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Unveiling Hidden Neural Codes: SIMPL – A Scalable and Fast Approach for Optimizing Latent Variables and Tuning Curves in Neural Population Data

Dr. Rishabh Pathak
This research paper presents SIMPL (Scalable Iterative Maximization of Population-coded Latents), a novel, computationally efficient algorithm designed to refine the estimation of latent variables and tuning curves from neural population activity. Latent variables in neural data represent essential low-dimensional quantities encoding behavioral or cognitive states, which neuroscientists seek to identify to understand brain computations better. Background and Motivation Traditional approaches commonly assume the observed behavioral variable as the latent neural code. However, this assumption can lead to inaccuracies because neural activity sometimes encodes internal cognitive states differing subtly from observable behavior (e.g., anticipation, mental simulation). Existing latent variable models face challenges such as high computational cost, poor scalability to large datasets, limited expressiveness of tuning models, or difficulties interpreting complex neural network-based functio...
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The Mathematical Models used in 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics.

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Dr. Rishabh Pathak


 

The mathematical models to the reconstruction of cardiac muscle fiber architecture in biventricular geometries and the development of a 3D cardiac electromechanical (EM) model coupled with a 0D closed-loop model for the cardiovascular system. Here is an overview of the mathematical models discussed in the document:

 1. Fiber Generation Methods: The document outlines the methods used to reconstruct the cardiac muscle fiber architecture in biventricular geometries. Specifically, Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) are employed to generate realistic fiber orientations within the heart. These methods involve solving Laplace boundary-value problems to determine the orientation of myocardial fibers based on boundary conditions on the heart's surfaces.

 2. 3D Cardiac EM Model: The document presents a detailed 3D cardiac electromechanical model that captures the biophysical processes involved in heart function. This model integrates aspects of electrophysiology, active contraction of cardiomyocytes, tissue mechanics, and blood circulation within the heart chambers. By considering these components, the model can simulate the electromechanical behavior of the heart in a comprehensive manner.

 3. 0D Closed-Loop Model: In addition to the 3D cardiac EM model, the document discusses the incorporation of a 0D closed-loop model for the cardiovascular system. This model represents the hemodynamics of the entire circulatory system using lumped parameters to simulate blood flow dynamics, pressure-volume relationships, and systemic interactions. The coupling of the 3D EM model with the 0D closed-loop model enables a holistic simulation of the heart's electromechanical activity in the context of circulatory dynamics.

 4. Numerical Approximation: The document also covers the numerical discretization strategies employed to solve the coupled 3D-0D model. This includes space and time discretizations using the Finite Element Method (FEM) with different mesh resolutions to handle the varying scales of electromechanical and hemodynamic processes. The Segregated-Intergrid-Staggered (SIS) approach is utilized to sequentially solve the core models contributing to cardiac EM and blood circulation.

 Overall, the mathematical models presented in the document provide a framework for simulating biventricular electromechanics and studying the complex interactions between the heart and the circulatory system. These models enable researchers to investigate cardiac function, electromechanical behavior, and hemodynamic responses in a comprehensive and integrated manner.


Piersanti, R., Regazzoni, F., Salvador, M., Corno, A. F., Dede', L., Vergara, C., & Quarteroni, A. (2021). 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics. *arXiv preprint arXiv:2108.01907*.

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