Non-invasive Pain Sensor Development for Advanced Control Strategy of

Anesthesia

A Conceptual Study

Dana Copot, Am

elie Chevalier, Clara M. Ionescu and Robin De Keyser

Department of Electrical energy, Systems and Automation, Ghent University,

Sint-Pietersnieuwstraat 41, Blok B2, 9000, Gent, Belgium

Keywords:

Compartmental Fractional Derivative Models, Fractional-Order Impedance Models (FOIM), Model-based

Predictive Control (MPC), Non-invasive Pain Sensor.

Abstract:

This paper introduces the mechanisms of pain perception in the human body in order to start the challenging

task of controlling analgesia as part of general anesthesia. This research proposes a pain sensor, which mea-

sures analgesia levels. For control purpose, a prediction model is needed in order to obtain a model-based

predictive control (MPC) strategy. This paper proposes to employ a compartmental fractional-order derivative

model as a prediction model for the diffusion process that occurs when a drug is taken up by the human body.

Simulations are preformed to investigate the effect of the fractional order on the diffusion of Propofol in the

human body.

1 INTRODUCTION

The main objective of a drug delivery system is to pro-

vide effective therapy by minimizing the side effects

and reducing deviation from the desired state of the

patient. To develop an advanced drug delivery sys-

tem, there is a need for a mathematical model, which

takes pharmacodynamic and pharmacokinetic effects

of the drugs into account.

Nowadays, the applications of control theory rely

mostly on deterministic assumptions where the gen-

eral approach of open-loop conﬁguration assumes

that the pharmacokinetic relations can be modeled

by a linear system with known parameters (Wagner,

1976). Nevertheless, these assumptions do not take

into account the individuality of each patient. Fur-

thermore, is the model optimization procedure based

on the average of a population which results in sub-

optimal solutions. Therefore, the challenge is to use

a closed-loop conﬁguration in order to formalize the

process of observation and intervention to provide a

better and more accurate control.

Moreover, some computer-control systems try to

predict the future drug effect in order to adjust the

parameters in advance (Absalom et al., 2011). As

anesthesia is neither a simple process nor a well-

understood process, it is a very challenging system

to control. Taking into account the difﬁculty in mod-

eling consciousness, the mechanism of anesthetic-

induced loss of consciousness is nowadays still con-

founding scientists. Current models for anesthe-

sia are mean ﬁeld models of drug action (Absalom

et al., 2011), which describe anesthetic phenomena

based on the electroencephalogram (EEG) and asso-

ciated with different brain states. A relationship be-

tween changes in EEG signals and depth of anes-

thesia was developed in order to control the deliv-

ery of intravenous drugs. Afterwards, this relation-

ship was used to inject liquid ether into an anes-

thetic circuit. The ﬁrst main impulse was given in the

early 70s with the introduction of physiology-based

compartment-models of uptake and action of anes-

thetic drugs (Zwart et al., 1972).

The advantage of automated closed loop control

of anesthesia is a continuous drug delivery contrary

to intermittent control, which is nowadays standard

practice. By having a continuous drug delivery, over-

dose or under-dose of hypnotic or analgesic drugs

can be avoided. Under-dosing patients can result in

sensing pain during the surgery without being able

to move. However, feedback information currently

presents a major problem for control algorithms be-

cause of the presence of artifacts (e.g. eye movement,

leg movement, etc.) or by patient mismatch, which

results in erroneous signals. Consequently, the qual-

ity of measured signals decreases, leading to complex

Copot D., Chevalier A., M. Ionescu C. and De Keyser R..

Non-invasive Pain Sensor Development for Advanced Control Strategy of Anesthesia - A Conceptual Study.

DOI: 10.5220/0004742800950101

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2014), pages 95-101

ISBN: 978-989-758-013-0

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

numerical ﬁltering.

The paper is structured as follows: in section II,

we describe how pain is perceived and transmitted

during anesthesia. The challenges coinciding the au-

tomated control of anesthesia are discussed in section

III, followed by the discussion of the proposed sensor.

Section IV shows the simulations and results. In the

last section conclusions are formulated.

