Fluid–Structure Interaction Simulation of Cardiac Leads in the Heart: Developing a Computational Model for Use in Medical Device Design1

Structural and fluid mechanics simulations have been developed for a wide range of applications, including bone mechanics and blood flow through arteries and veins. As these models improve, the next step is to couple fluid and structural simulations for a solution that can better capture the overall dynamics of a system [1]. The resulting fluid–structure interaction (FSI) problems require simultaneously solving the governing equations of fluid and solid mechanics, which can be accomplished via several approaches [2,3].This paper reports on the current progress and lessons learned by our interdisciplinary team, which is creating an “as accurate as possible” FSI model for simulating the dynamics of the right atrium (RA) of a real heart, with and without an implanted pacemaker wire. The RA structure is one of the preferred pathways for inserting pacemakers in the right ventricle. Although cardiac pacemakers have been employed for years, several open questions remain regarding the ideal design for these medical devices. For example, little is currently known about how exactly cardiac leads impact blood flow and stagnation inside the heart chambers, an issue often complicated by calcification. A stable and robust coupling of both flow and structure dynamics requires great care because the heart wall deforms rapidly in response to changing pressure and velocity fields in the heart [2–4].The model-development project described here fits into a larger program of research on virtual prototyping of medical devices by coupling supercomputer-based simulation with interactive visual design tools [5]. Our goal in this work is, therefore, to develop a computational model that fits appropriately into a simulation-based design workflow. With a robust computational model in hand, different parameters (e.g., lead wire geometry and mechanical properties) and scenarios (e.g., patient-specific anatomy) can be explored and visualized using innovative interactive design tools (e.g., see Ref. [6]).Our current model is implemented in abaqus and couples a solid and fluid solver along a prescribed surface. abaqus solvers were chosen to simulate all the FSI in this project. With the introduction of abaqus/cfd in version 6.10, the software provides advanced computational fluid dynamics (CFD) capabilities that address a broad range of nonlinear coupled fluid–structural problems in an integrated environment with support for preprocessing and postprocessing provided through abaqus/cae.A complete CT scan of a human heart obtained from the medical imaging was segmented into heart chambers. Only the RA was considered in this study.During the preprocessing phase, a series of geometry refinements and simplifications were performed. The original outer shape of the model was smoothed using a Lagrangian algorithm. Furthermore, the coronary sinus vein was removed, and the inlet was replaced by continuous solid elements. The heart wall, which is not perfectly regular in thickness, was replaced by a layer of shell elements of fixed thickness 2 mm.The tricuspid valve (TV) is not included in the model; its workings were simulated by the use of a pressure boundary condition.In our first model (without a lead), the interior of the RA is meshed with 663,264 tetrahedral elements for fluid analysis (FC3D4), and the solid heart wall is meshed with 35,974 shell elements (S3). The contacting surfaces are defined as the FSI boundary.Our second model includes a cardiac lead defined as a 1.4 mm isotropic, uniform wire, entering the RA through the superior venae cavae (SVC) and exiting through the TV. The geometry of the lead is a cubic spline, and the solid model used for the wire is also linearly elastic. In this case, the mesh of the fluid volume consists of 598,556 elements, while the heart wall and the pacemaker lead include 84,498 elements (S3 shell elements for the heart wall and C3D4 solid elements for the lead).For both of the resulting heart models, simulations were run over one heartbeat, estimated to last approximately 0.8 s for the average person. Mechanical properties of the materials (Table 1) are based upon recent studies [7,8].The inlet blood velocities at the superior and inferior venae cavae were adapted from the literature, as was the pressure profile at the TV outlet [2,7]. The inner surface of the heart wall was defined as the CFD–solid interaction surface.Four categories of simulations were performed: CFD-only simulations with and without a pacemaker lead, and FSI simulations with and without the lead. All the simulations were performed using a fully dynamic, implicit solver.Both the FSI and CFD-only simulation results are in agreement with physically observed values and phenomena. We achieved a computational stable solution for three of the four categories that converge. The FSI case with the pacemaker lead correctly mimics the desired behavior (e.g., correct displacement of the heart wall and reasonably accurate velocity field); however, it is sensitive to the selection of the mechanical properties of the lead wire (young modulus, Poisson's ratio, and density). The exact validation of the FSI for this case is still a work in progress. However, the model follows the expected physical behavior, and the velocities and pressures obtained are within the expected values. Figure 1 shows the successive plots of von Mises stress and the overall deformed shape of the RA throughout one cardiac cycle. The simulated behavior is in accordance with an initial relaxed state and the filling–filling–contraction–relaxation and refilling cycle, typical of the RA.It is important to note that this behavior cannot be obtained through CFD-only simulations, although they have significantly better and faster convergence, as expected. Figure 2(a) shows a sample fluid velocity data frame obtained from an FSI simulation. Vortical structures are observed forming and dissipating throughout the cycle, with one dominant vortex approximately in the center of the atrium and a secondary vortex forming near to the TV.Figure 2(b) shows the von Mises stress on a section of a simulated lead wire during the heart cycle. Here, it can be observed that the dominant deformation of the pacemaker lead is pure bending.This study demonstrates that a high-complexity coupled FSI model of a cardiac cycle is numerically stable under a reasonably wide array of conditions. The simulation converged successfully. It showed the gradual propagation of the two pressure waves (one at each outlet) and the vortex structures formed by their interaction. This corresponded well with the expected physical behavior seen in the in vivo experimental and numerical studies of cardiac flow in the RA [9]. Furthermore, it has been shown that the results of this model are within the expected physical parameters and that it is feasible to obtain the stress state of biomedical devices implanted in the patient heart. We believe these results can ultimately enable significant improvements in fatigue and fracture mechanics based design.With the increased use of computational modeling in the design of biomedical devices, we believe the present work offers a great prospect of expanding cardiac FSI simulations to patient-specific geometries and physical conditions, thus allowing physicians and biomedical device engineers an opportunity to precompute a wide array of hypothetical patient-specific cases for various types, placement, geometry, and properties of medical devices [5].The authors graciously acknowledge the support of Dr. Paul Iaizzo and the Visible Heart Lab for providing anatomical data for the models. This research was funded in part by NIH Grant No. R01 EB018205 and NSF Grant No. IIS-1251069.