A Model-Based Adaptive Blood Pressure Controller

Copyright © IFAC Jdf'ntifi cation and Systcm Paramcter Estimation 1982 . Washington D .e .. L'SA 1982

A MODEL-BASED ADAPTIVE BLOOD PRESSURE CONTROLLER

J.

B. Slate and L. C. Sheppard

Departments of Surgery and Biomedical Engineering, University of Alabama in Birmingham, USA

Abstract. Sodium nitroprusside is a fast-acting drug used to reduce blood pressure in hospitalized patients. A wide range of circulatory system responses to the drug is observed. For design of a controller for clinical use, a model of the system related to arterial pressure and its response to nitroprusside was developed and patient-care practices were analyzed. An adaptive, multiple-mode, multirate sampled-data controller was designed using model-based techniques and implemented with a microcomptuer system. Simulation results were verified by experiments in the animal laboratory. Results from clinical evaluations with postsurgical patients were superior to the performance of previous automated infusion systems. Keywords. Adaptive control; biomedical; blood pressure control; control engineering computer application; nonlinear control systems. INTRODUCTION Various closed-loop control systems have been used to automate the infusion of the fast-acting drug sodium nitroprusside for reducing blood pressure in hospitalized patients. Clinical experiences on over 1,300 postoperative open-heart patients with a nonlinear proportional-plus-integral-plusderivative controller (Reves, 1978) have shown that closed-loop control is safe, effective, and often superior to manual methods. Host patients can be satisfactorily controlled with this system; however, clinical experiences also indicated that system performance needed significant improvement for certain groups of patients, particularly those who are either sensitive or insensitive to the drug, and patients with blood pressure having large fluctuations. Therefore, a controller was designed that provides robust performance over the wide range of patient responses and has a band-limited response to disturbances introduced by disease and procedures related to patient care. Model-based control methods and interactive computer simulation were used to design and evaluate the improved system. The reader is referred to other reports (Slate 1979, 1980) for a review of other infusion systems and for more detailed descriptions of the model and controller design. Results with a nonlinear adaptive controller are presented from dog experiments

and patient evaluations. MODEL OF THE CONTROLLED PROCESS In the model, mean arterial pressure is considered to be the sum of the background pressure and chang~ in pressure due to the drug, which is related to the infusion rate by a linear transfer function. The background pressure consists of a constant term, a low amplitude sinusoid caused by respiration or mechanical ventilation, stochastic activity, and a component representing a reflex response to a reduction in pressure. Certain disturbances, such as those associated with changes in the patient's condition and patient-care related procedures, can be approximately modeled as step, ramp, or pulse changes in the background pressure. A transfer function with a proportional gain, first-order lag, and two pure time delays provided an adequate and parsimonious model of the human arterial pressure drug response. The gain, K, represents the patient's sensitivity to the drug. The firstorder lag results from the uptake, distribution, and biotransformation of the drug. The pure time delays represent an initial activation time (primarily due to transport from the injection site), and the recirculation time. Parameter value

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J. B. Slate and L. C. Sheppard

ranges were determined from measurements and observations and from extrapolation based upon physiological interpretations. The model realistically reproduces certain clinically observed features in patient responses during identification experiments and control. However, some patients exhibit complex behavior that is difficult to mathematically model. This behavior is not well understood but may result from the patient's physiological control systems being severely disturbed following openheart surgery. Thus, limitations exist in modeling on-line the background pressure of each patient.

control, and parameter adaptation. See Fig. 1. The infusion rate is cal culated at ten second intervals from the infusion rate incremental changes by an integrator with limits to prevent negative rates and exceeding the maximum recommended dose rate (Roche 1980). Quantization to the nearest integer rate is required by the digitally controlled pump. Depending upon the magnitude of the system states (the error and its derivative), either a linear regulator, nonlinear transient controller, or proportional transient controller is selected to calculate the increment. When the states are relatively small in magnitude ( I e l <8 mm Ilg and l e l.::. -1