2 PAIN PERCEPTION AND

TRANSMISSION DURING

ANESTHESIA

Anesthesia is the process of having sensation (includ-

ing the feeling of pain) blocked or temporarily taken

away. Adequate anesthesia can be deﬁned as a re-

versible pharmacological state where the three main

parts of anesthesia (muscle relaxation, hypnosis and

analgesia) are guaranteed. Good monitoring of anes-

thesia includes an attentive observation of the patient

during critical phases. There are several kinds of gen-

eral anesthetics, but those most commonly used en-

hance or mimic the action of the inhibitory neuro-

transmitter gamma-aminobutyric acid (GABA) (Gar-

cia et al., 2010).

The main components of anesthesia are: (1) mus-

cle relaxation, which is induced to prevent unwanted

movement or muscle tone and causes paralysis dur-

ing surgical procedures. EMG signals are used to

quantify the level of muscle relaxation. (2) hypno-

sis, which is a general term indicating unconscious-

ness and absence of post operative recall of events oc-

curred during surgery (Kuizenga et al., 2001). Level

of hypnosis is related with the infusion of drugs and

can be monitored by a BIS monitor (based on EEG)

and (3) analgesia (pain relief) which is an insensibil-

ity to pain without loss of consciousness i.e. a state

in which painful stimuli are not perceived or not in-

terpreted as pain. It is usually induced by an anal-

gesic drug, although trauma or a disease may produce

a general or regional analgesia. Figure 1 shows the

input-output variables of anesthesia. Notice, that the

three main parts of anesthesia are unmeasurable up

until now. However, relationships have been deﬁned

between unmeasurable and measurable outputs in or-

der quantify the levels of hypnosis and relaxation. For

analgesia levels ,however, these methods are insufﬁ-

cient.

Understanding pain perception and transmission

is necessary in order to measure analgesia during gen-

eral anesthesia. Pain receptors are distributed in the

superﬁcial layers of the skin (Figure 2) or in some

HUMAN BODY

i.v. ANESTHETICS

VOLATILE ANESTHETICS

MUSCLE RELAXANTS

VENTILATION PARAMETERS

NaCl

SURGICAL STIMULUS

BLOOD LOSS

MANIPULATED

VARIABLES

DISTURBANCES

HYPNOSIS

ANALGESIA

RELAXATION

EEG PATTERN

HEART RATE

CONC.

BLOOD PRESSURE

INSP/EXP CONC.

UNMEASUREABLE

OUTPUTS

MEASUREABLE

OUTPUTS

Figure 1: Schematic of input/output variables of anesthesia.

internal tissues. Five different types of receptors ex-

ist: (1) mechanoreceptors, which detect mechanical

deformation of the receptor or its adjacent cells; (2)

thermoreceptors, which detect changes in tempera-

ture; (3) nociceptors, which detect the damage of the

tissues, whether it be physical or chemical damage;

(4) electromagnetic receptors, which detect light on

the retina of the eye and (5) chemoreceptors, which

detect the taste in the mouth, smell in the nose, oxy-

gen levels in the arterial blood, carbon dioxide con-

centration and other factors that make up the chem-

istry of the body. Pain receptors are activated by ex-

tremes of pressure and temperature or as a veritable

soup of chemicals released from injured tissue. His-

tamine, K

, ATP (AdenasineTriPhosphate), acids and

bradykinin are among the most potent pain producing

chemicals (Keele, 1970).

Figure 2: Schematic overview of pain receptors in the skin

(Marieb and Hoehn, 2011).

Pain perception has three stages: (1) a peripheral

stage peripheral tissue sensitization, (2) a transmis-

sion stage - by specialized structures and (3) an inte-

gration of pain - can be conscious or not and involves

functions such as: attention, concentration, memory,

affect.

Peripheral stage - in this ﬁrst stage tissues are

damaged due to chemical, mechanical or thermal

stimuli followed by stimulation of pain receptor and

activation of the receptors by noxious stimuli. When

an inﬂammation appears the pain ﬁbers are subdued

to chemical aggression. Once the tissue is damaged,

the release of chemical substances (e.g. bardykinin)

takes place. This leads to a sensitization of nerve end-

ings that results in a pain signal and an increase in

local temperature (Marieb and Hoehn, 2011).

BIODEVICES2014-InternationalConferenceonBiomedicalElectronicsandDevices

Figure 3: Schematic representation of a biological pain pathway (right side) and general ﬂow chart of the pain perception

process (left side).

