Estimation of bone Calcium-to-Phosphorous mass ratio using dual-energy nonlinear polynomial functions

4th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Sotiropoulou, P.^1 ; Koukou, V.^1 ; Martini, N.^1 ; Michail, C.^2 ; Kounadi, E.^2 ; Kandarakis, I.^2 ; Nikiforidis, G.^1 ; Fountos, G.^2

Department of Medical Physics, Medical School University of Patras, Patras

265 00, Greece^1

Department of Medical Instruments Technology, Technological Educational Institution of Athens, Athens

122 10, Greece^2

关键词: Analytical approximation;    Fitting coefficient;    Intensity measurements;    Least squares estimation;    Nonlinear functions;    Nonlinear polynomials;    Photon counting detectors;    Quadratic function;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/633/1/012126/pdf
DOI  :  10.1088/1742-6596/633/1/012126

来源: IOP

【 摘 要 】

In this study an analytical approximation of dual-energy inverse functions is presented for the estimation of the calcium-to-phosphorous (Ca/P) mass ratio, which is a crucial parameter in bone health. Bone quality could be examined by the X-ray dual-energy method (XDEM), in terms of bone tissue material properties. Low- and high-energy, log-intensity measurements were combined by using a nonlinear function, to cancel out the soft tissue structures and generate the dual energy bone Ca/P mass ratio. The dual-energy simulated data were obtained using variable Ca and PO4thicknesses on a fixed total tissue thickness. The XDEM simulations were based on a bone phantom. Inverse fitting functions with least-squares estimation were used to obtain the fitting coefficients and to calculate the thickness of each material. The examined inverse mapping functions were linear, quadratic, and cubic. For every thickness, the nonlinear quadratic function provided the optimal fitting accuracy while requiring relative few terms. The dual-energy method, simulated in this work could be used to quantify bone Ca/P mass ratio with photon-counting detectors.