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Related Concept Videos

Navier–Stokes Equations01:28

Navier–Stokes Equations

705
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...
705
Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

362
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
362
Euler's Equations of Motion01:28

Euler's Equations of Motion

551
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains...
551
Shearing Stress01:19

Shearing Stress

834
Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
834
Stress: General Loading Conditions01:15

Stress: General Loading Conditions

372
To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
372
Principal Stresses01:24

Principal Stresses

356
The graphical depiction of normal and shearing stress equations is represented by a circle, demonstrating the interplay between these stresses under different angular conditions. The center of this circle C, located on the vertical axis, represents the average normal stress, while its radius shows the range of stress variations. At points A and B, where the circle intersects the horizontal axis, the maximum and minimum normal stresses are observed, occurring without shearing stress. These...
356

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Related Experiment Video

Updated: Sep 2, 2025

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
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Wall Shear Stress Estimation for 4D Flow MRI Using Navier-Stokes Equation Correction.

Jiacheng Zhang1, Sean M Rothenberger2, Melissa C Brindise3

  • 1School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA.

Annals of Biomedical Engineering
|August 9, 2022
PubMed
Summary

A new method enhances wall shear stress (WSS) accuracy in 4D flow MRI by correcting velocity gradients. This improved WSS estimation aids in predicting cardiovascular disease progression and blood vessel remodeling.

Keywords:
Cerebral aneurysmFluid dynamicsPhase-contrast MRIPressure field reconstructionThoracic aortaWall shear stress

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Area of Science:

  • Medical Imaging
  • Biomedical Engineering
  • Fluid Dynamics

Background:

  • Accurate wall shear stress (WSS) estimation is crucial for understanding cardiovascular diseases.
  • Current 4D flow MRI methods for WSS calculation have limitations in accuracy.

Purpose of the Study:

  • To develop and validate a novel WSS estimation method for 4D flow MRI.
  • To improve the accuracy of WSS quantification in cardiovascular applications.

Main Methods:

  • A new WSS estimation technique using reconstructed pressure gradients and flow-physics constraints.
  • Validation on synthetic Womersley flow and cerebral aneurysm data.
  • Application to in vivo cerebral aneurysm and aorta 4D flow MRI data.

Main Results:

  • Improved WSS accuracy by up to 100% for Womersley flow.
  • Reduced underestimation of mean WSS by 39-50% in synthetic aneurysms.
  • Higher WSS predictions in vivo for aneurysms (31-50%) and aortas (3-6x) compared to other methods.

Conclusions:

  • The proposed method significantly enhances WSS estimation accuracy from 4D flow MRI.
  • Accurate WSS data can improve predictions of blood vessel remodeling and cardiovascular disease progression.