Organized by: Paul A. Roberts, Jessica Crawshaw
Note: this minisymposia has multiple sessions. The other session is MS02-NEUR-1.

• Paul A. Roberts University of Birmingham (Centre for Systems Modelling and Quantitative Biomedicine)
  "Mathematical and Computational Ophthalmology: Coming of Age"
This talk will set the scene for those which follow in the Mathematical Ophthalmology minisymposium. I will begin by defining what we mean by the terms Mathematical Ophthalmology (a new term which I have coined) and Computational Ophthalmology (an existing term) and how these fields relate both to each other and to more established experimental and clinical disciplines. I shall give a brief history of these emerging fields, highlighting key case studies, and discuss their future prospects. I will also be announcing and inviting participation in a number of exciting opportunities and initiatives aimed at promoting these fields and supporting those working within them.
• Brendan C. Fry Metropolitan State University of Denver (Department of Mathematics and Statistics)
  "Modeling metabolic blood flow regulation and oxygenation in the human retinal microcirculation"
The retinal microcirculation perfuses the retinal cells responsible for vision, and impairments in retinal blood flow and oxygenation are involved in the progression of eye diseases such as glaucoma. Here, an established theoretical hybrid model of a retinal microvascular network will be presented and extended to include effects of local blood flow regulation on oxygenation. A heterogeneous description of the arterioles based on confocal microscopy images is combined with a compartmental representation of the downstream capillaries and venules. To simulate oxygen transport in the arterioles, a Green’s function method is used; in the capillary and venular compartments, a Krogh cylinder model is applied. Acute regulation of blood flow is simulated in response to changes in pressure, shear stress, and metabolism. The model results predict that both an increase in intraocular pressure and an impairment in blood flow regulation can lead to decreased tissue oxygenation, indicating that both mechanisms represent factors that can lead to the impaired oxygenation observed in eye disease. Results from the model further imply that the metabolic response mechanism reduces the fraction of poorly-oxygenated tissue, but that the pressure- and shear-stress-dependent response mechanisms may actually hinder the vascular response to changes in oxygenation. Importantly, the heterogeneity of the microvascular network structure demonstrates that traditionally-reported average values of tissue oxygen levels hide significant localized defects in tissue oxygenation that may be involved in eye disease processes. Going forward, the model framework will help provide comparisons to sectorial-specific clinical data, in order to better assess the role of impaired blood flow regulation in glaucoma.
• Julia Arciero Indiana University - Purdue University Indianapolis (Mathematical Sciences)
  "Predicting the impact of capillary density on retinal vessel and tissue oxygenation using a theoretical model"
Impairments in retinal blood flow and oxygenation have been shown to contribute to the progression of glaucoma. In this study, a theoretical model of the human retina is used to predict blood flow and tissue oxygenation in retinal vessels and tissue for varied levels of capillary density. The model includes a heterogeneous representation of retinal arterioles and a compartmental representation of capillaries and venules. A Green’s function method is used to model oxygen transport in the arterioles, and a Krogh cylinder model is used in the capillaries and venules. In our clinical observations, early glaucoma patients are shown to exhibit a 10-12% reduction in capillary density compared to healthy individuals. The model is simulated for capillary density values ranging from 250 to 750 capillaries/mm^2. Oxygen extraction fraction, defined as the ratio of oxygen consumption to oxygen delivery, is calculated for each model simulation. The model predicts a 6% and 53% decrease in mean PO_2 in retinal vessels immediately downstream of the capillaries when capillary density is decreased from its reference value of 500 capillaries/mm^2 by 10% and 50%, respectively. Ultimately, the mathematical model demonstrates the significant detrimental impact of such decreases in capillary density on the oxygenation of retinal tissues.
