Wall shear stress quantification from magnetic resonance imaging data using Lagrangian interpolation functions

摘要

Hemodynamic factors are hypothesized to be important in the maladaptive responses of vessels leading to arterial disease. There is evidence that wall shear stress conditions, including mean, peak, and oscillations of shear stress are the most consequential hemodynamic factors in the localization and progression of atherosclerotic lesions in mammalian arteries [1,2]. Considering the strong correlation between the localization of atherosclerosis and arterial wall shear stress, quantifying in vivo wall shear stress is important in understanding the development of arterial disease. For a Newtonian fluid, shear stresses can be computed from the gradient of velocity field distributions and the blood viscosity. Velocity can be measured in vivo non-invasively with Magnetic Resonance (MR). MR techniques offer several advantages over other modalities, including the quality of resolution and contrast, the fact that anatomic and velocity images can be acquired concurrently, and that these anatomic and velocity maps are coregistered. Polynomial curves and 3D paraboloids have been used to approximate velocity profiles and compute spatial velocity gradients, however, these methods rely on certain geometric assumptions [3,4]. We propose a new method to calculate wall shear stress using a level set method to segment the vessel lumen, and piecewise cubic Lagrangian basis functions defined on a band of elements that include the vessel boundary. With this method, we can temporally and spatially resolve variations in wall shear stress while requiring no assumptions in regards to lumen shape or cross-sectional velocity profile.