A new control system for left ventricular assist devices based on patient-specific physiological demand

Figures & data

Figure 1. Cardiovascular circuit model.

Table 1. Cardiovascular model parameters.

Parameters	Value	Physiological meaning
Resistances (mmHg s mL^−1)
RS	1.0000	Systemic vascular resistance (RS)
RM	0.0050	Mitral valve resistance
RA	0.0010	Aortic valve resistance
RC	0.0398	Characteristic resistance
Compliances (mL mmHg^−1)
C(t)	Time varying	Left ventricular compliance
CR	4.4000	Left atrial compliance
CS	1.3300	Systemic compliance
CA	0.0800	Aortic compliance
Inertances (mmHg s^2 mL^−1)
LS	0.0005	Inertance of blood in aorta

Figure 2. Elastance function E(t) = 1/C(t) of a healthy heart. (Cardiac cycle = 60/HR).

Table 2. Phases of the cardiac cycle.

Modes	Valves		Phases
	Mitral	Aortic
1	Closed	Closed	Isovolumic relaxation
2	Open	Closed	Filling
1	Closed	Closed	Isovolumic contraction
3	Closed	Open	Ejection
–	Open	Open	Not feasible

Figure 3. Combined cardiovascular and LVAD model.

Table 3. State variables in the cardiovascular model.

Variables	Name	Physiological meaning (units)
	LVP(t)	Left ventricle pressure (mmHg)
	LAP(t)	Left atrial pressure
	AP(t)	Arterial pressure (mmHg)
	AoP(t)	Aortic pressure (mmHg)
	QT(t)	Total flow (mL s^−1)
	QP(t)	Pump flow (mL s^−1)

Table 4. Parameter values in LVAD model.

Parameters	Value	Physiological meaning
Cannulae resistances (mmHg s mL^−1)
Ri	0.0677	Inlet cannula resistance
Rp	0.17070	Pump resistance
Ro	0.0677	Outflow cannula resistance
Cannulae inertances (mmHg s^2 mL^−1)
Li	0.0127	Inlet cannula inertance
Lp	0.02177	Pump inertance
Lo	0.0127	Outflow cannula inertance

Figure 4. Pump flow signals at i(t) = 0.18 amp for different R_S values.

Figure 5. Pump speed signals at i(t) = 0.18 amp for different R_S values.

Figure 6. Block diagram for the LVAD feedback controller.

Figure 7. Pump flow signal as R_S changes from 1 to 0.5.

Figure 8. Lower and upper brackets of the Fibonacci search converging to the estimate of R_S.

Figure 9. Upper and lower brackets of the Fibonacci search converging to the estimate of i_P.