10 mm Hg min ), a linear regulator is used. I f pressure is far below the setpoint (e > 20 mm IIg), a proportionSpecifications regarding system perforal term rapidly turns the infusion off. mance were determined based upon obserFor other values of the error and devations of patient-care practices and discussions with personnel in the Cardiac rivative, the incremental change is determined by a transient controller. Surgical Intensive Care Unit. After initiating control, mean arterial pres~ultirate filtering reduces the undesure should be lowered from the initial sirable effects of stochastic varia hypertensive level to the desired settions in the system states, but without point within 5 to 20 minutes, on a explicitly including a model of the smooth trajectory, and without more background pressure. The mean arterial than 5 to 10 mm Hg undershoot. The controller should maintain pressure near pressure obtained from the bedside monthe setpoint within ± 5 mm Hg. Incre- itor is sampled at one -se cond intervals. This signal is low-pass filtered and mental increses in the infusion rate sampled at two-second intervals to comshould be limited in magnitude to preA vent rapid decreases in pressure (Roche, pute the error and derivative. 1980) which in turn may cause undesirable three-point differentiator and lowpass filter attenuates high frequensecondary effects such as diminished These signals blood flows (Sheppard, 1976). Excessive cies in the derivative. are sampled at ten-second intervals variation in the infusion rate should be to calculate the infusion rate increavoided and changes in the rate made ment. Filter parameters were selected smoothly. to attenuate high frequency noise but without introducing excessive lag Significant variability among patient characteristics requires the use of a ro- which might compromise performance. bust controller. System performance should be reasonably insensitive to model The principles of variable structure systems (Itkis, 1076) and Smith's parameter variations and structural unmethod for time delay compensation certainty. However, a 30-to-1 range of (Smith, 1058) were applied to the dedrug gains are observed (Sheppard,1976) sign of the nonlinear transient com and this is a large parameter variation; troller. In this scheme, a relay-type therefore, adaptation is necessary. controller with a gain schedule and a Clinical application of an automated in- time delay compensator is used to fusion system necessitates criteria that compute the infusion rate increment from the filtered signals. A relay ensure safety. A conservative control element actuated by a switching func strategy is warranted that biases the tion produces an initial slewing controller towards decreasing the infuaction in the infusion rate for average sion rate, limits incremental infusion rate increases, and provides a quick re- or low drug gain patients and a system response that is satisfactory for high sponse to low pressure. drug gain patients. The slewing or CONTROLLER DESIGN DESIGN PRELIMINARIES

Design of an improved system used features of several digital methods including multirate filtering, multiple-mode

A Model-Based Adaptive Blood Pressure Controller

velocity-limiting action causes the infusion rate to increase in a ramplike manner; this feature prevents rapid decreases in pressure which are undesirable, unless pressure is very high. A dead band was included in the relay element to reduce the effects of chatter, producing a smooth control action and a faster response for low gain patients. The gain schedule provides a fast response to pressures that are below the setpoint level; this biases the controller to decrease the infusion rate. Time delay compensation reduces the adverse effects of the drug initial activation delay on the switching action of the relay controller. Compensator parameter values were selected to reduce the effects of mismatches among compensator and actual patient model parameters. To maintain pressure near the setpoint the increment is calculated by proportional-and-derivative error terms providing an overall proportional-plusintegral control action between the error signal and process input. The regualtor gains were iterativelv adjusted to achieve the desired response based upon families of time response simulations. This method produced a system response that is relatively insensitive to the drug initial activation delay, the drug time constant, and the structure of the background pressure model. A parameter adaptive mechanism adjusts the overall gain of regulator, the output levels of the relay element, and the time delay compensator gain. A recursive least-squares algorithm determines an estimate of the patient drug gain. Nominal values for the drug initial activation delay and time constant are assumed for the estimator model. The controller parameters are adjusted by an algorithm that includes rules which are nonlinear and a function of time in order to provide a conservative adaptation action. To overcome several of the limitations of on-line estimation that are encountered in clinical applications, adaptation is performed during a fifteen minute interval, which is usually during the initial period of control. It is assumed that during this period the mean arterial pressure is stationary. Allowable controller adjustments are limited to a range used in clinical studies where the overall gain of the nonlinear PID controller was manually adjusted (range: 0.15 to 2.5, Slate 1980). Simulations of the system for various combinations of patient model param-

