Application Of Fuzzy Logic Controller For Intensive Insulin Therapy In Tpye 1 Diabetic Mellitus Patient

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1 COMPUTERS and SMULATON in MOERN SCENCE, Volume Application Of Fuzzy Logic Contolle Fo ntensive nsulin Theapy n Tpye iabetic Mellitus Patient LALEH KARAR *, AL FALLAH, Shahia Ghaibzadeh, Fatollah Moztazadeh iomedical Engineeing Amikabi Univesity Of Technology RAN Abstact: - The wok we descibe hee is aimed at assisting out-patients affected by insulin dependent diabetes mellitus with an advisoy/contol algoithm. This advisoy/contol algoithm incopoates expet knowledge about the teatment of this disease by using Mamdani type fuzzy logic contolles to egulate the blood glucose level (GL). We poposed two-level achitectue fo contol system. The goal of the Low Level Module is to suggest the next insulin dosage of both shot and intemediate acting insulin (Regula and NPH) fomulation that ae pogammed in a thee-shots daily basis befoe meals, depending on the blood glucose measuement. The High Level Module adjusts the imum amounts of insulin povided to the patient in a time-scale of. This module aims to wok as a supeviso of the low level module. Simulations ae illustated, using a flow-limited model fo diabetes mellitus based on the wok of Puckett. Key-Wods: - iabetes mellitus, Fuzzy logic contolle, ntensive insulin theapy ntoduction Seveal ogans, homones and enzyme systems ae involved in the egulation of the blood glucose levels in human body. nsulin, a homone seceted by panceatic beta cells, is the most impotant homone in the egulation of blood glucose levels. t influences the ates of glucose utilization by the tissues and egulates the stoage of the fuel, theefoe helps to keep blood glucose concentations within a naow ange of about 9-3 mg/dl. iabetes mellitus is an endocine metabolic disode in which the body does not poduce o popely use insulin. The esults of the iabetes Contol and Complications Tial (CCT) [ showed that an intensive insulin theapy can educe the incidence of these illnesses in the long tem. Consequently, an intensive theapy is encouaged fo type diabetic mellitus (TM) patients pescibed eithe by a continuous subcutaneous insulin infusion (CS) pump, o a multiple daily injections egimen (MR). n this contibution, the latte one is studied, which is the most common scenaio in chonic patients, due to the high cost and availability of potable CS pumps. With this consideation, if an intensive theapy is followed by the patient, the pescibed insulin teatment must be caefully selected by the physician. t is then appealing to have an advisoy/contol system fo the patient in ode to update each daily dose of insulin [, [3, [, [5, [, [7. n the contol theoy field, the fuzzy logic has emeged as a poweful tool to incopoate expet knowledge about the systems into the contolles design [, [9, in paticula, the ability of synthesizing expet knowledge in the fuzzy logic famewok has aised a lot of attention in the biomedical engineeing field. The contol stategy pesented in this wok fomalizes expet knowledge in the fuzzy logic famewok. Section gives an oveview of the mathematical modeling of the insulin-glucose dynamics in a TM patient. Section 3 intoduces the synthesis of the knowledge-based (Mamdani-type) fuzzy contolles. Finally, Section intoduced the simulation esults. Section 5 pesents concluding emaks and futue wok. iabetic patient modeling The model to be pesented hee is a flow-limited model fo diabetes mellitus based on the wok of Puckett [. This model is constucted of two submodels. The glucose sub-model contains tissues including heat, bain, live, kidney and muscle whee the glucose is used fo enegy. The insulin sub-model includes subcutaneous tissue as a souce fo insulin. t is assumed that the panceas is completely lacking insulin poduction and changes in blood glucose and insulin concentations fo each tissue ae fast and the balances ae in a quasi-steady state (i.e. dg / ) shotly afte a distubance (i.e. the cabohydate intake).. nsulin sub-model nsulin tavels though seveal egions of the body as SSN: SN:

2 COMPUTERS and SMULATON in MOERN SCENCE, Volume it moves fom the injection depot to the taget cells. iabetic educatos usually teach patients to inject insulin into the subcutaneous tissue in such a way as to put it in the intestitial fluid and not a blood vessel. The insulin must then diffuse though the intestitial envionment to neaby capillaies. Afte cossing the capillay wall, it is caied to the main ciculation. The ciculating homone cosses the capillay wall in vaious tissues and diffuses though the intestitial milieu to the cell walls. nsulin s binding with eceptos in the cell membane then cause intacellula signals which activate appopiate changes in the cell s metabolism. Afte initiating the signal, the homone dissociates fom the ecepto, o the complex is intenalized. The intenalized insulin is eleased unalteed o degaded. The following thee pool model descibes the absoption fom an injection of shot acting insulin (egula) at t=: p = k p[ p [ p( t = ) = [ p (3) s V s = k p[ p ks[ s [ s( t = ) = [ s () V = ks[ s k[ + k[ (5) [ ( t = ) = [ p p τ = k, τ = V / k, τ = V / k s s s Whee, [ p is total amount of insulin in pocket, k p is ate constant fo the tanspot of insulin fom the pocket into the suounding intestitial fluid, [ p is injected insulin, [ s is insulin concentation in intestitial fluid, [ is concentation of insulin in the capillay blood, k s is ate constant fo the tanspot fom the intestitial egion to the capillay blood, V s is effective volume of the intestitial fluid, V is effective volume of ciculating blood, k is ate constant fo emoval of insulin in the live and kidney, τ p, τ s, τ ae time constants. The insulin sub-model paametes ae tabulated in Table. Table.Constant paametes of insulin Sub-model [ Paamete Value τ p (min) 3 τ s (min) 3 τ (min) [ ( μ U ) 7.5 [ s ( μ U ). Glucose sub-model Setting dg/ = in all tissues we get: V G = TGU GE + GA + LGP () n summay, we pesent the diffeent sub-models making up the glucose potion of the oveall model hee: Total Glucose Uptake (TGU) TGU = k[ A [ G + CNU (7) A = ([ [ A) TA () Whee, k is a constant value, [ A is effective insulin concentation, [G is ciculating blood glucose concentation, CNU is glucose and insulin independent uptake which is appoximately a constant, [ is ciculating blood insulin concentation delayed by the pue time delay T,TGU. Glucose Excetion (GE) dl mg mg GE =.5 ([ G 7 ) U ([ G 7 ) min dl dl (9) whee, U([G -7mg/dl) is step function indicating the theshold at appoximately 7 mg/dl. Glucose Absoption fom the small intestine (GA) dga F = GA + [ GG TA TATGE GA( t < t M ) = () GG = [ GG + [ CHOG TGE [ GG ( t < tm ) = () [ CHOG = CHOM ( t t M ) u( t t M ) min () CHOM ( t t M min ) u( t t M ) CHOM ( t t M min ) u( t t M ) + CHOM ( t t M min 5) u( t t M 5) Whee, [CHO G is total amount of hydolyzed meal cabohydate that have enteed the stomach, CHO M is cabohydate content of the meal (in mg/kg), t M is time of meal (in minutes), [G G is total amount of glucose in the stomach, F is faction of meal cabohydates that actually absob into the blood. Rate of Live Glucose Poduction (LGP) a ([ G a3 ) LGP = a( [ G a + a ) (3) G = k A ([ GL [ k A ([ GL [ 3 d [ G ) if [ GL [ d [ G ) if [ GL [ < [ G ( t = ) = [ G [ () SSN: SN:

3 COMPUTERS and SMULATON in MOERN SCENCE, Volume GA [ G L = [ G + (5) QL Whee, [G L is aveage glucose concentation enteing the live delayed by the pue time delay T,LGP, [ is ciculating blood insulin concentation delayed by the pue time delay T,LGP, [G is [G L [ delayed in a fist ode manne with a time constant /k A o /k, Q L is a constant value. The glucose sub-model paametes ae tabulated in table. Table.Constant paametes of glucose Sub-model [ Paamete Value V (dl/kg).75 T,TGU (min) 3 T A (min).3 k (/min).3 CNU (mg/kg-min).7 T GE (min) 5.59 T A (min) 3. F Q L (ml/min) a (mg/kg-min).3 a.3 a 3 ( mg μ U / dl ml ) 759 a ( mg μ U / dl ml ) 75 T,LGP (min) 3 k A (/min).37 k (/min).3 3 Poblem statement and contol method Thee meals ae consideed pe day: beakfast, lunch and dinne; whee the lunch is the majo one of the day. Roughly, thee is a time inteval of h between each meal. n the poposed injection plan, the insulin doses ae pogammed pevious to each meal, whee the NPH povides the basal insulin, and the tansient effects afte each meal (postpandial peaks) ae egulated by the egula. ecause of slow basal insulin absoption, the moning and lunch doses fo NPH ae skipped, and only egula is injected. The contol objective is then stated in Table 3. Table 3. Contol objective Plasma Glucose Nomal Taget efoe eating Less than 9 to 3 Two hous Less than Less than Afte eating eime Less than to 5 The advisoy/contol scheme pesented in this wok is based on a two-level achitectue, see Fig. 3. Supeviso Low level Contolle nsulin ose Patient GL Fig.. The oveall scheme fo contol system 3. Low Level Module The low level module is stuctued with a Mamdani type fuzzy achitectue and computes the egula ( ) and NPH ( ) insulin doses given to the patient befoe each meal. The input vaiables to this module ae: - Time of the day (t): the infomation of time is used to detemine whethe a NPH insulin dose is injected next o not. - Glucose measuement (G): the infomation of the GL is used fo the euglycemic analysis. - Pevious egula dose ( d ): the egula dose calculated in the pevious meal is used to analyze the glycemic contol. - Pevious NPH insulin dose ( d ): due to the absoption pocess of the NPH, its dose in the moning is consideed to evaluate also the glycemic contol. The two outputs egula ( ) and NPH doses ( ) ae nomalized to the inteval [,, and the actual injection pepaation ( a a ; ) is calculated when the amplitudes ae scaled accoding to the values nput nteval Table. nputs chaacteistics fo low level module Membeship Function t [, h Moning (SMF) Lunch (GCMF) Evening (SMF) G [, mg/dl Low (SMF) Nomal (GCMF) Medium (GCMF) High (SMF) d [, Small (SMF) Medium (GCMF) Lage (SMF) d [, Small (SMF) Medium (GCMF) Lage (SMF) output nteval Table 5. Outputs chaacteistics fo low level module Membeship Function [, None (TMF) Small (TMF) Medium (TMF) Lage (TMF) Vey Lage (TMF) [, None (TMF) Small (TMF) Medium (TMF) Lage (TMF) Vey Lage (TMF) SSN: SN:

4 COMPUTERS and SMULATON in MOERN SCENCE, Volume (imum egula insulin dosing) and (imum NPH insulin dosing) povided by the high level module. a a = = () The input and output chaacteistics ae shown in Table and 5 espectively, including the inteval of vaiation fo each vaiable and the fuzzy sets associated with the type of membeship function used (fuzzication method). y the definition of the input fuzzy set, a total of F-THEN ules wee defined. These ules wee of AN (minimum) type antecedent. The output (defuzzification method) is calculated by the centoid method. The majo tends in the ules desciption ae: - The moning and lunch doses of NPH insulin ae skipped. - The egula doses inceases as the GL inceases. - f the pevious dose of insulin is small and the GL is above nomal, then incease the doses. A sample of the poposed ules fo the low level module is detailed next: F Time=Moning and Glucose=Low and d =Lage and d =Lage THEN =Small and =Medium. 3. High Level Module The high level module is synthesized usingphysician knowledge [, [ by applying a Mamdani type fuzzy logic stuctue and egulates the amounts of insulin given to the patient by evaluating the glycemic contol in a time-scale of. Accoding to contol objective listed in Table 3, the systemic glucose deviation fom the taget glucose level (TGL) can be measued as: n J = θ ( (7) n k = whee n is the numbe of measuements used fo nput J J d d Δ Δ d evaluation, and θ ( (pointwise deviation fom TGL) is defined as: a) Fo GL measued befoe eating: G( 3 > 3 mg / dl θ ( = Γ.