Peripheral Route and of

1 downloads 0 Views 1MB Size Report
Aug 11, 1982 - at the Belfast College of Technology, Belfast,. Northern Ireland, and in .... and insulin independent glucose utilization by the central nervous ...

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-30, NO. 2, FEBRUARY 1983 S. J. CahiUl received the B.Sc. degree in electrical engineering and the M.Sc. degree in electronic engineering from Queen's University, Belfast, Northern Ireland, in 1970 and 1971, respectively. In 1971-1972 he was an Assistant Lecturer at the Belfast College of Technology, Belfast, Northern Ireland, and in 1972-1979 he was a Lecturer at Ulster College, Newtownabbey, Northern Ireland. He is currently a Senior Lecturer at Ulster Polytechnic, Newtown-

93

abbey, Northern Ireland, and Director of Cytel Instruments, Ltd., Belfast, Northern Ireland. His research interests include the development of teaching regimes for microprocessor engineering and the application of microprocessors to biomedical situations. Mr. Cahill is a member of the Institute of Electronic and Radio Engineers and the Ulster Biomedical Engineering Society. He is also a

Chartered Engineer of the United Kingdom.

G. McClure, photograph and biography not available at the time of

publication.

Evaluation of Portal/Peripheral Route and of Algorithms for Insulin Delivery in the Closed-Loop Control of Glucose in Diabetes-A Modeling Study CLAUDIO COBELLI AND ALFREDO RUGGERI

Abstract-In this paper we present an evaluation of portal versus peripheral routes for insulin delivery in diabetes with three representative closed-loop glucose control algorithms. A novel noninvasive approach is used which is based on a model of the blood glucose regulation system which simulates a Type I diabetic subject. The two routes and three algorithms are compared in controlling the simulated patient for 24 h, challenged with two dynamic glucose perturbations. The evaluation is performed by comparing both plasma accessible variables (e.g., glucose and insulin) and metabolic fluxes (e.g., glucose production and uptake, peripheral glucose utilization). Similar performances are achieved by the three algorithms both with peripheral and with portal infusions, especially in the postabsorptive steady state. An almost complete metabolic normalization is obtained with the portal route. With the peripheral route, normality is not restored; in particular, hyperinsulinemia and enhanced insulin-dependent glucose utilization are produced. From these simulation results, it is the site of insulin infusion, which appears to play an essential role in terms of the ability to normalize the metabolic state of a diabetic subject.

cose, and 2) open-loop systems, in which insulin is infused according to a preprogrammed scheme, that is, independent of the actual glucose concentrations. Several research groups have studied and implemented closed and open-loop systems (see, for example, the review papers [1] -[3] and the references therein). Not only are there differences between the various realizations with regard to their technological implementation, differences also exist with respect to the type of control algorithm used to predict the insulin infusion rate from glucose measurements or the type of preprogrammed schedule adopted for an open-loop insulin delivery. Moreover, different routes are available for insulin infusion, namely the peripheral, portal, peritoneal, muscular, and subcutaneous routes. There is, therefore, an obvious need to evaluate all these various regimens and routes of insulin delivery, not only in order to assess their cost effectiveness but also to provide further insight both into the limitations of available algorithms/routes as well as into a better design of I. INTRODUCTION both closed- and open-loop systems. This kind of quantitative IN recent years, much research effort has been devoted to evaluation is, however, hardly feasible in vivo on a diabetic attempting to achieve optimal control of glucose concentrasubject in the same metabolic conditions for obvious ethical tion in diabetes using external mechanical devices as opposed and practical reasons, and a model-based approach sounds to conventional therapy involving the subcutaneous injection of appropriate in order to gain quantitative insight into such insulin. Two types of devices have been developed: 1) closedproblems. loop systems (artificial pancreas), in which insulin and/or Recently, two groups have addressed via simulation studies other substances are infused according to appropriate control some of these problems focusing on closed-loop devices algorithms on the basis of a continuous measurement of glu[4] - [6] . In particular in [6], practically all the algorithms available for the closed-loop control of blood glucose via the Manuscript received February 1, 1982; revised August 11, 1982. peripheral route of insulin infusion have been compared and a The authors are with the Istituto di Elettrotecnica e di Elettronica, Universita di Padova, 35100 Padova, Italy, and LADSEB-CNR, 35100 lack of clearly important differences in the pattern of insulin delivery as provided by the different algorithms in response to Padova, Italy.

0018-9294/83/0200-0093$01.00 © 1983 IEEE

94

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-30, NO. 2, FEBRUARY 1983 Ra te of Appearance of Glucose A

Plasma Glucose

A tt.

