Model based parametric control and analysis of blood pressure

Presentation by
N. Vinoth
Under the guidance of
Dr. J. Krishnan,
Professor,
Dept. of Electronics and Instrumentation – Annamalai University

INTRODUCTION
MODEL BASED PARAMETRIC CONTROL AND ANALYSIS OF BLOOD PRESSURE
2
“The life of a single
human being is worth a
million times more than
all the property of the
richest man on earth”.
―Che Guevara
Heart is the powerful organ of
cardiovascular system which
pumps blood continuously.

INTRODUCTION
3
A heart works tirelessly over
a lifetime. During an average
life span, the heart beats
three billion times without a
single break.
Cardiovascular system
(CVS) is a highly complex
process in which
cardiovascular diseases
make disorders of the heart
and blood vessels and
leads to the malfunctioning
of the cardiovascular
system. It is the disturbing
effect which affects the
cardiovascular system.
From the perception of
Cardiovascular system, it
is intended provide a
solution to human society
related to cardiovascular
system.

INTRODUCTION
• CVS is identical to complex closed hydraulic system. Engineering
modeling of such important system has become a useful tool for
understanding the physiological and pathological problems.
• Computational modeling is a base tool for modeling physiological system.
This aids in the development of diagnostic and therapeutic procedures.
• Computational modeling describes and explains about the basic
mechanisms using comparatively simple models.
• Computational model of the cardiovascular system aids to understand the
fundamental biochemical, biophysical, electrical and mechanical functions
of the normal heart.
4

CARDIOVASCULAR SYSTEM
5

FUNCTIONS OF THE CVS
• Transporting Oxygen and Removing Carbon Dioxide
• Transporting Nutrients and Removing Wastes. Blood absorbs the waste
products made by cells, and transports them to the excretory organs for removal
from the body.
• Protect the body from infection and blood loss.
• Regulating Body Temperature, Temperature changes within the body are
detected by sensory receptors called thermoreceptors.
• Maintains fluid balance is by either dilating (widening) or constricting
(tightening) blood vessels to increase or decrease the amount of fluid that can be
lost through sweat.
6

CIRCULATION OF BLOOD IN HEART
7

BLOOD PRESSURE
8
Blood pressure is at its
highest value when the heart
beats (pumping the blood).
When the heart is at
rest, between beats,
your blood pressure
falls.
This is called SYSTOLIC pressure.
120/80
This is called DIASTOLIC pressure.
Bottom number
Blood pressure is the
force of blood
pushing against the
arteries.
Blood is carried to
all parts of your
body in vessels
called arteries.

MEAN ARTERIAL PRESSURE
• The Mean Arterial Pressure (MAP) is derived from a patient’s Systolic
Blood Pressure (SYS) and Diastolic Blood Pressure (DIAS).
• MAP is often used as a surrogate indicator of blood flow and believed to be
a better indicator of tissue perfusion than SYS.
• A MAP of 60 mmHg or greater is believed to be needed to maintain
adequate tissue perfusion, while normal range falls between 70 and
110 mmHg.
• The Mean arterial pressure is derived from systolic (SYS) and diastolic
(DIAS) pressure measurements (Klabunde RE, 2007).
9

ELECTRICAL AND HYDRAULIC
ACTIVITY OF THE CVS
• The hydraulic activity is also required to
study the cardiac pathologies.
• The hydraulic activity is under the
influence of electrical activity.
• The increase of the intercellular calcium
concentration leads to increase in the
pressure and flow of the ventricles, which
symbolizes the interaction of electrical
and hydraulic activity of the heart.
• Moreover during critical care situations the blood pressure is
(hydraulic activity) most important parameter and it is monitored.
10

MOTIVATION
• The major motivation for the study is to model a
hydraulic CVS model that is able to accurately
reproduce the steady state hemodynamic responses.
• In order to relive the workload of physician and
quick recovery of patient, it is aimed to automate the
drug delivery system.
• It is intended to make a simulation study, which aids
to have better understanding of physiological and
pathological problems.
11

OVERVIEW OF THE STUDY
• The overall work is categorized into three studies.
• Study 1: To obtain the hemodynamic parameters (BP, Flow
Volume) from the three different CVS models.
• Study 2: Automatic regulation of MAP during the post/pre
operative stage and surgery.
• Study 3: Automatic regulation of hypnosis by infusing
anesthetic agent during the surgery.
• Conclusion
12

OBJECTIVES
 Cardiovascular system is viewed in terms of electrical, mechanical and
hydraulic system.
 The prime objective is to study the CVS based on hydraulic activity.
 To simulate the performance of three cardiovascular models.
 To analyze the effects of the parameters and determine the most effective
parameters which affects Mean Arterial Pressure (MAP).
13

ROLE OF ARTERIAL SYSTEM
14
Aorta Arteries Arterioles Capillaries Tissues

ELECTRICAL ANALOGY OF
HYDRAULIC SYSTEM
15
Hydraulic
system
Electrical System
Pressure
Compliance
Laminar
resistance
Inertance
Valves

