Organized by: Mitchel J. Colebank (University of South Carolina), Vijay Rajagopal, The University of Melbourne, Australia

Note: this minisymposia has multiple sessions. The other sessions are: Part-2, Part-3, and Part-4.

1. Vijay Rajagopal University of Melbourne
   "Calcium-dependent regulation of physiological vs pathological cardiomyoctre hypertrophy"
Cardiomyocyte hypertrophic growth contributes to the adaptative response of the heart to meet sustained increases in hemodynamic demand. While hypertrophic responses to physiological cues maintains or enhances cardiac function, when triggered by pathological cues, this response is maladaptive, associated with compromised heart function, although initially, this response maybe adaptive with preserved function. Since cues and activated pathways associated with both forms of hypertrophy overlap, the question arises as to the mechanism that determines these different outcomes. Here we evaluate the hypothesis that cardiomyocyte Ca2+ signalling – a regulator of pathological hypertrophy - also signals physiological hypertrophy. We discuss how different Ca2+ profiles, in distinct subcellular organelles/microdomains, and interacting with other signalling pathways, provides a mechanism for Ca2+ to be decoded to induce distinct hypertrophic phenotypes. We discuss how integration of computational with rich structural and functional cellular measurements can be used to decipher the role of Ca2+ in hypertrophic gene programming.
2. Karin Leiderman University of North Carolina at Chapel Hill
   "A discrete platelet-bonding model for simulating platelet aggregation under flow"
Hemostasis is the healthy clotting response to a blood vessel injury. A major component of clotting is platelet aggregation, which involves the formation of platelet-platelet and platelet-wall bonds between platelet receptors (GPVI and GP1b), and platelet integrins ($alpha_2beta_1$ and $alpha_{IIb}beta_3$) with plasma-borne molecules (von Willebrand factor and fibrinogen) and wall adherent collagen. There are platelet disorders that decrease the number and/or functionality of $alpha_{IIb}beta_3$, which results in excessive bleeding. Current treatments exist but are not evidence based and are not always successful in restoring hemostasis. In the cases where hemostasis is restored, the aggregation mechanism without $alpha_{IIb}beta_3$ remains speculative. Our long-term goal is to uncover this mechanism with a mathematical and computational approach. As a first step, we simulated platelet aggregation using the molecular dynamics software, LAMMPS. We considered individual platelets and tracked the platelet-platelet and platelet-wall bonds that formed during aggregation. Currently, the strength of the bonds depends on the local shear rate of a prescribed background flow. Simulations show stable aggregation for healthy platelets under flow. Future work is to improve our modeling framework by parameterizing with experimental measurements and computationally coupling our platelet model to a dynamic flow.
3. Pradeep Keshavanarayana University College London, London, UK
   "Combination of shear stress and hydrostatic pressure dictates the temporal behaviour of vasculature permeability"
ndothelial cells form the inner lining of blood vessels, and their dysfunction, particularly at VE-cadherinbased cell-cell junctions, is associated with several life-threatening diseases. These cells are simultaneously exposed to various mechanical and chemical stimuli, with pathological conditions altering the balance of these stimuli, disrupting mechano-chemical equilibrium and cellular functions. Key mechanical stimuli include extracellular matrix (ECM)-dependent traction forces, shear stress from blood flow, and hydrostatic pressure within blood vessels. The simultaneous action of these forces disrupts cell-cell junctions, leading to changes in endothelial permeability. Increased permeability is not only linked to cardiovascular diseases but also impacts organs like the eyes and brain through the blood-retinal and blood-brain barriers. To investigate the effects of multiple mechanical stimuli