Drug Metabolism and Pharmacokinetics (DMPK) Advance Publication by J-STAGE Received; February 12, 2010 Published online; September 29, 2010 Accepted; June 15, 2010 doi; 10.2133/dmpk.DMPK-10-RG-017 1
Pharmacokinetic/pharmacodynamic modeling of glucose clamp effects of inhaled and subcutaneous insulin in healthy volunteers and diabetic patients
Cornelia B. Landersdorfer1,2 and William J. Jusko1
1Department of Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, NY 14260, USA 2Ordway Research Institute, Albany, NY, USA
Support: This work was supported by the UB-Pfizer Strategic Alliance.
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Running title: PK/PD of Inhaled Insulin
Address of correspondence: William J. Jusko, PhD, Department of Pharmaceutical Sciences, University at Buffalo State University of New York, 565 Hochstetter Hall Buffalo, NY 14260, USA. Phone: (716) 645-2855 x225 Fax: (716) 645-3693 E-mail: [email protected]
Number of text pages: 28
Number of tables: 2
Number of figures: 3
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Abstract
The pharmacokinetics and pharmacodynamics (PK/PD) of inhaled insulin in humans have not been modeled previously. We rationalized a model for the effects of inhaled insulin on glucose infusion rate during a euglycemic clamp study based on the mechanism of insulin action and compared parameter estimates between subcutaneous and inhaled insulin in healthy and diabetic subjects.
Published data from two studies in 11 healthy volunteers and 18 type 1 diabetes patients were digitized. The subjects received four different doses of inhaled insulin and one or three different doses subcutaneously at the start of a 10 h glucose clamp. All data were modeled simultaneously using NONMEM VI. Insulin pharmacokinetics were described by a one-compartment model with one (inhaled) or two (sc insulin) first-order absorption processes and first-order elimination.
Insulin effects on glucose were described by an indirect response model. A biophase direct effect equation for the glucose infusion rate was implemented.
Pharmacodynamic parameter estimates were 15.1 mg/min/kg for maximal glucose infusion rate (GIRmax) and 88.0 mIU/L for SC50 for diabetic and 62.9 mIU/L for healthy subjects. A PK/PD model based on fundamental principles of insulin action and glucose turnover suggests comparable potencies of inhaled and subcutaneous.
Keywords: Diabetes, insulin sensitivity, mechanism-based modeling, pharmacokinetics, pharmacodynamics
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Introduction
The number of diabetic patients is increasing and efforts are being made to improve therapy and develop new therapeutical approaches. Timely diagnosis and adequate treatment are vital for prevention or delay of long-term complications.
Type 2 diabetic patients suffer from both insulin resistance and β-cell failure [1].
Type 1 diabetes is mainly characterized by β-cell failure, however insulin resistance also plays a role [2]. Numerous different diagnostic tests are available for clinical use to evaluate β-cell function [3] and insulin sensitivity [4].
The hyperinsulinemic euglycemic glucose clamp technique, originally developed by DeFronzo et al. [5], is considered one of the gold standard methods to measure insulin sensitivity and used as reference for other methods [6, 7].
Generally, a constant rate insulin infusion is given which results in insulin concentrations higher than the physiological baseline. Blood glucose is measured frequently and maintained within the euglycemic range by glucose infusions with variable rates. As hepatic glucose production is assumed to be completely inhibited by the exogenous insulin infusion, glucose infusion rate (GIR) equals glucose utilization rate. Effects of exogenous insulin are often measured by comparing the areas under the GIR vs. time curve after various doses of insulin [8,
9]. With this approach, the doses in a study can be compared but effects of other doses or modes of administration cannot be accounted for and the underlying mechanism cannot be described.
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Timely initiation of insulin therapy is often the best way to improve glucose control in diabetic patients. Due to anxiety and resistance of patients towards injecting insulin, they frequently remain on therapy with oral antidiabetics although satisfactory blood glucose control may not be achieved [10]. To overcome this barrier, various formulations of inhaled insulin including powder and liquid aerosol inhalers were and are being developed by several companies. In a systematic literature review, inhaled insulin was found to be as effective clinically as injected short-acting insulin with a slightly faster onset of action and was preferred by most patients [11]. However costs are considerably higher with the inhaled formulation
[11]. A patient preference study in 344 Type 1 and 2 diabetic patients in the UK reported that 63 to 81% of the patients preferred inhaled over injected insulin [12].
Most recently, a two-year safety and efficacy study in type 2 diabetic (T2DM) patients found a small nonprogressive decrease in forced expiratory volume, similar improvement in HbA1c, lower fasting plasma glucose and lower weight gain with inhaled versus sc insulin [13]. Comparable efficacy and lung function were reported in pediatric T1DM patients who received inhaled or sc insulin for three months [14]. In general, similar safety and efficacy of inhaled and sc insulin, despite small changes in lung function was concluded [15].
The effect of spray instilled insulin in rats was modeled previously [16], however the effect of inhaled insulin in human healthy volunteers and diabetic patients has not been modeled. Therefore we sought to 1) rationalize a PK/PD model for the effects of inhaled insulin on glucose infusion rate during a
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euglycemic clamp study based on the mechanism of insulin action, 2) apply this model to literature data from glucose clamp studies to provide an example, and 3) compare the parameter estimates between subcutaneous (sc) and inhaled insulin in healthy volunteers and diabetic patients.
Methods
Data. Published data from two crossover studies [8, 9] were digitized (Graph-to-
Digital Data Converter: Graph Digitizer®, Version 2.0, http://www.geocities.com/graphdigitizer/.htm). Both studies reported average insulin concentrations and GIR for each dose and route of administration and had frequent sampling times; individual subject data were not available. In both studies regular human insulin was utilized.
The study by Brunner et al. [9] included 18 type 1 diabetic (T1DM) patients who were C-peptide negative and were on intensive insulin therapy. After an overnight fast, the patients received a variable insulin infusion over 5 h to achieve stable euglycemia (about 7.2, range 5.0-9.4 mmol/L). For inhaled insulin, the insulin infusion was stopped at the time of the dose and for sc insulin at 10 min after the sc dose. The patients received single doses of 0.3, 0.6, 1.2, and 1.8 IU of human regular insulin per kg body weight by inhalation and 0.12 IU / kg sc. Inhaled insulin was administered by a liquid aerosol device (AERx iDMS). Sc insulin was administered by Actrapid HM Penfill 100 U/mL (Novo Nordisk, A/S). After insulin administration the patients underwent a 10 h glucose clamp study during which glucose concentrations were held constant at 7.2 mmol/L. The mean (standard
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deviation) weight of the patients was 72.6 (8.8) kg, age was 35.4 (5.9) years, and
HbA1c (glycosylated hemoglobin) was 8.1 (0.9) %.
