Overview of the ParFE Project

Marzio Sala

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Outline of the Presentation

ParFE is used to perform μ-FE (micro finite element) analysis of trabecular bones, aiming to improve the understanding of diseases like osteoporosis. First, the presentation explains what a trabecular bone is, then why osteoporosis is important, finally what can be done with μ-FE analysis of trabecular bones. A few details on the software components of ParFE are also presented.

Cortical vs. trabecular bone

• Trabecular bone is one of two main types of bone. Trabecular bone is spongy, and makes up the bulk of the interior of most bones, including the vertebrae, while cortical bone is dense and forms the surface of bones.

Osteoporosis

• A disease of bone in which the bone mineral density is reduced, bone microarchitecture is disrupted, and the amount and variety of non-collagenous proteins in bone is changed. Osteoporotic bones are more susceptible to fracture.


• Common osteoporotic fracture sites, the wrist, the hip and the spine, have a relatively high trabecular bone to cortical bone ratio. These areas rely on trabecular bone for strength. (Content of this page from Wikipedia.)

Osteoporosis (cont'd)

• Lifetime risk for osteoporotic fractures in women is estimated close to 40%; in men risk is 13%
• Enormous impact on individual, society and health care social systems (as health care problem second only to cardiovascular diseases)
• For the clinician, the prediction of bone quality for individual patients is, so far, more or less restricted to the quantitative analysis of bone density alone, although there is convincing evidence that bone microarchitecture plays a significant role as well.
• Since global parameters like bone density do not admit to predict the fracture risk, patients have to be treated in a more individual way

μ-FE analysis of bones

Ideal procedure:

1. patient performs CT scan of bone under analysis
2. filtering of CT scan output
3. generation of finite element mesh w/ boundary conditions
4. quick problem solution (e.g., on CRAY XT3)
5. analysis of results: von Mises stresses, strains, statistical analysis, etc.
6. doctor's diagnosis to patient

μ-FE analysis of bones (cont'd)

This requires:

1. high-resolution CT scan + filtering software
2. a mathematical model for modeling trabecular bones
3. a scalable, robust and reliable parallel solver
4. data mining techniques

μ-FE analysis of bones (cont'd)

• We focus on the finite element discretization using piecewise trilinear polynomials, integrated using quadrature formula, and boundary conditions on displacements.
• After discretization, we have to solve the system of linear equations A x = b where A is is large sparse, symmetric positive definite, and a preconditioner is needed.
• We use preconditioned conjugate gradient method with algebraic multigrid preconditioners (smoothed aggregation)

ParFE Software Components

• ParFE is a fully-parallel code, featuring:
  • parallel I/O using HDF5
  • load balance using ParMETIS and Epetra's Import/Export
  • domain decomposition techniques for matrix assembly and linear system solves
  • algebraic multigrid preconditioners
• Smoothed aggregation preconditioner not too sensitive to jumps in coefficients
• Problems with 200'000'000 matrix rows can be solved in less than 100 seconds on the Cray XT3
• matrix-free algebraic multigrid preconditioner enables up to 1'000'000 matrix rows per processor on 1024 processor CRAY XT3.