Fast Finite Element Simulation Using GPGPU Technology in Soft Tissue Biomechanics

Finite element analysis (FEA) enjoys a variety of applications in the field of biomechanics, from simulated fatigue testing of an intramedullary rod to studying stresses in a displacement field generated within a single cell. The powerful generality of the finite element method implies that often no purpose-specific method or model need be developed to study a system, but regrettably also implies a certain computational cost. FEA-supported virtual reality surgical simulation, or intraoperative surgical simulation are examples of domains whose inherent requirement of (near-)real-time computation is directly contrasted by this fact. Similarly, other, research-oriented application areas such as optimization-driven material characterisation, rely on a large number of simulations. Here, reduced simulation time translates into more accurate characterisation or an expansion of the possible solution space. This thesis investigates the applicability of Graphics Processing Units (GPUs) to alleviate this computational burden, with particular focus on the biomechanics of soft tissues. The solution speed requirements motivate the selection of an appropriate FE formulation that maps well onto the fine-grained GPU parallel-processing paradigm. Initially, this thesis presents a custom GPU implementation of an explicit FE code solving the governing boundary value problem in nonlinear elasticity. The implementation is analyzed, and its advantages and limitations elucidated. Subsequently, a broad study using simple materials is conducted on a plethora of devices, examining the effect of several pertinent factors, such as mesh density or the use of single/double precision floating point computation on simulation times. Aggregate results reveal an encouraging 30-250x speedup against an industry established code. However, more complex, biofidelic, fiber-reinforced materials are needed. They are next included in this thesis, with a previously unreported implementation on GPUs. The use of these materials implies more complex Gaussian quadrature schemes, whose necessity heavily impacts GPU performance, more so than the added computation due to the inherent anisotropy alone. All factors related to fast simulation using these materials are elucidated in detail, including the scaling of the problem. Results reveal an approximate 10-35% slowdown duo to the fiber addition, in contrast to the 3-8x due to the nature of integration. Finally, an important test of clinical applicability is presented using five patient-specific simulations of an Abdominal Aortic Aneurysms (AAA). In this novel application it is found that the complex morphology-imposed aortic geometry, and the histology-imposed material model, severely impact the performance of the chosen method. Regardless, excellent overall speedup of 10-17x practically reduce solution times from approximately two days to two hours. Without recourse to simplifying assumptions and no accuracy loss, this is regarded as a significant result and further affirms the approach presented in this thesis. Altogether, this thesis presents engineering contributions to fast FEA computation directly applicable in several areas of biomechanics, particularly in surgical training, intraoperative mitigation of critical events and research applications. While doing so, the thesis objectively demonstrates the opportunities, challenges and limitations of the use of general purpose GPU technology in this context.status: publishe