WINDKESSEL MODEL
• Otto Frank in 1899.(heart and systemic arterial system)
• Compresses air
(Elasticity)
Resistance
(peripheral
Resistance)
• Arterial
Compliance
(ventricle pump)
16

MODELING OF WKM
17
I(t) sine wave
amplitude I0 during systole
I(t) zero otherwise
Tc is the period of the cardiac cycle in seconds
Ts is the period of systole, in seconds
Ts is assumed to be 2/5Tc
blood flow in one cardiac cycle is 90 cm3
I0 = 424.1 mL

FOUR COMPARTMENTAL MODEL
OF CVS
• The four-compartment Model comprises of the left heart, right
heart, pulmonary circulation and systemic circulation.
• The electrical analog model (lumped model) turns out as an
alternative of a hydraulic model for the cardiovascular system
18
Pulmonary
Circulation
Systemic
Circulation
Right HeartLeft Heart

ELECTRICAL ANALOGUE MODEL OF
CVS
19

FUNCTIONING OF VALVES
20

CVS PRESSURE OUTPUTS
21
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
50
100
150
200
Time (seconds)
Pressure(mmHg)
Left ventricle Pressure (Plv)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
10
20
30
40
Time (seconds)
Pressure(mmHg)
Right Ventricle Pressure (Prv)

CVS PRESSURE OUTPUTS (Contd.,)
22
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
2
3
4
5
6
7
8
9
Time (seconds)
Pressure(mmHg)
Left artrium Pressure (Pla)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
1
1.5
2
2.5
3
3.5
Time (seconds)
Pressure(mmHg)
Right atrium Pressue (Pra)

23
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
20
25
30
35
40
Time (seconds)
Pressure(mmHg)
Root arotic pulmonary Pressure (Pap)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
90
100
110
120
130
140
150
160
Time (seconds)
Pressure(mmHg)
Root arotic systemic Pressure (Pas)

24
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
70
80
90
100
110
120
130
Time (seconds)
Pressure(mmHg)
Arterial Pressure (Pa1)
0.8

CVS FLOW OUTPUTS
25
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-200
0
200
400
600
800
1000
Time (seconds)
Flow(ml/second)
Left ventricle outflow (QLV)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-200
-100
0
100
200
300
400
500
Time (seconds)
Flow(ml/second)
Right ventricle outflow (Qrv)

26
CVS FLOW OUTPUTS (Contd.,)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
50
100
150
200
250
300
350
400
450
Time (seconds)
Flow(ml/second)
Right atria outflow (Ql2)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
50
100
150
200
250
Time (seconds)
Flow(ml/second)
Left atria outflow (Qla)

CVS VALVE OUTPUTS
27
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0
0.2
0.4
0.6
0.8
1
Time (seconds)
PulmonaryValveoutput
Pulmonary Valve output
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0
0.2
0.4
0.6
0.8
1
Time (seconds)
Tricupsidvalveoutput
Tricuspid Valve output
0 0.5 1 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0
0.2
0.4
0.6
0.8
1
Time (seconds)
MitralValveoutput
Mitral Valve output
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
0.2
0.4
0.6
0.8
1
Time (seconds)
AtrialValveoutput
Aortic Valve output

CVS VOLUME OUTPUTS
28
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
60
80
100
120
140
Time (seconds)
Volume(ml)
Left ventriclular volume (Vlv)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
60
80
100
120
140
160
Time (seconds)
Volume(ml)
Right ventricular volume (Vrv)

CVS VOLUME OUTPUTS (contd.,)
29
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
20
40
60
80
100
120
Time (seconds)
Volume(ml)
Right atria volume (Vra)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
40
60
80
100
120
Time (seconds)
Volume(ml)
Left atria volume (Vla)

CVS ELSATANCE OUTPUTS
30
0 1 2 3 4 5
0
1
2
3
Time (seconds)
LeftVentricularElastance(mmHg/ml)
Elastance of left ventricle
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
Time (seconds)
RightVentricularElastance(mmHg/ml)
Elastance of right ventricle

• The parameters are varied from 30-70% from the
nominal value, to study effect of parameters on the MAP.
• The parameter values are varied in all the compartments
and the corresponding change in the MAP is tabulated.
• In the left heart, the parameters considered are LLa, RLa,
Ela, LLv, R0s and Elv.
• It is observed that Elv and R0s produce huge variations in
the MAP. Therefore Elv and R0s are the important
parameters of the left heart.
31
PARAMETRIC ANALYSIS

• Right heart the parameters Lra, Lrv, Era, Erv , Vunv and
R0p are varied and the corresponding changes in MAP
is noted.
• It is concluded from the tables that Vunv (unstressed
volume) and R0p are dominant parameter which affects
more on MAP
• Finally from the analysis it is derived that the Elv, R0s
and R0p are the important parameters which affect the
MAP than all the other parameters.
32
PARAMETRIC ANALYSIS (contd.,)

