity. These types of particles display trajectories of intriguing complexity, from regular (e.g. circular, helical, and so on) to irregular motions (run-tumble), the origin of which has remained elusive for over a century. This dynamics versatility is conventionally attributed to the shape asymmetry of the motile entity, to the suspending media, and/or to stochastic regulation. A universal approach highlighting that these movements are generic, occurring for a large class of cells and artificial microswimmers, without the need of invoking shape asymmetry nor stochasticity, but are encoded in their inherent nonlinear evolution. We show, in particular, that for a circular and spherical particle moving in a simple fluid, circular, helical and chaotic motions (akin to a persistent random walk) emerge naturally in different regions of parameter space. This establishes the operating principles for complex trajectories manifestation of motile systems, and offers a new vision with minimal ingredients.
  • Kirsty Wan (University of Exeter, United Kingdom)
    "Locomotor patterning in quadriflagellate microswimmers: lessons from quadrupeds and robots"
  • When animals first evolved from underwater to terrestrial living, they first had to overcome the formidable challenge of coordinating and controlling their limbs to generate effective legged locomotion involving gaits such as crawling, walking galloping. Surprisingly, it was recently discovered that many species of single-celled algae exhibit similar gaits for swimming, despite being only tens of micrometers across and lacking in a nervous system. Among these, species that have four flagella (whip-like appendages that can bend and deform actively in a fluid) are particularly abundant in nature. Species that appear morphologically similar may nonetheless be associated with distinct gaits and swimming speeds. In this talk i will discuss our recent efforts to integrate fluid dynamical modelling, live-cell experiments, and robophysical models to understand the swimming gaits of quadriflagellate algae. Continuing research into these microscopic swimmers may provide key insights into the evolutionary origins of decentralized locomotor control in living systems.
  • Hermes Gadêlha (Department of Engineering Mathematics and Bristol Robotics Laboratory, University of Bristol, United Kingdom)
    "Coarse-graining formulations for sperm swimming and other flagellates"
  • The inertialess fluid-structure interactions of active and passive inextensible filaments and slender-rods are ubiquitous in nature. The coupling between the geometry of deformation and the physical interaction governing the fluid dynamics is complex. Governing equations negotiate multi-scale interactions with non-holonomic constraints. Such systems are structurally convoluted, prone to numerical errors, often requiring penalization methods and high-order spatio-temporal propagators. In this talk we will discuss how the coarse-graining formulation greatly simplifies the several biophysical interactions and overcomes numerical instability. The dynamical system is straightforward and intuitive to implement, and allows for a fast and efficient computation. Only basic knowledge of systems of linear equations is required, and implementation achieved with any solver of choice. Generalizations for complex interaction of multiple rods, Brownian polymer dynamics, active filaments and non local hydrodynamics are also straightforward.
  • Ye Chen (New Jersey Institute of Technology, United States)
    "Helical locomotion in a porous medium"
  • Microorganisms and artificial microswimmers often need to swim through environments that are more complex than purely viscous liquids in their natural habitats or operational environments, such as gel-like mucus, wet soil and aquifer. The question of how properties of these complex environments affect locomotion has attracted considerable recent attention. In this work, we focus on helical locomotion for its ubiquity as a propulsion mechanism adopted by many swimming bacteria. We present a theoretical model to examine how the additional resistance due to the network of stationary obstacles in a porous medium affects helical locomotion. Compared with previous theoretical and experimental results, we will elucidate the effects of the resistance on various types of helical locomotion. We also remark on the limitations as well as potential connections of our results with experimental measurements of bacterial swimming speeds in polymeric solutions.

Mathematics of Microswimming

Organized by: Qixuan Wang (UC Riverside, United States), Bhargav Rallabandi (UC Riverside, United States), Mykhailo Potomkin (UC Riverside, United States)
Note: this minisymposia has multiple sessions. The second session is MS18-MMPB.

