J Global Clinical Engineering Vol.6 Special Issue 6: 2024 102 Conference Paper Deciphering Astroglial Dynamics and Interactions Through Multi-Scale Computational Modeling in Multiple Sclerosis Evolution Chrysoula Tsimperi1,*, Konstantinos Michmizos2 and Leontios Hadjileontiadis1 1 Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece. 2 Computational Brain Lab, Department of Computer Science, Rutgers University, Piscataway, NJ, United States. * Corresponding Author Email: xrysa97.tsiberi@gmail.com ABSTRACT Multiple sclerosis (MS) is a neurodegenerative disease affecting millions worldwide, highlighting the complex relationship between the immune system and the central nervous system. Astrocytes are recognized as significant contributors to the disease’s pathogenesis. In this work, a biophysically realistic astrocytic model was created to investigate astrocytes' role in MS develop- ment, focusing on their impact on axonal conduction and enhanced sodium channel facilitation in demyelinated axons. Through the advancement of comprehension about the involvement of astrocytes in the pathophysiology of MS, this study explores the processes underlying the disease. The study also examines the morphology of astrocytes and its influence on cellular activity, providing insights into cell instability drivers and the interaction between morphological changes and functional modifications. This approach aims to understand the complex connections between cellular characteristics and physiological attributes, en- hancing our understanding of multiple sclerosis and potentially developing groundbreaking therapies. Keywords—Astrocytes, Conduction velocity, In-Silico, Multiple sclerosis. Copyright © 2024. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY): Creative Commons - Attribution 4.0 International - CC BY 4.0. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduc- tion is permitted which does not comply with these terms. http://www.globalce.org http://globalce.org http://globalce.org https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ 103 J Global Clinical Engineering Vol.6 Special Issue 6: 2024 INTRODUCTION Astrocytes are key contributors to multiple sclerosis (MS) lesions, playing a crucial role in maintaining neural homeostasis and preventing neural tissue damage.1 They exhibit dual roles, responding adaptively or non-adaptively to the severity of injury.2,3 Their intricate morphology and adaptive responses are central to MS lesion development.4,5 However, this dual nature, providing both protection and potential hindrance, makes them complex therapeutic targets.6 In this study, our primary objective is to delve into the role of astrocytes in the development of MS le- sions, adopting a comprehensive approach through three distinct parts. The first part explores how astrocytes influence axonal conduction, with implications for MS- related functional deficits. The second part examines how astrocytes facilitate sodium channels in demyelinated axons, shedding light on potential MS pathophysiology mechanisms. The third part seeks to correlate the loss and recovery of astrocytes in the cerebral cortex with myelin loss due to conduction block in new MS lesions. Our approach involves creating biologically realistic models of two distinct astrocytic states, one representing physi- ological conditions and the other mimicking pathological scenarios. These models serve as the foundation for our study, enabling us to expand our understanding of various factors, including demyelinated and remyelinated axon conductance, the role of ions as signaling molecules (such as Ca2+, Na+, and K+), and the impact of inflammatory cy- tokines like IL1β/6 and TNFα . Our overarching goal is to develop comprehensive computational representations of astrocytes that encompass both their physiological and pathological behaviors within the neocortex area. By developing biophysically realistic models and incor- porating empirical data, we aim to accurately capture astrocyte morphology and functionality while exploring their behavior across different scales. METHODS In this study, we aimed to unravel the intricate ma- chinery underlying astroglial pathophysiology in MS by addressing the challenge of their complex, sponge-like morphology. This work systematically assessed the multi- scale morphology of astroglia to create a realistic multi- compartment cell model for biophysical interrogation within the NEURON computational environment. As