Detection of Organ Dysfunction in Type II Diabetic Patients

Transcription

1 211 Amercan Control Conference on O'Farrell Street, San Francsco, CA, USA June 29 - Jul 1, 211 Detecton of Organ Dsfuncton n Tpe II Dabetc Patents O. Vahd, R. B. Gopalun, and K.E. Ko Abstract Tpe II dabetes melltus s characterzed b several abnormaltes n dfferent bod organs such as the pancreas, the lver, muscles and adpose tssues. We have developed a technque to detect the dsfuncton of dfferent organs n a group of tpe II dabetc patents. The detecton of these abnormaltes s performed through euglcemc nsuln clamp and hperglcema clamp appled to a tpe II dabetes model developed n our prevous or [1]. Snce the perpheral nsuln and glucose concentratons are the onl common clncal measurements, e have used a partcle flterng algorthm to estmate the nsuln and glucose concentratons n dfferent parts of the bod. These concentratons reflect the pancreatc nsuln secreton rate as ell as the glucose metabolc rates n the lver, muscles and adpose tssues hch represent the functonal behavor of the correspondng organs. Our results sho that the proposed technque s capable of detectng defcences n the pancreatc nsuln producton, the perpheral glucose uptae, endogenous glucose producton and hepatc glucose uptae rates. The nformaton provded b the algorthm can, therefore, be used to choose a sutable detar program and/or prescrbe an effcent medcaton for tpe II dabetc patents. D I. INTRODUCTION IABETES melltus s characterzed b hgh blood glucose levels due to nsuln producton defcences n the slet beta cells of the pancreas and b the resstance of bod cells aganst the nsuln. Dabetes s one of the deadlest dseases and s the seventh leadng cause of death n the Unted States [2]. Tpe II dabetes or non-nsuln dependent dabetes melltus (NIDDM s the most common tpe of dabetes hch has affected 9% of the dabetes populaton orldde [3]. Multple abnormaltes n dfferent organs lead to the deteroraton of glucose homeostass n tpe II dabetc patents [4]. Resstance of muscles and adpose tssues aganst the secreted nsuln results n loer perpheral absorpton of the blood glucose hch n turn leads to accumulaton of glucose n blood [5]-[12]. Augmented or delaed endogenous glucose producton n dabetc patents due to mpared nsuln-nduced suppresson of hepatc glucose producton s ell documented [1]-[18]. Impared regulator effect of the lver on the glucose concentraton causes abnormal hepatc glucose uptae n tpe II dabetc patents [17]-[2]. Defcenc n pancreatc nsuln producton n response to a glucose stmulus leads to O. Vahd, R.B. Gopalun and K.E. Ko are th the department of chemcal and bologcal engneerng at Unverst of Brtsh Columba, Vancouver, BC, Canada V6T1Z3 (Correspondng author: ; e- mal: ovahd@chbe.ubc.ca. nsuffcent level of plasma nsuln concentratons [21]-[26]. Unle tpe I dabetc patents ho need nsuln njecton to mantan glucose concentraton at normal levels, elevated glucose concentratons n tpe II dabetes ma be controlled at normal levels b regular eercse and sutable detar program; hoever as the dsease progresses, medcaton s requred. Admnstraton of a sutable and effcent medcaton for an ndvdual patent needs accurate nformaton from the patent. In our prevous or [1], e developed a model for a group of tpe II dabetc patents. In the present or, e have appled dfferent tests to the developed model to dagnose and evaluate the abnormal behavor of dfferent organs n the same group. The nformaton obtaned from the tests ma be helpful n choosng a sutable detar program and n admnsterng sutable medcaton for the respectve patents. Dfferent detecton tests are common n dabetes research. We have emploed euglcemc nsuln clamp technque n slco to evaluate the nsuln medated effect on glucose uptae n the lver and perpheral tssues as ell as ts suppresson effect on hepatc glucose producton. Also, hperglcema clamp s appled n slco to nvestgate the glucose suppresson effect on hepatc glucose producton. Earl phase and overall nsuln secreton rate n response