  • Rishabh V. More (Mechanical Engineering, Purdue University, United States)
    "Micro-swimmer dynamics in stratified fluids"
  • Understanding the motion of microorganisms in aquatic bodies like lakes and oceans has been an active area of research for decades with wide ecological and environmental impacts. Especially, the upper layer of oceans which sustains an intense biological activity, observes a vertical variation in the density (stratification) which can either be due to variations in water temperature or salinity, or both. From our fully resolved numerical simulations, we show that fluid stratification affects the locomotion of an individual, interactions between a pair, and the dynamics of suspensions of marine micro-swimmers in interesting and non-intuitive ways. At low Re, the vertical migration of small organisms is hydrodynamically affected due to the rapid velocity decay as well as higher energy expenditure in stratified fluids. At a finite Re, stratification even leads to striking differences in the swimming speeds and stability of swimmers as compared to their motion in a homogeneous fluid. The reduced flow signature of a swimming organism due to stratification can save them from getting detected by predators. Stratification increases the contact time of two colliding swimmers, thus, increasing the probability of successful reproduction. These results can explain the commonly observed accumulation of phytoplankton in oceans. Finally, collective motion microorganisms alter the temperature microstructure and lead to higher mixing with increasing stratification. Insights obtained from the investigations for an individual swimmer's motion and interactions between a pair of swimmers in a stratified fluid explain these observations.
  • Jeffrey L. Moran (Department of Mechanical Engineering, George Mason University, United States)
    "Chemokinesis-driven Accumulation of Artificial Microswimmers in Low-Motility Regions of Fuel Gradients"
  • Motile cells often detect and respond to changes in their local chemical environment by changing their speed or direction, which allows them to carry out important functions including finding nutrients, immune response, or predator evasion. Two common examples are chemotaxis (motion up or down a chemical concentration gradient) and chemokinesis (dependence of speed on chemical concentration). Chemokinesis is distinct from chemotaxis in that no directional sensing or reorientation capabilities are required. Over the past 15+ years, researchers have developed 'artificial microswimmers' or 'microrobots' that move at speeds that usually depend on the concentration of a chemical 'fuel' (chemokinesis). However, the behavior of artificial microswimmers in fuel gradients has not been thoroughly characterized and the extent to which they exhibit chemotaxis is not fully known. Here, we study the behavior of half-platinum half-gold self-propelled rods in steady state, antiparallel gradients of hydrogen peroxide fuel and potassium chloride salt, which tend to increase and decrease the rods' speed, respectively. Brownian Dynamics simulations, a Fokker-Planck theoretical model, and experiments demonstrate that at steady state, the chemokinetic self-propelled rods accumulate in low-speed (salt-rich, peroxide poor) regions not because of chemotaxis, but because of chemokinesis. The agreement between simulations, model, and experiments bolsters the role of chemokinesis in this system and validates previous theoretical findings [Popescu et al., Nano Lett. 18, 9 (2018)] that chemokinesis alone cannot lead to chemotaxis. This work suggests a novel strategy of exploiting chemokinesis to effect the accumulation of artificial microswimmers in desired areas, which could find application in environmental remediation, wound healing, and drug delivery for cancer treatment.
  • Eva Kanso (University of Southern California, United States)
    "Emergent Waves in Ciliary Carpets"
  • Motile cilia often line internal epithelial surfaces with thousands of multiciliated cells, each containing hundreds of cilia. Their coordinated motion drives flows with important biological functions in the respiratory, cerebrospinal, and reproductive systems in humans. Cilia coordination has been studied extensively at the level of pairs of cilia, and even in collections of cilia with metachronal waves. However, a general theory for investigating the hydrodynamics of cilia coordination in large systems remains lacking. Here, starting from discrete arrays of cilia, wherein each cilium is represented by a well-known oscillator model, we devise a fast numerical algorithm for investigating the dynamics of thousands of hydrodynamically-coupled cilia. We then develop a continuum theory in the limit of infinitely many independently beating cilia by combining tools from active matter with classical Stokes flow methods. We analyze the stability of isotropic and synchronized states and show that they are unstable. Surprisingly, traveling wave patterns emerge in both the discrete and continuum theory regardless of initial conditions, indicating that these waves are global attractors.
  • David Saintillan (Mechanical and Aerospace Engineering, University of California San Diego, United States)
    "An Integrated Chemomechanical Model of Sperm Locomotion"
  • Mammalian sperm cells achieve locomotion by the spontaneous periodic oscillation of their flagellum. Dynein motors inside the flagellum consume energy from ATP to exert active sliding forces between microtubule doublets, thus creating bending waves along the flagellum and enabling the sperm cell to swim in a viscous medium. Using a sliding-control model of the axoneme that accounts for the coupling of motor kinetics with elastic deformations, we develop a chemomechanical model of a freely swimming sperm cell that accounts for the effect of non-local hydrodynamic interactions between the sperm head and flagellum. The model is shown to produce realistic beating patterns and swimming trajectories, which we analyze as a function of sperm number and motor activity. Remarkably, we find that the swimming velocity does not vary monotonically with motor activity, but instead displays two local maxima corresponding to distinct modes of swimming.