• Remi Hernandez University of Liverpool (Department of Cardiovascular and Metabolic Medicine)
  "Virtual populations of the retina to characterize hypoxia in wet AMD"
Retinal angiograms with high resolution are taken routinely in eye clinics. Several studies have highlighted the association between angiographic parameters and several retinal diseases, including wet age-related macular degeneration (wAMD). These parameters indicate a decline in retinal perfusion which may lead to hypoxia. Because hypoxia may be a trigger of the pathological angiogenesis seen in eyes with wAMD, quantifying it in diseased eyes is important to understand and model the disease and find optimal treatment strategies. We have created synthetic vasculatures using an algorithm mimicking angiogenesis along with convection and reaction-diffusion models of oxygen perfusion. We propose to develop a framework to computationally study hypoxia in 3-dimensional virtual populations of the retina, in health and disease.

Organized by: Paul A. Roberts, Jessica Crawshaw
Note: this minisymposia has multiple sessions. The other session is MS01-NEUR-1.

• Jessica Crawshaw University of Oxford (Mathematical Institute)
  "The role of hierarchical Bayesian inference in understanding macular degeneration treatment strategies"
Wet age-related macular degeneration (AMD) is a disease which slowly destroys ones’ central vision, with a huge impact on quality of life. It is the leading cause of central blindness worldwide. Wet AMD is characterised by neovascularisation, triggered by an unhealthy abundance of vascular endothelial growth factor (VEGF). These newly formed capillaries allow fluids to seep into the retina, damaging the local photoreceptors (critical light-sensing cells). Currently, there is no definitive cure for wet AMD. As such, intraocular injections of anti-angiogenic drugs to reduce the abundance of retinal VEGF is the clinical gold standard for disease management, slowing the progression of vision loss. However, injections into the eye are unpleasant, and the fluid dynamics within the eye leads to relatively rapid drug elimination, resulting in the need for regular intraocular injections. In this talk, we will present and analyse a pharmacokinetic/pharmacodynamic (PK/PD) model of a standard-of-care antibody, ranibizumab, targeting VEGF. This model has been developed to improve our understanding of the ocular pharmacology of ranibizumab and to provide a robust understanding of ranibizumab retention in the eye. Results from this PK/PD model are compared to published animal (cynomolgus monkey) and human data. We present a hierarchical Bayesian inference strategy to determine relevant parameter distributions. Using this strategy, we provide insight into the clinically observed inter-patient variability in VEGF suppression and drug retention. Finally, this model establishes the initial basis for a computational framework we are developing to mathematically compare the ocular PK/PD of ranibizumab with novel therapeutic strategies and other clinical anti-VEGF drugs in the treatment of AMD.
• Moussa A. Zouache University of Utah (John A. Moran Eye Center, Department of Ophthalmology & Visual Sciences)
  "Predicting Physiology from Structure in the Human Choriocapillaris"
The choroidal vasculature and its microvascular bed, the choriocapillaris, support the metabolic requirements of the outer half of the retina, which includes the photoreceptors, cells that have one of the highest metabolic rates of any cell of the human body. The choriocapillaris has evolved a vascular geometry that differs markedly from branched vasculatures. It consists of a layer of densely organized capillaries contained between two continuous and approximately parallel sheets. Blood enters and leaves the choriocapillaris through a set of arterioles and venules connected to capillaries perpendicularly to its plane. Because of this unusual geometry, theoretical and experimental approaches traditionally applied to characterize blood flow and mass exchange in branched microvasculatures are not adapted to the choriocapillaris. As a result, it has been difficult to assess the role that this vascular bed plays in the onset and progression of inflammatory and degenerative diseases of the back of the eye. We developed a framework to predict aspects of the physiology of the choriocapillaris from experimentally accessible vascular parameters. This framework relies on three-dimensional mathematical models of the choriocapillaris informed by the angioarchitecture of the choroid as observed through immunohistochemistry of human tissue. Blood was modelled as a Newtonian fluid, and analytical and numerical solutions for the blood flow were obtained by solving the Navier-Stokes equation. The salient features of mass exchange with the retina were determined by solving the advection-diffusion equation for a scalar while imposing either a Dirichlet or a Neumann boundary condition on the surface of the choriocapillaris. Topological analysis of the flow field revealed that the blood flow in the choriocapillaris is decomposed into contiguous subsets separated by separation surfaces across which there is no flow. This segmentation is at the origin of the previously unexplained lobular appearance of the choriocapillaris observed during fluorescent dye angiography. The segmentation of the blood flow is associated with spatially heterogeneous dominant transport mechanisms. The boundaries between subsets of the flow field form regions, where the transport of material is dominantly diffusive. These regions represent areas of reduced exchange with the outer retina and are ubiquitous across the choriocapillaris. The width of diffusion-limited regions is determined by the relative distribution of arteriolar and venular insertions into the choriocapillaris, arterial flow rate and molecular diffusivity. Salient characteristics of the blood flow and passive transport in the choriocapillaris differ markedly from branched vasculatures. The geometry of the choriocapillaris is associated with segmented blood flow and spatially heterogeneous exchange with the outer retina. This heterogeneity may explain the spatial selectivity in pathologies associated with retinal diseases.
