(2009)血流动力学参数集合

Sang-Wook Lee Biomedical Simulation Laboratory,

University of Toronto,

5King’s College Road Toronto,

Toronto,ON M5S3G8Canada;

School of Mechanical and Automotive

Engineering,

University of Ulsan,

Ulsan680-749,South Korea

Luca Antiga

Department of Bioengineering, Mario Negri Institute for Pharmacological

Research,

24020Ranica(BG),Italy David A.Steinman1

Biomedical Simulation Laboratory,

University of Toronto,

5King’s College Road Toronto,

Toronto,ON M5S3G8Canada e-mail:steinman@mie.utoronto.ca Correlations Among Indicators of Disturbed Flow at the Normal Carotid Bifurcation

A variety of hemodynamic wall parameters(HWP)has been proposed over the years to quantify hemodynamic disturbances as potential predictors or indicators of vascular wall dysfunction.The aim of this study was to determine whether some of these might,for practical purposes,be considered redundant.Image-based computationalfluid dynamics simulations were carried out for Nϭ50normal carotid bifurcations reconstructed from magnetic resonance imaging.Pairwise Spearman correlation analysis was performed for HWP quantifying wall shear stress magnitudes,spatial and temporal gradients,and harmonic contents.These were based on the spatial distributions of each HWP and,

harmonic(DH)parameter were found to depend on how the wall shear stress magnitude was defined in the presence offlow reversals.Many of the proposed HWP were found to provide essentially the same information about disturbedflow at the normal carotid bifurcation.RRT is recommended as a robust single metric of low and oscillating shear. On the other hand,gradient-based HWP may be of limited utility in light of possible redundancies with other HWP,and practical challenges in their measurement.Further investigations are encouraged before thesefindings should be extrapolated to other vas-cular territories.

͓DOI:10.1115/1.3127252͔

Keywords:wall shear stress,atherosclerosis,hemodynamic wall parameter,carotid bifurcation

1Introduction

There is much evidence suggesting that initiation and progres-sion of atherosclerotic disease is influenced by“disturbedflow”͓1͔.Notwithstanding the imprecise nature of this term͓2͔,various

metrics have been proposed over the years to quantifyflow dis-turbances.Originally focused on the magnitudes of wall shear stress͑WSS͓͒3,4͔these hemodynamic wall parameters͑HWP͒have since incorporated spatial and temporal gradients of WSS ͓5–8͔and,more recently,the harmonic content of time-varying WSS waveforms͓2,9͔.

In a recent computationalfluid dynamics͑CFD͒study of the relationship between geometry and disturbedflow at the carotid bifurcations of young adults͓10͔,we noted that ourfindings were relatively insensitive to the choice of either time-averaged wall shear stress magnitude͑TAWSS͒or oscillatory shear index͑OSI͒as metrics of disturbedflow.This was found to be explained by a strong and significant inverse correlation between these two quan-tities.Such correlations among HWP are not unexpected,as rec-ognized early by Friedman and Deters͓11͔;however,they have been little-investigated in light of the growth in the number and complexity of candidate HWP.

With this in mind,the objective of the present study was to use a representative sample of normal carotid bifurcation geometries to comprehensively test for correlations among established and recently-proposed HWP.Especially in the context of large-scale

studies of so-called geometric and hemodynamic risk factors in

atherosclerosis,we aimed to determine whether a subset of HWP,

or even a single HWP,might serve as a sufficiently robust marker

of disturbedflow.

2Materials and Methods

2.1Computational Fluid Dynamics.N=50anatomically re-alistic carotid bifurcation geometries were digitally reconstructed

from black blood magnetic resonance imaging͑MRI͒of25osten-

sibly healthy young adults,as described previously͓12͔.CFD

simulations were carried out using a well-validated in-house

finite-element-based CFD solver͓13–15͔.Quadratic tetrahedral-

element meshes were generated by a commercial mesh generator ͑ICEM-CFD;ANSYS,Berkeley,CA͒using a nominally uniform node spacing of0.2mm,previously shown to be sufficient for

resolving wall shear stresses to within10%accuracy͓16͔.Rigid

walls and Newtonian rheology were assumed.Pulsatileflow

boundary conditions were prescribed based on representative

waveform shapes and allometrically-scaled inlet and outletflow

rates.Further details of the CFD simulations are provided else-

where͓10͔.

For each tetrahedral element the vector WSS,␶w,was calcu-lated as the projection of the stress tensor onto the element’s sur-face at each node,using the element’s quadratic shape functions. As nodes are connected to multiple elements,contributions to each nodal␶w were averaged together.From these time-varying nodal WSS vectors,a variety of HWP were computed,as summa-rized in Table1,and detailed below.

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the J OUR-NAL OF B IOMECHANICAL E NGINEERING.Manuscript received August12,2008;final

manuscript received January1,2009;published online May11,2009.Review con-ducted by Fumihiko Kajiya.Paper presented at the2008Summer Bioengineering Conference͑SBC2008͒,Marco Island,FL,June25–29,2008.