to a glucose stmulus are also evaluated through hperglcema clamp. The glucose metabolc rates n the lver, muscles and adpose tssues as ell as the pancreatc nsuln secreton rate represent the behavor of those organs. In order to measure these rates, measurements of glucose and nsuln concentratons n dfferent parts of the bod are needed. Hoever, these measurements requre comple clncal facltes and n some cases ma rs the lfe of the patent. Therefore, clncal measurements of all requred concentratons are not possble. The commonl avalable clncal data nclude perpheral nsuln and glucose concentratons onl. Therefore, e propose usng a Sequental Monte Carlo (SMC flterng method called partcle flters on a nonlnear model of a group of dabetc patents to estmate the glucose and nsuln concentratons n dfferent parts of the bod. These estmates can then be used to measure the glucose metabolc rates n dfferent organs and nsuln secreton rate n the pancreas. Ths paper s organzed as follos. In Secton II, a bref descrpton of the mathematcal model that e have used here s provded. In the follong secton, fundamentals of partcle flterng algorthm are dscussed. The proposed technque for detectng the organ dsfuncton of a group of tpe II dabetc patents s eplaned n secton IV /11/$ AACC 4769

2 II. MATHEMATICAL MODEL In the present or, e have used a detaled compartmental model representng the hormonal effects of nsuln and glucagon on the plasma glucose concentraton n a group of tpe II dabetc patents. Ths model as developed n our prevous or [1]. Our model as based on an earler model proposed b Guton et al. [27] for a health human and modfed b Sorensen [28]. The model contans three sub-models hch represent blood glucose, nsuln and glucagon concentratons n the bod. Each submodel s dvded nto ndvdual compartments representng a specfc part or organ n the human bod. The number of compartments n each sub-model s dfferent. The nsuln sub-model s schematcall depcted n Fg. 1. The glucose sub-model has the same compartments as those of the nsuln sub-model ecept the pancreas compartment hch s not ncluded n the glucose sub-model. The glucagon sub-model treats the hole bod as one compartment. Muscles and adpose tssues are lumped nto the perpher compartment and gastrontestnal tract (ncludng the stomach and the ntestne s represented b the gut compartment. Subcompartments, such as those n the perpher compartment, are consdered here sgnfcant transport resstance beteen the capllares and ntersttal flud space ests [28]. Model equatons comprse mass balance equatons over ndvdual sub-compartments n each sub-model ecept for the pancreas compartment, hch has a separate mathematcal model. Detaled model equatons for a health human bod are provded n [28]. Prevousl, e used a set of clncal data obtaned from a group of tpe II dabetc patents to develop a model based on the Sorenson model. Based on our noledge of tpe II dabetc patents, e chose relevant parameters of the Sorenson model and estmated them usng the clncal data set from the patents. Complete detals on the estmaton of parameters n ths model are provded n [1]. To nvestgate the behavor of dfferent organs n tpe II dabetc patents and detect an abnormaltes, e need to compare the behavor of each organ th the same organ n a normal subject. The nsuln secreton rate from the pancreas and metabolc rates of glucose n dfferent organs reflect the behavor of those organs n response to an glucose stmulus. Comparson of these rates n tpe II dabetc patents th those of a normal subject ll allo us to detect an abnormal behavor of those organs. Snce the perpheral glucose and nsuln concentratons are commonl measured, e have used a partcle flterng algorthm to estmate the glucose and nsuln concentratons n dfferent part of the bod. The advantage of ths method s that ts accurac can be mproved b ncreasng the number of partcles used and moreover, s ndependent of the degree of nonlneart of the model unle etended Kalman flter. A bref descrpton of ths method s provded n