• Richard Braun University of Delaware (Department of Mathematical Sciences)
  "Semi-automated Tear Breakup Detection and Modeling on the Ocular Surface"
The tear film is a thin fluid multilayer left on the eye surface after a blink. A good tear film is essential for health and proper function of the eye. Millions of people have a condition called dry eye disease (DED) that is thought to be closely linked to the tear film. DED inhibits vision and may lead to inflammation and ocular surface damage. However, there is little quantitative data about tear film failure, often called tear break up (TBU). Currently, it is not possible to directly measure important variables such as tear osmolarity (saltiness) within areas of TBU. We present a mostly automatic method that we have developed to extract data from video of the tear film dyed with fluorescein (for visualization). We have extracted data for 15 healthy subjects resulting in 467 instances of TBU. Using parameter identification from fits to appropriate math models, we estimate which mechanisms are most important in each instance and determine critical variables such as osmolarity within regions of TBU. Not only is new data obtained, but far more data, enabling statistical methods to be applied. So far, the methods provide baseline data for TBU in healthy subjects; future work will produce data from DED subjects.

Organized by: Cheng Ly, Janet Best, Pamela Pyzza, Yangyang Wang
Note: this minisymposia has multiple sessions. The other session is MS07-NEUR-1.

• Krasimira Tsaneva-Atanasova University of Exeter (Mathematics and Statistics)
  "Mathematical modelling of GnRH pulse generator frequency modulation through the interaction between kisspeptin and GABA-glutamate in the posterodorsal medial amygdala"
Gonadotrophin releasing hormone (GnRH) pulsatile activity and the initiation of functional gonadotrophin secretion controlling reproductive competence are primarily driven by kisspeptin neurons located in the arcuate nucleus of the hypothalamus. Nevertheless, kisspeptin present in other brain regions, exerts a significant modulating effect on the hypothalamic kisspeptin population. In particular, a population of kisspeptin and its receptors has been found in the posterodorsal medial amygdala (MePD), where it acts as an upstream regulator of γ-aminobutyric acid (GABA) and glutamate sub-populations of neurons. We propose a coarse-grained network model that captures the cooperative and competitive dynamics between these sub-populations. We employ bifurcation analysis to study the effect of network connectivity strengths and the role of the afferent input from kisspeptin. This allows us to characterise the dynamical changes in the MePD output for different levels of kisspeptin. Our mathematical model, supported by experimental findings demonstrate that the effective modulation of the GnRH pulse generator by amygdala kisspeptin neurons is dependent on the functional neurotransmission of both GABA and glutamate.