MODELING THE CVS WITH PULSATILE
AND NON PULSATILE COMPONENTS
• The blood pressure difference is analogous to the
voltage, the blood flow impersonates current, the
stressed volume and the compliances of the blood
vessels play the role of an electric charge and
capacitors respectively.
• The blood flow is explained in terms of the mass
balance equations, i.e. the rate of change for the blood
volume V (t) in a compartment is the difference
between the flow into and out of the compartment. Fin
33

ELECTRICAL MODEL OF CVS
Qrv, Crv,
Rrv,Srv
Cap
Rap
Cvp
Rmv
Clv
Rav
Csa
Rsa1
Rsa2 Cfa
Rfa
CasCvs
Ras
34

Contd.,
• The flow F between two compartments can be
illustrated by Ohm's law. It depends on the pressure
difference between neighboring compartments and on
the resistances R against blood flow.
• The model is described as a system of coupled first
order ordinary differential equations representing
pressures in the systemic aorta, arterial systemic,
venous systemic, arterial pulmonary, left ventricle
compartments, right ventricular contractility.
35

CVS PRESSURE OUTPUTS (contd.,)
36
0 500 1000 1500
0
50
100
150
Left ventricle Pressure (Plv)
Time (seconds)
Pressure(mmHg)
1490 1492 1494 1496 1498 1500
0
50
100
150
Time (seconds)
Pressure(mmHg)
1498 1498.2 1498.4 1498.6 1498.8 1499
0
1
2
3
Left ventricular elastance function (Elv)
Time (seconds)
VentricularElastance(mmHg/mL)

37
0 500 1000 1500
100
120
140
160
Arterial Pressure (Pa)
Time (seconds)
pressure(mmHg)
1490 1492 1494 1496 1498 1500
100
120
140
160
Time (seconds)
Pressure(mmHg)
1497.61497.8 1498 1498.21498.41498.61498.8 1499 1499.21499.4
80
90
100
110
120
130
Systolic and Diastolic Pressure
Time (seconds)
Pressure(mmHg)
Psa
SYS & DIAS
Plv

CVS FLOW AND ELSATANCE
OUTPUTS
38
1497 1497.5 1498 1498.5 1499 1499.5
90
95
100
105
Systemic and Pulmonary Peripheral Flows
Time (seconds)
Flow(mL/second)
Systemic flow
Pulmonary flow
0 500 1000 1500
5.1
5.102
5.104
Venous systemic Pressure (Pvs)
Time (seconds)
Pressure(mmHg)
1490 1492 1494 1496 1498 1500
5.1
5.102
5.104
Time (seconds)
Pressure(mmHg)
0 500 1000 1500
3.8
3.9
4
4.1
4.2
Venous pulmonary Pressure (Pvp)
Time (seconds)
Pressure(mmHg)
1490 1492 1494 1496 1498 1500
3.8
4
4.2
Time (seconds)
Pressure(mmHg)

PARAMETRIC ANALYSIS
• The parameter variation analysis is carried out for this
CVS model. In this model, the parameters Csa, Cfa, Cas,
Cvs, Crv, Cap, Cvp, Rsc1, Rsc2, Rrv, Vd, Em and Rap were
varied and their effect on MAP is observed.
• It is observed from the tables that the Em, Rsc1, Rap and
Csa are the vital parameters that produce major effect
on MAP.
39

MODELING OF CVS USING A
ELECTRONIC CIRCUIT
• The model comprises of forty two sections signifying the
arterial system.
• The frequency of heart is chosen as 1 Hz and it is assumed
that the CVS functions are in stable state condition.
• The Ventricles are simulated as a variable capacitance and
the energy of systolic contraction of left and right ventricles
is represented by superposition of three ac power supplies
and diodes.
• The arteries blood vessel, ventricles, capillaries and
arterioles present in the CVS are represented as the
combination of basic electrical components (capacitor,
resistor and inductor).
40

41
BLOCK DIAGRAM OF THE CVS

42
ELECTRONIC CIRCUIT OF
CARDIOVASCULAR SYSTEM

Contd.,
• The pumping actions of the left and right ventricles are
attained by the pacmaker.
• The pacemaker comprise of three ac power supplies and a
pair of diode.
• An 8V dc voltage source is employed for the right ventricle
pacemaker to vary the voltage (pressure) of the ventricle
between 8V to 25V (mmHg).
• Another DC source with an amplitude of 7V is used for the
left ventricle to regulate the variation of pressure around 7–
120 volt (mmHg).
• The current generated from voltage supply is distributed to
left ventricle, aorta and upper body arteries.
43

Contd.,
• Thereafter the current passes toward the body arteries.
• The current from there passes the arterioles, capillaries
and veins and enters to right atrium.
• The required current is produced by additional
amplifier and pacemaker for circulation in the
pulmonary arteries and veins.
• At the end the current enters the left atrium.
• In this circuit there is no leakage of charge since the
output voltage is proportional to the input voltage.
44

