Patient-specific computational modeling of blood flow in the pulmonary arterial circulation

Abstract

Computational fluid dynamics (CFD) modeling of the pulmonary vasculature has the potential to reveal continuum metrics associated with the hemodynamic stress acting on the vascular endothelium. It is widely accepted that the endothelium responds to flow-induced stress by releasing vasoactive substances that can dilate and constrict blood vessels locally. The objectives of this study are to examine the extent of patient specificity required to obtain a significant association of CFD output metrics and clinical measures in models of the pulmonary arterial circulation, and to evaluate the potential correlation of wall shear stress (WSS) with established metrics indicative of right ventricular (RV) afterload in pulmonary hypertension (PH). Right Heart Catheterization (RHC) hemodynamic data and contrast-enhanced computed tomography (CT) imaging were retrospectively acquired for 10 PH patients and processed to simulate blood flow in the pulmonary arteries. While conducting CFD modeling of the reconstructed patient-specific vasculatures, we experimented with three different outflow boundary conditions to investigate the potential for using computationally derived spatially averaged wall shear stress (SAWSS) as a metric of RV afterload. SAWSS was correlated with both pulmonary vascular resistance (PVR) (R(2)=0.77, P<0.05) and arterial compliance (C) (R(2)=0.63, P<0.05), but the extent of the correlation was affected by the degree of patient specificity incorporated in the fluid flow boundary conditions. We found that decreasing the distal PVR alters the flow distribution and changes the local velocity profile in the distal vessels, thereby increasing the local WSS. Nevertheless, implementing generic outflow boundary conditions still resulted in statistically significant SAWSS correlations with respect to both metrics of RV afterload, suggesting that the CFD model could be executed without the need for complex outflow boundary conditions that require invasively obtained patient-specific data. A preliminary study investigating the relationship between outlet diameter and flow distribution in the pulmonary tree offers a potential computationally inexpensive alternative to pressure based outflow boundary conditions.

Keywords: Boundary conditions; Computational fluid dynamics; Hemodynamics; Pulmonary hypertension; Pulmonary vascular resistance; Vessel diameter.

Figure 1

Protocol for conducting patient-specific CFD analysis. CFD analysis is performed on the patient-specific vasculature reconstructed from CT scans yielding velocity (Vx, Vy, Vz, in the x, y, z directions, respectively) and pressure throughout the computational domain. In the Pre-Processing step, each outlet is extended by ten diameters and a volumetric non-uniform grid is generated during the meshing step.

Figure 2

WSS grid independence study results for an exemplary reconstructed pulmonary vasculature.

Figure 3

Structured tree outflow boundary condition: (a) a patient-specific model's unique α and β are determined to reconstruct the entire pulmonary vasculature equivalent to the RHC-measured PVR; (b) schematic of structured tree outflow boundary condition applied to three outlets of the computational domain. Reproduced with permission from [31].

Figure 4

Schematic showing how the structured tree outflow boundary condition computes a patient-specific function that relates outlet radius to the outflow resistance at that radius (example shown using α = β = 0.67).

Figure 5

Linear regression correlations of mPAP with PVR (a) and Compliance (b). PVR calculated from Eq. (1) revealed a linear correlation with mPAP of R² = 0.53. Compliance calculated from Eq. (2) reveled a linear correlation with mPAP of R² = 0.80. The two-tailed probability of all given correlations are below 0.05 (P < 0.05).

Figure 6

Exemplary CFD results, illustrating a WSS map for a patient-specific geometry simulated with a structured tree outflow boundary condition and patient-specific CO. Note: WSS is bounded at 50 dyn/cm².

Figure 7

Correlation of SAWSS with PVR and Compliance: (a) correlation when using patient-specific inlet CO and structured tree calculated from RHC-measured PVR; (b) correlation when using patient-specific inlet CO and zero-traction outflow BC; (c) correlation when using an inlet CO = 90 cm³/s and zero-traction outflow boundary condition. Note: Patient-specific HR was measured during CT scan.

Figure 7

Correlation of SAWSS with PVR and Compliance: (a) correlation when using patient-specific inlet CO and structured tree calculated from RHC-measured PVR; (b) correlation when using patient-specific inlet CO and zero-traction outflow BC; (c) correlation when using an inlet CO = 90 cm³/s and zero-traction outflow boundary condition. Note: Patient-specific HR was measured during CT scan.

Figure 8

Computational evidence of a flattened velocity profile in the proximal and distal vessels of the pulmonary vasculature with elevated PVR. The simulations were carried out using a structured tree outflow boundary condition on the geometry shown in (a). Local WSS is largely dependent on the gradient of the velocity profile (∂u/∂z) shown in (b). (c-e) show that the velocity profile is flattened for a larger PVR (lower curves) in the proximal and distal vessels.

Figure 9

Outlet volumetric flow rate (Q) vs. hydraulic diameter (D_h) for simulations conducted with (a) a healthy patient-specific vasculature (anterior and posterior views) for a Poiseuille inlet velocity profile corresponding to a constant flow rate of 95 cm³/s and three outflow boundary conditions: (b) zero traction; (c) a constant 40 dyn·s/cm² resistance at all outlets; and (d) a structured tree. The Q vs. D_h relationship from the structured tree model is shown fitted to both power and linear regression curves. This patient-specific model consisted of 274 outflow boundary surfaces.

Figure 9

Outlet volumetric flow rate (Q) vs. hydraulic diameter (D_h) for simulations conducted with (a) a healthy patient-specific vasculature (anterior and posterior views) for a Poiseuille inlet velocity profile corresponding to a constant flow rate of 95 cm³/s and three outflow boundary conditions: (b) zero traction; (c) a constant 40 dyn·s/cm² resistance at all outlets; and (d) a structured tree. The Q vs. D_h relationship from the structured tree model is shown fitted to both power and linear regression curves. This patient-specific model consisted of 274 outflow boundary surfaces.