on the endothelium, we developed a continuum model of an endothelial cell incorporating a strain-rate dependent active stress model. VE-cadherins, which connect neighbouring endothelial cells, are modelled using a traction-separation law. As traction forces on cell-cell junctions increase, the cohesive bonds weaken, resulting in loss of contact between cells. Our model considers both planar and cylindrical monolayers, revealing that monolayer geometry, in addition to mechanical stimuli, influences permeability. Recent in vitro studies have identified piezo-1 as a mechanotransduction pathway that regulates endothelial cell responses by altering cytoplasmic calcium concentration. Using a phenomenological law linking mechanical stimuli to calcium concentration and active stress, we demonstrate that endothelial permeability depends on shear stress and hydrostatic pressure magnitudes, and the duration of its application. Simulations show that permeability evolves over time based on shear stress magnitude. Under hydrostatic pressure, low shear stress initially results in lower permeability compared to high shear stress. However, over time, permeability under low shear stress surpasses that of high shear stress. This suggests that low shear stress is initially atheroprotective but becomes atheroprone over time, while high shear stress transitions from being atheroprone to relatively atheroprotective. Additionally, we analysed contact forces between endothelial cells under varying mechanical stimuli. For low shear stress, the median contact force is higher at the start than at the end, whereas for high shear stress, the median is higher at the end than at the start. These findings indicate that changes in shear stress magnitude affect VE-cadherin distribution and mechanical equilibrium. In vitro experiments further show that the morphology of VE-cadherin junctions—whether finger-like projections or smooth—depends on the magnitude and duration of mechanical stimuli. Furthermore, we expand the model to examine how increased vascular permeability influences diabetic macular oedema. Our findings indicate that the spatiotemporal progression of oedema is governed by the patientspecific distribution of retinal vasculature. Thus, our model provides insights into how multiple mechanical stimuli influence endothelial permeability and regulates tissue behaviour in physiological and pathological conditions.
4. Pim Oomen University of California, Irvine
   "One Size Does Not Fit All: Systems Biology Modeling of Sex-Specific Cardiac Remodeling"
While all hearts share the same fundamental properties and functions, no two hearts are truly the same. These differences are especially evident between female and male hearts. Interestingly, infant female hearts are initially slightly larger, with male hearts exceeding female heart size only after puberty. These relative changes coincide with major hormonal transitions during puberty and menopause, indicating a pivotal role for sex hormones in cardiac growth and remodeling. Yet, the precise mechanisms through which sex hormones such as estradiol and testosterone influence cardiac growth and remodeling remain elusive. Due to the complexity and intricate interplay of processes involved in cardiac growth and remodeling, computational models have proven useful in quantifying and analyzing these dynamics. However, there remains a critical need for models that consider sex hormones as biological variable. This critical gap prevents us from understanding the mechanisms behind sex-specific cardiac growth and remodeling and limits the effectiveness of using computational models to inform personalized therapies. In this talk, we will discuss how we used publicly available data to develop a multi-scale systems biology model of the interplay of sex hormones and cardiac remodeling. We use this model to understand the mechanisms that drive sex differences in cardiac remodeling, and demonstrate how these insights can be translated into personalized therapeutic approaches tailored to each patient, ultimately advancing the field toward precision cardiovascular medicine.

