import numpy as np
import dcmri.pk as pk
import dcmri.lib as lib
[docs]
def aif_tristan(
t: np.ndarray,
agent='gadoterate',
dose=0.2,
rate=3,
BAT=0,
weight=73,
CO=97,
E=0.07,
Thl=13,
Dhl=0.5,
Tp=25,
Te=350,
Ee=0.18,
dtol=0.01,
) -> np.ndarray:
"""Arterial input function with default parameters for young healthy
volunteers.
This AIF was measured in the TRISTAN project (Min et al 2024). The default
values are for young healthy volunteers but since the AIF is built on a
whole-body model of the circulation, they can be modified to generate
virtual populations.
Reference:
Thazin Min, Marta Tibiletti, Paul Hockings, Aleksandra Galetin,
Ebony Gunwhy, Gerry Kenna, Nicola Melillo, Geoff JM Parker,
Gunnar Schuetz, Daniel Scotcher, John Waterton, Ian Rowe, and
Steven Sourbron. *Measurement of liver function with dynamic
gadoxetate-enhanced MRI: a validation study in healthy volunteers*.
Proc Intl Soc Mag Reson Med, Singapore 2024.
Args:
t (np.ndarray): Array of time points
agent (str, optional): Contrast agent generic name. Defaults to
'gadoterate'.
dose (float, optional): Contrast agent dose in mL/kg. Defaults to 0.2.
rate (float, optional): Contrast agent injection rate in mL/sec.
Defaults to 3.
BAT (float, optional): Bolus arrival time in sec. Defaults to 0.
weight (float, optional): Subject weight in kg. Defaults to 73.
CO (float, optional): Cardiac output in mL/sec. Defaults to 97.
E (float, optional): Body extraction fraction. Defaults to 0.07.
Thl (float, optional): Mean transit time of the heart-lung system in
sec. Defaults to 13.
Dhl (float, optional): Transit time dispersion of the heart-lung
system. Defaults to 0.5.
Tp (float, optional): Plasma mean transit time in sec of the other
organs. Defaults to 25.
Te (float, optional): Extravascular mean transit time in sec.
Defaults to 350.
Ee (float, optional): Extraction fraction into the extravascular
space. Defaults to 0.18.
dtol (float, optional): Dose tolerance. Defaults to 0.01.
Returns:
np.ndarray: Aorta concentrations in mmol/mL.
Example:
Generate AIFs with different levels of cardiac output:
.. plot::
:include-source:
import matplotlib.pyplot as plt
import dcmri as dc
# Time points in sec
t = np.arange(0, 180, 2.0)
# Plot aifs with different levels of cardiac output, including the
# default of 100mL/sec.
plt.plot(t/60, 1000*dc.aif_tristan(t, BAT=30), 'r-', label='AIF (default)')
plt.plot(t/60, 1000*dc.aif_tristan(t, BAT=30, CO=150), 'g-',
label='AIF (increased cardiac output)')
plt.plot(t/60, 1000*dc.aif_tristan(t, BAT=30, CO=75), 'b-',
label='AIF (reduced cardiac output)')
plt.xlabel('Time (min)')
plt.ylabel('Concentration (mmol/mL)')
plt.legend()
plt.show()
"""
conc = lib.ca_conc(agent)
Ji = lib.ca_injection(t, weight,conc, dose, rate, BAT)
Jb = flux_aorta(Ji, t, E=E,
heartlung=['chain', (Thl, Dhl)],
organs=['2cxm', ([Tp, Te], Ee)],
tol=dtol)
return Jb/CO
[docs]
def flux_aorta(J_vena: np.ndarray,
t=None, dt=1.0, E=0.1, FFkl=0.0, FFk=0.5,
heartlung=['pfcomp', (10, 0.2)],
organs=['2cxm', ([20, 120], 0.15)],
kidneys=['comp', (10,)],
liver=['pfcomp', (10, 0.2)],
tol=0.001):
"""Whole-body model for indicator flux through the aorta.
