Non-invasive Stenotic Renal Artery Haemodynamics by in silico Medicine

Abstract

Background: Measuring the extent to which renal artery stenosis (RAS) alters renal haemodynamics may permit precision medicine by physiologically guided revascularization. This currently requires invasive intra-arterial pressure measurement with associated risks and is rarely performed. The present proof-of-concept study investigates an in silico approach that uses computational fluid dynamic (CFD) modeling to non-invasively estimate renal artery haemodynamics from routine anatomical computed tomography (CT) imaging of RAS. Methods: We evaluated 10 patients with RAS by CT angiography. Intra-arterial renal haemodynamics were invasively measured by a transducing catheter under resting and hyperaemic conditions, calculating the translesional ratio of distal to proximal pressure (Pd/Pa). The diagnostic and quantitative accuracy of the CFD-derived virtual Pd/Pa ratio (vPd/Pa) was evaluated against the invasively measured Pd/Pa ratio (mPd/Pa). Results: Hyperaemic haemodynamics was infeasible and CT angiography in 4 patients had insufficient image resolution. Resting flow data is thus reported for 7 stenosed arteries from 6 patients (one patient had bilateral RAS). The comparison showed a mean difference of 0.015 (95% confidence intervals of ± 0.08), mean absolute error of 0.064, and a Pearson correlation coefficient of 0.6, with diagnostic accuracy for a physiologically significant Pd/Pa of ≤ 0.9 at 86%. Conclusion: We describe the first in silico estimation of renal artery haemodynamics from CT angiography in patients with RAS, showing it is feasible and diagnostically accurate. This provides a methodological framework for larger prospective studies to ultimately develop non-invasive precision medicine approaches for studies and interventions of RAS and resistant hypertension.

Keywords: cardiovascular modeling; computational fluid dynamics; fractional flow reserve; in silico medicine; non-invasive diagnosis; precision medicine; renal artery haemodynamics.

FIGURE 1

Example of patient-specific CT images. Example CT images of each anatomical orientation for Patient 2: axial (i), coronal (ii), and sagittal (iii). The arrows in the axial and coronal slices, and the box in the sagittal slice indicate the approximate location of the renal stenosis for the specific case.

FIGURE 2

Typical volume mesh for the CFD simulations: (i) the mesh elements on the wall and on the inlet cross-section, and (ii) the tetrahedral elements inside the volume and the prismatic layers near the wall on a cut plane can be observed.

FIGURE 3

Boundary flow conditions for the set of simulations. The image summarizes the boundary flow conditions applied on the computational simulations: (1) for the comparative study between including and excluding the aortic segment (top row) and (2) for testing the accuracy of the workflow (bottom row) across the patient data set. The case of Patient 7 is used here for illustration purposes.

FIGURE 4

Downstream and upstream pressure monitoring cross-sections.

FIGURE 5

Resulting segmented patient renal geometries. Segmented volumes of renal arteries: unsuccessful segmentation examples based on the provided CT images are indicated by a red frame. The number for each image corresponds to patient number in Table 1.

FIGURE 6

Measured versus virtual Pd/Pa.

FIGURE 7

Bland Altman plot. The solid line represents the mean value of the difference between mPd/Pa and vPd/Pa, and the dotted lines create boundaries for ± 2 standard deviations from the mean difference. Each dot represents a stenosis and combines the knowledge for the difference and the mean value between the measured and the virtual calculations.

FIGURE 8

Correlation between mPd/Pa and vPd/Pa. The diagram plots mPd/Pa against vPd/Pa for each stenosis, where the segmented line in gray represents the points of exact agreement between measured and virtual calculations, while the solid line represent the data trendline of best-fit.

FIGURE 9

Velocity Vectors including and excluding the aorta. The figure shows the velocity vectors on a cross-sectional area of the renal artery close to the aorta for the simulation (i) that does not include the aortic geometry, and (ii) that does.

FIGURE 10

Examples from the CFD analysis. Pressure distributions (top row) and velocity streamlines (bottom row) are presented for the stenoses of three patients: 6 (left column), 7 (middle column), 10 (Right RAS, right column).