Rave et al. [8] administered doses of 60, 90, 120, and 150 IU of inhaled insulin to each of 11 healthy volunteers (HV) in a crossover fashion. Human insulin was delivered by a dry powder inhaler (SPIROS® blisterdisk inhaler, 11% micronized insulin crystals with carrier monohydrate NF, median particle size was
2-3 μm for insulin and 150 μm for lactose). In addition each healthy volunteer received two out of three doses of sc regular human insulin: 8, 14, or 20 IU
(Humulin® R) which was administered by syringe. Doses were given after an overnight fast. For 10 h after insulin administration, blood glucose was clamped at
5% below the individual mean baseline which was determined by measurement before insulin administration. The Biostator glucose-controlled insulin infusion system (GCIIS, Life Science Instruments, Elkhart, USA) was utilized to regulate glucose infusion rates in response to the changes of blood glucose levels. The healthy volunteers (eight female, five male) were between ages of 22 and 42 and required to have a BMI of ≤ 27 kg/m2.
.
Pharmacokinetics. For modeling the insulin concentrations, models with one and two disposition compartments, with and without an absorption lag-time, and with first-order, zero-order, mixed-order (Michaelis-Menten), parallel first-order and zero-order, first-order and mixed-order, two parallel first-order absorption compartments, sequential zero-order and first-order or first-order and first-order
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absorption were tested. For the modeling, the doses for T1DM patients were converted from IU/kg to IU by use of the reported average weight of 72.6 kg. The final PK model is depicted in Figure 1. Inhaled insulin PK in both T1DM and HV was described as:
dI Lung Ik (1) dt a_Inh Lung
dIs ILung CLT ka_Inh Is (2) dt V V where ILung is the amount of insulin at the absorption site in the lung, ka_Inh is the first-order absorption rate constant, Is is insulin plasma concentration, CLT is apparent clearance assuming the bioavailability of the sc dose is 100%, and V is apparent volume of distribution. The initial condition for ILung is 0. The initial condition of Is is Is(0) which was estimated. For healthy volunteers, at time = 0 the amount of (insulin dose · Finh) was put into compartment ILung, where Finh is the relative bioavailability of inhaled insulin. For T1DM patients at time = 5 h the amount of (insulin dose · F) was put into compartment ILung, e.g. (1.8 IU/kg ·
Finh_1.8), where Finh_1.8 is the relative bioavailability of inhaled insulin for the 1.8
IU/kg dose.
The PK of sc insulin in T1DM was described as:
dI 1sc Ik (3) dt 1sc_sc1a
dI 2sc Ik (4) dt 2sc_sc2a
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dIs I 1sc I 2sc CLT k _sc1a k _sc2a Is (5) dt V V V where Isc1 and Isc2 are the amounts of insulin at the sc absorption sites, ka_sc1 is the first-order absorption rate constant for the major part of the sc insulin dose for which absorption started immediately, and ka_sc2 is the first-order absorption rate constant for the rest of the sc insulin dose which was absorbed after a lag-time.
The fraction of insulin which was absorbed immediately (F1_sc) was estimated. The initial conditions for Isc1 and Isc2 are 0. The initial condition of Is is Is(0) which was estimated. At times t = 5 h and t = 5 h + Tlag_sc the amounts of (insulin dose · F1_sc) and (insulin dose · (1-F1_sc)) were put into compartments Isc1 and Isc2. The total bioavailability of sc insulin was assumed to be 100%.
The PK of sc insulin in HV was described as:
dI 1sc Ik (6) dt 1sca_sc
dI 2sc IIk (7) dt a_sc 1sc 2sc
dIs I 2sc CLT ka_sc Is (8) dt V V
Where Isc1 and Isc2 are the amounts of insulin in the sc depot and the sc soluble compartment (Figure 1), ka_sc is the first order absorption rate constant both from the depot to the soluble compartment and the soluble compartment to plasma. At time = 0 the amount of (insulin dose) was put into compartment Isc1. The total bioavailability of sc insulin was assumed to be 100%. The main objective of the
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absorption models was to provide an adequate description of the insulin profiles as input function for the PD model.
For all subjects the initial conditions for ILung, Isc1, and Isc2 are 0. The initial condition of Is is Is(0) which was estimated.
Pharmacodynamic model. Insulin affects glucose concentrations by both inhibition of glucose production and stimulation of glucose utilization. In a glucose clamp study the endogenous glucose production is assumed to be inhibited.
Therefore in equation (9) the effect of insulin is described by a stimulation of glucose utilization, using indirect response model IV [17]. In a glucose clamp study the glucose concentration is kept constant by a variable glucose infusion.
Therefore GG ss (G: glucose amount in plasma (mg/kg), Gss: glucose amount in plasma at steady-state (mg/kg)), and input and loss of glucose are equal. dG 0 )Is(IsS 1kk max 0G (9) in out 0 ss dt 50 )Is(IsSC
GIR Tissue utilization where 0 )Is(Is is the difference between insulin concentration and baseline insulin (pre-insulin dose) (mIU/L), kin is the rate of zero-order glucose input (mg ·
-1 -1 -1 min · kg ), and kout is the first-order disposition rate constant (h ). As insulin concentrations are high due to the exogenous insulin dose, in glucose clamp studies the endogenous glucose production is assumed to be completely inhibited
-1 -1 and kin equals the GIR (mg · min · kg ). The loss of glucose is due to glucose utilization in tissues. The Smax (-) is the maximum stimulation of glucose utilization
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-1 and SC50 (mIU · L ) is the insulin concentration which results in half-maximal stimulation of glucose utilization. Rearranging Eq. (9) yields:
0 )Is(IsS GIR 1k max G (10) out 0 ss 50 )Is(IsSC
At baseline of glucose and insulin, 0 0)Is(Is , Eq. (9) yields:
0 in out out GkGkk ss (11) where G0 is the glucose amount in plasma at baseline, i.e. before the insulin dose.
The delay in increase in GIR compared to the insulin concentrations was described by a hypothetical effect compartment which is assumed to receive insulin from plasma but does not affect the observed PK.