Fig. 1. A schematic representation of the simulated closed-loop experiment.

changing glycemia has been noted. The simulation approach did not consider, however, a real closed-loop situation, i.e., the simulated profiles of insulin delivery by the various algorithms have been obtained from a glucose time course previously obtained in a group of patients controlled by artificial pancreases. Preliminary but similar results on the comparison of a number of representative control algorithms have been also obtained in [51 using a different and more physiological approach, that is, by simulating a closed-loop situation with the diabetic patient described by a mathematical model. The effect of the portal versus the peripheral route of insulin on glucose disposal processes in the dog has been examined in [4] through a model of glucose metabolism challenged with square wave infusions of glucose, and also in [5] where preliminary results on a human glucose model challenged with oral glucose tolerance tests were communicated. Both studies emphasize the nonnormalization achieved through the peripheral route of insulin infusion, even if the agreement in the predictions of the nonnormalized glucose disposal processes was essentially qualitative

in nature. In this study, following the approach outlined in [5], we present a thorough investigation on the role of different algorithms and of the portal versus the peripheral route of insulin delivery for the closed-loop control of glucose in Type I diabetics. The closed-loop situation is simulated with the aid of a comprehensive mathematical model of the glucose regulation system [7], [8]. Support emerges from these studies to recent experimental findings in dogs [9] -[12], that it is the route of insulin delivery which appears to play an essential role in terms of the ability to normalize the metabolic state of a diabetic patient. The model provides some insight into the cause/effect mechanisms of the experimentally observed (in plasma) nonnormalization with the peripheral route; moreover, a quantitative prediction of the consequences of this nonnormalization at the level of the individual (inaccessible) unit processes of glucose metabolism (liver and peripheral uptake of glucose) is also allowed. As concerns comparative performance, the various closed-loop algorithms exhibit a substantially equivalent (especially in steady-state) behavior with both routes.

The outline of the paper is as follows. In Section II we describe the major features of the simulated closed-loop confi'guration; that is, the mathematical model used to describe the diabetic patient, the three algorithms for the external blood glucose control, and the test situation being considered. Simulation results are presented in Section III on the performance of the two routes and three algorithms in a diabetic subject challenged with dynamic glucose tolerance tests. The results are discussed in Section IV and some concluding remarks are drawn in Section V. II. SIMULATION OF THE CLOSED-LOOP CONTROL OF GLUCOSE IN DIABETES USING THE ARTIFICIAL PANCREAS A. Rationale The rationale of the situation being considered in this study is to externally control a Type I diabetic patient as represented by a mathematical model through either peripheral or portal administration of insulin according to a number of representative control algorithms. A schematic diagram of the simulated closed-loop control is shown in Fig. 1 and its components as well as the test situation being considered will now be discussed. B. A Mathematical Model of the Glucose Regulation and Its Use in Type I Diabetes The mathematical model used for simulating a patient with Type I diabetes (almost no insulin secretion from the ,B cells) is based on a previously validated comprehensive description of the glucose regulation system [7], [8] to which reference is made for all the details. The model consists of a glucose plant and a two-hormone controller, that is insulin and glucagon. Its basic structure is shown in Fig. 2. Briefly, the glucose subsystem is described by a single compartment representing the extracellular fluids. The nonlinear unit processes that have been explicitly considered are the liver glucose production and uptake, renal excretion, insulindependent glucose utilization by muscles and adipose tissues, and insulin independent glucose utilization by the central nervous system and the red blood cells. An exogenous glucose stimulus is allowed.

COBELLI AND RUGGERI: CLOSED-LOOP CONTROL OF GLUCOSE IN DIABETES Og

®i3

Test Input

C NS and RBC Utilization

I Liver Uptake Liver Production

GLUCOSE

INSULIN

SUBSYSTEM

r

r

0

0

F u d st

ElKidneiYio Elimination

Secretion t

F+

Muscular and Adipose Tissue Utilization

Extracellutar

0

0D

0D

SUBSYSTEM

95

Extracellula r F uids

Ii

GLUCAGON SUBSYSTEM

I Iv

1

(00

Fig. 2. Control system model of the glucose regulatory system including subsystems of glucose, insulin, and glucagon. Continuous lines represent fluxes of material; dashed lines represent control signals.

The insulin subsystem is described by a five compartment model representing, respectively, stored and promptly releasable insulin in the pancreas, liver and portal insulin, plasma insulin, and insulin in the interstitial fluids. Insulin synthesis and secretion are nonlinearly controlled by glucose. Two routes for insulin have been considered, namely, the peripheral and the portal route. The glucagon subsystem is described by a one compartmental model; its secretion is assumed to be controlled by glucose and insulin. For comparing the available routes of insulin infusion and the various algorithms, the model of Fig. 1 has been used to describe quantitatively the dynamics of the blood glucose regulatory system in a classical Type I diabetic state [13]. To simulate this- state, only the major defect of insulin-dependent diabetes has been taken into account, in line with experimental evidence; that is, insulin secretion has been suppressed. Insulin and glucagon kinetics have been assumed to be normal. Also, the action of insulin on peripheral glucose utilization has been assumed in the normal range. This model of Type I diabetes therefore constitutes an idealized, minimum-assumption description of this rather complicated pathological condition. We have successfully validated this model for a Type I diabetic subject first by comparing its response to an intravenous glucose injection with our available (unpublished) data. Further validation has been carried out by comparing the model predictions after a peripheral insulin infusion with a set of available experimental data [14] on the time course of plasma accessible variables (glucose, insulin, glucagon) and of unit processes behavior, for instance, NHGB.

