Module pk1Comp
Expand source code
#!/usr/bin/env python
# coding: utf-8
# In[1]:
# Import commands
from scipy.stats import gamma
import numpy as np
import matplotlib.pyplot as plt
#%matplotlib inline
from scipy.integrate import odeint
import math as math
class pk1Comp:
"""The pk1Comp object is a one compartment PK model that outputs graphs of mass of tracer over time."""
def __init__ (self, numParam = 4, Flow = 1, Vp = 0.1, Visf = 0.5, PS = 0.15):
"""Initializes the model with default parameter values for flow, Vp, Visf, and PS.
Parameters
----------
numParam: int
numParam is the number of parameters you want to optimize for the model. Defaults to 4.
Flow : double
Flow is the flow of plasma through the blood vessel in mL/(mL*min). Defaults to 1.
Vp : double
Vp is the volume of plasma in mL. Defaults to 0.1.
Visf : double
Visf is the volume of interstitial fluid in mL. Defaults to 0.5.
PS : double
PS is the permeability-surface area constant in mL/(g*min). Defaults to 0.15.
"""
# Declare Variables for initial conditions
self.numParam = numParam
self.Flow = Flow
self.Vp = Vp
self.Visf = Visf
self.PS = PS
C0 = 0 # Initial concentration of tracer in plasma
tmax = 10 #Time in seconds
dt = 0.1 #Time step
a = 2. # Alpha for gamma distribution
rv = gamma(a, loc = 2, scale = 0.65) #input function
# Define the time array
time = np.arange(0, tmax + dt, dt)
# Derivative function
def derivs(curr_vals, time):
"""Finds derivatives of ODEs.
Parameters
----------
curr_vals : double[]
curr_vals it he current values of the variables we wish to "update" from the curr_vals list.
time : double[]
time is our time array from 0 to tmax with timestep dt.
Returns
-------
dc_dt : double[]
contains the derivative of concentrations with respect to time.
"""
# Define value of input function Cin
Cin = rv.pdf(time)
# Unpack the current values of the variables we wish to "update" from the curr_vals list
C = curr_vals
# Right-hand side of odes, which are used to computer the derivative
dC_dt = flow*(Cin - C)/Vol
#Cout = C
return dC_dt
def getPlot(self):
"""Plots the solution of the solved ODEs.
Parameters
----------
self : self
Passes variables needed from self.
"""
# Plot the results using the values stored in the solution variable, "sol"
# Plot Cp using the "0" element from the solution
plt.figure(1)
plt.plot(time, rv.pdf(time), color = 'blue', label = 'Input Function')
plt.plot(time, sol[:,0],color="green", label = 'Cout')
# Plot Cisf using the "1" element from the solution
#plt.plot(time, sol[:,1],color="purple", label = 'Cisf')
plt.xlabel('Time [s]')
plt.ylabel('Concentration [mM]')
plt.legend(loc = 'best')
plt.grid()
def main(self):
"""Main function to run and solve ODEs"""
# Store the initial values in a list
init = [C0]
# Solve the odes with odeint
sol = odeint(derivs, init, time)
#Mass_plasma = Vp * sol[:,0] #mass of tracer in plasma
#Mass_isf = Visf * sol[:,1] #mass of tracer in isf
#Tp = Vp/(flow + PS) # mean transit time
#E = 1 - np.exp(-PS/flow) #extraction fraction
#Q = Mass_plasma + Mass_isf
#print('The mean transit time is ' + str(Tp))
#print('The extraction fraction is ' + str(E))
# Plot mass of tracer using the "2" element from the solution
#plt.figure(2)
#plt.plot(time, Mass_plasma,color="red", label = 'Plasma')
# Plot mass of tracer in tissue using the "3" element from the solution
#plt.plot(time, Mass_isf,color="black", label = 'Interstitial Space')
#plt.plot(time, Q, color="blue", label = 'Total mass')
#plt.xlabel('Time [s]')
#plt.ylabel('Mass [mg]')
#plt.legend(loc = 'best')
#plt.grid()
# In[ ]:Classes
class pk1Comp (numParam=4, Flow=1, Vp=0.1, Visf=0.5, PS=0.15)-
The pk1Comp object is a one compartment PK model that outputs graphs of mass of tracer over time.
Initializes the model with default parameter values for flow, Vp, Visf, and PS. Parameters
numParam: int numParam is the number of parameters you want to optimize for the model. Defaults to 4.
Flow : double Flow is the flow of plasma through the blood vessel in mL/(mL*min). Defaults to 1.
Vp : double Vp is the volume of plasma in mL. Defaults to 0.1.
Visf : double Visf is the volume of interstitial fluid in mL. Defaults to 0.5.