The difference between insulin concentration and insulin baseline in the effect compartment is CeCe 0 . From Eq. (10):
0 )Ce(CeS GIR 1k max G (12) out 0 ss SC50 )Ce(Ce
0 0 If Gss is set to G and CeCe 0 as in Eq. (11), then
0 in out out GkGkk ss
When kin is inserted into Eq. (12) instead of Gk ssout , a “direct effect” model with the biophase insulin concentration is obtained:
0 )Ce(CeS 1kGIR max in 0 (13) 50 )Ce(CeSC
Insulin concentrations in the biophase (Ce) are described by:
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dCe 0 0 )Ce(Ce)Is(Isk (14) dt eo where 0 )Is(Is is the difference between insulin concentration and its baseline in plasma. It is assumed that 0 CeIs 0 and 0 )Ce(Ce is protected by use of max 0 ),0Ce(Ce . The biophase equation (Eq. (14)) describes the delay between insulin concentrations and Eq. (12) describes the effect on kout. The amount of insulin in the biophase is assumed to be negligible. The first-order rate constant keo is the equilibrium constant between the plasma and biophase. At steady-state these concentrations are equal.
The limits of Eq. (13) are:
0 0 when GIR,0)Ce(Ce k in before insulin dose: GIR
0 0 when )Ce(Ce is large, GIR S1GIR max
The preferred method is to model the natural (observed or measured) data which are not baseline adjusted. When baseline values are not available, the baseline
0 0 adjusted GIR (GIRA) is calculated: GIR A GIRGIR , and GIR k in as in the limit to Eq. (13). Then it follows from insertion into Eq. (13) that
0 )Ce(CeSGIR GIR GIRGIR 0 max0 A 0 (15) SC50 )Ce(Ce
0 When SGIR max GIRmax the baseline adjusted GIR (GIRA) is:
GIR 0 )Ce(Ce GIR max A 0 (16) SC50 )Ce(Ce
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For the data from healthy volunteers, Eq. (13) was used to describe the GIR while, for the data from T1DM patients, Eq. (16) was used as no baseline data were available. First the data after inhaled insulin from the T1DM study were modeled, then the data after sc insulin in that study, followed by modeling of all doses in the
T1DM study simultaneously. Also for the healthy volunteer study first the two routes of administration were modeled separately and then were fitted simultaneously. Eventually all data from diabetic patients and healthy volunteers were modeled jointly. No parameters were fixed during that process. The final model is shown in Figure 1.
Parameter variability and observation model. As the data were average values from the literature, both studies were crossover design, and the goal was to describe all doses and routes of absorption with the same disposition parameters, we did not include any variability between treatment arms or studies in the model.
Including such variability on the parameters might result in masking systematic differences between healthy volunteers and diabetic patients or non-linear processes with regard to dose, as it cannot be distinguished between such variability and systematic differences between formulations or patients and volunteers. The residual unidentified variability was described by a combined additive and proportional error model for insulin concentrations and GIR.
Computation. NONMEM© version VI level 1.1 (NONMEM Project Group [18]) was used for all modeling and simulations. All PK and PD data (insulin concentrations and GIR) from healthy volunteers and patients were modeled
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simultaneously. The deconvolution method as implemented in WinNonlin Pro ® version 5.0.1 (Pharsight Corporation, Mountain View, CA, USA) was utilized to evaluate the time course of rate of absorption.
Model discrimination. Competing models were distinguished using the
NONMEM objective function, the χ2-test (addition of a parameter to the model is considered to significantly [p < 0.05] improve the fitting if it results in a reduction of the objective function by > 3.84), residual plots, standard goodness of fit plots, and comparison of population fittings to the observed time course of insulin and GIR.
Visual predictive checks were performed, however as BSV cannot be estimated from the available data the predicted variability would only represent the residual unexplained variability.
Results
Pharmacokinetics. The profiles of plasma insulin concentrations versus time for both T1DM and healthy subjects are shown in Figure 2. Goodness-of-fit plots are shown in Figure 3. The PK of inhaled insulin in T1DM patients was best described by a one-compartment disposition model with first-order absorption and elimination. The absorption of inhaled insulin was faster with the higher doses and the bioavailability decreased with dose (Table 1). Two parallel first-order absorption processes with a lag-time on one of them best described the PK after the sc insulin doses.
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In healthy volunteers the PK of inhaled insulin was described by a one- compartment disposition model with first-order absorption and elimination. The absorption of sc insulin was best described by two sequential first-order processes, i.e. administration of insulin into a depot compartment which represents insulin crystals, followed by first-order dissolution and first-order absorption into the systemic circulation (Figure 1). The other tested models did not fit the inhaled and sc data simultaneously (with same parameters for CL and V).
The time course of rate of absorption assessed by deconvolution suggested two consecutive first-order absorption steps and such a model fitted all data simultaneously. The estimates for both ka parameters for sc administration were identical; therefore only one parameter was used (ka_sc).
Apparent insulin clearance (clearance / bioavailability of the sc dose) was considerably higher in healthy volunteers (103 L/h) than in T1DM patients (20.8
L/h). Volume of distribution was slightly lower in T1DM patients when fitted separately but could be described with one parameter for healthy volunteers and patients which was estimated at 7.4 L. Bioavailability of inhaled insulin in HV was estimated to be about 7.9% relative to sc insulin. In T1DM patients relative bioavailability decreased from 17.2% for the 0.3 IU/kg dose to 6.9% for the 1.8
IU/kg dose. Absorption half-life increased from 3.0 h for the 1.8 IU/kg dose to 4.3 h at the 0.3 IU/kg dose. The slightly different sc absorption models between the two studies might be due to use of different injection devices or random variability. The
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profiles were adequately fitted for input into the PD model, which was the main objective of the absorption model.
Pharmacodynamics. The time-course of glucose infusion rates for the various doses of insulin are shown in Figure 2 for the T1DM and healthy subjects. These rates increased with the dose of insulin, but lagged behind the insulin profiles. For the data from T1DM patients, Eq. (16) was used, as these patients did not have endogenous insulin production and therefore no baseline GIR (GIR0). The PD parameter estimates for T1DM and healthy volunteers are shown in Table 2.