C. Algorithms for Closed-Loop Glucose Control A brief account will now be given of the principal features of the three control algorithms for the artificial pancreas we have

examined. These algorithms were chosen since they can be considered as representatives of a group of algorithms based on apparently different principles and we have considered their most recent version. 1) Biostator-Miles Algorithm: Three modes for infusing insulin are available in this commercial device [15] which realize, respectively, 1) a static mode, that is, the infusion of insulin is solely dependent upon the last measured value of glucose, 2) a dynamic mode, in which the insulin infusion rate depends upon the rate of change of glucose, and 3) a static plus dynamic mode. If we denote the insulin infusion rate by IR (t) and the measured glucose concentration by Yi, the three operating modes can be expressed through the following relations. Static Mode:

IR(t)=RI

(

I +11

IR(t)=0,y, ( QI

-B

y, (t) - BI QI

+ IBI

(3)

y 1 0, m < 0, respectively). An algorithm is also avail-

96

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-30, NO. 2, FEBRUARY 1983

PARAMETER VALUES

TABLE I

OF THE THREE ALGORITHMS FOR CLOSED-LOOP

BLOOD GLUCOSE CONTROL

Albisser

Biostator-Miles Algorithms B2 [17] B1 [161

91.5 30

BI

QI

RI

KR KF BD QD RDl

91.5 40

DR() DR(t=0,

BD - y X (t)

QD

1],

Al [201

16.4 (with IRpo) 16.4 (with IRpO) |21.2 (withIRpe) 21.2 (with IRpe) 165 45 60 30 15

70 45 60 30 15

able for the infusion of dextrose, whose rate is indicated by DR(t) in order to prevent hypoglycemic states: DR (t) = RD [BD-Yl(t) +

Algorithm

BD-yl(t)

+

1>0 (5)

QD

+I 0) is decreased (Table I). 3) Albisser Algorithm: Historically, the first algorithm for an artificial pancreas was proposed by Albisser and his colleagues [18]. In this case, the control algorithms for insulin and dextrose infusion are based on a hyperbolic description and are given, respectively, by

Imax 1GB

PI Dmax

IGD PD I K1 l K2

225

1160.3 (with IRpo) 155.7 (with IRpe) 42

200 50 31 100 10

mean of the differences of the last five glucose values and K1, K2 are empirical constants. The actual value of glucose concentration used for determining insulin and dextrose infusion rates through (7) and (8) is the projected glucose concentration given by

(10) Yip =y1(t) + Ay1, Values suggested in [20] have been used for the constant parameters and are also shown in Table I.

D. Test Situation The model of the diabetic patient together with the three external control algorithms has been implemented on an IBM370/158 using the CSMP-III simulation language. It is worth noting that a noise-free situation is considered. Evaluation of the alternative configurations (routes/algorithms) is carried out on the basis of results obtained from simulating the following dynamic tests which are widely adopted in studies of diabetes. A 24 h test period, during which control is maintained with the artificial pancreas, is considered, starting at 8:30 with two oral glucose tolerance tests each of 100 g at 12:00 and 18:00. The perturbation input of the model is therefore the rate of appearance (RA) of glucose in plasma (test input of Fig. 2), whose typical time course [21] is shown in Fig. 3(a). The evaluation of the peripheral and portal routes for insulin infusion (Fig. 2) for the three closedloop control algorithms is made by considering both their dynamic and static performance on the basis of a number of m I l+tah[ta ylt__-_GB ) IR(t)= Imax (7) indexes, including the quantity of insulin and dextrose infused during the study, glucose pattern ahd levels in plasma, insulin pattern and levels in plasma, liver, and interstitial fluids. For DR(t) = Dmax {I - tanh[Y )(t GD]} (8) generating a normal state reference for both system variables and fluxes, available 5 h plasma glucose and insulin measurewhere GB, PI, GD, and PD are empirical constants and Imax ments after an oral glucose tolerance test in a group of normal Dmax represent, respectively, the maximal infusion rates for subjects [22] have been used. insulin and dextrose. These characteristics realize only a static III. RESULTS mode of control. In order to take into account also the rate of The results obtained for the three algorithms, the Biostatorof in the insulin infusion a change glucose predicting rate, factor Ay, has been considered, which allows the estimation Miles (B 1), the modified Biostator-Miles (B 2), and the Albisser of a "projected glucose concentration." The factor Ay1 [19] algorithm (A 1), for the portal (IRp,) and peripheral (IRpe) is defined as routes of insulin delivery are summarized in Table II (the dextrose facility was practically never activated).

wherethr ocn ogo (9) A set of typical patterns obtained in the simulation studies where the rate of change of glucose i, is-computed as the with Bl by using the two routes of infusion are shown, to-

. _.*@_

COBELLI AND RUGGERI: CLOSED-LOOP CONTROL OF GLUCOSE IN DIABETES

97

z

0 o-

0

co

a

o.

9

15

12

18

21

TIME

HR)

24

(a)

I

-I

0

(.)

I

0 J 4

0 0 4

-a

A.

0

C4

6

(b)

_ .. *.

"

* *

**@

**

*-

* *@

..e

0 qt Cl

3.

w

_

_

C4

24,

4

.

0

21. 8S. TIME (HR)

**

* *-

* -

.. ***e

.. **. *-

.. **

-

:

*- *.* . ' ...* "

.

* *. -* *.. * -*

: . .* _

-J

0C ::...

0

z

t== .. ..

z 0 D

..* .

.. ..

II

0

0

L

9.

>- *.. *-:.* *-:

12.

.

15i.

21.

IS.

24.

3.

6.

