Surgical Simulations Involving Elastic Cardiac Geometries

A Novel Framework for Fluid/Structure Interaction in Subject-Specific Surgical Simulations Involving Elastic Cardiac Geometries

One of the most important applications of computational fluid dynamics has been simulation of blood flow. However, practical difficulties have limited the types and applicability of simulations performed, thus preventing numerical modeling of blood flow from reaching its full potential. Extreme computational expense, reduced order of accuracy due to complex geometry and lack of regularity in solutions have restricted the scale and scope of blood flow simulations. One exciting application currently outside the scope of existing methods is the simulation of surgeries designed to repair diseased and malfunctioning heart valves. The complexity of the valvular geometry and flow patterns in their vicinity complicate considerably the development of reliable and predicative numerical models.

The ability to deliver patient specific prognoses demands an algorithm that can accurately resolve these flows. However, cardiac geometry is highly complicated and must be represented with both volumetric and membraneous components, either of which might also exhibit intricate irregularities due to the patient's valvular disease. The solid/fluid coupling algorithm must have sufficient geometric flexibility to resolve these features and to adapt to the changes induced by the virtual surgery. Ultimately, to provide meaningful results the solid/fluid algorithm must deliver a certain level of accuracy and stability without sacrificing adaptability. Existing methods for fluid-solid interaction cannot guarantee this level of functionality. The general case sees geometric flexibility traded for higher order accuracy. Also, practical demands create the need for stable algorithms with minimal time step restrictions as the desire to accurately predict postoperative behavior comes with the inherent need to run simulations over longer time intervals.

The challenging nature of providing the functionality needed for effectively simulating valvular surgeries requires addressing all these issues simultaneously and existing methods cannot do this. The primary contribution of the proposed research will be the development and application of a tractable second-order numerical method capable of coupling a viscous incompressible fluid with thin and volumetric geometrically complex elastic solids represented with Lagrangian meshes. The fluid will be modeled by a Cartesian Eulerian grid in which the solid representations are embedded to avoid the prohibitive cost of re-meshing the computational domain at each time-step in the simulation. Regular grids will be used wherever possible. Geometric flexibility and the ability to impose a variety of boundary conditions on arbitrary moving surfaces throughout the fluid domain are key to accomplishing the stated goals and will be a primary guide in developing the higher-order accurate Navier-Stokes solver.

The benefits of patient-specific computational fluid dynamics simulations of blood flow near healthy and diseased heart valves can potentially revolutionize the treatment of certain pathologies. Such functionality could allow the surgeon to design new procedures tailored to the individual, to determine whether or not surgery is needed by numerically predicting postoperative results and could even be used to train surgical residents in state-of-the-art techniques. This effort will focus on the development of a numerical method for examining blood flow through such surgically altered tissues in the challenging case of corrective valvular surgery. Specifically, we target improvements in treatment for Tetralogy of Fallot and mitral valve repair. Patients born with Tetralogy of Fallot require artificial replacement valves with inherently finite lifespan and accurate determination of the time to replace these valves to correct for pulmonary regurgitation is a matter of life and death. With procedures such as mitral valve repair, the difficult choice lies in determining exactly which type of correction best suits a particular individual. The determination of when to make these critical decisions and many related others could potentially be improved with the successful application of this effort.

Joseph Teran, Ph.D., Mathematics
Dan Levi, MD, Umair Yousufi, M.D., Pediatric Cardiology and Fellow
Brian Reemtsen, MD, Cardiothoracic Surgery
Gregory Carman, Ph.D, Mechanical & Aerospace Engineering