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GIM.py
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# -*- coding: utf-8 -*-
"""
Created on Sun Jul 28 16:20:36 2013
@author: Ari Ramdial
"""
import numpy as np
import scipy as sp
from scipy.optimize import fsolve as solver
from scipy.integrate import ode
import math as math
# Initialze empty array of glucose results
X = np.zeros((1440,1))
def CobelliWrap(x,u,D,p,modelData):
xdot = Cobelli(0,x,u,D,p,modelData)
return xdot.T[0]
def Cobelli(t,x,u,D,p,modelData):
x = x
xdot = np.zeros((12,1))
G_p = x[0]
G_t = x[1]
I_l = x[2]
I_p = x[3]
Q_sto1 = x[4]
Q_sto2 = x[5]
Q_gut = x[6]
I_1 = x[7]
I_d = x[8]
X = x[9]
Y = x[10]
I_po = x[11]
# Constants
V_G = p[0]
k_1 = p[1]
k_2 = p[2]
V_I = p[3]
m_1 = p[4]
m_2 = p[5]
m_4 = p[6]
m_5 = p[7]
m_6 = p[8]
HE_b = p[9]
k_max = p[10]
k_min = p[11]
k_abs = p[12]
k_gri = p[13]
f = p[14]
a = p[15]
b = p[16]
c = p[17]
d = p[18]
k_p1 = p[19]
k_p2 = p[20]
k_p3 = p[21]
k_p4 = p[22]
k_i = p[23]
F_cns = p[24]
V_m0 = p[25]
V_mx = p[26]
K_m0 = p[27]
p_2U = p[28]
K = p[29]
alpha = p[30]
beta = p[31]
gamma = p[32]
k_e1 = p[33]
k_e2 = p[34]
BW = modelData[0]
#------------------------------------------------------------------
#------------------------------------------------TYPE 2 -------------
S = gamma*I_po
S_b =(m_6 - HE_b)/m_5
# Insulin basal state
I_b = 4.4 #basal insulin levels above 60pmol/l is considered insulin resistant.
h = 70 # = G_b = 4.4mmol/l
# Certain useful parameters are defined
HE = -m_5*S + m_6 #0.012243
m_3 = HE*m_1/(1- HE)
#GI Tract
Ra = (f*k_abs*Q_gut)/BW
Q_sto = Q_sto1 + Q_sto2
k_emptQ_sto = k_min +((k_max - k_min)/2)*((math.tanh(a*(Q_sto -b* D)) - math.tanh(c*(Q_sto -d*D))+2))
# Liver
EGP = sp.maximum(2.4, k_p1 - k_p2*G_p - k_p3*I_d - k_p4*I_po )# CHange 0 to 2.01 for test
# Muscle and Adipose Tissue
V_m = V_m0 + V_mx*X
K_m = K_m0
U_id = V_m*G_t/(K_m +G_t)
# Kidneys - Glucose Renal Excretion
if(G_p > k_e2):
E = k_e1*(G_p -k_e2)
else:
E = 0
# Brain - CNS Glucose Utilization
U_ii = F_cns
# Mass balances/ differential equations
xdot[0] = EGP + Ra - U_ii - E - k_1*G_p + k_2*G_t # dG_p
xdot[1] = -U_id + k_1*G_p - k_2*G_t # dG_t
xdot[2] = -(m_1 +m_3 )*I_l + m_2*I_p + S #dI_l
xdot[3] = -(m_2 +m_4 )*I_p + m_1*I_l #+ u #dI_p
G = G_p/V_G #G(t)
I = I_p/V_I
xdot[4] = D*d - k_gri*Q_sto1 #dQ_sto1
xdot[5] = k_gri*Q_sto1 - k_emptQ_sto*Q_sto2 #dQ_sto2
xdot[6] = k_emptQ_sto*Q_sto2 - k_abs*Q_gut #dQ_gut
xdot[7] = -k_i*(I_1 -I) #dI_1
xdot[8] = -k_i*(I_d -I_1 ) #dI_d
xdot[9] = p_2U*(I-I_b )-p_2U*X #dX
if(beta*(G-h) >= -S_b):
xdot[10] = -alpha*(Y-beta*(G-h)) #dY_t
