Regazzoni 2020 with a bleeding event

Regazzoni 2020 with a bleeding event#

In this example we will use the 0D model from [RSA+22] to simulate the cardiac cycle with a bleeding event. We use the Zenker model to find the heart rate for normal conditions and then we simulate a bleeding event and compute the new heart rate. Simularly we also adjust the systemic resistance and the contractility of the heart chambers to simulate the effects of bleeding.

from circulation.log import setup_logging
from circulation.regazzoni2020 import Regazzoni2020
from circulation.zenker import Zenker
import matplotlib.pyplot as plt
setup_logging()
# Run first Zenker to get the correct heart rate for normal conditions
zenker_normal = Zenker()
zenker_normal.solve(T=100.0, dt=1e-3, dt_eval=0.1)
history_zenker_normal = zenker_normal.history
HR_normal = history_zenker_normal["fHR"][-1]
R_TPR_normal = history_zenker_normal["R_TPR"][-1]
C_PRSW_normal = history_zenker_normal["C_PRSW"][-1]

[12/09/25 10:36:13] INFO     INFO:circulation.base:                                                                                                                                          base.py:134
                                           Circulation model parameters (Zenker)                                                                                                                        
                             ┏━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓                                                                                                          
                             ┃ Parameter        ┃ Value                                      ┃                                                                                                          
                             ┡━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩                                                                                                          
                             │ kE_LV            │ 0.066 / milliliter                         │                                                                                                          
                             │ V_ED0            │ 7.14 milliliter                            │                                                                                                          
                             │ P0_LV            │ 2.03 millimeter_Hg                         │                                                                                                          
                             │ tau_Baro         │ 20.0 second                                │                                                                                                          
                             │ k_width          │ 0.1838 / millimeter_Hg                     │                                                                                                          
                             │ Pa_set           │ 70.0 millimeter_Hg                         │                                                                                                          
                             │ Ca               │ 4.0 milliliter / millimeter_Hg             │                                                                                                          
                             │ Cv               │ 111.11 milliliter / millimeter_Hg          │                                                                                                          
                             │ Va0              │ 700 milliliter                             │                                                                                                          
                             │ Vv0_min          │ 2700 milliliter                            │                                                                                                          
                             │ Vv0_max          │ 3100 milliliter                            │                                                                                                          
                             │ R_TPR_min        │ 0.5335 millimeter_Hg * second / milliliter │                                                                                                          
                             │ R_TPR_max        │ 2.134 millimeter_Hg * second / milliliter  │                                                                                                          
                             │ T_sys            │ 0.26666666666666666 second                 │                                                                                                          
                             │ f_HR_min         │ 0.6666666666666666 / second                │                                                                                                          
                             │ f_HR_max         │ 3.0 / second                               │                                                                                                          
                             │ R_valve          │ 0.0025 millimeter_Hg * second / milliliter │                                                                                                          
                             │ C_PRSW_min       │ 25.9 millimeter_Hg                         │                                                                                                          
                             │ C_PRSW_max       │ 103.8 millimeter_Hg                        │                                                                                                          
                             │ start_withdrawal │ 0.0 second                                 │                                                                                                          
                             │ end_withdrawal   │ 0.0 second                                 │                                                                                                          
                             │ start_infusion   │ 0.0 second                                 │                                                                                                          
                             │ end_infusion     │ 0.0 second                                 │                                                                                                          
                             │ flow_withdrawal  │ 0.0 milliliter / second                    │                                                                                                          
                             │ flow_infusion    │ 0.0 milliliter / second                    │                                                                                                          
                             └──────────────────┴────────────────────────────────────────────┘                                                                                                          

                    INFO     INFO:circulation.base:                                                                                                                                          base.py:141
                             Circulation model initial states (Zenker)                                                                                                                                  
                             ┏━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓                                                                                                                                  
                             ┃ State ┃ Value                         ┃                                                                                                                                  
                             ┡━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩                                                                                                                                  
                             │ V_ES  │ 14.288 milliliter             │                                                                                                                                  
                             │ V_ED  │ 21.432000000000002 milliliter │                                                                                                                                  
                             │ S     │ 0.5 dimensionless             │                                                                                                                                  
                             │ Va    │ 938.1944444444443 milliliter  │                                                                                                                                  
                             │ Vv    │ 3886.805555555555 milliliter  │                                                                                                                                  
                             └───────┴───────────────────────────────┘                                                                                                                                  
                    INFO     INFO:circulation.base:Running circulation model                                                                                                                 base.py:333
                    INFO     INFO:circulation.base:Solving beat 0                                                                                                                            base.py:358
[12/09/25 10:36:16] INFO     INFO:circulation.base:Done running circulation model in 2.91 s                                                                                                  base.py:442
print(f"HR_normal = {HR_normal}, R_TPR_normal = {R_TPR_normal}, C_PRSW_normal = {C_PRSW_normal}")
HR_normal = 1.839239834801396, R_TPR_normal = 1.3378014381141288, C_PRSW_normal = 65.04719277044089
# # Now we will simulate a bleeding and compute a new heart rate
blood_loss_parameters = {"start_withdrawal": 1, "end_withdrawal": 2, "flow_withdrawal": -2000, "flow_infusion": 0}
zenker_bleed = Zenker(parameters=blood_loss_parameters)
zenker_bleed.solve(T=300.0, dt=1e-3, dt_eval=0.1, initial_state=zenker_normal.state)
history_zenker_bleed = zenker_bleed.history
HR_bleed = history_zenker_bleed["fHR"][-1]
R_TPR_bleed = history_zenker_bleed["R_TPR"][-1]
C_PRSW_bleed = history_zenker_bleed["C_PRSW"][-1]

