You are here: Home / Exposures / Komarova, Smith, Dixon, Sims, Wahl, 2003 / Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling: single bone remodeling cycle

Model Mathematics

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Component: environment

Component: x1

\frac{d}{d time} (x1) = alpha1 {x1}^{g11} {x2}^{g21} - (beta1 x1)

Component: x2

\frac{d}{d time} (x2) = alpha2 {x1}^{g12} {x2}^{g22} - (beta2 x2)

Component: z

\frac{d}{d time} (z) = k2 y2 - (k1 y1)

Component: y1

y1 = \{\begin{matrix} x1 - x1_bar if x1 > x1_bar \\ 0.0 otherwise \end{matrix}

Component: y2

y2 = \{\begin{matrix} x2 - x2_bar if x2 > x2_bar \\ 0.0 otherwise \end{matrix}

Component: x1_bar

x1_bar = {(\frac{beta1}{alpha1})}^{\frac{1.0 - g22}{gamma}} {(\frac{beta2}{alpha2})}^{\frac{g21}{gamma}}

Component: x2_bar

x2_bar = {(\frac{beta1}{alpha1})}^{\frac{g12}{gamma}} {(\frac{beta2}{alpha2})}^{\frac{1.0 - g11}{gamma}}

Component: model_parameters

gamma = g12 g21 - ((1.0 - g11) (1.0 - g22))

Source: Derived from workspace Komarova, Smith, Dixon, Sims and Wahl, 2003 at changeset cda7e45501eb.

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License: This work is licensed under a Creative Commons Attribution 3.0 Unported License.