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eters were used for tuning and evaluating the controller . Studies were made concerning the effects of parameter mismatches with respect to nominal values, stochastic activity, model components initially neglected during design (drug recirculation, reflex responses, and measurement filter), and different values of the level of the background pressure. The simulated system responses to closing the feedback loop for several values of the model drug gain are shown in Fig. 2. A smaller settling time compared to that of the nonlinear PID system (Slate, 1979) is observed for the relatively insensitive and average patients (for K -0.5 a 60% reduction in settling time and for K = -1 a 35% reduction). A stable response without undershoot is produced for the relatively sensitive patients (K = -5 and -8). System performance is not significantly affected over the range of model parameter values. EXPERIHENTAL AND CLINICAL EVALUATION System evaluations were made using a LSI-11 microcomputer system with a digitally controlled infusion pump. A feature was included to rapidly fill the infusion cannula with the drug; otherwise, the initial dead space volume would cause an unsatisfactory initial transient response and a drug gain estimate lower than the true value. An algorithm detects pressure measurements artifiacts, such as those caused by sampling blood or flushing the catheter, and holds the controller input and output constant. A simulation of the model was used for debugging software, checking hardware operations, system demonstrations, and for training clinical personnel to operate the system. Tests were conducted with five healthy dogs to ensure proper system operation and to validate simulation results. System responses were observed for different drug concentrations, setpoint changes, output disturbances, nonzero initial infusion rates, transfers of control from manual to automatic, and reinitialization of adaptation. Experimental and simulation results were in close agreement. The results for a range of drug sensitivities created by using solutions with different concentrations of nitroprusside are shown in Fig. 3 (compare to simulation results in Fig. 2). A concentration of 0.2 mg/ml produces a response comparable to that of the model for

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J . B. Sl.Jte and L. C. Sh"pp,-lr u

an av e r a g e drug g a in ( K = -1) . The effec ti ve n ess of th e n o nl i n ea r t r a nsien t co ntr ol l e r an d a d a pti ve mec hani s m ar e c l e arl y d e mo n st r ated u s in g high drug co n ce n t r at i ons ( 1. 0 a n d 1. 8 mg / ml) . A n o n ze r o in i ti a l i n fusio n r a t e rapidly l owers p r essure ~itho u t und e r s hoot e v e n ~ h en us in g a high drug c on ce n t r at i o n an d an i n itial rate l a rge r t h a n t h e val u e r equired during r e gu la ti o n . S u c h rapid de c re ases in p r ess ur e are u s u ally und es irabl e; howe v e r , if p r e ss u r e is ve r y h i gh , pr ess ur e mu st be qu i c kly l o ~ e r e d to a safe r l e v e l.

t hi s wa s as s um ed fo r co n t r o l l e r de sig n. I n th ese cases p e r s onn e l must be t r a in e d to r eco gn ize ~h e n to re ini t ial i z e a da p tatio n if p e r fo r ma n ce needs i mpr o v eme n t o r to re set th e I t mav c on trolle r g a in t o un it v. a l so b e d esi rab le i n s o~e S itua t i o ns t o in cl ud e a so ur ce of e x c itation. s u c h a s s et p n in t d i ther, during tran sfe r s o f co ntr ol f r om manual t o aUT omat i c . n es pi te i n acc urat e e stim at i o n fo r s ev e r al pa t i e nt s . s y s te m per forma n ce ~a s impr o v e d and ~ ell a cce p te d by cl in ical per s on n el.

In acc urat e dru g ga in est ima t es occ ur ed for 8 pati e nts. In t h ese c ases the r e sulting c ontroller g ai n was u sed i f pe rforman c e was a cc eptab le ( 4 pat i e n ts), o therwis e uni ty g a in was u se d (4 patient s ). Poo r est i ma tes r es u lte d f r om op e rat o r o r nur s ing e rr o r s (4 patie n ts) , larg e pr e s s ur e n o n s t a ti o n a r ities ( 3 patient s ), a nd f r o m inad eq u a t e e xc itation fo r estima ti o n dur i ng t r a n sfer from manual to aut o ma t i c ( 2 p atie n t s ). Operator and nursing e rr o r s , s u ch as f a iling to prime th e ca nnu la o r acc id e ntal bolus infusion o f ni t r op ru ss i de, ma y be eliminat e d by b e t te r t r a ining and exp e rience. Clin i cal per so nn e l will n ot alwa y s delay nonurgent pati e n t - ca re pr o cedures that may cause l a rg e p r ess ur e nonstati o naritie s o r bolu s i n f u sio ns ;