Pressure graph of right ventricle
Pressure graph of left ventricle
CVS PRESSURE OUTPUTS
45

Pressure graph of arterial pressure
CVS PRESSURE OUTPUT (contd.,)
46

SELECTION OF PROPER MODEL
• The first model (four compartmental CVS model) is
selected as CVS model for infusing the drugs.
• In Four compartment model Vunv , Elv, R0p and R0s are
the important parameters which affect the MAP than
all the other parameters.
• The drugs Dopamine and Sodium Nitroprusside
affects the same parameters in the heart, so it’s the
prime reason for the selection of the Four
compartment model.
47

OBJECTIVES
 To develop a drug delivery system with a view to
control MAP for the four compartmental model.
 To implement the intelligent control techniques for the
drug delivery system.
 Experimental verification of simulated system.
 Comparing the performance of controllers by
performance indices.
48

LITERATURE REVIWEW
• Slate et.al. (1982) formulated as a linear first-order transfer function with
two time delay components and a well-known model of dynamic
response of MAP to the SNP infusion.
• An adaptive control procedure for SNP regulation of arterial pressure
has been presented by James F Martin Alan (Martin, J. F et.al. 1987). The
theory of Smith predictor has been incorprated in the controller
effectively to remove the infusion delay time, thus simplifying the
control analysis and design.
• A multiple model adaptive predictive controller to simultaneously
regulate the mean arterial pressure and cardiac output in congestive
heart failure subjects by adjusting the infusion rates of nitroprusside
and dopamine has been designed by Yu (Yu et.al.1992).
• An adaptive PI and Fuzzy controllers for an automatic drug delivery
system to reduce the oscillatory change in MAP has been designed and
implemented by Jin Feng, Qu Bo and Zhu Kuanyi (Feng, J., Bo, Q., and
Kuanyi, Z, 2006).
49

• A fuzzy control strategy for two cardiovascular variables, blood
pressure and cardiac output has been illustrated by Cristian Boldişor
(Boldişor et.al.2010). The simulation has been done by making use of a
mathematical model describing the effects of drugs infusion rates on the
controlled variables and the performance reveal their satisfactory
behavior.
• An interval Type-2 Fuzzy Logic Control approach to control Mean
Arterial Pressure by controlling drug infusion has been designed by
Mohammed.Y.Hassan (Hassan M.Y. et.al. 2012).
• The work manages to distant itself from the current literature in the
sense it comes up with a novel control approach for control of MAP.
50

• On the duration of cardiac surgical treatment the
physician often make direct contact with the arterial
system. It causes difficulties during blood pressure
measurement and causes momentary variations in the
mean arterial pressure (van Geene W.J, 1993).
• The anesthesiologist could be so busy with additional
jobs that appropriate alteration of the infusion rate as the
patient's state varies may not be promising.
• It reduces intra operative bleeding, aiding a more
precise and quick operation, and results in less
consumption of drugs.
51
NEED FOR AUTOMATION

CARDIAC DRUGS
Cardiac Drugs
Inotropic
Affects myocardial
contractility
Chronotropic
Affect Heart
Rate
Dromotropic
Affects conduction
speed
52
Dopamine, Dobutamine, Nitroglycerin and Sodium
nitroprusside drugs are few examples for cardiac
drugs.

MULTI DRUG MODEL OF CVS
• The SNP and DP are selected to increase ventricular
contractility and decrease resistance to blood flow
respectively.
• The drugs DP and SNP are interchangeably infused into the
CVS model.
• The target sites of SNP are considered to be the main
parameters which affect the arterial blood pressure in the
CVS such as the Vus,v and Rsys.
• Both Emax,lv and Rsys are modified by the pharmacological
effects of DP which is a vasoconstrictor.
• SNP is a vasodilator and decreases resistance to blood flow
by decreasing Rsys and increasing Vus,v.
53

Contd..,
• The drug infusion therefore affects the controlled
variable MAP by these body parameters. An increase
in DP infusion increases MAP and an increase in SNP
infusion reduces MAP.
• The therapeutic range of SNP (0.0-10.0 μg/kg/min) is
used for both hypertension and acute congestive heart
failure.
• An intermediate infusion range of DP (2-6
μg/kg/min) is used for its inotropic effects and safety
provide during acute congestive heart failure
54

CONCEPTUAL DIAGRAM OF THE
CARDIOVASCULAR SYSTEM WITH
DRUG EFFECTS
55
Cardiovascular
system
DNP
SNP
Drug
effects
Emax
Rsys
Vus_ven
MAP

MODELLING THE DRUG
EFFECT CVS MODEL
• The drug effects of SNP and DP are modeled with the
four compartmental CVS model which is selected.
• The SNP is infused at the 9th second and travels to
lower the MAP. Meanwhile DP is infused on 19th
second and serves to increase the MAP.
56
5 10 15 20 25 30 35
80
82
84
86
88
90
92
94
Time (seconds)
MeanArterialPressure(mmHg)
Open loop response

