dcmri.relax_tissue#

dcmri.relax_tissue(ca: ndarray, R10: float, r1: float, t=None, dt=1.0, kinetics='2CX', water_exchange='FF', **params)[source]#

Free relaxation rates for a 2-site exchange tissue. For more detail see Exchange tissues.

Note: the free relaxation rates are the relaxation rates of the tissue compartments in the absence of water exchange between them.

Parameters:

  • ca (array-like) – concentration in the blood of the arterial input.

  • R10 (float) – precontrast relaxation rate. The tissue is assumed to be in fast exchange before injection of contrast agent.

  • r1 (float) – contrast agent relaxivity.

  • t (array_like, optional) – the time points in sec of the input function ca. If t is not provided, the time points are assumed to be uniformly spaced with spacing dt. Defaults to None.

  • dt (float, optional) – spacing in seconds between time points for uniformly spaced time points. This parameter is ignored if t is explicity provided. Defaults to 1.0.

  • kinetics (str, optional) – Tracer-kinetic model. Possible values are ‘2CX’, ‘2CU’, ‘HF’, ‘HFU’, ‘NX’, ‘FX’, ‘WV’, ‘U’. Defaults to ‘2CX’.

  • water_exchange (str, optional) – Water exchange regime, Any combination of two of the letters ‘F’, ‘N’, ‘R’ is allowed. Defaults to ‘FF’.

  • params (dict) – values for the parameters of the tissue, specified as keyword parameters. See table Parameters by configuration for more detail on the parameters that are relevant in each regime.

Returns:

relaxation rates

In the fast water exchange limit, the relaxation rates are a 1D array. In all other situations, relaxation rates are a 2D-array with dimensions (k,n), where k is the number of compartments and n is the number of time points in ca.

volume fractions

the volume fractions of the tissue compartments. Returns None in ‘FF’ regime.

water flows

2D array with water exchange rates between tissue compartments. Returns None in ‘FF’ regime.

Return type:

numpy.ndarray

Example

Compare the free relaxation rates without water exchange against relaxation rates in fast exchange:

>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> import dcmri as dc

Generate a population-average input function:

>>> t = np.arange(0, 300, 1.5)
>>> ca = dc.aif_parker(t, BAT=20)

Define constants and model parameters:

>>> R10, r1 = 1/dc.T1(), dc.relaxivity()
>>> pf = {'H':0.5, 'vb':0.05, 'vi':0.3, 'Fb':0.01, 'PS':0.005}
>>> pn = {'H':0.5, 'vb':0.1, 'vi':0.3, 'Fb':0.01, 'PS':0.005}

Calculate tissue relaxation rates without water exchange, and also in the fast exchange limit for comparison:

>>> R1f, _, _ = dc.relax_tissue(ca, R10, r1, t=t, water_exchange='FF', **pf)
>>> R1n, _, _ = dc.relax_tissue(ca, R10, r1, t=t, water_exchange='NN', **pn)

Plot the relaxation rates in the three compartments, and compare against the fast exchange result:

>>> fig, (ax0, ax1) = plt.subplots(1,2,figsize=(12,5))

Plot restricted water exchange in the left panel:

>>> ax0.set_title('Restricted water exchange')
>>> ax0.plot(t/60, R1n[0,:], linestyle='-',
>>>          linewidth=2.0, color='darkred', label='Blood')
>>> ax0.plot(t/60, R1n[1,:], linestyle='-',
>>>          linewidth=2.0, color='darkblue', label='Interstitium')
>>> ax0.plot(t/60, R1n[2,:], linestyle='-',
>>>          linewidth=2.0, color='grey', label='Cells')
>>> ax0.set_xlabel('Time (min)')
>>> ax0.set_ylabel('Compartment relaxation rate (1/sec)')
>>> ax0.legend()

Plot fast water exchange in the right panel:

>>> ax1.set_title('Fast water exchange')
>>> ax1.plot(t/60, R1f, linestyle='-',
>>>          linewidth=2.0, color='black', label='Tissue')
>>> ax1.set_xlabel('Time (min)')
>>> ax1.set_ylabel('Tissue relaxation rate (1/sec)')
>>> ax1.legend()
>>> plt.show()

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

../../_images/dcmri-relax_tissue-1.png