• Andrea K. Barreiro Southern Methodist University (Mathematics)
  "Fluid dynamics as a driver of retronasal olfaction"
Flavor perception is a fundamental governing factor of feeding behaviors and associated diseases such as obesity. Smells that enter the nose retronasally, i.e. from the back of the nasal cavity, play an essential role in flavor perception. Previous studies have demonstrated that orthonasal olfaction (nasally inhaled smells) and retronasal olfaction involve distinctly different brain activation, even for identical odors. Differences are evident at the glomerular layer in the olfactory bulb (Gautam et al. 2012, Sanganahalli et al. 2020) and can even be identified in the synaptic inputs to the bulb (Furudono et al. 2013). Why does the bulb receive different input based on the direction of the air flow? We hypothesize that this difference originates from fluid mechanical forces at the periphery: olfactory receptor neurons respond to mechanical, as well as chemical stimuli (Grosmaitre et al, 2007, Iwata et al, 2017). To investigate this, we use computational fluid dynamics to simulate and analyze shear stress patterns during natural inhalation and sniffing. We will show preliminary results demonstrating that shear stress forces differ for orthonasal vs. retronasal air flow; i.e. inspiration vs. exhalation, in a model of the nasal cavity, and connect these findings to our earlier work on directional selectivity in neural network models of the olfactory bulb (Craft et al. 2021).
• Madeline Edwards University of Pittsburgh (Department of Neuroscience)
  "Exploring the Roles of Interneuron Subtypes in Network Dynamics"
Neuronal responses to sensory stimuli can be strongly modulated by animal's brain state. Three distinct subtypes of inhibitory interneurons, parvalbumin (PV), somatostatin (SOM), and vasoactive intestinal peptide (VIP) expressing cells, have been identified as key players of flexibly modulating network activity. The three interneuron populations have specialized local microcircuit motifs and are targeted differentially by top-down inputs from higher-order cortical areas and neuromodulators. Optogenetic stimulation of different interneuron cell types demonstrates different impacts on neuronal population responses, such as firing rate and network synchrony. In this work, we systematically study the function of each interneuron cell type at controlling network dynamics in a spatially ordered spiking neuron network. We model top down and neuromodulatory inputs as static current applied to each neuron population. We find that the network transitions through three distinct network states, from subcircuit to weak synchrony to strong synchrony state, as we activate the excitatory or SOM population or inactivate the PV or VIP population. Further, we investigate how network responses to modulatory inputs depend on the connectivity of the SOM cells. This work provides a foundational understanding for the modulation of network activity with respect to four unique populations and testable predictions for future experiments.
• Andrea Welsh University of Pittsburgh (Department of Mathematics)
  "Modeling Mouse Colon Non-propulsion Dynamics"
Colon motility, the spontaneous self-generated movement and motion of the colon muscle and its cells, is produced by activity in different types of cells such as myenteric neurons of the enteric nervous system (ENS), neurons of the autonomic nervous system (ANS) and interstitial cells of Cajal (ICC). Two colon motor patterns measured experimentally are motor complexes (MC) often associated with the propulsion of fecal contents, and ripple contractions which are involved in mixing and absorption. It has been observed that the MCs can occur without fecal matter present, but it is poorly understood how these spontaneous CMs occur. How ICC and neurons of the ENS and ANS interact to initiate and influence colon motility is still not completely understood. This makes it difficult to develop new therapies to restore function in pathological conditions. This talk will discuss the data-driven modeling of the ICCs and neurons that also capture the spontaneous global dynamics that are observed in the colon and give insight into how these dynamical features may occur.

Organized by: Cheng Ly, Janet Best, Pamela Pyzza, Yangyang Wang
Note: this minisymposia has multiple sessions. The other session is MS06-NEUR-1.

• Ngoc Anh Phan University of Iowa (Department of Mathematics)
  "Robustness of mixed mode oscillations and mixed mode bursting oscillations in three-timescale neuronal systems."