Organized by: Mitchel J. Colebank (University of South Carolina), Vijay Rajagopal, The University of Melbourne, Australia

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-3, and Part-4.

1. Ishraq U Ahmed University of Sydney
   "Free cholesterol toxicity and impaired cell recycling in a lipid-structured model of atherosclerosis"
The resolution of chronic inflammation involves a dynamic balance between cell death and the clearance of dying cells via efferocytosis. In nonresolving atherosclerotic plaques, this balance is disrupted due to the accumulation of high levels of intracellular cholesterol. Cholesterol is initially stored within the cell in the form of cholesterol esters, but some of this is hydrolysed to form free cholesterol. Excess free cholesterol is cytotoxic to macrophages, and impairs their efferocytic ability and promotes necrotic cell death. In nonresolving plaques, the impairment of cellular function and increase in cell death rates can lead to the formation of a necrotic core. In this talk, we present a preliminary partial integro-differential equation model for the early development of atherosclerotic tissue, where the cell population is structured by cholesterol content. Cells can accumulate cholesterol by ingesting it from LDL or dead cells, and can reduce their cholesterol load by proliferating. The model includes cell death via both apoptosis and necrosis, where necrotic material is ingested by live cells more slowly than apoptotic material. Death rates themselves depend on the levels of esterified and free cholesterol, where the relative levels of each are obtained from a coupled single-cell ODE model that describes intracellular cholesterol processing. With this model, we study how free cholesterol-induced cell death can lead to full tissue necrosis if efferocytosis rates are insufficient. We also consider how cell proliferation can help mitigate tissue necrosis by lowering intracellular cholesterol loads.
2. Pak-Wing Fok University of Delaware
   "Impact of Medial Calcification on Arterial Mechanics and Hemodynamics"
Medial Arterial Calcification (MAC) often occurs in aging arteries, promoted by diabetes mellitus and chronic kidney disease. Advanced MAC represents a frequent cause of chronic limb-threatening ischemia and limb amputation. Through a 1D haemodynamics simulation, we study how the mechanical properties of calcified arterial tissue and hydraulic resistance in the peripheral circulation jointly impact hemodynamics as MAC develops. We find that (i) there is a greater drop in systolic pressure across calcified arteries compared to healthy arteries, but this drop can be offset by greater peripheral resistance, provided left ventricular function is intact, (ii) both calcification and enhanced peripheral resistance lead to reduced flow rates, reduced peripheral perfusion, and peripheral tissue hypoxemia and (iii) pressurized calcified arteries present lumen areas that are smaller compared to healthy arteries, even though they are larger when unpressurized. Our simulations suggest that the increased impedance in calcified arteries results from smaller in-vivo lumen areas. This can reduce the outflow rate, but the effect is complicated by arteriole closures, vessel geometry, and global pressure. These findings confirm previously reported observations of flow reduction in calcified arteries.
3. Laura Ellwein Fix Virginia Commonwealth University
   "A closed-loop system-level model of cerebrovascular reactivity"
Cerebrovascular reactivity (CVR) is a metric of the ability of cerebral blood vessel tone to respond to stimuli for regulating blood flow and metabolism in the brain. In one such mechanism, the cerebrovasculature dilates to lower resistance in response to increased arterial carbon dioxide (CO2), thereby increasing blood flow to wash out the CO2. However, the integration of this with other processes and the implications for the systemic circulation are still not fully understood. Previously, Ellwein et al. developed a closed-loop system-level circulation model, in which cerebrovascular resistance was modeled using a piecewise linear function parameterized empirically using available data for blood flow velocity in the middle cerebral artery, arterial blood pressure, and expired CO2. In the current work we replaced the piecewise linear function with a more mechanistic representation of cerebral resistance as a function of partial pressure of CO2 together with a first-order control equation. Initial model simulated dynamics compare well to those previously achieved by Ellwein et al., with improved physiological fidelity. We also incorporated systemic responses to CO2 and optimized model parameters against a new cohort of data obtained under CO2 rebreathing conditions. These model adaptations will improve understanding of the system-level integration of mechanisms behind CBF regulation and CVR.
4. Liam Murray The University of Melbourne
   "Myofibril networks produce shear stress in sheep cardiomyocytes"
Myofibril arrangement is critical to cardiac muscle function in health, exercise, and disease. Historically, analysis of myofibril organisation impact on force and cell contraction has relied on the assumption of parallel, longitudinal arrays. However, improvements in imaging indicate that myofibrils may form complex networks. How these anisotropic networks modulate cell-contraction and force has yet to be explored. Here, morphological analysis of sheep cardiomyocytes has informed finite element models of cell contraction. Analysis of U-NET++ segmentations of Z-Discs demonstrate that myofibrils have a distribution of orientation throughout the cell. Simulations have similarly produced unique deformation patterns for geometries informed by myofibril orientations. These patterns highlight the physiological impact of myofibril structure and update understanding of uniaxial contraction to consider shear stress.

Organized by: Mitchel J. Colebank (University of South Carolina), Vijay Rajagopal, The University of Melbourne, Australia

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-2, and Part-4.

