Computer Methods and Programs in Biomedicine, 32 (1990) 195-214 Elsevier
195
COMMET 01101
Computer-assisted diabetic management: a complex approach T. Deutsch 1,2, E.R. Carson
2.3, F.E.
Harvey 3.2, E.D. Lehmann 3, P.H. Sonksen G. Whitney 2 and C.D. Williams 3
3.2, G. Tamas
4,
I Computer Centre, Semmelweis University, Budapest, Hungary, 2 Department of Systems Science, Centre for Measurement and Information in Medicine, City University, London, U.K., 3 Department of Endocrinology and Chemical Pathology, UMDS, St. Thomas's Hospital, London, U.K., 4 1st Clinic, Semmelweis University, Budapest, Hungary.
This paper describes the architecture of, and the main reasoning methods involved in, a computer system developed to assist in diabetic management. The system integrates (i) a database module used for blood glucose moni'~oring, (ii) an interpreter module used to analyse the adequacy of diet and insulin treatment for diabetics, and (iii~ an advisory module suggesting alterations in diet and/or insulin regimen in order to improve glycaemic control. The analysis of blood glucose profiles and hypoglycaemic episodes, as well as the suggestions for altered diet and insulin therapy, are based on qualitative and quantitative models of insulin effect and carbohydrate absorption using meal-time related glucose balance and distance from the preselected target (DFT) glucose values as focal concepts in the reasoning process. During the sequence of consultations with the system, a dynamic model of carbohydrate metabolism is gradually adjusted in order to constitute an appropriate simulation for the specific patient. This model is used to confirm the suggestions made by the ADVISOR program and to assist the health care professional in selecting the best control action by predicting the blood glucose profiles resulting from alternative control policies. Decision support system; Diabetes; Insulin therapy; Dynamic simulation; Knowledge-based system
1. Introduction
Diabetes mellitus is one of the major chronic diseases in Western societies and as such it constitutes a major medical challenge. For patients requiring insulin therapy the blood glucose level can be well controlled by maintaining a careful balance between diet, physical activity and insulin administration. The meticulous adjustment of these main components of diabetic management, however, requires a level of clinical expertise which, although available in the specialist diabetic clinic, is not always to be found in other sectors of the health care system.
Correspondence: Dr. T. Deutsch, Computer Centre, Semmelweis University, Kulich Gy. ter. 5, H-1089 Budapest, Hungary.
One approach to making more widely available the required expertise for the management of diabetes is to make use of computer-based systems. A broad range of computer-based approaches have been developed including expert systems to advise on patient management in the out-patient clinic (e.g. [5,11-13]; computer algorithms for adjusting insulin dosage when using intensive conventional insulin therapy or pump treatment (e.g. [6,15,1822]) and selecting individually tailored diet plans [25]; mathematical models to interpret glucose tolerance tests and predict blood glucose excursions (e.g. [4,7-9]); and approaches drawing upon optimal and adaptive control assuming the patient to be treated by some kind of glucose-controlled insulin infusion device, an 'artificial pancreas' (e.g. [17,23]). The approach described here is different. It is not based upon mathematical modelling or the use
0169-2607/90/$03.50 © 1990 Elsevier Science Publishers B.V. (Biomedical Division)
196
of computer algorithms, but rather adopts a complex approach to tackle the information processing and decision making activity associated with diabetic management. The current system takes full account not only of insulin treatment, but also of the interactions with diet planning. At this stage, the liiestyle (e.g. exercise), however, is not included as a variable, but is assumed to remain relatively constant during the adjustment process. 2. A l t e r n a t i v e m e t h o d s f o r c o m p u t e r - a s s i s t e d diabetic
management
The techniques mentioned above can be classified as 'feature-oriented' and 'whole-profile-oriented' approaches depending on the way in which the patient's response to the current therapy is analysed and the results of this analysis are used to define appropriate control actions. The 'if feature X present then do action Y' type decision rules are common to the different clinical algorithms. These algorithms allow efficient decision making in typical situations, representing explicitly routine dosage adjustment practice. The typical situations as 'features' are extracted from the blood glucose profiles and hypoglycaemic episodes as responses to the current therapy observed on two or more consecutive days. A control action is activated when a particular feature or a combination of features are present or absent in the observed blood glucose profile. A set of such decision rules is given below, extracted from those published in [22]: - if pre-hinch blood glucose is greater than 130 mg/dl for 2-4 days in a row, increase your pre-breakfast regular insulin by I or 2 units; - if pre-supper blood glucose is greater than 130 mg/dl for 2-4 days in a row, increase your pre-lunch regular insulin by 1 or 2 units; - if pre-lunch blood glucose is less than 70 m g / d l or if you have a hypoglycaemic reaction between breakfast and lunch, reduce your prebreakfast~ regular insulin by 1 or 2 units; - if pre-lunch blood glucose is less then 70 m g / d l or if you have a hypoglycaemic reaction between lunch and supper, reduce your pre-lunch regular insulin by 1 or 2 units. (1)
Although such algorithms are easy to program and usually well accepted they do have some fundamental limitations. The major one is that the rule set is not complete, i.e. it does not contain any information about possible control actions for situations which are either not explicitly stated or in which more than one feature requiring control action occurs (hypoglycaemia and hyperglycaemia in different periods of the day). Although the different features are inter-related and a control action, in fact, has impact in each period of the day due to the domino effect, the foimulation of rules defining control action for any combination of specific features would lead to a combinatorial explosion. Moreover, such algorithms provide single decisions instead of suggesting possible alternatives and do not allow the building of consistent knowledge about the patient during the sequence of consultations (the lack of a learning capability). All of these limitations directly follow from the way in which such systems determine control action in the presence of a specific feature or combination of features. Since clinical algorithms do not contain any explicit knowledge about the timing of insulin action or carbohydrate absorption, they must link control actions directly to specific features. Thus the rules in such algorithms are to a great extent redundant, i.e. adequate control actions could be deduced from a compact set of more general rules reflecting the dynamics of insulin action. For example, the rules given by (1) should not be formulated separately since all of them could be deduced from 'deep' knowledge related to the time course of the effect of the short-acting insulin preparation, Actrapid. If one assumes Actrapid to have maximal effect between 2 and 6 h after injection, and the intensity of the effect increases (decreases) with increasing (decreasing) dose of this (any) insulin preparation, the appropriate control actions for situations formulated in the condition part of (1) directly follow from insulin pharmacodynamics. In contrast to clinical algorithms, the different model-based control strategies apply 'whole-profile-oriented' approaches to determine optimal control actions. Such mathematical models which reflect the underlying (patho)physiology of insulin
197
action and carbohydrate absorption in quantitative terms such as insulin sensitivity, volume ~,~-~ distribution, maximal absorption rate, etc. - - in principle, can provide a suitable framework to characterise diabetic patients quantitatively and predict the blood glucose profile which is expected to be produced by any adjustment in the diet a n d / o r insulin dosage regimen. Unfortunately, however, such 'stand-alone' dynamic mathematical models are not very useful in real clinical situations. If the model is not sufficiently comprehensive, it will be unable to provide accurate predictions in real-life conditions, although the parameters in such models can be adjusted for individual patients in idealised test conditions (e.g. IVGTT). The parameters assessed in such tests are subject to diurnal variations, hence their value cannot be directly used for simulating blood glucose excursions in periods/ conditions which differ from the test conditions. On the other hand, if the model is comprehensive enough to contain sufficient detail about insulin and glucose handling in :.he hum~.n body, it becomes useless in clinical situatioas due to the inability to adjust all the appropriate parameters to correspond to the particular patient even in artificial test conditions. As we shall show later, however, an appropriately selected model could usefully perform as a 'simulated patient' in an integrated diabetes management system. Our approach differs from both the methodologies discussed above. This approach uses 'periodoriented' reasoning to analyse blood glucose profiles and hypoglycaemic episodes, seeking to incorporate the dynamics of glucose and insulin in a manner which reflects their clinical importance. As such it is influenced by the earlier work of Deutsch et al. [10] which attempted to introduce a qualitative insulin algebra to predict the change in the blood glucose profile brought about by any changes in the insulin regimen. The results achieved with that previous system have led us to a modified version in which the selection of an appropriate control action is based on the patient's response to the current therapy. We attempted to integrate a semi-quantitative method for suggesting control decisions in qualitative terms and a dynamic mathematical model of carbohydrate
metabolism to assign quantitative values for the model parameters and to assist quantitative adjustment in the treatment plan.
