The presentation was delivered by me at Electrical Engineering department of IIT KGP as a part of best project contest. The presentation is about design and development of a rate responsive cardiac pacemaker based on SO2 saturation level in blood.

1. 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.

2. 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.
•

3. 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.

4. BLOCK DIAGRAM OF PMCV SYSTEM

5. 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 bpm
At a workload of 50 watts ------- HR = 77 bpm
At a workload of 100 watts------ HR = 86 bpm

6. 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

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

8. NON-LINEAR DYNAMICAL SIMULATION OF THE PMCV SYSTEM
The differential equations governing the system are:
d
14x1+14τ1 dt (X1) = P --------(1)
d
X2 + τ3 dt (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)
d
X3 + τ2 dt (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)
d
Hence, X3 + τ2 dt (X3) = [0.2 – (OXC0+X2)/{0.16 HROP – 4.53 -0.08K(SO2ref –
M*X4)}] --------(3)
d
Let (X4) = X5 -------- (4)
dt
d
And (X5) = X6 -------- (5)
dt
d
(X6) = -(68*X6+11.65*X5+X4-X3)/263 --------(6)
dt

9. 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.

10. 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.