TIME (HR)

(c)

Fig. 3. Time courses of plasma glucose and insulin in a normal and in a diabetic subject controlled by artificial pancreas (BI algorithm) after two oral glucose loads. (a) Shows the rate of appearance of glucose in the plasma following these two oral loads, (b) and (c) show, respectively, the predicted time courses of plasma glucose and insulin. The continuous line refers to a normal subject, while the dashed and dotted lines refer, respectively, to the portal and peripheral route of insulin delivery in a diabetic subject.

gether with the "normal state" reference, in Figs. 3-6. More were equally able to restore the diabetic patient to a normal precisely, in Fig. 3(b) and (c), plasma glucose and insulin time postabsorptive steady state (PAS), both with respect to concourses are reported; Fig. 4 depicts the predicted time course centrations of glucose, insulin, and glucagon in the various of insulin-dependent peripheral glucose utilization, and finally, compartments and to the various metabolic unit processes Figs. 5 and 6 show the prediction of the liver unit processes (liver output and uptake, peripheral utilization, etc.). As concerns the dynamic mode, none of the algorithms was behavior, glucose production and uptake, respectively. Using the. portal route for insulin delivery, all the algorithms able to reproduce exactly the "normal reference" pattern of

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-30, NO. 2, FEBRUARY 1983

98

RESULTS OBTAINED WITH

THE

TABLE II THREE ALGORITHMS B1, B2, AND A 1 BY USING THE PORTAL (IRpo) ROUTE FOR INSULIN INFUSION B11

Pn2

Al

91.5 91.5

91.5 91.5

91.5 91.5

Liver Uptake (PAS, mg/min/kg

Plasma Insulin (PAS, pU/mk)

11.0 26.8

11.0 26.8

11.0 26.8

Peripheral Uptake (PAS, mg/min/lcg B.W)

Liver Insuilin

30.0 26.4

30.0 26.4

30.0 26.4

9.8

Plasma Clucose (PAS, mf /]00 m k)

IR P0 IR

(PAS, PU/mt) Interstiti.l Fliid Instulin

AND THE

PERIPHERAL (IRpe)

131

n2

Al

0.05 0.05

0.05 0.05

0.05 0.05

0.41 0.60

0.41 0.60

0.41 0.60

Plasma Glucose (lst OGTT peak, mg/100 m9)

139 134

156 148

141 138

Ali)

IR Po IR e

(PAS, pU/mW.)

23.9

9.8 23.9

9.8 23.9

Plasma Insulin (lst OGTT peak, PU/mQ)

105 298

90 287

94 316

Glucagon (PAS, pg/mQ)

75 74

75 74

75 74

Liver Insulin (lst OGTT peak, pU/ml)

317 279

268 265

297 271

16.4 21.2

16.4 21.2

16.4 21.2

Interstitial Fluid Insulin (lst OGTT peak, PU/mi)

60 108

58 105

60 108

54.2 55.9

50.4

53.4 55.3

Insulini Infusion Rate (PAS, sU/min) Liver Production (PAS, ispmmg/kgm i

2.11

I)

2.30

2.11 2.30

2.11 2.30

Total Insulin Infused

(U/24h)

52.5

0-

z

a Iw x A.O

n

A.

w .4

0

TIME (HR)

Fig. 4. Time course of insulin-dependent peripheral glucose utilization in a normal and in a diabetic subject (same situation as Fig. 3).

plasma variables and of liver and peripheral glucose unit processes even if the achieved control may be judged able to restore a normal metabolic portrait of the diabetic patient. Insulin-dependent glucose disposal processes during an oral glucose tolerance load is practically normal [8], i.e., the total amount of glucose taken up by the peripheral tissues is predicted to be 23 percent of the glucose load while the liver takes up 54 percent of the load (normal values are, respectively, 21 and 56 percent). As concerns the various algorithms, the B2 algorithm exhibited a better performance, the insulin levels being lower than those achieved with BI or A 1.

Using the peripheral (plasma) route for the external infusion of insulin, none of the algorithms was able to normalize the metabolic state of the patient. In the postabsorptive state, glucose is normal, but an elevated insulin concentration is present in plasma in order to establish a concentration of portal insulin such that liver output is almost normalized (no liver-plasma gradient can be established for insulin through the peripheral route). This in turn causes remarkably enhanced insulin-dependent peripheral utilization of glucose. In the dynamic mode, severe nonnormalization of plasma insulin and of glucose unit processes is a common feature of

99

COBELLI AND RUGGERI: CLOSED-LOOP CONTROL OF GLUCOSE IN DIABETES

12.

15.

18.

21.

24.

3.

6.

TIME (HR)

Fig. 5. Time course of liver glucose production in a normal and in a diabetic subject (same situation as Fig. 3).

2

wI-.

a a -

3.

TIME (HR)

Fig. 6. Time

of liver glucose uptake in a normal and in betic subject (same situation as Fig. 3).

course

a

dia-

all the algorithms, in particular, insulin-dependent peripheral distinguishable from A 1, and has, for the sake of clarity, not glucose utilization is remarkably enhanced. Accordingly, been shown). insulin-dependent glucose disposal processes are not norIV. DISCUSSION malized, in particular, the amounts of the glucose load taken Increasing experimental evidence is becoming available on up by peripheral tissues and by the liver are, respectively, 57 -and 21 percent, which indicates a remarkable abnormal the inability of closed-loop external glucose control systems to handling of the glucose load when compared to the portal obtain full normalization of metabolic profiles of a Type I route discussed above. As concerns the various algorithms, diabetic subject despite a satisfactory control of plasma glucose both in and out of steady state. In particular, hypera somewhat better performance for the B2 algorithm may still be noted. With this respect in Fig. 7, the plasma glucose and insulinemia has been reported by several authors both in insulin time courses obtained with the B2 and Al algorithms human as well in animal studies [9] [12], [20], [23] [25] are shown (the profile obtained with BI is practically in- after artificial pancreas treatment (infusion in plasma). More-

-

100

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-30, NO. 2, FEBRUARY 1983

0J 0 7-

4 4

-j

a. 15

TIME (HR)

18

(a) 0

co

0

CM

0 N

CM

0 0.

