Principle of transformation groups - Revision history

en>Markhurd: Disambiguate Jacobian to Jacobian matrix and determinant using popups

2014-07-02T15:45:17Z

Disambiguate Jacobian to Jacobian matrix and determinant using popups

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	In [[bone\|bone physiology]], the '''bone remodeling period''' describes the temporal duration (i.e. lifespan) of the basic multicellular unit (BMU) that is responsible for bone turnover. Historically, this was referred to ~~as the '''sigma (σ)''' or '''sigma period''',<ref>Frost, HM~~. <u>~~Tetracycline-based histological analysis of bone remodeling</u>. ''Calc Tiss Res'' 1969;3:211-237.</ref> but the terminology is now outdated.~~		Not much to write about myself at all.<br>Hurrey Im here and a member of this site.<br>I really hope I am useful at all<br><br>my page ... [http://tinyurl.com/q3sw2ql Celine Handbags]

	~~==Bone remodeling==~~
	~~Although bone may appear superficially as~~ a ~~static tissue, it is actually very dynamic, undergoing constant [[bone remodeling\|remodeling]] throughout the life~~ of the vertebrate organism. This occurs with the synchronized action of [[osteoclast]]s and [[osteoblast]]s, cells that resorb and deposit bone, respectively. Bone remodeling also occurs in response to trauma, such as that following accidental bone fracture or the placement of [[dental implant]]s into the jaw bones.

	~~==The remodeling period==~~
	The remodeling period consists of the combined duration of the [[bone resorption\|resorption]], the osteoclastic reversal (the phase marked by shifting of resorption processes into formative processes) and the [[bone formation\|formation]] periods of bone growth and development.<ref>Burr, DB. <u>The effects of altered strain environments on bone tissue kinetics</u>. ''Bone'' 1989;10:215-221.<~~/ref~~> ~~This period refers to the average total duration of a single cycle of [[bone remodeling]]~~ at ~~any point on a bone surface.~~<~~ref~~>~~Parfitt, AM, et al.~~ <u>~~Bone histomorphometry: standardization of nomenclature, symbols, and units</u>. ''J Bone Miner Res'' 1987;'''2''':595-610.</ref>~~

	~~<div style="float:right; margin:5px;">~~
	~~{\| class="wikitable" style="text-align:center"~~
	~~\|+ Remodeling duration (in wks)~~
	~~! !!Resorption !!Reversal !!Formation !!Total~~
	\|-
	~~!Rabbits~~
	~~\| 1~~
	~~\| 0.5~~
	~~\| 4.5~~
	~~\| 6~~
	\|-
	~~!Dogs~~
	~~\| 1.5~~
	~~\| 0.5~~
	~~\| 10~~
	~~\| 12~~
	\|-
	~~!Humans~~
	~~\| 2~~
	~~\| 2~~
	~~\| 13~~
	~~\| 17~~
	\|-
	\|}

	For the remodeling to occur, appropriate cell signaling occurs to trigger osteoclasts to resorb the surface of the bone, followed by deposition of bone by osteoblasts. Together, the cells in any given particular region of the bone surface that are responsible for bone remodeling are known as the basic multicellular unit (BMU), and it is the average lifespan of the BMU that is referred to as the ''remodeling period''.<ref>Doll, B; et al. Overview of fracture repair. In Pietrzak, WS; editor: ''Musculoskeletal tissue regeneration: biological materials and methods'', New Jersey: Humana Press, 2008. ISBN 1-58829-909-0 page ~~48</ref> The size of a BMU is roughly 200μm in diameter, defined by the 100μm diffusion capability in bone.~~

