Compartmental cardiovascular indicator dilution model based on Rideout_IndicatorDilution with systemic flow used as constant reference. Also in MATLAB.

Description

This model simulates the human cardiovascular loop. It can simulate
a healthy or deseased heart. Both Ventricular Septal Defect (VSD) and
Atrial Septal Defect (ASD) are modeled. To simulate a healthy heart,
set both shunt flows Fvsd and Fasd to zero. To investigate a deseased
heart set either or both to a positive flow.

Unlike Rideout's original model (Rideout_IndicatorDilution), this model
keeps the systemic flow (Fs) as constant reference. This is more
analogous to real life and is needed to keep us alive. When the systemic
flow Fs is held constant, intracardiac flows must rise when there is a
shunt, and observations of pulmonary hypertension and heart failure are
easy to understand.

The model is made of 10 compartments which combine perfect mixing and
delay compartments. The anatomy represented by each compartment, as
well as its volume and time constant are shown in the table above. This
is a simple model which ignores capillary diffusion. An indicator bolus
is injected into the pulmonary artery (compartment 1) and recirculates
through the compartments. By conservation of mass, the total amount of
indicator in all compartments is fixed. In a healthy heart there are no
internal loops. Blood flows from compartment to compartment in series.
We expect to see the concentration peak in each compartment with the
accumulated delays as shown in the table. The Transport Time around the
loop is 40 sec. We expect all compartments to show a peak-to-peak delay
of ~40 sec (as long as the second peak can be distinguished). Indicator
concentrations eventually flatten into a unified concentration in all
compartments.

In a diseased heart, there is an additional inner loop which flows in
parallel to the outer loop and disrupts normal function. Ventricular
Septal Defect (VSD) includes a shunt from the left ventricle
(compartment 3) to the right ventricle (compartment 0). Atrial Septal
Defect (ASD) includes a shunt from the left atrium (compartment 2) to
the right atrium (compartment 7). Figure 1 shows indicator dilution C0
when the VSD shunt aperture is swept from 0 to 60 ml/s, which is 60% of
the default systemic reference flow (100 ml/s). Note that in VSD, an
early peak in the right ventricle is visible and increases in amplitude
as the shunt aperture is increased. ASD creates a similar effect, where
indicator dilution C7 shows an early peak.

Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.