                    INFO     INFO:circulation.base:                                                                                                                                          base.py:134
                                           Circulation model parameters (Zenker)                                                                                                                        
                             ┏━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓                                                                                                          
                             ┃ Parameter        ┃ Value                                      ┃                                                                                                          
                             ┡━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩                                                                                                          
                             │ kE_LV            │ 0.066 / milliliter                         │                                                                                                          
                             │ V_ED0            │ 7.14 milliliter                            │                                                                                                          
                             │ P0_LV            │ 2.03 millimeter_Hg                         │                                                                                                          
                             │ tau_Baro         │ 20.0 second                                │                                                                                                          
                             │ k_width          │ 0.1838 / millimeter_Hg                     │                                                                                                          
                             │ Pa_set           │ 70.0 millimeter_Hg                         │                                                                                                          
                             │ Ca               │ 4.0 milliliter / millimeter_Hg             │                                                                                                          
                             │ Cv               │ 111.11 milliliter / millimeter_Hg          │                                                                                                          
                             │ Va0              │ 700 milliliter                             │                                                                                                          
                             │ Vv0_min          │ 2700 milliliter                            │                                                                                                          
                             │ Vv0_max          │ 3100 milliliter                            │                                                                                                          
                             │ R_TPR_min        │ 0.5335 millimeter_Hg * second / milliliter │                                                                                                          
                             │ R_TPR_max        │ 2.134 millimeter_Hg * second / milliliter  │                                                                                                          
                             │ T_sys            │ 0.26666666666666666 second                 │                                                                                                          
                             │ f_HR_min         │ 0.6666666666666666 / second                │                                                                                                          
                             │ f_HR_max         │ 3.0 / second                               │                                                                                                          
                             │ R_valve          │ 0.0025 millimeter_Hg * second / milliliter │                                                                                                          
                             │ C_PRSW_min       │ 25.9 millimeter_Hg                         │                                                                                                          
                             │ C_PRSW_max       │ 103.8 millimeter_Hg                        │                                                                                                          
                             │ start_withdrawal │ 1           
                             │ end_withdrawal   │ 2           
                             │ start_infusion   │ 0.0 second                                 │                                                                                                          
                             │ end_infusion     │ 0.0 second                                 │                                                                                                          
                             │ flow_withdrawal  │ -2000           
                             │ flow_infusion    │ 0           
                             └──────────────────┴────────────────────────────────────────────┘                                                                                                          

                    INFO     INFO:circulation.base:                                                                                                                                          base.py:141
                             Circulation model initial states (Zenker)                                                                                                                                  
                             ┏━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓                                                                                                                                  
                             ┃ State ┃ Value                         ┃                                                                                                                                  
                             ┡━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩                                                                                                                                  
                             │ V_ES  │ 14.288 milliliter             │                                                                                                                                  
                             │ V_ED  │ 21.432000000000002 milliliter │                                                                                                                                  
                             │ S     │ 0.5 dimensionless             │                                                                                                                                  
                             │ Va    │ 938.1944444444443 milliliter  │                                                                                                                                  
                             │ Vv    │ 3886.805555555555 milliliter  │                                                                                                                                  
                             └───────┴───────────────────────────────┘                                                                                                                                  
                    INFO     INFO:circulation.base:Running circulation model                                                                                                                 base.py:333
                    INFO     INFO:circulation.base:Solving beat 0                                                                                                                            base.py:358
[12/09/25 10:36:24] INFO     INFO:circulation.base:Done running circulation model in 7.53 s                                                                                                  base.py:442
print(f"HR_bleed = {HR_bleed}, R_TPR_bleed = {R_TPR_bleed}, C_PRSW_bleed = {C_PRSW_bleed}")
HR_bleed = 2.999997254656593, R_TPR_bleed = 2.1339981168905187, C_PRSW_bleed = 103.79990834474941
HR_factor = HR_bleed / HR_normal
R_TPR_factor = R_TPR_bleed / R_TPR_normal
C_PRSW_factor = C_PRSW_bleed / C_PRSW_normal
regazzoni_normal_parmeters = Regazzoni2020.default_parameters()
regazzoni_normal_parmeters["HR"] = 1.0
regazzoni_normal = Regazzoni2020(parameters=regazzoni_normal_parmeters)
regazzoni_normal.print_info()

