High performance multi-platform computing for large-scale image-based finite element modeling of bone

Background: Image-based finite element (FE) modeling of bone is a non-invasive method to estimate bone stiffness and strength. High-resolution imaging data as input allows for inclusion of bone microarchitecture but results in large amounts of data unsuitable for traditional FE solvers. Bone-specific mesh-free solvers have been developed over the past 20 years to improve on memory efficiency in simulated bone loading applications. The objective of this study was to provide linear performance benchmarking for a bone-specific, mesh-free solver (FAIM) using µCT and HR-pQCT image data on Mac, Linux, and Windows operating systems using both single- and multi-thread CPU and GPU processing.

Methods: The focus is on the linear gradient-descent solver using standardized uniaxial loading of bone models from µCT, and first- and second-generation HR-pQCT scans of the radius and tibia. Convergence, speedup, memory, and batch performance tests were completed using CPUs and GPUs on three laboratory-based systems with Windows, Linux, and Mac operating systems.

Results: Although varying by system and model size, time-per-iteration was as low as 0.03 s when an HR-pQCT-based radius model (6.45 million DOF) was solved with 3 GPUs. Strong scaling was achieved with GPU and CPU parallel processing, with strong parallel efficiencies when models were solved using 3 GPUs or ≤ 10 CPU threads. Errors in force, strain energy density, and Von Mises stress were as low as 0.1% when a convergence tolerance of 10^-3 or smaller was used.

Conclusion: The results of this study indicate that to maximize computational efficiency and minimize model solution times using FAIM software under the standardized tested conditions using µCT, XCT1 and XCT2 HR-pQCT image data, convergence tolerance set to 10^-4, and 10 threads or 2 GPUs are sufficient for efficient solution times. Less strict convergence tolerances will improve solution times but will introduce more error in the outcome measures.