256IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 2, APRIL 2009
Control of Drug Administration During Monitored
Antonello L. G. Caruso, Thomas W. Bouillon,
Peter M. Schumacher, Eleonora Zanderigo, and Manfred Morari
Abstract—Monitored anesthesia care (MAC) is increasingly used to
provide patient comfort for diagnostic and minor surgical procedures.
The drugs used in this setting can cause profound respiratory depression
even in the therapeutic concentration range. Titration to effect suffers
from the difficulty to predict adequate analgesia prior to application of
a stimulus, making titration to a continuously measurable side effect an
attractive alternative. Exploiting the fact that respiratory depression and
analgesia occur at similar drug concentrations, we suggest to administer
opioids and propofol during MAC using a feedback control system with
transcutaneously measured partial pressures of CO ?PtcCO? as the
controlled variable. To investigate this dosing paradigm, we developed
a comprehensive model of human metabolism and cardiorespiratory
regulation, including a compartmental pharmacokinetic and a pharmaco-
dynamic model for the fast acting opioid remifentanil. Model simulations
are ingoodagreementwithventilatoryexperimentaldata, bothin presence
and absence of drug. Closed-loop simulations show that the controller
maintains a predefined CO target in the face of surgical stimulation and
variable patient sensitivity. It prevents dangerous hypoventilation and
delivers concentrations associated with analgosedation. The proposed
control system for MAC could improve clinical practice titrating drug ad-
ministration to a surrogate endpoint and actively limiting the occurrence
Note to Practitioners—We describe a system minimizing the risks
associated with the delivery of respiratory depressants to spontaneously
breathing patients during medical procedures. In this setting, several
factors can contribute to the occurrence of patient injuries: overdosing
leading to profound respiratory depression, especially in the nonsteady
state (bolus administration); inadequate monitoring of physiological
parameters; delayed or inadequate resuscitation. We propose to monitor
the respiratory gases (O
CO ? as effective indicators of the patient’s
ventilatory state and to automatically titrate drug delivery based on this
information. We tested the performance of the control system in a soft-
ware environment with a comprehensive mathematical model of human
metabolism and cardiorespiratory regulation. Using a PtcCO
of 50 mmHg, the system delivered drug concentrations in the accepted
therapeutic range for analgesia and prevented the occurrence of severe
(transient and steady-state) respiratory depression, coping with interindi-
vidual variability. Since the drugs and the hardware necessary for the
proposed system are commercially available, developing a medical device
for the automatic delivery of sedatives/analgesics would be relatively inex-
pensive. In our opinion, the safety of monitored anesthesia care, especially
when performed by non-anesthesiologists, would be profoundly enhanced.
Future research will be directed towards the design of an algorithm for
robust detection of sensor malfunction and the clinical evaluation of the
Index Terms—Automatic drug dosing, blood gases, pharmacoki-
netic-pharmacodynamic modeling, respiratory depression,transcutaneous
monitoring, ventilatory regulation modeling.
Manuscript received July 10, 2007; revised January 07, 2008. First published
February 27, 2009; current version published April 01, 2009. This paper was
recommended forpublication by AssociateEditor M. Zhang andEditor D. Mel-
drum upon evaluation of the reviewers’ comments.
Laboratory, ETH Zurich, CH-8092 Zurich, Switzerland (e-mail: caruso@con-
trol.ee.ethz.ch; firstname.lastname@example.org; email@example.com).
T. W. Bouillon and P. M. Schumacher are with the Department of Anes-
thesiology, University Hospital Bern, 3010 Bern, Switzerland (e-mail: thomas.
Digital Object Identifier 10.1109/TASE.2008.2009088
Sedation techniques are used to provide analgesia and reduce
anxiety during diagnostic and minor surgical procedures such as
endoscopy, bronchoscopy, extracorporeal shockwave lithotripsy, and
wounds/burns debridement . Monitored anesthesia care (MAC) is
defined as a medically controlled state of depressed consciousness that
allows protective reflexes (cardiorespiratory control) to be maintained.
The moderate depression of consciousness is intended to facilitate the
performance of the medical procedure, while ensuring patient comfort
and cooperation. The sedated patient retains the ability to breathe
autonomously and to protect his airways; depending on the depth of
sedation, he can respond to verbal commands and tactile stimulation
with different degrees of purposefulness .