[ G( 9 < 9 mg / dl () 9 G( 3 mg / dl b) Fo GL measued hous afte eating: G( > mg / dl θ ( = (9) Othewise c) Fo GL measued at beime: G( 5 > 5 mg / dl θ ( = Γ.[ G( < mg / dl () G( 5 mg / dl Whee Γ is a constant that includes an additional weight fo low glucose concentations (hypoglycemic scenaios). Consequently, the high level module must adjust the insulin dosing in thee global scenaios: - ncease it, if an hypeglycemic condition is detected. - ecease it, in the case of an hypoglycemic condition. - Maintain it, fo a nomal condition. These dosing adjustments ae pefomed in a timescale of, whee they could be specified pe day o week accoding to the physician's advise. The adjustment is done the next moning by modifying the scaling factos type of updating ule: whee ( i) = ( i) = ( i ) + Δ ( i ) + Δ Δ and and using an integal () Δ ae the adjustments given by the high level module. The index i- efes to the old scaling facto, and i to the new adjusted one. The input infomation used by the high level module includes details of the glycemic contol duing the pevious, and the pevious insulin adjustments, this is: Table. nputs chaacteistics fo high level module nteval Membeship Function [-, mg/dl Negative (SMF) Zeo (GCMF) Positive (SMF) [-, mg/dl Negative (SMF) Zeo (GCMF) Positive (SMF) [-, U Negative (SMF) Zeo (GCMF) Positive (SMF) [-, U Negative (SMF) Zeo (GCMF) Positive (SMF) Output Δ Δ Table 7. Outputs chaacteistics fo high level module nteval Membeship Function [-, U Vey Negative Negative Zeo Positive (SMF) (TMF) (TMF) (TMF) [-, U Vey Negative Negative Zeo Positive (SMF) (TMF) (TMF) (TMF) Vey Positive (SMF) Vey Positive (SMF) SSN: SN:

5 COMPUTERS and SMULATON in MOERN SCENCE, Volume - The glucose deviation (J) in (7). - Memoy of the pevious deviation (J d ). - The pevious adjustments Δ and Δ. The input and output chaacteistics ae shown in Table and 7 espectively, including the inteval of vaiation fo each vaiable and the fuzzy sets associated with the type of membeship function used (fuzzication method). y the definition of the input fuzzy set, a total of F-THEN ules wee defined. These ules wee of AN (minimum) type antecedent. The output (defuzzification method) is calculated by the centoid method. The pemise of these ules can be summaized in thee points: - f thee is a tendency fo the glucose deviation to incease above the TGL, then incease the scaling factos. - f thee is a tendency to decease below the TGL, then educe the scaling factos. - f the glucose deviation is in the TGL, then ty to decease the scaling facto without leaving the TGL. A sample of the poposed ules fo the low level module is detailed next: F J d =Negative and J=Negative and Δ d =Zeo and Δ d =Zeo THEN Δ =Negative and Δ =Negative. Simulations The numeical simulation was implemented in MATLA/Simulink using the Fuzzy Logic Toolbox. A total of 5 (T = 3 min) wee simulated with thee meals pe day: beakfast: h, lunch: h, and dinne: h. Thee boluses of insulin ae pogammed pe day by a subcutaneous injection, whee a combination of Regula and NPH insulin is pogammed. The high level module supevises intensively the low level module evey day to adjust the scaling factos. uing the simulation peiod (5 ), a total of doses ae computed. The hypoglycemic weight Γ in () and () was selected to 5 [5 duing the computation of glucose deviation J. At the fist case of ou simulation, the patient stats with small scaling factos fo both types of insulin, poducing small insulin doses and high glucose levels. The algoithm adjusts the insulin dosages in ode to each the TGL. Fo this scenaio, a ± 5 % eo (typical eo in commecial devices) in each of the glucose measuements is assumed. At the second case of ou simulation, in ode to analyze the effect of heavy vaiations in the meal intakes, the patient vaies his cabohydate intake duing meals by 5% fom the nominal ones, using a unifom distibution. Fig. and Fig.3 pesent simulations fo the case and espectively: meal cabohydates intakes, blood glucose concentation, glucose deviation function, and insulin doses. t is obseved that thee is no instability in the system although the measuement eo can be as high as 5%, and meal intakes can have up to 5% vaiation. Hypoglycemia was detected when the GL deceased below mg/dl duing simulations, and no hypoglycemic conditions ae detected. Fo both two cases studied, the advisoy/contol algoithm is able of egulate the plasma glucose aound the TGL despite initially low scaling factos and measuement eos (case ) and vaiable cabohydates intake (case ). 