Deterministic and stochastic models for complex cardiovascular phenomena

Organized by: Martina Bukac (University of Notre Dame, United States), Daniele Schiavazzi (University of Notre Dame, United States)
Note: this minisymposia has multiple sessions. The second session is MS14-MMPB.

  • Mitchel Colebank (North Carolina State University, United States)
    "Modeling and simulation of fluid dynamics in chronic thromboembolic pulmonary hypertension"
  • A compromised pulmonary vasculature can lead to pulmonary hypertension (PH), defined by a mean pulmonary arterial blood pressure (mPAP) exceeding 20 mmHg. Though there have been advances in PH treatments, only chronic thromboembolic pulmonary hypertension (CTEPH) is considered curable. CTEPH is characterized by multiple recurrent or unresolved pulmonary emboli that impede flow to the alveoli. The disease causes perfusion defects, causing small vessel disease in both obstructed and unobstructed territories. Those with lesions in the smaller arteries are treated by balloon pulmonary angioplasty (BPA), though treatment planning is clinic dependent. To address this, we propose a multiscale model of CTEPH hemodynamics that couples a one-dimensional computational fluid dynamics model (1D CFD) of the large arteries to a linearized CFD model of the small arteries and arterioles. The former is conducted in an image based geometry, while the latter fluid dynamics are simulated in a fractal, structured tree. We also integrate two pressure-loss models, mimicking typical CTEPH lesions. Our results show that the model framework predicts common phenotypes of CTEPH, including perfusion deficits, small vessel flow imbalances, and elevated mPAP. Lastly, we use the 1D model to predict hemodynamic improvements after virtual BPA, laying the foundation for an in-clinic treatment planning tool.
  • Charles Puelz (Baylor College of Medicine and Texas Children's Hospital, United States)
    "A fluid/structure interaction model of the human heart"
  • This talk will focus on our efforts towards building a computational model of the entire human heart, including the blood, valves, heart chambers, great vessels, and peripheral circulations. The heart tissues are assumed to be anisotropic hyperelastic materials immersed in blood, and blood itself is modeled as a viscous incompressible Newtonian fluid. The equations of motion are solved using the immersed finite element method. In this numerical approach, tissue displacements and forces are approximated on finite element meshes and blood velocities and pressures are approximated on a fixed and possibly locally refined Cartesian grid. Tissue geometries are generally imaged based, and constitutive laws for the tissues depend on fiber directions calculated using Poisson interpolation. Peripheral circulations in the form of 3-element Windkessel models provide boundary conditions for the heart model.
  • Jae Lee (Johns Hopkins University, United States)
    "Fluid-structure interaction models of bioprosthetic heart valves to study leaflet kinematics"
  • Bioprosthetic heart valves (BHVs) are commonly used in surgical and percutaneous valve replacement. The durability of percutaneous valve replacement is unknown, but surgical valves have been shown to require reintervention after 10--15 years. Further, smaller-diameter surgical BHVs generally experience higher rates of prosthesis-patient mismatch (PPM), which leads to higher rates of failure. Bioprosthetic aortic valves can flutter in systole, and fluttering is associated with fatigue and failure in flexible structures. The determinants of flutter in BHVs have not been well characterized, however, despite their potential to impact durability. We use an experimental pulse duplicator and a computational fluid-structure interaction model of this system to study the role of device geometry on BHV dynamics. The experimental system mimics physiological conditions, and the computational model enables precise control of leaflet biomechanics and flow conditions to isolate the effects of variations in BHV geometry on leaflet dynamics. We systematically characterize the impact of BHV diameter and leaflet thickness on fluttering dynamics. Ultimately, understanding the effects of device geometry on leaflet kinematics may lead to more durable valve replacements.
  • Zachary Sexton (Stanford University, United States)
    "Multiscale Hemodynamics of Autogenerated Cardiovascular Networks"
  • Recapitulating the complex topologies and flow physics of meso/microvascular circulation precedes the manufacturing of functional, biofabricated tissues. In this work we leverage stochastic constrained constructive optimization (CCO) methods to automatically vascularize proposed cardiac tissue perfusion volumes. This approach seeks to optimize vascular topologies with respect to costs functions derived from total hydraulic resistance and blood volume constrained to geometric assumptions imposed by Murray’s law. We introduce techniques to partially bind intermediate network solutions to accelerate the optimization process while improving algorithmic precision compared to recent literature. To assess hemodynamics within these networks, we utilize multiscale 0D-3D models for computational fluid dynamics simulations with prescribed pulsatile inflows. We compare time-averaged pressures and volumetric flow rates across CCO models constructed with varying power law constraints and cost function formulations. Furthermore, we predict hemodynamic metrics crucial in wall homeostasis and adaptation including time-averaged wall shear stress, oscillatory shear index, and regions of low shear to better identify viable network topologies for biofabrication. Our pipeline will serve as an end-to-end, open-source solution for autogenerating vascular networks and verifying local flow behavior in future engineered tissues.

