J Pharmacokinet Pharmacodyn (2011) 38:713–725
`DOI 10.1007/s10928-011-9216-2
`
`Mechanism-based population modelling for assessment
`of L-cell function based on total GLP-1 response
`following an oral glucose tolerance test
`
`Jonas B. Møller • William J. Jusko • Wei Gao •
`Torben Hansen • Oluf Pedersen • Jens J. Holst •
`Rune V. Overgaard • Henrik Madsen •
`Steen H. Ingwersen
`
`Received: 13 December 2010 / Accepted: 8 September 2011 / Published online: 16 September 2011
`Ó Springer Science+Business Media, LLC 2011
`
`Abstract GLP-1 is an insulinotropic hormone that synergistically with glucose
`gives rise to an increased insulin response. Its secretion is increased following a
`meal and it is thus of interest to describe the secretion of this hormone following an
`oral glucose tolerance test (OGTT). The aim of this study was to build a mecha-
`nism-based population model that describes the time course of total GLP-1 and
`provides indices for capability of secretion in each subject. The goal was thus to
`model the secretion of GLP-1, and not its effect on insulin production. Single 75 g
`doses of glucose were administered orally to a mixed group of subjects ranging from
`healthy volunteers to patients with type 2 diabetes (T2D). Glucose, insulin, and total
`GLP-1 concentrations were measured. Prior population data analysis on measure-
`ments of glucose and insulin were performed in order to estimate the glucose
`absorption rate. The individual estimates of absorption rate constants were used in
`the model for GLP-1 secretion. Estimation of parameters was performed using the
`FOCE method with interaction implemented in NONMEM VI. The final transit/
`
`J. B. Møller (&) R. V. Overgaard S. H. Ingwersen
`Quantitative Clinical Pharmacology, Novo Nordisk A/S, Søborg, Denmark
`e-mail: jbem@novonordisk.com
`W. J. Jusko W. Gao
`Department of Pharmaceutical Sciences, State University of New York at Buffalo,
`Buffalo, NY, USA
`T. Hansen O. Pedersen
`Hagedorn Research Institute, Gentofte, Denmark
`
`J. J. Holst
`Department of Medical Physiology, Panum Institute, University of Copenhagen,
`Copenhagen, Denmark
`
`H. Madsen
`Department of Informatics and Mathematical Modelling, Technical University of Denmark,
`Lyngby, Denmark
`
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`indirect-response model obtained for GLP-1 production following an OGTT
`included two stimulation components (fast, slow) for the zero-order production rate.
`The fast stimulation was estimated to be faster than the glucose absorption rate,
`supporting the presence of a proximal–distal loop for fast secretion from L-cells. The
`fast component (st3 = 8.64 10-5 [mg-1]) was estimated to peak around 25 min
`after glucose ingestion, whereas the slower component (st4 = 26.2 10-5 [mg-1])
`was estimated to peak around 100 min. Elimination of total GLP-1 was charac-
`terised by a first-order loss. The individual values of the early phase GLP-1
`secretion parameter (st3) were correlated (r = 0.52) with the AUC(0–60 min.) for
`GLP-1. A mechanistic population model was successfully developed to describe
`total GLP-1 concentrations over time observed after an OGTT. The model provides
`indices related to different mechanisms of subject abilities to secrete GLP-1. The
`model provides a good basis to study influence of different demographic factors on
`these components, presented mainly by indices of the fast- and slow phases of GLP-
`1 response.
`Keywords GLP-1 L-cells Oral glucose tolerance test (OGTT)
`Indirect response model NONMEM
`
`Introduction
`
`Type 2 diabetes (T2D) is a result of decreased insulin sensitivity combined with
`decreased beta-cell function. The beta-cell function is described by the ability of the
`beta-cells to provide an insulin response to a given glucose load.
`One of the main determinants of beta-cell function is the presence of the
`insulinotropic hormone glucagon-like-peptide 1 (GLP-1) [1, 2] in combination with
`glucose. More specifically Brandt et al.
`[2] demonstrated in vivo glucose
`dependency of the action of postprandial physiological concentrations of GLP-1
`in healthy subjects over the plasma glucose range of 5–10 mM.