PS : double PS is the permeability-surface area constant in mL/(g*min). Defaults to 0.15.
Expand source code
class pk1Comp: """The pk1Comp object is a one compartment PK model that outputs graphs of mass of tracer over time.""" def __init__ (self, numParam = 4, Flow = 1, Vp = 0.1, Visf = 0.5, PS = 0.15): """Initializes the model with default parameter values for flow, Vp, Visf, and PS. Parameters ---------- numParam: int numParam is the number of parameters you want to optimize for the model. Defaults to 4. Flow : double Flow is the flow of plasma through the blood vessel in mL/(mL*min). Defaults to 1. Vp : double Vp is the volume of plasma in mL. Defaults to 0.1. Visf : double Visf is the volume of interstitial fluid in mL. Defaults to 0.5. PS : double PS is the permeability-surface area constant in mL/(g*min). Defaults to 0.15. """ # Declare Variables for initial conditions self.numParam = numParam self.Flow = Flow self.Vp = Vp self.Visf = Visf self.PS = PS C0 = 0 # Initial concentration of tracer in plasma tmax = 10 #Time in seconds dt = 0.1 #Time step a = 2. # Alpha for gamma distribution rv = gamma(a, loc = 2, scale = 0.65) #input function # Define the time array time = np.arange(0, tmax + dt, dt) # Derivative function def derivs(curr_vals, time): """Finds derivatives of ODEs. Parameters ---------- curr_vals : double[] curr_vals it he current values of the variables we wish to "update" from the curr_vals list. time : double[] time is our time array from 0 to tmax with timestep dt. Returns ------- dc_dt : double[] contains the derivative of concentrations with respect to time. """ # Define value of input function Cin Cin = rv.pdf(time) # Unpack the current values of the variables we wish to "update" from the curr_vals list C = curr_vals # Right-hand side of odes, which are used to computer the derivative dC_dt = flow*(Cin - C)/Vol #Cout = C return dC_dt def getPlot(self): """Plots the solution of the solved ODEs. Parameters ---------- self : self Passes variables needed from self. """ # Plot the results using the values stored in the solution variable, "sol" # Plot Cp using the "0" element from the solution plt.figure(1) plt.plot(time, rv.pdf(time), color = 'blue', label = 'Input Function') plt.plot(time, sol[:,0],color="green", label = 'Cout') # Plot Cisf using the "1" element from the solution #plt.plot(time, sol[:,1],color="purple", label = 'Cisf') plt.xlabel('Time [s]') plt.ylabel('Concentration [mM]') plt.legend(loc = 'best') plt.grid() def main(self): """Main function to run and solve ODEs""" # Store the initial values in a list init = [C0] # Solve the odes with odeint sol = odeint(derivs, init, time)Methods
def derivs(curr_vals, time)-
Finds derivatives of ODEs.
Parameters
curr_vals : double[] curr_vals it he current values of the variables we wish to "update" from the curr_vals list.
time : double[] time is our time array from 0 to tmax with timestep dt.
Returns
dc_dt:double[]- contains the derivative of concentrations with respect to time.
Expand source code
def derivs(curr_vals, time): """Finds derivatives of ODEs. Parameters ---------- curr_vals : double[] curr_vals it he current values of the variables we wish to "update" from the curr_vals list. time : double[] time is our time array from 0 to tmax with timestep dt. Returns ------- dc_dt : double[] contains the derivative of concentrations with respect to time. """ # Define value of input function Cin Cin = rv.pdf(time) # Unpack the current values of the variables we wish to "update" from the curr_vals list C = curr_vals # Right-hand side of odes, which are used to computer the derivative dC_dt = flow*(Cin - C)/Vol #Cout = C return dC_dt def getPlot(self)-
Plots the solution of the solved ODEs.
Parameters
self : self Passes variables needed from self.
Expand source code
def getPlot(self): """Plots the solution of the solved ODEs. Parameters ---------- self : self Passes variables needed from self. """ # Plot the results using the values stored in the solution variable, "sol" # Plot Cp using the "0" element from the solution plt.figure(1) plt.plot(time, rv.pdf(time), color = 'blue', label = 'Input Function') plt.plot(time, sol[:,0],color="green", label = 'Cout') # Plot Cisf using the "1" element from the solution #plt.plot(time, sol[:,1],color="purple", label = 'Cisf') plt.xlabel('Time [s]') plt.ylabel('Concentration [mM]') plt.legend(loc = 'best') plt.grid() def main(self)-
Main function to run and solve ODEs
Expand source code
def main(self): """Main function to run and solve ODEs""" # Store the initial values in a list init = [C0] # Solve the odes with odeint sol = odeint(derivs, init, time)