Th e auth o rs gra t ef ul ly ac kno~l e dg e t h e a d vice and su p port of P r o f . V . C . Ride o u t and Dr. I . Il. Bla c kston e . Sp ecial t h a n ks go to ~ r . F . D. ~allace f or tech n ical assi st an c e , to 'I es s rs C . ~ allace and W. Trac y fo r ass i s ta n c e in tbe a n imal l aboratory, a n d to ' 11' . I. Br i.ll fo r s o ftll'are con s u l t ati o n s . ~e are g r ateful f or the c ollaborat i o n of Dr s . R . B . Karp, J . ~. Ki rk l i n, X .T . Kouchoukos . and G. L . Zo r n a nd for the cooperatio n of the personnel of t he Ca r diac Int ens i ve Ca r e l;n i t.

CO\' CLl" S IO\' S Eva lu at i o n s we r e p e rf o rm e d o n 33 Clini c a ll y a cce p ta bl e p e r fo rm a n c e p os t o p e r at i ve o p e n-h ea r t patients ~a s a c hi e v e d fo r a ~ i d e r a ng e of fo r a t o tal dur at i o n of 152 h ou r s . patient c h a r ac t e rist ics by u s ing a Fig. 4 s h ows a comp ar i s o n bet~ e e n ga i n - adaptiv e, multip le - mo d e, multi manu al co ntr ol by a nu rse a nd com ra te s a mp l e d - d ata co ntr o ll e r . pu te r co ntr ol . Th e mea n er r or dur S i mu l at io n s, a n im a l e xp e rim e nt s , and ing ma nu a l co n trol was -1 9. 1 DUll Hg c lini c a l e valu a ti o n s indicat e d that a nd th e pr ess ur e wi th i n ± 1 0 mm Il g t h i s sy s t e m ha s i mpro v e d performance o f t h e se tp o in t 17% of t he t ime , co mpar e d t o p re vi o u s co ntr o ller d e wh e r e a s t h e mea n e rr or d u ri n g c o m~ o d e lin g a nd simu l at i o n s ig n s. put e r co ntr o l was - 0 .27 mm Hg a n d p r o vid e d p o ~ e r f u l t oo ls fo r d es ign pre ss ur e 100% wit hi n ± 1 0 mm Hg ing the c o ntro ll e r and tes ting th e (92 % ± 5 mm Hg) . Osc i llatio n s i n i mplement a ti o n , and ~i l l be of pr e s s ure that a r e n ot in duced by great valu e in t raining c linical infu s i o n rat e f lu ct uati o n s we r e perso nnel h o ~ t o u s e th e sy s tem with Th is o bser ve d with thi s pati e n t. out the n e ed f o r l earning o n sick typ e of ph e n o me na ca n b e r ep r odu c patient s . ' Io d el - ba sed adaptive c o n e d with t h e mod e l during r eflex r e t rol t ec hniqu e s wer e u s efu l in im sponse s to a r e du ct i o n i n pr essur e pr o v in g s y s t e m p e rf o rmance; ho wever , (Slate , 19 8 0) . Th e system r espo n ses c ertain probl e ms c an b e enco un tere d for a pati e n t h a ving a l ow d ru g se n si in c lini c a l appli ca ti o n s which ma y t i vity and pr ess ur e wi t h la r ge r a n dom requir e ope r ator interactio n. fluctuations a r e s h own in F i g. 5. Evalua t ions ar e ~arran te d in which The o utpu t di s turban ce cau sed by bathing this pati e nt was q u ickly t r ac k ed cl i nical personn el o p e rate the syste m wi thou t the p r ese n c e of t h e d esig n er . b e cause of th e high co ntr o l le r gai n For this ~e are dev e l o pi n g a n inex (improv e d r es p o n se t im e compared to pensive, compact, mic r ocompu te r i mth e n o nlin ea r PID system) . Th e co n trol plementation, ~hich will al s o be u s e d a c ti o n i s smooth d es p ite the la r ge pr ess ure f lu c tua tio n s . Fo r th i s pa ti e n t , i n t h e o p e r ating r o om du r i n g a n d immedia te l y a f t e r o pen - h e art s ur g e r y . the mean erro r was 0 . 68 mm Hg a nd th e pre ss ur e wa s 100% within ± 1 0 mm Hg (95 ~ ACK\'O~LEDG E ~ E X T S ± 5 mm Hg).

