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# Use of Factor Analysis to Characterize Arterial Geometry and Predict Hemodynamic Risk: Application to the Human Carotid Bifurcation

[+] Author and Article Information
Qi Zhang

Department of Electronic and Information Engineering, Shanghai University, 200072, Shanghai, China; Department of Biomedical Engineering, Duke University, Durham, NC 27708

David A. Steinman

Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8 Canada

Morton H. Friedman1

Department of Biomedical Engineering, Duke University, Durham, NC 27708; Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052mhfriedm@gwu.edu

1

Corresponding author.

J Biomech Eng 132(11), 114505 (Oct 27, 2010) (5 pages) doi:10.1115/1.4002538 History: Received July 30, 2010; Revised August 19, 2010; Posted September 10, 2010; Published October 27, 2010; Online October 27, 2010

## Abstract

The detailed geometry of atherosclerosis-prone vascular segments may influence their susceptibility by mediating local hemodynamics. An appreciation of the role of specific geometric variables is complicated by the considerable correlation among the many parameters that can be used to describe arterial shape and size. Factor analysis is a useful tool for identifying the essential features of such an inter-related data set, as well as for predicting hemodynamic risk in terms of these features and for interpreting the role of specific geometric variables. Here, factor analysis is applied to a set of 14 geometric variables obtained from magnetic resonance images of 50 human carotid bifurcations. Two factors alone were capable of predicting 12 hemodynamic metrics related to shear and near-wall residence time with adjusted squared Pearson’s correlation coefficient as high as 0.54 and $P$-values less than 0.0001. One factor measures cross-sectional expansion at the bifurcation; the other measures the colinearity of the common and internal carotid artery axes at the bifurcation. The factors explain the apparent lack of an effect of branch angle on hemodynamic risk. The relative risk among the 50 bifurcations, based on time-average wall shear stress, could be predicted with a sensitivity and specificity as high as 0.84. The predictability of the hemodynamic metrics and relative risk is only modestly sensitive to assumptions about flow rates and flow partitions in the bifurcation.

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## Figures

Figure 1

Predicted versus true ranking of values of WSS90% for the 50 carotid bifurcations. Lowest rank corresponds to highest risk, that is, the lowest value of WSS90%. The predicted rankings are based on the assumption of CCA-ICA allometrically scaled flow; the true rankings are based on flow calculations assuming (a) CCA-ICA allometrically scaled flow, (b) CCA allometrically scaled flow, and (c) nonallometric flow.

Figure 2

Four pairs of bifurcations with similar values of factor F1, but opposite extremes of F3. Beside each bifurcation, its case number is labeled as used in Ref. 4, as well as its F1-value and F3-value. Bifurcations on the top row have low F3-values (F3<−1.2) and bifurcations at the bottom row have high F3-values (F3>1.3); the pair of bifurcations in each column have similar F1-values (difference <0.09). Regions shown in yellow and red indicate at-risk areas exposed to high RRT outside the 80th and 90th percentiles, respectively. Light shading designates at-risk areas on the hidden side of the bifurcation.

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