We are concerned with two types of complex oscillatory dynamics that frequently occur in multiple-timescale dynamical systems, namely mixed mode oscillations (MMOs) and mixed mode bursting oscillations (MMBOs). These phenomena involve the alternation of small-amplitude oscillations (SAOs) and large-amplitude oscillations or bursting oscillations. SAOs during the silent phase can arise from canard dynamics associated with folded singularities or a slow passage through a delayed Andronov-Hopf bifurcation (DHB) of the fast subsystem. In this work, we investigate the dynamic mechanisms underlying MMOs and MMBOs in two three-timescale neuronal systems. We identify the conditions under which the two separate mechanisms in the two-timescale setting, canard and DHB, can interact in the three-timescale context to produce more robust MMOs or MMBOs. This work can shed light on the fundamental principles governing these complex oscillatory behaviors in multiple-timescale systems.
• Sushmita John University of Pittsburgh (Mathematics)
  "Slow negative feedback enhances robustness of square-wave bursting"
Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.
• Victoria Booth University of Michigan (Mathematics)
  "Neural rhythms generated by spatially heterogeneous neuromodulation"
Oscillatory neural firing activity or neural rhythms, have been shown to play critical roles in perception, attention, learning, and memory, especially rhythms in the theta (5-10 Hz) and gamma (30-100Hz) frequency bands. Available data suggest that forebrain acetylcholine (ACh) signaling promotes gamma and theta rhythms, although the mechanism has not been identified. Recent evidence suggests that cholinergic signaling is both temporally and spatially constrained, in contrast to the traditional notion of slow, spatially homogeneous, and diffuse neuromodulation. Using biophysically-based excitatory-inhibitory (E-I) neural network models, we find that spatially constrained cholinergic stimulation can generate theta-modulated gamma rhythms. We simulate the effects of ACh on neural excitability by varying the conductance of a muscarinic receptor-regulated K+ current. In E-I networks with local excitatory connectivity and global inhibitory connectivity, we demonstrate that stable gamma- modulated firing arises within regions with high ACh signaling, while theta or mixed theta- gamma activity occurs at the peripheries of these regions. High gamma activity also alternates between different high ACh regions, at theta frequency. Our results are the first to indicate a causal role for spatially heterogenous ACh signaling in the emergence of theta-gamma rhythmicity.
• Fernando Antoneli Universidade Federal de Sao Paulo (Centro de Bioinformatica Medica)
  "Network Dynamics: Theory and Examples"
A coupled cell system is a network of interacting dynamical systems. Dynamical network models assume that the output from each node is important and that signals from two or more nodes can be compared so that a notion of pattern of synchrony makes sense. One may ask: How does network architecture (who is talking to whom) affect the kinds of synchronous solutions that are expected in network equations. This talk will discuss necessary and sufficient conditions for synchrony in terms of network architecture, spatio-temporal symmetries of periodic solutions, as well as some curious synchrony-breaking bifurcations.

Organized by: Richard Bertram

• Wilfredo Blanco Figuerola State University of Rio Grande do Norte (Department of Computer Science)
  "Population Bursting in Modular Neural Networks"
Population bursts are observed in developing neural systems and in some fully developed neural systems. These can be achieved in networks in which synaptic connections are fully excitable, with no inhibitory connections. We have previously shown mechanisms and properties of such population bursts in purely excitatory neural systems, but only in unstructured networks, as would be expected in developing neural systems. In this presentation, we explore emergent dynamics in modular networks, focusing on how both intra- and inter-cluster connectivity impacts the behavior of the full population of cells.