Sub-group contributed talks

MMPB Subgroup Contributed Talks

  • Brendan Fry Metropolitan State University of Denver
    "A hybrid model for metabolic signaling in the human retinal microcirculation"
  • Impaired blood flow regulation and oxygenation have been implicated as contributors to glaucomatous damage in the retina. Here, a mathematical model is presented that combines an image-based heterogeneous representation of the retinal arteriolar vasculature with a compartmental description of the downstream capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. This hybrid model is used to predict blood flow and oxygenation throughout the entire retinal microcirculation; in addition, a metabolic wall signal is calculated in each vessel from blood and tissue oxygen levels, and is conducted upstream to communicate the metabolic status of the retina to the arterioles. Model results predict a wide range of metabolic signals generated throughout the microvascular network, dependent both on oxygen levels and vascular path lengths. Overall, the model predicts that a higher metabolic wall signal is generated in pathways with a lower oxygen level at the terminal arteriole. This model framework will be used in the future to simulate blood flow regulation in a realistic, spatially non-uniform representation of the human retina, in order to assess the role of metabolic blood flow dysregulation in glaucoma.
  • Thomas Bury McGill University
    "Long ECGs reveal rich and robust dynamical regimes in patients with frequent premature ventricular complexes."
  • Heart disease is one of the leading causes of disability and death. One manifestation of heart disease is abnormal heart rhythms, called arrhythmia. A very common arrhythmia consists of abnormal extra heart beats called premature ventricular complexes (PVCs). Though considered benign in most cases, recent studies have shown that frequent PVCs pose an increased risk for more serious arrhythmia that can lead to sudden cardiac death. Risk stratification for these patients remains a significant challenge in part since the mechanism generating the PVCs is usually unknown. In this talk, we will show how analysis of multi-day ECGs reveal robust dynamical regimes in PVC dynamics that vary as a function of heart rate and hour of the day. This analysis facilitates the development of basic mathematical models that can help reveal the underlying mechanism of PVCs. With the current advances in wearable technology and corresponding influx of ECG data, such approaches can bring about a dynamics-based personalised medicine.
  • Jeungeun Park University of Cincinnati
    "A swimming strategy of polarly-flagellated bacteria"
  • Flagellar bacteria swim through fluid by rotating their flagella that are connected to rotary motors in their cell wall. The physical, geometrical, and material properties of flagella characterize bacterial swimming patterns. In this talk, we present a mathematical model of a lophotrichous bacterium swimming through fluid. We introduce a recently reported swimming mode in which a bacterium undergoes a slow swimming phase by wrapping its flagella around the cell body. By using our mathematical model, we investigate the mechanism of wrapping motion, and suggest benefits of the motion in bacterial native habitats. Furthermore, we compare our numerical examples with experimental observations.
  • Dongheon Lee Department of Biomedical Engineering, Duke University
    "Hybrid Data-driven Mechanistic Modeling Approach to Describe Uncertain Intracellular Signaling Pathways"
  • Developing an accurate mechanistic model is important in analyzing an intracellular signaling pathway. However, a model is difficult to be developed since it requires in-depth understandings. Since underlying mechanisms are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a mechanistic model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability.