Drugs used for MAC are propofol, benzodiazepines or opioids, all
of which are respiratory depressants. The magnitude of this effect de-
pends on dosing history (rate of administration, cumulation, coadmin-
istration of other drugs) and individual sensitivity to the drug(s). Drug
combinations, high doses and/or rapid administration rates can dan-
gerously blunt the respiratory drive and lead to serious cardiorespira-
tory depression in both adults and children –. Hypoxia, poten-
tially progressing towards cardiocirculatory arrest is the most feared
consequence. Oxygenation is usually supported via provision of sup-
plemental oxygen. However, sufficient oxygenation does not imply ad-
equate ventilation and, therefore, hypercarbia and respiratory acidosis
may still develop.
Serious injuries and cardiorespiratory events associated with drug
overdosing during MAC have significant social and economic reper-
cussions. A recent survey of surgical anesthesia malpractice claims
over the years 1990–2002 concluded that monitored anesthesia care
has the highest proportion of claims for death/permanent brain damage
(MAC: 41%; general anesthesia: 37%; regional anesthesia: 21%) and
the highest median payment to the plaintiff (MAC: 159 kUSD; GA:
140 kUSD; RA: 127 kUSD) . The survey identified oversedation
leading to respiratory depression as the main mechanism of patient
injuries during MAC and suggested improved monitoring through
capnography and vigilance to reduce morbidity.
changing surgical stimulus mandate the continuous evaluation of the
pharmacologic effects and the individualization of drug delivery. The
goal is to optimize the desired effects (i.e., analgesia, sedation, and re-
duction of anxiety and agitation), while minimizing the occurrence of
adverse effects (cardiorespiratory depression) . Titration to effect is
compounded by the lack of a preemptive indicator of analgesia and se-
dation. In fact, the therapeutic effects of MAC are difficult to quantify;
analgesia, for instance, can only be assessed after the patient has been
exposed to a noxious stimulus. It has been suggested to use EEG-de-
tems, MA) to provide a continuous measurement of the desired effects,
however, EEG-derived parameters display pronounced fluctuations in
moderately sedated patients and are insensitive to opioids in the thera-
peutic concentration range –. Clinical sedation scales (e.g., the
VAS scale, the OASS scale) are user-dependent classifications and are
during shallow breathing and partial airway obstruction and it is diffi-
cult to assess without a tight fitting, low dead-space mask. A simple,
objective, and robust measure of the therapeutic effects is therefore not
available .Titration toside effectas an alternative dosing paradigm
1545-5955/$25.00 © 2009 IEEE
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 2, APRIL 2009 257
piratory depression. Apnea is not rapidly detected by MAC providers
without continuous monitoring of ???. Recognition of apnea or
hypoventilation in patients who receive supplemental oxygen may also
be delayed if oxygen saturation ??????? alone is monitored .
We advocate the combined use of transcutaneous ??? tension
?????? ? and ?????for respiratory monitoring during MAC. The re-
liability of ????? readings is independent of airway status and pulse
oximetry provides information on the adequacy of peripheral oxygena-
tion. A device combining transcutaneous ??? and ????? sensing
has been recently introduced into anesthetic practice. Its favorable
dynamic properties ????? ???????? ?? ????? ?????? ? ???? ????
enable it to detect the onset of apnea significantly faster than pulse
oximetry alone –. Beyond serving as a monitor for patient
safety, such a device could also provide an objective, continuously
accessible and therapeutically meaningful surrogate endpoint for the
automatic titration of opioids and propofol during sedation. In fact,
the desired and undesired effects are mediated by the same receptors,
therefore drug induced respiratory depression always correlates with
analgosedation, and vice versa  (with the exception of opioid tol-
erant subjects, for whom this remains to be established). Mu receptors
in the brainstem and the thalamus mediate both the analgesic and the
respiratory depressant effect of highly potent opioids ,  so
that the two effects share important pharmacodynamic characteristics
 and exhibit similar plasma-effect site equilibration properties
, . Benzodiazepines and propofol exert their sedative effect
at gamma-aminobutyric acid (GABA) receptors, that have also been
fect relationships for the desired and undesired effect are similar, we
believe that deliberately targeting moderate levels of hypercapnia is a
viable approach for MAC. The degree of hypercapnia can be selected
by the care provider within a safe range (45–60 mmHg) and serves as
the setpoint of a feedback infusion system. Such a system would both
simplify the titration task and protect against lapses caused by lack of
vigilance in a highly dynamic environment.
