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Determination of spatially dependent diffusion parameters in bovine bone using Kalman filter.

Shokry, Abdallah LU ; Ståhle, Per LU and Svensson, Ingrid LU (2015) In Journal of Theoretical Biology 384. p.10-18
Abstract
Although many studies have been made for homogenous constant diffusion, bone is an inhomogeneous material. It has been suggested that bone porosity decreases from the inner boundaries to the outer boundaries of the long bones. The diffusivity of substances in the bone matrix is believed to increase as the bone porosity increases. In this study, an experimental set up is used where bovine bone samples, saturated with potassium chloride (KCl), were put into distilled water and the conductivity of the water was followed. Chloride ions in the bone samples escaped out in the water through diffusion and the increase of the conductivity was measured. A one-dimensional, spatially dependent mathematical model describing the diffusion process is... (More)
Although many studies have been made for homogenous constant diffusion, bone is an inhomogeneous material. It has been suggested that bone porosity decreases from the inner boundaries to the outer boundaries of the long bones. The diffusivity of substances in the bone matrix is believed to increase as the bone porosity increases. In this study, an experimental set up is used where bovine bone samples, saturated with potassium chloride (KCl), were put into distilled water and the conductivity of the water was followed. Chloride ions in the bone samples escaped out in the water through diffusion and the increase of the conductivity was measured. A one-dimensional, spatially dependent mathematical model describing the diffusion process is used. The diffusion parameters in the model are determined using a Kalman filter technique. The parameters for spatially dependent at endosteal and periosteal surfaces are found to be (12.8±4.7)×10(-11) and (5±3.5)×10(-11)m(2)/s respectively. The mathematical model function using the obtained diffusion parameters fits very well with the experimental data with mean square error varies from 0.06×10(-6) to 0.183×10(-6)(μS/m)(2). (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Theoretical Biology
volume
384
pages
10 - 18
publisher
Academic Press
external identifiers
  • pmid:26275499
  • wos:000362613400002
  • scopus:84940025894
ISSN
1095-8541
DOI
10.1016/j.jtbi.2015.07.025
language
English
LU publication?
yes
id
af8a290f-2dab-4768-b0e8-5f66e54fb16d (old id 7841055)
date added to LUP
2015-09-10 10:48:24
date last changed
2017-01-01 03:30:37
@article{af8a290f-2dab-4768-b0e8-5f66e54fb16d,
  abstract     = {Although many studies have been made for homogenous constant diffusion, bone is an inhomogeneous material. It has been suggested that bone porosity decreases from the inner boundaries to the outer boundaries of the long bones. The diffusivity of substances in the bone matrix is believed to increase as the bone porosity increases. In this study, an experimental set up is used where bovine bone samples, saturated with potassium chloride (KCl), were put into distilled water and the conductivity of the water was followed. Chloride ions in the bone samples escaped out in the water through diffusion and the increase of the conductivity was measured. A one-dimensional, spatially dependent mathematical model describing the diffusion process is used. The diffusion parameters in the model are determined using a Kalman filter technique. The parameters for spatially dependent at endosteal and periosteal surfaces are found to be (12.8±4.7)×10(-11) and (5±3.5)×10(-11)m(2)/s respectively. The mathematical model function using the obtained diffusion parameters fits very well with the experimental data with mean square error varies from 0.06×10(-6) to 0.183×10(-6)(μS/m)(2).},
  author       = {Shokry, Abdallah and Ståhle, Per and Svensson, Ingrid},
  issn         = {1095-8541},
  language     = {eng},
  pages        = {10--18},
  publisher    = {Academic Press},
  series       = {Journal of Theoretical Biology},
  title        = {Determination of spatially dependent diffusion parameters in bovine bone using Kalman filter.},
  url          = {http://dx.doi.org/10.1016/j.jtbi.2015.07.025},
  volume       = {384},
  year         = {2015},
}