the net sesson. In order to appl the partcle flterng algorthm, the nonlnear model n [1] s rertten n a dscrete tme stochastc nonlnear state space format as follos: Fg. 1.Schematc dagram of nsuln compartmental sub-model. ( θ + ν (1 = f 1, u 1, = g(, u, θ + ω (2 here f and g are the state and measurement dnamc functons, respectvel; denotes a tme step; s the vector of states, u s the vector of nputs and s the vector of measurements; θ denotes a vector of model parameters hch are constant values; ν and ω are state and measurement nose sequences th non probablt denst functons (PDF th zero mean. We assume that the state and measurement noses affect the model n a lnear manner. The states of the model correspond to the nsuln and glucose concentratons n dfferent organs of the bod. Our mathematcal model contans 22 states and to measurements. Therefore, szes of and are respectvel 22 and 2. The model nputs are the glucose and nsuln nfuson rates to the bod and therefore, the sze of u s 2. III. PARTICLE FILTERS A SEQUENTIAL MONTE CARLO METHOD The Sequental Monte Carlo (SMC approach s a recursve Baesan estmaton method for nonlnear and non- Gaussan flterng problems. The basc frameor of the SMC approach s presented belo. A. Recursve Baesan Estmaton The SMC approach n flterng problems s based on calculaton of the probablt denst functon of the model states at the current tme step (.e., gven a sequence of the measurements up to tme (.e. 1: ={ 1, 2,..., }. The 477

3 Baesan soluton to ths flterng problem s to calculate the probablt denst functon (PDF of gven 1:, 1:, for each teraton. The denst 1: s calculated recursvel nto to steps - predcton and update. In the predcton step, the PDF of s calculated gven the sequence of the measurements up to tme -1 through the follong equaton: p ( 1: 1 = 1 1 1: 1 d 1 (3 In the update step, the denst 1: s calculated va the follong equaton: 1: 1 1: = (4 1: 1 It s assumed that the PDF of the ntal tme step,, s non. Equatons (3 and (4 do not have analtcal solutons ecept for lnear processes th Gaussan nose. In most cases the ntegrals n equaton (3 are comple and ntractable. For general non-lnear, non-gaussan sstems descrbed b equatons (1 and (2, there s no smple a to proceed. The sequental Monte Carlo algorthms mae these comple ntegrals tractable through the use of effcent samplng strateges [29], [3]. B. Sequental Monte Carlo Salmond et al. [31] ntroduced Sequental Monte Carlo methods for the frst tme n 1993 and later on the SMC algorthm has been further developed and adapted to man dfferent applcatons [3]. It has appeared n the lterature n dfferent names such as bootstrap flterng [31], partcle flterng [32] and nteractng partcle appromatons [33]. The basc dea of SMC follos the frameor of Baesan recursve estmaton descrbed above. In ths approach the recursve computaton of relevant probablt dstrbutons s accomplshed usng the concepts of mportance samplng and appromaton of probablt dstrbutons b a set of random samples th assocated eghts. Consderng the model equatons represented b equatons (1 and (2, the Baesan recursve estmaton s appled va a SMC algorthm nstead of analtcall solvng the equatons (3 and (4. At each tme step, to peces of nformaton are requred for estmatng the PDF: the samples and ther assocated eghts. Samples are assumed to be generated from a non PDF called mportance denst functon, q( 1:. Then, the correspondng eghts of the samples are calculated from the follong equaton: 1: = (5 q( 1: and the eghts after normalzaton are: = N (6 = 1 here N s the number of partcles used. If the mportance denst functon s chosen to be factorzed such that: q( 1: = q( 1, 1: q( 1 1: 1 (7 then the samples at tme step, ~ q( 1:, are computed b multplng the estng samples, -1 ~ q( -1 1:-1, and the ne state, ~ q( -1, 1:. The correspondng eghts are updated usng the follong equaton: 1 1 (8 q(, 1 1: In common cases hen onl a fltered estmate of 1: s requred, t s useful to assume that q( -1, 1: = q( -1, and then, the mportance denst onl depends