else:
xdot[10] = -alpha*(Y+S_b)
# Pancreas/ Beta -Cell
if(xdot[0]/V_G > 0):
S_po = Y + S_b + K*(xdot[0]/V_G)
else:
S_po = Y + S_b
xdot[11] = S_po - S #dI_po
return xdot
def SimulateCobelliDay(modelData):
# modelData = np.zeros((22,1))
eatingTime = 30 # [min ]
# Data is unpacked
bHour = modelData[1]
bMin = modelData[2]
bCHO = 1000*modelData[3]*18.018 # converted to mg
bInsulin = 6.945*modelData[4]/1000 # converted from IU/L to pmol/L
lHour = modelData[5]
lMin = modelData[6]
lCHO = 1000*modelData[7]*18.018 # converted to mg
lInsulin = 6.945*modelData[8]/1000 # converted to pmol/L
dHour = modelData[9]
dMin = modelData[10]
dCHO = 1000*modelData[11]*18.018 # converted to mg
dInsulin = 6.945*modelData[12]/1000 # converted to pmol/L
insulinTime = modelData[13]
# Initialize the time vector
t = np.zeros((11,1))
# Relevant moments are calculated
t[0] = 0
t[1] = bHour*60 + bMin - insulinTime
t[2] = bHour*60 + bMin
t[3] = bHour*60 + bMin + eatingTime
t[4] = lHour*60 + lMin - insulinTime
t[5] = lHour*60 + lMin
t[6] = lHour*60 + lMin + eatingTime
t[7] = dHour*60 + dMin - insulinTime
t[8] = dHour*60 + dMin
t[9] = dHour*60 + dMin + eatingTime
t[10] = 24*60
V_G = 1.88 #1.49 # [dL/kg]
k_1 = 0.065 #0.042 # [min ^-1]
k_2 = 0.079 #0.071 # [min ^-1]
V_I = 0.05 #0.04 # [L/kg]
m_1 = 0.190 #0.379 # [min ^-1]
m_2 = 0.484 #0.673 # [min ^-1]
m_4 = 0.194 #0.269 # [min ^-1]
m_5 = 0.0304 #0.0526 # [min *kg/pmol ]
m_6 = 0.6471 #0.8118 # [-]
HE_b = 0.6 # [-]
k_max = 0.0558 #0.0465 # [min ^-1]
k_min = 0.0080 #0.0076 # [min ^-1]
k_abs = 0.057 #0.023 # [min ^-1]
k_gri = 0.0558 #0.0465 # [min ^-1]
f = 0.90 # [-]
a = 0.00013 #0.00006 # [mg ^-1]
b = 0.82 #0.68 # [-]
c = 0.00236 #0.00023 # [mg ^-1]
d = 0.010 # 0.09 # [-]
k_p1 = 2.70 #3.09 # [mg/kg/min ]
k_p2 = 0.0021 #0.0007 # [min ^-1]
k_p3 = 0.009 #0.005 # [mg/kg/min per pmol/L]
k_p4 = 0.0618 #0.0786 # [mg/kg/min per pmol/kg]
k_i = 0.0079 #0.0066 # [min ^-1]
F_cns = 1 # [mg/kg/min ]
V_m0 = 2.50 #4.65 # [mg/kg/min ]
V_mx = 0.047 #0.034 # [mg/kg/min per pmol/L]
K_m0 = 225.59 #466.21 # [mg/kg]
p_2U = .0331 #0.084 # [min ^-1]
K = 2.30 #0.99 # [pmol/kg per mg/dL]
alpha = 0.050 #0.013 # [min ^-1]
beta = 0.11 #0.05 # [pmol/kg/min per mg/dL]
gamma = 0.5 # [min ^-1]
k_e1 = 0.0005 #0.0007 # [min ^-1]
k_e2 = 339 #269 # [mg/kg]
p = [V_G ,k_1 ,k_2 , V_I ,m_1 ,m_2 ,m_4 ,m_5 ,m_6 ,HE_b, k_max , k_min , k_abs ,
k_gri,f,a,b,c,d, k_p1,k_p2, k_p3, k_p4,k_i , F_cns , V_m0,V_mx ,K_m0, p_2U,K,
alpha,beta, gamma , k_e1, k_e2]
u = 0 #0.0954119*BW, #7.15
X = []
# Calculate the steady state values
xStart = [90,90,54.18,54.18,0,0,0,4.4,4.4,0,0,0] #zeros(16,1) ,
