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Related Concept Videos

Bernoulli's Equation: Problem Solving01:16

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A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
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Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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In the middle of the nineteenth century, it was observed that two trains passing each other at a high relative speed get pulled towards each other. The same occurs when two cars pass each other at a high relative speed. The reason is that the fluid pressure drops in the region where the fluid speeds up. As the air between the trains or the cars increases in speed, its pressure reduces. The pressure on the outer parts of the vehicles is still the atmospheric pressure, while the resultant...
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Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
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Bernoulli's Principle: Applications01:17

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There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices include, but are not limited to, entrainment devices and fluid flow measuring devices.
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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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In Silico Clinical Trials for Cardiovascular Disease
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Bayesian Optimization-Based Inverse Finite Element Analysis for Atrioventricular Heart Valves.

Colton J Ross1, Devin W Laurence2, Ankush Aggarwal3

  • 1Biomechanics & Biomaterials Design Laboratory, School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK, USA.

Annals of Biomedical Engineering
|November 22, 2023
PubMed
Summary

Bayesian optimization improves inverse finite element analysis for atrioventricular heart valves, enabling accurate in-vivo mechanical response predictions. This method enhances understanding of heart valve function, even with complex congenital defects.

Keywords:
Constitutive model parametersHeart valve biomechanicsIn-silico modelingStatistics-based modeling

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Area of Science:

  • Biomedical Engineering
  • Computational Mechanics
  • Cardiovascular Research

Background:

  • Inverse finite element analysis (iFEA) offers insights into in-vivo heart valve function but faces limitations in predicting patient-specific leaflet mechanics.
  • Current iFEA methods are not widely adopted for clinical applications due to these challenges.

Purpose of the Study:

  • To explore the application of Bayesian optimization (BO) for in-vivo atrioventricular heart valve (AHV) functional behavior analysis.
  • To assess BO's efficacy in estimating material coefficients for AHV models.
  • To develop and apply a BO-integrated iFEA framework for patient-specific AHV leaflet property prediction.

Main Methods:

  • Utilized Bayesian optimization (BO) to estimate isotropic Lee-Sacks material coefficients in benchmark problems (inflation test, leaflet contact, idealized AHV model).
  • Developed a BO-iFEA framework and applied it to a patient-specific tricuspid valve with congenital heart defects.
  • Evaluated an in-silico modeling approach substituting chordae with displacement boundary conditions for improved iFEA convergence.

Main Results:

  • BO accurately constructed objective function surfaces, outperforming traditional grid search analysis.
  • The BO-iFEA framework achieved average element errors below 0.02 mm/mm for material parameter predictions.
  • Identified non-unique solutions due to objective function valleys, indicating functionally equivalent outcomes.

Conclusions:

  • Demonstrated the first-time use of Bayesian optimization for atrioventricular heart valve inverse finite element analysis.
  • The proposed BO-iFEA framework shows promise for accurate in-vivo AHV mechanical response prediction.
  • Substituting chordae with boundary conditions improved iFEA convergence and objective surface smoothness.