3. Information processing and control in diabetic management
In healthy subjects, elevated levels of blood glucose are restored to normal principally by the action of the hormone insulin. In insulin-dependent diabetics, however, adequate quantities of insulin are no longer secreted by the pancreas, and external control action has to be taken involving clinical decision-making related to diet and insulin administration. A range of situations can exist with different control goals and different time scales of control action and subsequent monitoring. Here we are concerned with established diabetics requiring sequential re-stabilisation of their blood glucose level. In such patients, blood glucose levels are monitored at home several times a day and these measurements along with the registered occurr, uces of hypoglycaemia represent the observations upon which the insulin regimen a n d / o r diet plan are adjusted in order to seek an improved degree of control. The so-called 'basic' management plan is produced as the result of the sequential modification of the current insulin dosage and meal plan on a 2-day basis using blood glucose monitoring and the occurrence of hypoglycaemic episodes as indicatcrs of the patient's carbohydrate metabolism. The scheme of this sequential adjustment process is illustrated in Fig. 1. The main characteristics of this sequential control process are as follows: (i) the lack of precise definition of therapeutic targets, i.e. the optimal control, (ii) the existence of alternative adjustment strategies (sequences) leading from an initial state to the desired target state of control, (iii) the need for a relatively long period (for example 2-4 days) to assess the characteristic response of the patient to the current treatment regimen due to the high intra-individual variations, (iv) the constraints on making only small adjustments in order to avoid large changes in the patient's carbohydrate metabolism, (v) the presence of large inter-individ-
198
ual variations, and (vi) the existence of several factors and practical difficulties in defining even the controllable variables (absorption patterns of diet and insulin) in quantitative terms. All of these characteristics should be taken into account when selecting the most appropriate technique for adjusting the inter-related components of diabetes therapy. The information flow and the inter-relationship between the patient-specific database, analysis (interpretation) of the data and the decision-making process are illustrated in Fig. 2. The patient-specific database contains permanent (demographic and history) data and dynamic data associated with (i) the momentary and longterm indicators of carbohydrate metabolism (blood glucose profiles, glycosylated haemoglobin, HbA1 levels, urine glucose if any, etc.), and (ii) the sequence of control actions (diet and insulin dosage regimen). Interpretation has the task (i) of judging the adequacy of the current diet plan, (ii) checking the blood glucose readings for consistency, (iii) extracting the 'modal day' blood glucose profile from individual blood glucose profiles registered
Initial stab~ ½
1
SeleeU°n tal~ta °r t h e ~ i e
~
k
f re~
[,,
to therapy
i t th~r~
t E~almtion/snaly~i~
Terntina~ ~ d ~ Fig. 1. Scheme of the sequential treatment adjustment procedure.
as responses to the same treatment on two or more subsequent days, (iv) assessing the quality of blood glucose control in the different time periods in terms of glucose balance and distance from pre-selected targets, and (v) building and updating a patient-specific mathematical model of the impaired carbohydrate metabolism. Decision making is based on the 'modal day' blood glucose response of the patient to the current therapy. This process involves (i) the setting of nutritional and blood glucose-related targets, (ii) the selection of the times for blood glucose observations needed to assess the patient's response to the current therapy, and (iii) suggestions of how to modify the current treatment plan in order to improve glycaemic control. The complex system outlined in the next section is intended to perform all the tasks involved in database management, in interpretation and clinical decision making.
4. Overview of the system
In the management of diabetes, the decision-making process involves the three components of insulin therapy, meal plan and physical activity selected by the patient, dietitian and physician in a sequential manner. The final version of the system is intended to support all aspects of this complex management process. The current version, however, only provides advice in adjusting the diet plan and insulin dosage assuming the patient's physical activity as related to his/her life-style to be relatively constant. Before giving a detailed description of the structure of the system and of the concepts and methods employed, a short list of the fundamental assumptions adopted is provided in order to clarify the basic conditions for its clinical use: (i) the energy demand must be supplied via the diet plan corresponding to the energy expenditure of the 'routine' physical activity of the patient; (ii) any type of insulin dosage regimen and meal plan can be adjusted provided that the dynamic effect of each component involved in these management (control) variables (short-
199
- Pe.,~. ~. ,L Data ~ c data (aqe. sex, ere) diabetes history (creeL, previous therapy, e ~ )
-l~m~ent - Related data diet plan msmi. D
A I A
~
reqim~
-Hortitorir~ - Related Data current s t ~ m a r ~ r s bland ¢Jlutmse p r o f i l e
hypsql~c
epi.,~-~
r j l u r ~ e~cretion in LI~ urine period markers t ~ l level ct~al icaLit~s
Data - L,-~-~-
(PAliOm)
(Pt~slc[~R/
Interpretation (m~SlCL~¢
DI['IIII/~)
DI~ITI/~)
Dacisim mkirq
D E C
I
of larqets nutritiorel tart]eta mrmOyca~c ~ t s
.Selection -
-
Nutritional - Oriented - t o t a l ererry rec~renent - ~te/fat/pmtein
ratio
I S
I 0
-Selection o f Observations
N
Diabetes - Oriented - check for data Consist_~L~/ - q e ~ r a t i o n o f '~rrial d e / ' p r o f i l e
H -Selection o f Ctmtrol /~tions
A K
- cliet
I
- insulin ~
adjustment adjustmmt
-Pesesstemt o f the [ ~ l i t v Blood C,],~nse Control
of
N C
- Char~terisaLion of the Patient in Terms of Nodal Parameters Fig. 2. Informationprocessing in diabetic management.
