Shear stress, inflammation and Atherosclerosis

Imperatives of Mathematical Model of Arterial Blood Dynamics for Interpretation of Doppler Velocimetry: A Narrative Review

Clinicians frequently study arterial Doppler velocimetric waveforms depicted by Doppler sonography of the kidneys, the heart, the brain, and the feto-maternal circulation to assess the well-being of the aforementioned vital organs. The waveform interpretation of the Doppler indices can be studied using a mathematical model. The developed models serve as teaching tools and for easy comprehension of the regulatory mechanism of the organs. It will also obtain accurate wall shear stress (WSS) and likely atherosclerotic sites can be predicted early. The aim of this review is to reveal the imperatives of mathematical models in the study of the physical interpretation of Doppler velocimetry. The models will explore sonographic Doppler velocimetry and computational fluid dynamics (CFD) in determining the segments of the arteries that are prone to the development of atheromatous plaque. It will be achieved by comparing and computing the measurement differences of the WSS. A thorough literature review was carried out between 1971 and 2021 on the mathematical modeling of blood dynamics and Doppler velocimetry of different blood vessels, across various electronic databases including NC AHEC Digital Library, PUBMED, ERIC, MEDLINE, Free Medical Journals, and EMBASE. The results of the literature search were presented using the PRISMA flow chat. The narrative review of the mathematical models of arterial blood dynamics is based on incompressible Navier-Stokes equations, the Windkessel model, and CFD. It was deduced that the blood flow velocity decreased with time across the varying frequency from 0.2Hz to 0.50Hz in the interlobar arterial channels. The review also revealed that adult humans' Doppler indices of the renal-interlobar artery agree with developed models of renal interlobar arterial blood dynamics. The mathematical model measurements of the great vessels matched the sonographic Doppler velocimetry with <15% variation. In our fast-paced world of epidemiological transition, the imperatives of mathematical modeling of arterial flow dynamics based on the Navier-Stokes equations to represent various physiologic and pathologic situations cannot be overstated. The practical consequences include the possibility of mathematical models to acquire precise WSS distribution and early detection of potential atherosclerotic sites during cardiovascular Doppler sonography.

Measuring wall shear stress distribution in the carotid artery in an African population: Computational fluid dynamics versus ultrasound doppler velocimetry

INTRODUCTION

Computational fluid dynamics (CFD) and ultrasound Doppler velocimetry are diagnostic tools useful for determining carotid artery segments susceptible to atheromatous plaque development. This study computes and compares the difference in Wall Shear Stress (WSS) measurements between these two methods.

METHODS

The carotid artery of 204 volunteers selected using simple random sampling were scanned using standard carotid doppler protocols. Four segments of the carotid artery - the common, internal, external carotid, and the carotid bulb were sonographically assessed. The intima-media thickness, diameter, peak systolic velocity, and end-diastolic velocity were measured at a point 2 cm away from the carotid bifurcation for the three segments, while the carotid bulb was measured at the bifurcation. A 2D incompressible Navier-Stokes Equation for modelling Newtonian, pulsatile, and laminar flow in a viscoelastic pipe was applied to model velocity flow across the carotid artery using COMSOL software. WSS values were computed for experimental and CFD measurements and the results were compared.

RESULTS

The WSS values generated by the model had respectively peak and average values of 19.81 N/cm² and 15.76 ± 1.81 N/cm² for the common carotid, 10.77 N/cm² and 7.57 ± 1.66 N/cm² for the internal carotid, 11.51 N/cm² and 8.05 ± 1.65 N/cm² for the external carotid, 37.55 N/cm² and 26.55 ± 6.62 N/cm² for the carotid bifurcation, 1.39 N/cm² and 3.13 ± 1.34 N/cm² for the carotid bulb. The model measurements matched doppler velocimetry measurements with <15% variation.

CONCLUSION

Model based WSS values were higher but comparable with doppler velocimetry measurements. The carotid bulb had low WSS and is therefore the segment highly disposed to atheromatous plaque formation.

IMPLICATIONS FOR PRACTICE

Subject-specific mathematical models could be incorporated during cardiovascular scan work up for accurate WSS distribution and early prediction of possible atherosclerotic sites.