Zenker#
This example shows how to use the Zenker model [ZRC19]. The Zenker model is a 0D model that simulates the cardiac cycle.
from circulation.log import setup_logging
from circulation.zenker import Zenker
import matplotlib.pyplot as plt
import numpy as np
setup_logging()
circulation = Zenker(
parameters={
"start_withdrawal": 100,
"end_withdrawal": 200,
"start_infusion": 400,
"end_infusion": 500,
"flow_withdrawal": -1,
"flow_infusion": 1,
"Vv0_min": 1000,
"Vv0_max": 2000,
}
)
history = circulation.solve(T=700.0, dt=1e-3, dt_eval=0.1)
start_plot = 0
time = history["time"][start_plot:]
[11/28/24 20:30:27] INFO INFO:circulation.base: base.py:131 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 │ 1000 │ │ Vv0_max │ 2000 │ │ 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 │ 100 │ │ end_withdrawal │ 200 │ │ start_infusion │ 400 │ │ end_infusion │ 500 │ │ flow_withdrawal │ -1 │ │ flow_infusion │ 1 │ └──────────────────┴────────────────────────────────────────────┘
[11/28/24 20:30:28] INFO INFO:circulation.base: base.py:137 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 │ └───────┴───────────────────────────────┘
fig, ax = plt.subplots(5, 2, sharex=True, figsize=(10, 10))
ax[0, 0].plot(time, history["Vv"][start_plot:])
ax[0, 0].set_ylabel("Vv [mL]")
ax[1, 0].plot(time, history["Va"][start_plot:])
ax[1, 0].set_ylabel("Va [mL]")
ax[2, 0].plot(time, history["V_ED"][start_plot:])
ax[2, 0].set_ylabel("V_ED [mL]")
ax[3, 0].plot(time, history["V_ES"][start_plot:])
ax[3, 0].set_ylabel("V_ES [mL]")
SV = np.subtract(history["V_ED"], history["V_ES"])
ax[4, 0].plot(time, SV[start_plot:], label="SV")
ax[4, 0].set_ylabel("Stroke volume [mL]")
ax[0, 1].plot(time, history["fHR"][start_plot:])
ax[0, 1].set_ylabel("fHR [Hz]")
CO = SV * history["fHR"]
ax[1, 1].plot(time, CO[start_plot:], label="CO")
ax[1, 1].set_ylabel("Cardiac output [mL/s]")
ax[2, 1].plot(time, history["Pa"][start_plot:])
ax[2, 1].set_ylabel("Pa [mmHg]")
ax[3, 1].plot(time, history["S"][start_plot:])
ax[3, 1].set_ylabel("S")
ax[4, 1].plot(time, history["Pcvp"][start_plot:])
ax[4, 1].set_ylabel("Pcvp [mmHg]")
ax[4, 0].set_xlabel("Time [s]")
ax[4, 1].set_xlabel("Time [s]")
# plt.show()
fig.savefig("zenker.png")
References#
[ZRC19]
Sven Zenker, Jonathan Rubin, and Gilles Clermont. Correction: from inverse problems in mathematical physiology to quantitative differential diagnoses. PLoS Computational Biology, 15(6):e1007155, 2019.