A Novel Method for Improving the Accuracy of MR-derived Patient-specific Vascular Models using X-ray Angiography

Abstract

MR imaging, a noninvasive radiation-free imaging modality commonly used during clinical follow up, has been widely utilized to reconstruct realistic 3D vascular models for patient-specific analysis. In recent work, we used patient-specific hemodynamic analysis of the circle of Willis to noninvasively assess stroke risk in pediatric Moyamoya disease (MMD)-a progressive steno-occlusive cerebrovascular disorder that leads to recurrent stroke. The objective was to identify vascular regions with critically high wall shear rate (WSR) that signifies elevated stroke risk. However, sources of error such as insufficient resolution of MR images can negatively impact vascular model accuracy, especially in areas of severe pathological narrowing, and thus diminish clinical relevance of simulation results, as local hemodynamics are sensitive to vessel geometry. To improve the accuracy of MR-derived vascular models, we have developed a novel method for adjusting model vessel geometry utilizing 2D X-ray angiography (XA), which is considered the gold standard for clinically assessing vessel caliber. In this workflow, "virtual angiographies" (VAs) of 3D MR-derived vascular models are conducted, producing 2D projections that are compared with corresponding XA images to guide the local adjustment of modeled vessels. This VA-comparison-adjustment loop is iterated until the two agree, as confirmed by an expert neuroradiologist. Using this method, we generated models of the circle of Willis of two patients with a history of unilateral stroke. Blood flow simulations were performed using a Navier-Stokes solver within an isogeometric analysis framework, and WSR distributions were quantified. Results for one patient show as much as 45% underestimation of local WSR in the stenotic left anterior cerebral artery (LACA), and up to a 56% underestimation in the right anterior cerebral artery when using the initial MR-derived model compared to the XA-adjusted model. To evaluate whether XA-based adjustment improves model accuracy, vessel cross-sectional areas of the pre- and post-adjustment models were compared to those seen in 3D CTA images of the same patient. CTA has superior resolution and signal-to-noise ratio compared to MR imaging but is not commonly used in the clinic due to radiation exposure concerns, especially in pediatric patients. While the vessels in the initial model had normalized root mean squared deviations (NRMSDs) ranging from 26% to 182% and 31% to 69% in two patients with respect to CTA, the adjusted vessel NRMSDs were comparatively smaller (32% to 53% and 11% to 42%). In the mildly stenotic LACA of patient 1, the NRMSDs for the pre- and post-adjusted models were 49% and 32%, respectively. These findings suggest that our XA-based adjustment method can considerably improve the accuracy of vascular models, and thus, stroke-risk prediction. An accurate, individualized assessment of stroke risk would be of substantial help in guiding the timing of preventive surgical interventions in pediatric MMD patients.

Keywords: Computer-aided-design; Image-based modeling; Segmentation; Stroke; Wall shear rate.

Fig. 1

Graphical flow chart showing processes for model creation and XA-based adjustment. (A) An initial model is created by segmenting an MR TOF image stack. (B) Model centerlines are used to align the model relative to a virtual x-ray source and detector mimicking clinical XA image acquisition. (C) A virtual angiogram is computed of the model and (D) compared to the corresponding clinical XA image. If the virtual angiogram of the model and the clinical angiogram differ, the model is locally adjusted (E), and a new virtual angiogram is computed. The adjust-virtual angiography-compare steps (C-D-E) are iteratively repeated until there is good agreement between the two angiograms. (F) Comparison of final adjusted model to initial model.

Fig. 2

The vascular modeling pipeline. The Circle of Willis vasculature is segmented from MR TOF images (A) as a triangulated surface mesh (B) using 3D Slicer. 2D projections of the segmented mesh are registered to (C) XA images. The vessel diameters along the mesh are locally adjusted to match XA images. (D) shows the adjustments made across the entire mesh. Adjustments made along the LACA are highlighted in the insets. The adjusted surface mesh is used to generate the NURBS mesh (E). Each vessel corresponds to a volumetric NURBS patch. The insets show the NURBS patch, control net, and a cross section for the RACA.

Fig. 3

A volumetric NURBS mesh of the CoW (A) is generated from the adjusted CoW surface mesh. A close-up of a bifurcation (B) is shown to highlight the mesh quality and refinement used in the computation. The cross-section of the NURBS mesh (C) is shown to highlight the boundary layer refinement (D) used in the simulation. The equations and boundary conditions for the blood-flow simulation is presented, where u represents velocity, p is pressure, f is the external force, μ is dynamic viscosity, ρ is density, t is time, and n is the unit normal. A pulsatile inflow condition[21] is prescribed at the three inlets. The inflow at the two ICAs and BA are given by the red and blue waveforms respectively. A no-slip boundary condition is imposed along the vessel walls, and a traction-free boundary condition is applied at each outlet.

Fig. 4

Overview of XA-adjustment verification strategy. (A) Several planes (yellow) along the length of a vessel of the 3D model (RMCA of the initial patient 1 model shown), perpendicular to its centerline, are used to extract vessel cross sections (red curves). (B) An example CTA slice corresponding to one of the perpendicular planes in (A). The cross section of the model superimposed on the CTA slice is shown by the red curve. Determination of the vessel lumen boundary on the CTA slice (blue curve) is guided by assessment of lumen extent provided by a trained neuroradiologist (green dots). (C) Cross-sectional areas of the model vessel and CTA vessel are computed in each slice and plotted against the position along the vessel centerline. The top plot compares the initial model (red curve) to the CTA-extracted lumen area (blue curve) and the bottom plot compares the adjusted model (red curve) to the CTA images (blue curve). These curves are used to compute the RMSD for each vessel.

Fig. 5

Comparison of initial (blue) and XA-adjusted models (green) for patient 1 (top panels) and patient 2 (bottom panels) shown in posterior (left) and anterior views (right).

Fig. 6

Comparison of predicted WSR (above 5000 s⁻¹ coagulation limit) distributions for the initial (left panels) and XA-adjusted (right panels) models of patient 1 (top) and patient 2 (bottom).

Fig. 7

Comparison of NRMSD values for each vessel before (blue bars) and after XA-based adjustment (green bars) for (A) patient 1 and (B) patient 2.