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Insulin Dosage Adjustment Using Time Series Analysis and Rule-Based Reasoning
Copyright © IFAC 12th Triennial World Congress. Sydney, Australia, 1993
INSULIN DOSAGE ADJUSTMENT USING TIME SERIES ANALYSIS AND RULE-BASED REASONING E.R. Carson*, T. Deutsch*'**, A.V. Roudsari* and A. Sali** 'Centre/or Measurement and Information in Medicine. Department o/Systems Science. City University, Northampton Square. London EC IV OHB. UK "Computing Centre, Semmelweis University 0/ Medicine. Kalvaria fcr 5. H-I089 Budapesf. Hunfiary
Abstract. The management of a chronic disease such as diahetes is a classic example of the need for external control action to compensate for the malfunctioing of internal physiological control loops. It is shown that the use of advanced time series analysis can aid the intelligent interpretation of long-term patterns of blood glucose variation, which in turn can assist in the provision of more appropriate insulin treatment regimens. In the selection of this treatment (control action). the role of a qualitative, rule-based, reasoning strategy is demonstrated. Key Words. Physiological control systems; diahetes mellitus; clinical decision support system; timeseries analysis; rule-based reasoning; insulin therapy adjustment.
I. INTRODUCTION
PATIENT DATA I
In the healthy subject, the islet cells of the endocrine pancreas continuously monitor the blood glucose level and respond to any glucose disturbance by secreting an appropriate amount of insulin into the bloodstream. Impaired functioning of the endocrine pancreas leads to diabetes mellitus which, along with its neurological or metabolic complications. affects approximately one hundred million people worldwide (EURODIABETA, 1990). Insulin-dependent (type I) diabetes results from the complete failure of the pancreas to produce insulin in response to elevated blood glucose levels. The management of this disease requires the regular monitoring of the status of the patient's carbohydrate metabolism and includes the need for insulin injections to replace the impaired internal control loop. Effective control of the patient's blood glucose level may help to minimise the progression of the disease, and hence reduce the risk of later complications. Patient monitoring and treatment involve intensive data and knowledge manipulation. This, in turn, requires skills and expertise which although available in specialised clinics, are not always found in other health care settings. This paper discusses the role of time series analysis and rule-based reasoning used, within a comprehensive diabetes management system, for assessing the patient's response to ongoing therapy and for selecting control actions to improve control of the patient's blood glucose level. This is the use of time series analysis to aid intelligent interpretation of the data, and a qualitative advisor. incorporating rule-based reasoning, for therapy planning. The interrelationship between the patient-specific database, analysis (interpretation) of the data and decision-making is summarised in Fig. I.
2. CHRONIC DIABETES MANAGEMENT AS A CONTROL PROBLEM The diabetic patient can be regarded as a multi-input/multi-output physiological system with several controllable and measurable variables, as well as other factors which are not directly observable and hence, as such, are
J61
Pemlaoenl Data d~mographlc data
(age. sex, l'IC.) diabt:lcs history (onsel. pn.:vious therapy. elc.)
MQojloring-Rc1aled Data current Slage markers blood glucose profile hypoglycaemic episodes glucose excretion in the urine
I Period Markers lIbAllevel complications
Manag(~lIIcnt-Rrlals;dDala
diel plan insulin dosage regimen
D
~
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Fig. I.
NytritiQnal - QrieOled - total energy requirement - carbohydrate/fat/protein! ratiQ Djabetes - Oriented - check fQr data consistency - genen\lion of "modal day" pro me Assessment of the Duality Qf Blood Glucose CQnlm! CharacterisatiQn Qf Ihe patjenl jn lerms Qf Model Parnmele[$
The inter-relationship between the patient-specific database, analysis (interpretation) of the data, and the decision making process.
beyond Ihe clinician's control. The patient's diet (the carhohydrate content of which will directly elevate blood glucose level) and the dosage of insulin administered can be regarded as control variables to be adjusted in order to maintain a balance between energy supply and expenditure with blood glucose heing regulated at levels set by the clinician The insulin dosage required to (Carson et al., 1990). maintain a reasonable degree of control, when keeping food intake and energy expenditure relatively constant in the absence
of intercurrent illness or psychological stress, is called the basal insulin dose. This basal insulin dose may vary during specific times of the week or month, e.g. with increased activity at weekends or, in the case of women, during menstruation. Long term diabetes management involves temporary readjustment of a patient's therapy whenever his or her home monitoring blood glucose data show evidence of deviation from preselected therapeutic targets. Patients with Type I diabetes striving to optimise their treatment must monitor blood glucose (BG) levels frequently. To support patient monitoring, computerised blood glucose recording devices with non-volatile memory for receiving, storing, and processing patient-entered data with respect to self-measured glucose concentrations and treatment data such as insulin doses given and meals consumed, are becoming widely available commercially (Piwernetz, 1988).
to all reports. The first contains one line "bullet" summaries of the key findings that are presented in more detail in the remainder of the report (focusing on key issues such as the average blood glucose value being higher than the upper limit of the patient's prescribed target range, and the times of occurrence of extremely low blood glucose values). The lower section provides a concise graphical summary of the quantity and quality of patient data available for analysis (including high, low and mean daily blood glucose values together with details of insulin injections, as well as markers indicating extreme values, hypoglycaemic (low blood glucose) symptoms and other relevant life style information). Conceptually there are two categories of quantitative methods aimed at describing a sequence of observed data. Time series methods seek to identify historical patterns using time as a reference, while explanatory methods seek to identify the relationships that lead (caused) observed outcomes in the past and then forecast by applying these relationships to the future. The mechanism for capturing the relationship between inputs such as insulin injection regimen and diet and outputs such as blood glucose response is to build a mathematical model and fit it to the observed data. In such cases the variability in the raw blood glucose data can be mapped into the uncertainty of some of the patient specific model parameters, e.g. insulin sensitivity, using causal probabilistic networks to represent input-output relationships (Andreassen et al., 1991).
