BACKGROUND AND OBJECTIVE: Capturing 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. METHODS: Random 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. RESULTS: The 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. CONCLUSIONS: The 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.

Department of Anatomy Faculty of Medicine in Hradec Králové Charles University Šimkova 870 Hradec Králové 500 03 Czech Republic

Department of Macroscopic and Clinical Anatomy Medical University of Graz Auenbruggerpl 2 Graz 8036 Austria; Department of Orthopedic and Trauma Surgery University of Leipzig Leipzig Germany; Fraunhofer Institute for Machine Tools and Forming Technology IWU Nöthnitzer Straße 44 01187 Dresden Germany

Institut für Rechtsmedizin Universitätsklinikum Hamburg Eppendorf Butenfeld 34 Hamburg 22529 Germany

Institute of New Technologies and Applied Informatics Faculty of Mechatronics Informatics and Interdisciplinary Studies Technical University of Liberec Studentskí 1402 2 Liberec 461 17 Czech Republic

Institute of Structural Mechanics Faculty of Civil Engineering Brno University of Technology Veveří 331 95 Brno 602 00 Czech Republic

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