MMPB Subgroup Contributed Talks

  • Jonathan Miller University of Dundee
    "Modelling firing characteristics of T6SS"
  • In this talk I will develop a mathematical model of of the Type VI bacterial secretion system. The Type VI Secretion System (T6SS) is a transmembrane macro-molecular contractile machine able to dynamically and repeatedly compete against both prokaryotes and eukaryotes. Whilst many of the core molecular components of the T6SS have been identified, there are open questions regarding how the T6SS is regulated in response to stimuli. Here I develop a stochastic differential equation model that describes post-translational regulation of the T6SS. The model is solved numerically and used to explore how the time between successive firing events allows for spatial reorientation of firing and thus for a bacterium to respond to spatially localised external stimuli.
  • Divyoj Singh Indian Institute of Science
    "Continuum model for Planar cell polarity"
  • Planar Cell Polarity (PCP) is an evolutionary conserved phenomenon in which cells in an epithelium are polarized within the plane of the tissue. Disruptions in PCP can often lead to developmental abnormalities such as defects in neural tube formation and atypical organ shape. The emergent multi-scale dynamics of PCP has been investigated experimentally and computationally through focusing on different modules (set of molecular players) revealing asymmetric protein localisation on cell boundaries as the primary PCP mechanism. Additional ingredient in the PCP establishment is the global cue in the form of tissue-wide protein concentrations. Despite multiple mechanistic modelling attempts, an analytic understanding of the system has not yet been comprehensively achieved. Here, we present a minimal continuum model, derived from the microscopic interactions of the proteins, to study the emergence of macroscopic tissue-wide polarity. We obtain necessary and sufficient conditions and diverse parameter regimes for different cases of establishing PCP and its disruptions. We also solve the model numerically to study the model where analytic solution is not possible. Finally, we compare the model results to other existing mechanistic approaches to draw conceptual parallels between them, with the goal of identifying design principles of PCP.
  • Ushasi Roy Indian Institute of Science Bangalore, India
    "Does intermediate intercellular adhesion leads to faster migration of a multicellular cluster?"
  • Diverse biological processes like embryogenesis, morphogenesis, neurogenesis, regeneration, wound healing, and disease propagation like cancer-metastasis involve numerous cells exhibiting coherent migration. Multicellular clusters undergo dynamic rearrangement while relocating — bigger clusters split, smaller sub-clusters collide and reassemble, gaps continually appear and disappear, and cells (and the clusters as a whole) undergo variations in shape and orientation. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. To unveil the underlying mechanics of collective migration of two-dimensional cell clusters concertedly tracking chemical gradients, we develop a generic computational framework based on the cellular Potts model which captures cell shape changes and cluster rearrangement. We find that cells have an optimal adhesion strength that maximizes cluster migration speed. The optimum negotiates a tradeoff between preserving cell-cell contact and maintaining configurational freedom, and we identify maximal variability in the cluster aspect ratio as a revealing signature. Our results suggest a collective benefit for intermediate cell-cell adhesion.U. Roy and A. Mugler. Phys. Rev. E 103, 032410 (2021).
  • Tsuyoshi Mizuguchi Osaka Prefecture University
    "Inhomogeneity of Japanese name distribution"
  • The size distributions of persons' names, i.e., how many people share a certain name, obeys Zipf's law in various countries or areas. There is, however, a regionality for each country or area, and the ingredients of the distributions differ from each other. We statistically analyze the distributions of persons' family and given names obtained from a telephone directory to characterize their heterogeneities. By using Kullback–Leibler divergence, the inhomogeneity of name distribution are analyzed both from the viewpoint of person and prefecture.