The transfer function model of SNP and DP on MAP
is given by
57
Contd.,

CLOSED LOOP STUDY
• The performances of the SNP and DP model are analyzed in
closed loop to bring out a comparative study is made with
the different controllers.
• The widespread industrially accepted conventional Ziegler-
Nicholas Proportional-Integral (PI) controller, Fuzzy logic
controller (FLC) and Internal Model Controller (IMC) are
incorporated.
58
Controller
Controller Settings
Kc Ti (s)
ZN-PI SNP -0.2183 -0.5994
ZN-PI DP 0.27 0.6660
ZN-PI Controller settings

Contd.,
• During the pre/post operative state the range of MAP
may be in the range between 100 to 160mmHg.
• At this stage SNP and DP are infused to maintain the
MAP at 93.3mmHg.
• The pre/post operative pressure state scenario is
simulated by keeping the initial MAP as 110mmHg.
• During the anesthetic state (cardiac surgery) the
pressure will be drop down to the range of 65 to
80mmHg in order to relieve the patient from
perceiving pain during surgery.
59

MAP RESPONSE FOR PI
CONTROLLER
60
0 10 20 30 40
85
90
95
100
105
110
Time (seconds)
MAP response to SNP infusion under pre/post operative condition
0 10 20 30 40 50
60
70
80
90
100
110
Time (seconds)
MAP response to ZN-PI based DP infusion under pre/post operative condition

61
Contd.,
0 5 10 15 20
60
65
70
75
80
85
Time (seconds)
MAP response to ZN-PI based DP infusion under anesthetic condition
0 2 4 6 8 10 12 14 16 18 20
65
70
75
80
85
90
95
100
Time (seconds)
MAP response to ZN-PI based SNP infusion under anesthetic condition

MAP RESPONSE TO FLC
62
0 500 1000 1500
90
95
100
105
110
Time (seconds)
MAP response to FLC based SNP infusion under pre/ post operative condition
0 500 1000 1500
64
66
68
70
72
74
76
Time (seconds)
MAP response to FLC based DP infusion under anesthetic condition

Contd.,
630 500 1000 1500
64
66
68
70
72
74
76
Time (seconds)
MAP response to FLC based DP infusion under anesthetic condition
0 500 1000 1500 2000
75
80
85
90
95
Time (seconds)
MAP response to FLC based SNP infusion under anesthetic condition

64
MAP RESPONSE TO IMC
0 20 40 60 80 100 120 140 160 180 200
92
94
96
98
100
102
104
106
108
110
Time (seconds)
MAP response to IMC based SNP infusion under pre/post operative condition.
0 20 40 60 80 100 120
65
70
75
80
85
90
95
Time (seconds)
MeanArterialPressure(mmHg) MAP response to IMC based DP infusion under pre/post operative condition.

Contd.,
65
0 50 100 150 200
75
80
85
90
95
Time (seconds)
MAP response to IMC based SNP infusion under anesthetic condition
0 20 40 60 80 100
65
66
67
68
69
70
71
72
73
74
75
Time (seconds)
MAP response to IMC based DP infusion under anesthetic condition

COMPARISON OF CONTROLLERS
66
0 100 200 300 400
85
90
95
100
105
110
Time (seconds)
Comparison of SNP effect on MAP to controllers
ZN-PI
IMC
FUZZY
0 20 40 60 80 100
60
70
80
90
100
110
Time (seconds)
Comparison of DP effect on MAP response to controllers

PERFOMANCE INDICES
Controller ISE % Overshoot Settling time (s
econds)
PI (SNP) 76.79 6.0021 4.6
FLC (SNP) 26.86 0 300
IMC (SNP) 111.60 0 74
PI (DP) 286.20 16 6.7
FLC (DP) 147.5 0 160
IMC (DP) 162.00 0 56
67

SWITCHING OF CONTROLLER
• The design of switching control strategy guaranteeing that,
at each instant of time, only one control is activated.
• When the error is greater than zero, the SNP based
controller is activated. While the error is less than zero, the
DP based controller is activated.
68
SNP
DNP
Switch
+
-
MAPref
Error
MAP

MAP RESPONSE TO FLC
69
0 500 1000 1500 2000 2500 3000
90
95
100
105
110
Time (seconds)
MAP response to switching of FLC controller for pre/post operative condition
0 500 1000 1500 2000 2500 3000
70
75
80
85
90
95
Time (seconds)
MAP response to switching of FLC controller for anesthetic condition

MAP RESPONSE TO IMC
70
0 50 100 150 200 250
90
95
100
105
110
Time (seconds)
MAP response to switching of IMC controller for pre/post operative condition
0 50 100 150 200 250
70
75
80
85
90
95
Time (seconds)
MAP response to switching of IMC controller for anesthetic condition

