Bone microarchitecture characterization based on fractal analysis in spatial frequency domain imaging

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>This paper suggests a new technique for trabecular bone characterization using fractal analysis of X-Ray and MRI texture images for osteoporosis diagnosis. Osteoporosis is a chronic disease characterized by a decrease in bone density that can lead to fracture and disability. In essence, the proposed fractal model makes use of the differential box-counting method (DBCM) to estimate the fractal dimension (<em>FD</em>) after an appropriate image preprocessing stage that ensures a robust estimation process. In this study, we showed that within the frequency domain generated through discrete cosine transform (DCT), only a quarter of DCT coefficients are enough to characterize osteoporotic tissues. The algorithmic complexity of the developed approach is of the order of \(\frac{N}{8} \log_2 \frac{N}{8}\) where \(N\) stands for the size of the image, which, in turn, likely yields important gain in terms of medication cost. We report a successful separation of healthy and pathological cases in term of both <em>P</em>-value (using statistical Wilcoxon rank sum test) and margin difference. A comparative statistical analysis has been performed using a publicly available database that contains a set of MRI and X-Ray texture images of both healthy and osteoporotic bone tissues. The statistical results demonstrated the feasibility and accepted performance level of our fractal model-based diagnosis to discriminate healthy and unhealthy trabecular bone tissues. The developed approach has been implemented on a medical device prototype.</p></div>