DO

z DO 4

O

UM 0

0 Uco

18.

TIME (HR)

(b)

Fig. 7. Plasma glucose and insulin response in a diabetic subject controlled by two artiflcial pancreas algorithms after an oral glucose load. Predicted glucose (a) and insulin (b) time courses are shown for the Albisser algorithm (dotted line) and Biostator 2 algorithm (continuous line).

over, experimental evidence has been reported in dog studies [9] - [121 that it is the nonphysiological route of insulin delivery (peripheral instead of portal) that causes incomplete metabolic normalization despite the fact that normoglycemic levels are achieved, even if a significant difference between the two routes of insulin administration has not been found in other studies [261. One important component of a closed-loop device for external blood glucose control is the computer algorithm which predicts the time course of the insulin delivery rate from glucose measurements. Several algorithms have been proposed, ranging from reasonably simple and pragmatic to more so-

phisticated (see [1], [2], [6] for reviews). From time to time, claims have been made on the superiority or inferiority of certain realizations as compared to others, but recent evidence from simulation studies indicates substantially equivalent performance of a number of representative algorithms [5],

[6].

The evaluation of alternative routes and algorithms for insulin delivery is difficult to tackle in vivo for rather obvious ethical and technical reasons. Moreover, an experimental approach seems necessary which is able not only to provide quantitative insight on the time course of plasma accessible variables, but also on unit processes behavior, e.g., liver and

COBELLI AND RUGGERI: CLOSED-LOOP CONTROL OF GLUCOSE IN DIABETES

peripheral glucose fluxes, in order, for instance, to understand more deeply the cause/effect mechanisms of the observed nonnormalization with peripheral closed-loop insulin infusion. In this respect, the modeling/simulation approach constitutes an appealing noninvasive methodology to provide, in a sort of ideally controlled noise-free experimental situation, quantitative insight into the problems outlined above, i.e., the optimal route of insulin delivery and a comparative evaluation of different control algorithms. In this study, we have used such a model-based approach by simulating a classical situation for external blood glucose control in Type I diabetes (Fig. 1). Type I diabetes has been described through a previously validated mathematical model of the glucose regulation system [7], [8] which allows insulin to be infused either peripherally or portally. The simulated diabetic subject has been externally controlled with the two routes by three representative algorithms during a 24 h test situation with two dynamic glucose perturbations. This modeling and simulation approach has obviously required a number of simplifications (idealizations), e.g., a sort of ideal Type I diabetic state with normal insulin kinetics and action, and glucose-meal dynamic perturbations have been considered. Nevertheless, the major features of Type I diabetes have been incorporated and the simulated closed-loop situation seems to provide a sufficiently rich dyrLamic framework for understanding the cost effectiveness of portal versus peripheral routes for insulin delivery and the performance of the various closed-loop algorithms. In particular, one of the goals of this simulation rationale may be seen as hypothesis testing/heuristic potential, i.e., can the experimentally observed hyperinsulinemia (with peripheral infusion) be explained in terms of site of infusion and if yes, to what extent do the various metabolic glucose fluxes deviate from normal? These simulation studies on the portal versus the peripheral route which are, in terms of plasma accessible variables (glucose, insulin, glucagon), in agreement with experimental studies in dogs [9] - [12], indicate that it is the site of insulin infusion that plays an essential role in terms of the ability to normalize the metabolic state of a diabetic patient. On the contrary, the various closed-loop algorithms exhibit a substantially equivalent (especially in steady-state) performance with both routes. The portal route is able to restore near normality both in terms of plasma variables and metabolic fluxes. This is completely true for the postabsorptive steady state, while a difference in phase (not in amplitude) from the "normal reference" pattern can be seen in the metabolic profiles during the dynamic perturbation. These abnormalities in the waveform shape are very likely to be due to the still incomplete restoration which is achieved in terms of the physiology of glucose control, i.e., the role of the gastrointestinal tract is neglected, even if one could argue that the available algorithms were originally designed for peripheral infusion only. Another feature which has been noted is the presence in some metabolic profiles of rather high-frequency components (as compared to the peripheral route), which could be related to the kinetic r'ole of the portal compartment from which insulin is