When SC50 was estimated separately for inhaled and sc in T1DM patients, it was
29% higher for inhaled than sc insulin. In healthy volunteers, however, the SC50 for inhaled insulin was 16% lower than for sc insulin. As the goodness of fit did not improve by estimating different SC50 values for inhaled and sc insulin, and the differences were small, we used the same SC50 parameter for both routes of administration in our final model. All data could be described with one keo and one
GIRmax. Baseline insulin concentration in the biophase above which glucose utilization is stimulated was considerably higher in T1DM patients than in healthy volunteers.
For the sc doses in healthy volunteers, the peak of the model-predicted GIR was earlier than in the observed data (Figure 3), which is a weakness of analysis and was not improved by fitting more complex models. However apart from this limitation, the model adequately fitted the data, considering these were average
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data from two studies, healthy volunteers and T1DM patients and also different doses and routes of administration which were fitted simultaneously.
In summary, the absorption parameters were different between sc and inhaled insulin. Using two different parameters for CL, Ce(Is0), and SC50 for healthy volunteers and T1DM patients resulted in significantly better model fittings
(p < 0.05 based on the χ2 test). For CL and Ce(Is0) this difference was also significant based on 95% confidence intervals estimated from asymptotic standard errors ($COV step as implemented in NONMEM IV).
Discussion
The hyperinsulinemic euglycemic clamp and the intravenous glucose tolerance test are the two methods for determination of insulin resistance considered as ‘gold standard’ by the American Diabetes Association [4]. Whereas results from the intravenous glucose tolerance test are routinely analyzed by the well-known Minimal Model [19] or more recently developed extensions of this model [20, 21], a non-compartmental analysis is usually performed for glucose clamp studies. The latter provides information about the total effect of each dose of insulin on glucose utilization and the time and value of maximum GIR, but does not consider the full time course of the effect. By PK/PD modeling, parameter estimates can be compared between formulations, patient populations, or both, and the underlying reasons for differences in the GIR time profiles may be explored.
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We developed a mechanism-based model from basic principles of insulin action on glucose. The basis of glucose clamp experiments is the assumption that
GIR equals glucose utilization rate which is a measure of insulin sensitivity. From this assumption a direct effect model was derived. As the physiological feedback between glucose and insulin is disrupted due to the clamp, feedback loops need not be included in the model and the model can be considerably simplified to Eq.
(16). Such a model has been suggested previously [22, 23]. However those authors chose the model based on a hysteresis plot and concluded that, due to the presence of a delay between insulin concentrations and effect on glucose, the effect compartment model [24] would be suitable to describe the data. Tornoe et al. [22] focused on the mathematical method of ‘grey box’ modeling instead of use of structural and mechanism-based models. On the contrary, our model is based on an indirect response process [17] which describes stimulation of glucose utilization by insulin as is physiologically realistic. Such models can describe drug effects by stimulation or inhibition of production or loss of an endogenous substance. Insulin action includes both inhibition of glucose production and stimulation of glucose utilization. However, during a euglycemic clamp endogenous glucose production is assumed to be suppressed and therefore insulin mainly acts on glucose utilization. The stimulation of glucose utilization by insulin was described by Indirect Response Model (IDR) IV (Eq. (9)). From this model which describes the mechanism of action of insulin, we derived Eq. (13)
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and (16) by considering the fundamental assumptions of the glucose clamp and thereby provide the theoretical framework for this choice of the structural model.
In the past several authors have chosen biophase or effect compartment models combined with an Emax function to describe effects on glucose and insulin when an IDR might have been the more suitable choice [25-29]. However many of these papers were published before IDR models became widely known.
Hysteresis in plotting response versus concentration alone does not necessarily mean that an effect compartment model is suitable, but only indicates that a delay between drug concentrations and response is present. Both models result in a delay of the PD response compared plasma concentrations of the drug. However, in an indirect response model the delay is due to inhibition or stimulation of production of an endogenous substance, in this case inhibition of glucose utilization by insulin, which mirrors the mechanism of action of insulin. In contrast the effect compartment model assumes distribution of a drug to its site of action as the main reason for the delay. Authors who employed biophase models for antidiabetic drug effects when IDR models would have been the more adequate starting point, reported that separate PD parameter sets were necessary to model different rates of infusion [25], or dose levels [27] of insulin within one study. These are indications that the model could not adequately and fully describe the system.
More recently, many authors employed IDR models to describe effects of insulin [16, 30] and antidiabetic drugs [31-37] and were able to model various doses and routes of administration simultaneously. Also in the present report, the
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same set of PD parameters could be used to describe insulin effects on glucose after different doses and routes of administration within one study population. A complex model for data from IVGTT and glucose clamp studies was developed by
Silber et al. [38]. However a dataset with clamp data only cannot provide enough information to estimate all the parameters in the model from Silber et al. [38]. In contrast to the more complex model by Silber et al. the model reported here does not represent the complexities of the glucose insulin system, but is a simplified model based on the assumption that glucose concentrations are constant during a clamp study.
This report shows that the use of a ‘biophase direct effect model’ is appropriate for the special situation of the glucose clamp by derivation of the equations based on an indirect response model (Methods section). This model is also supported by its ability to describe multiple doses and routes of administration by use of one set of universal PD parameters.
A model of inhaled insulin in humans has not been published previously.
Recently, the effect of three different formulations of intratracheally administered insulin microparticles and sc insulin in streptozocin-induced diabetic rats was modeled by the Minimal Model of glucose disappearance [39]. Despite its wide usage, several limitations of the Minimal Model [19] have been pointed out [20, 37,
40, 41]. The authors modeled all four formulations with only one set of PK/PD parameters, except for bioavailability. Despite utilizing PK/PD modeling, a measure of efficiency which might have also been derived from non-
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compartmental analysis (area above the effect curve / insulin AUC) was used to compare the efficiency between formulations. The same efficiency was concluded for all formulations. Another PK/PD model for spray-instilled insulin in rats was reported previously [16]. The authors modeled the effect of insulin on glucose concentrations by an IDR for stimulation of glucose utilization which adequately describes the mechanism of action of insulin. However the authors did not estimate the SC50 for insulin effect on glucose utilization but fixed it to a value from the literature. This value was taken from a publication which was not a clamp study and where the effect of insulin on glucose concentrations was described by a simple effect compartment model [25]. The authors reported increasing values of
SC50 (drug potency) with dose and rate of infusion [25], which is physiologically not reasonable.