These home monitoring data can be used in two different ways. Adjustments in insulin dosage can be made on a daily basis which means that the device at the time of each injection scans its memory and analyses past as well as current blood glucose and insulin data. The corresponding control action (such as an increase in the short-acting insulin component of the current basic treatment regimen) is activated when a particular feature (such as persisting high blood glucose level before lunch which cannot be explained by alterations in food intake or activity) is present on two or more consecutive days in the patient's blood glucose profile (Pernick and Rodbard, 1986). In practice it is more usual to adjust the basic insulin dosage less frequently; only at times when the patient visits a physician. During such visits: (i) the physician must examine this collection of data for specific features such as the presence of a rise or fall throughout the different daily periods, or excessive values after meals, and (ii) suggest modifications in the current treatment which would be expected to produce improved control of blood glucose level whenever it is necessary.
The blood glucose regulatory system involves many variables, most of which are non-observable and as such beyond the physician's control. Therefore, it may be preferable to adopt time series analysis for home monitoring blood glucose data. This assumes that some pattern, or combination of patterns, is recurring over time, and treats the system as a blood glucose generating process which is not sufficiently understood and as such makes no attempt to quantify the factors affecting its behaviour. That is, it is more appropriate to try to discover the regularities and random components directly in the original data without referring to any non-observable quantity or any specific parameter incorporated in any particular mathematical model. Thus it would appear to be reasonable to characterise the patient's blood glucose response at the four landmark times of the day by the averages of the blood glucose readings made at these time points. This assessment, however, does not consider the effect of the missing data on the different means, and, more importantly, the calculated mean values do not represent the patient's 'true' response unless the raw data are concentrated around that mean value. The basic assumption underlying the use of any time series analysis method is that the actual value will be determined by some pattern plus some random influences. That is:
3. TIME SERIES ANALYSIS FOR CHARACTERISING LONG-TERM CONTROL OF BLOOD GLUCOSE LEVEL Plarming in diabetes therapy involves the forecasting of blood glucose levels to help make good decisions about the most attractive treatment alternative for the patient. Forecasting is generally used to predict (describe) what will happen given a set of circumstances based on gathering and analysing repeated observations. In most cases the registered blood glucose data show systematic variations, but these patterns are usually rather difficult to extract from the highly variable monitored data. In the following, it will be assumed that blood glucose measurements are made four times per day, before the three main meals and at bedtime. Some of the data, however, may be missing. Furthermore, the basic insulin dosage will be assumed to be constant over the whole monitoring period.
observed data = pattern
+ randomness
(I)
One useful way of approaching the identification of patterns in blood glucose time series is to treat these data as comprising four elements: daily-pattern, trend, cyclicity, and randomness:
The patient specific database also contains information on diet and insulin regimen when they differ from their basic values. These data serve to identify possible causes of out of range findings, e.g. a very high blood glucose level resulting from, for example, an extra meal or missing insulin injection. Such 'outliers' do not imply a need for any adjustment in the basic insulin dosage. Analysis of large quantities of data requires that they should first be summarised (processed) and then interpreted. In contrast to summarising data (e.g. computing means and standard deviations), intepretation seeks to discover regularities (clinically important patterns) within the data that point to therapeutic opportunities for improving diabetes management (Kahn et al., 1991).
(2) where G, is the observed blood glucose value at time ti, and Di,C"T, and Ri are the daily-pattern, cyclical component, trend component and random noise at time ti (Kendall and Ord, 1990). The explicit functional relationship, f, used to relate these four sub-patterns can take a variety of forms. The most straightforward are additive (simply adding the elements) and multiplicative (taking the product of the four elements). A trend pattern, representing long-run behaviour, exists when there is a general increase or decrease in the blood glucose values over time (if there is no trend in the data, the time series is said to be stationary). A significant trend may indicate a change in the patient's condition, also resulting in the need for preventive clinical measures as appropriate. A
For example, the program developed by Kahn and colleagues (199 I) accepts patient data in an electronic file, interprets those data using symbolic and numerical methods, and produces a paper-based report of its findings. Two sections are common 162
daily-pattern (seasonality in time series analysis terminology) exists when the blood glucose data observed on different days fluctuate according to some daily rhythm. Seasonality means periodic fluctuations of constant length which are repeated at fixed intervals. This may occur for reasons related to an internal diurnal rhythm, or inadequacy in the current insulin therapy. The daily pallern is analogous to the so-called modal day aggregation of daily blood glucose measurements, frequently used to assess the "mean response" of the patient to the current therapy, and which also serves as a guide for adjusting insulin dosage when necessary. This pattern reflects the patient's mean daily response to the current therapy once any long term trend and cyclicity have been removed. A cyclical pattern is similar to a seasonal pattern, but the length of a single cycle is generally longer. This component is difficult to predict, because its duration may vary from cycle to cycle. It often follows the pattern of a wave, passing from a large to a small value and back again to a large value. Blood glucose time series may contain such cyclicity arising as the difference between workdays and weekends (I week cyclicity) or corresponding to the menstrual cycle in women. The identification of cyclical patterns in a blood glucose time series may lead to fine tuning of the basic insuln dosage according to long term fluctuations of insulin demand of the patient. Although, by definition, randomness cannot be predicted, once it has been isolated its magnitude can be estimated and used to determine the extent of variation likely between actual and predicted blood glucose levels.