200
acting insulin, intermediate-acting insulin, meals, etc.) on the net glucose balance is defined in (semi)quantitative terms; (iii) the patient's blood glucose response to the current therapy can be monitored on a daily basis; (iv) the possible control actions during the adjustment process are as follows: - wait and observe, - modify the insulin dose, modify the time of the insulin injection, - change the insulin injection regimen, modify the meal time, - modify the glycaemic index of the meal consumed, - conclude the adjustment process; (v) in any control decision only one modification in the treatment is allowed (simultaneous changes in insulin dose, timing, carbohydrate content, meal times, etc. are excluded); (vi) the control actions must be based on a careful analysis of the blood glucose responses registered on two or more consecutive days; (vii) the treatment plan is considered as acceptable, if normoglycaemic responses are registered on two consecutive days (the condition which terminates the adjustment process). The main modules and data involved in the complex system are shown in Fig. 3. All oper-
-
landqere~
IT
"
" ] 0~tmaim
•
t,,,
data rilter~ ]
[ INILIII~c.i ~ Fig. 3. Overview of the complex diabetic management system.
ations and data transfer are supervised and controlled by the CONTROL program. Data related to home blood glucose monitoring and insulin dosage can be loaded from the CAMIT system into the database. The CAMIT system [3,16] is a method for measuring a patient's blood glucose concentration. It consists of three parts: a portable blood glucose meter; a portable data storage device; and a software program for data analysis. The data storage device can be connected to an IBM PC or compatible computer and also to the blood glucose meter. Thus direct transfer of data can be performed. The data transmitted consist primarily of the patient's blood glucose measurements, but the system also contains a series of event markers. These mark the times of occurrences such as meals or episodes of hypoglycaemia. If the blood glucose data contra-indicate a marked event then it will be over-ruled. Data related to the meal plan of the patient can be entered into the MICRODIET program which allows the composition (carbohydrate, fat and protein content), glycaemic index and energy content of the different meals constituting the current diet plan to be calculated on the basis of a built-in nutritional data base. All of the original data and the data calculated by the MICRODIET program are automatically transferred into the patientspecific data base for further use. MICRODIET, developed at Salford University [1], is the most commonly used dietary software package in the U.K. The version adopted allows foods to be entered by name, rather than by the McCance and Widdowson reference numbers [14,241, and also contains sections for comprehensive diet analysis, and for diet design. Meals entered can be analysed either for their nutritional value alone or with reference to the 1979 U.K. Department of Health and Social Security Recommended Dietary Allowances. For any fo~ds that do not exist in the database, 'recipies' can be created. If the diet does not meet the dietary standard chosen, MICRODIET has the facility to recommend alterations in the quantities of the different foods eaten, so that the diet does meet the standard. To allow the system to be used independently of the CAMIT and MICRODIET programs, data can also be entered directly into the database from
201 the keyboard bypassing the computer programs developed for storing home blood glucose monitoring data and analysing meal plans. Raw data stored by the CAMIT system are transferred to the 'MODAL-DAY GENERATOR' module for filtering and analysis which yield the characteristic response of the patient to the current therapy as needed by the ADVISOR and DYNAMIC-MODEL modules. The 'modal day' blood glucose profile is generated as a weighted average of the individual blood glucose profiles taking into account the event-markers associated with the blood glucose readings as well as the times of the hypoglycaemic episodes registered on two or more subsequent days and stored in the database (Fig. 4). The event-markers (e.g. excess carbohydrate intake, emotional upset, missed injection, etc.) serve to indicate conditions which may produce abnormal (hyperglycaemic or hypoglycaemic) findings, albeit that the current regimen is appropriate. The generation of the 'modal day' blood glucose profile is a very difficult problem which involves careful analysis of the sequence of blood
glucose profiles, dealing with the different rebound phenomena (if applicable) following hypoglycaemic episodes, the propagation of disturbances through the readings on to the subsequent readings, and so on. In the current version of the system the modal day blood glucose profile is computed simply by taking the average of the blood glucose observations in response to the same treatment regimen. The analysis of the current meal plan of the patient is performed by the DIET-ANALYSER ]nodule. This module comprises a suite of programs which enters patient information, produces diet sheets and accesses the MICRODIET package [26]. Thew are two major elements in this program suite. The ";rst ~ been developed to make the provision of diet sheets by the dietitian easier and to provide a record of the recommended diet sheet. The second provides the necessary information for the ADVISOR module. The focal point of the system is the ADVISOR module. The task of this module is to suggest possible alterations in the insulin dosage and diet plan which are expected to produce improvement
,~ d i n
dmn~
¢/,,
I'll
blood glucose '~al
I~'
filtering
I t.i~
ar~lysis time
time Nan Fig. 4. Generation of the 'modal day' response to current therapy. Symbolsare event markers: (o) missinginjection; (z~)emotional disturbance; (D) missingmeal.
2o2 in the glycaemic control of the patient. The reasoning method used to make such suggestions is described in the next section. The interpretation of blood glucose profiles and the selection of appropriate control actions are assisted by a DYNAMIC-MODEL module which allows the estimation of the patient's insulin sensitivity from observed blood glucose data as well as the simulation of the blood glucose excursions expected to be produced by any treatment plan.
5. Decision-making in diabetes management From a control system viewpoint insulin is administered as a control agent in order to produce a blood glucose profile that corresponds as closely as possible to normoglycaemia, seeking a balance between endogenous glucose production and utilisation (physical activity), and exogenous glucose input (food intake). Blood glucose level is a state variable which reflects the status of carbohydrate metabolism and can be used as a measure of normality, that is the effectiveness of the control action. Blood glucose concentration data, obtained by home monitoring, together with the times of occurrence of any hypoglycaemic episodes constitute the observed variables. Insulin dosage and the meal plan are the controlling variables which are to be adjusted to ensure normoglycaemic control. 5.1. State variables and control variables
In terms of the MicroPROLOG syntax which is adopted in the computer implementatic!n of the diabetes management system, the variables in the control system are described as followt. The characteristic ('modal day') blood glucose profile response to the current therapy is defined as a set of statements (PROLOG clauses) of the form
bLood-gLucose(_time _bg)
(2)
where _time represents the meal-related time at which the blood glucose level, _bg has been ob-
~min ~
~mJn
"shm'tafter" ~.~/] "-~,.- "
"slhm'tbef~'
time
1 2 qg,
t
'
~ 4. -
~
~
5
:-
6
7
#.