For the present report previously published average data [8, 9] from euglycemic clamp studies with inhaled and sc insulin were modeled due to lack of availability of individual data. The studies [8, 9] were chosen as in other published studies the observation periods were too short, i.e. insulin concentrations, GIR, or both, did not go back to baseline, and confounding variables such as smoking or asthma were present.
An objective of the present work was to compare the SC50 between inhaled and sc insulin. As discussed, it is not physiologically reasonable to estimate different SC50 for different doses of the same drug administered by the same route. Also for most drugs the route of administration is not expected to influence
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the PD. However for inhaled insulin it has been reported that, despite similar overall arterial and hepatic insulin exposures (AUC), the amount of glucose required to maintain euglycemia was greater after inhaled than sc insulin [42]. In another study, enhanced nonhepatic glucose clearance associated with inhaled insulin was found compared to intravenous insulin [43]. Subsequently, considerably greater whole-body glucose disposal was reported after inhaled compared to sc insulin, although arterial and hepatic insulin AUC were similar for both routes of administration. In addition, inhaled insulin resulted in increased insulin sensitivity in non-hepatic but not hepatic tissues compared with sc administration [44]. Mechanisms that have been postulated to explain these findings are blockade of ACE activity in the lungs and subsequent increase of NO concentrations which ultimately results in increased GLUT-4 transporter translocation in skeletal muscle [44].
Our modeling results suggest similar potency of inhaled and sc insulin. In
T1DM patients the potency of inhaled insulin was estimated to be slightly higher than in sc, whereas from the healthy volunteer data the opposite was found.
Therefore the results of our model do not support potential differences in potency between inhaled and sc insulin. Clinical trials have concluded similar efficacy of sc and inhaled insulin based on long-term changes HbA1c and fasting plasma glucose, but did not measure insulin concentrations. However the efficacy is described by Smax (GIRmax) whereas the SC50 describes the potency. In a study in type 2 diabetic patients [47] an AUC of 7.6 mU·min/ml after inhaled insulin and an
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AUC of 8.1 mU·min/ml after subcutaneous insulin resulted in the same AUC for
GIR (1100 mg/kg) which suggests similar potency of inhaled and subcutaneous insulin, although in such an approximate comparison the time course of insulin and
GIR are not taken into account. A population analysis of individual subject data would be necessary to confirm or reject potential differences in potency between inhaled and sc insulin with greater certainty.
However, the time delay between peak insulin concentrations and peak GIR is larger for the sc than the inhaled route in both studies [8, 9], most obviously in the healthy volunteer study. Assuming that the lungs are a site of action of insulin
[44], the signaling cascade which eventually results in enhanced glucose utilization could be started already before plasma insulin concentrations increase. This could explain the difference in onset of action and time of maximum action if the sc site is not a site of action of insulin. Most recently, average times of maximum GIR that occurred even slightly earlier than average peak insulin concentrations after inhalation were reported in healthy volunteers and asthma patients [45]. However, in other publications, the delay between peak insulin and peak GIR was longer for inhaled than sc insulin; therefore this observation does not appear to be consistent between studies.
We compared the disposition and effect of insulin in T1DM patients to healthy volunteers by modeling all data simultaneously. Use of different absorption models for sc insulin was the only component necessary to adequately describe the data. As reported previously, insulin clearance was decreased in T1DM
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compared to healthy volunteers. The decreased clearance might be due to a lower renal function and decreased uptake of insulin by insulin receptors into cells in the diabetic patients, a lower bioavailability of the sc formulation used in the healthy volunteer study, or both. However, there are conflicting reports in the literature about whether insulin clearance is decreased, unchanged, or even increased compared to healthy subjects [46]. The relative bioavailability of inhaled insulin relative to sc insulin was 8% in healthy volunteers and 7 to 17% in diabetic patients. This agrees with the 9 to 22% relative bioavailability of inhaled insulin previously reported in literature [47]. Volume of distribution could be modeled with a common parameter for both groups (Table 1). The SC50 was slightly higher in
T1DM than in HV which might suggest a small degree of insulin resistance.
However the difference was not statistically significant as the asymptotic standard errors were greater than 30% for both estimates. The misfit for the sc doses in the healthy volunteers might have slightly affected the SC50 estimate. Insulin resistance in T1DM was found previously [2] and the author concluded that it plays a larger role than commonly recognized. With our model GIRmax was slightly lower in T1DM than in HV when modeled separately but could also be described by a common parameter. The insulin concentration in the biophase which is needed to stimulate glucose utilization (Ce0) was considerably higher in T1DM than in healthy volunteers, which could also indicate some insulin resistance, but is more likely an artifact due to the study design in T1DM.
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A limitation of our assessment is that only average data were available and therefore it was not feasible to perform a population analysis. Also there was no insulin infusion given during the studies, and therefore endogenous glucose production might not have been suppressed completely. Glucose concentrations are generally not reported from clamp studies as, on average, glucose is held constant. However fluctuations necessarily occur as concentrations are monitored every few minutes and then the glucose infusion is changed accordingly. Also it is not known whether glucose concentrations in T1DM rose above the baseline of
7.2 mmol/L during the time when GIR was zero. It does not seem plausible for
T1DM patients without endogenous insulin secretion to be able to keep their insulin at baseline constant which would be the conclusion from the continued GIR equaling zero. It is likely that in glucose clamp studies a GIR of 0 is reported when the glucose concentrations in fact increase above the baseline and theoretically a
“negative GIR” (i.e. an insulin dose) would be necessary to keep glucose at baseline. These concerns are not only applicable to modeling but may be even more relevant to conventional non-compartmental analysis (NCA). Also, while
NCA is faster, it does not allow extrapolation to other doses and does not adequately describe nonlinear processes. The approach described here is a simplified model for the case that glucose concentrations are not known and approximately constant. While the GIR in clamp studies should be adjusted every few minutes, the latter assumption might not hold true over the whole study period in clamp studies where a single dose of insulin is given. In the case of
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considerable changes in the glucose concentrations during a clamp study and the glucose concentrations being reported, they could be employed in Eq. (9) and the model could account for the fluctuations in glucose. However glucose concentrations are usually not reported from clamp studies. Including a feedback of glucose on insulin would still not be necessary as long as the assumption of suppressed endogenous insulin production due to the insulin infusion holds true, or constant endogenous insulin production can be assumed. In general more detailed reporting of clamp studies would be beneficial to be able to judge whether those assumptions can be made. Deviations could be taken into account by modeling more adequately than by NCA. Our model allows us to compare effects of insulin on glucose utilization between different formulations, routes of administration, and doses.