	~~===Determining the bone remodeling period===~~
	In calculating the bone remodeling period, a two-dimensional model is examined, referring to the time it takes for the area in question to be eroded and then filled in with new bone (sigma will be used here for simplicity's sake). The bone formation portion (σ<sub>f</sub>) of the bone remodeling period is calculated as follows:<ref name="JAW">Jaworski, ZFC: Bone histomorphometry: Outline of theory and practice. ~~In Simmons, OJ; Kunin AS; editors: ''Skeletal Research'', Volume 2. New York: Academic Press, 1983~~. ~~ISBN 0-12-429002-7 pages 237-276~~.~~</ref>~~

	:~~<math>\sigma_{f} = \frac{MWT}{M_{f}}</math>~~

	in which MWT refers to the mean wall thickness of the completed bone unit and M<sub>f</sub> refers to the prevailing mean effective bone appositional rate. In other words, what this formula means is that the bone remodeling period is equivalent to the thickness of the microscopic segment of bone being formed divided by the rate at which it forms. If the mean linear rate of bone resorption is known, the bone resorption portion (σ<sub>r</sub>) can be similarly calculated:<ref name="JAW"/>

	~~:<math>\sigma_{r} = \frac{MWT}{M_{r}}</math>~~

	~~Consequently, the entire bone remodeling period (σ<sub>r + f</sub>, equivalent to σ) can be represented by the following formula:<ref name="JAW"/>~~

	~~:<math>\sigma_{(r + f)} = \frac{MWT}{M_{r}} + \frac{MWT}{M_{f}}<~~/~~math>~~

	~~The linear bone resorption rate (M<sub>r<~~/~~sub>) cannot be measured directly, but it approximates a third of σ<sub>f</sub>.<ref>Frost, HM~~. ~~"Bone dynamics in osteoporosis and in osteomalacia." Thomas, Springfield, Illinois - 1966.<~~/~~ref>~~

	~~==Interspecies differences==~~
	Each vertebrate species exhibits a distinct duration of bone regeneration and remodeling, and it appears as though there is an inversely proportional relationship between the rate of bone regeneration and the phylogenetic evolution of the animal.<ref>Martınez-Gonzalez, JM, et al. <u>Evaluation of minipigs as an animal model for alveolar distraction</u>. ''Oral Surg Oral Med Oral Pathol Oral Radiol Endod'' 2005;99:11-6</ref> Each remodeling period lasts 3–6 months in humans, 3 months in dogs, and 6 weeks in rabbits.<ref>Roberts WE, et al. Fisiologia y metabolismo oseo. In: Misch C, editor: ''Implantologia contemporanea''. Madrid: Mosby, 1995. ISBN 84-8086-384-6 pages 324-350.</ref>

	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Skeletal system]]~~
	~~[[Category:Animal physiology]~~]

en>Wikijmf: Capitalised Cauchy; although in this case there is no ambiguity.

2012-03-01T22:35:47Z

Capitalised Cauchy; although in this case there is no ambiguity.

New page

In [[bone|bone physiology]], the '''bone remodeling period''' describes the temporal duration (i.e. lifespan) of the basic multicellular unit (BMU) that is responsible for bone turnover. Historically, this was referred to as the '''sigma (σ)''' or '''sigma period''',<ref>Frost, HM. Tetracycline-based histological analysis of bone remodeling. ''Calc Tiss Res'' 1969;3:211-237.</ref> but the terminology is now outdated.

==Bone remodeling==
Although bone may appear superficially as a static tissue, it is actually very dynamic, undergoing constant [[bone remodeling|remodeling]] throughout the life of the vertebrate organism. This occurs with the synchronized action of [[osteoclast]]s and [[osteoblast]]s, cells that resorb and deposit bone, respectively. Bone remodeling also occurs in response to trauma, such as that following accidental bone fracture or the placement of [[dental implant]]s into the jaw bones.

