The Heterogeneous Mineral Content of Bone—Using Stochastic Arguments and Simulations to Overcome Experimental Limitations
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  • 作者：C. Lukas (1)
    P. Kollmannsberger (1)
    D. Ruffoni (2)
    P. Roschger (3)
    P. Fratzl (1)
    R. Weinkamer (1) richard.weinkamer@mpikg.mpg.de
  • 关键词：Bone – Mineralization – Material heterogeneity – Counting statistics – Bone mineralization density distribution – Quantitative backscattered electron imaging – Tikhonov regularization
  • 刊名：Journal of Statistical Physics
  • 出版年：2011
  • 出版时间：July 2011
  • 年：2011
  • 卷：144
  • 期：2
  • 页码：316-331
  • 全文大小：781.2 KB
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  • 作者单位：1. Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany2. Institute for Biomechanics, ETH Zurich, Zurich, Switzerland3. Ludwig Boltzmann Institute of Osteology at Hanusch Hospital of WGKK and AUVA Trauma Centre Meidling, 1st Medical Dept., Hanusch Hospital, 1140 Vienna, Austria
  • 刊物类别：Physics and Astronomy
  • 刊物主题：Physics
    Statistical Physics
    Mathematical and Computational Physics
    Physical Chemistry
    Quantum Physics
  • 出版者：Springer Netherlands
  • ISSN：1572-9613
文摘
On a sub-millimeter length scale, bone is a very heterogeneous material with varying mineral content. This heterogeneity can be measured by quantitative backscattered electron imaging (qBEI) and quantified by a probability distribution called the bone mineralization density distribution (BMDD). The stochastic nature of the backscattering of electrons during the measurement makes the results dependent on the acquisition time. In this work the influence of the measurement conditions was quantified and was corrected for using Tikhonov regularization. Deconvolution reduces the width of the BMDD and allows a more precise definition of a reference BMDD for healthy adults. The corrected information was used as input for a mathematical model that predicts the time evolution of the BMDD. Simulations of osteoporosis treatment reveal a double peak in the BMDD that is not observed in experiments due to limited acquisition time. Our method allows determining the necessary acquisition time to resolve such double peaks.

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