Conclusions
This report focuses on the clarification of modeling theory and provides model equations to capture the full time course of insulin concentrations and glucose infusion rates during glucose clamp studies for different routes of administration and for both healthy volunteers and diabetic patients. The model equations were derived from basic principles of insulin action and turnover of glucose. To provide an example and to illustrate the application of those equations, the model was applied to literature data, due to lack of availability of individual data. Our modeling results suggest that inhaled insulin has similar potency as sc insulin, both in healthy volunteers and in T1DM patients. Application
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of the model to datasets of individual measurements in a population analysis is warranted and would provide further insights into the relative potency of inhaled and subcutaneous insulin in healthy volunteers and diabetic patients.
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References
1. LeRoith, D.: Beta-cell dysfunction and insulin resistance in type 2 diabetes: role of metabolic and genetic abnormalities. Am. J. Med., 113 Suppl 6A: 3S-11S (2002). 2. Greenbaum, C.J.: Insulin resistance in type 1 diabetes. Diabetes Metab. Res. Rev., 18: 192-200 (2002). 3. Kjems, L.L, Christiansen, E., Volund, A., Bergman, R.N., Madsbad, S.: Validation of methods for measurement of insulin secretion in humans in vivo. Diabetes, 49: 580-588 (2000). 4. Monzillo, L.U., Hamdy, O.: Evaluation of insulin sensitivity in clinical practice and in research settings. Nutr. Rev., 61: 397-412 (2003). 5. DeFronzo, R.A., Tobin, J.D., Andres, R.: Glucose clamp technique: a method for quantifying insulin secretion and resistance. Am. J. Physiol., 237: E214-E223 (1979). 6. Muniyappa, R., Lee, S., Chen, H., Quon. M.J.: Current approaches for assessing insulin sensitivity and resistance in vivo: advantages, limitations, and appropriate usage. Am. J. Physiol. Endocrinol. Metab., 294: E15-E26 (2008). 7. Lee, S., Muniyappa, R., Yan, X., Chen, H., Yue, L.Q., Hong, E.G., Kim, J.K., Quon, M.J.: Comparison between surrogate indexes of insulin sensitivity and resistance and hyperinsulinemic euglycemic clamp estimates in mice. Am. J. Physiol. Endocrinol. Metab., 294: E261-E270 (2008). 8. Rave, K., Nosek, L., Heinemann, L., Gonzales, C., Ernest, C.S., Chien, J., Muchmore, D.: Inhaled micronized crystalline human insulin using a dry powder inhaler: dose-response and time-action profiles. Diabet. Med. 21: 763-768 (2004). 9. Brunner, G.A., Balent, B., Ellmerer, M., Schaupp, L., Siebenhofer, A., Jendle, J.H., Okikawa, J., Pieber, T.R.: Dose-response relation of liquid aerosol inhaled insulin in type I diabetic patients. Diabetologia, 44: 305-308 (2001). 10. Arnolds, S., Heise, T.: Inhaled insulin. Best Pract. Res. Clin. Endocrinol. Metab., 21: 555-571 (2007). 11. Black, C., Cummins, E., Royle, P., Philip, S., Waugh, N.: The clinical effectiveness and cost-effectiveness of inhaled insulin in diabetes mellitus: a systematic review and economic evaluation. Health Technol. Assess., 11: 1-126 (2007). 12. Chancellor, J., Aballea, S., Lawrence, A., Sheldon, R., Cure, S., Plun- Favreau, J., Marchant, N.: Preferences of patients with diabetes mellitus for inhaled versus injectable insulin regimens. Pharmacoeconomics, 26: 217-234 (2008). 13. Rosenstock, J., Cefalu, W.T., Hollander, P.A., Belanger, A., Eliaschewitz, F.G., Gross, J.L., Klioze, S.S., St Aubin. L.B., Foyt, H., Ogawa, M., Duggan, W.T.: Two-year pulmonary safety and efficacy of inhaled human insulin (Exubera) in adult patients with type 2 diabetes. Diabetes Care, 31: 1723-1728 (2008). 14. White, N.H., Quattrin, T., St Aubin, L.B., Duggan, W.T., England, R.D., Fryburg, J.S.: Efficacy and safety of inhaled human insulin (Exubera) compared to
Drug Metabolism and Pharmacokinetics (DMPK) Advance Publication by J-STAGE
29
subcutaneous insulin in children ages 6 to 11 years with type 1 diabetes mellitus: results of a 3-month, randomized, parallel trial. J. Pediatr. Endocrinol. Metab., 21: 555-568 (2008). 15. Roach, P.: New insulin analogues and routes of delivery : pharmacodynamic and clinical considerations. Clin. Pharmacokinet., 47: 595-610 (2008). 16. Gopalakrishnan, M., Suarez, S., Hickey, A.J., Gobburu, J.V.: Population pharmacokinetic-pharmacodynamic modeling of subcutaneous and pulmonary insulin in rats. J. Pharmacokinet. Pharmacodyn., 32: 485-500 (2005). 17. Dayneka, N.L., Garg, V., Jusko, W.J.: Comparison of four basic models of indirect pharmacodynamic responses. J. Pharmacokinet. Biopharm., 21: 457-478 (1993). 18. Beal, S.L., Boeckmann, A.J., Sheiner, L.B., NONMEM Project Group.: NONMEM Users Guides. Version VI ed. San Francisco: University of California at San Francisco, 2007. 19. Bergman, R.N., Ider, Y.Z., Bowden, C.R., Cobelli, C.: Quantitative estimation of insulin sensitivity. Am. J. Physiol., 236: E667-E677 (1979). 20. Mari, A.: Mathematical modeling in glucose metabolism and insulin secretion. Curr. Opin. Clin. Nutr. Metab. Care, 5: 495-501 (2002). 21. Krudys, K.M., Dodds, M.G., Nissen, S.M., Vicini, P.: Integrated model of hepatic and peripheral glucose regulation for estimation of endogenous glucose production during the hot IVGTT. Am. J. Physiol. Endocrinol. Metab., 288: E1038- E1046 (2005). 22. Tornoe, C.W., Jacobsen, J.L., Madsen, H.: Grey-box pharmacokinetic/pharmacodynamic modelling of a euglycaemic clamp study. J. Math. Biol., 48: 591-604 (2004). 23. Woodworth, J.R., Howey, D.C., Bowsher, R.R.: Establishment of time- action profiles for regular and NPH insulin using pharmacodynamic modeling. Diabetes Care, 17: 64-69 (1994). 24. Sheiner, L.B., Stanski, D.R., Vozeh, S., Miller, R.D., Ham, J.: Simultaneous modeling of pharmacokinetics and pharmacodynamics: application to d- tubocurarine. Clin. Pharmacol. Ther., 25: 358-371 (1979). 25. Miyazaki, M., Mukai, H., Iwanaga, K., Morimoto, K., Kakemi, M.: Pharmacokinetic-pharmacodynamic modelling of human insulin: validity of pharmacological availability as a substitute for extent of bioavailability. J. Pharm. Pharmacol., 53: 1235-1246 (2001). 26. Brown, S.A., Nelson, R.W., Bottoms, G.D.: Models for the pharmacokinetics and pharmacodynamics of insulin in alloxan-induced diabetic dogs. J. Pharm. Sci., 76: 295-299 (1987). 27. Colburn, W.A., Gottlieb, A.B., Koda, J., Kolterman, O.G.: Pharmacokinetics and pharmacodynamics of AC137 (25,28,29 tripro-amylin, human) after intravenous bolus and infusion doses in patients with insulin-dependent diabetes. J. Clin. Pharmacol., 36: 13-24 (1996).
