calc_srtm_tac

petpal.kinetic_modeling.reference_tissue_models.calc_srtm_tac(tac_times_in_minutes: numpy.ndarray, ref_tac_vals: numpy.ndarray, r1: float, k2: float, bp: float) → numpy.ndarray

Calculate the Time Activity Curve (TAC) using the Simplified Reference Tissue Model (SRTM) with the given reference TAC and kinetic parameters.

Important

This function assumes that the reference TAC is uniformly sampled with respect to time since we perform convolutions.

The SRTM TAC can be calculated as:

\[C(t)=R_{1}C_\mathrm{R}(t) + \left(k_{2} - \frac{R_{1}k_{2}}{1+\mathrm{BP}}\right) C_\mathrm{R}(t)\otimes\exp\left(- \frac{k_{2}t}{1+\mathrm{BP}}\right),\]

where \(C_\mathrm{R}(t)\) is the reference TAC, \(R_{1}=\frac{k_1^\prime}{k_1}\), \(k_{2}\) is the rate-constant from the tissue compartment to plasma, and \(\mathrm{BP}\) is the binding potential.

Parameters:

• tac_times_in_minutes (np.ndarray) – The array representing the time-points for both TACs.

• r1 (float) – The ratio of the clearance rate of tracer from plasma to the reference to the transfer rate of the tracer from plasma to the tissue; \(R_{1}\equiv\frac{k_1^\prime}{k_1}\).

• k2 (float) – The rate constant for the transfer of the tracer from tissue compartment to plasma.

• bp (float) – The binding potential of the tracer in the tissue.

• ref_tac_vals (np.ndarray) – The values of the reference TAC.

Returns:

np.ndarray – TAC values calculated using SRTM.

Raises:

AssertionError – If the reference TAC and times are different dimensions.