response_function_serial_2tcm_c1#

petpal.kinetic_modeling.tcms_as_convolutions.response_function_serial_2tcm_c1(t: numpy.ndarray, k1: float, k2: float, k3: float, k4: float) → numpy.ndarray#

The response function for first compartment in the serial 2TCM.

\[f(t) = \frac{k_{1}}{\Delta \alpha} \left[ (k_{4}-\alpha_{1})e^{-\alpha_{1}t} + (\alpha_{2}-k_{4})e^{-\alpha_{2}t}\right]\]

where

\[\begin{split}a&= k_{2}+k_{3}+k_{4}\\ \alpha_{1}&=\frac{a-\sqrt{a^{2}-4k_{2}k_{4}}}{2}\\ \alpha_{1}&=\frac{a+\sqrt{a^{2}-4k_{2}k_{4}}}{2}\\ \Delta \alpha&=\alpha_2 - \alpha_1\end{split}\]
Parameters:

  • t (np.ndarray) – Array containing time-points where \(t\geq0\).

  • k1 (float) – Rate constant for transport from plasma/blood to tissue compartment.

  • k2 (float) – Rate constant for transport from first tissue compartment back to plasma/blood.

  • k3 (float) – Rate constant for transport from first tissue compartment to second tissue compartment.

  • k4 (float) – Rate constant for transport from second tissue compartment back to first tissue compartment.

Returns:

(np.ndarray) – Array containing response function values for first compartment given the constants.

See also