forked from Le0Meyer/Red_Blood_Cell
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathred_cell.py
More file actions
182 lines (128 loc) · 5.57 KB
/
red_cell.py
File metadata and controls
182 lines (128 loc) · 5.57 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
#premier essai pour le stage
from scipy.integrate import odeint
import numpy as np
import matplotlib.pyplot as plt
def func(y,t,Ht,PhiMaxNa,PLNa,PLK,PGNa,PGK,PGA,F,R,T,kCo,kHA,d,fHb,QHb,QMg,QX,KB) :
# Le vecteur y est égal à (QNa,QK,QA,QH,Vw,CmNa,CmK,CmA,CmH,CmHB,CmB,CmY)
# #QNa,QK,QA,QH,Vw,CmNa,CmK,CmA,CmH,CmHB,CmB,CmY = y
#QNa,QK,QA,QH,Vw,CmNa,CmK,CmA,CmHB,CmB,CmY = y
#QNa,QK,QA,QH,Vw,CmNa,CmK,CmA,CmH,CmHB,CmB,CmY = y
QNa,QK,QA,QH,Vw,CmNa,CmK,CmA,CmHB,CmB,CmY,Q_ = y
# Equation des différents flux
FluxPNa = -PhiMaxNa*(((QNa/Vw)/((QNa/Vw)+0.2*(1+(QK/(Vw*8.3)))))**3) * ((CmK/(CmK + 0.1 * (1 + (CmK/18))))**2)
FluxPK = -FluxPNa/1.5
FluxLNa = -PLNa * ((QNa/Vw) - CmNa)
FluxLK = -PLK * ((QK/Vw) - CmK)
# Equation des flux électro-diffusifs
E = - R*T/F * np.log(( PGNa*QNa/Vw + PGK*QK/Vw + PGA*CmA ) / ( PGNa*CmNa + PGK*CmK + PGA*QA/Vw ))
FluxGNa = -PGNa * FsurRT * E * (QNa/Vw - CmNa * np.exp(- FsurRT * E))/(1 - np.exp(- FsurRT * E))
FluxGK = -PGK * FsurRT * E * (QK/Vw - CmK * np.exp(- FsurRT * E))/(1 - np.exp(- FsurRT * E))
FluxGA = +PGA * FsurRT * E * (QA/Vw - CmA * np.exp(+ FsurRT * E))/(1 - np.exp(+ FsurRT * E))
# Equation ...
FluxCo = -kCo * (((QA/Vw)**2) * (QNa/Vw) * (QK/Vw) - d * (CmA**2) * CmNa * CmK)
# Equation du flux HA
CmH = KB * CmHB / ( CmB - CmHB )
FluxHA = -kHA * (((QA * QH)/(Vw**2))- CmA * CmH)
# Variation des quantités Q
dQNadt = FluxPNa + FluxLNa + FluxGNa + FluxCo
dQKdt = FluxPK + FluxLK + FluxGK + FluxCo
dQAdt = FluxGA + FluxHA + FluxCo
dQHdt = FluxHA
dQ_dt = dQHdt
# Variation du volume intra-cellulaire
#dVwdt = ((CmNa + CmK + CmA + CmB + CmY)*(dQNadt + dQKdt + dQAdt) - (fHb * QHb + QNa + QK + QA + QMg + QX) * (dCmNadt + dCmKdt + dCmAdt + dCmBdt + dCmYdt))/((CmNa + CmK + CmA + CmB + CmY)**2)
#avec formule léna
#dVwdt = ((dQNadt + dQKdt + dQAdt)/(CmNa + CmK + CmA + CmB + CmY))
# Formule avec fHb :
#dVwdt = ( (dQKdt + dQAdt) * ( (CmNa + CmK + CmA + CmB + CmY) + ( (fHb*QHb + QNa + QK + QA + QMg + QX) * (Ht/1-Ht) ) ) ) / ( (CmNa + CmK + CmA + CmB + CmY) * ( (CmNa + CmK + CmA + CmB + CmY) + ( (fHb*QHb + QNa + QK + QA + QMg + QX) * (Ht/1-Ht) ) + (b*(QHb**2)/(Vw**2) ) + (2*c*(QHb**3)/(Vw**3) ) ) )