therapeutic targets set by the physician, a diagnostic problem can be associated with that period as follows: problem (strong excess-in-glucose-supply) (breakfast lunch) (3)
The different types of problem, and periods in which they are found, can be rank-ordered according to the priorities assigned to them (for example a shortage in glucose supply is of greater priority than an excess of it due to the increased risk of a very low blood glucose level). To select the appropriate decision, a simplified model of insulin pharmacodynamics is defined which gives the intensity of insulin action in 3 hour periods following injection in terms of the three categories: strong, mild and none. For example the eight element list for regular insulin is as follows : effect (regular (strong strong mild none none none none none)) (4)
indicating that the total effect of such an insulin injection is completed within a period of nine hours, there having been a strong effect in the first six hours, followed by a mild effect during the period from six to nine hours after injection. The search for appropriate control actions which can modify the timing and/or dosage of the insulin injections, including a change in the type of the insulin regimen, is performed in two steps. First, control decisions are generated in qualitative terms, defining only the direction of the adjustment required. The extent of the required adjustment is calculated in the second step, based on a dynamic model of carbohydrate metabolism which is tailored to the individual patient. The procedural knowledge needed to propose control decisions to "cure" problems in glucose supply in different daily periods has been defined by production rules. The search for appropriate control actions which can modify the timing and/or dosage of the insulin injections in qualitative terms (increase dose, inject later, etc.) is controlled by a
Analysing and interpreting blood glucose time series involves decomposition into sub-pallerns that identify each component of the time series separately. This decomposition may help to achieve an understand of the behaviour of the series. The range of time series modelling approaches includes aUloregressive/moving average (ARMA) methods, Parzen's ARARMA models, AEP and Kalman filtering, Lewandowski's FORSYS structural modelling and BATS (Bayesian time series analysis) some of which aim to isolate each component of the series as accurately as possible (Kendall and Ord, 1990; Harvey, 1989). Fig. 2 shows a blood glucose time series decomposed into components with clinical significance.
"
Trend
(A)
-~
- -
~
15 ---- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
4. SELECTION OF CONTROL ACTIONS
10
A broad range of computer-based approaches including expert systems, computer algorithms and model-based methods have been developed to assist diabetes management (e.g. Albisser et al., 1986; Boroujerdi et al., 1987; Carson et al., 1990; Cobelli and Ruggeri, 1983; Levy et al., 1989; Sivitz et al., 1989). The approach adopted here merges logical and model-based reasoning to reach therapeutic conclusions, dividing the original complex problem (what to do, given the non-appropriate response resulting from the current therapy) into sub-problems which are solvable in a more rational and objective manner. Deficiencies in the patient's modal day blood glucose profile as assessed by the above time series analysis can be considered as problems in the glucose supply in the different daily periods (Deutsch et aI., 1990). The severity of such problems can be evaluated with respect to the therapeutic targets formulated in terms of allowable ranges for the blood glucose level for each meal-related characteristic time of the day. Obviously the therapeutic objectives can be set in different ways for different patients depending on factors such as age, pregnancy, complications, etc.
5
,~
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---
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2.5 BG(mmolll)
Four Periods a Day
2 ------.------------
o ---------------12~J.l12:H 12:1il12:14 12:)4 12:14 12:-10112:1" 12:14 12~1'112:1'11 :!:l4 123<1 12:14 1234
Four Periods
The quality of the control of blood glucose in a daily period (e.g. between breakfast and lunch) is defined by the "distance from the target" parameter which reflects the absolute values of, and the changes in, the blood glucose values (glucose balance) in the given period (Deutsch et al., 1990). If this distance is too high (or too low), i.e. if the blood glucose values in a daily period are outside the therapeutic range and/or the trend over this period does not correspond to the
Fig. 2.
163
B
J
234
Day
Blood glucose time series data, corresponding to four daily periods, decomposed into components of clinical significance. A) Blood glucose and estimated trend (since there is no cycle in this case, trend effectively corresponds to a combination of cycle and trend). B) Irregular and seasonal components.
backward-chaining, rule-based inference engine. A control action is proposed if it is expected to solve a problem, but not to create another one, for example by carrying a high risk of very low blood glucose level. The following rules define indications related to adjustment of dose (Sa) and shift of injection time (5b), respectively: is-indicated (decrease-dose((beforeMeal)Type» if problem ((" -" Any-extent) Period) (Sa) and has-strong-effect (((before Meal) Type) Period) is-indicated (inject-earlier ((before Meal) short-acting» (5b) if problem ((" +" X) (post-prandial Meal»
Rule (6) defines control actions which might produce an hypoglycaemic episode (low blood glucose level): may-cause-hypo (increase-dose ((before Meal) Type)) if has-strong-effect (((before Meal) Type) period) (6) and blood-glucose (T Subperiod Bg) and Bg<4 and is-included (Subperiod Period) Three different adjustment strategies can be selected by the user. The "worst first strategy" selects control actions to improve the control in the worst controlled period. The "user own choice" option allows the user to choose target periods for control actions. The "all at one time" strategy attempts to generate a combination of adjustments which are expected to solve all problems diagnosed in the different daily periods. Fig. 3 shows a sample data file and advice. 5.