==The remodeling period==
The remodeling period consists of the combined duration of the [[bone resorption|resorption]], the osteoclastic reversal (the phase marked by shifting of resorption processes into formative processes) and the [[bone formation|formation]] periods of bone growth and development.<ref>Burr, DB. The effects of altered strain environments on bone tissue kinetics. ''Bone'' 1989;10:215-221.</ref> This period refers to the average total duration of a single cycle of [[bone remodeling]] at any point on a bone surface.<ref>Parfitt, AM, et al. Bone histomorphometry: standardization of nomenclature, symbols, and units. ''J Bone Miner Res'' 1987;'''2''':595-610.</ref>

<div style="float:right; margin:5px;">
{| class="wikitable" style="text-align:center"
|+ Remodeling duration (in wks)
! !!Resorption !!Reversal !!Formation !!Total
|-
!Rabbits
| 1
| 0.5
| 4.5
| 6
|-
!Dogs
| 1.5
| 0.5
| 10
| 12
|-
!Humans
| 2
| 2
| 13
| 17
|-
|}

For the remodeling to occur, appropriate cell signaling occurs to trigger osteoclasts to resorb the surface of the bone, followed by deposition of bone by osteoblasts. Together, the cells in any given particular region of the bone surface that are responsible for bone remodeling are known as the basic multicellular unit (BMU), and it is the average lifespan of the BMU that is referred to as the ''remodeling period''.<ref>Doll, B; et al. Overview of fracture repair. In Pietrzak, WS; editor: ''Musculoskeletal tissue regeneration: biological materials and methods'', New Jersey: Humana Press, 2008. ISBN 1-58829-909-0 page 48</ref> The size of a BMU is roughly 200μm in diameter, defined by the 100μm diffusion capability in bone.

===Determining the bone remodeling period===
In calculating the bone remodeling period, a two-dimensional model is examined, referring to the time it takes for the area in question to be eroded and then filled in with new bone (sigma will be used here for simplicity's sake). The bone formation portion (σf) of the bone remodeling period is calculated as follows:<ref name="JAW">Jaworski, ZFC: Bone histomorphometry: Outline of theory and practice. In Simmons, OJ; Kunin AS; editors: ''Skeletal Research'', Volume 2. New York: Academic Press, 1983. ISBN 0-12-429002-7 pages 237-276.</ref>

:<math>\sigma_{f} = \frac{MWT}{M_{f}}</math>

in which MWT refers to the mean wall thickness of the completed bone unit and Mf refers to the prevailing mean effective bone appositional rate. In other words, what this formula means is that the bone remodeling period is equivalent to the thickness of the microscopic segment of bone being formed divided by the rate at which it forms. If the mean linear rate of bone resorption is known, the bone resorption portion (σr) can be similarly calculated:<ref name="JAW"/>

:<math>\sigma_{r} = \frac{MWT}{M_{r}}</math>

Consequently, the entire bone remodeling period (σr + f, equivalent to σ) can be represented by the following formula:<ref name="JAW"/>

:<math>\sigma_{(r + f)} = \frac{MWT}{M_{r}} + \frac{MWT}{M_{f}}</math>

The linear bone resorption rate (Mr) cannot be measured directly, but it approximates a third of σf.<ref>Frost, HM. "Bone dynamics in osteoporosis and in osteomalacia." Thomas, Springfield, Illinois - 1966.</ref>

==Interspecies differences==
Each vertebrate species exhibits a distinct duration of bone regeneration and remodeling, and it appears as though there is an inversely proportional relationship between the rate of bone regeneration and the phylogenetic evolution of the animal.<ref>Martınez-Gonzalez, JM, et al. Evaluation of minipigs as an animal model for alveolar distraction. ''Oral Surg Oral Med Oral Pathol Oral Radiol Endod'' 2005;99:11-6</ref> Each remodeling period lasts 3–6 months in humans, 3 months in dogs, and 6 weeks in rabbits.<ref>Roberts WE, et al. Fisiologia y metabolismo oseo. In: Misch C, editor: ''Implantologia contemporanea''. Madrid: Mosby, 1995. ISBN 84-8086-384-6 pages 324-350.</ref>

==References==
{{reflist}}

[[Category:Skeletal system]]
[[Category:Animal physiology]]