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Commit 3acf51d9 authored by Tu, Ethan's avatar Tu, Ethan
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pk_optimizer/2_Comp_Model_PK.ipynb 0 → 100644
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%% Cell type:code id: tags:
``` python
# Put your code here
# 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
# Derivative function
def derivs(curr_vals, time):
# Unpack the current values of the variables we wish to "update" from the curr_vals list
Cp, Cisf = curr_vals
# Define value of input function Cin
Cin = rv.pdf(time)
# Right-hand side of odes, which are used to computer the derivative
dCp_dt = (flow/Vp)*(Cin - Cp) + (PS/Vp)*(Cisf - Cp)
dCisf_dt = (PS/Visf)*(Cp - Cisf)
return dCp_dt, dCisf_dt
# Declare Variables for initial conditions
flow = 1/60 # Flow into capillary
Vp = 0.05 # Volume of plasma
Visf = 0.15 # Volume of interstitial space
PS = 1/60 # Permeability-Surface area product
Cp0 = 0 # Initial concentration of tracer in plasma
Cisf0 = 0 # Initial concentration of tracer in interstitial space
tmax = 10 #Time in seconds
dt = 0.1 #Time step
a = 2. # Alpha for gamma distribution
rv = gamma(a, loc = 2, scale = 0.55) #input function
# Define the time array
time = np.arange(0, tmax + dt, dt)
# Store the initial values in a list
init = [Cp0, Cisf0]
# 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 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 = 'Cp')
# 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()
# 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()
print('Cp at 10 sec is ' + str(sol[100,0]))
print('Cisf at 10 sec is ' + str(sol[100,1]))
```
%% Output
The mean transit time is 1.5
The extraction fraction is 0.6321205588285577
Cp at 10 sec is 0.023400076577464173
Cisf at 10 sec is 0.038131979959528696
%% Cell type:code id: tags:
``` python
Q[99]
```
%% Output
0.007018384196576239
%% Cell type:code id: tags:
``` python
```
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