-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathlpm.py
189 lines (152 loc) · 10 KB
/
lpm.py
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
183
184
185
186
187
188
189
"""
Lumped parameter model of cardiovascular system.
This is the main code for the modeling.
It computes pressures/flows from a systems of ODEs.
First, it calculates the initiate values of each compartment (pressure, volume)
Then, it calculates the pressure derivative and volume derivative (by calculating the flow in a first place)
Finally, it resolves the system of equations.
"""
import jax
import jax.numpy as jnp
from jax import jit
import diffrax
import state_eq
def model_solve(timeTree, paramsModel, cardiacCyc, P0, V0, ECMO, CRRT, LVAD):
""" Manages the solving of the model system equations.
It first gets the initial values (volume, pressure) of each compartment from model_init()
It then gets the pressure and volume differential from model_ODE.
Finally it launches the solving and calculates the solution.
Args:
Every input parameters come from the initTree
- timeTree: dict() -> time tree
- paramsModel: dict() -> parameters of the lpm
- cardiacCyc: dict() -> parameters of the current cardiac cycle
- V0: dict() -> initial volumes of the model
- ECMO: dict() -> extracorporeal circuit ECMO properties
- CRRT: dict() -> extracorporeal circuit CRRT properties
Returns:
The solution of the model.
To access the pressures and flows from model_main:
- solutionODE.ys[0]=dict() of pressures
- solutionODE.ys[1]=dict() of volumes
- solutionODE.ys[2]=dict() of flows
"""
initialVolumes={'Vra': V0['Vra'], 'Vrv': V0['Vrv'], 'Vla': V0['Vla'], 'Vlv': V0['Vlv']}
initialFlows={'Qao': 0, 'Qsart': 0, 'Qpas': 0, 'Qpart': 0,
'Qecmotudp': 0, 'Qecmotupo': 0, 'Qecmotuor': 0,
'Qcrrttuin': 0, 'Qcrrttupf': 0, 'Qcrrttuout': 0,
'Qlvadpump': 0}
initialQuantities=[P0, initialVolumes, dict(sorted(initialFlows.items()))]
sol = diffrax.diffeqsolve(terms=diffrax.ODETerm(model_ODE),
solver=diffrax.Dopri8(),
t0=timeTree['tSet']['tmin'], t1=timeTree['tSet']['tmax'],
dt0=timeTree['tSet']['h'],
y0=initialQuantities,
stepsize_controller=diffrax.PIDController(rtol=1e-6, atol=1e-8, dtmin=1e-5, pcoeff=0.1, icoeff=1.0, dcoeff=0),
args=[paramsModel, cardiacCyc, ECMO, CRRT, LVAD],
max_steps = 16**7,
saveat=diffrax.SaveAt(ts=timeTree['T']),
)
return sol
def model_ODE(t, y, args):
""" Calculates the differential (dP_i/dt and dV_i/dt) of the quantities (pressures and volumes).
CVS + Lungs mechanics
Args:
- t: [array] -> time of computation
- y: list(dict()) -> pressures and volumes (quantities of the model)
- args: list() -> arguments sent from the model_solve()
Returns:
[dict(), dict()] -> Pressures and volumes differential which is an input of the ODE solver.