a proof of concept, we simulated two neocortex astrocytes in a virtual environment, subjecting them to a series of imaging experiments. This allowed us to reveal crucial aspects of astroglial pathophysiology that are challeng- ing to access through empirical methods. These findings encompassed spatiotemporal dynamics of intracellular K+ and Na+ redistribution, essential Ca2+ buffering properties, as well as the effects of demyelinated and remyelinated axon conductance and the influence of inflammatory cy- tokines such as IL1β/6 and TNFα. We aimed to create a modeling approach that faithfully replicates the intricate morphology of astrocytes across multiple scales while retaining the full capabilities of biophysical simulations provided by NEURON. A. Significance of Morphology in MS Brain astroglia has a distinct morphology compared to nerve cells due to their complex system of nanoscopic processes that fill tissue volume between branches.3,7 They are often seen as a cloudy structure around thicker branches and do not overlap in tissue domains.8,9 In MS lesions, astroglia plays complex roles, influencing inflam- mation and neuronal repair. The nervous system influences the shapeshifting properties of reactive astrocytes, which can be influenced by damage severity. Traumatic brain injuries can increase GFAP levels, leading to cell-body hypertrophy and hot spots of cell proliferation (Figure 1). The presence of astrocytes near focal lesions can lead to “palisades” and decreased astrogliosis hallmarks.3,10,11   To develop effective therapies targeting astrocytes, a deeper understanding of their subtypes and functions is essential. Super-resolution imaging techniques hold promise in unraveling astrocyte behavior in MS.12 Due to the varying cellular mechanisms and morphological features of astroglia, it is important to develop a model that can explore astroglial functions under pathological conditions. B. Data Selection In this study, we employed a multifaceted approach to investigate the role of cortical astrocytes in the context of neocortical lesions associated with MS. Using datasets from mouse models, we harnessed advanced imaging http://www.globalce.org http://globalce.org http://globalce.org J Global Clinical Engineering Vol.6 Special Issue 6: 2024 104 techniques to visualize the intricate morphological changes of astrocytes within the cortex when neocortical lesions are present. For this work, it was selected two datasets of astrocytes (physiology and pathophysiology) from the neocortex area from the NEUROMORPHO database (Tables 1 and 2) for the development of an interactive realistic model.13 FIGURE 1. Function of the Astrocyte from Homeostasis to Pathology. TABLE 1. Measurements of physiology cell. Measurements Data Soma Surface 67.05 µm2 Number of Stems 13 Number of Bifurcations 742 Number of Branches* 1497 Overall Width 44.67 µm Overall Height 52.97 µm Overall Depth 51.07 µm Average Diameter 0.51 µm Total Length 8281.73 µm Total Surface** 11237.8 µm2 Total Volume** 2672.6 µm3 Max Euclidean Distance 41.74 µm Max Path Distance 63.29 µm Max Branch Order 27 Average Contraction 0.87 Total Fragmentation 7466 Partition Asymmetry 0.65 Average Rall’s Ratio 1.9 Average Bifurcation Angle Local 65.21° Average Bifurcation Angle Remote 77.33° Fractal Dimension 1.1 * Rows highlighted in blue represent the number of branches. ** Rows highlighted in red correspond to surface area and volume parameters, which are utilized in calculating the surface-to-volume ratio (SVR). TABLE 2. Measurements of pathology cell. Measurements Data Soma Surface 126.98 µm2 Number of Stems 6 Number of Bifurcations 267 Number of Branches* 540 Overall Width 24.57 µm Overall Height 67.02 µm Overall Depth 51.54 µm Average Diameter 0.64 µm Total Length 3160.88 µm Total Surface** 5575.83 µm2 Total Volume** 2820.8 µm3 Max Euclidean Distance 46.74 µm Max Path Distance 62.2 µm Max Branch Order 26 Average Contraction 0.83 Total Fragmentation 3764 Partition Asymmetry 0.62 Average Rall’s Ratio 2.08 Average Bifurcation Angle Local 69.86° Average Bifurcation Angle Remote 75.01° Fractal Dimension 1.11 * Rows highlighted in blue represent the number of branches. ** Rows highlighted in red correspond to surface area and volume parameters, which are utilized in calculating the surface-to-volume ratio (SVR). http://www.globalce.org http://globalce.org http://globalce.org 105 J Global Clinical Engineering Vol.6 Special Issue 6: 2024 C. Incorporation