Drug Metabolism and Pharmacokinetics (DMPK) Advance Publication by J-STAGE
30
28. Rydberg, T., Jonsson, A., Karlsson, M.O., Melander, A.: Concentration- effect relations of glibenclamide and its active metabolites in man: modelling of pharmacokinetics and pharmacodynamics. Br. J. Clin. Pharmacol., 43: 373-381 (1997). 29. Frey, N., Laveille, C., Paraire, M., Francillard, M., Holford, N.H., Jochemsen, R.: Population PKPD modelling of the long-term hypoglycaemic effect of gliclazide given as a once-a-day modified release (MR) formulation. Br. J. Clin. Pharmacol., 55: 147-157 (2003). 30. Lin, S., Chien, Y.W.: Pharmacokinetic-pharmacodynamic modelling of insulin: comparison of indirect pharmacodynamic response with effect- compartment link models. J. Pharm. Pharmacol., 54: 791-800 (2002). 31. Lee, S.H., Kwon, K.I.: Pharmacokinetic-pharmacodynamic modeling for the relationship between glucose-lowering effect and plasma concentration of metformin in volunteers. Arch. Pharm. Res., 27: 806-810 (2004). 32. de Winter, W., DeJongh, J., Post, T., Ploeger, B., Urquhart, R., Moules, I., Eckland, D., Danhof, M.: A mechanism-based disease progression model for comparison of long-term effects of pioglitazone, metformin and gliclazide on disease processes underlying Type 2 Diabetes Mellitus. J. Pharmacokinet. Pharmacodyn., 33: 313-343 (2006). 33. Stepensky, D., Friedman, M., Raz, I., Hoffman, A.: Pharmacokinetic- pharmacodynamic analysis of the glucose-lowering effect of metformin in diabetic rats reveals first-pass pharmacodynamic effect. Drug Metab. Dispos., 30: 861-868 (2002). 34. Benincosa, L., Jusko, W.J.: Inventors: Novel Method of Treatment. World Intellectual Property Organization Publ. No. W0 00/27341. 1999. 35. Yun, H.Y., Park, H.C., Kang, W., Kwon, K.I.: Pharmacokinetic and pharmacodynamic modelling of the effects of glimepiride on insulin secretion and glucose lowering in healthy humans. J. Clin. Pharm. Ther., 31: 469-476 (2006). 36. Hamren, B., Bjork, E., Sunzel, M., Karlsson, M.: Models for plasma glucose, HbA1c, and hemoglobin interrelationships in patients with type 2 diabetes following tesaglitazar treatment. Clin. Pharmacol. Ther., 84: 228-235 (2008). 37. Landersdorfer, C.B., Jusko, W.J.: Pharmacokinetic/pharmacodynamic modelling in diabetes mellitus. Clin. Pharmacokinet., 47: 417-448 (2008). 38. Silber, H.E., Jauslin, P.M., Frey, N., Gieschke, R., Simonsson, U.S., Karlsson, M.O.: An integrated model for glucose and insulin regulation in healthy volunteers and type 2 diabetic patients following intravenous glucose provocations. J. Clin. Pharmacol., 47: 1159-1171 (2007). 39. Amidi, M., Krudys, K.M., Snel, C.J., Crommelin, D.J., Della Pasqua, O.E., Hennink, W.E., Jiskoot, W.: Efficacy of pulmonary insulin delivery in diabetic rats: use of a model-based approach in the evaluation of insulin powder formulations. J. Control Release, 127: 257-266 (2008). 40. Ferrannini, E., Mari, A.: How to measure insulin sensitivity. J. Hypertens., 16: 895-906 (1998).
Drug Metabolism and Pharmacokinetics (DMPK) Advance Publication by J-STAGE
31
41. De Gaetano, A., Arino, O.: Mathematical modelling of the intravenous glucose tolerance test. J. Math. Biol., 40: 136-168 (2000). 42. Cherrington, A.D., Neal, D.W., Edgerton, D.S., Glass, D., Bowen, L., Hobbs, C.H., Leach, C., Rosskamp, R., Strack, T.R.: Inhalation of insulin in dogs: assessment of insulin levels and comparison to subcutaneous injection. Diabetes, 53: 877-881 (2004). 43. Edgerton, D.S., Neal, D.W., Scott, M., Bowen, L., Wilson, W., Hobbs, C.H., Leach, C., Sivakumaran, S., Strack, T.R., Cherrington, A.D.: Inhalation of insulin (Exubera) is associated with augmented disposal of portally infused glucose in dogs. Diabetes, 54: 1164-1170 (2005). 44. Edgerton, D.S., Stettler, K.M., Neal, D.W., Scott, M., Bowen, L., Wilson, W., Hobbs, C.H., Leach, C., Strack, T.R., Cherrington, A.D.: Inhalation of human insulin is associated with improved insulin action compared with subcutaneous injection and endogenous secretion in dogs. J. Pharmacol. Exp. Ther., 319: 1258- 1264 (2006). 45. Wolzt, M., de la Pena, A., Berclaz, P.Y., Tibaldi, F.S., Gates, J.R., Muchmore, D.B.: AIR inhaled insulin versus subcutaneous insulin: pharmacokinetics, glucodynamics, and pulmonary function in asthma. Diabetes Care, 31: 735-740 (2008). 46. Kotronen, A., Juurinen, L., Tiikkainen, M., Vehkavaara, S., Yki-Jarvinen, H.: Increased liver fat, impaired insulin clearance, and hepatic and adipose tissue insulin resistance in type 2 diabetes. Gastroenterology, 135: 122-130 (2008). 47. Patton, J.S., Bukar, J.G., Eldon, M.A.: Clinical pharmacokinetics and pharmacodynamics of inhaled insulin. Clin. Pharmacokinet., 43: 781-801 (2004).