A
i j before brenkf~-°c afte~aBt af'ter-]trch herm'e-st~after-eUpper bed~ Fig. 5. Characteristic times and location of hypoglycaemic episodes. The times are: (1) before-breakfast;(2) after-breakfast; (3) before-lunch;(4) after-lunch; (5) before-supper;(6) after-supper; (7) bedtime;(8) night. served. The characteristic time points distinguished in the system are shown in Fig. 5. The blood glucose of the patient should be measured at several of these times. Blood glucose readings observed at any other time of the day will be disregarded by the program. The before-breakfast, before-lunch and before-supper observations refer to times immediately before the corresponding main meals; the after-breakfast, after-lunch and after-supper values are to be registered at approximately 1.5 h following the ingestion of the conesponding main meal. Night is defined as the period between 2 and 4 a.m. In addition to the blood glucose profiles, the times of the hypoglycaemic episodes (if any) constitute the observations on which adjustment should be based. During the day the hypoglycaemic episodes are located in the different between-meal periods, whereas during the night the episodes of hypoglycaemia are located in time periods of length approximately 3 h. The definitions of the between-meal periods depend on the current meal plan and involve the main meals as well as the snacks as limits for these characteristic time periods. Since the specific location of a hypogl,ycaemic episode within a time period has implications for
203
its interpretation and the control actions to be carried out in this period, three types of hypoglyeaemia are distinguished according to the distance of the time of the episode with respect to the limits of that time period (Fig. 5). The 'short-after-meal' type hypoglycaemie episodes occur within 20 rain following the ingestion of a meal, whereas the 'short-before-meal' type of hypoglycaemic events are observed within the 20 rain period before the next meal. All other hypoglycaemic episodes are referred to as 'betweenmeals' type hypoglycaemia. Assuming breakfast time to be 7.30 a.m., midmorning-snaek time to be 10.30 a.m. and a hypoglycaemic episode occurring at 10.15 a.m., then the corresponding PROLOG clause has the form of
hypoglycaemia ((breakfast midmorningsnack) short-before)
5.2. Glucose balance and therapeutic targets The therapeutic objectives of the therapy are formulated in terms of allowable ranges for the blood glucose level (_ l owe r - l i mi t _upper - 11 mi t) for each meal-related characteristic time (_time), ~n addition to the basic requirement that no, hypoglycaemic episodes should occur at ~ny time. Obviously the therapeutic o~ectives zax, be se~ in different ways for different patients depending on age, pregnancy, complications, etc.
(3)
The current insulin dosage which represents one of the controllable factors in the adjustment process is stored as a set of PROLOG clauses in the form of
insulin-injection (_no _inj-time (_type1 _type2) (_dose1 _dose2))
sents the carbohydrate content of the corresponding meal, while _g l y e - i n d e x stands f.~r the glycaemic index of the meal. The calculation of the glycaemic index of a meal, based on the published glycaemic indices of their constituents, is not considered in this paper.
(4)
blood-glucose- target (_time (_towerlimi t _upper- limi t)) (6)
For example, the normoglycaernic conditions (in mmol/l) for the before-breakfast time are given by
blood-glucose-target (before-breakfast (4 7))
where _no represents the serial -~mhe,- of the injection (1st, 2nd, etc.); _i nj - t i me contains the time of the _no-th insulin injection; t y p e 1 and t y p e 2 denote the different insulin preparations contained in the _no-th injection (short-acting, intermediate-acting, etc.); while d o s e 1 and _dose2 represent the corresponding doses of these insulin preparations, respectively. (If only one insulin preparation is injected, t y p e 2 is empty and _dose2 is equal to zero.) The current meal plan is stored as a set of facts about the individual meals (main meals and snacks)
meal (_meal-name _meal-time _chocontent _g lyc- index)
(5)
where _meal-name represents the meal (breakfast, lunch, bedtime-snack, etc.), _meal-time is the time of meal ingestion, _ c h o - c o n t e n t repre-
(7)
and for the after-breakfast time blood- glucose- target (after-breakfast (5 9)) (8)
The above limits for the respective blood glucose levels implicitly contain another requirement relating to the allowable changes in blood glucose level between two adjacent time points. In each meal period one wishes the blood glucose level to return nearly to its pre-prandial value, while obviously one sets greater than zero limits for the difference between post-prandial and pre-prandial blood glucose concentrations. This type of objective can be formulated in terms of glucose balances between two adjacent characteristic time points (Fig. 6). If the blood glucose concentration at the end of a time period is Gi+ 1 and is G, at the beginning of that interval,
204 fii+l I~1
,-,,,,F
~t
/
L
B= Gi÷l- Gi q!,r,me balan~)
f:.lm~ |
ti
ti+l
~Lime
Fig. 6. Glucose balance and target levels.
the glucose balance, B;, for this interval is defined simply as the difference between the corresponding terminal and starting values B,
=
Gi+ 1
-
Gt
(9)
The target in the different between-meal periods, and between bedtime and night and between night and breakfast, with respect to this glucose balance is nearly zero (values in the range - 2 to + 2 mmol/l are allowed) glucose-balance-target ((_before-meal1 .before-meal2) ( - 2 2)) glucose-balance-target ( - 2 2))
((bedtime n i g h t )
glucose-balance-target ((night beforebreakfast) ( - 2 2)) (10)
Consider a time period [t, t~+l] at the limits of which the modal day blood glucose concentrations are G~ = 6.2 m m o l / l and G~+l = 13.5 m m o l / l respectivdy. Assume ti and t~+~ correspond to before-breakfast and before-lunch, hence the respective targets for Gi and G~+1 are [4 7], whereas the target for the glucose balance in this period is [ - 2 + 2]. How good (or bad) is the blood glucose control in that period with the current regimen? Clearly the blood glucose response in that period is hyperglycaemic due to the high before-lunch blood glucose reading. Moreover, there is a large increase in that period in the blood glucose concentration which is in sharp contrast to the objective to achieve a nearly zero glucose balance between any two pre-prandial time points. It seems reasonable to define the quality of control as the sum of the average differences of the observed blood glucose levels and glucose balance in that period from their respective target values: D = Ds + D b
where Dg represents the average distance of Gi and G,+I from the [4 7] normoglycaemic range, while D b denotes the distance of the balance, B = Gi+ t - G~-- 13.5 - 6.2 = 7.3 mmol/1 from its target range [ - 2 + 2]. The definition of the distance of a quantity X, D~,, from its respective target range [X low X.,p] is given by the following expressions: Dx = X -
where meal1 and meal2 represent successive meals. On the other hand, a range of 1-5 mmol/1 is allowed for the change in blood glucose level in any (before-meal)-(after-meal) period glucose-balance-target ((_before-meal _after-meal) (1 5)) (11) Using the concept of targets related to the blood glucose levels and glucose balances in characteristic time periods we are able to introduce a quantitative criterion to judge the quality of glycaemic control achieved with the current regimen.