MMPB Subgroup Contributed Talks

  • Juliana Curty Faria CFisUC, University of Coimbra
    "Fibrinogen-Mediated Erythrocyte Adhesion"
  • Peripheral vascular disease (PVD) is an abnormal condition of blood vessels, where they become completely or partially blocked due to atherosclerosis, which is associated with increased serum levels of fibrinogen. High levels of fibrinogen may result in increased erythrocyte aggregation, leading to changes in blood rheology. Here we combine experimental micropipette assays with mathematical modeling to gain insight into the role of fibrinogen in mediating erythrocyte adhesion. The micropipette assay permits the direct visualization of the deformation of two erythrocytes as a function of fibrinogen concentration as they adhere while being pulled apart. The computational phase-field model we implement permits us to relate the morphology of the adhered erythrocytes with the pulling force they exert on each other. By comparing the erythrocyte deformations observed in the two methodologies we are able to estimate the forces the two cells exert on each other during the micropipette assay. We further compare this value with the forces measured by AFM between fibrinogen covered spheres and erythrocytes.
  • Tânia Sousa Department of Life Sciences University of Coimbra, Coimbra, Portugal
    "How far can hydrogen peroxide travel in microcirculation?"
  • In response to a mechanical or other stimuli, vascular endothelial cells release superoxide to the extracellular medium. Part of this superoxide is readily dismutated into hydrogen peroxide, which can act as an autocrine and/or a paracrine signalling agent. In this work we developed a computer simulation to quantify the restrictions of hydrogen peroxide signalling in capillaries and arterioles. This computer simulation considered the following processes: the superoxide dismutation; the superoxide/hydrogen peroxide release by endothelial cells and uptake by erythrocytes and endothelial cells; and the diffusion and transport of hydrogen peroxide/superoxide by the blood flow. It is assumed that superoxide is produced in a ring of endothelial cells with 20μm length. For plausible cellular rates of superoxide production, local hydrogen peroxide concentrations in blood plasma may reach ~0.1 μM. Maximal concentrations occur within 10 μm and 500μm of the start of the superoxide production domains, in capillaries and arterioles, respectively. We conclude that (i) signalling through superoxide/hydrogen peroxide release to the circulation can only be autocrine in the case of the capillaries and may be paracrine in arterioles; (ii) hypothetical signalling mechanisms must be sensitive to sub-μM extracellular hydrogen peroxide concentrations, which requires peroxiredoxins or peroxidases acting as hydrogen peroxide receptors.
  • Gustavo Taiji Naozuka Laboratório Nacional de Computação Científica
    "Discovery of a dynamical system from simulated tumor growth data of a hybrid multiscale model"
  • Data-driven methods via machine learning have been useful for predicting the behavior of several complex systems in science and engineering. Recently, the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method has been proposed to discover underlying governing equations from measurement data. This approach assumes that most physical systems have only a few relevant terms to the dynamics and depends on determining the best value for a threshold parameter, which eliminates non-important terms of the governing equations. However, this choice needs to be performed exhaustively, evaluating the Pareto frontier that balances model complexity and accuracy. On the other hand, sensitivity analysis (SA) is a technique that allows ranking the importance of the parameters with respect to the quantity of interest. In this work, we modify the original SINDy implementation replacing the definition of the threshold parameter with a sensitivity analysis method. The SINDy-SA method is applied to capture the dynamical system from time evolution data of different tumor phenotypes. The data are collected from a simulation of a hybrid multiscale model for tumor growth. Besides retrieving the governing equations from data, the proposed approach is automated and able to reduce high complexity models to low complexity systems of ordinary differential equations.
  • Rui Travasso CFisUC, University of Coimbra
    "Adhesion modulates cell morphology and migration within dense fibrous networks"
  • Cell movement involves the coordination between mechanical forces, biochemical regulatory pathways and environmental cues. In particular, epithelial cancer cells have to employ mechanical strategies in order to migrate through the tissue's basement membrane and infiltrate the bloodstream during the invasion stage of metastasis. In this work we explore how mechanical interactions such as spatial restriction and adhesion affect migration of a self-propelled droplet in dense fibrous media. We have performed a systematic analysis using the phase-field model and a vertex model, and we propose a novel approach to simulate cell migration with dissipative particle dynamics modelling. With this purpose we have measured in our simulation the cell's velocity and quantified its morphology as a function of the fibre density and of its adhesiveness to the matrix fibres. Furthermore, we have compared our results to a previous in vitro migration assay of fibrosarcoma cells in fibrous matrices. Our results indicate that adhesiveness is critical for cell migration, by modulating cell morphology in crowded environments and by enhancing cell velocity. In addition, we explore the morphology of epithelial tissues after multiple events of cell extrusion.