                    INFO     INFO:circulation.base:                                                                                                                                          base.py:134
                                                    Circulation model parameters (Regazzoni2020)                                                                                                        
                             ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓                                                                                
                             ┃ Parameter                             ┃ Value                                           ┃                                                                                
                             ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩                                                                                
                             │ HR                                    │ 1.0           
                             │ chambers.LA.EA                        │ 0.07 millimeter_Hg / milliliter                 │                                                                                
                             │ chambers.LA.EB                        │ 0.18 millimeter_Hg / milliliter                 │                                                                                
                             │ chambers.LA.TC                        │ 0.17 second                                     │                                                                                
                             │ chambers.LA.TR                        │ 0.17 second                                     │                                                                                
                             │ chambers.LA.tC                        │ 0.9 second                                      │                                                                                
                             │ chambers.LA.V0                        │ 4.0 milliliter                                  │                                                                                
                             │ chambers.LV.EA                        │ 4.482 millimeter_Hg / milliliter                │                                                                                
                             │ chambers.LV.EB                        │ 0.17 millimeter_Hg / milliliter                 │                                                                                
                             │ chambers.LV.TC                        │ 0.25 second                                     │                                                                                
                             │ chambers.LV.TR                        │ 0.4 second                                      │                                                                                
                             │ chambers.LV.tC                        │ 0.1 second                                      │                                                                                
                             │ chambers.LV.V0                        │ 42.0 milliliter                                 │                                                                                
                             │ chambers.RA.EA                        │ 0.06 millimeter_Hg / milliliter                 │                                                                                
                             │ chambers.RA.EB                        │ 0.07 millimeter_Hg / milliliter                 │                                                                                
                             │ chambers.RA.TC                        │ 0.17 second                                     │                                                                                
                             │ chambers.RA.TR                        │ 0.17 second                                     │                                                                                
                             │ chambers.RA.tC                        │ 0.9 second                                      │                                                                                
                             │ chambers.RA.V0                        │ 4.0 milliliter                                  │                                                                                
                             │ chambers.RV.EA                        │ 0.2 millimeter_Hg / milliliter                  │                                                                                
                             │ chambers.RV.EB                        │ 0.029 millimeter_Hg / milliliter                │                                                                                
                             │ chambers.RV.TC                        │ 0.25 second                                     │                                                                                
                             │ chambers.RV.TR                        │ 0.4 second                                      │                                                                                
                             │ chambers.RV.tC                        │ 0.1 second                                      │                                                                                
                             │ chambers.RV.V0                        │ 16.0 milliliter                                 │                                                                                
                             │ valves.MV.Rmin                        │ 0.0075 millimeter_Hg * second / milliliter      │                                                                                
                             │ valves.MV.Rmax                        │ 75006.2 millimeter_Hg * second / milliliter     │                                                                                
                             │ valves.AV.Rmin                        │ 0.0075 millimeter_Hg * second / milliliter      │                                                                                
                             │ valves.AV.Rmax                        │ 75006.2 millimeter_Hg * second / milliliter     │                                                                                
                             │ valves.TV.Rmin                        │ 0.0075 millimeter_Hg * second / milliliter      │                                                                                
                             │ valves.TV.Rmax                        │ 75006.2 millimeter_Hg * second / milliliter     │                                                                                
                             │ valves.PV.Rmin                        │ 0.0075 millimeter_Hg * second / milliliter      │                                                                                
                             │ valves.PV.Rmax                        │ 75006.2 millimeter_Hg * second / milliliter     │                                                                                
                             │ circulation.SYS.R_AR                  │ 0.733 millimeter_Hg * second / milliliter       │                                                                                
                             │ circulation.SYS.C_AR                  │ 1.372 milliliter / millimeter_Hg                │                                                                                
                             │ circulation.SYS.R_VEN                 │ 0.32 millimeter_Hg * second / milliliter        │                                                                                
                             │ circulation.SYS.C_VEN                 │ 11.363 milliliter / millimeter_Hg               │                                                                                
                             │ circulation.SYS.L_AR                  │ 0.005 millimeter_Hg * second ** 2 / milliliter  │                                                                                
                             │ circulation.SYS.L_VEN                 │ 0.0005 millimeter_Hg * second ** 2 / milliliter │                                                                                
                             │ circulation.PUL.R_AR                  │ 0.046 millimeter_Hg * second / milliliter       │                                                                                
                             │ circulation.PUL.C_AR                  │ 20.0 milliliter / millimeter_Hg                 │                                                                                
                             │ circulation.PUL.R_VEN                 │ 0.0015 millimeter_Hg * second / milliliter      │                                                                                
                             │ circulation.PUL.C_VEN                 │ 16.0 milliliter / millimeter_Hg                 │                                                                                
                             │ circulation.PUL.L_AR                  │ 0.0005 millimeter_Hg * second ** 2 / milliliter │                                                                                
                             │ circulation.PUL.L_VEN                 │ 0.0005 millimeter_Hg * second ** 2 / milliliter │                                                                                
                             │ circulation.external.start_withdrawal │ 0.0 second                                      │                                                                                
                             │ circulation.external.end_withdrawal   │ 0.0 second                                      │                                                                                
                             │ circulation.external.start_infusion   │ 0.0 second                                      │                                                                                
                             │ circulation.external.end_infusion     │ 0.0 second                                      │                                                                                
                             │ circulation.external.flow_withdrawal  │ 0.0 milliliter / second                         │                                                                                
                             │ circulation.external.flow_infusion    │ 0.0 milliliter / second                         │                                                                                
                             └───────────────────────────────────────┴─────────────────────────────────────────────────┘                                                                                