Aim of this work, is to implement the proposed dosing paradigm
into a feedback control system, i.e., to design a system for the auto-
matic delivery of monitored anesthesia care based on transcutaneous
?????and ???monitoring. The system should achieve and maintain
drug concentrations corresponding to adequate sedation and analgesia,
avoiding marked respiratory depression. The present study focuses on
proof of concept in a software environment, using remifentanil, a po-
tent, fast-acting opioid. In particular, we will:
i) develop a comprehensive model of human respiratory control
ii) integrate the ventilatory model with the pharmacokinetics (PK)
and pharmacodynamics (PD) of remifentanil, specifically to
achieve a suitable quantitative description of the respiratory
depressant effect of the opioid (= virtual patient);
iii) design a control strategy for the automatic performance of
sedation that individualizes drug delivery, manages surgical
stimulation, and prevents the occurrence of severe respiratory
iv) analyze the performance of the system adopting the virtual pa-
tient as a substrate for simulations.
The manuscript is structured as follows. First, the components of the
the ventilatory control system, the remifentanil PKPD model, the
of monitored anesthesia care is described. Finally, simulation results of
and discussed. Preliminary results were reported in  and .
Fig. 1. The metabolic model and its relationship to the ventilatory and cardio-
vascular control systems. Model inputs are the metabolic rates of oxygen con-
respiratory gases in inspired air ????
rial, cerebral, tissue, transcutaneous partial pressure of carbon dioxide (equiv-
alent notation for oxygen). Shaded blocks depict the structure of the remifen-
tanil PKPD model. ?, ? , and ?
are the infusion rate, plasma, and effect site
concentrations of the opioid, respectively. E: pharmacologic depressant effect
on ventilation;?? : baseline ventilation;?? : minute ventilation;?? : alveolar
ventilation; Q: cardiac output. The dead space indicates the fraction of minute
ventilation that does not participate in gas exchange ???
, ? ? ?, b, t, tc: arte-
? ??????? ?.
In order to investigate the feasibility of the proposed drug delivery
paradigm, a comprehensive yet parsimonious respiratory model is de-
veloped in the first part of this section. Several studies are available
in the literature describing isolated respiratory mechanisms –,
or the influence of anesthetics on those , . Few attempts have
been made at modeling the PD of propofol and opioid induced respi-
ratory depression , , particularly in the non-steady state ,
. No model is currently available, however, providing an integrated
picture of human metabolism, gas exchange and transport, cardiorespi-
stimuli and sedative drugs. In the following, we propose a consistent
unified framework of regulatory physiology and respiratory drug ef-
fects, that will later be used as a test bed for control of drug infusion
during MAC. The control algorithm for the automatic delivery of se-
dation is described in the second part of this section.
A. The Gas Exchange System
To describe human metabolism and ventilatory gas exchange, we
adopted a previously published model that characterizes the disposi-
tion of oxygen and carbon dioxide in the tissues , . The model
the other tissues (lumped into one compartment). Mass balance equa-
tions for ??and ???are written for each compartment taking into ac-
count ?? and ???exchange with blood, ??consumption, and ???
production in tissues. The partial pressures of ?? and ??? in the in-
spired air and the metabolic rates constitute the inputs to the model.
Local blood flow to the tissues is modulated by a cardiovascular con-
tion of gas exchange and cardiovascular regulation and for the model
equations and parameters. Fig. 1 depicts the structure of the metabolic
model and its links to the ventilatory control system.
258IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 2, APRIL 2009
PARAMETER VALUES IN THE PATIENT SIMULATOR EQUATIONS
Oxygen and carbon dioxide transport in blood is described with a
mathematical representation of ?? and ??? dissociation curves that
accounts for the Bohr and Haldane effects . The agreement with
experimental data measured in whole blood (?????????? ??????? ?
