Cardiac Cycle: pV-loopsfew.vu.nl/~ivo/BMS/Mathematica/20181002BMS.pdf · complete cardiac cycle in the circulation consisting of: 1. Systemic & pulmonary circulation, with for each,

"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.