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Strain driven transport for bone modeling at the periosteal surface.

Banks-Sills, Leslie LU ; Ståhle, Per LU ; Svensson, Ingrid LU and Eliaz, Noam (2011) In Mathematical Biosciences 230. p.37-44
Abstract
Bone modeling and remodeling has been the subject of extensive experimental studies. There have been several mathematical models proposed to explain the observed behavior, as well. A different approach is taken here in which the bone is treated from a macroscopic view point. In this investigation, a one-dimensional analytical model is used to shed light on the factors which play the greatest role in modeling or growth of cortical bone at the periosteal surface. It is presumed that bone growth is promoted when increased amounts of bone nutrients, such as nitric oxide synthase (NOS) or messenger molecules, such as prostaglandin E(2) (PGE(2)), seep out to the periosteal surface of cortical bone and are absorbed by osteoblasts. The transport... (More)
Bone modeling and remodeling has been the subject of extensive experimental studies. There have been several mathematical models proposed to explain the observed behavior, as well. A different approach is taken here in which the bone is treated from a macroscopic view point. In this investigation, a one-dimensional analytical model is used to shed light on the factors which play the greatest role in modeling or growth of cortical bone at the periosteal surface. It is presumed that bone growth is promoted when increased amounts of bone nutrients, such as nitric oxide synthase (NOS) or messenger molecules, such as prostaglandin E(2) (PGE(2)), seep out to the periosteal surface of cortical bone and are absorbed by osteoblasts. The transport of the bone nutrients is assumed to be a strain controlled process. Equations for the flux of these nutrients are written for a one-dimensional model of a long bone. The obtained partial differential equation is linearized and solved analytically. Based upon the seepage of nutrients out of the bone, the effect of loading frequency, number of cycles and strain level is examined for several experiments that were found in the literature. It is seen that bone nutrient seepage is greatest on the tensile side of the bone; this location coincides with the greatest amount of bone modeling. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Mathematical Biosciences
volume
230
pages
37 - 44
publisher
Elsevier
external identifiers
  • wos:000288630100004
  • pmid:21199660
  • scopus:79951769042
ISSN
0025-5564
DOI
10.1016/j.mbs.2010.12.008
language
English
LU publication?
yes
id
87179cc0-da8b-476e-96c4-b102c349f292 (old id 1777887)
date added to LUP
2011-02-04 09:54:38
date last changed
2017-01-01 06:13:50
@article{87179cc0-da8b-476e-96c4-b102c349f292,
  abstract     = {Bone modeling and remodeling has been the subject of extensive experimental studies. There have been several mathematical models proposed to explain the observed behavior, as well. A different approach is taken here in which the bone is treated from a macroscopic view point. In this investigation, a one-dimensional analytical model is used to shed light on the factors which play the greatest role in modeling or growth of cortical bone at the periosteal surface. It is presumed that bone growth is promoted when increased amounts of bone nutrients, such as nitric oxide synthase (NOS) or messenger molecules, such as prostaglandin E(2) (PGE(2)), seep out to the periosteal surface of cortical bone and are absorbed by osteoblasts. The transport of the bone nutrients is assumed to be a strain controlled process. Equations for the flux of these nutrients are written for a one-dimensional model of a long bone. The obtained partial differential equation is linearized and solved analytically. Based upon the seepage of nutrients out of the bone, the effect of loading frequency, number of cycles and strain level is examined for several experiments that were found in the literature. It is seen that bone nutrient seepage is greatest on the tensile side of the bone; this location coincides with the greatest amount of bone modeling.},
  author       = {Banks-Sills, Leslie and Ståhle, Per and Svensson, Ingrid and Eliaz, Noam},
  issn         = {0025-5564},
  language     = {eng},
  pages        = {37--44},
  publisher    = {Elsevier},
  series       = {Mathematical Biosciences},
  title        = {Strain driven transport for bone modeling at the periosteal surface.},
  url          = {http://dx.doi.org/10.1016/j.mbs.2010.12.008},
  volume       = {230},
  year         = {2011},
}