?? ? ??? ??, ???? ?????? ? ? ????? at 37??) is adequate between
0–120 mmHg ?? and 0–80 mmHg ??? . The dissociation curve ex-
pressions disregard the amount of oxygen carried in dissolved form.
This term becomes significant when breathing oxygen enriched air, a
condition that is relevant to our study. Therefore, we modify the orig-
inal equation describing ??molar concentration in blood as a function
of ?? and ??? ([33, eq. (4)]) as follows:
?? ? ??
? ? ??
?? ?? ??
where the ?? ??
oxygen (in accord with Henry’s law) to total blood content and ??
is the oxygen solubility in blood. Linear least-squares fit values of
the parameters in (1) are given in Table I. ?? has a physiological
meaning since it corresponds to the molar oxygen concentration
achieved in blood with 100% saturated hemoglobin. Because the max-
imum ??capacity of human Hb is ???? ???? ? ????? ?????? and
the typical Hb content in blood is 150 g/l, ?? is assigned a value of
8.848 mmol/l. The modified dissociation curve equation matches well
the experimental data over the whole ?? range that is meaningful for
the present investigation (0–700 mmHg).
term represents the contribution of dissolved
B. Ventilatory Regulation
Multiple studies are available in the literature investigating the
human hypercarbic and hypoxic ventilatory drive , , ,
and the regulatory activity of chemoreceptors , . However,
most experimental paradigms are geared towards isolating physiologic
phenomena in order to obtain reliable and interpretable data of the
respiratory subsystems. Consequently, they are not suitable for simu-
lating the global ventilatory response to oxygen and carbon dioxide.
We propose to integrate the available knowledge into a parsimonious
interaction model to achieve a unified picture of human respiratory
control under different clinically relevant conditions (hypercapnia and
hypoxia being the most significant).
Respiratory control in man predominantly depends on chemical
signals stimulating the peripheral and central chemoreceptors .
Peripheral chemosensitive areas are located at the bifurcation of the
common carotid arteries and respond to changes in arterial ?? and
??? . The central chemoreceptors lie on the anterolateral surface of
the medulla and respond primarily to changes in cerebrospinal fluid
??? partial pressure . According to experimental results, the two
chemoreflex mechanisms exert an additive effect on ventilation ,
therefore the ventilatory response to ?? and ??? can be partitioned
into a peripheral and a central dynamic component , . We use
the following equation:
??? ??????? ? ??
where???? is baseline minute ventilation, C and P are the central and
peripheral fractional contributions to minute ventilation, respectively.
Under basal conditions ? ? ??? and ? ? ???, in accordance with
the clinical results reported in , , and  indicating that the
peripheral chemoreceptors contribute approximately 30% to the total
ventilatory drive under normoxia.
We describe the output of the central chemoreflex loop, C, with the
??? ? ? ??????? ?? ? ??? ? ??
the stimulus to the central chemoreceptors. The parameter ?? is the
??? sensitivity, B the apneic threshold (or the extrapolated pressure
(lung-receptor transit time), respectively.
We propose to describe the contribution of the peripheral chemore-
flex mechanism to minute ventilation as follows:
??? ? ???
??? ????? ????
???? ?? ? ??? ? ??
???? ???? ????? ?? ? ??? ? ??
??? ?????? ???
? is the output of the peripheral chemoreflex loop; it comprises an
oxygen-dependent term ???? ?, a carbon dioxide-dependent term
????? ?, and an ??????multiplicative interaction factor ?????. The
parameters ?? and ?? in (4) are the ??? sensitivity and the compo-
nent time constant, respectively. The peripheral ventilatory response to
??under isocapnic conditions is described with the expression in (5),
where ??? ??? ??? is the arterial stimulus delayed by the peripheral
transport time ??, . The peripheral drive to carbon dioxide is
linearly dependent on the difference between ???? and the apneic
threshold B [(6)] , . The ??? ???interaction [(7)] accounts
for the ventilatory response under hypoxia being greater than the sum
of the response to be expected from the rise in ???? and the fall in
??? if considered separately, as reported in  and .
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 2, APRIL 2009 259
Least-squares estimates of the ventilatory model parameters are in
good agreement with clinical experimental data regarding chemore-
ceptive gains, thresholds, time constants, and time delays: ?? ? ?????
