Highlights
- •Unified least-squares-based framework for fast “nodal” and “element” strategies of mapping scalar CT voxel densities onto finite element mesh.
- •Approximation of density by finite element method using least squares projection.
- •The discontinuous variant of the finite element method is more suitable for density approximation than the continuous variant in terms of accuracy and efficiency.
- •The discontinuous zero-order finite element method preserves the density spectrum better than the continuous one.
Abstract
Background
The spatially varying mechanical properties in finite element models of bone are most
often derived from bone density data obtained via quantitative computed tomography.
The key step is to accurately and efficiently map the density given in voxels to the
finite element mesh.
Methods
The density projection is first formulated in least-squares terms and then discretized
using a continuous and discontinuous variant of the finite element method. Both discretization
variants are compared with the nodal and element approaches known from the literature.
Findings
In terms of accuracy in the L2 norm, energy distance and efficiency, the discontinuous
zero-order variant appears to be the most advantageous. The proposed variant sufficiently
preserves the spectrum of density at the edges, while keeping computational cost low.
Interpretation
The continuous finite element method is analogous to the nodal formulation in the
literature, while the discontinuous finite element method is analogous to the element
formulation. The two variants differ in terms of implementation, computational cost
and ability to preserve the density spectrum. These differences cannot be described
and measured by known indirect methods from the literature.
Keywords
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Article Info
Publication History
Published online: June 14, 2022
Accepted:
June 7,
2022
Received in revised form:
March 23,
2022
Received:
November 19,
2021
Identification
Copyright
© 2022 Elsevier Ltd. All rights reserved.