1. Mette Olufsen North Carolina State University
   "An uncertainty aware framework for generating vascular networks from imaging"
A well-calibrated mathematical model and an understanding of uncertainties in model predictions are essential for generating a digital twin. Creating a patient-specific cardiovascular model typically involves two key steps: (i) constructing the vascular domain and (ii) performing hemodynamic simulations. The vascular domain is usually obtained by segmenting CT or MRI scans to reconstruct the vascular network. Once constructed, hemodynamic simulations are conducted using inferred model parameters that minimize discrepancies between computed results and available physiological data. This talk will addres challenges in generating 1D network models with multiple branching generations and detecting abnormalities within these networks. One significant challenge is the automatic extraction of vessel centerlines, which is crucial for 1D modeling. We focus on a skeletonization-based method for centerline extraction, which iteratively removes voxels until only a single-voxel-wide path remains within each vessel. Using statistical change-point analysis, we construct a labeled directed graph (a tree) that encodes vessel connectivity, radii, and lengths. By sampling from normal distributions of these quantities with a 1D fluid dynamics model, we explore how uncertainties in geometry affect hemodynamic predictions. Our results emphasize the importance of accounting for image-based uncertainty in medical modeling.
2. Sara Johnson University of Puget Sound
   "Modeling Microglial Response to MCAO-Induced Ischemic Stroke"
Neuroinflammation immediately follows the onset of ischemic stroke in the middle cerebral artery. During this process, microglial cells are activated in and recruited to the penumbra. Microglial cells can be activated into two different phenotypes: M1, which can worsen brain injury; or M2, which can aid in long-term recovery. In this study, we contribute a summary of experimental data on microglial cell counts in the penumbra following ischemic stroke induced by middle cerebral artery occlusion (MCAO) in mice and compile available data sets into a single set suitable for time series analysis. Further, we formulate a mathematical model of microglial cells in the penumbra during ischemic stroke due to MCAO. Through use of global sensitivity analysis and Markov Chain Monte Carlo (MCMC)-based parameter estimation, we analyze the effects of the model parameters on the number of M1 and M2 cells in the penumbra and fit identifiable parameters to the compiled experimental data set. We utilize results from MCMC parameter estimation to ascertain uncertainty bounds and forward predictions for the number of M1 and M2 microglial cells over time. Results demonstrate the significance of parameters related to M1 and M2 activation on the number of M1 and M2 microglial cells. Simulations further suggest that potential outliers in the observed data may be omitted and forecast predictions suggest a lingering inflammatory response.
3. Simon Walker-Samuel University College London
   "Using physics-informed deep generative learning to model blood flow in the retina"
Disruption of retinal vasculature is linked to various diseases, including diabetic retinopathy and macular degeneration, leading to vision loss. We present here a novel algorithmic approach that generates highly realistic digital models of human retinal blood vessels, based on established biophysical principles, including fully-connected arterial and venous trees with a single inlet and outlet. This approach, using physics-informed generative adversarial networks (PI-GAN), enables the segmentation and reconstruction of blood vessel networks with no human input and which out-performs human labelling. Segmentation of DRIVE and STARE retina photograph datasets provided near state-of-the-art vessel segmentation, with training on only a small (n = 100) simulated dataset. Our findings highlight the potential of PI-GAN for accurate retinal vasculature characterization, with implications for improving early disease detection, monitoring disease progression, and improving patient care.
4. Mitchel Colebank University of South Carolina
   "Effects of vasomotor tone on systemic vascular wave reflections"
One-dimensional, pulse-wave propagation models are able to replicate hemodynamic waveforms that are representative of measured data. While these models are a potential tool in the era of digital twins, few models have considered the role of smooth muscle vasoactivity and its effects on blood pressure and flow. This is especially important for understanding cerebrovascular function, especially in diseases like dementia and Alzheimer's, where cerebral vasoactivity is known to be a cause and consequence of altered mechanical stimuli. Thus, there is a need for new computational models that explicitly account for vascular tone during hemodynamic simulation. Here, we implement a relatively simplistic exponential model of the proximal vasculature pressure-area relationship which incorporates extracellular matrix stiffness, vascular smooth muscle cell stiffness, the degree of vasomotor tone in comparison to some reference tone, and the reference pressure. We couple this vasoactive large vessel model to the structured tree boundary condition, which represents the microvascular beds. To differentiate between proximal and small vessel vasoconstriction, we also introduce a vasodilation factor in the structured tree that controls microvascular radii. We analyze the model using global sensitivity analysis, and provide insight into the distinct contributions of large and small vessel vasoactivity in an idealized systemic arterial network. Our results show that microvascular vasoconstriction is more impactful that proximal vessel vasotone, but that stress-strain behavior in the large vessels can be modulated divergently depending on the relative magnitudes of ECM and smooth muscle stiffness. This study lays the foundation for future studies investigating the effects of vasoactivity on hemodynamic outcomes.