on -1 and. Under ths assumpton, equaton (8 can be rertten as: 1 1 (9 q(, 1 and the fltered denst 1: can be appromated b the follong equaton: p N ( 1 : δ ( (1 = 1 here δ s the Drac delta functon, s the th sample that appromates the dstrbuton, and the coeffcent s the correspondng eght. As N, the above denst appromaton approaches the true fltered denst 1:. IV. DETECTION OF ORGAN DYSFUNCTION There are some technques that are commonl used n dabetes research to evaluate ho ell an ndvdual metabolzes glucose, ho ell an ndvdual s bod responds to glucose, and ho resstant an ndvdual s aganst nsuln. Glucose clamp s a commonl used technque proposed b Defronzo et al. [34] n The proposed to tpes of clamps called hperglcema clamp and euglcemc nsuln clamp hch have been del used n dabetes research. We have appled these to tests n slco to detect and evaluate the defcences (f the est n dfferent organs of a group of tpe II dabetc patents usng the model of tpe II dabetes developed for these patents. The same tests have also been appled to the Sorensen model to obtan smlar nformaton on a health subject. Comparng the glucose and nsuln concentratons n dfferent organs of dabetc patents th those obtaned from health ndvduals ll provde nsght nto an organ defcences n the patents. The flterng algorthm as mplemented th 25 partcles n all tests. A. Euglcemc nsuln clamp Ths technque as developed b Defronzo et al. [34] n In ths technque, the plasma nsuln concentraton s rased and clamped at around mu/l b a contnuous nfuson of nsuln. At the same tme, the plasma glucose concentraton s held constant at basal levels b glucose njecton va a negatve feedbac prncple. At stead state condtons, snce the endogenous glucose producton s decreased to a neglgble level, the rate of glucose nfuson s appromatel equal to rate of glucose uptae b all bod tssues and s therefore a measure of tssue nsuln senstvt. The nformaton obtaned from partcle flterng 4771

4 Perperal Glucose Uptae Rate (mg/mn Hepatc Glucose Uptae Rate (mg/mn Hepatc Glucose Producton Rate (mg/mn Tme (mn Tme (mn Tme (mn Fg. 2. Varatons of dfferent glucose metabolc rates durng the euglcemc nsuln clamp, NIDDM ( and normal subjects ( -- helps n measurng the uptae rate of glucose n dfferent organs hch n turn ll allo us to determne the senstvt of that organ to nsuln. In our prevous or, e used the data provded b Nagasaa et al. [35] to develop our model. The same basal condtons for both control subjects and dabetc patents are used here. The perpheral nsuln and glucose concentratons at the basal condton for the dabetc group ere reported to be 4.5 ±. 4 mu/l and 117 ± 7 mg/dl, respectvel. The correspondng values reported for control subjects ere 5.1±.3 mu/l and 91 ± 8 mg/dl for the perpheral nsuln and glucose concentratons, respectvel. To perform euglcemc nsuln clamp, the rate of nsuln nfuson s set to mu/mn and mu/mn, and the glucose nfuson rate s set to 27.8 mg/mn and mg/mn for the dabetc patents and control subjects, respectvel. These values are obtaned b tral and error to mantan the nsuln concentratons at mu/l and the glucose concentratons at ts basal value. Consderng the decreased rate of endogenous glucose producton due to hpernsulnema, the overall glucose nfuson rate shos that the overall senstvt of the bod to nsuln s decreased b appromatel 63% n dabetc patents. It reflects sever nsuln resstance n ther bod tssues. To evaluate the nsuln senstvt n dfferent parts of the (a (b (c Perpheral Glucose Uptae Rate (mg/mn Hepatc Glucose Uptae Rate (mg/mn Hepatc Glucose Producton Rate (mg/mn Tme (mn Tme (mn Tme (mn Fg. 3. Varatons of dfferent glucose metabolc rates durng the hperglcemc clamp, NIDDM ( and normal subjects ( -- bod, the glucose metabolc rates n perpheral tssues and the lver are provded n Fg. 2. Accordng to Fg. 2 (a, the perpheral glucose uptae rate s decreased b appromatel 63% due to lo nsuln senstvt n perpheral tssues. The same appromate amount of decrease n glucose uptae rate s observed n the lver (see Fg. 2 (b. It shos