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Applications of Integration to Find Blood Flow

Applications of Integration to Find Blood Flow

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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Thrombus Profiling Assay: A Microfluidics-Based Platform for Comprehensively Characterizing Biomechanical Thrombogenesis

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Haemodynamic forces on in vitro thrombi: a numerical analysis.

Christopher J Butler¹, Kris Ryan, Gregory J Sheard

¹Fluids Laboratory for Aeronautical and Industrial Research-FLAIR, Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia.

Medical & Biological Engineering & Computing

|March 16, 2012

Summary

This study models blood flow around a thrombus analogue using computational fluid dynamics. Local shear rate variations near the thrombus suggest a potential mechanism for limiting its growth and influencing platelet interactions.

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Area of Science:

* Computational fluid dynamics
* Biomedical engineering
* Thrombosis research

Background:

* Blood flow dynamics are crucial in understanding thrombosis.
* Thrombus formation and growth are complex processes influenced by fluid shear stress.
* Previous studies have simplified flow conditions around thrombi.

Purpose of the Study:

* To compute blood flow past an axisymmetric thrombus analogue.
* To investigate platelet behavior and shear rate variations.
* To explore thrombus growth-limiting mechanisms.

Main Methods:

* Solution of discrete three-dimensional Navier-Stokes equations.
* Particle tracking to model thrombocyte (platelet) behavior.
* Analysis of shear rate and temporal gradients under varying flow conditions.

Main Results:

* Local shear rate variations exceeded double Poiseuille flow conditions.
* Non-linear shear rate variations were observed at low Reynolds numbers.
* Topological transitions in shear rate suggest thrombus growth limitation.
* Peak shear rate gradients were found in multiple flow regions, indicating widespread platelet interaction.

Conclusions:

* Idealized thrombi induce significant local shear rate variations.
* These variations may play a role in limiting thrombus growth.
* Platelet interactions extend beyond the immediate thrombus surface.