MMPB Subgroup Contributed Talks

  • Ahmed Abdelhamid
    "Computational modeling of external versus internal fibrinolysis in contracted blood clots"
  • Minseo Kim Arnold O. Beckman High School
    "Revealing the Effect of Hydration on Kidney Stone Formation Through Singular Perturbation Analysis"
  • Kidney stones, also known as renal calculi, are hard deposits of salts and minerals that form in the kidney. When the stones get stuck in the urinary tract and obstruct the path of urine, they may cause excruciating pain in the lower abdomen. The most common type of kidney stones is made of calcium and oxalate, and they form during the bodily process of creating urine, especially when the urine becomes supersaturated and does not allow minerals to dissolve. In fact, recent studies have shown that drinking plenty of water dilutes the substances in urine and thereby reduces the likelihood of contracting kidney stones. Overall, this project devises two mathematical models that accurately and systematically determine the behavior of chemicals in the system. Then, we present a quantitative mechanism, namely the method of matched asymptotic expansions, and different modeling techniques to explain how an increase in fluid consumption decreases the amount of calcium-oxalate complex in the body and consequently the risk of contracting kidney stones.
  • Valeri Barsegov Department of Chemistry, University of Massachusetts, Lowell
    "Biomechanics, Thermodynamics and Mechanisms of Rupture of Fibrin Clots"
  • Fibrin is the main determinant of the mechanical stability of blood clots and thrombi. Here, we explored the rupture of blood clots, emulating thrombus breakage by stretching fibrin gels with single-edge cracks. The stress-strain profiles display the weakly non-linear regime I of the gel due to alignment of fibrin fibers; linear elastic regime II owing to reversible stretching of fibers; and the rupture regime III for large deformations, during which irreversible breakage of fibers occurs. These dynamic mechanical regimes correlate with structural changes in the fibrin network. To model the stress-strain curves, we developed the Fluctuating Spring model, which maps the fibrin alignment, elastic network stretching, and cooperative rupture of coupled fibrin fibers into a mathematical framework to obtain a formula for stress as a function of strain. Cracks render network rupture stochastic. The free energy change for fiber deformation and rupture decreases with the crack size, thereby making the network rupture more spontaneously, but mechanical cooperativity due to the inter-fiber coupling strengthens the fibrin network. These results provide a basis for understanding of blood clot breakage that underlies thrombotic embolization. The mathematical Fluctuating Spring model can be used to characterize the dynamics of mechanical deformation of other protein networks.