Transmission stage - the second stage includes:

peripheral receptors, nervous tracts, spinal mecha-

nisms, ascending and descending pathways, brain-

stem, thalamus and the cortex. According to control

theory of pain (Melzack, 2011), the mechanism in

the brain acts as a gate to increase/decrease the ﬂow of

nerve signals from the peripheral receptors to the cen-

tral nervous system. Pain transmission is inﬂuenced

by many factors such as: (a) a continuous increase of

duration and amplitude of the action potentials in the

dorsal horn, this phenomenon is named wind-up phe-

nomenon, (b) a correlation of the ampliﬁcation phe-

nomenon according to the stimulation of ﬁbers. Clin-

ically, this results in hyperalgesia or secondary pain

and the phenomenon is described as a temporal sum-

mation and (c) a central hypersensitivation, this rep-

resents the pathophysiological mechanism of chronic

pain.

Integration stage - the last stage involves com-

ponents such as brainstem, thalamus, hypothalamus,

subcortical nuclei and brain cortex. These structures

take care of ﬂexion reﬂexes, pain sensation and its

perception, responses, etc. Pain control depends on

the thalamus and the gate system.

A schematic representation of the pain pathway is

presented in ﬁgure 3. The incoming pain ﬁbers excite

second-order neurons that send long ﬁbers to the op-

posite side of the cord and then upward to the brain

as can be observed in ﬁgure 3 (right hand side). Fig-

ure 3 (left hand side) shows a general ﬂow chart that

describes the pain perception process.

3 CHALLENGES FOR

AUTOMATED CONTROL OF

ANESTHESIA

The development of a pain sensor to measure analge-

sia levels during general anesthesia has several chal-

lenges.

• The ﬁrst step is to obtain a suitable patient model.

Taking into account the individuality of each pa-

tient the identiﬁcation is very challenging.

• The second challenge of this research is that this

model has to be generalized.

To control the depth of the anesthesia, there is a

need for a sensor that can measure the level of analge-

sia. The degree to which a person reacts to pain varies

tremendously. A robust controller should handle the

nonlinear response proﬁle and inter- and intra-patient

variation of the patient’s analgesic state to infusion

of an analgesic drug (e.g. Reminfetanil, Propofol).

An ideal controller guides the induction of anesthesia

in order to reach the target as fast as possible with-

out initial overshoot and maintains the desired tar-

get. Therefore, from control engineering viewpoint,

model-based predictive control (MPC) plays a crucial

role in solving such complex problems.

Non-invasivePainSensorDevelopmentforAdvancedControlStrategyof

Anesthesia-AConceptualStudy

One proposed beneﬁt of automated, closed-loop

drug delivery systems is that continuous, responsive

control of the clinical and therapeutic effect may im-

prove quality of care compared to intermittent control.

3.1 Non-invasive Pain Sensor

Development

Pain is a complex response to the interaction of mul-

tiple inﬂammatory mediators that are released at the

point of injury. Clinical assessment of pain is neces-

sary to diagnose, manage and choose treatment op-

tions, as well as for the evaluation of the most efﬁ-

cient treatment. Current methods of assessing pain

include visual analog, Wong-Baker faces and verbal

numeric scales (Hemmerling et al., 2007). However,

studies have shown that these methods may be sub-

jective and discrepancies are likely to be recorded for

similar pain intensity measurements. Hence, there is

a need to develop a more objective scale that relies on

the fundamentals of biochemical mechanisms of pain

transduction.

General anesthesia consists of three components

acting simultaneously on the patient’s vital signs:

hypnosis, analgesia and neuromuscular blockade.

Hypnosis and neuromuscular blockade are relatively

well-characterized and can be quantiﬁed by respec-

tively electroencephalogram (EEG) and electromyo-

gram (EMG) data. By contrast, analgesia is far from

being well-characterized and no sensor is available for

measuring the pain relief levels that the patient ex-

periences during general anesthesia. The challenge

originates from unavailability of models that charac-

terize pain perception in the neural dynamics. Un-

like the well-understood dose-response relationship

for the hypnotic component of sedation, the dose-

response relationship for the analgesic component of

sedation needs further study.

Figure 4 shows the three main parts proposed for

a pain sensor: the role of biological recognition ele-

ments (receptors, enzymes, antibodies, etc.) is to dif-

ferentiate the target molecules in the presence of var-

ious chemicals, the transducer electrochemical, opti-

cal, magnetic, etc.) converts the bio-recognition event

into a measurable signal, the signal processing part

converts the signal into a readable form.