RIF EREXCES I tk i s, l· .

(19 7 6) .

Control Systems of

A Model-Based Adaptive Blood Pressure Controller

Variable Structure. John Wiley & Sons.

~ew

York:

Thesis , University of London. Slate, J.B. (1980). ~odel-based design of a controller for infusing sodium nitroprusside during post-surgical hypertension, Ph.D. Thesis, University of Wisconsin in ~adison.

Reves, J.G., L.C. Sheppard, R. Wallach, and W.A. Lell (1978) "Therapeutic uses of sodium nitroprusside and an automated method of administration," Int. Anesth. Clin., Vol. 16, ~o. 2-,-pp. 51-88. Roche

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Slate, J.B., L.C. Sheppard, V.C. Rideout, and E.H. Blackstone (1979). "A model for design of a blood pressure controller for hypertensive patients," 5th IFAC Symp. on Identification and System Parameter Estimation, pp. 867-874.

(1980) "~ipride (sodium nitroprusside)." ~utley, ~ew Jersey: Hoffman-La Roche, Inc.

Sheppard, L.C. (1976). Correlation analysis of arterial blood pressure responses to vasoactive drug, with particular reference to clinioal surveillance of the post surgical cardiac patient. Ph.D.

Smith, O.J.~I. (1958). Feedback Control Systems. ~ew York: hlcGraw-Hill Book Co., Inc.

Selpoinl Infuslon

Rile Ineremenlll Chlnge

'-------_1------------Mean Arterial Pressure

Fig. 1.

From Bedside Monilor

The configuration of the multiple-mode, adaptive, multirate controller is shown schematically in this block diagram. MODEL DRUG GAIN K'

INSENSITIVE

AVERAGE

-0.5

-10

-5.0

Infusion Rote (ml/hJ

-8.0

JHl llfP 9 111 11&11 Hfl lll ll t~fUil l. ~ ~11~!!~!I~II~II~li

o

15

o

15

-l·

o

TtME(minJ

Fig. 2.

SENSITIVE

150

15

The simulated system responses to closing the feedback loop for a patient model with a 30s initial drug activation delay and several values of the patient drug gain, but without stochastic activity in the background pressure. Sustained oscillations having a low frequency occur for high drug gain patients because the minimum change in the infusion rate (1 ml/h) is relatively large. The setpoint was 100 mm Hg.

J. B. Sl a t e and L. C. She ppard

1442

SE NSI Tiv E

AVERAGE

•

:~~-,~<;~ ~ I~ '\f=-"-~"s~"'<>

=

,\~~::, :f'. /,-- r'~---- ~ g~/

,,,.m,'"

Druq Go,"

Con~I

I

·'t -,------ -----~

j

---1:-

-.

..

,:[--L-- - ----- ------I o

L l'~ '"---- ,,,R'-----\_,_ _ __

.,

I .'-. ------- -.. .

---'----....:----'--~-"-'-""'---

---, --.",.---~~

--.,.-----~"

Ti M[ (m.n )

Fig. 3.

Results of do g experiment #5 comparing the initial r e sponses to closing the feedback loop for different concentrations of nitroprusside (which creates different drug sensitivities). The 0.2 mg/ml concentration is the standard strength used in the intensive care unit. The high infusion rate before initiating control primes the infusion cannula in order to eliminate the initial dead space volume. The setpoint was 100 mm Hg.

Mean Arterial Pressure (mmH9)

Infusion Rote (ml / h)

':~I"lllI·11I :1111111111111111111111. •

,

,t"

-90

"

t

!

o

' 60

TIME(min)

Fig. 4.

t,

60

90

Estimated drug gain =-1.1 Controller gain = 0 _9

The performance of the controller in maintaining pressure near the desired level is superior compared to manual control by nurses. ~8ATH~

80

Infusion Ra t e (ml / h)

40' t-<-!---+--+-+---r---i-i--4--+-++--i~H---+--+-+-+----""f.,.b--I----kI

I

o~~- ~ - ~~ , ~, o

:le

60

90

120

150

TIME (min)

Fig. 5.

The infusion was transferred from manual to automatic control shortly after arriving in the intensive care unit. Multirate filtering and adaptation provided a smooth control action despite large pressure variations and good tracking of the disturbance resulting from giving this patient a bath. The estimated drug gain was -0.25 and controller gain 2.5.