• Mehran Fazli Henry M. Jackson Foundation for the Advancement of Military > Medicine, Inc., Bethesda, MD, USA (Austere Environments Consortium for Enhanced Sepsis Outcomes (ACESO))
  "Gene bundling: a new approach to clustering and reversed engineering of gene expression network"
Sepsis, responsible for one in five deaths globally, results from the body's response to inflammation caused by infection and can lead to life-threatening tissue damage. Detecting gene expression patterns that signify infection severity or type may improve patient diagnosis and care. The Austere environments Consortium for Enhanced Sepsis Outcomes (ACESO) conducts an international observational study to boost sepsis patient survival rates. In this research, we develop a new parameter-free algorithm for gene correlation-based clustering, founded on graph-theoretic concepts and spectral clustering. Blood samples collected upon hospital admission from 505 participants at ACESO sites in the United States, Ghana, and Cambodia are used for this algorithm. The subsequent transcriptomic data is employed to create and evaluate this innovative clustering approach. A single dataset can yield various clustering configurations, each highlighting distinct aspects of the data. Our primary aim is to build the necessary mechanisms to capture these aspects and achieve optimal gene clusters composed of genes that co-cluster in the most prevalent clustering schemes using spectral theory. This method, referred to as gene bundling, is both straightforward and versatile, permitting the analysis of diverse clustering scales to determine the optimal gene clustering. Using our sepsis dataset, we found that gene bundles have a strong connection to known biological pathways. Furthermore, by utilizing 28-day mortality data and a scoring system, we identified gene bundles that distinguish survivors and non-survivors within the entire population. Employing a multi-layered bundling scheme allows us to reverse-engineer the bundle-bundle interaction network. This algorithm holds promise for deepening our understanding of biological pathway interaction networks in sepsis patients, ultimately contributing to progress in sepsis diagnosis, prognosis, and therapy.
• Bhargav Karamched Florida State University (Mathematics)
  "How do Heterogeneity and Correlated Information Affect Decision-Making in Social Networks?"
Normative models are often used to describe how humans and animals make decisions. These models treat deliberation as the accumulation of uncertain evidence that terminates with a commitment to a choice. Such models exhibit two major limitations: (1) they model decision-making by individuals in isolation; (2) they assume observations are conditionally independent. Humans and animals often make decisions based on their own observations in conjunction with information provided by their peers. How should classical drift-diffusion models of decision-making be generalized to situations where decisions are made by networks of individuals? How does heterogeneity in network makeup affect collective decisions? We find that heterogeneous networks collectively make faster and more accurate decisions than homogeneous networks of identical observers. Moreover, individuals rarely observe independent data in making a decision. How does correlated information affect decision-making in networks? Surprisingly, we find that early decisions are less accurate than later decisions even in networks of identical agents who have the same criteria to make a decision! Our models are for idealized situations but can provide insight into strategies for optimizing individual and collective decision-making.
• Brad Peercy University of Maryland, Baltimore County (UMBC) (Mathematics and Statistics)
  "Loss of Synchrony to Silencing in Networks of Excitable Cells: Impact of Cell and Coupling Heterogeneity in Small Network Examples"
Experiments on pancreatic islets have raised a question about the potential unitary impact of certain cells in islet synchrony. Previous modeling to corroborate these findings under the suggested conditions proved unfruitful, but wide parameter searches did identify cases where silencing or ablating individual beta cells could completely or nearly completely silence islet behavior. We term such islets as 'switch' islets and such critical cells as 'switch' cells. We describe our efforts to create minimal examples representative of 'switch' behavior. This includes three cell beta cell networks and a small 2D grid network of simpler two-variable excitable cells. We find examples of 'switch' behavior in each case.

• Allison Cruikshank Duke University
  "Dynamical Questions in Volume Transmission"
In volume transmission (or neuromodulation) neurons do not make one-to-one connections to other neurons, but instead simply release neurotransmitter into the extracellular space from numerous varicosities. Many well-known neurotransmitters including serotonin (5HT), dopamine (DA), histamine (HA), Gamma-Aminobutyric Acid (GABA) and acetylcholine (ACh) participate in volume transmission. Typically, the cell bodies are in one volume and the axons project to a distant volume in the brain releasing the neurotransmitter there. We introduce volume transmission and describe mathematically two natural homeostatic mechanisms. In some brain regions several neurotransmitters in the extracellular space affect each others' release. We investigate the dynamics created by this comodulation in two different cases: serotonin and histamine; and the comodulation of 4 neurotransmitters in the striatum and we compare to experimental data. This kind of comodulation poses new dynamical questions as well as the question of how these biochemical networks influence the electrophysiological networks in the brain.