`GLP-1 is a gut derived peptide secreted from intestinal L-cells [3] and circulating
`levels increase after a meal or an oral glucose load [4, 5]. It is derived from a
`transcription product of the proglucagon gene and the active molecule is identified
`as GLP-1 (7–36). Once in the circulation it has a very short half-life estimated to be
`around 2–3 min in healthy volunteers [4].
`The GLP-1 response in terms of area under the curve from 0 to 240 min. after the
`start of the meal is significantly decreased in most patients with type 2 diabetes [6].
`Combined with the finding that the short half-life of GLP-1 does not seem to differ
`in healthy volunteers and patients with T2D [1], this suggests that the decreased
`GLP-1 response observed in patients with T2 diabetes is due to a lower post-
`prandial secretion. This also seems to be the case comparing patients with impaired
`glucose tolerance (IGT) and healthy volunteers [5]. In general we believe that
`analysis of the GLP-1 response observed after an OGTT would be valuable in
`understanding the mechanisms underlying the post-prandial secretion profile.
`The overall aim of this study was to develop a mechanism-based population
`model providing descriptive indices of the observed GLP-1 secretion following an
`
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`OGTT. The goal was thus not to model the GLP-1 effect on insulin secretion, but
`rather to build a model providing indices for capability of GLP-1 secretion. Based
`on the mechanisms of action, we propose to model the stimulation of GLP-1, using
`an indirect response model [7]. Compared to earlier non-compartmental analysis (as
`in [8]) of the GLP-1 secretion profiles observed after an OGTT, a compartmental
`population model approach takes into account variability in measurements and time
`(compartmental) and variability between subjects (population). This kind of model
`further provides a good basis for
`future inclusion of covariates (such as
`demographic factors) on obtained model parameters.
`
`Methods
`
`Study participants
`
`The data applied in this study is a subset of the dataset originally described in [9]. In
`this study available plasma GLP-1 profiles obtained after an oral glucose load are
`included. Only full profiles were included and seven profiles were removed because
`of erratic behaviour inconsistent with basic physiology and the dynamics of the rest
`of the population. The cleaned dataset applied here thus consisted of samples taken
`from 135 individuals distributed as presented in Table 1. The classification of
`individuals was categorized according to concentrations of plasma glucose (FPG)
`fasting and 2 h after glucose ingestion (OGTT120) measured in mmol/L. The
`classification criteria, agreed with the ones described in [10]. The study was
`approved by the Ethical Committee of Copenhagen and was in accordance with the
`principles of the Declaration of Helsinki.
`
`Study conditions
`
`All participants underwent a standardized and extended 75-g frequently sampled
`OGTT. After a 12-h overnight fast, venous blood samples were drawn in duplicate
`at -30, -10, 0 before the glucose intake and then at 10, 20, 30, 40, 50, 60, 75, 90,
`105, 120, 140, 160, 180, 210, 240. Plasma glucose and serum insulin were
`measured. The plasma glucose concentration was analyzed by a glucose oxidase
`method (Granutest; Merck, Darmstadt, Germany). Serum insulin was determined by
`
`Table 1 Mean and standard deviation (SD) of demographics of study subjects
`
`Normal
`
`IFG-IGT-T2D
`
`Total
`
`135
`
`42.3 (11.6)
`
`95.3 (10.5)
`
`6.26 (4.6)
`
`5.26 (3.2)
`
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`
`Subjects
`
`Number
`
`Age [yr]
`Fasting plasma glucose [mg dl-1]
`Fasting plasma insulin [pmol l-1]
`Fasting plasma GLP-1(total) [pmol l-1]
`
`117
`
`41.8 (11.4)
`
`93.0 (8.1)
`
`5.43 (3.1)
`
`5.35 (3.3)
`
`18
`
`45.6 (12.7)
`
`109.8 (13)
`
`11.66 (8.4)
`
`4.61 (2.6)
`
`IFG Impaired fasting glucose, IGT Impaired glucose tolerance, T2D Type 2 diabetics
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`enzyme-linked immunoadsorbent assay with a narrow specificity excluding des (31,
`32)-proinsulin and intact proinsulin (DAKO Diagnostics, Ely, UK) [11].