REALIZATION OF THE SNP AND DP
MODEL- EXPERIMENTAL SETUP
• The pressure output of the model in terms of voltage
signal is given to PC based control system through
ADC port of VMAT01 interface board.
71

Electronic equivalent model of DP
Electronic equivalent model of SNP
+
_
+
_
+
_
From ADC
10kohm
TO DAC
1kohm
11.68kohm
10kohm
50uF
1kohm
1kohm
10uF 10uF 10uF
6kohm 6kohm 6kohm
+
_
+
_
From ADC
10kohm
TO DAC
1kohm
17kohm
100kohm
10uF
10uF 10uF 10uF
6kohm 6kohm 6kohm
72
ELECTRONIC EQUIVALENT
OF SNP AND DP

MAP RESPONSE TO FLC
73
50 100 150 200 250
65
70
75
80
85
90
95
Experimental simulation of MAP response to FLC
Time (seconds)
50 100 150 200 250 300
85
90
95
100
105
110
115
MAP response to switching controller
Time (seconds)

MAP RESPONSE TO IMC
10 20 30 40 50 60 70 80 90 100
94
96
98
100
102
104
106
108
110
Time (seconds)
74
10 20 30 40 50 60 70 80 90 100
65
69
73
77
81
85
89
93
97
Time (seconds)
Experimental simulation of MAP response to IMC based SNP
under pre/post operative condition
Experimental simulation of MAP response to IMC based DP
under pre/post operative condition

OBJECTIVES
 To study the effect of isoflurane in CVS in terms of mathematical
modeling based on PharmacoKinetic- PharmacoDynamic effect.
 To implement PI, FLC, IMC and NN-IMC control techniques for
PK-PD model to control Bispectral Index (measure of level of
hypnosis)
 Comparison of controller based on the performance indices.
75

LITERATURE REVIEW
• A control algorithm that consists of a cascaded Internal Model Controller (IMC) the aims at
regulating BIS has been proposed by Gentilini (Gentilini et.al. 2001). The model-based
control approaches has been allowed to relate a transparent reconfiguration of the control
algorithm on the basis of the identified patient’s parameters.
• The control of depth of anesthesia has been examined by Atieh Bamdadian (Bamdadian
et.al.2008) with a constrained generalized predictive control (GPC) method. The BIS has
been taken as a patient endpoint and Propofol as an anesthetic agent.
• The clinical aspect and engineering view of measuring, interpreting, modeling, and
controlling of general anesthesia has been reviewed by Jheng-yan Lan (Jheng-yan Lan, J.
Y.et.al.2012).
• A procedure to find the impact of the time delay (TD) of the patient and instrumentations
(bispectral index (BIS) monitor, depth of anaesthesia) during surgery has been projected by
Shahab A. Abdulla (Abdulla, S. et.al.2012). The Smith Predictive Control has been
introduced to estimate the TD.
• The work manages to distant itself from the current literature in the sense it comes up with
a novel controller in this field for control of BIS.
76

HYPNOSIS AND ANALGESIA
• Hypnosis describes the state of anesthesia related to
unconsciousness of the patient and enumerates the
disability of the patient to remember experiences that
occurred during surgery.
• The consciousness can be a disturbing experience, which
may be avoided by maintaining satisfactory hypnosis level
in the patient.
• A suitable metric to measure the depth of hypnosis is the
bispectral index (BIS).
• Analgesia describes the disability of the patient to realize
pain. Surgical practices are painful and can cause
uneasiness to the patient. It is provided by management of
analgesics.
77

BISPECTRAL INDEX (BIS)
• BIS is one of several technologies used to monitor
depth of anesthesia.
• Allows the anesthetist to adjust the amount of
anesthetic agent to the needs of the patient.
78

MODELING OF HYPNOSIS BY
PK-PD
79
The five compartment model comprising of Lungs,
Liver, Muscles, other organs and fat tissues

Contd.,
• The relation between inspired anesthetic drug
concentration Cinsp (g/mL) to the fresh anesthetic gas
concentration Cin (vol. g/mL) and parameters of the
breathing system are given by
• Where Cout is the concentration of isoflurane stream
(g/mL), Qin is the inlet flow rate (mL/min), ΔQ are the
losses (mL/min), V is the volume of the respiratory
system (mL), fR is the respiratory frequency (min-1), VT
is the tidal volume (mL) and Δ is the physiological
dead space (mL).
80

PHARMACOKINETIC MODEL
• The resulting mass balance for isoflurane in the central
compartment is given by
• The Elimination of isoflurane by exhalation and
metabolism in liver which is the 2nd compartment, is
given by
• The remaining compartments mass balance is given by
81

PHARMACODYNAMIC
MODEL
• A PD model is relates the consequence of drug on
the hypnotic level (BIS) .
• The PK model is attached to an effect-site
compartment model which signifies the time lag
between the delivery of drug and its effect on BIS.
• The action of isoflurane on BIS can be expressed
82

