Stresses in Carotid Plaques using MRI-based Fluid Structure Interaction Models

Stresses in Carotid Plaques using MRI-based Fluid Structure Interaction models

Samuel A. Kock¹, Ernst-Torben Fründ², Won Y. Kim^1,3 and Jens V. Nygaard⁴

¹MR-Center, Aarhus University Hospital, Denmark, ²Dept. of Biomechanical Engineering, Aarhus University Hospital, Denmark, ³Dept. of Cardiology, Aarhus University Hospital, Denmark, ⁴Interdisciplinary Nanoscience Center, Aarhus University, Denmark

Introduction

Atherosclerosis is the main cause of death and severe disability in the world (1). The disease generates fatty deposits inside vessel walls (lipid cores) covered by a protective fibrous cap – the atherosclerotic plaque. If the cap ruptures blood clots are formed which may be carried down-stream to lodge in small-diameter blood vessels. Disrupted blood flow results causing heart attacks or strokes. Currently the risk of cap rupture is assessed using the degree of luminal narrowing (2). This fails to take the morphology of the plaque into account. Indeed, unstable or vulnerable plaques are known to possess large lipid cores and thin fibrous caps (3). A morphology such as this generates severe internal stresses in the fibrous cap. In vitro studies have shown that cap rupture predominantly occur when static stresses exceed 300 kPa. The ability to estimate stress magnitudes in the fibrous cap is thus expected to improve risk assessment.

Methods

A patient with severe atherosclerosis was scanned using magnetic resonance imaging (MRI). The plaque was segmented into lipid core, fibrous cap, vessel wall, and blood stream and inflow velocities were measured. The splines surrounding the segmented components were imported into Matlab and collected into a single 3D matrix using interpolation and smoothing (figure 1). The 3D model was intersected using a non-uniform rational B-sline (NURBS) surface. The intersections between the iso-surfaces from the MRI-scans and the NURBS surface resulted in a 2D surface which was imported into COMSOL (figure 2). The blood-stream was simulated using the Navier-Stokes module (ρ=1050, ν=0.005) and a parabolic inflow with a maximal central velocity of 1.35 m/s. The pressure in the pressure outlets was set to 10666 Pa. The Neo-Hookean hyper-elastic model was used to specify the material properties (5) of surrounding tissue (µ=6.20e6, κ=1.24e8, ρ=960) and vessel wall (µ=7.20e5, κ=1.44e7, ρ=1200). Lipid was treated as an isotropic materiel (6) with Young’s modulus set to 1/100 of that of the equivalent Young’s modulus of the vessel wall (E=1e5, ν=0.45, ρ=900). To facilitate convergence, the fluid was simulated using artificial high viscosity and low velocity which were gradually changed to the correct values. An initial simulation employing the stationary linear solver SPOOLES was performed using adaptive mesh refinement which was switched to non-linear on attaining convergence. Subsequently the vessel wall, lipid pool, and surrounding tissue were added to the simulation using the Structural Mechanics Module. Pressure was used to couple the fluid to the structural components along the vessel-wall/blood-stream interface (one-way coupling).

Results

First principal stresses are depicted in figure 3. The soft lipid pool generated severe stresses (max. 350 kPa) in the overlaying fibrous cap, most prominent in the “shoulder region” i.e. the region of the fibrous cap adjacent to the vessel wall immediately below the large zone of recirculation overlying this area. A stagnation point is visible at the flow divider as well as a marked jet resulting from the severe luminal narrowing. The jet results in large areas of recirculating or slowly moving blood, which is a known progenitor of further plaque deposition.

Conclusion

The maximal stresses found in the fibrous cap exceed established criteria for caps at risk of rupture. Indeed, the patient exhibited symp-toms consistent with a stroke judged to be the result of a previous cap rupture. The fibrous cap was thus demonstrably vulnerable and our findings corroborated the clinical picture. The technique is therefore deemed feasible.