`Fasting plasma GLP-1 were analysed in duplicate and at single measurements
`post glucose load at time points 10, 20, 30, 40, 60, 90, 120, 180, and 240 min. All
`blood samples for GLP-1 analysis were kept on ice, and the protease inhibitor
`aprotinin (Novo Nordisk, Denmark) was added in a concentration of 0.08 mg/ml
`blood. The GLP-1 concentrations were measured after extraction of plasma with
`70% ethanol (vol/vol). The plasma concentrations of GLP-1 were measured [12]
`using standards of synthetic GLP-1 7–36 amide using antiserum code no. 89390,
`which is specific for the amidated C-terminus of GLP-1 and therefore mainly reacts
`with GLP-1 derived from the intestine. The results of the assay reflect the rate of
`secretion of GLP-1 because the assay measures the sum of intact GLP-1 and the
`primary metabolite, GLP-1 9–36 amide, into which GLP-1 is rapidly converted [13].
`The assay sensitivity was below 1 pmol/l, intra-assay coefficient of variation below
`0.06 at 20 pmol/l, and recovery of standard added to plasma before extraction was
`100% when corrected for losses inherent in the plasma extraction procedure. Very
`few samples were under the LLOQ, and these were not included in analysis.
`
`Non-compartmental analysis
`
`The individual incremental areas under the curve for GLP-1 were calculated using a
`linear up/linear down trapezoidal method. Peak AUCs identified in the report as
`AUCPGLP-1 were calculated as incremental AUCs up to 60 min. The software
`S-plus was used for this part of the analysis.
`
`Compartmental population modelling
`
`For preliminary analysis, the absorption rate constant (ka) of glucose was obtained
`from glucose and insulin data by applying the model presented by Lima et al. [14],
`using two compartments for description of absorption rate according to Eq. (3) and
`(4). This was done in order not to bias the estimation of this parameter towards the
`fitting of GLP-1.
`Baseline GLP-1 values were calculated as the average from pre-dose samples for
`each individual. Considering the fact that the inclusion of these baseline values as
`either fixed or estimated can influence the bias of other parameters [15], we
`implemented these values as either fixed, fixed with a variance, or estimated. In
`general the GLP-1 data was modelled using a population model build in NONMEM
`VI using the FOCE Inter method. Model selection was based on individual/
`population predicted profiles, variance and independence of residuals, and obtained
`objective function value (OFV), and inspection of visual predictive check (VPC).
`
`Structural model
`
`The final structural models for glucose/insulin and secretion of GLP-1 are presented
`in Fig. 1. The glucose/insulin model was applied in order to obtain estimates of
`glucose absorption rate. The model for the GLP-1 secretion reflects an indirect
`
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`
` (A)
`
`Glucose
`dose
`
`A2
`
`kin_Gluc
`
`A3
`
`ka
`
`Glucose
`Abs.rate
`
`ka
`
`Glucose
`above basal
`
`kout_Gluc
`
` (B)
`Glucose
`Abs.rate
`
`Glucose
`Dose
`(Signal)
`
`A4
`
`A1
`
`kb
`
`kc
`
`st1
`
`st2
`
`kin_Ins
`
`Insulin
`above basal
`
`kout Ins
`
`A5
`
`. . .
`
`A7
`
`kb
`
`S2
`
`kb
`
`S1
`
`kc
`
`st3
`
`kin_GLP1
`
`st4
`
` Total GLP-1
`
`Fig. 1 a Diagram of glucose/insulin model for estimation of glucose absorption rate constant, b GLP-1
`secretion model. Absorption rate for glucose is identical to that estimated in the glucose/insulin model.
`Symbols are defined in Table 2
`
`response model with zero-order input and first-order loss. The zero-order input was
`found to be stimulated by two mechanisms differentiated by time of onset. The first
`part was estimated to be faster than the absorption of glucose and caused a peak in
`the GLP-1 concentration around 40 min as also identified in [16]. The ingestion
`signal was included as being proportional to the glucose dose size as:
`¼ kc A1; A1ð0Þ ¼ Dose
`
`ð1Þ
`
`dA1
`dt
`¼ kc A1 kc S1;
`dS1
`dt
`
`S1ð0Þ ¼ 0
`
`ð2Þ
`
`where 1/kc [min] determines the length of the signal caused by the intake of the
`amount of glucose, defined by Dose. The A1 and S1 define the first and second transit
`compartments in the early response signal originating from ingestion of glucose.
`The second part was related to a delayed version of the absorption of glucose in gut.
`The delay was implemented with the use of transit compartments.