SUMMARY
The problem of insulin adjustment in the insulin-dependent diabetic patient provides the opportunity to combine qualitative and quantitative approaches in solving this control problem. Two problems have been considered. The first is that of characterising the long term control of blood glucose in an intelligent manner, where the day-to-day variability in blood glucose data is amenable to techniques of time series analysis. Secondly, a qualitative, rule-based approach, incorporating daily period-based reasoning, has been shown to be effective in tackling the control problem of advising in insulin adjustment. This qualitative reasoning has been linked to an individually-tailored dynamic model of carbohydrate metabolism in the AIDA (Automated Insulin Dosage Advisor) system for generating alternative control actions which are expected to improve the patient's metabolic control (Lehmann et al., 1993). This complex system is currently being tested and evaluated at the SI. Thomas' Hospital, London. 6.
computer-based decision support in diabetic management, Comput. Meth. Prog. Biomed., 32, 179-188. Cobelli, e. and A. Ruggeri (1983) Evaluation of portal/peripheral route and of algorithms for insulin delivery in the closed-loop control of glucose in diabetes. A modelling study, IEEE Trans. Biomed. Eng., BME-30, 93-103. Deutsch, T., E.R. Carson, F.E. Harvey, E.D. Lehmann, P.H. S6nksen, G. Tamas, G. Whitney, and C.D. Williams (1990) Computer assisted diabetes management. A complex approach, Comput. Meth. Prog. Biomed., 32, 195-214. EURODIABETA (1990) Information technology for diabetes care in Europe: the EURODIABETA initiative, Diabetic Medicine, 7, 639-650. Harvey, A.e. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press. Kahn, M.G., e.B. Abrams, M.J. Orland, J.C. Beard, J.P. Miller, and J.W. Santiago (1991) Intelligent computer-based interpretation and graphical presentation of self-monitored blood glucose and insulin data Diabetes, Nutrition and Metabolism, 4 (suppl. 1),99-107. Kendall, M., and J.K. Ord (1990) Time Series (3rd edition). London: Edward Arnold. Lehmann, E.D., T. Deutsch, E.R. Carson, and P.H. S6nksen (1993) Combining rule-based reasoning and mathematical modelling in diabetes care. System overview and clinical assessment, Artif. Intell. Med. (in press). M., P. Ferrand, and V. Chirat (1989) Levy, SESAM-DIABETE, an expert system for insulin-requiring diabetic patient education, Comput. Biomed. Res., 22, 442-453. Pernick, N., and D. Rodbard (1986) Personal computer programs to assist with home monitoring of blood glucose and self-adjustment of insulin dosage, Diabetes Care, 9, 61-69. Piwernetz, K.R. (1988) Camit: a new diabetes data management system, Diabetes News, 9, 10-12. Sivitz, W.!., P.e. Davidson, D. Steed, B. Bode, and P. Richardson (1989) Computer-assisted instruction in intense insulin therapy using a mathematical model for clinical simulation with a clinical algorithm and flow sheet, Diabetes Education, 15, 77-79. patient VM, sex: f, age: 32 meal bre 0800 30 meal mms 1100 10 meal lun 1300 45 meal afs 1600 15 meal sup 1800 30 meal bts 2300 10 ins 0745 Actrapid NPH 0 25 ins 1750 Actrapid NPH 0 IS bg 0800 4.1 bg 1300 8.0 bg 1800 10.9 bg 2300 9.3
REFERENCES
Suggestions for changcs in theraoy
Albisser, A.M., A. Schiffrin, M. Schulz, J. Tiran, and B.S. Leibel (1986) Insulin dosage adjustment using manual methods and computer algorithms: a comparative study, Med. BioI. Eng. Comput., 24, 577-584. Andreassen, S., R. Hovorka, J.J. Benn, K.G. Olesen, and E.R. Carson (1991) A model-based approach to insulin adjustment, In: Proc. AIME 91, (M.Stefanelli, A.Hasman, M.Fieschi and J.Talmon, Eds.), Berlin: Springer-Verlag, pp. 239-249. Boroujerdi, M.A., e.D. Williams, E.R. Carson, K. Piwernetz, K.D. Hepp, and P.H. S6nksen (1987) A simulation approach for planning insulin regimes, In: Proc. Internat. Symp. on Advanced Models for Therapy of Insulin-Dependent Diabetes (Serona Symposium No. 37), (P.Brunetti and W.K.Waldhaust, Eds.) New York: Raven Press, pp. 41-46. Carson, E.R., S. Carey, F.E. Harvey, P.H. S6nksen, S. Till, and e.D. Williams (1990) Information technology and
Decrease the before-supper NPH dose by 2 units explanation: the adjustment is aimed to reduce glucose utIlIsatIOn between bedtime and morning, since there is a shortage of glucose in that period.
2
Fig. 3.
164
Increase the beforc-breakfast NPH dose by 2 units explanation: the adjustment is aimed to increase glucose utIlIsatIon between breakfast and lunch, since thcre is an excess of glucose supply in that period.