??????????, ? ? ????? ????, ?? ? ??? ? and ?? ? ??? ?,
?? ? ???? ? and ?? ? ??? ? , , ; ? ? ?? ???? .
All values of the parameters in (2)–(7) are listed in Table I.
For the sake of mimicking intraoperative noxious stimulation, we
incorporate into the physiological model a description of human venti-
latory response to pain. The effect of painful stimulation on the human
body is modeled as a 10% increase in ??? metabolism and a 10%
decrease of the apneic threshold. As a result, pain determines a 15%
increase in minute ventilation compared to baseline. These effects re-
flect the experimental observations on the ventilatory response to pain
in man reported in the literature –.
C. Transcutaneous ??? Sensing
The proposed dosing paradigm includes titration of drug according
to ????? . Therefore, the physiological model must incorporate an ex-
plicitdescriptionofthetranscutaneous ???signal.Inaprevious study
(SenTec AG, Switzerland), a Severinghaus-type device for the transcu-
taneous monitoring of the partial pressure of carbon dioxide ?????? ?.
It was concluded that the ????? response of the sensor can be related
to end-expiratory ??? by means of a two compartment model with
?????????????????? ???? ????????? ? ???? ?????, and a 20 s time
lag. This ????? model is included into the respiratory simulator to
test the feasibility of the proposed sedation system.
D. PKPD Modeling
In order to describe the respiratory depressant effect of remifentanil,
apharmacokinetic/pharmacodynamic modelis addedto thephysiolog-
PK is described by means of a customary three-compartment mammil-
lary model; the PK model is augmented with a first-order transfer to
the effect site (link model) . PK parameters are listed in Table I.
In a recent study , Magosso et al. simulated the ventilatory re-
sponse to the opioid fentanyl, proposing a detailed description of drug
effects on the different mechanisms that regulate ventilation. However,
we believe this level of detail is not sufficiently supported by the liter-
ature. In fact, it would be nearly impossible to design an experimental
paradigm in man geared towards simultaneously determining ?? and
???dynamics and drug PD at each regulatory subsystem. Therefore,
we opt for a more parsimonious structure, expressing the effect as a
concentration-dependent depression of the total ventilatory drive. PD
modeling is performed using the fractional sigmoidal ????model for
the effectonminuteventilation.Thechoice of afractional????model
. Effect quantitation is achieved through
? ? ?? ? ?
where ?is theminuteventilationasfunctionofthedrug concentration,
?? the baseline value in absence of drug ??? the drug concentration
causing 50% depression of minute ventilation under isohypercapnia,
? the sigmoidicity (Hill) factor. ??? is set to a value of 1 ng/ml in
agreement with the literature (: 0.92 ng/ml, : 1.12 ng/ml, :
1.17 ng/ml); ? ? ???? . Since ? is normalized to baseline venti-
lation (that is, ?? ? ?), the dynamic effect of the drug is determined
with a minimal number of parameters.
Fig. 2. Configuration for the closed-loop control of sedation delivery. I: drug
: estimated measurement; ?
system enforces the ???? , ? , ?
: control setpoint. The override
thresholds to maximize the safety of
E. Control Strategy
Aim of the control algorithm, is to manage drug administration for
induction of sedation and maintenance of the ????? setpoint defined
by the anesthesiologist. Adequate management of intraoperative
painful stimuli, surgical disturbances, and interpatient variability is
required. An endpoint of 50 mmHg is selected for paradigm validation
because in volunteers it corresponds to mild respiratory depression and
plasma concentrations well in the analgesic range . The control
algorithm must fulfil the following conservative constraints to ensure
patient safety: ????? ? ???; remifentanil ??, ??? ? ? ?????. In
a safety override stops the automatic infusion and reverts the responsi-
bility of dosing to the care provider, still providing information about
plasma and effect compartment concentrations.
of the model to stepwise changes in ??? is approximately linear and
of first order, so the requirements in terms of controller sophistication
is selected. A two-degree-of-freedom control structure is employed to
improvetracking performancewhile ensuring rapidsuppression ofdis-
turbance effects. Further considerations on the choice of this control
algorithm over more sophisticated ones are included in the Discussion
and Conclusions section.
