The Extended Tofts model

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==================== The Extended Tofts model ====================

Simulating tissue concentrations from extended Tofts model with different settings.

import matplotlib.pyplot as plt

Import necessary packages

import numpy as np
import osipi

Generate Parker AIF with default settings.

# Define time points in units of seconds - in this case we use a time
# resolution of 1 sec and a total duration of 6 minutes.
t = np.arange(0, 6 * 60, 1)

# Create an AIF with default settings
ca = osipi.aif_parker(t)

Plot the tissue concentrations for an extracellular volume fraction of 0.2 and 3 different plasma volumes of 0.05, 0.2 and 0.6

Ktrans = 0.2  # in units of 1/min
ve = 0.2  # volume fraction between 0 and 1
vp = [0.05, 0.2, 0.6]  # volume fraction between 0 and 1
ct = osipi.extended_tofts(t, ca, Ktrans, ve, vp[0])
plt.plot(t, ct, "b-", label=f"vp = {vp[0]}")
ct = osipi.extended_tofts(t, ca, Ktrans, ve, vp[1])
plt.plot(t, ct, "g-", label=f"vp = {vp[1]}")
ct = osipi.extended_tofts(t, ca, Ktrans, ve, vp[2])
plt.plot(t, ct, "m-", label=f"vp = {vp[2]}")
plt.xlabel("Time (sec)")
plt.ylabel("Tissue concentration (mM)")
plt.legend()
plt.show()

plot extended tofts

Comparing different discretization methods for an extracellular volume fraction of 0.2, Ktrans of 0.2 /min and vp of 0.05

ct = osipi.extended_tofts(t, ca, Ktrans, ve, vp[0])  # Defaults to Convolution
plt.plot(t, ct, "b-", label="Convolution")
ct = osipi.extended_tofts(t, ca, Ktrans, ve, vp[0], discretization_method="exp")
plt.plot(t, ct, "g-", label="Exponential Convolution")
plt.title(f"Ktrans = {Ktrans} /min")
plt.xlabel("Time (sec)")
plt.ylabel("Tissue concentration (mM)")
plt.legend()
plt.show()

# Choose the last image as a thumbnail for the gallery
# sphinx_gallery_thumbnail_number = -1