A sample data file, together with suggestions for changes in therapy.
INSULIN DOSAGE ADJUSTMENT USING TIME SERIES ANALYSIS AND RULE-BASED REASONING E.R. Carson*, T. Deutsch*'**, A.V. Roudsari* and A. Sali** 'Centre/or Measurement and Information in Medicine. Department o/Systems Science. City University, Northampton Square. London EC IV OHB. UK "Computing Centre, Semmelweis University 0/ Medicine. Kalvaria fcr 5. H-I089 Budapesf. Hunfiary
Abstract. The management of a chronic disease such as diahetes is a classic example of the need for external control action to compensate for the malfunctioing of internal physiological control loops. It is shown that the use of advanced time series analysis can aid the intelligent interpretation of long-term patterns of blood glucose variation, which in turn can assist in the provision of more appropriate insulin treatment regimens. In the selection of this treatment (control action). the role of a qualitative, rule-based, reasoning strategy is demonstrated. Key Words. Physiological control systems; diahetes mellitus; clinical decision support system; timeseries analysis; rule-based reasoning; insulin therapy adjustment.
I. INTRODUCTION
PATIENT DATA I
In the healthy subject, the islet cells of the endocrine pancreas continuously monitor the blood glucose level and respond to any glucose disturbance by secreting an appropriate amount of insulin into the bloodstream. Impaired functioning of the endocrine pancreas leads to diabetes mellitus which, along with its neurological or metabolic complications. affects approximately one hundred million people worldwide (EURODIABETA, 1990). Insulin-dependent (type I) diabetes results from the complete failure of the pancreas to produce insulin in response to elevated blood glucose levels. The management of this disease requires the regular monitoring of the status of the patient's carbohydrate metabolism and includes the need for insulin injections to replace the impaired internal control loop. Effective control of the patient's blood glucose level may help to minimise the progression of the disease, and hence reduce the risk of later complications. Patient monitoring and treatment involve intensive data and knowledge manipulation. This, in turn, requires skills and expertise which although available in specialised clinics, are not always found in other health care settings. This paper discusses the role of time series analysis and rule-based reasoning used, within a comprehensive diabetes management system, for assessing the patient's response to ongoing therapy and for selecting control actions to improve control of the patient's blood glucose level. This is the use of time series analysis to aid intelligent interpretation of the data, and a qualitative advisor. incorporating rule-based reasoning, for therapy planning. The interrelationship between the patient-specific database, analysis (interpretation) of the data and decision-making is summarised in Fig. I.
2. CHRONIC DIABETES MANAGEMENT AS A CONTROL PROBLEM The diabetic patient can be regarded as a multi-input/multi-output physiological system with several controllable and measurable variables, as well as other factors which are not directly observable and hence, as such, are
J61
Pemlaoenl Data d~mographlc data
(age. sex, l'IC.) diabt:lcs history (onsel. pn.:vious therapy. elc.)
MQojloring-Rc1aled Data current Slage markers blood glucose profile hypoglycaemic episodes glucose excretion in the urine
I Period Markers lIbAllevel complications
Manag(~lIIcnt-Rrlals;dDala
diel plan insulin dosage regimen
D
~
M A
t
I N
T
Selec!jpn QfTargl"ls - nutnIJonal targets - nonnoglycaemic targels
I K
SelectjQn Qf Qbsayatjons
N
Se!
1~
E R P
R E T A
T I
o
N
Fig. I.
NytritiQnal - QrieOled - total energy requirement - carbohydrate/fat/protein! ratiQ Djabetes - Oriented - check fQr data consistency - genen\lion of "modal day" pro me Assessment of the Duality Qf Blood Glucose CQnlm! CharacterisatiQn Qf Ihe patjenl jn lerms Qf Model Parnmele[$
The inter-relationship between the patient-specific database, analysis (interpretation) of the data, and the decision making process.
beyond Ihe clinician's control. The patient's diet (the carhohydrate content of which will directly elevate blood glucose level) and the dosage of insulin administered can be regarded as control variables to be adjusted in order to maintain a balance between energy supply and expenditure with blood glucose heing regulated at levels set by the clinician The insulin dosage required to (Carson et al., 1990). maintain a reasonable degree of control, when keeping food intake and energy expenditure relatively constant in the absence
of intercurrent illness or psychological stress, is called the basal insulin dose. This basal insulin dose may vary during specific times of the week or month, e.g. with increased activity at weekends or, in the case of women, during menstruation. Long term diabetes management involves temporary readjustment of a patient's therapy whenever his or her home monitoring blood glucose data show evidence of deviation from preselected therapeutic targets. Patients with Type I diabetes striving to optimise their treatment must monitor blood glucose (BG) levels frequently. To support patient monitoring, computerised blood glucose recording devices with non-volatile memory for receiving, storing, and processing patient-entered data with respect to self-measured glucose concentrations and treatment data such as insulin doses given and meals consumed, are becoming widely available commercially (Piwernetz, 1988).
to all reports. The first contains one line "bullet" summaries of the key findings that are presented in more detail in the remainder of the report (focusing on key issues such as the average blood glucose value being higher than the upper limit of the patient's prescribed target range, and the times of occurrence of extremely low blood glucose values). The lower section provides a concise graphical summary of the quantity and quality of patient data available for analysis (including high, low and mean daily blood glucose values together with details of insulin injections, as well as markers indicating extreme values, hypoglycaemic (low blood glucose) symptoms and other relevant life style information). Conceptually there are two categories of quantitative methods aimed at describing a sequence of observed data. Time series methods seek to identify historical patterns using time as a reference, while explanatory methods seek to identify the relationships that lead (caused) observed outcomes in the past and then forecast by applying these relationships to the future. The mechanism for capturing the relationship between inputs such as insulin injection regimen and diet and outputs such as blood glucose response is to build a mathematical model and fit it to the observed data. In such cases the variability in the raw blood glucose data can be mapped into the uncertainty of some of the patient specific model parameters, e.g. insulin sensitivity, using causal probabilistic networks to represent input-output relationships (Andreassen et al., 1991).