Organized by: Mitchel J. Colebank (University of South Carolina), Vijay Rajagopal, The University of Melbourne, Australia

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-2, and Part-3.

Note: this minisymposia has been accepted, but the abstracts have not yet been finalized.

Organized by: Ning Wei (Purdue University)

1. Igor Vorobyov University of California, Davis
   "Digital twins for cardiac safety pharmacology and neuromodulation: from the atom to the rhythm"
It is increasingly clear that individual variability may be a key factor in determining the emergence of rare disease phenotypes in the setting of inherited and acquired disease. To begin to address personalized susceptibility to disease and drug responses, we have been working to develop a transformative experimentally informed and validated digital twin technology for patient-specific prediction of physiological processes and pharmacological interventions. Here we will describe such digital twins approach for prediction of the cardiotoxicity of drugs and efficacy of neuromodulation therapy in individuals. We established atomic-protein-structure digital twins of the cardiac ion channels including hERG, a major drug anti-target, which plays a critical role in the cardiac action potential. We used multiple machine learning based molecular modeling approaches including AlphaFold for predictions of physiologically and pharmacologically important conformational states of the hERG channel and its state-specific drug interactions. We used enhanced sampling molecular dynamics (MD) simulations to estimate hERG - drug binding affinities and rates, which were used to parameterize new digital twin representations at the cardiac protein, cell and tissue function scales to predict emergent drug-induced arrhythmia risks. Recently we expanded this multiscale digital twins pipeline to include multi-protein drug effects and acute effects of sex hormones on cardiac ion channel – drug interactions for more accurate predictions of arrhythmogenesis. We used a similar multiscale digital twins approach for the prediction of the autonomic nervous system stimulation effects to combat arrhythmia in the diseased heart tissue as an alternative to anti-arrhythmic medications. At the molecular level we focused on beta-adrenergic receptor – neurotransmitter interactions, a key event in the sympathetic nervous system stimulation. As a result of our studies, we aim to develop robust and efficient experimentally validated multiscale digital twins pipeline for an accurate prediction of arrhythmia risks starting from drug chemical structures and patients’ genetic information.
2. Karli Gillette University of Utah
   "Generation of cardiac digital twins of whole-heart electrophysiology under normal sinus rhythm"
Introduction: Personalized medicine using cardiac digital twins of cardiac electrophysiology has shown great promise for enhancing diagnostics and therapy planning for cardiac arrhythmias. Whole-heart cardiac digital twins, however, are challenging to personalize in terms of both anatomy and function. We present a novel computational pipeline for generating single snapshots of cardiac digital twins of whole-heart electrophysiology based on non-invasive clinical imaging and 12 lead electrocardiogram (ECG) data. Methods: Our computational pipeline produces anatomically highly detailed heart-torso models of patient hearts from clinical cardiac magnetic resonance images and calibrates their electrophysiological model properties to replicate the measured 12 lead ECGs. Efficient modeling pipelines in the atria and ventricles are deployed with modifications for atrioventricular entities. We utilize a novel optimization approach termed Geodesic-BP to infer ventricular activation during normal sinus rhythm based on the QRS complex. T-wave morphology is based on ventricular repolarization gradients related to activation, and the P-wave depends on fitted atrial electrophysiology through electrophysiological parameters. The method is demonstrated for two healthy subjects under normal sinus rhythm. Results: The novel computational pipeline can generate cardiac digital twins of whole-heart electrophysiology