5 Conclusion n this study, a fuzzy logic contolle has been poposed to maintain the nomoglycaemic fo diabetic patient of type. The teatment stategy is based on a fou-daily doses of egula and NPH insulin and which is applied though a subcutaneous oute. n ode to incopoate knowledge about patient teatment, the contolles ae designed using a Mamdani-type fuzzy scheme. Simulation esults with a physiological model of the TM patient show the effectiveness of stuctue fo blood glucose egulation. Hence the esults pesented ae encouaging fo clinical studies, howeve in that case, some othe physiological factos not addessed in the TM mathematical model could affect the actual pefomance, and futhe tuning could be necessay accoding with the esults achieved in each patient. As shown in this pape, the fuzzy logic famewok has the potential to synthesize expet knowledge to teat diseases. Theefoe, the appoach and methodology intoduced could be a valuable tool fo educational puposes. Moeove, in futue wok, the inclusion of an execise egime in the oveall model of the TM patient in ode to have a moe ealistic simulation will be consideed. Refeences: [ CCT,.The effect of intensive teatment of diabetes on the development and pogession of long-tem complications in insulin-dependent diabetes mellitus,. N. Engl. J. Med., vol. 39, pp , 993. [ J. M. ailey and W. M. Haddad,.ug dosing contol in clinical phamacology,. EEE Contol Systems Magazine, vol. 5, no., pp. 35.5, 5. [3 R. ellazzi,.electonic management systems in diabetes mellitus: mpact on patient outcomes,. isease Management & Health Outcomes, vol., no. 3, pp. 59.7, 3. [ R. ellazzi, G. Nucci, and G. Cobelli,.The subcutaneous oute to insulin-dependent diabetes SSN: SN:

6 COMPUTERS and SMULATON in MOERN SCENCE, Volume theapy,. EEE Engineeing in Medicine and iology, vol., pp. 5., junuay/febuay. [5. U. Campos-elgado, R. Femat, M. Hen andez- Odonez, and A. Godillo-Moscoso,.Self-tuning insulin adjustment algoithm fo type diabetic patients based on multi-doses egime,. Applied ionics & iomechanics, vol., no., pp..7, 5. [. U. Campos-elgado, R. Femat, E. Ruiz- Vel azquez, and A. Godillo-Moscoso,.Knowledge-based contolles fo blood glucose egulation in type diabetic patients by subcutaneous oute,. in Poc. of the nt. Symp. on nteligent Cont., Houston, USA, octobe 3. [7 K. Miyako, R. Kuomau, H. Kohno, and T. Haa,.mpoved diabetes contol by using close adjustment algoithms,. Pediatics ntenational, vol., pp. 7.,. [. iankov, H. Hellendoon, and M. Reinfank, An ntoduction to Fuzzy Contol, nd ed. Spinge-Velag elin Heidelbeg, 99. [9 L. X. Wang, A Couse in Fuzzy Systems and Contol. Uppe Saddle Rive, New Jesey: Pentice Hall nc., 997. [ AA,.Standads of medical cae fo patients with diabetes mellitus, iabetes Cae, vol. 5, supplement, pp ,. [ K. Miyako, R. Kuomau, H. Kohno, and T. Haa,.mpoved diabetes contol by using close adjustment algoithms, Pediatics ntenational, vol., pp. 7.,. [ W.R. Puckett. ynamic modelling of diabetes mellitus. Ph Thesis, Univesity of Wisconsin - Madison, 99. NPH insulin doses(u) eviation Function (mg/dl) Cabohydates Content(mg/kg) lood Glucose Concentation(mg/dl) Fig.. Simulation fo a 5 peiod: case beakfast lunch dinne Cabohydates Content(mg/kg) lood Glucose Concentation(mg/dl) Regula insulin doses(u) beakfast lunch dinne time() -beak -lunch i-dinne Regula insulin doses(u) NPH insulin doses(u) eviation Function(mg/dl) Fig. 3. Simulation fo a 5 peiod: case -beak -lunch i-dinne SSN: SN: