You are here: Home / Exposures / Shrestha, Hollot, Chipkin, Schmitt, Chait, 2010 / A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans

Model Mathematics

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Component: environment

Component: x1

\frac{d}{d time} (x1) = k - (lambda_Ca x1 + lambda1 x1)

Component: lambda_Ca

lambda_Ca = \frac{A - B}{1 + {(\frac{Ca}{S})}^{m_Ca}} + B

Component: m_Ca

m_Ca = \frac{m1}{1 + ⅇ^{(- beta) (R - Ca)}} + m2

Component: x2

\frac{d}{d time} (x2) = lambda_Ca x1 - (lambda2 x2)

PTH = \frac{x2}{2.75}

Component: Ca

Ca = \{\begin{matrix} Ca_0 if time < t0 \\ Ca_0 - (Ca_1 (1 - (ⅇ^{(- alpha) (time - t0)}))) otherwise \end{matrix}

Component: k

k = lambda2 x2_n + lambda1 x1_n

Component: S

S = Ca_0 {(- (\frac{x1_n B - (lambda2 x2_n)}{x1_n A - (lambda2 x2_n)}))}^{\frac{1}{m_Ca}}

Component: A

A = \frac{lambda1 lambda2 x2_max}{k - (lambda2 x2_max)}

Component: B

B = \frac{lambda1 lambda2 x2_min}{k - (lambda2 x2_min)}

Component: model_parameters

Source: Derived from workspace Shrestha, Hollot, Chipkin, Schmitt and Chait 2010 at changeset da21662a6c52.

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A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans