Diagnosing osteoporosis: A new perspective on estimating bone density

Osteoporosis may be characterized by low bone density and its significance is expected to grow as the population of the world both increases and ages. Our purpose here is to model human bone mineral density estimated through dual-energy x  -ray absorptiometry, using local volumetric distance spline interpolants. Interpolating the values means the construction of a function F(x,y,z)F(x,y,z) that mimics the relationship implied by the data (xi,yi,zi;fi)(xi,yi,zi;fi), in such a way that F(xi,yi,zi)=fiF(xi,yi,zi)=fi, i=1,2,…,ni=1,2,…,n, where x,yx,y and z represent, respectively, age, weight and height. This strategy greatly enhances the ability to accurately express the patient's bone density measurements, with the potential to become a framework for bone densitometry in clinical practice. The usefulness of our model is demonstrated in 424 patients and the relevance of our results for diagnosing osteoporosis is discussed.