These home monitoring data can be used in two different ways. Adjustments in insulin dosage can be made on a daily basis which means that the device at the time of each injection scans its memory and analyses past as well as current blood glucose and insulin data. The corresponding control action (such as an increase in the short-acting insulin component of the current basic treatment regimen) is activated when a particular feature (such as persisting high blood glucose level before lunch which cannot be explained by alterations in food intake or activity) is present on two or more consecutive days in the patient's blood glucose profile (Pernick and Rodbard, 1986). In practice it is more usual to adjust the basic insulin dosage less frequently; only at times when the patient visits a physician. During such visits: (i) the physician must examine this collection of data for specific features such as the presence of a rise or fall throughout the different daily periods, or excessive values after meals, and (ii) suggest modifications in the current treatment which would be expected to produce improved control of blood glucose level whenever it is necessary.
The blood glucose regulatory system involves many variables, most of which are non-observable and as such beyond the physician's control. Therefore, it may be preferable to adopt time series analysis for home monitoring blood glucose data. This assumes that some pattern, or combination of patterns, is recurring over time, and treats the system as a blood glucose generating process which is not sufficiently understood and as such makes no attempt to quantify the factors affecting its behaviour. That is, it is more appropriate to try to discover the regularities and random components directly in the original data without referring to any non-observable quantity or any specific parameter incorporated in any particular mathematical model. Thus it would appear to be reasonable to characterise the patient's blood glucose response at the four landmark times of the day by the averages of the blood glucose readings made at these time points. This assessment, however, does not consider the effect of the missing data on the different means, and, more importantly, the calculated mean values do not represent the patient's 'true' response unless the raw data are concentrated around that mean value. The basic assumption underlying the use of any time series analysis method is that the actual value will be determined by some pattern plus some random influences. That is:
3. TIME SERIES ANALYSIS FOR CHARACTERISING LONG-TERM CONTROL OF BLOOD GLUCOSE LEVEL Plarming in diabetes therapy involves the forecasting of blood glucose levels to help make good decisions about the most attractive treatment alternative for the patient. Forecasting is generally used to predict (describe) what will happen given a set of circumstances based on gathering and analysing repeated observations. In most cases the registered blood glucose data show systematic variations, but these patterns are usually rather difficult to extract from the highly variable monitored data. In the following, it will be assumed that blood glucose measurements are made four times per day, before the three main meals and at bedtime. Some of the data, however, may be missing. Furthermore, the basic insulin dosage will be assumed to be constant over the whole monitoring period.
observed data = pattern
+ randomness
(I)
One useful way of approaching the identification of patterns in blood glucose time series is to treat these data as comprising four elements: daily-pattern, trend, cyclicity, and randomness:
The patient specific database also contains information on diet and insulin regimen when they differ from their basic values. These data serve to identify possible causes of out of range findings, e.g. a very high blood glucose level resulting from, for example, an extra meal or missing insulin injection. Such 'outliers' do not imply a need for any adjustment in the basic insulin dosage. Analysis of large quantities of data requires that they should first be summarised (processed) and then interpreted. In contrast to summarising data (e.g. computing means and standard deviations), intepretation seeks to discover regularities (clinically important patterns) within the data that point to therapeutic opportunities for improving diabetes management (Kahn et al., 1991).
(2) where G, is the observed blood glucose value at time ti, and Di,C"T, and Ri are the daily-pattern, cyclical component, trend component and random noise at time ti (Kendall and Ord, 1990). The explicit functional relationship, f, used to relate these four sub-patterns can take a variety of forms. The most straightforward are additive (simply adding the elements) and multiplicative (taking the product of the four elements). A trend pattern, representing long-run behaviour, exists when there is a general increase or decrease in the blood glucose values over time (if there is no trend in the data, the time series is said to be stationary). A significant trend may indicate a change in the patient's condition, also resulting in the need for preventive clinical measures as appropriate. A
For example, the program developed by Kahn and colleagues (199 I) accepts patient data in an electronic file, interprets those data using symbolic and numerical methods, and produces a paper-based report of its findings. Two sections are common 162
daily-pattern (seasonality in time series analysis terminology) exists when the blood glucose data observed on different days fluctuate according to some daily rhythm. Seasonality means periodic fluctuations of constant length which are repeated at fixed intervals. This may occur for reasons related to an internal diurnal rhythm, or inadequacy in the current insulin therapy. The daily pallern is analogous to the so-called modal day aggregation of daily blood glucose measurements, frequently used to assess the "mean response" of the patient to the current therapy, and which also serves as a guide for adjusting insulin dosage when necessary. This pattern reflects the patient's mean daily response to the current therapy once any long term trend and cyclicity have been removed. A cyclical pattern is similar to a seasonal pattern, but the length of a single cycle is generally longer. This component is difficult to predict, because its duration may vary from cycle to cycle. It often follows the pattern of a wave, passing from a large to a small value and back again to a large value. Blood glucose time series may contain such cyclicity arising as the difference between workdays and weekends (I week cyclicity) or corresponding to the menstrual cycle in women. The identification of cyclical patterns in a blood glucose time series may lead to fine tuning of the basic insuln dosage according to long term fluctuations of insulin demand of the patient. Although, by definition, randomness cannot be predicted, once it has been isolated its magnitude can be estimated and used to determine the extent of variation likely between actual and predicted blood glucose levels.
