Population variability and correlations in bone mineral density can be described by a spatial random field, which can be inferred from the routine computed tomography (CT) data. Random fields were simulated by transforming pairwise uncorrelated Gaussian random variables into correlated variables through the spectral decomposition of age-detrended correlation matrix estimated from CT. The validity of random field model was demonstrated on spatio-temporal analysis of bone mineral density and bone mineral content. The similarity of CT samples and that generated from random fields was analyzed with energy distance metric. It was found that the bone mineral density random field was approximately Gaussian/slightly left-skewed/strongly right-skewed in various locations. However, bone mineral content could be well simulated with the proposed Gaussian random field and that of energy distance, i.e., a measure to quantify discrepancies between two distribution functions, is convergent with respect to the number of correlation eigenpairs. The proposed random field allows for enriching computational biomechanical models with variability in bone mineral density, which could increase the model usability and provide a step forward in digital twin paradigm.
Random field assessment of inhomogeneous bone mineral density from DXA scans can enhance the differentiation between postmenopausal women with and without hip fractures