# (xStart,u,0,p,modelData)
xInitial0 = solver(CobelliWrap,xStart,args=(u,0,p,modelData))
# Midnight to first insulinshot
r = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial0, t[0]).set_f_params(u ,0,p,modelData)
while r.successful() and r.t < t[1]:
r.integrate(r.t+1)
X.append(r.y[0])
# Insulinshot before breakfast
xInitial1 = r.y.T
xInitial1[2] = xInitial1[2] + bInsulin
r1 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial1, t[1]).set_f_params(u ,0,p,modelData)
while r1.successful() and r1.t < t[2]:
r1.integrate(r1.t+1)
X.append(r1.y[0])
# Breakfast start
xInitial2 = r1.y.T
r2 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial2, t[2]).set_f_params(u ,bCHO/(eatingTime),p,modelData)
while r2.successful() and r2.t < t[3]:
r2.integrate(r2.t+1)
X.append(r2.y[0])
# Breakfast stop
xInitial3 = r2.y.T
r3 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial3, t[3]).set_f_params(u ,0,p,modelData)
while r3.successful() and r3.t < t[4]:
r3.integrate(r3.t+1)
X.append(r3.y[0])
# Insulinshot before lunch
xInitial4 = r3.y.T
xInitial4[2] = xInitial4[2] + lInsulin
r4 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial4, t[4]).set_f_params(u ,0,p,modelData)
while r4.successful() and r4.t < t[5]:
r4.integrate(r4.t+1)
X.append(r4.y[0])
# Lunch start
xInitial5 = r4.y.T
r5 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial5, t[5]).set_f_params(u ,lCHO/(eatingTime),p,modelData)
while r5.successful() and r5.t < t[6]:
r5.integrate(r5.t+1)
X.append(r5.y[0])
# Lunch stop
xInitial6 = r5.y.T
r6 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial6, t[6]).set_f_params(u ,0,p,modelData)
while r6.successful() and r6.t < t[7]:
r6.integrate(r6.t+1)
X.append(r6.y[0])
# Insulinshot before dinner
xInitial7 = r6.y.T
xInitial7[2] = xInitial7[2] + dInsulin
r7 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial7, t[7]).set_f_params(u ,0,p,modelData)
while r7.successful() and r7.t < t[8]:
r7.integrate(r7.t+1)
X.append(r7.y[0])
# Dinner start
xInitial8 = r7.y.T
r8 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial8, t[8]).set_f_params(u ,dCHO/(eatingTime),p,modelData)
while r8.successful() and r8.t < t[9]:
r8.integrate(r8.t+1)
X.append(r8.y[0])
# Dinner stop
xInitial9 = r8.y.T
r9 = ode(Cobelli).set_integrator('vode', method='bdf', order=15).set_initial_value(xInitial9, t[9]).set_f_params(u ,0,p,modelData)
while r9.successful() and r9.t < t[10]:
r9.integrate(r9.t+1)
X.append(r9.y[0])
#sys.exit(0)
# Collects all the simulated intervals
G = [x / V_G for x in X]
T = r.t
return (T,G,t)