                    INFO     INFO:circulation.base:                                                                                                                                          base.py:141
                                  Circulation model initial states                                                                                                                                      
                                           (Regazzoni2020)                                                                                                                                              
                             ┏━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓                                                                                                                                
                             ┃ State     ┃ Value                       ┃                                                                                                                                
                             ┡━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩                                                                                                                                
                             │ V_LA      │ 87.183 milliliter           │                                                                                                                                
                             │ V_LV      │ 118.52 milliliter           │                                                                                                                                
                             │ V_RA      │ 86.833 milliliter           │                                                                                                                                
                             │ V_RV      │ 166.177 milliliter          │                                                                                                                                
                             │ p_AR_SYS  │ 87.675 millimeter_Hg        │                                                                                                                                
                             │ p_VEN_SYS │ 35.898 millimeter_Hg        │                                                                                                                                
                             │ p_AR_PUL  │ 19.545 millimeter_Hg        │                                                                                                                                
                             │ p_VEN_PUL │ 15.004 millimeter_Hg        │                                                                                                                                
                             │ Q_AR_SYS  │ 71.104 milliliter / second  │                                                                                                                                
                             │ Q_VEN_SYS │ 94.039 milliliter / second  │                                                                                                                                
                             │ Q_AR_PUL  │ 94.084 milliliter / second  │                                                                                                                                
                             │ Q_VEN_PUL │ 473.279 milliliter / second │                                                                                                                                
                             └───────────┴─────────────────────────────┘                                                                                                                                



                    INFO     INFO:circulation.base:                                                                                                                                          base.py:508
                                                                                        Volumes                                                                                                         
                             ┏━━━━━━━━┳━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━┓                                             
                             ┃ V_LA   ┃ V_LV    ┃ V_RA   ┃ V_RV    ┃ V_AR_SYS ┃ V_VEN_SYS ┃ V_AR_PUL ┃ V_VEN_PUL ┃ Heart   ┃ SYS     ┃ PUL     ┃ Total    ┃                                             
                             ┡━━━━━━━━╇━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━┩                                             
                    87.183118.52086.833166.177120.290407.909390.900240.064458.713528.199630.9641617.876           
                             └────────┴─────────┴────────┴─────────┴──────────┴───────────┴──────────┴───────────┴─────────┴─────────┴─────────┴──────────┘                                             
                                                                Pressures                                                                                                                               
                             ┏━━━━━━━┳━━━━━━━┳━━━━━━━┳━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┓                                                                                            
                             ┃ p_LA  ┃ p_LV  ┃ p_RA  ┃ p_RV  ┃ p_AR_SYS ┃ p_VEN_SYS ┃ p_AR_PUL ┃ p_VEN_PUL ┃                                                                                            
                             ┡━━━━━━━╇━━━━━━━╇━━━━━━━╇━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━┩                                                                                            
                    0.0000.0000.0000.00087.67535.89819.54515.004           
                             └───────┴───────┴───────┴───────┴──────────┴───────────┴──────────┴───────────┘                                                                                            
                                                                  Flows                                                                                                                                 
                             ┏━━━━━━━┳━━━━━━━┳━━━━━━━┳━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┓                                                                                            
                             ┃ Q_MV  ┃ Q_AV  ┃ Q_TV  ┃ Q_PV  ┃ Q_AR_SYS ┃ Q_VEN_SYS ┃ Q_AR_PUL ┃ Q_VEN_PUL ┃                                                                                            
                             ┡━━━━━━━╇━━━━━━━╇━━━━━━━╇━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━┩                                                                                            
                    0.0000.0000.0000.00071.10494.03994.084473.279           
                             └───────┴───────┴───────┴───────┴──────────┴───────────┴──────────┴───────────┘                                                                                            
dt_eval = 0.01
regazzoni_normal.solve(num_beats=20, dt_eval=dt_eval)
N_normal = int(regazzoni_normal.HR / dt_eval)
                    INFO     INFO:circulation.base:Running circulation model                                                                                                                 base.py:333
                    INFO     INFO:circulation.base:Solving beat 0                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 1                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 2                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 3                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 4                                                                                                                            base.py:358
[12/09/25 10:36:25] INFO     INFO:circulation.base:Solving beat 5                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 6                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 7                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 8                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 9                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 10                                                                                                                           base.py:358
[12/09/25 10:36:26] INFO     INFO:circulation.base:Solving beat 11                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 12                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 13                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 14                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 15                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 16                                                                                                                           base.py:358
[12/09/25 10:36:27] INFO     INFO:circulation.base:Solving beat 17                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 18                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 19                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Done running circulation model in 3.32 s                                                                                                  base.py:442
regazzoni_bleed_parmeters = Regazzoni2020.default_parameters()
regazzoni_bleed_parmeters["HR"] = HR_factor
regazzoni_bleed_parmeters["circulation"]["SYS"]["R_AR"] *= R_TPR_factor
regazzoni_bleed_parmeters["circulation"]["SYS"]["R_VEN"] *= R_TPR_factor
for chamber in ["LA", "LV", "RA", "RV"]:
    regazzoni_bleed_parmeters["chambers"][chamber]["EA"] *= C_PRSW_factor
    regazzoni_bleed_parmeters["chambers"][chamber]["EB"] *= C_PRSW_factor
regazzoni_bleed_parmeters["circulation"]["external"] = blood_loss_parameters
regazzoni_bleed = Regazzoni2020(parameters=regazzoni_bleed_parmeters)
regazzoni_bleed.solve(num_beats=100, initial_state=regazzoni_normal.state, dt_eval=dt_eval)
regazzoni_bleed.print_info()
N_bleed = int(regazzoni_bleed.HR / dt_eval)
history_regazzoni_normal = regazzoni_normal.history
history_regazzoni_bleed = regazzoni_bleed.history

