Bone structure analysis with GPGPU

The aging of the human population made the number of bone fractures due to osteoporosis increase considerably. In Switzerland, the risk for an osteoporotic fracture in women above 50 years is about 50%, for men the risk is about 20%1. Not surprisingly, research concerning osteoporosis plays a prominent role in health science. Often, large scale computer simulations are conducted to improve the understanding of the bone structure and bone strength [1]. These simulations are based on voxel models of the bone that are obtained by high-resolution CT scans. The voxel model constitutes a structure that is investigated for its elastic properties. The structures are composed by millions of tiny cubes (voxels), see the image on the left. Our simulations are based on finite element discretizations for linear or non-linear elasticity and lead to very large linear or non-linear systems of equations with hundreds of millions or even billions of unknowns [1–3, 7, 8]. The typically symmetric positive definite linear systems are solved by the preconditioned conjugate gradient algorithm on large parallel computers [4]. In recent years we have developed a computer program called ParFE that solves these problems very efficiently, in terms of computing time and in terms of memory space [2, 3, 6]. The program combines the conjugate gradient algorithm with a smoothed aggregation-based multilevel preconditioner. More recently, we have developed codes that are similarly fast as ParFE but much memory-efficient [7,8]. One of the approaches, that we called the full-space approach, is very well suited for general purpose graphics processing units (GPGPUs) [8]. In the full-space approach the void space between the bone is filled by a very soft material that does not affect (much) the elastic properties of the bone. Linear elasticity is then applied to the filled bone. The computational domain in this appraoch extends to a cuboid that encases the original bone.