`The optimal number of transit compartments for description of the delay was
`determined based on an explicit solution [17] together with the obtained OF Vs.
`
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`From the obtained number of compartments and rate constants, this signal was
`identified to peak around 100 min. The equations below define the glucose
`absorption rate (ka A3) and the stimulus of GLP-1 production related to the
`absorption rate (S2).
`
`¼ ka A2;
`
`A2ð0Þ ¼ Dose f
`
`¼ ka A2 ka A3; A3ð0Þ ¼ 0
`
`¼ ka A3 kb A4; A4ð0Þ ¼ 0
`
`¼ kb A4 kb A5; A5ð0Þ ¼ 0
`
`dA2
`dt
`dA3
`dt
`dA4
`dt
`dA5
`dt
`
`ð3Þ
`
`ð4Þ
`
`ð5Þ
`
`ð6Þ
`
`.
`..
`¼ kb A6 kb S2;
`
`S2ð0Þ ¼ 0
`
`dS2
`dt
`The value of f was fixed to 0.722 based on the bioavailability of glucose observed
`from an OGTT in healthy subjects [18].
`Specifically A2 presents the glucose at absorption site, and ka A3 the glucose
`absorption rate as stated above. The absorption rate constant ka was estimated using
`the compartment absorption structure of glucose (A2 and A3) connected to an
`indirect response model for the interaction between glucose and insulin [14], see
`Fig. 1. The rate constant kb defines the delay between glucose absorption rate and
`stimulation of late-phase GLP-1 secretion. The S2 thus defines the signal related to
`stimulation of GLP-1 production by glucose absorption.
`The elimination of GLP-1 was implemented as a first-order process. In total, the
`concentration of total GLP-1 following the OGTT is described by
`¼ kin GLP1 1 þ st3 S1 þ st4 S2
`½
`Š kout GLP1 CGLP1;
`dCGLP1
`dt
`CGLP1ð0Þ ¼ BGLP1
`where kin_GLP1 (pmol l-1 min-1) is the endogenous production rate of GLP-1 and
`kout_GLP1 (min-1) the first-order rate constant of GLP-1 elimination with the steady-
`state condition defined by
`
`ð7Þ
`
`ð8Þ
`
`kin GLP1 ¼ BGLP1 kout GLP1
`where BGLP1 is the baseline level of GLP-1. The parameters st3 and st4 present first-
`and second-phase stimulation factors related to the first- and second phase
`stimulation signals (S1 and S2).
`
`ð9Þ
`
`Individual model
`
`Inclusion of Inter-individual variability (IIV) was done according to a log-normal
`distribution of individual parameters. The IIV was included for all estimated
`
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`
`parameters except kout_GLP1 which is experimentally found not to vary significantly
`between subjects [1]. Due to a high correlation, the same random effect was used for
`st3 and st4, and these were estimated according to
`ð10Þ
`st3 ¼ h1 expðg1Þ
`ð11Þ
`st4 ¼ h2 expðj g1Þ
`where h1 is the typical value of st3 and g1 the random effects parameter related to
`the inter-subject variability of st3 and similar for st4. Note that the inter-variability
`between the individual estimates of st4 is proportional to the inter-variability of the
`st3 estimates using the constant j.
`
`Residual error model
`
`Additive, proportional, and combined error models were tested. The combined error
`model appeared superior.
`
`Results
`
`Four individual GLP-1 concentration versus time profiles together with model
`predictions are shown in Fig. 2. High variability in the profiles is present both for
`the baseline and in the dynamics of the GLP-1 hormone.
`Figure 3 presents population predictions together with individual observations
`and their mean. Figure 4 presents the autocorrelation function (ACF) of residuals
`[19]. A visual predictive check (VPC) of the model is presented in Fig. 5. These
`figures indicate that
`the model seems to adequately capture the main GLP-1
`dynamics measured in the studied population. There is no need to implement the
`presented model using stochastic differential equations (SDEs). This is augmented
`by the fact that for all lags [0 there is small correlation and only the correlation at
`lag = 2 (corresponding to the correlation between residuals shifted two time-points)
`is significant (See Fig. 4).
`Interpretation, estimated values, and inter-individual variability (IIV) of each
`parameter is presented in Table 2. For each parameter estimated with IIV we have
`also reported the g-shrinkages (shr) as these measures are of importance e.g. for a
`study incorporating covariate effects [20]. The shrinkage on the residual error was
`found to be very small.