(12)
X,p
Dx = 0 and
Dx=X-XIo
if X > )(up if Xlo w
195
COMMET 01101
Computer-assisted diabetic management: a complex approach T. Deutsch 1,2, E.R. Carson
2.3, F.E.
Harvey 3.2, E.D. Lehmann 3, P.H. Sonksen G. Whitney 2 and C.D. Williams 3
3.2, G. Tamas
4,
I Computer Centre, Semmelweis University, Budapest, Hungary, 2 Department of Systems Science, Centre for Measurement and Information in Medicine, City University, London, U.K., 3 Department of Endocrinology and Chemical Pathology, UMDS, St. Thomas's Hospital, London, U.K., 4 1st Clinic, Semmelweis University, Budapest, Hungary.
This paper describes the architecture of, and the main reasoning methods involved in, a computer system developed to assist in diabetic management. The system integrates (i) a database module used for blood glucose moni'~oring, (ii) an interpreter module used to analyse the adequacy of diet and insulin treatment for diabetics, and (iii~ an advisory module suggesting alterations in diet and/or insulin regimen in order to improve glycaemic control. The analysis of blood glucose profiles and hypoglycaemic episodes, as well as the suggestions for altered diet and insulin therapy, are based on qualitative and quantitative models of insulin effect and carbohydrate absorption using meal-time related glucose balance and distance from the preselected target (DFT) glucose values as focal concepts in the reasoning process. During the sequence of consultations with the system, a dynamic model of carbohydrate metabolism is gradually adjusted in order to constitute an appropriate simulation for the specific patient. This model is used to confirm the suggestions made by the ADVISOR program and to assist the health care professional in selecting the best control action by predicting the blood glucose profiles resulting from alternative control policies. Decision support system; Diabetes; Insulin therapy; Dynamic simulation; Knowledge-based system
1. Introduction
Diabetes mellitus is one of the major chronic diseases in Western societies and as such it constitutes a major medical challenge. For patients requiring insulin therapy the blood glucose level can be well controlled by maintaining a careful balance between diet, physical activity and insulin administration. The meticulous adjustment of these main components of diabetic management, however, requires a level of clinical expertise which, although available in the specialist diabetic clinic, is not always to be found in other sectors of the health care system.
Correspondence: Dr. T. Deutsch, Computer Centre, Semmelweis University, Kulich Gy. ter. 5, H-1089 Budapest, Hungary.
One approach to making more widely available the required expertise for the management of diabetes is to make use of computer-based systems. A broad range of computer-based approaches have been developed including expert systems to advise on patient management in the out-patient clinic (e.g. [5,11-13]; computer algorithms for adjusting insulin dosage when using intensive conventional insulin therapy or pump treatment (e.g. [6,15,1822]) and selecting individually tailored diet plans [25]; mathematical models to interpret glucose tolerance tests and predict blood glucose excursions (e.g. [4,7-9]); and approaches drawing upon optimal and adaptive control assuming the patient to be treated by some kind of glucose-controlled insulin infusion device, an 'artificial pancreas' (e.g. [17,23]). The approach described here is different. It is not based upon mathematical modelling or the use
0169-2607/90/$03.50 © 1990 Elsevier Science Publishers B.V. (Biomedical Division)
196
of computer algorithms, but rather adopts a complex approach to tackle the information processing and decision making activity associated with diabetic management. The current system takes full account not only of insulin treatment, but also of the interactions with diet planning. At this stage, the liiestyle (e.g. exercise), however, is not included as a variable, but is assumed to remain relatively constant during the adjustment process. 2. A l t e r n a t i v e m e t h o d s f o r c o m p u t e r - a s s i s t e d diabetic
management
The techniques mentioned above can be classified as 'feature-oriented' and 'whole-profile-oriented' approaches depending on the way in which the patient's response to the current therapy is analysed and the results of this analysis are used to define appropriate control actions. The 'if feature X present then do action Y' type decision rules are common to the different clinical algorithms. These algorithms allow efficient decision making in typical situations, representing explicitly routine dosage adjustment practice. The typical situations as 'features' are extracted from the blood glucose profiles and hypoglycaemic episodes as responses to the current therapy observed on two or more consecutive days. A control action is activated when a particular feature or a combination of features are present or absent in the observed blood glucose profile. A set of such decision rules is given below, extracted from those published in [22]: - if pre-hinch blood glucose is greater than 130 mg/dl for 2-4 days in a row, increase your pre-breakfast regular insulin by I or 2 units; - if pre-supper blood glucose is greater than 130 mg/dl for 2-4 days in a row, increase your pre-lunch regular insulin by 1 or 2 units; - if pre-lunch blood glucose is less than 70 m g / d l or if you have a hypoglycaemic reaction between breakfast and lunch, reduce your prebreakfast~ regular insulin by 1 or 2 units; - if pre-lunch blood glucose is less then 70 m g / d l or if you have a hypoglycaemic reaction between lunch and supper, reduce your pre-lunch regular insulin by 1 or 2 units. (1)
Although such algorithms are easy to program and usually well accepted they do have some fundamental limitations. The major one is that the rule set is not complete, i.e. it does not contain any information about possible control actions for situations which are either not explicitly stated or in which more than one feature requiring control action occurs (hypoglycaemia and hyperglycaemia in different periods of the day). Although the different features are inter-related and a control action, in fact, has impact in each period of the day due to the domino effect, the foimulation of rules defining control action for any combination of specific features would lead to a combinatorial explosion. Moreover, such algorithms provide single decisions instead of suggesting possible alternatives and do not allow the building of consistent knowledge about the patient during the sequence of consultations (the lack of a learning capability). All of these limitations directly follow from the way in which such systems determine control action in the presence of a specific feature or combination of features. Since clinical algorithms do not contain any explicit knowledge about the timing of insulin action or carbohydrate absorption, they must link control actions directly to specific features. Thus the rules in such algorithms are to a great extent redundant, i.e. adequate control actions could be deduced from a compact set of more general rules reflecting the dynamics of insulin action. For example, the rules given by (1) should not be formulated separately since all of them could be deduced from 'deep' knowledge related to the time course of the effect of the short-acting insulin preparation, Actrapid. If one assumes Actrapid to have maximal effect between 2 and 6 h after injection, and the intensity of the effect increases (decreases) with increasing (decreasing) dose of this (any) insulin preparation, the appropriate control actions for situations formulated in the condition part of (1) directly follow from insulin pharmacodynamics. In contrast to clinical algorithms, the different model-based control strategies apply 'whole-profile-oriented' approaches to determine optimal control actions. Such mathematical models which reflect the underlying (patho)physiology of insulin
197
action and carbohydrate absorption in quantitative terms such as insulin sensitivity, volume ~,~-~ distribution, maximal absorption rate, etc. - - in principle, can provide a suitable framework to characterise diabetic patients quantitatively and predict the blood glucose profile which is expected to be produced by any adjustment in the diet a n d / o r insulin dosage regimen. Unfortunately, however, such 'stand-alone' dynamic mathematical models are not very useful in real clinical situations. If the model is not sufficiently comprehensive, it will be unable to provide accurate predictions in real-life conditions, although the parameters in such models can be adjusted for individual patients in idealised test conditions (e.g. IVGTT). The parameters assessed in such tests are subject to diurnal variations, hence their value cannot be directly used for simulating blood glucose excursions in periods/ conditions which differ from the test conditions. On the other hand, if the model is comprehensive enough to contain sufficient detail about insulin and glucose handling in :.he hum~.n body, it becomes useless in clinical situatioas due to the inability to adjust all the appropriate parameters to correspond to the particular patient even in artificial test conditions. As we shall show later, however, an appropriately selected model could usefully perform as a 'simulated patient' in an integrated diabetes management system. Our approach differs from both the methodologies discussed above. This approach uses 'periodoriented' reasoning to analyse blood glucose profiles and hypoglycaemic episodes, seeking to incorporate the dynamics of glucose and insulin in a manner which reflects their clinical importance. As such it is influenced by the earlier work of Deutsch et al. [10] which attempted to introduce a qualitative insulin algebra to predict the change in the blood glucose profile brought about by any changes in the insulin regimen. The results achieved with that previous system have led us to a modified version in which the selection of an appropriate control action is based on the patient's response to the current therapy. We attempted to integrate a semi-quantitative method for suggesting control decisions in qualitative terms and a dynamic mathematical model of carbohydrate
metabolism to assign quantitative values for the model parameters and to assist quantitative adjustment in the treatment plan.