See section :ref:`whole-body-tissues` for a more detailed description of
this model.
Args:
J_vena (np.ndarray): Indicator influx (mmol/sec) into the veins.
t (np.ndarray, optional): Array of time points (sec), must be of
equal size as J_vena. If not provided, the time points are uniformly
sampled with interval dt. Defaults to None.
dt (float, optional): Sampling interval in sec. Defaults to 1.0.
E (float, optional): Body extraction fraction. Defaults to 0.1.
FFkl (float, optional): Fraction of the cardiac output that passes
through kidney and liver. Set FFkl=0 for a whole body model without
explicit kidney and liver spaces. Defaults to 0.0.
FFk (float, optional): Kidney fraction of the flow to kidney and liver.
With FFk=0, only the liver is modelled. With FFk=1, only the kidneys
are modelled. Defaults to 0.5.
heartlung (list): 3-element list specifying the model to use for the
heart-lung system (see notes for detail).
organs (list): 3-element list specifying the model to use for the
organs (see notes for detail).
kidneys (list): 3-element list specifying the model to use for the
kidneys (see notes for detail). This keyword is ignored if FFkl=0
or FFk=0.
liver (list): 3-element list specifying the model to use for the
liver (see notes for detail). This keyword is ignored if FFkl=0
or FFk=1.
tol (float, optional): Dose tolerance in the solution. The solution
propagates the input through the system, until the dose that is
left in the system is given by tol*dose0, where dose0 is the
initial dose. Defaults to 0.001.
Returns:
tuple: Indicator fluxes (mmol/sec) through the vena cava and aorta.
Notes:
The lists specifying each organ system consist of 3 elements: the
model (str), its parameters (tuple) and any keyword parameters (dict).
Any of the basic pharmacokinetic blocks can be used. For instance,
*chain*, *plug-flow compartment*, and *compartment* would be specified
as follows:
- **chain**: ['chain', (Thl, Dhl), {'solver':'step'}]
- **plug-flow compartment**: ['pfcomp', (Thl, Dhl), {'solver':'interp'}}
- **compartment**: ['comp', Thl]
- **2cxm**: ['2cxm', ([To, Te], Eo)]
Example:
Generate flux through aorta:
.. plot::
:include-source:
import matplotlib.pyplot as plt
import dcmri as dc
# Generate a stepwise injection:
t = np.arange(0, 120, 2.0)
Ji = dc.ca_injection(t, 70, 0.5, 0.2, 3, 30)
# Calculate the fluxes in mmol/sec:
Ja = dc.flux_aorta(Ji, t)
# Plot the fluxes:
plt.plot(t/60, Ja, 'r-', label='Aorta')
plt.xlabel('Time (min)')
plt.ylabel('Indicator flux (mmol/sec)')
plt.legend()
plt.show()
"""
dose = np.trapezoid(J_vena, x=t, dx=dt)
min_dose = tol*dose
# Residuals of each pathway
Rk = FFk*FFkl*(1-E)
Rl = (1-FFk)*FFkl*(1-E)
Ro = (1-FFkl)*(1-E)
# Initialize output
J_aorta_total = np.zeros(J_vena.size)
while dose > min_dose:
# Aorta flux of the current pass
J_aorta = pk.flux(
J_vena, *heartlung[1], t=t, dt=dt, model=heartlung[0])
# Add to the total aorta flux
J_aorta_total += J_aorta
# Venous flux of the current pass
J_vena = Ro * pk.flux(
J_aorta, *organs[1], t=t, dt=dt, model=organs[0])
if Rl > 0:
J_vena += Rl * pk.flux(
J_aorta, *liver[1], t=t, dt=dt, model=liver[0])
if Rk > 0:
J_vena += Rk * pk.flux(
J_aorta, *kidneys[1], t=t, dt=dt, model=kidneys[0])
# Get residual dose in current pass
dose = np.trapezoid(J_vena, x=t, dx=dt)
return J_aorta_total