3.2 A Prediction Model for

Model-based Predictive Control

Model-based Predictive Control (MPC) refers to a

family of control algorithms that compute a sequence

of manipulated variables by solving an optimiza-

tion problem, incorporating explicit knowledge of the

Figure 4: Three main parts of the proposed sensor.

plant model and incorporating feedback information

(De Keyser, 2003). Due to the properties of MPC

(its ability to handle nonlinear, constrained, and mul-

tivariable systems but also its severe computational

requirements), it has primarily been used in the chem-

ical process industries. Thus, while MPC remains an

open and growing area of research in systems and

control, there are somewhat limited applications re-

ported outside the processes industries. More re-

cently, there has been considerable interest in ex-

panding the applicability of MPC to other domains

of engineering which were traditionally considered

unsuitable for MPC due to their small physical size

and fast dynamics. The MPC strategy can be visual-

ized by the block-scheme in Figure 5 (De Keyser and

Van Cauwenberghe, 1981; D’hulster et al., 1983).

Model

Optimizer

Cost Function

Constraints

Future Errors

Future Inputs

Past Inputs

and Outputs

Predicted

Outputs

Reference

Trajectory

Figure 5: MPC block-scheme.

The success of MPC as a computer control

paradigm can be attributed to three important factors.

First and foremost is the incorporation of an explicit

process model into the control calculation; this allows

the controller to deal directly with all signiﬁcant fea-

tures of the system dynamics. Second, the MPC al-

gorithm predicts the system behavior over a future

horizon in time. This means that the effects of distur-

bances can be anticipated and removed, allowing the

controller to drive the system more closely along the

desired trajectory. Finally, the MPC controller con-

BIODEVICES2014-InternationalConferenceonBiomedicalElectronicsandDevices

siders input, state and output constraints directly in

the control calculation. This means that constraint vi-

olations are far less likely, resulting in tighter control

around the optimal operating point of the system.

Standard models include step response models,

transfer function models and linear state space mod-

els, however, these models do not sufﬁce in model-

ing the dynamics of the diffusion processes that oc-

cur in the human body. To model the diffusion pro-

cesses in the human body, we use compartmental

models in combination with fractional-order deriva-

tives i.e. Fractional Calculus (Dokomuetzidis et al.,

2010). Two compartments are used in this diffusion

model: plasma (blood) and muscle.

3.2.1 Fractional Calculus Principles

Fractional Calculus is a generalization of integration

and derivation to non-integer (fractional) order oper-

ators (West, 1990). At ﬁrst, we generalize the dif-

ferential and integral operators into one fundamental

operator D

(n is the operation order) which is known

as fractional calculus. Several deﬁnitions of this op-

erator have been proposed. All of them generalize

the standard differentialintegral operator in two main

groups: (a) they become the standard differential inte-

gral operator of any order when n is an integer; (b) the

Laplace transform of the operator D

is s

(provided

zero initial conditions), and hence the frequency char-

acteristic of this operator is ( jω)

. The latter is very

appealing for the design of parametric modeling and

control algorithms by using speciﬁcations in the fre-

quency domain. A fundamental D

operator, a gener-

alization of integral and differential operators (differ-

integration operator), as shown in equation (1).







, n > 0

1, n = 0

(dα)

−n

, n < 0

(1)

In this equation n is the fractional order (FO) and

dα is the derivative function. Since the entire re-

search will focus on the frequency domain approach

for fractional order derivatives and integrals, we shall

not introduce the complex mathematics for time do-

main analysis. The Laplace transform for integral and

derivative order n are, respectively:

L{D

−n

f (t)} = s

−n

F(s) (2)

L{D

f (t)} = s

F(s) (3)

where F(s) = L{ f (t)} and s is the Laplace complex

variable. The Fourier transform can be obtained by

replacing s by jω in the Laplace transform and the

equivalent frequency-domain expressions are:

( jω)



cos

nπ

− jsin

nπ



(4)

( jω)

= ω



cos

nπ

+ jsin

nπ



(5)

Thus, the modulus and the argument of the FO terms

are given by:

Modulus(dB) = 20 log



( jω)

∓n



= ∓20nlog

(6)

Phase(rad) = arg



( jω)

∓n



= ∓n

(7)

resulting in a straight line with a slope of ∓20n pass-

ing through 0 dB for ω = 1 for the magnitude (dB

vs. log-frequency), respectively a horizontal line,

thus independent with frequency, with value ∓n

for

the phase (rad vs. log-frequency). The respective

sketches are given in ﬁgure 6.