3. Information processing and control in diabetic management
In healthy subjects, elevated levels of blood glucose are restored to normal principally by the action of the hormone insulin. In insulin-dependent diabetics, however, adequate quantities of insulin are no longer secreted by the pancreas, and external control action has to be taken involving clinical decision-making related to diet and insulin administration. A range of situations can exist with different control goals and different time scales of control action and subsequent monitoring. Here we are concerned with established diabetics requiring sequential re-stabilisation of their blood glucose level. In such patients, blood glucose levels are monitored at home several times a day and these measurements along with the registered occurr, uces of hypoglycaemia represent the observations upon which the insulin regimen a n d / o r diet plan are adjusted in order to seek an improved degree of control. The so-called 'basic' management plan is produced as the result of the sequential modification of the current insulin dosage and meal plan on a 2-day basis using blood glucose monitoring and the occurrence of hypoglycaemic episodes as indicatcrs of the patient's carbohydrate metabolism. The scheme of this sequential adjustment process is illustrated in Fig. 1. The main characteristics of this sequential control process are as follows: (i) the lack of precise definition of therapeutic targets, i.e. the optimal control, (ii) the existence of alternative adjustment strategies (sequences) leading from an initial state to the desired target state of control, (iii) the need for a relatively long period (for example 2-4 days) to assess the characteristic response of the patient to the current treatment regimen due to the high intra-individual variations, (iv) the constraints on making only small adjustments in order to avoid large changes in the patient's carbohydrate metabolism, (v) the presence of large inter-individ-
198
ual variations, and (vi) the existence of several factors and practical difficulties in defining even the controllable variables (absorption patterns of diet and insulin) in quantitative terms. All of these characteristics should be taken into account when selecting the most appropriate technique for adjusting the inter-related components of diabetes therapy. The information flow and the inter-relationship between the patient-specific database, analysis (interpretation) of the data and the decision-making process are illustrated in Fig. 2. The patient-specific database contains permanent (demographic and history) data and dynamic data associated with (i) the momentary and longterm indicators of carbohydrate metabolism (blood glucose profiles, glycosylated haemoglobin, HbA1 levels, urine glucose if any, etc.), and (ii) the sequence of control actions (diet and insulin dosage regimen). Interpretation has the task (i) of judging the adequacy of the current diet plan, (ii) checking the blood glucose readings for consistency, (iii) extracting the 'modal day' blood glucose profile from individual blood glucose profiles registered
Initial stab~ ½
1
SeleeU°n tal~ta °r t h e ~ i e
~
k
f re~
[,,
to therapy
i t th~r~
t E~almtion/snaly~i~
Terntina~ ~ d ~ Fig. 1. Scheme of the sequential treatment adjustment procedure.
as responses to the same treatment on two or more subsequent days, (iv) assessing the quality of blood glucose control in the different time periods in terms of glucose balance and distance from pre-selected targets, and (v) building and updating a patient-specific mathematical model of the impaired carbohydrate metabolism. Decision making is based on the 'modal day' blood glucose response of the patient to the current therapy. This process involves (i) the setting of nutritional and blood glucose-related targets, (ii) the selection of the times for blood glucose observations needed to assess the patient's response to the current therapy, and (iii) suggestions of how to modify the current treatment plan in order to improve glycaemic control. The complex system outlined in the next section is intended to perform all the tasks involved in database management, in interpretation and clinical decision making.
4. Overview of the system
In the management of diabetes, the decision-making process involves the three components of insulin therapy, meal plan and physical activity selected by the patient, dietitian and physician in a sequential manner. The final version of the system is intended to support all aspects of this complex management process. The current version, however, only provides advice in adjusting the diet plan and insulin dosage assuming the patient's physical activity as related to his/her life-style to be relatively constant. Before giving a detailed description of the structure of the system and of the concepts and methods employed, a short list of the fundamental assumptions adopted is provided in order to clarify the basic conditions for its clinical use: (i) the energy demand must be supplied via the diet plan corresponding to the energy expenditure of the 'routine' physical activity of the patient; (ii) any type of insulin dosage regimen and meal plan can be adjusted provided that the dynamic effect of each component involved in these management (control) variables (short-
199
- Pe.,~. ~. ,L Data ~ c data (aqe. sex, ere) diabetes history (creeL, previous therapy, e ~ )
-l~m~ent - Related data diet plan msmi. D
A I A
~
reqim~
-Hortitorir~ - Related Data current s t ~ m a r ~ r s bland ¢Jlutmse p r o f i l e
hypsql~c
epi.,~-~
r j l u r ~ e~cretion in LI~ urine period markers t ~ l level ct~al icaLit~s
Data - L,-~-~-
(PAliOm)
(Pt~slc[~R/
Interpretation (m~SlCL~¢
DI['IIII/~)
DI~ITI/~)
Dacisim mkirq
D E C
I
of larqets nutritiorel tart]eta mrmOyca~c ~ t s
.Selection -
-
Nutritional - Oriented - t o t a l ererry rec~renent - ~te/fat/pmtein
ratio
I S
I 0
-Selection o f Observations
N
Diabetes - Oriented - check for data Consist_~L~/ - q e ~ r a t i o n o f '~rrial d e / ' p r o f i l e
H -Selection o f Ctmtrol /~tions
A K
- cliet
I
- insulin ~
adjustment adjustmmt
-Pesesstemt o f the [ ~ l i t v Blood C,],~nse Control
of
N C
- Char~terisaLion of the Patient in Terms of Nodal Parameters Fig. 2. Informationprocessing in diabetic management.