F. Kalman Filtering
A state observer is included in the sedation system to perform fil-
tering of the ????? signal. As observer the Kalman filter is selected
because we do not rule out the presence of stochastic noise in the
????? signal. The positioning of the Kalman filter within the control
loop and the configuration of the MAC delivery system are depicted in
The use of Kalman ?????
estimates is also intended to assist
in sensor failure/disconnection detection . For instance, during
the medical procedure, it may happen that the sensing element is
displaced from its measurement site on the patient. The ????? mea-
surements would then rapidly approach a value of zero because the
??? ??????? ?? ??????????? ??? ? ?????. A significant mismatch
between the sensed and the estimated ????? would be observed. In
the sedation system, excessive estimation residuals are interpreted as
being indicative of a fault.We establish that the systemdetects asensor
failure/disconnection if the sensor output undershoots the estimated
value by 7 mmHg or more. Following the detection of a fault, the
system rejects the sensor output. The prediction at each time step is
then based on the previous estimate and the current control command
only. In the clinical implementation a warning message would be
issued at this stage, drawing the attention of the care provider. The
260IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 2, APRIL 2009
Fig. 3. Left diagrams—the ventilatory response to hypercapnia measured in healthy volunteers is plotted versus time (top: symbols are single minute ventilation
measurements reported in ; middle and bottom: symbols are ???? ? ???? ). The hypercapnic stimulus is applied under hyperoxic, euoxic and hypoxic
conditions (? ? ???, 100, 53 mmHg, respectively). Right diagrams—simulated minute ventilation versus time (thick line) in response to a square change
in ?? partial pressure (thin line). The simulations are performed under ?
minute ventilation is 12 l/min under hyperoxia and 8.7 l/min under normoxia and hypoxia in accordance with the experimental observations.
conditions identical to those of the clinical experiments. Baseline
system does not discard measurement information when the sensor
reading is higher than the estimated value, since false high readings
revert the virtual patient to a safe state decreasing the infusion rate.
Simulation results relative to the ventilatory response to ??? chal-
lenges, the ventilatory response to remifentanil administration, and the
feedback control of drug delivery are described in the following.
A. Ventilatory Response to Oxygen and Carbon Dioxide
The ventilatory response of the model to a square wave change of
end-tidal ??? partial pressure for different oxygen concentrations is
shown in Fig. 3 (hyperoxia: ????
? ??? ????, middle; hypoxia: ????
bottom). Simulation results are in good agreement with the average
responses measured in volunteers reported in  (top diagram) and
? ??? ????, top diagram; eu-
? ?? ????,
 (middle, bottom). In accordance with respiratory physiology, the
response of the model to a hypercapnic challenge is stronger under
hypoxia (approximately a threefold increase of baseline ventilation),
while hyperoxia has a mild respiratory depressant effect . Under
due to the effect of low oxygen tension on ventilatory regulation ,
; this effect is visible in the model output but it cannot be clearly
discerned in the experimental results (middle, bottom diagrams).
The clinical data show a fast initial increase of minute ventilation in
response to the ??? change, followed by the contribution of a slower
respiratory component. This biphasic behavior is typical of human res-
piratory patterns and it is produced by the different time constant and
time delay (lung-receptor transit time) that characterize the response of
the slow ventilatory mechanism , , . In the model, the two
chemoreflex loops determine additively minute ventilation [(2)]; their
contributions generate the ventilatory patterns displayed in Fig. 3. The
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 2, APRIL 2009261
Fig. 4. The open-loop arterial ?
remifentanil plasma concentration is displayed versus time for two different
subjects. Filled circles: remifentanil plasma concentration ?? ? measurements;
empty circles: arterial carbon dioxide tension ??
experimental data are compared with simulation results. Solid lines: ?
input to the model that reproduces the experimental administration schedule;
dashed lines: ?
resulting from model simulations with population PD
parameters (? ? ? ?????, ? ? ????, ?
from simulations with individual fit of PD parameters (top:
? ? ??? ?????, ? ? ???, ? ? ? ???
? ? ????, ? ? ???? ???
response to stepwise changes of
? measurements. The
? ???? ???
; bottom: ? ? ??? ?????,
present the same dynamics, in agreement with the clinical findings re-
ported in  and .