                    INFO     INFO:circulation.base:                                                                                                                                          base.py:134
                                                        Circulation model parameters (Regazzoni2020)                                                                                                    
                             ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓                                                                         
                             ┃ Parameter                             ┃ Value                                                  ┃                                                                         
                             ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩                                                                         
                             │ HR                                    │ 1.6311071551908496           
                             │ chambers.LA.EA                        │ 0.11170341523845612 millimeter_Hg / milliliter         │                                                                         
                             │ chambers.LA.EB                        │ 0.2872373534703157 millimeter_Hg / milliliter          │                                                                         
                             │ chambers.LA.TC                        │ 0.17 second                                            │                                                                         
                             │ chambers.LA.TR                        │ 0.17 second                                            │                                                                         
                             │ chambers.LA.tC                        │ 0.9 second                                             │                                                                         
                             │ chambers.LA.V0                        │ 4.0 milliliter                                         │                                                                         
                             │ chambers.LV.EA                        │ 7.152210101410861 millimeter_Hg / milliliter           │                                                                         
                             │ chambers.LV.EB                        │ 0.2712797227219649 millimeter_Hg / milliliter          │                                                                         
                             │ chambers.LV.TC                        │ 0.25 second                                            │                                                                         
                             │ chambers.LV.TR                        │ 0.4 second                                             │                                                                         
                             │ chambers.LV.tC                        │ 0.1 second                                             │                                                                         
                             │ chambers.LV.V0                        │ 42.0 milliliter                                        │                                                                         
                             │ chambers.RA.EA                        │ 0.09574578449010523 millimeter_Hg / milliliter         │                                                                         
                             │ chambers.RA.EB                        │ 0.11170341523845612 millimeter_Hg / milliliter         │                                                                         
                             │ chambers.RA.TC                        │ 0.17 second                                            │                                                                         
                             │ chambers.RA.TR                        │ 0.17 second                                            │                                                                         
                             │ chambers.RA.tC                        │ 0.9 second                                             │                                                                         
                             │ chambers.RA.V0                        │ 4.0 milliliter                                         │                                                                         
                             │ chambers.RV.EA                        │ 0.31915261496701747 millimeter_Hg / milliliter         │                                                                         
                             │ chambers.RV.EB                        │ 0.046277129170217535 millimeter_Hg / milliliter        │                                                                         
                             │ chambers.RV.TC                        │ 0.25 second                                            │                                                                         
                             │ chambers.RV.TR                        │ 0.4 second                                             │                                                                         
                             │ chambers.RV.tC                        │ 0.1 second                                             │                                                                         
                             │ chambers.RV.V0                        │ 16.0 milliliter                                        │                                                                         
                             │ valves.MV.Rmin                        │ 0.0075 millimeter_Hg * second / milliliter             │                                                                         
                             │ valves.MV.Rmax                        │ 75006.2 millimeter_Hg * second / milliliter            │                                                                         
                             │ valves.AV.Rmin                        │ 0.0075 millimeter_Hg * second / milliliter             │                                                                         
                             │ valves.AV.Rmax                        │ 75006.2 millimeter_Hg * second / milliliter            │                                                                         
                             │ valves.TV.Rmin                        │ 0.0075 millimeter_Hg * second / milliliter             │                                                                         
                             │ valves.TV.Rmax                        │ 75006.2 millimeter_Hg * second / milliliter            │                                                                         
                             │ valves.PV.Rmin                        │ 0.0075 millimeter_Hg * second / milliliter             │                                                                         
                             │ valves.PV.Rmax                        │ 75006.2 millimeter_Hg * second / milliliter            │                                                                         
                             │ circulation.SYS.R_AR                  │ 1.169247225422182 millimeter_Hg * second / milliliter  │                                                                         
                             │ circulation.SYS.C_AR                  │ 1.372 milliliter / millimeter_Hg                       │                                                                         
                             │ circulation.SYS.R_VEN                 │ 0.5104489933630263 millimeter_Hg * second / milliliter │                                                                         
                             │ circulation.SYS.C_VEN                 │ 11.363 milliliter / millimeter_Hg                      │                                                                         
                             │ circulation.SYS.L_AR                  │ 0.005 millimeter_Hg * second ** 2 / milliliter         │                                                                         
                             │ circulation.SYS.L_VEN                 │ 0.0005 millimeter_Hg * second ** 2 / milliliter        │                                                                         
                             │ circulation.PUL.R_AR                  │ 0.046 millimeter_Hg * second / milliliter              │                                                                         
                             │ circulation.PUL.C_AR                  │ 20.0 milliliter / millimeter_Hg                        │                                                                         
                             │ circulation.PUL.R_VEN                 │ 0.0015 millimeter_Hg * second / milliliter             │                                                                         
                             │ circulation.PUL.C_VEN                 │ 16.0 milliliter / millimeter_Hg                        │                                                                         
                             │ circulation.PUL.L_AR                  │ 0.0005 millimeter_Hg * second ** 2 / milliliter        │                                                                         
                             │ circulation.PUL.L_VEN                 │ 0.0005 millimeter_Hg * second ** 2 / milliliter        │                                                                         
                             │ circulation.external.start_withdrawal │ 1           
                             │ circulation.external.end_withdrawal   │ 2           
                             │ circulation.external.start_infusion   │ 0.0 second                                             │                                                                         
                             │ circulation.external.end_infusion     │ 0.0 second                                             │                                                                         
                             │ circulation.external.flow_withdrawal  │ -2000           
                             │ circulation.external.flow_infusion    │ 0           
                             └───────────────────────────────────────┴────────────────────────────────────────────────────────┘                                                                         

