"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018 Cardiac Cycle: pV-loops Leycom Time (s) Volume (ml) Pressure (mmHg) Volume (ml) Pressure (mmHg) Derivative of Pressure ECG (volt) pV loop
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"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018
Cardiac Cycle: pV-loops
Leycom
Time (s) Volume (ml)
Pres
sure
(mm
Hg)
Volume (ml)
Pressure (mmHg)
Derivative of Pressure
ECG (volt)
pV loop
"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018
Elastance model: pV-loops
Sagawa (1988) pp 374, 392; (1978) p. 444
0P t E t V t V
Pragmatic modelling: A Pulsatile Windkessel Model
Time-varying elastance Pulm. Art. FlowPulm. Art. Pressure
J-W. Lankhaar (2002),
pp. 20, 25, 26
"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018
CVS-model: Open & Half Circulation
Implement: Faes & Kerkhof (2015), appendix provides detailsPossible extensions: 1) Closed & Full Circulation; 2) Interaction &Tamponade
Tamponade
"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018
End Assignment Tamponade
Develop a Matlab/Mathematica programme to simulate the complete cardiac cycle in the circulation consisting of:
1. Elastance models of ventricle and atrium & five-element windkessel model of a closed double circulation (additional text available with differential equations for an open single circulation)
2. Add a tamponade to the model & simulate3. Deliver: 1) plots with pressures, volumes and flows as
function of time, 2) ventricular PV-loop, 3) influence of cardiac tamponade on pressures, volumes and flows.
"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018
End Assignment Closed & Full CirculationDevelop a Matlab/Mathematica programme to simulate the
complete cardiac cycle in the circulation consisting of: 1. Systemic & pulmonary circulation, with for each, Elastance
models of ventricle and atrium & five-element windkesselmodel of a closed double circulation (additional text available with differential equations for an open single circulation)
2. Trim model3. Deliver: 1) plots with pressures, volumes and flows as
function of time, 2) ventricular PV-loop, 3) influence of cardiac tamponade on pressures, volumes and flows.
End-Assignment Thermo-dilution
"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018
Source: Netter (1971) vol. 5, pp. 43
Area under curve
End-Assignment Thermo-dilution
"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018
Source: Netter (1971) vol. 5, pp. 43
Area under curve
Assumptions: • A constant vessel volume, i.e., VV (t) = VV = constant;• A complete thermal isolation i.e., no energy exchange with the
body;• A well-mixed condition i.e., saline and blood are mixed
instantaneously and completely; • A constant bolus injection i.e., during the injection, the bolus
flow rate is constant; • Non-pulsatile blood flow, meaning that in- and outflow are
time-independent, i.e., FI(t) = FI = constant and FO(t) = FO = constant.
• The temperature of the inflowing blood is constant, i.e., TI(t) = TI = constant
End-Assignment Thermo-dilution
"BM&S: CVS", Th.J.C. Faes, VUmc. Oct. 2018
Source: Netter (1971) vol. 5, pp. 43
Area under curve
Model & Simulate Thermo-dilution for: • Pulsatile blood flow, meaning FI(t) and FO(t)• A varying vessel volume, i.e., VV (t) • An incomplete thermal isolation• A non-constant bolus injection i.e., during the injection, the
bolus flow rate is constant.
Validate by drawing scatter-plots & Bland&Altman-plots for true and simulated Cardiac output while varying key model-parameters
See Lecture Notes for model & Canvas for End-assignment description.
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