DESIGN OF A CONTROLLER FOR A RATE-RESPONSIVE CARDIAC PACEMAKER

Presented by: Somnath Banerjee

Presented by Somnath Banerjee at Electrical Engineering Department, IIT Kharagpur as a part of “Best B.Tech Project” contest. The project was selected among best 5 projects in a department of 80+ students.

KEY TERMS AND CONCEPTS:

Cardiac Pacemaker. Rate-responsive pacing.

Closed loop and Open loop pacemaker controller.

Cardiovascular plant and its dynamics.

Heart rate (HR) and Cardiac Output (CO).

Oxygen Supply (OXS) and Oxygen Consumption (OXC).

Oxygen Saturation Level (SO2) near the ventricle.

OBJECTIVES OF THE PROJECT

Development of a block diagram of the Pacemaker – Cardiovascular (PMCV) system.

Design of a closed loop controller based on sensing venous oxygen saturation level.

Steady state simulation of the PMCV system.

Approximate linear dynamic simulation of PMCV system.

Non-linear dynamic simulation of PMCV system.

BLOCK DIAGRAM OF PMCV SYSTEM

DESIGN OF CONTROLLER AND STEADY STATE SIMULATION:

After much iteration, we fixed the proportional controller gain at 1000 and feedback gain at 0.6. For this combination, the steady state simulation shows:

At a workload of 0 watt ---------- HR = 61 bpmAt a workload of 50 watts ------- HR = 77 bpmAt a workload of 100 watts------ HR = 86 bpm

LINEAR DYNAMIC SIMULATION:

Removing the non-linearities:

It is assumed that HR never goes beyond HROP.

To remove the non-linearity due to (1/CO) term, the system is simulated for small changes in workload around a fixed point.

Transfer Functions:

T1(S) = ΔSO2/ ΔP = (A1S+A2)(0.1717-S)/14(300S2+40S+1)(15S2+A3S+A4)

T2(S) = ΔHR/ ΔP = -K*M*(A1S+A2)(0.1717-S)/ 14(300S2+40S+1)(15S2+A3S+A4)

Where, A1 = 30g1-1.75g2 A2 = g1-0.175g2

A3 = 2.5755-0.16*K*M*g1

A4 = 0.1717+0.027*K*M*g1

g1 = [OXC/(CO)2] and g2 = 1 / CO

Plot 1: Unit step response of T2(S) at operating point P = 0W. Change of HR due to unit change in workload.

NON-LINEAR DYNAMICAL SIMULATION OF THE PMCV SYSTEM

The differential equations governing the system are:

14x1+14τ1 (X1) = P --------(1)

X2 + τ3 (X2) = 0.0125P ------- (2)

When HR<= HROP,

X3(S) = [0.2 – (OXC0+X2(S))/{0.16K(SO2ref – M*X4(S))-4.53+X1(S)}]/(1+Sτ2)

X3 + τ2 (X3) = [0.2 – (OXC0+X2)/{0.16K(SO2ref – M*X4)-4.53+X1}]

When HR> HROP,X3(S) = [0.2 – (OXC0+X2(S))/{0.16 HROP – 4.53 -0.08K(SO2ref –

M*X4(S))}]/(1+Sτ2)

Hence, X3 + τ2 (X3) = [0.2 – (OXC0+X2)/{0.16 HROP – 4.53 -0.08K(SO2ref –

M*X4)}] --------(3)

Let (X4) = X5 -------- (4)

And (X5) = X6 -------- (5)

(X6) = -(68*X6+11.65*X5+X4-X3)/263 --------(6)

Plot 1 : The variation of HR for a step change in P from 0 to 100W. Values of OXC0

and SO2ref remain constant at 0.269 and 0.15 respectively. Initial condition was HR = 61 bpm.

REFERENCES

[1] Leslie Cromewell, Fred J. Weibell, Erich A. Pfeiffer, “Biomedical Instrumentation and Measurements”, Prentice-Hall of India Private Limited, New Delhi, second edition, December 2001.

[2] John G. Webster, Editor, “Medical Instrumentation – Application and Design”, John Wiley & Sons (Asia) Private Limited, Third Edition, 1999.

[3] Gideon f. Inbar, R.Heinze, Klass N. Hoekstein, Hans-Dieter Liess, K. Stangl, and A.Wirtzfeld, “Development of a Closed-Loop Pacemaker Controller Regulating Mixed Venous Oxygen Saturation Level”, IEEE transactions on Biomedical Engineering, Vol. 35, No. 9, pp. 679-690, September 1988.

[4] George K. Hung, member, IEEE, “Application of Root Locus Technique to the Closed-Loop SO2 Pacemaker-Cardiovascular System”, IEEE transactions on Biomedical Engineering, Vol. 37, No. 6, pp. 549-555, June 1990.

[5] Benjamin C. Kuo, “Automatic Control Systems”, Prentice-Hall of India Private Limited, Prentice-Hall of India Private Limited, New Delhi, Seventh Edition, 2000.

[6] Michael C. K. Khoo, “ Physiological Control Systems – Analysis, Simulation, and Estimation”, IEEE Press, Prentice-Hall of India Private Limited, 2001.