200
acting insulin, intermediate-acting insulin, meals, etc.) on the net glucose balance is defined in (semi)quantitative terms; (iii) the patient's blood glucose response to the current therapy can be monitored on a daily basis; (iv) the possible control actions during the adjustment process are as follows: - wait and observe, - modify the insulin dose, modify the time of the insulin injection, - change the insulin injection regimen, modify the meal time, - modify the glycaemic index of the meal consumed, - conclude the adjustment process; (v) in any control decision only one modification in the treatment is allowed (simultaneous changes in insulin dose, timing, carbohydrate content, meal times, etc. are excluded); (vi) the control actions must be based on a careful analysis of the blood glucose responses registered on two or more consecutive days; (vii) the treatment plan is considered as acceptable, if normoglycaemic responses are registered on two consecutive days (the condition which terminates the adjustment process). The main modules and data involved in the complex system are shown in Fig. 3. All oper-
-
landqere~
IT
"
" ] 0~tmaim
•
t,,,
data rilter~ ]
[ INILIII~c.i ~ Fig. 3. Overview of the complex diabetic management system.
ations and data transfer are supervised and controlled by the CONTROL program. Data related to home blood glucose monitoring and insulin dosage can be loaded from the CAMIT system into the database. The CAMIT system [3,16] is a method for measuring a patient's blood glucose concentration. It consists of three parts: a portable blood glucose meter; a portable data storage device; and a software program for data analysis. The data storage device can be connected to an IBM PC or compatible computer and also to the blood glucose meter. Thus direct transfer of data can be performed. The data transmitted consist primarily of the patient's blood glucose measurements, but the system also contains a series of event markers. These mark the times of occurrences such as meals or episodes of hypoglycaemia. If the blood glucose data contra-indicate a marked event then it will be over-ruled. Data related to the meal plan of the patient can be entered into the MICRODIET program which allows the composition (carbohydrate, fat and protein content), glycaemic index and energy content of the different meals constituting the current diet plan to be calculated on the basis of a built-in nutritional data base. All of the original data and the data calculated by the MICRODIET program are automatically transferred into the patientspecific data base for further use. MICRODIET, developed at Salford University [1], is the most commonly used dietary software package in the U.K. The version adopted allows foods to be entered by name, rather than by the McCance and Widdowson reference numbers [14,241, and also contains sections for comprehensive diet analysis, and for diet design. Meals entered can be analysed either for their nutritional value alone or with reference to the 1979 U.K. Department of Health and Social Security Recommended Dietary Allowances. For any fo~ds that do not exist in the database, 'recipies' can be created. If the diet does not meet the dietary standard chosen, MICRODIET has the facility to recommend alterations in the quantities of the different foods eaten, so that the diet does meet the standard. To allow the system to be used independently of the CAMIT and MICRODIET programs, data can also be entered directly into the database from
201 the keyboard bypassing the computer programs developed for storing home blood glucose monitoring data and analysing meal plans. Raw data stored by the CAMIT system are transferred to the 'MODAL-DAY GENERATOR' module for filtering and analysis which yield the characteristic response of the patient to the current therapy as needed by the ADVISOR and DYNAMIC-MODEL modules. The 'modal day' blood glucose profile is generated as a weighted average of the individual blood glucose profiles taking into account the event-markers associated with the blood glucose readings as well as the times of the hypoglycaemic episodes registered on two or more subsequent days and stored in the database (Fig. 4). The event-markers (e.g. excess carbohydrate intake, emotional upset, missed injection, etc.) serve to indicate conditions which may produce abnormal (hyperglycaemic or hypoglycaemic) findings, albeit that the current regimen is appropriate. The generation of the 'modal day' blood glucose profile is a very difficult problem which involves careful analysis of the sequence of blood
glucose profiles, dealing with the different rebound phenomena (if applicable) following hypoglycaemic episodes, the propagation of disturbances through the readings on to the subsequent readings, and so on. In the current version of the system the modal day blood glucose profile is computed simply by taking the average of the blood glucose observations in response to the same treatment regimen. The analysis of the current meal plan of the patient is performed by the DIET-ANALYSER ]nodule. This module comprises a suite of programs which enters patient information, produces diet sheets and accesses the MICRODIET package [26]. Thew are two major elements in this program suite. The ";rst ~ been developed to make the provision of diet sheets by the dietitian easier and to provide a record of the recommended diet sheet. The second provides the necessary information for the ADVISOR module. The focal point of the system is the ADVISOR module. The task of this module is to suggest possible alterations in the insulin dosage and diet plan which are expected to produce improvement
,~ d i n
dmn~
¢/,,
I'll
blood glucose '~al
I~'
filtering
I t.i~
ar~lysis time
time Nan Fig. 4. Generation of the 'modal day' response to current therapy. Symbolsare event markers: (o) missinginjection; (z~)emotional disturbance; (D) missingmeal.
2o2 in the glycaemic control of the patient. The reasoning method used to make such suggestions is described in the next section. The interpretation of blood glucose profiles and the selection of appropriate control actions are assisted by a DYNAMIC-MODEL module which allows the estimation of the patient's insulin sensitivity from observed blood glucose data as well as the simulation of the blood glucose excursions expected to be produced by any treatment plan.
5. Decision-making in diabetes management From a control system viewpoint insulin is administered as a control agent in order to produce a blood glucose profile that corresponds as closely as possible to normoglycaemia, seeking a balance between endogenous glucose production and utilisation (physical activity), and exogenous glucose input (food intake). Blood glucose level is a state variable which reflects the status of carbohydrate metabolism and can be used as a measure of normality, that is the effectiveness of the control action. Blood glucose concentration data, obtained by home monitoring, together with the times of occurrence of any hypoglycaemic episodes constitute the observed variables. Insulin dosage and the meal plan are the controlling variables which are to be adjusted to ensure normoglycaemic control. 5.1. State variables and control variables
In terms of the MicroPROLOG syntax which is adopted in the computer implementatic!n of the diabetes management system, the variables in the control system are described as followt. The characteristic ('modal day') blood glucose profile response to the current therapy is defined as a set of statements (PROLOG clauses) of the form
bLood-gLucose(_time _bg)
(2)
where _time represents the meal-related time at which the blood glucose level, _bg has been ob-
~min ~
~mJn
"shm'tafter" ~.~/] "-~,.- "
"slhm'tbef~'
time
1 2 qg,
t
'
~ 4. -
~
~
5
:-
6
7
#.
