Mathematical network model for bone mineral density (BMD) and bone quality assessment

The bone fractures can appear in a patient as a result of an exceeding stress level at a specific anatomic site, depending the failure on fatigue phenomena, high loads or on a low value of bone density. Indeed, independently from physiological conditions or specific pathologies such as osteoporotic ones, bone mineral density (BMD) constitutes the main responsible of the strength of a selected bone region. In this respect, the standard and routine approach for the diagnosis of osteoporosis is to assess BMD shown to be a possible indicator of fracture risk. However, a major limitation of BMD is that it incompletely reflects variation in bone strength. Other factors like bone microarchitecture contribute substantially to bone strength and their evaluation can improve determination of bone quality and strength; yet, structural assessment has not been implemented in clinical routine because of the lack of a mathematical model for analyzing bone structure. In this paper, we develop a mathematical network model for bone microstructure which is capable of quantitative assessment of bone mineral density and bone micro-architecture. First, we design a bone continuum model by analyzing bone image profile of dual-energy X-ray absorptiometry (DXA) scan. Next, we introduce a mathematical network model of bone microstructure which allows us to calculate BMDmodel as well as the density distribution of bone microstructure for patients. Last, we present realizations of the mathematical network model based on DXA scan images of two different patients as a representative example of bone network model. Our study provides an initial framework of mathematical network bone model along with BMDmodel that can enhance the diagnosis ability of bone disease such as osteoporosis. Eventually, it would be useful for a theoretical testing framework of bone remodeling dynamics to leverage new drug development for future treatments.