Indiana University-Purdue University Indianapolis (IUPUI) / The interplay between biomechanics and blood perfusion in the optic nerve head (ONH) has a critical role in ocular pathologies, especially glaucomatous optic neuropathy. Elucidating the complex interactions of ONH perfusion and tissue structure in health and disease using current imaging methodologies is difficult, and mathematical modeling provides an approach to address these limitations. The biophysical phenomena governing the ONH physiology occur at different scales in time and space and porous media theory provides an ideal framework to model them. We critically review fundamentals of porous media theory, paying particular attention to the assumptions leading to a continuum biphasic model for the phenomenological description of fluid flow through biological tissues exhibiting viscoelastic behavior. The resulting system of equations is solved via a numerical method based on a novel hybridizable discontinuous Galerkin finite element discretization that allows accurate approximations of stresses and discharge velocities, in addition to solid displacement and fluid pressure. The model is used to theoretically investigate the influence of tissue viscoelasticity on the blood perfusion of the lamina cribrosa in the ONH. Our results suggest that changes in viscoelastic properties of the lamina may compromise tissue perfusion in response to sudden variations of intraocular pressure, possibly leading to optic disc hemorrhages.

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Heart disease is the main cause of death today, and studying causes and treatments are of great interest. Blood flow simulations using computational fluid dynamics shows promise in providing insight into this area. This study builds upon previous work by Larsson et al. and Kronborg et al. who have developed a program for simulating the blood flow through patient specific left ventricles. More specifically we aimed to improve the accuracy of their blood flow simulation by accounting for the protruding structure of the endocardial wall, previously disregarded in the model due to the limitations in spacial accuracy of echocardiography. These structures, consisting of trabeculae carneae and papillary muscles, have been shown to have a significant impact on the blood flow. In a recent study, Sacco et al. proposed a solution were a porous layer could mimic the effects on the blood flow from these structures in a rigid heart model. Our study aimed to apply this modification to the left ventricle of the dynamic model using the Navier-Stokes-Brinkman flow equation and a subdomain defining the porous region. This study has been working towards the end goal of fully implementing the porous layer into the heart simulation. The equations needed have been formulated and simulations have been run on flow in a more simple setting to verify the model. The simulations show promise in being able to recreate the results from Sacco et al. but further development is needed before the porous model can be tested in the dynamic left ventricle model, most notably defining the porous subdomain in the dynamic model. We conclude that the porous domain will affect the flow, possibly breaking up vortices and reducing the wall shear stress. Confirming this requires additional studies, but the implementation of a porous domain would likely result in a more accurate simulation.

The goal of this project was to determine whether i) fused deposition modeling could be employed to manufacture molds for vascular constructs, ii) whether vascular constructs could be created from these molds, and iii) to verify practical equivalence between observed fluid velocities. Dye tracking was to be employed to characterize fluid velocity profiles through the in vitro vascular constructs, including a half-vessel model and a full vessel model of an iliac artery aneurysm. A PDMS half-vessel construct was manufactured, and the movement of dye through the construct was tracked by a cellphone camera. Thresholds were applied to each video in HSB or YUV mode in ImageJ, and analyzed to determine the velocity of the fluid through the construct. COMSOL simulations of the half-vessel were conducted for comparison to the empirical observations. Plots describing the flow velocities along the maximum streamline path length were generated, and a one sample t-test was conducted at a 5% significance level to determine whether there was a significant difference between velocity values obtained by dye tracking and the COMSOL simulations. It was determined that the empirical dye tracking trials failed to demonstrate agreement between the measured and predicted flow rates. A full vessel construct was not completed due to unforeseen time constraints. Dye tracking was not determined to be reliable as a means of measuring the maximum velocity of fluid. Discrepancies between the empirical observations and the COMSOL simulation are discussed. The discrepancy was attributed to limitations in the experimental protocol; low frame rate, poor control over lighting conditions, and the subjectivity involved in image processing. Methods of improving upon the manufacturing and experimental protocols used for the half-vessel are proposed for future work, such as improving control over lighting conditions, choosing a camera with a higher frame rate, constructing a more stable fixture, exploring PIV. Additionally, the technical problems leading to the failure to complete the full vessel model are discussed, and changes in the manufacturing process are proposed to allow dissolution or removal of the aneurysm model.

With the high mortality rate of cardiovascular disease, it is important to study the early signs. The early detection of cardiovascular disease can lead to saved lives. Currently the most prevalent detection methods are the Framingham Risk Score and the carotid intima media thickness, both of which are insufficient. The necessary tool for early detection requires a uniform quantification system. The stimulus leading to endothelial dysfunction, the most significant predictor of a major adverse cardiovascular event (MACE)—and subsequently subclinical atherosclerosis—is reduced shear stress. Increased surface relative roughness affects the flow profile transition from laminar to turbulent resulting in reduced shear rate. The relationship between the shear stress and the relative roughness was studied using a computer model for fluid flow. A model of the brachial artery was generated to study its hemodynamics. Roughness values for both laminar and turbulent flow were calculated to use with the governing equations programmed in COMSOL Multiphysics. With all other factors remaining constant in the model, the roughness values were changed. From the model profile plots, line graphs, and numeral data are generated. This data provides information about how the shear stress and the shear rate change with respect to the relative roughness value. The models with different wall boundary conditions—slip versus Navier slip—were unable to be directly compared due to the differences in value magnitude. When the flow profile transitions from laminar to turbulent, there is a corresponding drop in both the shear stress and the shear rate values. Additional testing is required to determine a critical relative roughness value for this change in cumulative shear.

This project offers a multidisciplinary approach towards the acquisition, analysis and visualization of experimental data that pertain to cardiovascular applications. First and foremost, the capabilities of our Time-Resolved Digital Particle Image Velocimetry (TRDPIV) system were improved, allowing near-wall wall TRDPIV on compliant, dynamically moving boundaries. As a result, false flow-field vectors due to reflections from the boundary walls were eliminated, and allowing measurement of wall shear stress, wall shear rate, and oscillating shear index within as little as fifty microns of the boundary. Similar in-vitro measurements have not been reported to date by any other group. Second, an immersive, virtual environment (VE) was developed for the investigation and analysis of vortical, spatio-temporally developing flows with complex fluid-structure interactions. This VE was used to study flows in the cardiovascular system, particularly for flow through mechanical heart valves and inside the heart left ventricle (LV). The simulation provides three-dimensional (3-D) visualization of in-vitro heart flow mechanics, allowing global, volumetric flow analysis, and a useful environment for comparison with in-vivo MRI velocimetry data. 3-D glyphs (symbols representing informational parameters) are used to visually represent the flow parameters in the form of an ellipse attached to a cone, where the ellipse represents a second-order Reynolds stress tensor, and the cone represents the velocity magnitude and direction at a particular point in space, and the color corresponds to an out-of-plane vorticity. This new system has a major advantage over conventional 2-D systems in that it successfully doubles the number of visualized parameters, and allows for visualization of a time-dependent series of flow data in the Virginia Tech CAVETM immersive VE. The user controls his/her viewpoint, and can thus navigate through the simulation and view the flow field from any perspective in the immersive VE. Finally, an edge detection algorithm was developed to determine the inner and outer myocardial boundaries, and from this information calculate the local thickness distribution of the myocardium and a myocardial area approximation. This information is important in validating our in-vitro system, and is integral to the evaluation and diagnosis of congestive heart disease and its progression. / Master of Science

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