B. Drug Induced Ventilatory Depression
Fig. 4 displays the ventilatory depressant effect of remifentanil on
two healthy volunteers in terms of arterial ??? changes. The experi-
mental data reported here is from a clinical study aimed at identifying
the inhibitory effect of remifentanil on ventilation . Remifentanil
end-tidal ???exceeded 65 mmHg and/or apnea periods of more than
decrease to 1 ng/ml. During the infusion, arterial blood samples were
drawn to determine remifentanil plasma concentrations and ???? .
expected, open-loop simulation results based on population PD param-
eters do not always adequately describe the data due to the pronounced
interindividual variability (Fig. 4, top). Since individualization of the
parameters leads to an adequate fit, the model structure is acceptable.
C. Control of Drug Infusion During MAC
In order to validate the proposed dosing paradigm for sedation,
we simulated titration to and maintenance of a target ?????
the physiological model described in the above as a virtual patient.
Closed-loop results for a ?????
????????? ?? ?????? ?? ???????? ???? ? ??? in three differently
sensitive virtual patients (highly sensitive, averagely sensitive, insen-
sitive) are displayed in Fig. 5. To mimic the nuisance effects that often
occur in the operating theater during MAC delivery, the following
disturbances were reproduced in the simulation studies:
i) a painful stimulus at ? ? ?? ???;
ii) a generic surgical disturbance at ? ? ??? ??? that causes an
abrupt increase of 4 mmHg in arterial ??? (to mimic for in-
stance the effect of tourniquet release);
iii) the disconnection of the sensor at ? ? ??? ???.
The ?? versus time diagram in Fig. 5 shows that the control algo-
rithm adjusts drug dosing to track the reference signal, to reject the
disturbances and to individualize drug delivery depending on the spe-
cific sensitivity of the virtual patient. Remifentanil plasma concentra-
tions delivered by the controller (1–2.5 ng/ml) lie within the analgesic
curs, the ????? signal quickly drops to zero; thereafter at each time
step the Kalman filter outputs a ????? estimate based on the previous
estimate and the current control command only (no estimate update
with measurement information since the sensor is detached). Minute
ventilation is displayed as another indicator of drug induced respira-
tory depression. It remains at safe levels, both transiently and at steady
state. Throughout the entire simulated procedure the hypoxic override
remains inactive since blood oxygenation stays always above the 93%
target of 50 mmHg and ????
IV. DISCUSSION AND CONCLUSION
The ability of opioids to provide adequate analgesia is limited by
breathing patients. Therefore, quantitation of drug induced ventilatory
depression is a pharmacokinetic-pharmacodynamic problem relevant
to the practice of anesthesia and in particular to the delivery of moni-
tored anesthesia care.
Aim of this study, was to address the problem of drug delivery in
the spontaneously breathing patient and to provide a solution that en-
hances safety in clinical practice. Dosing during MAC is critical be-
cause there is no direct, objective measurement of the therapeutic ef-
fect and the drug induced adverse effects are life threatening. We pre-
sented an innovative dosing strategy that entails the measurement of
the pharmacologic side effect rather than the evaluation of the thera-
peutic effect to provide guidance for the automatic control of drug de-
livery (surrogate endpoint based dosing paradigm). More specifically,
we suggested titrating the administration of sedatives and analgesics
to the individual sensitivity based on transcutaneous measurements of
??? . We demonstrated the dosing paradigm by means of computer
simulations. The results in Fig. 5 show that the control algorithm indi-
vidualizes drug infusion, titrates to effect and delivers concentrations
within the analgesic range. Closed-loop control may be effective and
robust to intraoperative disturbances, individual drug sensitivity, and
sensor disconnection. Improved safety, reliable and adequate therapy,
and manpower would be the most prominent results of implementing
the proposed dosing paradigm into a therapeutic device for use during
MAC. The system has, therefore, the potential to be converted into a
commercial healthcare device because it may fulfil the clinical demand
for improved sedation care and the technology of the single compo-
nents (sensor, actuator, processing and control unit) is available and
relatively inexpensive compared to anesthesia workstations. However,
a second, independent sensor (e.g., a nasal thermistor) is needed to de-
tect ongoing breathing and identify possible single fault conditions.