at scale within clinical time frames under 10 hours. Segmentation and optimization of the ventricular activation constituted the highest temporal costs. Simulated 12 lead ECGs are high fidelity with a mechanistic basis, especially in the QRS complex. Discussion: Our robust and non-invasive computational pipeline facilitates the generation of cardiac digital twins based on non-invasive clinical data. The method is scalable for additional subjects. In future work, we aim to generate time-integrated cardiac digital twins and apply the cardiac digital twins across various cardiac arrhythmias. Depending on the application, a detailed His-Purkinje system must be incorporated, and further optimization of atrial parameters may be needed.
3. Trine Krogh-Madsen Weill Cornell Medical College
   "Population modeling to explain heterogeneity of single stem cell-derived cardiomyocytes"
Human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) are a promising tool to study arrhythmia-related factors, but the variability of action potential (AP) recordings from these cells limits their use as an in vitro model. We have recently developed an efficient voltage clamp protocol to quantify the relative size of key ionic currents within a single cardiomyocyte. Applying this protocol to tens of cells, correlating features of the recorded current to AP recordings from the same cells, and using computational models, we can generate mechanistic insights into the ionic currents contributing to AP heterogeneity.
4. Ning Wei Purdue University
   "The impact of ephaptic coupling and ionic electrodiffusion on arrhythmogenesis in the heart"
Cardiac myocytes synchronize through electrical signaling to contract heart muscles, facilitated by gap junctions (GJs) in the intercalated disc (ID). GJs provide low-resistance pathways for electrical impulse propagation between myocytes, serving as the primary mechanism for electrical communication in the heart. However, research indicates that conduction can persist without GJs. For instance, GJ knockout mice still exhibit slow, discontinuous electrical propagation, suggesting alternative communication mechanisms. Ephaptic coupling (EpC) serves as an alternative way for cell communication, relying on electrical fields within narrow clefts between neighboring myocytes. Studies show that EpC can enhance conduction velocity (CV) and reduce conduction block (CB), especially when GJs are compromised. Reduced GJs and significant electrochemical gradients are prevalent in various heart diseases. However, existing models often fail to capture their combined influence on cardiac conduction, which limits our understanding of both the physiological and pathological aspects of the heart. Our study aims to address this gap by developing a two-dimensional (2D) multidomain electrodiffusion model that incorporates EpC. This is the first model to capture the dynamics of all ions across multiple domains, enabling us to reveal the impact of EpC in the heart. In particular, we investigated the interplay between ionic electrodiffusion and EpC on action potential propagation, morphology, electrochemical properties and arrhythmogenesis in both healthy and ischemic hearts. Our findings indicate that ionic electrodiffusion enhances CV and reduces CB under strong EpC. Specifically, the electrodiffusion of Ca$^{2+}$ and K$^+$ intensifies the effects of EpC on action potential morphology, whereas Na$^+$ diffusion mitigates these effects. Ionic electrodiffusion also facilitates action potential propagation into ischemic regions when EpC is substantial. Moreover, strong EpC can effectively terminate reentry, prevent its initiation, and lower the maximum dominant frequency (max DF), irrespective of GJ functionality. However, weak EpC may help counteract proarrhythmic effects when GJ coupling is slightly to moderately reduced, contributing to the stabilization of conduction patterns. Additionally, strong EpC notably alters ionic concentrations in the cleft, significantly increasing [K$^+$] and nearly depleting [Ca$^{2+}$], while causing moderate changes in [Na$^+$]. This multidomain electrodiffusion model sheds light on the mechanisms of EpC in the heart.