therapeutic targets set by the physician, a diagnostic problem can be associated with that period as follows: problem (strong excess-in-glucose-supply) (breakfast lunch) (3)
The different types of problem, and periods in which they are found, can be rank-ordered according to the priorities assigned to them (for example a shortage in glucose supply is of greater priority than an excess of it due to the increased risk of a very low blood glucose level). To select the appropriate decision, a simplified model of insulin pharmacodynamics is defined which gives the intensity of insulin action in 3 hour periods following injection in terms of the three categories: strong, mild and none. For example the eight element list for regular insulin is as follows : effect (regular (strong strong mild none none none none none)) (4)
indicating that the total effect of such an insulin injection is completed within a period of nine hours, there having been a strong effect in the first six hours, followed by a mild effect during the period from six to nine hours after injection. The search for appropriate control actions which can modify the timing and/or dosage of the insulin injections, including a change in the type of the insulin regimen, is performed in two steps. First, control decisions are generated in qualitative terms, defining only the direction of the adjustment required. The extent of the required adjustment is calculated in the second step, based on a dynamic model of carbohydrate metabolism which is tailored to the individual patient. The procedural knowledge needed to propose control decisions to "cure" problems in glucose supply in different daily periods has been defined by production rules. The search for appropriate control actions which can modify the timing and/or dosage of the insulin injections in qualitative terms (increase dose, inject later, etc.) is controlled by a
Analysing and interpreting blood glucose time series involves decomposition into sub-pallerns that identify each component of the time series separately. This decomposition may help to achieve an understand of the behaviour of the series. The range of time series modelling approaches includes aUloregressive/moving average (ARMA) methods, Parzen's ARARMA models, AEP and Kalman filtering, Lewandowski's FORSYS structural modelling and BATS (Bayesian time series analysis) some of which aim to isolate each component of the series as accurately as possible (Kendall and Ord, 1990; Harvey, 1989). Fig. 2 shows a blood glucose time series decomposed into components with clinical significance.
"
Trend
(A)
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- -
~
15 ---- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
4. SELECTION OF CONTROL ACTIONS
10
A broad range of computer-based approaches including expert systems, computer algorithms and model-based methods have been developed to assist diabetes management (e.g. Albisser et al., 1986; Boroujerdi et al., 1987; Carson et al., 1990; Cobelli and Ruggeri, 1983; Levy et al., 1989; Sivitz et al., 1989). The approach adopted here merges logical and model-based reasoning to reach therapeutic conclusions, dividing the original complex problem (what to do, given the non-appropriate response resulting from the current therapy) into sub-problems which are solvable in a more rational and objective manner. Deficiencies in the patient's modal day blood glucose profile as assessed by the above time series analysis can be considered as problems in the glucose supply in the different daily periods (Deutsch et aI., 1990). The severity of such problems can be evaluated with respect to the therapeutic targets formulated in terms of allowable ranges for the blood glucose level for each meal-related characteristic time of the day. Obviously the therapeutic objectives can be set in different ways for different patients depending on factors such as age, pregnancy, complications, etc.
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Four Periods
The quality of the control of blood glucose in a daily period (e.g. between breakfast and lunch) is defined by the "distance from the target" parameter which reflects the absolute values of, and the changes in, the blood glucose values (glucose balance) in the given period (Deutsch et al., 1990). If this distance is too high (or too low), i.e. if the blood glucose values in a daily period are outside the therapeutic range and/or the trend over this period does not correspond to the
Fig. 2.
163
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234
Day
Blood glucose time series data, corresponding to four daily periods, decomposed into components of clinical significance. A) Blood glucose and estimated trend (since there is no cycle in this case, trend effectively corresponds to a combination of cycle and trend). B) Irregular and seasonal components.
backward-chaining, rule-based inference engine. A control action is proposed if it is expected to solve a problem, but not to create another one, for example by carrying a high risk of very low blood glucose level. The following rules define indications related to adjustment of dose (Sa) and shift of injection time (5b), respectively: is-indicated (decrease-dose((beforeMeal)Type» if problem ((" -" Any-extent) Period) (Sa) and has-strong-effect (((before Meal) Type) Period) is-indicated (inject-earlier ((before Meal) short-acting» (5b) if problem ((" +" X) (post-prandial Meal»
Rule (6) defines control actions which might produce an hypoglycaemic episode (low blood glucose level): may-cause-hypo (increase-dose ((before Meal) Type)) if has-strong-effect (((before Meal) Type) period) (6) and blood-glucose (T Subperiod Bg) and Bg<4 and is-included (Subperiod Period) Three different adjustment strategies can be selected by the user. The "worst first strategy" selects control actions to improve the control in the worst controlled period. The "user own choice" option allows the user to choose target periods for control actions. The "all at one time" strategy attempts to generate a combination of adjustments which are expected to solve all problems diagnosed in the different daily periods. Fig. 3 shows a sample data file and advice. 5.