of Astrocyte Mechanisms This section discusses the versatility of models built, emphasizing their ability to incorporate numerous NEU- RON-enabled channel and transporter kinetic mechanisms validated through experiments and simulations. Formal descriptions of these algorithms are accessible through the extensive NEURON database, SenseLab. The model includes various channel current and diffusion-reaction mechanisms tailored to this study. These mechanisms encompass the Kir4.1 potassium current, intracellular K+ and Na+ diffusion, the demyelination and remyelination axon conductance mechanism, and K+/Na+ extrusion.14, 15 Gap junction mechanisms are also incorporated, offering options for current leakage or diffuse escape.8 Also, we delve into the simulation algorithms that govern intracel- lular Ca2+ dynamics in MSASTRO, including the diffusion of Ca2+ among compartments of different sizes. These algorithms draw from NEURON Book 24 and are adapted from the modified cadifus.mod file.16 D. Generating Complete Astrocyte Morphology The study’s methods involved setting up the NEURON environment, generating astrocyte stem trees through various options, and simulating the nanoscopic processes within the MSASTRO system.7 Stem trees were selected from libraries, generated with endfoot structures, or loaded from reconstructed files. Nanoscopic process geometry was determined using default statistics or built-in tools. Parameters for membrane conductance and dendritic geometry were adjusted for accurate simulations. The resulting astrocyte models were compared to empirical data, and their morphology was refined to achieve align- ment. Computer simulations were used to analyze sodium uptake mechanisms, focusing on the electrochemical properties of astrocytes and the Na+, K⁺-ATPase (Figure 2). High-affinity Ca2+ indicators were employed to trans- late fluorescence signals into intracellular Ca2+ dynamics, requiring in-silico modeling of Ca2+ entry, diffusion, and buffering mechanisms. The clustering of Ca2+ channels was studied to reveal spatial dynamics and the role of channel clusters in Ca2+ signaling (Figure 3). Architectural characteristics of astroglia were investi- gated through the examination of tissue volume fraction FIGURE 2. Summed distribution of astrocyte intermediate forms binding Na+ and K+ versus membrane potential. FIGURE 3. The visualization of the internal dynamics of Ca2+ in a cell is done through the use of dendrites. The black circle shows the area of interest, while the right shows the dendrites’ d1 and d2. http://www.globalce.org http://globalce.org http://globalce.org J Global Clinical Engineering Vol.6 Special Issue 6: 2024 106 (VF) and surface-to-volume ratios (SVR), providing insights into morphology and interactions with the surrounding environment (Figure 4). Computational modeling of cy- tokine signaling was conducted, focusing on interactions between microglial cytokines and their effects on astroglial behavior. Using an ordinary differential equation (ODE) model (Equation 1), the research explored the effects of autocrine/paracrine microglial cytokine interactions, particularly those involved MS, such as TNFα, IL-1β, and IL-6. We used a classic S-systems model formulation to simulate the expression dynamics of each cytokine (Figure 5a). where Cx = Cx(t) is the expression of cytokine x (TNFα, IL-1β, IL-6) that is produced at rate kx upon activation by cytokine Ci at time = t − τd,ix. Thus the delay term τd,ix is time between the activation of Ci and its subsequent activation of Cx. The activation of Cx depends on Ci according to a Hill function characterized by half-maximal activation constant Kix and cooperativity coefficient nix. Similarly, inhibitory cytokine Cj reduces Cx production with time delay τd,jx ac- cording to a decreasing sigmoidal function characterized by Kjx and njx. The degradation of Cx occurred with both concentration-dependent and concentration-independent components determined by rate constants γx and γss,x, respectively. The concentration-independent degradation term encompassed the initial value of cytokine x, which was set to Css,x = 0.1 for all cytokines, and a degradation constant that was set to maintain a constant steady state 17 in the absence of stimulation. Lastly, the study explored the requirements for effective conduction within astroglia particularly the influence of internodal distance on conduction velocity, and assessed the impact of parameters