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Figure legends
Figure 1. Model diagram for pharmacokinetics of insulin and pharmacodynamics of glucose. Symbols are defined in the text and tables.
Figure 2. Population predictions and observed insulin concentrations and glucose infusion rates (GIR) versus time after administration of inhaled or sc insulin.
Doses in healthy volunteers are: 150 IU inhaled, 120 IU inhaled, 90
IU inhaled, 60 IU inhaled, 20 IU sc, 14 IU sc, and 8 IU sc.
Doses in T1DM patients are: 1.8 IU/kg inhaled, 1.2 IU/kg inhaled,
0.6 IU/kg inhaled, 0.3 IU/kg inhaled, and 0.12 IU/kg sc.
Figure 3. Observed versus population fitted insulin concentrations and glucose infusion rates (GIR) in healthy volunteers and T1DM patients
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Table 1. Pharmacokinetic parameter estimates
Parameter Definition Estimate SE (%) (unit) Healthy volunteers and T1DM Apparent volume of distribution assuming absolute V (L) 7.4 12.6 bioavailability of sc dose is 100% Healthy volunteers Apparent clearance assuming absolute bioavailability of sc CL ° (L h-1)a 103 8.0 T dose is 100%
FInh (%) Relative bioavailability of inhaled insulin 7.9 5.0 -1 ka_inh (h ) First-order absorption rate constant for inhaled insulin 0.252 6.7 -1 ka_sc (h ) First-order absorption rate constant for sc insulin 0.582 8.4
CVC (-) Proportional residual error for plasma insulin 0.12 41 -1 SDC (mIU L ) Additive residual error for plasma insulin 0.58 79 T1DM Apparent clearance assuming absolute bioavailability of CL (L h-1)a 20.8 5.5 T the sc doses is 100% b Finh_1.8 (%) 6.9 1.5 Relative bioavailability of 1.8, 1.2, 0.6, and Finh_1.2 (%) 7.9 3.8 0.3 IU/kg doses of inhaled insulin b Finh_0.6 (%) 11.7 2.9 b Finh_0.3 (%) 17.2 4.2 -1 c ka_1.8 (h ) 0.233 1.3 -1 First-order absorption rate constants for ka_1.2 (h ) 0.203 6.9 -1 c ka_0.6 (h ) 1.8, 1.2, 0.6, and 0.3 IU/kg doses of inhaled insulin 0.154 2.4 -1 c ka_0.3 (h ) 0.163 2.8
-1 First-order absorption rate constant for most of the sc c k (h ) 0.086 6.1 a1_sc insulin dose First-order absorption rate constant for a small part of the k (h-1) 1.95 22.5 a2_sc sc insulin dose
Tlag_sc (h) Lag-time for small part of the sc insulin dose 1.82 0.6
CVC (-) Proportional residual error for plasma insulin 0.027 105 -1 SDC (mIU L ) Additive residual error for plasma insulin 3.15 37 a Parameter estimate significantly different (based on 95% confidence intervals estimated from asymptotic standard errors [$COV]) between T1DM patients and healthy volunteers. b Parameterized as factor proportional to F1.2. c Parameterized as factor proportional to ka_1.2.
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Table 2. Pharmacodynamic parameter estimatesc
Estimate Parameter (unit) Definition SE (%) Healthy Healthy volunteers and T1DM GIR Maximum GIR achievable by stimulation of max 15.1 b - (mg min-1 kg-1) glucose utilization by insulin a First-order equilibrium constant between plasma k (h-1) 1.37 22.0 eo and effect compartment Healthy volunteers k in Rate of zero-order glucose input 0.22 7.7 (mg min-1 kg-1) Maximum stimulation of glucose utilization by S (-) 68.2 23.5 max insulin (factor) Insulin concentration in biophase needed to Ce0 -1 d stimulate glucose utilization and increase GIR 4.44 10.3 (mIU L ) 0 above GIR
-1 Insulin concentration which results in half-maximal SC (mIU L ) 62.9 34.0 50 stimulation of GIR
CVGIR (-) Proportional residual error for the GIR 0.19 35 -1 SDGIR(mIU L ) Additive residual error for the GIR 0.081 91 T1DM patients Insulin concentration in biophase needed to Ce0 stimulate glucose utilization and increase GIR 15.0 4.7 (mIU L-1)d above GIR0 Insulin concentration which results in half-maximal SC (mIU L-1) 88.0 32.6 50 stimulation of GIR after inhaled and sc insulin
CVGIR (-) Proportional residual error for the GIR 0.23 37 -1 SDGIR (mIU L ) Additive residual error for the GIR 0.068 86 a Note: GIRmax in reports where GIR is not modeled means maximum stimulation seen with a particular dose, not the maximum achievable GIR. b Calculated from kin · Smax (equation (16)). c All parameters are for both inhaled and sc insulin. The PD could be described by one set of parameters after both routes of administration. d As described in Table 1.
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Figure 1. Model diagram for pharmacokinetics of insulin and pharmacodynamics of glucose
Symbols are defined in the text and tables.
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Figure 2. Population predictions and observed insulin concentrations and glucose infusion rates (GIR) versus time after administration of inhaled or sc insulin
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Doses in healthy volunteers are: 150 IU inhaled, 120 IU inhaled, 90
IU inhaled, 60 IU inhaled, 20 IU sc, 14 IU sc, and 8 IU sc.
Doses in T1DM patients are: 1.8 IU/kg inhaled, 1.2 IU/kg inhaled,
0.6 IU/kg inhaled, 0.3 IU/kg inhaled, and 0.12 IU/kg sc.
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Figure 3. Observed versus population fitted insulin concentrations and glucose infusion rates (GIR) in healthy volunteers and T1DM patients
T1DM Healthy volunteers