SUMMARY
The problem of insulin adjustment in the insulin-dependent diabetic patient provides the opportunity to combine qualitative and quantitative approaches in solving this control problem. Two problems have been considered. The first is that of characterising the long term control of blood glucose in an intelligent manner, where the day-to-day variability in blood glucose data is amenable to techniques of time series analysis. Secondly, a qualitative, rule-based approach, incorporating daily period-based reasoning, has been shown to be effective in tackling the control problem of advising in insulin adjustment. This qualitative reasoning has been linked to an individually-tailored dynamic model of carbohydrate metabolism in the AIDA (Automated Insulin Dosage Advisor) system for generating alternative control actions which are expected to improve the patient's metabolic control (Lehmann et al., 1993). This complex system is currently being tested and evaluated at the SI. Thomas' Hospital, London. 6.
computer-based decision support in diabetic management, Comput. Meth. Prog. Biomed., 32, 179-188. Cobelli, e. and A. Ruggeri (1983) Evaluation of portal/peripheral route and of algorithms for insulin delivery in the closed-loop control of glucose in diabetes. A modelling study, IEEE Trans. Biomed. Eng., BME-30, 93-103. Deutsch, T., E.R. Carson, F.E. Harvey, E.D. Lehmann, P.H. S6nksen, G. Tamas, G. Whitney, and C.D. Williams (1990) Computer assisted diabetes management. A complex approach, Comput. Meth. Prog. Biomed., 32, 195-214. EURODIABETA (1990) Information technology for diabetes care in Europe: the EURODIABETA initiative, Diabetic Medicine, 7, 639-650. Harvey, A.e. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press. Kahn, M.G., e.B. Abrams, M.J. Orland, J.C. Beard, J.P. Miller, and J.W. Santiago (1991) Intelligent computer-based interpretation and graphical presentation of self-monitored blood glucose and insulin data Diabetes, Nutrition and Metabolism, 4 (suppl. 1),99-107. Kendall, M., and J.K. Ord (1990) Time Series (3rd edition). London: Edward Arnold. Lehmann, E.D., T. Deutsch, E.R. Carson, and P.H. S6nksen (1993) Combining rule-based reasoning and mathematical modelling in diabetes care. System overview and clinical assessment, Artif. Intell. Med. (in press). M., P. Ferrand, and V. Chirat (1989) Levy, SESAM-DIABETE, an expert system for insulin-requiring diabetic patient education, Comput. Biomed. Res., 22, 442-453. Pernick, N., and D. Rodbard (1986) Personal computer programs to assist with home monitoring of blood glucose and self-adjustment of insulin dosage, Diabetes Care, 9, 61-69. Piwernetz, K.R. (1988) Camit: a new diabetes data management system, Diabetes News, 9, 10-12. Sivitz, W.!., P.e. Davidson, D. Steed, B. Bode, and P. Richardson (1989) Computer-assisted instruction in intense insulin therapy using a mathematical model for clinical simulation with a clinical algorithm and flow sheet, Diabetes Education, 15, 77-79. patient VM, sex: f, age: 32 meal bre 0800 30 meal mms 1100 10 meal lun 1300 45 meal afs 1600 15 meal sup 1800 30 meal bts 2300 10 ins 0745 Actrapid NPH 0 25 ins 1750 Actrapid NPH 0 IS bg 0800 4.1 bg 1300 8.0 bg 1800 10.9 bg 2300 9.3
REFERENCES
Suggestions for changcs in theraoy
Albisser, A.M., A. Schiffrin, M. Schulz, J. Tiran, and B.S. Leibel (1986) Insulin dosage adjustment using manual methods and computer algorithms: a comparative study, Med. BioI. Eng. Comput., 24, 577-584. Andreassen, S., R. Hovorka, J.J. Benn, K.G. Olesen, and E.R. Carson (1991) A model-based approach to insulin adjustment, In: Proc. AIME 91, (M.Stefanelli, A.Hasman, M.Fieschi and J.Talmon, Eds.), Berlin: Springer-Verlag, pp. 239-249. Boroujerdi, M.A., e.D. Williams, E.R. Carson, K. Piwernetz, K.D. Hepp, and P.H. S6nksen (1987) A simulation approach for planning insulin regimes, In: Proc. Internat. Symp. on Advanced Models for Therapy of Insulin-Dependent Diabetes (Serona Symposium No. 37), (P.Brunetti and W.K.Waldhaust, Eds.) New York: Raven Press, pp. 41-46. Carson, E.R., S. Carey, F.E. Harvey, P.H. S6nksen, S. Till, and e.D. Williams (1990) Information technology and
Decrease the before-supper NPH dose by 2 units explanation: the adjustment is aimed to reduce glucose utIlIsatIOn between bedtime and morning, since there is a shortage of glucose in that period.
2
Fig. 3.
164
Increase the beforc-breakfast NPH dose by 2 units explanation: the adjustment is aimed to increase glucose utIlIsatIon between breakfast and lunch, since thcre is an excess of glucose supply in that period.
A sample data file, together with suggestions for changes in therapy.