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Model Mathematics

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Component: environment

Component: intracellular_glucose

\frac{d}{d time} (G_i) = \frac{R1 + R2 - Rm}{rho}

Component: extracellular_glucose

\frac{\partial}{\partial time} (G) = \frac{(- R1) + (- R2)}{1.0 - rho} + D_G A + (- (G B)) \frac{\partial^{2.0}}{\partial x^{2.0}} (G) = A \frac{\partial}{\partial x} (G) = B

Component: insulin

\frac{\partial}{\partial time} (I) = Rs + D_I C + (- (V D)) \frac{\partial^{2.0}}{\partial x^{2.0}} (I) = C \frac{\partial}{\partial x} (I) = D

Component: insulin_inhibition

\frac{d}{d time} (J) = J_tau (J_infinity - J) J_infinity = \frac{K_inh}{K_inh + I}

Component: glucose_metabolism

Rm = rho \frac{Vm G_i}{Km + G_i}

Component: GLUT_1_transporter

R1 = rho \frac{V1 (G - G_i)}{(K1 + G_i) (1.0 + \frac{G}{K1})} \frac{I}{Ki + I}

Component: GLUT_2_transporter

R2 = rho \frac{V2 (G Jm - G_i)}{(K2 + G_i) (1.0 + \frac{G}{K2})}

Component: insulin_secretion

Rs = \frac{Vs ({Rm}^{4.0} + {rho}^{4.0} L^{4.0})}{{Rm}^{4.0} + {rho}^{4.0} {Ks}^{4.0} + {rho}^{4.0} L^{4.0}}

Source: Derived from workspace Keener, 2001 at changeset 6c8cc275ab29.

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Diffusion Induced Oscillatory Insulin Secretion