like Na+ and K+ channel density (1) (4) (5) (2) (3) FIGURE 4. NEURON-based astrocyte model: determining volumetric quantities. FIGURE 5. Network model and mathematical simulation of complex signaling dynamics cytokines. (a) The literature-based network model depicts the activation and inhibition of cytokine production. (b) The results of our calibrated model are shown along with a saturating stimulus of LPS = 1000 & t = 0. http://www.globalce.org http://globalce.org http://globalce.org 107 J Global Clinical Engineering Vol.6 Special Issue 6: 2024 on conduction. In astroglia, ion dynamics is a relatively slow process and the simulation trial normally requires needs at least 100 seconds. RESULTS AND DISCUSSION The results showcased that the chosen rate coefficients for isolated astrocytes and the current-voltage (I-V) relation were consistent with the physiological implica- tions of the electrogenic sodium pump. This provided a fundamental understanding of sodium dynamics in these cells (Figure 2). No step involving binding or dissociation between Na+ or K+ and the astrocytes is directly influenced by voltage. There is a considerable indirect effect of volt- age on the binding of Na+ or K+ to the astrocytes, owing to the voltage-dependent distribution of intermediates. Moving beyond sodium uptake, the research delved into the intricate world of astroglial calcium waves. While traditionally, slow global calcium elevations were the primary indicators of astroglial activity, recent advance- ments in high-sensitivity Ca2+ imaging revealed faster and more localized Ca2+ signals prevalent in smaller processes (Figure 3). The VF, which describes the proportion of local tissue occupied by astrocytes, was examined to provide insights into astrocyte morphology. Similarly, the SVR, a key biophysical determinant of a cell's function, was ana- lyzed to evaluate how astrocyte morphology aligns with its surrounding environment. It is not known how SVR ranges in neocortex astroglial cells. However, we decided to evaluate surface area-to-volume ratios, which can be considered a measure of how much the morphology of a cell is adapted to interact with its environment. (Tables 1 and 2) (SVRphysiology = 4.205 μm−1 & SVRpathology = 1.977 μm−1). This provided quantitative data that shed light on the physical interact interactions between astrocytes and their surroundings (Figure 4). The model provided insights into how these cytokines may influence astroglial responses under pathological conditions, paving the way for a deeper understanding of complex cellular interactions (Figure 5). By focusing on incorporating relevant mechanisms into the model, the study aimed to explore the requirements for effective con- duction within astroglia. Notably, experimental evidence suggests a low Na+ channel density within the internodal axolemma (2–6%), potentially acting as a mediator between demyelinated regions. Several simulations were conducted to scrutinize this possibility. In constructing the model, a 12-node axon was designed, with each node divided into regions representing demyelinated or remyelinated phases. The presence of new Ranvier nodes emerged in internodal regions during remyelination, creating short internodes. As the remyelination process progressed and the lamellae increased, the likelihood of successful Ranvier conduction escalated rapidly, although the conduction velocity remained low. The relationship between internodal conduction time (ICT) and velocity exhibited a linear trend for small and large internodal lengths (L), with the increase in velocity observed only for L below 2000 μm (Figure 6). This study suggests the significance of internodal distance in conduc- tion velocity and emphasizes the delicate balance between nodal and internodal currents for effective propagation. CONCLUSION In summary, this study uses advanced computational modeling to explore astroglial physiology and interac- tions, providing insights into astrocyte function, calcium dynamics, tissue architecture, and cytokine signaling. It raises questions about how specific inflammatory stimuli influence disease outcomes and whether modulating FIGURE 6. NEURON-based astrocyte model: determining volumetric quantities. http://www.globalce.org http://globalce.org http://globalce.org J Global Clinical Engineering Vol.6 Special Issue 6: 2024 108 astrocyte responses could have therapeutic potential. 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