101

cleared at a very high rate; again, it may be worth remarking that no modifications have been introduced into the algorithms originally designed for the peripheral route to take care of this alternative route. The peripheral route is not able to normalize the metabolic state of the simulated Type I diabetic patient. More specifically, elevated plasma insulin levels are produced throughout the test (e.g., almost 150 percent greater than normal in PAS), thus supporting the view that hyperinsulinemia as reported in a number of human studies [20], [22] - [24] can be explained largely in terms of the route employed for insulin delivery. The simulation rationale also provides some quantitative insight into the consequences on the individual glucose disposal processes of this nonnormalization at the plasma level. In particular, the role of the liver and of the peripheral tissues in handling the glucose load is roughly interchanged if compared to a normal state (and to the portal route of infusion); that is, the peripheral uptake approaches normal liver uptake percentages (56 percent) while the liver uptake approaches normal peripheral uptake percentages (21 percent). In particular, insulin-dependent glucose utilization is remarkably enhanced due to the highly increased interstitial fluid insulin levels. Indirect support for these model predictions are provided by the experimentally observed [24], [25] elevated lactate and pyruvate plasma levels after artificial pancreas treatment. The model's ability to explicitly predict the individual glucose disposal processes cannot be overemphasized as for instance, total turnover studies focusing on total glucose utilization and production, respectively [26] , may easily underrate the role of the nonnormalization of the single processes. The various control algorithms exhibit a substantially equivalent performance. This is completely true as concerns the steady state; in the nonsteady state, the optimized Biostator algorithm (B2) is the most satisfactory, being capable of producing lower levels of insulin in the various compartments at the expense of moderate, more pronounced glycemic excursions. As a consequence, the amount of insulin infused is less than that infused with either Bl or A 1, while it is confirmed that the portal route requires a somewhat less amount of insulin as compared to the peripheral, in agreement with the findings in pancreatectomized dogs [ 12]. In conclusion, this simulation study shows that the peripheral route of intravascular insulin delivery exhibits an intrinsic limitation for all the available closed- and hence, open-loop algorithms. Alternative portal-like ways of delivering insulin should therefore be considered in order to avoid elevated levels of insulin in the postabsorptive state, thus preventing the incomplete metabolic normalization seen with the intravenous route. V. CONCLUSIONS A novel noninvasive approach for evaluation of alternative routes of insulin delivery and of the performance of various closed-loop algorithms for external glucose control in diabetes has been presented. The approach is based on the use of a mathematical model of the glucose regulation system in a Type I diabetic state. This kind of evaluation is practically in-

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-30, NO. 2, FEBRUARY 1983

102

feasible in vivo in humans for obvious ethical and technical reasons. Our results show that the route of insulin delivery plays an essential role in terms of the ability of normalizing the metabolic state of a diabetic patient. On the contrary, all the closed-loop algorithms exhibit a substantially equivalent performance and of particular relevance, none of the algorithms is able to maintain in the postabsorptive state a normal insulin concentration in plasma when the peripheral route for insulin delivery is used. This in turn causes nonnormalization, for instance, of the insulin-dependent glucose utilization. The ability of the portal route to practically normalize the metabolic state of a diabetic patient should encourage further research into alternative "portal-like" routes of insulin delivery. Note Added in Proof: We also recently examined the performance of the algorithm proposed by Fisher et al. (Diabetologia, vol. 18, pp. 97-107, 1980), as it can be considered representative of a different class of algorithms. More specifically, the rate of insulin infusion has three components: one glucose independent (parameter a,) and two linear functions of the glucose level and of its rate of change (parameters a1 and a2, respectively). The adopted parameter values were aO = 16.4 for portal and aO = 21.2 for peripheral insulin infusion;a, = 1.09 and a2 = 7.16 for both routes of infusion. In PAS, exactly the same performance exhibited by the other three algorithms has been observed, both with the portal and peripheral routes of infusion. As concerns the dynamic mode (first OGTT peak, see Table II), higher plasma glucose (193 mg/100 ml with IRpo and 208 mg/100 ml with IRpe), lower plasma insulin (80 MU/ml with IRpo and 173 pU/ml with IRpe), and liver (227 pU/ml with IRpo and 171 pU/ml with IRpe) concentrations were observed. Interstitial fluid insulin was practically unchanged (58 ,uU/ml with IRpo and 108 PU/ml with IRpe). Total insulin infused was 52.5 U with IRpo and 54.2 U with IRpe. These results indicate that this algorithm is less sensitive to glucose changes, resulting in relatively less adequate normalization of blood glucose, and these findings are in close agreement with those presented in [6]. We also observed a rather different (with respect to Bl, B2, and A 1) dynamic performance in the time courses of glucose fluxes. In particular, the peak in peripheral glucose uptake was 2.67 mg/min/kg with IRpo and 9.32 mg/min/kg with IRpe (see Fig. 4), and the peak in liver uptake was 6.93 mg/min/kg with IRpo and 3.66 with IRpe (see Fig. 6).

[41

[5]

[6]

[71 [8]

191 [101

[11] [121 [131

[14] [151

[161

[17]

[181

[191

ACKNOWLEDGMENT We would like to thank Dr. R. Nosadini of the Istituto di Medicina Clinica, Dipartimento di Gerontologia e Malattie del Ricambio, Universit'a di Padova, Padova, Italy, for many helpful discussions during the development of this study.

[201

REFERENCES

[221

[11 A. M. Albisser, "Devices for the control of diabetes mellitus," Proc. IEEE, vol. 67, pp. 1308-1320, 1979. [21 J. V. Santiago, A. H. Clemens, W. C. Clarke, and D. M. Kipnis, "Closed-loop devices for blood glucose control in normal and diabetic subjects," Diabetes, vol. 28, pp. 71-84, 1979. [31 W. J. Spencer, "A review of programmed insulin delivery systems," IEEE Trans. Biomed. Eng., vol. BME-28, pp. 237-251, Mar. 1981.