"""
paramsModel = args[0]
cardiacCyc = args[1]
ECMO=args[2]
CRRT=args[3]
LVAD=args[4]
###### Calculate atrial and ventricular activity #######
ea=state_eq.act_atrium(t,cardiacCyc['Tcyc'],cardiacCyc['Tpwb_atr'],cardiacCyc['Tpww_atr'])
ev=state_eq.act_ventricle(t,cardiacCyc['Tcyc'],cardiacCyc['Ts1_ven'],cardiacCyc['Ts2_ven'])
###### Calculate flows in each compartment #######
# Aorta + Systemic vessels
dQao=(y[0]['Pao']-y[0]['Psart']-paramsModel['Rao']*y[2]['Qao'])/paramsModel['Lao']
dQsart=(y[0]['Psart']-y[0]['Psvn']-(paramsModel['Rsart']+paramsModel['Rmc'])*y[2]['Qsart'])/paramsModel['Lsart']
Qsvn=state_eq.Q(y[0]['Psvn'],y[0]['Pra'],paramsModel['Rsvn'])
# Right heart
Qra=state_eq.Q_valves(y[0]['Pra'], y[0]['Prv'], paramsModel['CQtri'])
Qrv=state_eq.Q_valves(y[0]['Prv'], y[0]['Ppas'], paramsModel['CQpa'])
# Pulmonary circulation
dQpas=(y[0]['Ppas']-y[0]['Ppart']-paramsModel['Rpas']*y[2]['Qpas'])/paramsModel['Lpas']
dQpart=(y[0]['Ppart']-y[0]['Ppvn']-(paramsModel['Rpart']+paramsModel['Rpmc'])*y[2]['Qpart'])/paramsModel['Lpart']
Qpvn=state_eq.Q(y[0]['Ppvn'], y[0]['Pla'], paramsModel['Rpvn'])
# Left heart
Qla=state_eq.Q_valves(y[0]['Pla'], y[0]['Plv'], paramsModel['CQmi'])
Qlv=state_eq.Q_valves(y[0]['Plv'], y[0]['Pao'], paramsModel['CQao'])
# Extracorporeal circuits
Qecmodrain, dQecmotudp, Qecmopump, dQecmotupo, Qecmooxy, dQecmotuor, Qecmoreturn= jnp.where(
jnp.equal(ECMO['status'], 0.0), 0.,
state_eq.Q_ECMO(y, paramsModel, ECMO))
dQlvadpump = jnp.where(
jnp.equal(LVAD['status'], 0.0), 0.,
state_eq.Q_LVAD(y, LVAD))
dQcrrttuin, Qcrrtpump, dQcrrttupf, Qcrrtfil, dQcrrttuout = jnp.where(
jnp.equal(CRRT['status'], 0.0), 0.,
state_eq.Q_CRRT(y, paramsModel, CRRT))
###### Build system of ODEs (dP/dt and dV/dt) #######
# Get the access and the flows of extracorporeal circuits to connect them to the CVS
access={'ECMO': ECMO['access'], 'CRRT': CRRT['access'], 'LVAD': LVAD['access']}
flows={'ECMO': {'drain': Qecmodrain, 'return': Qecmoreturn},
'CRRT': {'drain': y[2]['Qcrrttuin'], 'return': y[2]['Qcrrttuout']},
'LVAD': {'drain': y[2]['Qlvadpump'], 'return': y[2]['Qlvadpump']}}
### ---------------------- Cardiovascular system -----------------------###
# Vessels
dPao=state_eq.dP('ao', Qlv, y[2]['Qao'], paramsModel['Cao'], access, flows) # Circ0: Aorta
dPsart=state_eq.dP('sart', y[2]['Qao'], y[2]['Qsart'], paramsModel['Csart'], access, flows) # Circ1: Syst. Art.
dPsvn=state_eq.dP('svn', y[2]['Qsart'], Qsvn, paramsModel['Csvn'], access, flows) # Circ2: Syst. Ven.
# New dP for pulmonary
dPpas=state_eq.dP('pas', Qrv, y[2]['Qpas'],paramsModel['Cpas'], access, flows)
dPpart=state_eq.dP('part', y[2]['Qpas'], y[2]['Qpart'],paramsModel['Cpart'], access, flows)
dPpvn=state_eq.dP('pvn', y[2]['Qpart'], Qpvn, paramsModel['Cpvn'], access, flows)
# End Vessels
# Heart cavities
dPla=(state_eq.P_atrium(ea,paramsModel['Emaxla'],
paramsModel['Edla'],y[1]['Vla'])-y[0]['Pla'])/8E-5 # Left heart: Left Atrium P
dPlv=(state_eq.P_ventricle(ev,paramsModel['Emaxlv'],
paramsModel['LV_Pd_beta'],paramsModel['LV_Pd_kappa'],