• Gurpreet Jagdev Toronto Metropolitan University
  "The interplay between asymmetric noise and uneven coupling of two coupled neuronal oscillators"
Two ubiquitous components, coupling and noise, may drive complex neural networks to exhibit emergence dynamics. While the roles of equal coupling and symmetric noise have been extensively studied, the general mechanisms of unequal coupling strength and asymmetric noise remain unclear. In this work, we investigate the simultaneous interplay of unequal coupling and asymmetric noise in the simplest network motif of two bi-directionally coupled neural oscillators, each with its own intrinsic noise. Our findings show that noise-induced synchrony can be maximized when one oscillator (source) with weak intrinsic noise is strongly connected to the other oscillator (receiver) with strong intrinsic noise. Furthermore, we extend our study to three coupled neural oscillators with a feed-forward-loop schematic. These results shed new light on the complex interplay between coupling and noise in neural networks.
• Marina Chugunova University of Waterloo, Canada
  "Modelling duality of the exocytosis initiation in GnRH neurons"
Gonadotropin-releasing hormone (GnRH) neurons work as a trigger of the reproductive axis in mammals. These neurons exhibit two types of exocytosis: a surge and a pulsatile one. Traditionally, changes in the neuron dynamics are connected to and explained by changes in parameters of the action potential, transmitted by a neuron's membrane. However, in case of GnRH neurons, the experimental data demonstrates that the switch in the type of the hormone release is determined rather by the location of the GnRH neuron activation. Action potential initiated in the proximity of soma is necessary for the surge of GnRH. The second type, the pulsatile release of GnRH, is driven by the synaptic activities on the distal part of the neurons. Both types of the exocytosis initiation target the intracellular calcium dynamics. The increase in calcium ions due to the electrical spikes near soma is short-lived. On the other hand, the increase in calcium ions in the distal parts of the GnRH neurons lasts for tens of minutes. We have built the mathematical and computational models of the electrical and chemical dynamics in GnRH neurons. The model, in silico, reveals the connection between the action potential, neuropeptides, and calcium ion dynamics. In addition, our model confirms the functionality of the bundling between multiple GnRH neurons and its effect on exocytosis synchronization.
• Zhuo-Cheng Xiao New York University
  "Efficient models of the cortex via coarse-grained interactions and local response functions"
Modeling the human cortex is challenging due to its structural and dynamic complexity. Spiking neuron models can incorporate many details of cortical circuits but are computationally costly and difficult to scale up, limiting their scope to small patches of cortex and restricting the range of phenomena that can be studied. Alternatively, one can use simpler phenomenological models, which are easier to build and run but are more difficult to compare directly to experimental data. This talk presents an efficient modeling strategy that aims to strike a balance between biological realism and computational efficiency. The proposed modeling strategy combines a coarse-grained representation with local circuit dynamics to compute the steady-state cortical response to external stimuli. A crucial observation is that as a consequence of anatomical structures and the nature of neuronal interactions, potential local responses can be computed independently of dynamics on the coarse-grained level. We first precompute a library of steady-state local responses driven by possible lateral and external input. Then, the fixed point of the coarse-grained model can be computed by an iterative scheme combined with fast library lookup. Our approach is tested on a model of primate primary visual cortex (V1) and successfully captures essential V1 features such as orientation selectivity. Time permitting, I will also discuss a related project in which we devised an efficient way to explore the parameter space of a primate V1 model, identifying the set of viable parameters as a 'thickened' codimension-1 submanifold of parameter space.

