You are here: Home / Exposures / Komarova, 2005 / Mathematical model of paracrine interactions between osteoclasts and osteoblasts predicts anabolic action of parathyroid hormone on bone

Model Mathematics

Component based math viewer is available

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))

g21 = \{\begin{matrix} 0.15 if time \geq 1.0 \land time < 2.00 \\ -0.5 otherwise \end{matrix}

Source: Derived from workspace Komarova 2005 at changeset 27939ead9d0c.

Collaboration: To begin collaborating on this work, please use your git client and issue this command:

Downloads

Views Available

Tools

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

Mathematical model of paracrine interactions between osteoclasts and osteoblasts predicts anabolic action of parathyroid hormone on bone