Contd.,
• Where EC50 is the concentration of drug at half-
maximal effect and represents the patient’s
sensitivity to the drug, and γ is a dimensionless
parameter that determines the degree of
nonlinearity.
• The BIS has the range between 0 and 100, where
BIS0 = 100 denotes a fully conscious state and
BISMAX = 0 denotes deep coma.
83

BIS OPEN LOOP RESPONSE
84
0 500 1000 1500 2000 2500 3000 3500 4000
40
50
60
70
80
90
100
Time (seconds)
BispectralIndex
Open loop response of BIS

BIS RESPONSE TO PI
CONTROLLER
85
0 50 100 150 200
20
40
60
80
100
Time (senconds)
BispectralIndex
BIS response to PI controller
20 40 60 80 100 120 140 160 180 200
-10
0
10
20
30
40
Time (seconds)
Isofluraneinfusionrate(g/ml)
PI controller output

BIS RESPONSE TO FLC
86
0 50 100 150 200 250 300 350
50
60
70
80
90
100
Time (seconds)
BispectralIndex
Closed loop response of FLC
50 100 150 200 250 300 350
-10
-5
0
5
10
15
20
Time (seconds)
IsofluraneInfusionrate(g/ml)
FLC Controller output

BIS RESPONSE TO IMC
87
0 500 1000 1500 2000 2500 3000
50
60
70
80
90
100
Time (seconds)
BispectralIndex
BIS response for IMC
0 500 1000 1500 2000 2500 3000
0.5
1
1.5
2
2.5
3
3.5
4
Time (seconds)
Isofluraneinfusionrate(g/ml)
IMC controller output

NN-IMC MODELING STEPS
88
Design of neural network internal model controller
Training and validation of Inverse neural model.
Training and validation of Forward neural model
Generation of input-output data

GENERATION OF
INPUT-OUTPUT DATA
• By changing the infusion rate as random number
sequence as input to the PK-PD the corresponding
output is obtained. The identification data set, contains
N = 1000 samples with sampling time of 15 sec.
89
0 200 400 600 800 1000 1200 1400 1600 1800 2000
0
0.5
1
1.5
Time(samples)
Druginfusionrate(g/ml)
0 200 400 600 800 1000 1200 1400 1600 1800 2000
40
50
60
70
80
90
100
Time(samples)
BispectralIndex
Random input to PK-PD model BIS response to random input

Forward Neural Model of PK-PD
model
• The neural network approach is trained to represent
the forward dynamics of the PK-PD model.
• The network is trained using delayed outputs and
current input. The Activation function for the hidden
layer is tansigmoidal, while for the output layer linear
function is selected and they are bipolar in nature.
90
PK-PD model
Inverse neural model
Z-2
Z-1
LM algorithm
u(k)
e(k)
BIS(k)
u ( k )
+
-

TRAINING AND VALIDATION
OF FORWARD NEURAL MODEL
• During training the NN learns the forward of the PK-
PD dynamics by fitting the input-output data pairs. It
is achieved by using the Levenberg Marquardt
algorithm.
It is observed that forward model output exactly
matches with the output of the actual process. Hence,
the neural network has the ability to model forward
dynamics of the PK-PD model.
91
0 200 400 600 800 1000 1200 1400 1600 1800 2000
40
50
60
70
80
90
100
Time (samples)
BispectralIndex
Actual Output
Forward model Output

DIRECT INVERSE NEURAL
MODEL OF PK-PD MODEL
• The neural network approach is also trained to capture
the inverse dynamics of the PK-PD model. The
network is trained using delayed sample of outputs
and delayed input of PK-PD model.
92
PK-PD model
Z-1
Inverse neural model
Z-2
Z-1
LM algorithm
u(k)
e(k)
BIS(k)
u ( k )
u'(k)

TRAINING AND VALIDATION
OF INVERSE NEURAL MODEL
• Inverse model output exactly matches with input
of the actual model.
93
0 200 400 600 800 1000 1200 1400 1600 1800 2000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Time(samples)
Druginfusionrate(g/ml)
Actual input
Inverse model output

DESIGN OF NEURAL INTERNAL
MODEL CONTROLLER
• The neural internal model control approach is similar
to the direct inverse control approach above except for
two additions.
• The first is the addition of the forward model placed in
parallel with the plant, to cater for plant or model
mismatches and the second is that the error between
the plant output and the neural net forward model is
subtracted from the set point before being fed into the
inverse model.
• A filter can be introduced prior to the controller to
obtain robustness in the feedback system.
94

Inverse neural model PK-PD model
Z-2
Z-1
Forward model
BIS(k)
u ( k )
-
+
Z-2
Z-1
Z-1
+
-
Ysp
NEURAL INTERNAL MODEL
CONTROLLER
95