                    INFO     INFO:circulation.base:                                                                                                                                          base.py:141
                                  Circulation model initial states                                                                                                                                      
                                           (Regazzoni2020)                                                                                                                                              
                             ┏━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓                                                                                                                                
                             ┃ State     ┃ Value                       ┃                                                                                                                                
                             ┡━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩                                                                                                                                
                             │ V_LA      │ 87.183 milliliter           │                                                                                                                                
                             │ V_LV      │ 118.52 milliliter           │                                                                                                                                
                             │ V_RA      │ 86.833 milliliter           │                                                                                                                                
                             │ V_RV      │ 166.177 milliliter          │                                                                                                                                
                             │ p_AR_SYS  │ 87.675 millimeter_Hg        │                                                                                                                                
                             │ p_VEN_SYS │ 35.898 millimeter_Hg        │                                                                                                                                
                             │ p_AR_PUL  │ 19.545 millimeter_Hg        │                                                                                                                                
                             │ p_VEN_PUL │ 15.004 millimeter_Hg        │                                                                                                                                
                             │ Q_AR_SYS  │ 71.104 milliliter / second  │                                                                                                                                
                             │ Q_VEN_SYS │ 94.039 milliliter / second  │                                                                                                                                
                             │ Q_AR_PUL  │ 94.084 milliliter / second  │                                                                                                                                
                             │ Q_VEN_PUL │ 473.279 milliliter / second │                                                                                                                                
                             └───────────┴─────────────────────────────┘                                                                                                                                
                    INFO     INFO:circulation.base:Running circulation model                                                                                                                 base.py:333
                    INFO     INFO:circulation.base:Solving beat 0                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 1                                                                                                                            base.py:358
[12/09/25 10:36:28] INFO     INFO:circulation.base:Solving beat 2                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 3                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 4                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 5                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 6                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 7                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 8                                                                                                                            base.py:358
[12/09/25 10:36:29] INFO     INFO:circulation.base:Solving beat 9                                                                                                                            base.py:358
                    INFO     INFO:circulation.base:Solving beat 10                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 11                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 12                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 13                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 14                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 15                                                                                                                           base.py:358
[12/09/25 10:36:30] INFO     INFO:circulation.base:Solving beat 16                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 17                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 18                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 19                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 20                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 21                                                                                                                           base.py:358
[12/09/25 10:36:31] INFO     INFO:circulation.base:Solving beat 22                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 23                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 24                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 25                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 26                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 27                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 28                                                                                                                           base.py:358
[12/09/25 10:36:32] INFO     INFO:circulation.base:Solving beat 29                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 30                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 31                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 32                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 33                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 34                                                                                                                           base.py:358
[12/09/25 10:36:33] INFO     INFO:circulation.base:Solving beat 35                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 36                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 37                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 38                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 39                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 40                                                                                                                           base.py:358
[12/09/25 10:36:34] INFO     INFO:circulation.base:Solving beat 41                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 42                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 43                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 44                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 45                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 46                                                                                                                           base.py:358
[12/09/25 10:36:35] INFO     INFO:circulation.base:Solving beat 47                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 48                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 49                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 50                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 51                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 52                                                                                                                           base.py:358
[12/09/25 10:36:36] INFO     INFO:circulation.base:Solving beat 53                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 54                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 55                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 56                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 57                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 58                                                                                                                           base.py:358
[12/09/25 10:36:37] INFO     INFO:circulation.base:Solving beat 59                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 60                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 61                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 62                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 63                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 64                                                                                                                           base.py:358
[12/09/25 10:36:38] INFO     INFO:circulation.base:Solving beat 65                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 66                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 67                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 68                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 69                                                                                                                           base.py:358
[12/09/25 10:36:39] INFO     INFO:circulation.base:Solving beat 70                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 71                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 72                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 73                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 74                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 75                                                                                                                           base.py:358
[12/09/25 10:36:40] INFO     INFO:circulation.base:Solving beat 76                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 77                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 78                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 79                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 80                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 81                                                                                                                           base.py:358
[12/09/25 10:36:41] INFO     INFO:circulation.base:Solving beat 82                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 83                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 84                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 85                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 86                                                                                                                           base.py:358
[12/09/25 10:36:42] INFO     INFO:circulation.base:Solving beat 87                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 88                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 89                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 90                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 91                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 92                                                                                                                           base.py:358
[12/09/25 10:36:43] INFO     INFO:circulation.base:Solving beat 93                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 94                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 95                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 96                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 97                                                                                                                           base.py:358
[12/09/25 10:36:44] INFO     INFO:circulation.base:Solving beat 98                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Solving beat 99                                                                                                                           base.py:358
                    INFO     INFO:circulation.base:Done running circulation model in 16.74 s                                                                                                 base.py:442