[211

[231

[24]

A. M. Albisser, Y. Yamasaki, H. Broekhuyse, and J. Tiran, "Hypercomplex models of insulin and glucose dynamics: Do they predict experimental results?," Ann. Biomed. Eng., vol. 2, pp. 539-557, 1980. C. Cobelli, G. Pacini, A. Ruggeri, E. Duner, S. Del Prato, R. Nosadini, and A. Tiengo, "Algorithms for closed-loop glucose control (artificial pancreas) in diabetes. A novel noninvasive approach for their comparative evaluation based on mathematical modeling," in Preprints IFAC 8th World Congress, vol. XXI, pp.89-94,1981. H. M. Broekhuyse, J. D. Nelson, B. Zinman, and A. M. Albisser, "Comparison of algorithms for the closed-loop control of blood glucose using the artificial beta cell," IEEE Trans. Biomed. Eng., vol. BME-28, pp. 678-687, Oct. 1981. C. Cobelli, G. Federspil, G. Pacini, A. Salvan, and C. Scandellari, "An integrated model of blood glucose dynamics control," Math. Biosci., vol. 58, pp. 27-60, 1982. C. Cobelli and A. Mari, "Validation of mathematical models of complex endocrine-metabolic systems. A case study on a model of glucose regulation," Med. Biol. Eng. Comput., in press. A. M. Albisser, C. K. Botz, and B. S. Leibel, "Blood glucose regulatiopl using an open-loop insulin delivery system in pancreatectomized dogs given glucose infusions. I. Portal square waves," Diabetologia, vol. 16, pp. 129-133, 1979. C. K. Botz, E. B. Marliss, and A. M. Albisser, "Blood glucose regulation using closed- and open-loop insulin delivery systems. II. Peripheral primed square wave infusions," Diabetologia, vol. 17, pp. 45-49, 1979. Y. Goriya, A. Bahoric, E. B. Marliss, B. Zinman, and A. M. Albisser, "Blood glucose control arid insulin clearance in unrestrained diabetic dogs portally infused with a portable insulin system," Diabetologia, vol. 19, pp. 452-457, 1980. , "The metabolic and hormonal responses to a mixed meal in unrestrained pancreatectomized dogs chronically treated by portal or peripheral insulin infusion," Diabetologia, vol. 21, pp. 58-64, 1981. National Diabetes Data Group, "Classification and diagnosis of diabetes mellitus and other categories of glucose intolerance," Diabetes, vol. 28, pp. 1039-1057, 1979. L. Sacca, R. Sherwin, R. Hendler, and P. Felig, "Influence of continuous physiologic hyperinsulinemia on glucose kinetics and counterregulatory hormones in normal and diabetic humans," J. Clin. Invest., vol. 63, pp. 849-857, 1979. A. H. Clemens, "Feedback control dynamics for glucose controlled insulin infusion system," Med. Progr. Technol., vol. 6, pp. 91-98, 1979. -Biostator® Glucose Controlled Insulin Infusion System, Operating Manual, Miles Lab., Inc., 1976. J. S. Christiansen, P. A. Svendsen, E. Mathiesen, P. Rubin, and B. Rann, "Studies in order to optimize constants used in the algorithms of the Biostator GCIIS," in Proc. Wksp. Artificial Beta Cells Diabetes Res. Management, Heviz, Hungary, Sept. 1979, D-11. A. M. Albisser, B. S. Leibel, T. G. Ewart, Z. Davidovac, C. K. Botz, and W. Zingg, "An artificial endocrine pancreas," Diabetes, vol. 23, pp. 389-396, 1974. C. K. Botz, "An. improved control algorithm for an artifical B-cell," IEEE Trans. Biomed. Eng., vol. BME-23, pp. 252-255, May 1976. A. K. Hanna, B. Zinman, A. F. Nakhooda, H. L. Minuk, E. F. Stokes, A. M. Albisser, B. S. Leibel, and E. B. Marliss, "Insulin, glucagon and amino acids during glycemic control by the artificial pancreas in diabetic man," Metabolism, vol. 29, pp. 321-332, 1980. J. Radziuk, T. J. McDonald, D. Rubenstein, and J. Dupre, "Initial splanchnic extraction of ingested glucose in normal man," Metabolism, vol. 27, pp. 657-669, 1978. 0. P. Ganda, J. L. Day, J. S. Soeldner, J. J. Connon, and R. E. Gleason, "Reproducibility and comparative analysis of repeated intravenous and oral glucose tolerance tests," Diabetes, vol. 27, pp. 715-725, 1978. D. L. Horwitz, A. Zeidler, B. Gonen, and J. B. Jaspan, "Hyperinsulinism complicating control of diabetes mellitus by an artificial beta-cell," Diabetes Care, vol. 3, pp. 274-277, 1980. R. Nosadini, G. A. Noy, M. Nattras, K.G.M.M. Alberti, D. G. Johnston, P. D. Home, and H. Orskov, "The metabolic and hormonal response to acute normoglycemia in Type 1 (insulin-

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME -30, NO. 2, FEBRUARY 1983

dependent) diabetes: Studies with a glucose controlled insulin infusion system (artificial endocrine pancreas)," Diabetologia, vol. 23, pp. 220-228, 1982. [251 B. Zinman, E. F. Stokes, A. M. Albisser, A. K. Hanna, H. L. Minuk, A. N. Stein, B. J. Leibel, and E. B. Marliss, "The metabolic response to glycemic control by the artificial pancreas in diabetic man,"Metabolism, vol. 28, pp. 511-518, 1979. [261 R. A. Rizza, R. E. Westland, L. D. Hall, G. S. Patton, M. W. Haymond, A. H. Clemens, J. E. Gerich, and F. J. Service, "Effect of peripheral hyperglycemia and glucose turnover in alloxan-diabetic dogs," Mayo Clin. Proc., vol. 56, pp. 434 -438, 1981.

