Improved prediction of disturbed flow via hemodynamically-inspired geometric variables

Abstract

Arterial geometry has long been considered as a pragmatic alternative for inferring arterial flow disturbances, and their impact on the natural history and treatment of vascular diseases. Traditionally, definition of geometric variables is based on convenient shape descriptors, with only superficial consideration of their influence on flow and wall shear stress patterns. In the present study we demonstrate that a more studied consideration of the actual (cf. nominal) local hemodynamics can lead to substantial improvements in the prediction of disturbed flow by geometry. Starting from a well-characterized computational fluid dynamics (CFD) dataset of 50 normal carotid bifurcations, we observed that disturbed flow tended to be confined proximal to the flow divider, whereas geometric variables previously shown to be significant predictors of disturbed flow included features distal to the flow divider in their definitions. Flaring of the bifurcation leading to flow separation was redefined as the maximum relative expansion of the common carotid artery (CCA), proximal to the flow divider. The beneficial effect of primary curvature on flow inertia, via suppression of flow separation, was characterized by the in-plane tortuosity of CCA as it enters the flare region. Multiple linear regressions of these redefined geometric variables against various metrics of disturbed flow revealed R(2) values approaching 0.6, better than the roughly 0.3 achieved using the conventional shape-based variables, while maintaining their demonstrated real-world reproducibility. Such a hemodynamically-inspired approach to the definition of geometric variables may reap benefits for other applications where geometry is used as a surrogate marker of local hemodynamics.

Figure 1

Elements in the definition of geometric variables, as described in the Methods. In panels A and B, planes normal to the centerlines are used to define the original area ratio (AR1) and redefined flare (FlareA) variables. In panel B, the thin solid line is the average of the (dotted) ICA and ECA centerlines; the thicker (red) dashed lines identify the major axes used to compute FlareM, and the distance between planes for compute FlareR. In panel C, the thick (red) solid line identifies the centerline segment used to compute the original Tortuosity. In panel D, the pivot is identified as the point of maximum rate of change of the Frenet normals (vector direction), or equivalently the maximum torsion (vector colour). The thick (red) line identifies the centerline segment used as the basis for the redefined tortuosity, Tort3D. The projection of this centerline onto the best-fit plane is used to determine Tort2D or Curv2D.

Figure 2

Scatter plots illustrating the improved prediction of SA_rel using the original (AR1 and Tortuosity) vs. redefined (FlareA and Tort2D) geometric variables. The upper left of each plot shows the regression equation used to generate the predictions; the lower right shows the coefficient of determination (R² _adj) and standardized regression coefficients for the respective flare and tortuosity variables (β_F and β_T).

Figure 3

Distribution of disturbed flow for a representative case. Yellow highlights regions exposed to low WSS or high OSI beyond the respective the 80^th percentile value; red narrows this area to the 90^th percentile value. Dark grey identifies the surface area used to normalize the SA exposed to disturbed flow. Panel C isolates the disturbed flow and normalizing surface area to the outer wall of the CCA-ICA tract, as described in the Discussion.