that the nsuln senstvt of perpheral tssues and the lver s mpared at the same level n the group of dabetc patents. Fg. 2 (c ndcates that the nsuln-nduced suppresson of hepatc glucose producton at hpernsulnema condton s not mpared n the group of dabetc patents. Our results are n agreement th the dscusson b Defronzo [4] hch ndcates normal suppresson of hepatc glucose producton due to hpernsulnema over phsologcal range (~ mu/l. Nevertheless, Defronzo [4] has argued that the doseresponse curve shong the relatonshp beteen hepatc glucose producton and the plasma nsuln concentraton s shfted to the rght hch ndcates relatve resstance to the suppresson effect of the nsuln on hepatc glucose producton at phsologcal concentratons B. Hperglcemc clamp Ths technque as also proposed b Defronzo et al. [34] n In ths technque, the plasma glucose concentraton s rased and mantaned at 125 mg/dl above basal levels b a (c (a (b 4772

5 Perpheral Insuln Concentraton (mu/l Perpheral Glucose Concentraton (mg/dl contnuous nfuson of glucose. Snce the plasma glucose concentraton s clamped at hperglcema level, the glucose nfuson rate s an nde of nsuln secreton capact and also shos ho the glucose s metabolzed. More detaled nformaton about the pancreatc nsuln secreton rate and ts acuteness n response to a glucose stmulus can be obtaned from the flterng results. Here, the perpheral nsuln and concentratons at basal condton are the same as prevous secton. Hperglcema clamp s performed for both groups of dabetc patents and control subjects at a glucose nfuson rate of 33.8 mg/mn for dabetc patents and 1229 mg/mn for control subjects. The values for glucose nfuson rates are obtaned b tral and error to mantan the perpheral glucose concentratons at 125 mg/dl above the basal level for both groups. The glucose nfuson rate of the dabetc group shos that the hole bod absorpton of glucose s sgnfcantl lo th respect to normal subjects. Euglcemc nsuln clamp technque ndcated that ths group of patents had hgh resstance aganst nsuln. In the current eperment, lo nsuln senstvt of the patents s supplemented b the lo plasma nsuln concentraton due to the defcences n the pancreatc nsuln secreton. These to factors together have Insuln Secreton Rate (mu/mn Tme (mn Tme (mn Fg. 4 Perpheral nsuln and glucose concentratons durng hperglcema clamp, NIDDM ( and health bod ( Tme (mn Fg. 5. Pancreatc nsuln secreton rate durng hperglcemc clamp, NIDDM ( and health bod ( -- (a (b Insuln Secreton Rate (mu/mn Tme (mn Fg. 6. Earl phase of pancreatc nsuln secreton rate due to glucose nfuson for 5 mg/mn, NIDDM ( and health bod ( -- resulted n sgnfcantl loer overall bod glucose uptae n the dabetc group. As Fg. 3 (a and (b sho, the perpheral glucose uptae rate and the hepatc glucose uptae rate of the dabetc group are appromatel 8% loer than the correspondng values for the normal group. Agan, t suggests the same nsuln resstance n perpheral tssues and the lver of the dabetc group. Accordng to Fg. 3 (c, the hepatc glucose producton n both groups of dabetc patents and normal subjects s suppressed sgnfcantl due to the ncrease n plasma glucose concentratons. It suggests normal glucose-nduced suppresson of hepatc glucose producton n the dabetc group hch agrees th the nvestgatons b Del Prato et al. [36] and Nelsen et al. [37]. Snce the plasma glucose concentraton has rsen faster n the normal group than that of dabetc patents (Fg. 4 (b, suppresson of hepatc glucose producton s faster n the normal group. As Fg. 3 (c shos, the fnal amount of suppresson s hgher n the normal group than that of the dabetc group due to loer plasma nsuln concentratons (Fg 4 (a and due to the nsuln resstance at lo nsuln concentratons. It s consstent th the results dscussed n the prevous secton. The hperglcema clamp results also ndcate defected pancreatc nsuln secreton n the dabetc group. As Fg. 5 shos, the pancreatc nsuln secreton rate s reduced b appromatel 6% n ths dabetc group hch n turn resulted n lo plasma nsuln concentratons (see Fg 4 (a. Snce the magntude of eogenous glucose stmulus durng the hperglcema clamp s not the same for both dabetc and normal groups, the profle of pancreatc nsuln secreton rate (Fg 5 ll not reflect the actual defcenc n the earl phase of nsuln secreton. Therefore, another glcemc clamp s performed to compare the earl phase nsuln secreton rate for both groups. Fg. 6 shos the frst mn of the pancreatc nsuln secreton rate due to 5 mg/mn glucose nfuson for both dabetc and normal subjects. As epected, the earl phase pancreatc nsuln secreton rate s reduced b about 65% n the dabetc group th respect to the normal group. V. CONCLUSION In ths stud, e used a model of a group of tpe II dabetc patents developed n our prevous or to dagnose the defcences n ther bodes. We emploed partcle 4773

6 flterng method to estmate the model states as ell as the glucose metabolc rates n dfferent organs and pancreatc nsuln secreton rate. Abnormal behavor of dfferent organs s detected va euglcemc nsuln clamp and hperglcema clamp n slco. Implementaton of these technques together th a mathematcal model and a nonlnear flterng method s effcent n detectng the abnormaltes n the lver, the pancreas and perpheral tssues of tpe II dabetc patents. REFERENCES [1] O. Vahd, K. E. Ko, R. B. Gopalun, and L. Sun, " Developng a phsologcal model for tpe II dabetes melltus," Bochem. Eng. J, n Press, 211 [2] Natonal Dabetes Informaton Clearnghouse. Avalable at: [3] World Health Organzaton. Avalable at: [4] R. A. Defronzo, Pathogeness of tpe 2 dabetes melltus, Med. Cln. N. Am., vol. 88, pp , 4. [5] E. Ferrannn, D. C. Smonson, L. D. Katz, G. Rechard, S. Bevlacqua, E. J. Barrett, M. Olsson, R. A. DeFronzo, The dsposal of an oral glucose load n patents th non-nsuln-dependent dabetes, Metabolsm, vol. 37, pp , [6] R.A. DeFronzo, R.C. Bonadonna, E. Ferrannn, Pathogeness of NIDDM. A balanced overve, Dabetes Care, vol. 15, pp , [7] L. C. Groop, E. Wden, E. Ferrannn, Insuln resstance and nsuln defcenc n the pathogeness of tpe 2 (non-nsuln-dependent dabetes melltus: errors of metabolsm or of methods, Dabetologa, vol. 36, pp , [8] A Basu, A Alzad, S Dnneen, A Caumo, C Cobell, R A Rzza, Effects of a change n the pattern of nsuln delver on carbohdrate tolerance n dabetc and nondabetc humans n the presence of dfferng degrees of nsuln resstance, J. Cln. Invest., vol. 97, pp , [9] A. Basu, R. Basu, P. Shah, A. Vella, C.M. Johnson, K.S. Nar, M.D. Jensen, W.F. Schen, R.A. Rzza, Effects of tpe 2 dabetes on the ablt of nsuln and glucose to regulate splanchnc and muscle glucose metabolsm. Evdence for a defect n hepatc gluconase actvt, Dabetes, vol. 49, pp ,. [1] P. J. Campbell, L. J. Mandarno, J. E. Gerch, Quantfcaton of the relatve mparment n actons of nsuln on hepatc glucose producton and perpheral glucose uptae n non-nsuln-dependent dabetes melltus, Metabolsm, vol. 37, pp , [11] R. A. DeFronzo, E. Ferrannn, D. C. Smonson, Fastng hperglcema n non-nsuln-dependent dabetes melltus: contrbuton of ecessve hepatc glucose producton and mpared tssue glucose uptae, Metabolsm, vol. 38, pp , [12] A. Mtraou, D. Kelle, T. Veneman, T. Jenssen, T. Pangburn, J. Rell, J. Gerch, Contrbuton of abnormal muscle and lver glucose metabolsm to postprandal hperglcema n NIDDM, Dabetes, vol. 39, pp , 199. [13] A. Consol, N. Nurjhan, F. Capan, J. Gerch, Predomnant role of gluconeogeness n ncreased hepatc glucose producton n NIDDM, Dabetes, vol. 38, pp , [14] A. A. Alzad, S. F. Dnneen, D. J. Tur, A. Caumo, C. Cobell, R. A. Rzza, Assessment of nsuln acton and glucose effectveness n dabetc and nondabetc humans, J. Cln. Invest., vol. 94, pp , [15] R. Basu, W. F. Schen, R. A. Rzza, Both fastng glucose producton and dsappearance are abnormal n people th mld and severe tpe 2 dabetes, Am. J. Phsol. Endocrnol. Metab., vol. 287 pp , 4. [16] R. Basu, V. Chandramoul, B. Dce, B. Landau, R. Rzza, Obest and tpe 2 dabetes mpar nsuln-nduced suppresson of glcogenolss as ell as gluconeogeness, Dabetes, vol. 54, pp , 