_calc_simplified_frtm_tac

petpal.kinetic_modeling.reference_tissue_models._calc_simplified_frtm_tac(tac_times_in_minutes: numpy.ndarray, ref_tac_vals: numpy.ndarray, r1: float, a1: float, a2: float, alpha_1: float, alpha_2: float) → numpy.ndarray

Calculate the Time Activity Curve (TAC) for the Full Reference Tissue Model (FRTM) given the reference TAC and simplified coefficients. The coefficients can be generated from kinetic constants using _calc_frtm_params_from_kinetic_params()

Important

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

We use a more compact form for the FRTM:

\[C(t) = R_{1}C_\mathrm{R}(t) + \left[ A_{1}e^{-\alpha_{1}t} + A_{2}e^{-\alpha_{2}t} \right] \otimes C_\mathrm{R}(t),\]

where \(R_{1}\equiv\frac{k_1^\prime}{k_1}\), and \(A_{1},\,A_{2},\,\alpha_1,\,\alpha_2\) can be calculated from the underlying kinetic constants. See _calc_frtm_params_from_kinetic_params() for more details about the parameter calculation.

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; \(R_{1}\equiv\frac{k_1^\prime}{k_1}\).

• a1 (float) – Coefficient of the first exponential term.

• a2 (float) – Coefficient of the second exponential term.

• alpha_1 (float) – Coefficient inside the first exponential.

• alpha_2 (float) – Coefficient inside the second exponential.

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

Returns:

np.ndarray – TAC values calculated using FRTM.

Raises:

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