Tac Interpolation

This module provides classes for time-activity curve (TAC) interpolation for Positron Emission Tomography (PET) data. It enables the resampling of data evenly with respect to time, which is particularly useful when performing convolutions with respect to time. We use scipy.interpolate.interp1d for the interpolation.

The module comprises two classes: EvenlyInterpolate and EvenlyInterpolateWithMax.

The EvenlyInterpolate class takes in TAC times and values and a specified delta time, \(\Delta t\), to resample data by interpolating TACs evenly with respect to time.

The EvenlyInterpolateWithMax class extends the functionality of EvenlyInterpolate by modifying the calculation of delta time, \(\Delta t\), to explicitly sample the maximum value of the TAC.

Example

In the proceeding example, we shall use the two classes to resample a fake TAC. For better visualization, we shall plot the resampled TACs shifted in the y-direction.

import numpy as np
from petpal.kinetic_modeling.tac_interpolation import EvenlyInterpolate, EvenlyInterpolateWithMax
import matplotlib.pyplot as plt

# define some dummy TAC times and values
tac_times_in_minutes = np.array([0., 1., 2.5, 4.1, 7., 15.0])
tac_values = np.array([0., 0.8, 2., 1.5, 0.6, 0.0])

# instantiate EvenlyInterpolate object and resample TAC (and add shift for better visualization)
even_interp = EvenlyInterpolate(tac_times=tac_times_in_minutes, tac_values=tac_values+0.25, delta_time=1.0)
resampled_tac = even_interp.get_resampled_tac()

# instantiate EvenlyInterpolateWithMax object and resample TAC (and add shift for better visualization)
even_interp_max = EvenlyInterpolateWithMax(tac_times=tac_times_in_minutes, tac_values=tac_values+0.5, samples_before_max=3)
resampled_tac_max = even_interp_max.get_resampled_tac()

# plot the TAC and the resampled TACs
fig, ax = plt.subplots(1,1, constrained_layout=True, figsize=(8,4))
plt.plot(tac_times_in_minutes, tac_values, 'ko--', label='Raw TAC', zorder=2)
plt.plot(*resampled_tac, 'ro-', label='Evenly Resampled TAC', zorder=1)
plt.plot(*resampled_tac_max, 'bo-', label='Evenly Resampled TAC w/ Max', zorder=0)
ax.text(s='resampled TACS are \nshifted for visual clarity',
        x=0.95, y=0.95, ha='right', va='top', transform=ax.transAxes, fontsize=16)
plt.xlabel('Time (s)', fontsize=16)
plt.ylabel('TAC Value', fontsize=16)
plt.legend(bbox_to_anchor=(1.0, 0.5), loc='center left')
plt.show()

(Source code, png, hires.png, pdf)

Evenly interpolating TACs can sometimes miss the maximum value of the provided TAC given the time-step. Therefore, we can explicitly include the maximum value by modifying the time-step.

Note

This module utilises scipy.interpolate.interp1d for linear interpolation. Ensure Scipy is installed for this package to function.

Todo

• Test if the classes work correctly if the max value of the TAC is at the first or last time-point.

Classes

EvenlyInterpolate	A class for basic evenly interpolating TACs with respect to time
EvenlyInterpolateWithMax	A class, extends EvenlyInterpolate, and modifies the \(\Delta t\) calculation such that the