Figure 6: Sketch representation of the FO integral and

derivator operators in frequency domain, by means of the

Bode plots (magnitude above and phase below).

3.2.2 Principles of Compartmental Fractional

Derivative Models

A two-compartmental fractional derivative model can

be used to model the diffusion process in the human

body (Popovic et al., 2010; Beneken and van Oost-

rom, 1998). The model is formulated so that the mass

balance is preserved. In ﬁgure 7, we see a conceptual

schematic of a model.

Figure 7: Conceptual schematic of a two compartment

model.

The ﬁrst compartment represents the plasma or

any other region in the body where the kinetics of

the drug are uniform. The second compartment repre-

sents the place where the drug is applied i.e. muscle,

subcutaneous tissue or digestive tract. Traditionally,

Non-invasivePainSensorDevelopmentforAdvancedControlStrategyof

Anesthesia-AConceptualStudy

the two compartments are described by a system of

differential equations of integer order.

˙q

(t) = −K

(t) (8)

˙q

(t) = K

(t) − K

(t) (9)

Recently, the fractional-order models seem to better

suit the dynamics of biological systems than the in-

teger one (Magin, 2010). A simple model of a two-

compartmental system is then given by the following

equations:

−1

(t) = −K

(t), (10)

−1

(t) = K

(t) − K

(t), (11)

where we assumed K

= 0, K

= 0 and with the ini-

tial conditions q

(0) = dose, and q

(0) = 0. In these

equations τ

and τ

are time constants which repre-

sent the speed of diffusion, while n

and n

represent

a non-integer between 0 and 1 and characterize the

type of diffusion (sub-, super-, etc).

4 SIMULATIONS AND RESULTS

In this section we presents a ﬁrst attempt in using

the fractional order derivatives in modelling Propo-

fol concentration. Based on the fractional-order two-

compartmental model mentioned in the previous sec-

tion, simulations are performed. In our simulations,

the anesthetic drug is Propofol. The objective of

this simulations is to investigate the inﬂuence of the

fractional-order derivatives on the Propofol concen-

tration in a target organ i.e. the muscle.

We simulate the diffusion of Propofol in a patient

of 45 years old that weighs 90 kg and has a height of

184 m. We take a bolus injection of 3.33 mg/s during

a period of 15 seconds, which corresponds with an

injected amount of drug of 50 mg.

The values of K

and K

are dependent on the

age of the patient and are calculated as follows:

= 1.29 − 0.024 ∗ (age − 53) (12)

(13)

with v

the volume of blood in liters (v

= 4,27`).

Figure 8 shows the amount of Propofol in com-

partment 1, i.e. the bloodstream, as a function of time

and the fractional order α. In ﬁgure 9 we see the

amount of drug for compartment 2, i.e. the muscle,

in function of time at distinct values of α. From ﬁg-

ure 8 we can conclude that the decay of the numerical

solution changes in function of α. For lower values

of α, we observe higher decay rates, which show that

fractional-order models can capture inter-patient vari-

ability. In ﬁgure 9 we can see that the higher values

of α will result in higher amounts of drug taken up

by the muscle. This can be explained by the slower

decay rates in the bloodstream resulting in more time

for the drug to diffuse through the membrane.

Figure 8: Amount of drug in compartment 1 as a function

of α and time.

Figure 9: Amount of drug in compartment 2 as a function

of α and time.

5 CONCLUSIONS

Controlling analgesia levels during general anesthe-

sia is of great importance for the patient’s quality of

treatment. This research gives a overview of the com-

plexity of the neurophysiological pain perception pro-

cess needed to understand analgesia. A non-invasive

pain sensor has to be developed to ensure feedback in

the analgesia control strategy. The main challenges in

this development is the patient model. A model-based

predictive control strategy is proposed for the analge-

sia process based on a two-compartmental fractional

derivative model. Simulations show the effect of the

fractional order on the concentration of Propofol in

a patient. We conclude that different values for the

fractional order of the model can capture inter-patient

variability, making compartmental fractional deriva-

BIODEVICES2014-InternationalConferenceonBiomedicalElectronicsandDevices

100

tive models suitable to model the diffusion process in

the human body.

ACKNOWLEDGEMENTS

C. M. Ionescu acknowledges the Flanders Research

Center (FWO) for its ﬁnancial support. This re-

search is supported by Flemish Research Foundation

-Research Project FWOPR2013 005101.

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