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Showing posts with the label Hemodynamics

Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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How does the 0D closed-loop model of the whole cardiovascular system contribute to the overall accuracy of the simulation?

Dr. Rishabh Pathak
  The 0D closed-loop model of the whole cardiovascular system plays a crucial role in enhancing the overall accuracy of simulations in the context of biventricular electromechanics. Here are some key ways in which the 0D closed-loop model contributes to the accuracy of the simulation:   1. Comprehensive Representation: The 0D closed-loop model provides a comprehensive representation of the entire cardiovascular system, including systemic circulation, arterial and venous compartments, and interactions between the heart and the vasculature. By capturing the dynamics of blood flow, pressure-volume relationships, and vascular resistances, the model offers a holistic view of circulatory physiology.   2. Integration of Hemodynamics: By integrating hemodynamic considerations into the simulation, the 0D closed-loop model allows for a more realistic representation of the interactions between cardiac mechanics and circulatory dynamics. This integration enables the simulation ...
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The Mathematical Models used in 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics.

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 electrophysiolog...
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What is the significance of reconstructing the muscular fiber architecture in accurately simulating cardiac electromechanics?

Dr. Rishabh Pathak
  1. **Impact on Electrophysiology**: The orientation and arrangement of myocardial fibers play a significant role in the propagation of electrical signals within the heart. By accurately representing the fiber architecture, electromechanical models can better simulate the initiation and propagation of action potentials, which are essential for coordinating the heart's contraction.   2. **Influence on Contraction**: The alignment of cardiac muscle fibers determines the direction in which the heart contracts during systole. By incorporating realistic fiber orientations, electromechanical models can accurately predict the mechanical behavior of the heart, including the generation of contractile forces and the resulting changes in chamber volumes.   3. **Effect on Mechanical Function**: The architecture of myocardial fibers directly influences the mechanical properties of the heart, such as its stiffness, compliance, and contractile efficiency. By capturing the intric...
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The 3D biventricular electromechanical model in account for the interaction between the heart and the circulatory system.

Dr. Rishabh Pathak
     The 3D biventricular electromechanical model described in the PDF file incorporates a detailed representation of the interaction between the heart and the circulatory system. This model couples the electromechanical behavior of the heart with a 0D closed-loop (lumped parameters) hemodynamical model of the entire cardiovascular system, including blood flow dynamics. By integrating these two components, the model can simulate the complex interplay between cardiac mechanics and circulatory dynamics. Specifically, the electromechanical aspect of the model accounts for processes such as cardiac electrophysiology, active contraction of cardiomyocytes, tissue mechanics, and blood circulation within the heart chambers. These core models capture the molecular, cellular, tissue, and organ-level processes involved in the heart's pumping function. The coupling between these electromechanical components and the closed-loop hemodynamical model is achieved through suitable interf...
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What is Laplace Dirichlet-Rule-Based-Methods (LDRBMs)?

Dr. Rishabh Pathak
  Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) are a class of Rule-Based-Methods (RBMs) used to generate cardiac muscle fiber orientations in electromechanical models. These methods define the orientation of myocardial fibers within the heart by solving Laplace boundary-value problems. Specifically, LDRBMs determine the transmural, apico-basal, and inter-ventricular distances as solutions to Laplace equations within the computational domain. By prescribing boundary conditions on the epicardial, endocardial, and base surfaces of the heart, LDRBMs provide a mathematical framework for generating realistic fiber architectures that play a crucial role in electric signal propagation and myocardial contraction. These methods are essential for accurately modeling the biomechanics of the heart and are widely used in computational cardiac electromechanics research.   Piersanti, R., Regazzoni, F., Salvador, M., Corno, A. F., Dede', L., Vergara, C., & Quarteroni, A. (202...
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3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics

Dr. Rishabh Pathak
  The article presents a comprehensive study on a 3D-0D closed-loop model for simulating biventricular electromechanics in the context of the heart and circulatory system interaction. The model incorporates detailed descriptions of the muscular fiber architecture within the heart to accurately represent cardiac activity. By considering the interaction between the left and right ventricles, the study highlights the importance of a biventricular approach over a stand-alone left ventricle model. The model accounts for active tension along different directions within the heart, showing how it impacts cardiac work and efficiency. Additionally, the article discusses the distribution of stress on the ventricular base and the implications of different stress distribution approaches. Overall, the study emphasizes the significance of a holistic approach to simulating cardiac electromechanics, considering both ventricles and their interplay within the cardiovascular system.   ...
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