                    INFO     INFO:circulation.base:                                                                                                                                          base.py:508
                                                                                       Volumes                                                                                                          
                             ┏━━━━━━━━┳━━━━━━━━┳━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━┓                                               
                             ┃ V_LA   ┃ V_LV   ┃ V_RA   ┃ V_RV   ┃ V_AR_SYS ┃ V_VEN_SYS ┃ V_AR_PUL ┃ V_VEN_PUL ┃ Heart   ┃ SYS     ┃ PUL     ┃ Total    ┃                                               
                             ┡━━━━━━━━╇━━━━━━━━╇━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━┩                                               
                    86.56154.60581.50583.044116.073377.923476.532341.632305.716493.997818.1631617.876           
                             └────────┴────────┴────────┴────────┴──────────┴───────────┴──────────┴───────────┴─────────┴─────────┴─────────┴──────────┘                                               
                                                                 Pressures                                                                                                                              
                             ┏━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┓                                                                                          
                             ┃ p_LA   ┃ p_LV   ┃ p_RA  ┃ p_RV  ┃ p_AR_SYS ┃ p_VEN_SYS ┃ p_AR_PUL ┃ p_VEN_PUL ┃                                                                                          
                             ┡━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━┩                                                                                          
                    23.77527.0928.7758.72084.60233.25923.82721.352           
                             └────────┴────────┴───────┴───────┴──────────┴───────────┴──────────┴───────────┘                                                                                          
                                                                   Flows                                                                                                                                
                             ┏━━━━━━━━┳━━━━━━━━┳━━━━━━━┳━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┓                                                                                         
                             ┃ Q_MV   ┃ Q_AV   ┃ Q_TV  ┃ Q_PV   ┃ Q_AR_SYS ┃ Q_VEN_SYS ┃ Q_AR_PUL ┃ Q_VEN_PUL ┃                                                                                         
                             ┡━━━━━━━━╇━━━━━━━━╇━━━━━━━╇━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━┩                                                                                         
                    -0.000-0.0015.403-0.00044.02747.96749.742311.617           
                             └────────┴────────┴───────┴────────┴──────────┴───────────┴──────────┴───────────┘                                                                                         
V_LV_normal = history_regazzoni_normal["V_LV"][-N_normal:]
V_LV_ED = max(V_LV_normal)
V_LV_ES = min(V_LV_normal)
SV_normal = V_LV_ED - V_LV_ES
V_LV_bleed = history_regazzoni_bleed["V_LV"][-N_bleed:]
V_LV_ED = max(V_LV_bleed)
V_LV_ES = min(V_LV_bleed)
SV_bleed = V_LV_ED - V_LV_ES
print(f"SV_normal = {SV_normal}, SV_bleed = {SV_bleed}")
SV_normal = 83.03587846770604, SV_bleed = 28.594868076205486
fig, ax = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10, 5))
ax[0, 0].set_title("Normal")
ax[0, 0].plot(history_regazzoni_normal["V_LV"], history_regazzoni_normal["p_LV"], label="LV")
ax[0, 0].plot(history_regazzoni_normal["V_RV"], history_regazzoni_normal["p_RV"], label="RV")
ax[1, 0].plot(history_regazzoni_normal["V_LV"][-N_normal:], history_regazzoni_normal["p_LV"][-N_normal:], label="LV")
ax[1, 0].plot(history_regazzoni_normal["V_RV"][-N_normal:], history_regazzoni_normal["p_RV"][-N_normal:], label="RV")
ax[0, 1].set_title("Bleeding")
ax[0, 1].plot(history_regazzoni_bleed["V_LV"], history_regazzoni_bleed["p_LV"], label="LV")
ax[0, 1].plot(history_regazzoni_bleed["V_RV"], history_regazzoni_bleed["p_RV"], label="RV")
ax[1, 1].plot(history_regazzoni_bleed["V_LV"][-N_bleed:], history_regazzoni_bleed["p_LV"][-N_bleed:], label="LV")
ax[1, 1].plot(history_regazzoni_bleed["V_RV"][-N_bleed:], history_regazzoni_bleed["p_RV"][-N_bleed:], label="RV")
[<matplotlib.lines.Line2D at 0x7f9b08f8b380>]
../_images/56019d95a508eff98ec392ed1709b5e39e57d4eb90298af40203e949449fa50e.png
ax[0, 0].set_ylabel("p [mmHg]")
ax[1, 0].set_ylabel("p [mmHg]")
ax[1, 0].set_xlabel("V [mL]")
ax[1, 1].set_xlabel("V [mL]")
Text(0.5, 4.444444444444445, 'V [mL]')
for axi in ax.flatten():
    axi.grid()
    axi.legend()
pressure_keys = ['p_AR_SYS', 'p_VEN_SYS', 'p_AR_PUL', 'p_VEN_PUL', 'p_LV', 'p_RV', 'p_LA', 'p_RA']
flow_keys = ["Q_MV","Q_AV", "Q_TV", "Q_PV" ,"I_ext", "Q_AR_SYS", "Q_VEN_SYS" ,  "Q_AR_PUL",  "Q_VEN_PUL"]
for case, obj in [("normal",regazzoni_normal), ("bleed", regazzoni_bleed)]:
    history = obj.history
    fig, ax = plt.subplots(3, 3, sharex=True, figsize=(10, 8))
    for axi, key in zip(ax.flatten(), flow_keys):
        axi.plot(history["time"], history[key])
        axi.set_title(key)
    fig.suptitle(f"Flow {case}")

