fit_mrtm2_2003_to_tac#

petpal.kinetic_modeling.reference_tissue_models.fit_mrtm2_2003_to_tac(tac_times_in_minutes: numpy.ndarray, tgt_tac_vals: numpy.ndarray, ref_tac_vals: numpy.ndarray, t_thresh_in_mins: float, k2_prime: float, weights: numpy.ndarray = None)#

Fit the second version of Multilinear Reference Tissue Model (MRTM2) to the provided target Time Activity Curve (TAC) values given the reference TAC, times, threshold time (in minutes), and k2_prime. The data are fit for all values beyond the threshold. We assume that the target TAC and reference TAC are sampled at the same times.

Important

This function assumes that both TACs are sampled at the same time, and that the time is in minutes.

We have the following multilinear regression:

\[C(T) = -\frac{V}{V^{\prime}b}\left(\int_{0}^{T}C^{\prime}(t)\mathrm{d}t -\frac{1}{k_{2}^{\prime}}C^{\prime}(T) \right) + \frac{1}{b} \int_{0}^{T}C(t)\mathrm{d}t\]
Parameters:

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

  • tgt_tac_vals (np.ndarray) – Target TAC values to fit the MRTM2.

  • ref_tac_vals (np.ndarray) – Reference TAC values.

  • t_thresh_in_mins (float) – Threshold time in minutes.

  • k2_prime (float) – Kinetic parameter: washout rate for the reference region.

  • weights (np.ndarray) – Weights applied to each frame. Default None.

Returns:

np.ndarray –

Array containing fit results. (\(-\frac{V}{V^{\prime}b}\),

\(\frac{1}{b}\))

Note

This function is implemented with numba for improved performance.

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