1. Jared Barber IU Indianapolis
   "Mathematical model of blood flow in the brain after a major arterial occlusion."
Blood vessel adaptation plays an important role in maintaining healthy and well-oxygenated tissue throughout the body. This is especially true for the brain. To better characterize how blood flow changes when the brain suffers a major arterial occlusion (e.g. during a stroke) and to identify major factors that may affect flow restoration to downstream regions, we created a mathematical model of blood flow in the brain. The network is modeled as multiple larger vessels interconnected with multiple compartments of smaller vessels with each compartment consisting of identical vessels situated in parallel. The model further includes vessel adaptation in response to changes in pressure (myogenic response), wall shear stress (shear response), and oxygen saturation (metabolic response). By varying tissue oxygen demand and incoming pressure, we are able to identify that the number of collateral vessels moving flow from unobstructed to obstructed regions is a major factor. We also predicted a loss of normal function particularly reflected by a shift in the “autoregulation curve”, a curve that reflects the ability of vessels to reasonably respond to increases in pressure. Such results were consistent with experiment and reinforce the appropriateness of treatments that raise flow and oxygenation by minimizing tissue oxygen demand and raising vascular pressure.
2. Cory Brunson University of Florida
   "Testing hypotheses of glomerular capillary development with geometric and topological data analysis"
Blood filtration occurs in renal capillary tufts called glomeruli, the internal structure of which bears on questions of function, development, evolution, and pathology. Due to the low resolution and labor-intensity of imaging technology, only a handful of studies reaching back decades have examined the spatial structure of glomerular capillaries. Several common features have been described, including lobular topology, plausibly associated with robustness to vascular damage, and circuitous geometry, hypothesized to ensure consistent filtration. However, these properties have been neither mathematically defined nor statistically confirmed. Recent developments in serial scanning electron microscopy and virtual reality enabled us to reconstruct the capillary networks of twelve murine glomeruli and trace spatial graph models. We used circuit analysis to represent these as Reeb graphs, the fundamental theorem of calculus to describe a mean trajectory and its curvature, and principal components analysis to reveal lateral and transverse symmetry. Separately, we built a non-spatial random graph growth model based on two mechanisms, angiogenesis and intussusception, which provided evidence that both contribute to development. We then introduced several topological measures of lobularity and found, surprisingly, that empirical glomeruli tend to be less lobular than those generated by our model. Ongoing work focuses on simulation-based attack tolerance and the development of a spatial growth model.

1. Brendan Fry Metropolitan State University of Denver
   "Modeling the effects of vascular impairments on blood flow autoregulation in the retinal microcirculation"
The retinal microcirculation supplies blood and oxygen to the cells responsible for vision, and vascular impairments – including compromised flow regulation, reduced capillary density, and elevated intraocular pressure – are involved in the progression of eye diseases such as glaucoma. Here, an established theoretical model of a retinal microvascular network will be presented and extended to investigate the effects of these impairments on retinal blood flow and oxygenation as intraluminal pressure is varied. A heterogeneous description of the arterioles based on confocal microscopy images is combined with a compartmental representation of the downstream capillaries and venules. A Green’s function method is used to simulate oxygen transport in the arterioles, and a Krogh cylinder model is used in the capillary and venular compartments. Acute blood flow autoregulation is simulated in response to changes in pressure, shear stress, and metabolism. The model predicts that impaired flow regulation mechanisms, decreased capillary density, and increased intraocular pressure all cause a loss in the autoregulation plateau over the baseline range of intraluminal pressures (meaning that blood flow is not maintained constant over those pressures), leading to a corresponding decrease in oxygenation in that range. Small impairments in capillary density or intraocular pressure are predicted to mostly be offset by functional flow regulation; however, larger changes and/or combinations of vascular impairments lead to a significant decrease in oxygenation. Clinically, since poor retinal tissue oxygenation could lead to vision loss in advanced glaucoma, model results suggest early identification of vascular changes to prevent these impairments from progressing.