`In order to check that our model was consistent with NCA-analysis, we plotted
`the fast stimulation index st3 versus AUCPGLP-1 which has been used previously
`[21] to measure the size of the fast response (see Fig. 6). A significant correlation
`between the two measures (r = 0.52) was obtained.
`Figure 7 presents the time course of mean signals related to the fast and the slow
`GLP-1 responses (simulation of compartment S1 and S2 above using the estimated
`typical values of ka, kb and kc) together with the mean of simulated A3, the
`presenting compartment related to glucose absorption rate. For the fast response a
`
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`Fig. 2 Measurements and individual predictions of total GLP-1 versus time after the oral dose of
`glucose. Left: Normal glucose tolerant subjects (NGT). Right: Impaired glucose tolerant subjects (IGT)
`
`Fig. 3 Comparison between
`mean DV and population
`prediction. Black small dots:
`plasma concentrations of GLP-1
`versus time for all subjects.
`Large dots: mean observed
`GLP-1 concentrations. Gray
`curve: population prediction
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`Fig. 4 Autocorrelation function
`(ACF) calculated based on
`appended residuals from each
`subject
`
`Fig. 5 Visual predictive check
`(VPC) of GLP-1 measurements
`versus time. Shaded area defines
`the 5–95th percentiles of
`predictions and dotted line, the
`10–90th percentiles for
`predictions. Full line presents
`median of prediction, whereas
`dots represent data points
`
`peak around 25 min is observed, whereas the slow response peaked around
`100 min.
`
`Discussion
`
`In this study we modelled the sum of intact GLP-1 and the primary metabolite,
`GLP-1 (9–36), into which GLP-1 is rapidly converted. This sum therefore reflects the
`rate of secretion of GLP-1. The obtained total GLP-1 concentrations following the
`OGTT could be described by an indirect response model with zero-order production
`rate and first-order
`loss. Stimulation of GLP-1 production by glucose was
`characterized with a fast stimulation signal and a signal related to a delayed version
`of the absorption rate of glucose. Elimination was characterized by a non-saturable
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`Table 2 Obtained parameter estimates for GLP-1 dynamics
`
`Parameter
`
`Interpretation
`
`f (-)
`ka (min-1)
`kb (min-1)
`kc (min-1)
`kout_GLP1 (min-1)
`
`j [-]
`st3 [mg-1]
`
`st4 [mg-1]
`
`Absorption fraction
`
`Abs. rate constant
`
`Transit rate constant
`
`Neural signal rate constant
`
`First-order elimination rate constant of
`GLP-1
`Proportionality between IIV on st3 and st4
`Stimulation factor of GLP-1 production
`by early signal
`
`Stimulation factor of GLP-1 production
`by late signal
`
`SDglp [pmol l-1]
`CVglp (%)
`[pmol l-1]
`
`Additive error
`
`Proportional error
`
`Value
`
`SEM
`(%)
`
`IIV
`(CV%)
`
`0.722
`
`0.0359
`
`0.0962
`
`0.0566
`
`0.0644
`
`0.775
`8.64 10-5
`
`26.2 10-5
`
`0.998
`
`9
`
`–
`
`2
`
`8
`
`11
`
`18
`
`10
`
`10
`
`3
`
`5
`
`–
`
`–
`
`0.0581(24)
`
`0.0357(12)
`
`0.270(52)
`
`0 FIXED
`
`0 FIXED
`
`0.939(97)
`
`–
`
`–
`
`–
`
`Shr
`(%)
`
`–
`
`5
`
`20
`
`20
`
`–
`
`–
`
`6
`
`–
`
`–
`
`–
`
`The f is obtained from Ref. [18] and ka is estimated from glucose/insulin data
`
`Fig. 6 Individual predictions of parameter st3 versus AUCPGLP-1 calculated as AUC from 0–60 min.
`above baseline values. Open circles: NGTs, Gray filled circles: IFG-IGT-T2Ds. Line presents relation:
`st3 = 0.03 AUCPGLP-1, obtained using perpendicular least squares
`
`elimination pathway. The model for glucose/insulin was estimated separately from
`the GLP-1 secretion model. This was done in order not to bias the estimation of
`glucose absorption towards the prediction of GLP-1 concentrations. Besides, the
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`Fig. 7 Normalized mean of
`simulations of compartments S1,
`A3 and S2 versus time
`
`simultaneous estimation was very time-consuming causing separate estimation to be
`preferred.
