The Mathematical Models used in 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics.

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*.

Comments

Different Methods for recoding the Brain Signals of the Brain?

The various methods for recording brain signals in detail, focusing on both non-invasive and invasive techniques. 1. Electroencephalography (EEG) Type : Non-invasive Description : EEG involves placing electrodes on the scalp to capture electrical activity generated by neurons. It records voltage fluctuations resulting from ionic current flows within the neurons of the brain. This method provides high temporal resolution (millisecond scale), allowing for the monitoring of rapid changes in brain activity. Advantages : Relatively low cost and easy to set up. Portable, making it suitable for various applications, including clinical and research settings. Disadvantages : Lacks spatial resolution; it cannot precisely locate where the brain activity originates, often leading to ambiguous results. Signals may be contaminated by artifacts like muscle activity and electrical noise. Developments : ...

Predicting Probabilities

1. What is Predicting Probabilities? The predict_proba method estimates the probability that a given input belongs to each class. It returns values in the range [0, 1] , representing the model's confidence as probabilities. The sum of predicted probabilities across all classes for a sample is always 1 (i.e., they form a valid probability distribution). 2. Output Shape of predict_proba For binary classification , the shape of the output is (n_samples, 2) : Column 0: Probability of the sample belonging to the negative class. Column 1: Probability of the sample belonging to the positive class. For multiclass classification , the shape is (n_samples, n_classes) , with each column corresponding to the probability of the sample belonging to that class. 3. Interpretation of predict_proba Output The probability reflects how confidently the model believes a data point belongs to each class. For example, in ...

How does the 0D closed-loop model of the whole cardiovascular system contribute to the overall accuracy of the simulation?

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 ...

LPFC Functions

The lateral prefrontal cortex (LPFC) plays a crucial role in various cognitive functions, particularly those related to executive control, working memory, decision-making, and goal-directed behavior. Here are key functions associated with the lateral prefrontal cortex: 1. Executive Functions : o The LPFC is central to executive functions, which encompass higher-order cognitive processes involved in goal setting, planning, problem-solving, cognitive flexibility, and inhibitory control. o It is responsible for coordinating and regulating other brain regions to support complex cognitive tasks, such as task switching, attentional control, and response inhibition, essential for adaptive behavior in changing environments. 2. Working Memory : o The LPFC is critical for working memory processes, which involve the temporary storage and manipulation of information to guide behavior and decis...

Prerequisite Knowledge for a Quantitative Analysis

To conduct a quantitative analysis in biomechanics, researchers and practitioners require a solid foundation in various key areas. Here are some prerequisite knowledge areas essential for performing quantitative analysis in biomechanics: 1. Anatomy and Physiology : o Understanding the structure and function of the human body, including bones, muscles, joints, and organs, is crucial for biomechanical analysis. o Knowledge of anatomical terminology, muscle actions, joint movements, and physiological processes provides the basis for analyzing human movement. 2. Physics : o Knowledge of classical mechanics, including concepts of force, motion, energy, and momentum, is fundamental for understanding the principles underlying biomechanical analysis. o Understanding Newton's laws of motion, principles of equilibrium, and concepts of work, energy, and power is essential for quantifyi...

Mashtishk Vigyan Anusandhan

Search This Blog