103

endocrine systems, with emphasis on carbohydrate, lipid, and protein metabolism. He is coeditor (with Dr. R. N. Bergman) of Carbohydrate Metabolism: Quantitative Physiology and Mathematical Modelirig (Chichester, England: Wiley, 1981), and is coauthor (with Dr. E. R. Carson and Prof. L. Finkelstein) of The Mathematical Modeling of Metabolic and Endocrine Systems: Model Formulation, Identification and Validation (New York: Wiley, 1982). He is on the Editorial Boards of Mathematical Biosciences and the American Journal of Physiology: Regulatory, Integrative and Comparative Physiology, ModelingMethodology Forum. Dr. Cobelli is a member of the Biomedical Engineering Society and the Society for Mathematical Biology.

Claudio Cobelli was born in Bressanone, Italy,

on February 21, 1946. He received the Doctoral degree (Laurea in Ingegneria Elettronica) in 1970 from the University of Padova, Padova,

Italy.

From 1970 to 1980 he was a Research Fellow * of the Institute of System Dynamics and Bioengineering, National Research Council (LADSEBCNR), Padova, Italy. In 1980 he joined the Istituto di Elettrotecnica e di Elettronica, Uni-

versity of Padova, where he is Full Professor of Biomedical Engineering. Since then he has also maintained an Associate Research position at LADSEB-CNR. His research activity is in the field of kinetic modeling and system identification of metabolic and

R

Alfredo Ruggeri was born in Vicenza, Italy, in 1955. He received his Doctoral degree (Laurea in Ingegneria Elettronica) from the University of Padova, Padova, Italy, in 1979. Since 1979 he has been associated with the Istituto di Elettrotecnica e di Elettronica, University of Padova, where he is presently a Research Fellow in Biomedical Engineering. His main research activity is in the field of ___l__ modeling of metabolic and endocrine systems, with emphasis on the use of simulation, system identification techniques, and optimal experimental design.

Voltage Clamp Processor System HITOSHI YAMAGATA, NOZOMU HOSHIMIYA, MEMBER, IEEE, AND HACHIRO INOMATA

Abstract-A new method of voltage clamping of biological membranes is developed. Usually, series resistance (Rs) is inevitably introduced to the membrane and Rs makes it difficult to control the membrane voltage. The purpose of this study is to compensate undesirable effects of Rs, and to develop an improved voltage clamp system. If the membrane is driven by a current source, it is possible to calculate the voltage drop across Rs and the true membrane voltage (Vm). Then, if the current injection from the current source to the membrane is controlled by voltage feedback, the difference voltage between the command voltage and Vm becomes small enough. This principle was utilized in the present voltage clamp processor system, which was composed of analog-digital hybrid circuits with the support of a high-speed microprocessor, Intel-8086 (16-bit, 8 MHz). With this new hybrid system it was possible to remove the parasitic oscillation associated with the conventional analog feedback control system. The microprocessor performed the compensation and clamping algorithm by using its arithmetic functions. The performance of this system has been tested and confirmed on the electronic excitable membrane model which had similar V-I-t character-

istics to those of actual biological membranes. The speed of this clamp circuit was appropriate for slow currents such as in smooth muscle membranes.

1. INTRODUCTION THE voltage clamp method is very important in the study the ionic mechanisms underlying the excitation of biological membranes [1], [2]. By using this method it has been possible to control the membrane voltage at a desired "command" level and to observe the membrane current (Im) corresponding to the activation/inactivation process of ionic channels. However, there has been a serious problem of the effect of series resistance (Rs), which is inevitably introduced to the membrane. Because of the presence of Rs, the membrane voltage (Vm) differs from the measured voltage (V) by the voltage drop Im Rs produced by the membrane current flowing across Rs. In this paper, we consider a double sucrose gap technique [31 for recording Vm and Im from a restricted Manuscript received February 5, 1982; revised August 19, 1982. This work was supported in part by the Ministry of Education, Science and, region of multicellular tissues such as cardiac and smooth Culture of Japan under Grant-in-Aid 587031 (1980) for Developmental muscle. In the case of this technique, it can be considered that Scientific Research and Grant-in-Aid 56490002 (1981) for Sdentific the effective Rs is mainly due to the resistance in the multiResearch. H. Yamagata and N. Hoshimiya are with the Department of Electronic cellular clefts in a bundle, and is approximately in inverse Engineering, Faculty of Engineering, Tohoku University, Sendai 980, proportion to the node width, where the node is an active Japan. H. Inomata is with the Department of Applied Physiology, School of small region isolated from the rest of the cells by high resistance of sucrose gap. Medicine, Tohoku University, Sendai 980, Japan.

Tof

-

0018-9294/83/0200-0103$01.00 © 1983 IEEE