It is relevant to mention that the dosing paradigm object of investi-
gation was here exemplified selecting ????? as the feedback signal
262IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 2, APRIL 2009
Fig. 5. Simulated closed-loop induction and maintenance of sedation ???? ? ?????. Model results in terms of estimated ?
tanil plasma concentration, and normalized minute ventilation are displayed. The reference ?
?????, thereby activating the controller and initiating drug infusion. A painful stimulation and a generic surgical disturbance occur for 10 min at time ? ? ?????
and ? ? ??? ???, respectively. At ? ? ?????? ?
signal loss occurs (reproducing, e.g., the detachment of the sensor). The sequence of events is simulated
for three different levels of drug sensitivity: high sensitivity (? ? ??? ?????, dotted line), average sensitivity (?
(? ? ??? ?????, dash-dotted line).
, measured ?
signal is changed from baseline to 50 mmHg at time ? ?
? ? ?????, solid line), low sensitivity
and remifentanil as the anesthetic drug. However, in principle, the par-
adigm can be applied to other ventilatory measurements (e.g., ???
via end-expiratory capnography) and/or other sedative/analgesic drugs
with respiratory depressant side effects (for instance, opioids such as
fentanyl and alfentanil; propofol; combinations of drugs).
The physiological model presented herein combines several isolated
pharmacological and physiological aspects of respiratory regulation
and drug induced respiratory depression under various conditions.
Several studies in the literature address the effect of chemical stimuli
and anesthetics on specific respiratory and metabolic subsystems. Our
work integrates and thereby expands that knowledge providing, for the
first time, a unified picture of respiratory regulation and drug effects
on breathing under different clinically relevant conditions. The model
serves as a simulator/test bed for both drug tolerability and control
issues under non-steady-state conditions.
The patient simulator expresses drug induced respiratory depression
as a concentration-dependent effect on minute ventilation. It does not
describe the pharmacologiceffects on tidal volume and respiratoryrate
separately, although it has been shown that their dynamics are different
. Modeling these two ventilatory components may improve the ca-
pability to predict apneic events and is, therefore, going to be the sub-
ject of further investigation.
The main objective of this work was to investigate the feasibility of
employing a surrogate measurement of analgesia for automatic drug
dosing during sedation. As it is often the case for physiological sys-
tems, the most critical decision for the success of the control scheme is
the right choice of the controlled and actuated variable(s), and not the
level of sophistication of the algorithm. The specific control strategy
we adopted is undoubtedly simple, but the simulation results in Fig. 5
show that a higher degree of complexity is not required to deliver con-
centrations in the analgesic range even in the presence of pronounced
interindividual physiological variability and the occurrence of various
disturbances. We strongly suspect a more complex control algorithm
would not contribute substantially to the theoretical or clinical rele-
vance of our results. In fact, more sophisticated control strategies such
as model predictive control (MPC)  and cascade control (being
????? and ????? the controlled variables) were tested in the sim-
ulation environment, but did not deliver a significant improvement in
the performance of the system. Therefore, we concluded that the use of
more sophisticated control algorithms is not justified. From our track
record in collaborations with anesthesiologists, we also believe that
simpler control structures are considerably more likely to be accepted
and successfully introduced in the clinical practice.
This study modeled the effect of remifentanil on breathing and did
not consider coadministration of other drugs. Polypharmacy of seda-
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 6, NO. 2, APRIL 2009263
macologic interaction of the drugs. However, coadministration of an-
other respiratory depressant would lead to more pronounced hyper-
capnia and, therefore, reduce administration of the automatically ad-
ministered drug, thereby protecting the patient. This hypothesis will be
tested in a prospective clinical study that aims at validating the pro-
posed dosing paradigm for MAC in the clinical practice.
Future developments of the research also include the design of a
robust algorithm for detection of single fault conditions of the sensor
and/or the control system. A hardware implementation of the sedation
system will be pursued for the performance of the clinical study di-
rected at confirming the validity of our findings in patients. The major
challenges there will be posed by the ???sensor and the pronounced
patient variability, rather than by the implementation of the controller.
The authors would like to thank Dr. C. Jones (Automatic Control
Laboratory, ETH Zurich, Zurich, Switzerland) for his valuable collab-
oration during the study.
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