# ... mais rajouter fHb dans le vecteur !
dVwdt = ((dQKdt + dQAdt)/(CmNa + CmK + CmA + CmB + CmY))
# Variation des concentrations extra-cellulaires Cm
dCmNadt = (Ht/(1 - Ht)) * (dVwdt*CmNa - dQNadt)
dCmKdt = (Ht/(1 - Ht)) * (dVwdt*CmK - dQKdt)
dCmAdt = (Ht/(1 - Ht)) * (dVwdt*CmA - dQAdt)
dCmHBdt = (Ht/(1 - Ht)) * (dVwdt*CmHB - dQHdt)
dCmBdt = (Ht/(1 - Ht)) * (dVwdt*CmB)
# dCmHdt = KB * ((dCmHBdt * CmB - dCmBdt * CmHB)/((CmB-CmHB)**2))
dCmYdt = (Ht/(1 - Ht)) * (dVwdt*CmY)
# Vecteur final dydt issu de y = (QNa,QK,QA,QH,Vw,CmNa,CmK,CmA,CmH,CmHB,CmB,CmY)
# dydt = [dQNadt,dQKdt,dQAdt,dQHdt,dVwdt,dCmNadt,dCmKdt,dCmAdt,dCmHdt,dCmHBdt,dCmBdt,dCmYdt]
dydt = [dQNadt,dQKdt,dQAdt,dQHdt,dVwdt,dCmNadt,dCmKdt,dCmAdt,dCmHBdt,dCmBdt,dCmYdt,dQ_dt]
return dydt
# Valeurs initiales
# On fixe les constantes
Ht = 0.1 # 1
PhiMaxNa= 8.99 # mmol/l*h
F = 96485
E = -0.0086 # V
R = 8.314
T = 310 # K
FsurRT = F / (R * T) # 1/V
d = 1.05 # 1
fHb = 2.78 # 1
QHb = 5 # mmol/l
QMg = 2.5 # mmol/l
QX = 19.2 # mmol/l
KB = 10**-4.55 # mmol/l
Vw0 = 0.7 # 1
# Constante qui varie
PGA = 0.2 # 1/h # 0.2 a 200
# Constantes qui changent d'un cas à l'autre
# Cas 1 : avec fG = 0.1 et mode 'off'
#PLNa = 0.0180 # 1/h
#PLK = 0.0116 # 1/h
#PGNa = 0.0017 # 1/h
#PGK = 0.0015 # 1/h
#kCo = 10**-9 # 1
#kHA = 1 # 1
# Cas 2 : avec fG = 0.9 et mode 'on'
PLNa = 0.0020 # 1/h
PLK = 0.0013 # 1/h
PGNa = 0.0151 # 1/h
PGK = 0.0138 # 1/h
kCo = 10**-6 # 1
kHA = 10**9 # 1
# Vecteur initial
## ( QNa, QK, QA, QH, Vw, CmNa,CmK, CmA,
#y0 = np.array([10 * Vw0, 140 * Vw0, 95 * Vw0, 1000 * 10**(-7.26) * Vw0, Vw0, 140., 5., 131.,
#1000 * 10**(-7.4), 5.86, 10., 10.])
## CmH, CmHB, CmB, CmY)
# ( QNa, QK, QA, QH, Vw, CmNa,CmK, CmA,
#y0 = np.array([10 * Vw0, 140 * Vw0, 95 * Vw0, 1000 * 10**(-7.26) * Vw0, Vw0, 140., 5., 130.9,
#5.86, 10., 10.])
# CmHB, CmB, CmY)
## CmH, CmHB, CmB, CmY)
# ( QNa, QK, QA, QH, Vw, CmNa,CmK, CmA,
y0 = np.array([10 * Vw0, 140 * Vw0, 95 * Vw0, 1000 * 10**(-7.26) * Vw0, Vw0, 140., 5., 5.,
5.86, 10., 135.9, 38.5])
# CmHB, CmB, CmY, Q_)
t = np.linspace(0.,1.,1001)
sol = odeint(func, y0, t, args=(Ht,PhiMaxNa,PLNa,PLK,PGNa,PGK,PGA,F,R,T,kCo,kHA,d,fHb,QHb,QMg,QX,KB))
E = - R*T/F * np.log(( PGNa*sol[:,0]/sol[:,4] + PGK*sol[:,1]/sol[:,4] + PGA*sol[:,7] ) / ( PGNa*sol[:,5] + PGK*sol[:,6] + PGA*sol[:,2]/sol[:,4] ))
plt.figure()
plt.subplot(2, 2, 1)
#plt.plot(t, sol[:,0] , 'green', label='QNa')
#plt.plot(t, sol[:,1] , 'black', label='QK')
plt.plot(t, sol[:,2] , label='QA')
#plt.plot(t, sol[:,4] , label='Vw')
#plt.plot(t, sol[:,8] , label='CmHB')
#plt.plot(t, sol[:,9] , label='CmB')
#plt.plot(t, sol[:,11] , label='Q_')
plt.plot(t,E,label='E')
plt.legend(loc='best')
plt.grid()
plt.subplot(2, 2, 2)
plt.plot(t, - np.log10(sol[:,3]/(1000*sol[:,4])), label='pHc') # pHc = - log10(QH/(1000*Vw))
plt.plot(t, 6.85 + (sol[:,11] + 18) / (-10 * 5), label='pHcT')
plt.plot(t, - np.log10(KB *0.001* sol[:,8] / ( sol[:,9] - sol[:,8] )), label='pHm')
plt.legend(loc='best')
plt.grid()
plt.subplot(2, 2, 3)
plt.plot(t, sol[:,4]/Vw0, label ='V/V0')
plt.legend(loc='best')
plt.grid()
plt.subplot(2,2,4)
plt.plot(t,1 + 0.0645 * (5/sol[:,4]) + 0.026 * (5/sol[:,4])**2, label='fHb')
plt.legend(loc='best')
plt.grid()
plt.show()