Neuromon's cardiovascular simulation is built from two components: capacitances and resistances. There are many ways to implement these components so in the model an arbitrary choice had to be made. The parameters for optimal finetuning of the model have been found by trial and error. First, the fundamental charactertics of the two components will be described and then the criteria for optimization of parameter values will be explained.
Capacitances
Capacitances have been modeled by an exponential relationship between volume (m3) and pressure (hPa) according to the formula:
Pressure(hPa) = exp(volume(m3) / capacitance) - 1;
Resistances
Resistances have been used to calculated the Flow per time unit from capacitance A to capacitance B according to the following equation:
flow (m3/s) = (pressure A (hPa) - pressure B (hPa)) / resistance (hPa * s/m3)
3 Capacitances connected by 2 Resistances
For every timestep (variabel between 2-10 ms) the flow from capacitance A to B and the flow from capacitance A to C cannot be calculated in sequence since any flow from A to B will result in a decrease in pressure difference from A to C. To find a solution calculating the flow from A to B and from A to C 'simultaneously' the Runge-Kutta method for complex polynomial relations was applied.
Note that for brain circulation flow was also possible from C to B (see figure) but this was handled after calculating the flow from A to B and A to C.
Optimization of parameter values
For optimization the following criteria have been established:
1. total blood volume (the sum of the volumes of all capacitances together) is 5000 ml
2. when there is no heart activity (and the pressure in all capacitances is equal and close to zero) blood will distribute with approximately 1000 ml in the small circulation versus 4000 ml (80%) in the systemic circulation. Of the 4000 ml in the systemic circulation the arterial capacitances hold approximately 400 ml (10%) with the rest of the blood held in the venous compartment (90%). These volumes can be checked when selecting cardiac arrest in the Scenario menu and bringing the window for immutable parameter values to the front:
During cardiac arrest only the parameters for capacitances can be set since resistances only become relevant when there are pressure differences, and for this de model needs to be dynamic with the heart actively pumping.
Under basic conditions (50 years old male, arterial acceleration off, no reflexes active) the heart pumps with a cardiac output of 4200 ml/min with a stroke volume of approximately 62ml at a heart rate of 69 BPM. Under dynamic circumstances the arterial compartment of the systemic circulation contains 620ml at a pressure of 116/86mmHg with the resistances from the last arterial capacitances to the venous compartment as most important determinants of arterial blood pressure.
Starting off from these basic parameter values for resistances and capacitances further finetuning was required to obtain the average flow velocity waveform calculated for an age of 50 years based upon a study in 105 healthy Dutch volunteers (with acceleration turned on). This was monitored in the Z-score graph by aiming at a Z-score of zero for all flow velocity determinants: Sys1, Sys2, D560 and HR.