NN-IMC RESPONSE FOR BIS
96
0 1000 2000 3000 4000 5000 6000
50
60
70
80
90
100
110
BIS response to NN-IMC
Time (seconds)
BispectralIndex

COMPARISON OF
CONTROLLER PERFOMANCES
97
0 500 1000 1500 2000 2500
20
40
60
80
100
120
Time (seconds)
BispectralIndex
Comparison of controllers
CONV PI
FUZZY
NN-IMC
IMC

PERFORMANCE INDICES
Controller ISE % Overshoot Settling time (s
econds)
PI (SNP) 7.06 x105 30 140
FLC (SNP) 5.22 x105 0 760
IMC (SNP) 1.42 x107 0.9 2100
NN-IMC 1.12 x105 0 3920
98

CONCLUSION
• Based on parametric analysis, it is inferred that four
compartmental CVS has been chosen to be best for
drug infusion.
• Besides it has been also observed that Elv, Vus and
R0p turn out to be the dominant parameter which
affects MAP at different operating points with these
control strategies.
• The drugs SNP and DP have been infused to study the
effect on the chosen CVS model and illustrate its effect
on Elv (Maximum elastance of left ventricle), Vus
(Unstressed volume) and Rsys (Systemic resistance).
99

Contd.,
• The ranking of the different control strategies have been
summarised
• The IMC has been found to work well with higher
performances compared to other control strategies for CVS
drug model.
• The ZN-PI has been seen to offer a relatively poor
performance among the strategies attempted.
• Fuzzy logic has been projects to stand second in
performance.
• For the PK-PD model NN-IMC outperforms the mediocre
performance of fuzzy logic and poor performance of PI
controller.
100

SCOPE FOR FUTURE RESEARCH
• The Modeling of CVS can be done by including the
effects of baroreceptor and chemocepteor on MAP.
• The receptors can act as a sensor to effect changes in
pressure.
• The extensions to construct Multi Input Multi Output
(MIMO) system can be considered through the control
of heart rate, cardiac output and mean pulmonary
arterial pressure.
101

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Contd.,

LIST OF PUBLICATIONS
International Journal
• N.Vinoth, J.Krishnan, R.Malathi, “Modeling and Analysis of
Sinoatrial Cell using SIMULINK - A Computational Approach”,
International Journal of Engineering Research and Applications, Vol. 3,
No.1, pp826-831, Jan –Feb, 2013. ISSN 2248-9622. Impact factor: 1.325.
• N.Vinoth, J.Krishnan, R.Malathi,“Modelling of Four Compartment
Model of Cardiovascular System Using Simulation”, CiiT International
Journal of Biometrics and Bioinformatics, Vol 5, No.1, pp 1-6,Jan 2013.
ISSN 0974 – 9675. Impact factor: 0.361.
• N.Vinoth, J.Krishnan, R.Malathi, “Performance analysis of neural
network based control of hypnosis and analgesia during anesthesia by
employing a PharmacoKinetic-PharmacoDynamic model”,
International Journal of Current Research, Vol.5, No.10, pp.3133-3139,
Oct, 2013. ISSN 0975-833X. Impact factor: 0.455
• N.Vinoth, J.Krishnan, R.Malathi ,“Control of mean arterial
pressure by cardiac drug infusion system using fuzzy logic
controller”, Asian Journal of Science and Technology, Vol. 5, Issue 2, pp.
148-152, February, 2014. ISSN 0976-3376. Impact factor: 0.552.
110

International Conferences
• N.Vinoth, L.abunesan and J.Krishnan Parameter Estimation
of Cardiovascular Model With Pulsatile And Non-Pulsatile
Components, International Conference on “Biomaterials,
Implant Devices and Tissue Engineering (BIDTE)”, Rajalakshmi
Engineering College, Chennai, India, Jan. 6-8, 2012.
• N. Vinoth, M.Kirubakaran, J.Krishnan and R.Malathi “Fuzzy
logic based Multidrug infusion for blood pressure control”,
TIMA –MIT Campus, Anna university, pp190-194, Dec 2013.
National Conference
• N.Vinoth, and J.Krishnan “Simulation study of baroreceptor
activity and control of heart rate”, proceedings of the 36th
National System Conference, pp 138-141, Dec 2012.
111

112

• The segments of the CVS are listed as, 1-Left Atrium;
2-Left Ventricle; 3, 4, 5, 12, 13, 14, 15, 16- different
Aorta Sections; 6 to 11, A, B-Carotid and Subclavin
Arteries; 17 to 22- Femoral and Iliac Arteries
sections; 23-Hepatic; 24-Gastric; 25-Splentic;26-Left
Renal;27-Right Renal; 28-Superior Mesenteric; 29-
Inferior Mesenteric; 30-Arterioles; 31-Capillaries; 32
and 33- Veins; 34-Right Atrium; 35-Right Ventricle;
C, D, E-Pulmonary Artery Sections; F,G-Pulmonary
Veins.
113
DETAILS OF CVS
MODEL SEGMENTS

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