    fig, ax = plt.subplots(4, 2, sharex=True, figsize=(10, 8))
    for axi, key in zip(ax.flatten(), pressure_keys):
        axi.plot(history["time"], history[key])
        axi.set_title(key)
    fig.suptitle(f"Pressure {case}")

    volumes = Regazzoni2020.compute_volumes(obj.parameters, obj.results_state)

    fig, ax = plt.subplots(4, 3, sharex=True, figsize=(10, 8))
    for axi, (key, v) in zip(ax.flatten(), volumes.items()):
        axi.plot(history["time"], v)
        axi.set_title(key)
    fig.suptitle(f"Volumes {case}")
../_images/ba7f2c2d21c4b19d480c872fe7c2347060b0fd444562e3761fc17102a1de5248.png ../_images/6f4e7c89ae8ce37d61c91029dcee1dd59f870504511a3b033d270de12c10c980.png ../_images/d07f29f1f17f9a4ac03245c1da61007f761e55e47bbbbdf516eb283735c5df9d.png ../_images/6006380f899c77a79164d099a469c0f2fb8727903fab2076ec3033fd34d10845.png ../_images/7292c2f5fd2b17ea169ce586251240d69bd97d00be13ddad6e2700253fcdd0ed.png ../_images/8dbe62f56842ac80f837f2afb6a4e9407049e2d55992cf463739b17ee3c56df9.png
plt.show()

References#

[RSA+22]

Francesco Regazzoni, Matteo Salvador, Pasquale Claudio Africa, Marco Fedele, Luca Dedè, and Alfio Quarteroni. A cardiac electromechanical model coupled with a lumped-parameter model for closed-loop blood circulation. Journal of Computational Physics, 457:111083, 2022.