• Amy Cochran University of Wisconsin Madison
  "Multidimensionality in reinforcement learning models of human decision-making"
Temporal difference learning models, once developed as computer algorithms, have transformed how we study human decision-making and related brain activity. These models describe how a person updates their valuation of a decision according to an error in predicted rewards. While these valuations have conventionally been one-dimensional, recent experiments and theories suggest that these valuations might be multi-dimensional. In this talk, I will give a brief introduction to conventional modeling of human decision-making and discuss recent work to extend current reinforcement learning models to capture multi-dimensional valuations. Further, I will demonstrate the advantage of these extended models, from the perspective of what a person learns and the decisions they make, and connect these models to recent experiments. Last, I will discuss how these ideas can inform the design of future experiments
• Seokjoo Chae KAIST
  "Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping"
The circadian (~24h) clock is based on a negative feedback loop centered around the PERIOD protein (PER) that is translated in the cytoplasm and then enters the nucleus to repress its own transcription at the right time of day. Such precise nucleus entry is mysterious because thousands of PER molecules transit through crowded cytoplasm and arrive at the perinucleus across several hours. To understand this, we developed a mathematical model describing the complex spatiotemporal dynamics of PER as a single random time delay. We find that the spatially coordinated bistable phosphoswitch of PER, which triggers the phosphorylation of accumulated PER at the perinucleus, leads to the synchronous and precise nuclear entry of PER. This leads to robust circadian rhythms even when PER arrival times are heterogenous and perturbed due to changes in cell crowdedness, cell size, and transcriptional activator levels. This shows how the circadian clock compensates for spatiotemporal noise.
• Shaharina Shoha Western Kentucky University
  "A Comparison of Computational Perfusion Imaging Techniques."
Perfusion imaging is valuable because it is used to help grade tumors; differentiate between tumor types; differentiate tumors from nonneoplastic lesions; guide intraoperative sampling; most importantly, determine the efficacy of treatment. Computational techniques combined with the imaged data can help identify important biological parameters. For example, key parameters include cerebral blood flow (CBF), cerebral blood volume (CBV) and mean transit time (MTT) . These parameters can help distinguish between the likely salvageable tissue and irreversiblydamaged infarctcore.Theparametersarecalculateddeconvolvingcontrast-time curves with the arterial inlet input function. A common approach employed with the deconvolution method is a singular value decomposition (SVD). However, these algorithms are very sensitive to noise and artifacts in the source image which may introduce additional distortions in the output parameters. For this reason, we will employ machine learning algorithms to aid in the measurements of perfusion parameters from CT imaging and compare to parameter measurement using SVD with regularization.
• Iulia Martina Bulai University of Sassari
  "Wavelet packets and graph neuronal signal processing"
Nowadays graphs have become of significant importance given their use to describe complex system dynamics, with important applications to real world problems, e.g. graph representation of the brain, social networks, biological networks, spreading of a disease, etc.. In this work, [4], we introduce a novel graph wavelet packets construction, to our knowledge different from the ones known in literature. We get inspired by the Spectral Graph Wavelet Transform defined by Hammond et all. in [1], based on a spectral graph wavelet at scale s > 0, centered on vertex n, and a spectral graph scaling function, respectively. Moreover, after defining the wavelet packet spaces, and the associated tree, we obtain a dictionary of frames for R^N; with known lower and upper bounds. We will give some concrete examples on how the wavelet packets can be used for compressing, denoising and reconstruction by considering a signal, given by the fRMI (functional magnetic resonance imaging) data, on the nodes of voxel-wise brain graph G with 900760 nodes (representing the brain voxels) defined in [2]-[3]. References [1] D. K. Hammond, P. Vandergheynst , and R. Gribonval, Wavelets on graphs via spectral graph theory, Appl. Comput. Harmon. Anal. 30 (2011) 129-150. [2] A. Tarun, D. Abramian, M. Larsson, H. Behjat, and D. Van De Ville, Voxel-Wise Brain Graphs from Diffusion-Weighted MRI: Spectral Analysis and Application to Functional MRI, preprint (2021). [3] A. Tarun, H. Behjat, T. Bolton, D. Abramian, D. Van De Ville, Structural mediation of human brain activity revealed by white-matter interpolation of fMRI, NeuroImage 213 (2020) 116718.[4] I.M. Bulai, S. Saliani, Spectral graph wavelet packets frames, Applied and Computational Harmonic Analysis (2023).