5. [17] R. Basu, A. Basu, C. M. Johnson, W. F. Schen, R. A. Rzza1, Insuln Dose-Response Curves for Stmulaton of splanchnc glucose uptae and suppresson of endogenous glucose producton dffer n nondabetc humans and are abnormal n people th tpe 2 dabetes, Dabetes, vol. 53, pp , 4. [18] A. Basu, C. D. Man, R. Basu, G. Toffolo, C Cobell, R.A. Rzza, Effects of tpe 2 dabetes on nsuln secreton, nsuln acton, glucose effectveness, and postprandal glucose metabolsm, Dabetes Care, vol. 32, pp , 9. [19] P. Iozzo, K. Hallsten, V. Oonen, K.A. Vrtanen, J. Kemppanen, O. Soln, E. Ferrannn, J. Knuut, P. Nuutla, Insuln-medated hepatc glucose uptae s mpared n tpe 2 dabetes: evdence for a relatonshp th glcemc control, J. Cln. Endocrnol. Metab., Vol. 88, pp , 3. [2] R. Borraa, R. Lautamä, R. Parolaa, M. Komu, P. E. Sjens, K. Hällsten, J. Bergman, P. Iozzo, P. Nuutl, Inverse assocaton beteen lver fat content and hepatc glucose uptae n patents th tpe 2 dabetes melltus, Metab. Cln. Ep., vol. 57 pp , 8. [21] M. A. Pfeffer, J. B. Halter, D. Porte, Insuln secreton n dabetes melltus, Am. J. Med., vol. 7, pp , [22] K. S. Polons, B. D. Gven, L. J. Hrsch, H. Tlll, E. T. Shapro, C. Beebe, B. H. Fran, J. A. Galloa, E. V. Cauter, Abnormal patterns of nsuln secreton n non-nsuln-dependent dabetes melltus, N. Engl. J. Med., vol. 318, pp , [23] L Luz and R. A. DeFronzo, Effect of loss of frst-phase nsuln secreton on hepatc glucose producton and tssue glucose dsposal n humans, Am. J. Phsol. Endocrnol. Metab., vol. 257, pp. E241- E246, [24] C. Weer, C. Bogardus, D. M. Mott, R. E. Pratle, The natural hstor of nsuln secretor dsfuncton and nsuln resstance n the pathogeness of tpe 2 dabetes melltus, J.Cln. Invest., vol. 14, pp , [25] J. L. Leah, Pathogeness of Tpe 2 Dabetes Melltus, Arch. Med. Res., vol. 36, pp , 5. [26] P.J. Gullausseau, T. Meas, M. Vrall, M. Lalo-Mcheln, V. Médeau, J.P. Kevoran, Abnormaltes n nsuln secreton n tpe 2 dabetes melltus, Dabetes Metab., vol. 34, pp. S43-S48, 8. [27] J. R. Guton, R. O. Foster, J. S. Soeldner, M. H. Tan, C. B. Kahn, L. Koncz, R. E. Gleason, A model of glucose-nsuln homeostass n man that ncorporates the heterogeneous fast pool theor of pancreatc nsuln release, Dabetes, vol. 27, pp , [28] J. T. Sorensen, A phsologcal model of glucose metabolsm n man and ts use to desgn and assess mproved nsuln therapes for dabetes, PhD Thess, Massachusetts Insttute of Technolog, [29] A. Doucet, S. Godsll, and C. Andreu, On sequental monte carlo samplng methods for baesan flterng, Statst. Comput., vol. 1, pp ,. [3] S. Masell M. Arulampalam and N. Gordon, A tutoral on partcle flters for onlne nonlnear/non-gaussan baesan tracng, IEEE Trans. Sg. Proc., vol. 5, pp , 2. [31] D. Salmond N. Gordon and A. Smth, Novel Approach to Nonlnear/Non-Gaussan Baesan State Estmaton, Radar Sgnal Process., IEE Proc. F, vol. 14, pp , [32] J. Carpenter, P. Clfford, and P. Fearnhead An mproved partcle flter for non-lnear problems, Radar Sonar Navg., IEE Proc., vol. 146, pp. 2 7, [33] D. Crsan, P. Del Moral, and T. Lons Interactng partcle sstems appromatons of the ushner stratonovtch equaton Adv. Appl. Prob., vol. 31, pp , [34] R. A. DeFronzo, T. D. Tobn, and R. Andres, Glucose Clamp Technque: a Method for Quantfng Insuln Secreton and Resstance. Am. J. Phsol., vol. 237, pp. E214 E223, [35] S. Nagasaa, K. Touama, I. Kusaa, H. Haash, K. Roau, T. Naamura, A. Kaaam, M. Hgashama, S. Ishaa, T. Sato, Endogenous glucose producton and glucose effectveness n tpe 2 dabetc subjects derved from stable-labeled mnmal model approach Dabetes, vol. 48, pp , [36] S. Del Prato, M. Matsuda, D.C. Smonson, L.C. Groop, P. Sheeha, F. Leonett, R.C. Bonadonna, R.A. DeFronzo, Studes on the mass acton effect of glucose n NIDDM and IDDM: evdence for glucose resstance, Dabetologa, vol. 4, pp , [37] M F Nelsen, R Basu, S Wse, A Caumo, C Cobell and R A Rzza, Normal glucose-nduced suppresson of glucose producton but mpared stmulaton of glucose dsposal n tpe 2 dabetes: evdence for a concentraton-dependent defect n uptae, Dabetes, vol. 47, pp ,