A
i j before brenkf~-°c afte~aBt af'ter-]trch herm'e-st~after-eUpper bed~ Fig. 5. Characteristic times and location of hypoglycaemic episodes. The times are: (1) before-breakfast;(2) after-breakfast; (3) before-lunch;(4) after-lunch; (5) before-supper;(6) after-supper; (7) bedtime;(8) night. served. The characteristic time points distinguished in the system are shown in Fig. 5. The blood glucose of the patient should be measured at several of these times. Blood glucose readings observed at any other time of the day will be disregarded by the program. The before-breakfast, before-lunch and before-supper observations refer to times immediately before the corresponding main meals; the after-breakfast, after-lunch and after-supper values are to be registered at approximately 1.5 h following the ingestion of the conesponding main meal. Night is defined as the period between 2 and 4 a.m. In addition to the blood glucose profiles, the times of the hypoglycaemic episodes (if any) constitute the observations on which adjustment should be based. During the day the hypoglycaemic episodes are located in the different between-meal periods, whereas during the night the episodes of hypoglycaemia are located in time periods of length approximately 3 h. The definitions of the between-meal periods depend on the current meal plan and involve the main meals as well as the snacks as limits for these characteristic time periods. Since the specific location of a hypogl,ycaemic episode within a time period has implications for
203
its interpretation and the control actions to be carried out in this period, three types of hypoglyeaemia are distinguished according to the distance of the time of the episode with respect to the limits of that time period (Fig. 5). The 'short-after-meal' type hypoglycaemie episodes occur within 20 rain following the ingestion of a meal, whereas the 'short-before-meal' type of hypoglycaemic events are observed within the 20 rain period before the next meal. All other hypoglycaemic episodes are referred to as 'betweenmeals' type hypoglycaemia. Assuming breakfast time to be 7.30 a.m., midmorning-snaek time to be 10.30 a.m. and a hypoglycaemic episode occurring at 10.15 a.m., then the corresponding PROLOG clause has the form of
hypoglycaemia ((breakfast midmorningsnack) short-before)
5.2. Glucose balance and therapeutic targets The therapeutic objectives of the therapy are formulated in terms of allowable ranges for the blood glucose level (_ l owe r - l i mi t _upper - 11 mi t) for each meal-related characteristic time (_time), ~n addition to the basic requirement that no, hypoglycaemic episodes should occur at ~ny time. Obviously the therapeutic o~ectives zax, be se~ in different ways for different patients depending on age, pregnancy, complications, etc.
(3)
The current insulin dosage which represents one of the controllable factors in the adjustment process is stored as a set of PROLOG clauses in the form of
insulin-injection (_no _inj-time (_type1 _type2) (_dose1 _dose2))
sents the carbohydrate content of the corresponding meal, while _g l y e - i n d e x stands f.~r the glycaemic index of the meal. The calculation of the glycaemic index of a meal, based on the published glycaemic indices of their constituents, is not considered in this paper.
(4)
blood-glucose- target (_time (_towerlimi t _upper- limi t)) (6)
For example, the normoglycaernic conditions (in mmol/l) for the before-breakfast time are given by
blood-glucose-target (before-breakfast (4 7))
where _no represents the serial -~mhe,- of the injection (1st, 2nd, etc.); _i nj - t i me contains the time of the _no-th insulin injection; t y p e 1 and t y p e 2 denote the different insulin preparations contained in the _no-th injection (short-acting, intermediate-acting, etc.); while d o s e 1 and _dose2 represent the corresponding doses of these insulin preparations, respectively. (If only one insulin preparation is injected, t y p e 2 is empty and _dose2 is equal to zero.) The current meal plan is stored as a set of facts about the individual meals (main meals and snacks)
meal (_meal-name _meal-time _chocontent _g lyc- index)
(5)
where _meal-name represents the meal (breakfast, lunch, bedtime-snack, etc.), _meal-time is the time of meal ingestion, _ c h o - c o n t e n t repre-
(7)
and for the after-breakfast time blood- glucose- target (after-breakfast (5 9)) (8)
The above limits for the respective blood glucose levels implicitly contain another requirement relating to the allowable changes in blood glucose level between two adjacent time points. In each meal period one wishes the blood glucose level to return nearly to its pre-prandial value, while obviously one sets greater than zero limits for the difference between post-prandial and pre-prandial blood glucose concentrations. This type of objective can be formulated in terms of glucose balances between two adjacent characteristic time points (Fig. 6). If the blood glucose concentration at the end of a time period is Gi+ 1 and is G, at the beginning of that interval,
204 fii+l I~1
,-,,,,F
~t
/
L
B= Gi÷l- Gi q!,r,me balan~)
f:.lm~ |
ti
ti+l
~Lime
Fig. 6. Glucose balance and target levels.
the glucose balance, B;, for this interval is defined simply as the difference between the corresponding terminal and starting values B,
=
Gi+ 1
-
Gt
(9)
The target in the different between-meal periods, and between bedtime and night and between night and breakfast, with respect to this glucose balance is nearly zero (values in the range - 2 to + 2 mmol/l are allowed) glucose-balance-target ((_before-meal1 .before-meal2) ( - 2 2)) glucose-balance-target ( - 2 2))
((bedtime n i g h t )
glucose-balance-target ((night beforebreakfast) ( - 2 2)) (10)
Consider a time period [t, t~+l] at the limits of which the modal day blood glucose concentrations are G~ = 6.2 m m o l / l and G~+l = 13.5 m m o l / l respectivdy. Assume ti and t~+~ correspond to before-breakfast and before-lunch, hence the respective targets for Gi and G~+1 are [4 7], whereas the target for the glucose balance in this period is [ - 2 + 2]. How good (or bad) is the blood glucose control in that period with the current regimen? Clearly the blood glucose response in that period is hyperglycaemic due to the high before-lunch blood glucose reading. Moreover, there is a large increase in that period in the blood glucose concentration which is in sharp contrast to the objective to achieve a nearly zero glucose balance between any two pre-prandial time points. It seems reasonable to define the quality of control as the sum of the average differences of the observed blood glucose levels and glucose balance in that period from their respective target values: D = Ds + D b
where Dg represents the average distance of Gi and G,+I from the [4 7] normoglycaemic range, while D b denotes the distance of the balance, B = Gi+ t - G~-- 13.5 - 6.2 = 7.3 mmol/1 from its target range [ - 2 + 2]. The definition of the distance of a quantity X, D~,, from its respective target range [X low X.,p] is given by the following expressions: Dx = X -
where meal1 and meal2 represent successive meals. On the other hand, a range of 1-5 mmol/1 is allowed for the change in blood glucose level in any (before-meal)-(after-meal) period glucose-balance-target ((_before-meal _after-meal) (1 5)) (11) Using the concept of targets related to the blood glucose levels and glucose balances in characteristic time periods we are able to introduce a quantitative criterion to judge the quality of glycaemic control achieved with the current regimen.
(12)
X,p
Dx = 0 and
Dx=X-XIo
if X > )(up if Xlo w
