Hammer, N. | bioRxiv Science

bioRxiv2021

Mechanical Metric for Skeletal Biomechanics Derived from Spectral Analysis of Stiffness matrix

A new metric for the quantitative and qualitative evaluation of bone stiffness is introduced. It is based on the spectral decomposition of stiffness matrix computed with finite element method. The here proposed metric is defined as an amplitude rescaled eigenvalues of stiffness matrix. The metric contains unique information on the principal stiffness of bone and reflects both bone shape and material properties. The metric was compared with anthropometrical measures and was tested for sex sensitivity on pelvis bone. Further, the smallest stiffness of pelvis was computed under a certain loading condition and analyzed with respect to sex and direction. The metric complements anthropometrical measures and provides a unique information about the smallest bone stiffness independent from the loading configuration and can be easily computed by state-of-the-art subject specified finite element algorithms.

bioinformatics↗

bioRxiv2021

Bone Mineral Density modelled as a Random Field: a Feasibility Study on Pelvic Bone

Background and ObjectiveCapturing the population variability of bone properties is of paramount importance to biomedical engineering. The aim of the present paper is to describe variability and correlations in bone mineral density with a spatial random field inferred from routine computed tomography data. MethodsRandom fields were simulated by transforming pairwise uncorrelated Gaussian random variables into correlated variables through the spectral decomposition of an age-detrended correlation matrix. The validity of the random field model was demonstrated in the spatiotemporal analysis of bone mineral density. The similarity between the computed tomography samples and those generated via random fields was analyzed with the energy distance metric. ResultsThe random field of bone mineral density was found to be approximately Gaussian/slightly left-skewed/strongly right-skewed at various locations. However, average bone density could be simulated well with the proposed Gaussian random field for which the energy distance, i.e., a measure that quantifies discrepancies between two distribution functions, is convergent with respect to the number of correlation eigenpairs. ConclusionsThe proposed random field model allows the enhancement of computational biomechanical models with variability in bone mineral density, which could increase the usability of the model and provides a step forward in in-silico medicine.

biophysics↗