paramsModel['LV_Pd_alpha'],y[1]['Vlv'])-y[0]['Plv'])/8E-5 # Left heart: Left Ventricle P
dPra = (state_eq.P_atrium(ea,paramsModel['Emaxra'],
paramsModel['Edra'],y[1]['Vra'])-y[0]['Pra'])/8E-5 # Right heart: Right Atrium P
dPrv = (state_eq.P_ventricle(ev,paramsModel['Emaxrv'],
paramsModel['RV_Pd_beta'],paramsModel['RV_Pd_kappa'],
paramsModel['RV_Pd_alpha'],y[1]['Vrv'])-y[0]['Prv'])/8E-5 # Right heart: Right Ventricle P
dVla=state_eq.dV('la', Qpvn, Qla, access, flows) # Left heart: Left Atrium V
dVlv=state_eq.dV('lv', Qla, Qlv, access, flows) # Left heart: Left Ventricle V
dVra=state_eq.dV('ra', Qsvn, Qra, access, flows) # Right heart: Right Atrium V
dVrv=state_eq.dV('rv', Qra, Qrv, access, flows) # Right heart: Right Ventricle V
# End Heart cavities
### ---------------------- End Cardiovascular System ----------------------###
### ---------------------- Extracorporeal Circuits ------------------------###
# ECMO
dPecmodrain=state_eq.dP('ecmodrain', Qecmodrain, y[2]['Qecmotudp'], paramsModel['Cecmodrain'], access, flows) # ECMO: Drain cannula
dPecmotudp=state_eq.dP('ecmotudp', y[2]['Qecmotudp'], Qecmopump, paramsModel['Cecmotudp'], access, flows) # ECMO: Tubing Drain-Pump
dPecmotupo=state_eq.dP('ecmotupo', Qecmopump, y[2]['Qecmotupo'], paramsModel['Cecmotupo'], access, flows) # ECMO: Tubing Pump-Oxy
dPecmooxy=state_eq.dP('ecmooxy', y[2]['Qecmotupo'], Qecmooxy, paramsModel['Cecmooxy'], access, flows) # ECMO: Oxygenator
dPecmotuor=state_eq.dP('ecmotuor', Qecmooxy, y[2]['Qecmotuor'], paramsModel['Cecmotuor'], access, flows) # ECMO: Tubing Oxy-Return
dPecmoreturn=state_eq.dP('ecmoreturn', y[2]['Qecmotuor'], Qecmoreturn, paramsModel['Cecmoreturn'], access, flows) # ECMO: Return cannula
# ECMO end ##
# CRRT
dPcrrttuin=state_eq.dP('crrttuin', y[2]['Qcrrttuin'], Qcrrtpump, paramsModel['Ccrrttuin'], access, flows) # CRRT: Drain tube/Tube in
dPcrrttupf=state_eq.dP('crrttupf', Qcrrtpump, y[2]['Qcrrttupf'], paramsModel['Ccrrttupf'], access, flows) # CRRT: Tubing pump/filter
dPcrrtfil=state_eq.dP('crrtfil', y[2]['Qcrrttupf'], Qcrrtfil, paramsModel['Ccrrtfil'], access, flows) # CRRT: Filter
dPcrrttuout=state_eq.dP('crrttuout', Qcrrtfil, y[2]['Qcrrttuout'], paramsModel['Ccrrttuout'], access, flows) # CRRT: Return tube/Tube out
# CRRT end ##
### ---------------------- End Extracorporeal Circuits ---------------------###
dtPressures = {'Pao': dPao, 'Psart': dPsart, 'Psvn': dPsvn, 'Ppas': dPpas, 'Ppart': dPpart, 'Ppvn': dPpvn,
'Pecmodrain': dPecmodrain, 'Pecmotudp': dPecmotudp,'Pecmotupo': dPecmotupo, 'Pecmooxy': dPecmooxy, 'Pecmotuor': dPecmotuor, 'Pecmoreturn': dPecmoreturn,
'Pcrrttuin': dPcrrttuin, 'Pcrrttupf': dPcrrttupf,'Pcrrtfil': dPcrrtfil, 'Pcrrttuout' : dPcrrttuout,
'Pra': dPra, 'Prv': dPrv, 'Pla': dPla, 'Plv': dPlv}
dtVolumes = {'Vra': dVra, 'Vrv': dVrv, 'Vla': dVla, 'Vlv': dVlv}
dtFlows={'Qao': dQao, 'Qsart': dQsart, 'Qpas': dQpas, 'Qpart': dQpart,
'Qecmotudp': dQecmotudp, 'Qecmotupo': dQecmotupo, 'Qecmotuor': dQecmotuor,
'Qcrrttuin': dQcrrttuin, 'Qcrrttupf': dQcrrttupf, 'Qcrrttuout': dQcrrttuout,
'Qlvadpump': dQlvadpump}
return [dtPressures, dtVolumes, dtFlows]