Image-based Modeling and Clinical Applications

 Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive  networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.

Patient-specific cerebral vascular models with realistic morphological characteristics constructed from non-invasively acquired MRI data using growth based optimization were shown to predict perfusion territories of healthy and stroke patients realistically.

Computational Fluid Dynamics

Abdominal aortic aneurysm can exhibit transitional flow characteristics in laminar flow regimes. To report transitional flow characteristics, we examined the convergence of phase-averaged solutions by executing blood flow simulations of a patient-specific abdominal aortic aneurysmal model for 257 cardiac cycles with periodic, pulsatile boundary conditions. The phase-averaged solutions were computed by averaging the solutions over various numbers of cardiac cycles and compared against the ones averaged over 124 cycles. The phase-averaged solutions reported small differences when they were averaged over a large number of cardiac cycles. The instantaneous solutions, however, failed to exhibit fluctuations reported in the phase-averaged solutions. To study transitional blood flows in the aneurysmal region we need to report phase-averaged solutions as they exhibit non-periodic, disturbed flow characteristics. Additionally, when reporting phase-averaged solutions it is preferred to compute an average over a large number of cardiac cycles to be able to represent flow structures of the converged phase-averaged solutions.

Cardiovascular Biomechanics

Computational Methods

Computational fluid dynamic methods are currently being used clinically to simulate blood flow and pressure and predict the functional significance of atherosclerotic lesions in patient-specific models of the coronary arteries extracted from noninvasive coronary computed tomography angiography data. One such technology, or noninvasive fractional flow reserve derived from CT data, has demonstrated high diagnostic accuracy as compared to invasively measured fractional flow reserve (FFR) obtained with a pressure wire inserted in the coronary arteries during diagnostic cardiac catheterization. However, uncertainties in modeling as well as measurement results in differences between these predicted and measured hemodynamic indices. Uncertainty in modeling can manifest in two forms – anatomic uncertainty resulting in error of the reconstructed 3D model and physiologic uncertainty resulting in errors in boundary conditions or blood viscosity. We present a data-driven framework for modeling these uncertainties and study their impact on blood flow simulations. The incompressible Navier–Stokes equations are used to model blood flow and an adaptive stochastic collocation method is used to model uncertainty propagation in the Navier–Stokes equations. We perform uncertainty quantification in two geometries, an idealized stenosis model and a patient specific model. We show that uncertainty in minimum lumen diameter (MLD) has the largest impact on hemodynamic simulations, followed by boundary resistance, viscosity and lesion length. We show that near the diagnostic cutoff, the uncertainty due to the latter three variables are lower than measurement uncertainty, while the uncertainty due to MLD is only slightly higher than measurement uncertainty. We also show that uncertainties are not additive but only slightly higher than the highest single parameter uncertainty. The method presented here can be used to output interval estimates of hemodynamic indices and visualize patient-specific maps of sensitivities.

Research Projects

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