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Related Concept Videos

Eulerian and Lagrangian Flow Descriptions01:22

Eulerian and Lagrangian Flow Descriptions

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Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
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Applications of Integration to Find Blood Flow01:27

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Blood flow through a cylindrical blood vessel can be mathematically described using the principles of laminar flow, a regime in which fluid moves smoothly in parallel layers. In this model, the velocity of the blood is not uniform across the cross-section of the vessel; rather, it varies with the radial distance from the center. The maximum velocity occurs along the central axis, decreasing progressively toward the vessel walls, where it reaches zero due to viscous drag.Approximating Blood...
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Bernoulli's Equation for Flow Along a Streamline01:30

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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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Autoregulation of Blood Flow01:17

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Autoregulation mechanisms are characterized by their inherent capacity for self-regulation without necessitating specific nervous stimulation or endocrine control. These mechanisms facilitate the adjustment of blood flow and, therefore, perfusion specific to each tissue region. This self-regulation encompasses chemical signals and myogenic controls.
Chemical Signaling in Autoregulation
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Bernoulli's Equation for Flow Normal to a Streamline01:16

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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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Energy Line and Hydraulic Gradient Line01:27

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Based on Bernoulli's equation, the energy line (EL) and hydraulic grade line (HGL) provide graphical representations of energy distribution in a fluid flow system. For steady, incompressible, inviscid flows, Bernoulli's equation is expressed as:
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Particle Image Velocimetry Investigation of Hemodynamics via Aortic Phantom
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Lagrangian postprocessing of computational hemodynamics.

Shawn C Shadden1, Amirhossein Arzani

  • 1Department of Mechanical Engineering, University of California, 5126 Etcheverry Hall, Berkeley, CA , 94720-1740, USA, shadden@berkeley.edu.

Annals of Biomedical Engineering
|July 26, 2014
PubMed
Summary
This summary is machine-generated.

Lagrangian methods are essential for analyzing complex cardiovascular blood flow data. This review explores their use in understanding vascular health and disease from fluid mechanics principles.

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Area of Science:

  • Cardiovascular science
  • Fluid mechanics
  • Biomedical engineering

Background:

  • Recent advances in imaging, modeling, and computing enhance hemodynamic analysis in large vessels.
  • Cardiovascular flow data, particularly velocity fields, contains under-utilized information.
  • Complex blood flow in the heart and arteries requires advanced analysis techniques.

Purpose of the Study:

  • To review Lagrangian methods for post-processing cardiovascular velocity data.
  • To highlight the necessity of Lagrangian approaches for understanding transient hemodynamic conditions.
  • To elucidate the role of these methods in assessing vascular function and health.

Main Methods:

  • Review of existing literature on Lagrangian methods in cardiovascular fluid dynamics.
  • Focus on Lagrangian particle tracking and related post-processing techniques.
  • Application of fluid mechanics principles to interpret hemodynamic data.

Main Results:

  • Lagrangian methods are crucial for interpreting complex, time-varying velocity fields.
  • These techniques enable a deeper understanding of the biomechanical factors influencing vascular health.
  • The review consolidates knowledge on applying Lagrangian methods to cardiovascular flows.

Conclusions:

  • Lagrangian methods are indispensable for fully utilizing cardiovascular flow data.
  • Understanding transient hemodynamics via Lagrangian analysis is key to diagnosing and treating vascular conditions.
  • This review provides a foundation for future research in cardiovascular fluid mechanics.