Mechanical metric for skeletal biomechanics derived from spectral analysis of stiffness matrix

Petr Henyš,Michal Kuchař,Niels Hammer,Petr Hájek

doi:10.1038/s41598-021-94998-5

Abstract

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.

Highlights

A new metric for the quantitative and qualitative evaluation of bone stiffness is introduced
The resultant eigenpairs composed from eigenvalues and associated eigenvectors contain a unique information about the modal as well as static stiffness
This mix of unique bone properties is highly individual and its precise capturing seems a paramount of current in silico biomedical engineering

Summary

Introduction

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 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 computed by state-of-the-art subject specified finite element algorithms. The resultant eigenpairs composed from eigenvalues and associated eigenvectors contain a unique information about the modal as well as static stiffness.

Methods

Results

Conclusion