MMPB Subgroup Contributed Talks

  • Gabriella Bretti IAC-CNR
    "A mathematical simulation algorithm for the dynamics on cells on microfluidic chips"
  • The present work was inspired by the recent developments in laboratory experiments made on microfluidic chip, where culturing of multiple human cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis, and takes into account the interactions among cell populations and the possibility of drug administration.A simulation tool that is able to reproduce the chemotactic movement was developed and the interactions between different cell species (immune and cancer cells) living in microfluidic chip environment was simulated. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving condition involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains. We finally find that the qualitative behavior of the solutions obtained by our simulation algorithm is comparable with the experimental observations.
  • Andrew Mair Heriot-Watt University
    "Modelling the influence of plant root systems on soil moisture transport"
  • Understanding the effect of vegetation on the hydraulic properties of soil is an important aspect of land management. Plants grow complex root systems to acquire water and nutrients. There is strong evidence that the presence of these root systems increases the hydraulic conductivity of soil. The famous Richards' equation is the standard model for moisture transport through soil. In this work we modify Richards' equation to propose a model which incorporates preferential flow along the axes of the roots which occupy the soil. This accounts for the influence of the explicit structure of a root system on soil moisture transport. We calibrate our model with respect to experimental data on the saturated hydraulic conductivity of vegetated soils and use Bayesian optimisation to do this. Our calibration results suggest that preferential moisture flow does occur along root axes. They also support the hypothesis that this preferential flow plays a key role in the observed differences between the hydraulic properties of vegetated and bare soil.
  • Mohit Dalwadi University of Oxford
    "Emergent robustness of bacterial quorum sensing in fluid flow"
  • Bacteria use intercellular signalling, or quorum sensing (QS), to share information and respond collectively to aspects of their surroundings. The autoinducers that carry this information are exposed to the external environment. Consequently, they are susceptible to removal through fluid flow, a ubiquitous feature of bacterial habitats ranging from the gut and lungs to lakes and oceans.We develop and apply a general theory that identifies and quantifies the conditions required for QS activation in fluid flow by systematically linking cell- and population-level genetic and physical processes. By exploring the dynamics across an imperfect transcritical bifurcation in the system, we predict that cell-level positive feedback promotes a robust collective response, and can act as a low-pass filter at the population level in oscillatory flow, responding only to changes over slow enough timescales. Moreover, we use our model to predict how bacterial populations can discern between increases in cell density and decreases in flow rate.[1] Emergent robustness of bacterial quorum sensing in fluid flow, MP Dalwadi and P Pearce, PNAS, 118, e2022312118; DOI: 10.1073/pnas.2022312118
  • Bente Hilde Bakker Universiteit Leiden
    "Cellular Potts model with discrete fibrous extracellular matrix replicates strain-stiffening"
  • The extracellular matrix is the biological mortar that holds cells together. A major class of matrix proteins form molecularly crosslinked fibres. The fibre network has non-trivial topology and displays strain-stiffening, which affects cell migration. Cell-based models such as cellular Potts generally treat mechanical interactions between cells and the extracellular matrix with mean-field approaches, e.g. finite element models, but these have the downside that they average fibre network topology.To address this gap, we developed a cellular Potts model with discrete extracellular matrix fibres. The model was implemented by interfacing the cellular Potts software library Tissue Simulation Toolkit with the molecular mechanics framework HOOMD-blue via a Python bridge. Fibres are modelled using a bead-spring chain with linear elastic potentials between consecutive beads and linear bending potentials between consecutive bead triplets. Fibres can be mechanically coupled via crosslinkers, and cellular Potts cells link to fibres via discrete focal adhesion-like sites.We simulate how a single contractile cellular Potts cell strains a pre-defined fibre network. We compare how parameters including fibre number, fibre crosslinks, and number of adhesion sites affect network strain and local fibre density. Using in silico atomic force microscopy, we measure spatial variation in network stiffness and detect strain-stiffening.','In this contribution, we present the mathematical modelling tools needed to address an open question in biology: How do interactions between cells and the extracellular matrix affect cell behaviour?Our chosen modelling formalism is a hybrid combination of discrete-space cellular Potts and continuous-space molecular dynamics. These two types of models have been used to great success in isolation to address various biological questions.Combining these techniques is crucial for understanding cell migration during angiogenesis and metastasis.