`The GLP-1 secretion model was successfully applied to a mixed-effects model
`setting using NONMEM VI, thus providing both information about intra-variability
`and inter-variability in the studied population.
`To our knowledge compartmental modelling of GLP-1 secretion following an
`OGTT has not been performed previously. As observed from our individual profiles
`there is very high variability between subjects and the response is considered
`complex which relates to the fact that determinants of the secretion are not fully
`understood. Based on this we initially started out using a simple indirect response
`model using one stimulus related solely to the glucose absorption rate. This stimulus
`was not adequate to describe the GLP-1 secretion and we observed that two phases
`of secretion could be identified. Based on the estimation of the rate constants kb and
`kc, the peaks of these stimuli were observed to be around 25 and 100 min. This
`seems to be consistent with the GLP-1 profiles following a mixed meal [21]
`indicating maximum GLP-1 concentrations shortly after the peak stimulation times.
`The fast response (peak around 25 min.) is hypothesized to be caused mainly by
`nutrients in the duodenum activating a proximal—distal neuroendocrine loop
`stimulating GLP-1 secretion from L-cells and colon (3). In our study we estimated
`the rate constant (kc) related to the first-phase to be significantly faster than the rate
`(ka)
`related to glucose absorption. This provides evidence for
`the
`constant
`possibility of the neuroendocrine regulation of L-cell secretion (3), although more
`insights could be gained from further experiments.
`In this study we chose not to perform covariate analysis on the individual
`parameters for secretion, and did thus also not analyse the effect of disease state on
`the obtained estimates. Such an analysis belongs to another study, and must be
`performed with data that has more subjects identified with T2D.
`The developed model should be seen as a tool that in future can be applied to
`investigate factors such as disease state, drug effect, or ethnicity on the parameters
`characterizing GLP-1 secretion.
`
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`724
`
`J Pharmacokinet Pharmacodyn (2011) 38:713–725
`
`Estimating the rate of absorption of glucose without the use of tracer has been a
`subject in various publications [18, 22]. We applied a simple approach using only
`one parameter without information from tracer kinetics.
`In order to investigate the dependence of our approach on different glucose
`absorption models, we implemented two alternative models [18, 22]. The objective
`function values, population fittings and correlation obtained between st3 and
`AUCPGLP-1 appeared similar to the present results. A clear drawback of our study is
`that the absorption rate for glucose is not necessarily captured with high accuracy. It
`will be of future interest to see how the model performs knowing the rate of
`absorption obtained with a tracer [22, 23].
`Another limitation of this study is that only one dose level of the OGTT was
`administered. Possible non-linearities in the GLP-1 response are thus unidentifiable.
`For further model development it would be informative to repeat the experiments
`performed in this analysis with different glucose doses.
`the
`Regarding the number of transit compartments one could argue that
`possibility of having different individual numbers would be reasonable. This was
`tested using an explicit solution [17], but was found to cause the model not to be
`uniquely identifiable thus causing unstable estimation of parameters. Instead we
`chose to have IIV on kb, thus enabling individual differences in time of onset of S2.
`In spite of the fact that IIV was only 12% in kb values, we observed significantly
`higher OFV and a worse model fit. That was the reason for having kb not fixed to 0.
`The value of kout_GLP1 indicates a half-life of total GLP-1 of around 10 min. This
`agrees with values in the range of 3–11 min obtained experimentally in vivo [13],
`although it seems to be slightly higher than values obtained for active GLP-1
`(7–36), specifically measured in humans [4, 24, 25]. As Holst et al. [16] describe,
`there are different types of GLP-1 and in this study the measured concentration
`reflects the sum of the active GLP-1 (7–36) and the inactive form, GLP-1 (9–37).
`The inactive form has a much longer half-life [16] which will be the main
`determinant for the half-life. In general it is important to note that the degradation of
`GLP-1 (7–36) is known to be fairly complex and involves both an inactivation in the
`gut and degradation in liver which is not taken into account here. It would thus be of
`future interest to build a more complex model based on data obtained in different
`tissues and from the different metabolites.
`
`Acknowledgments This study was partly supported by NIH Grant GM 57980 for WJJ and WG.
`
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