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Abstract

Objective:

Model-based metabolic tests require accurate identification of subject-specific parameters from measured assays. Insulin assays are used to identify insulin kinetics parameters, such as general and first-pass hepatic clearances. This study assesses the impact of intravenous insulin boluses on parameter identification precision.

Method:

Insulin and C-peptide data from two intravenous glucose tolerance test (IVGTT) trials of healthy adults (N = 10 × 2; denoted A and B), with (A) and without (B) insulin modification, were used to identify insulin kinetics parameters using a grid search. Monte Carlo analysis (N = 1000) quantifies variation in simulation error for insulin assay errors of 5%. A region of parameter values around the optimum was identified whose errors are within variation due to assay error. A smaller optimal region indicates more precise practical identifiability. Trial results were compared to assess identifiability and precision.

Results:

Trial B, without insulin modification, has optimal parameter regions 4.7 times larger on average than Trial A, with 1-U insulin bolus modification. Ranges of optimal parameter values between trials A and B increase from 0.04 to 0.12 min^-1 for hepatic clearance and from 0.07 to 0.14 for first-pass clearance on average. Trial B’s optimal values frequently lie outside physiological ranges, further indicating lack of distinct identifiability.

Conclusions:

A small 1-U insulin bolus improves identification of hepatic clearance parameters by providing a smaller region of optimal parameter values. Adding an insulin bolus in metabolic tests can significantly improve identifiability and outcome test precision. Assay errors necessitate insulin modification in clinical tests to ensure identifiability and precision.

Keywords

insulin kinetics hepatic clearance identification IVGTT assay error insulin modified identification error

Introduction

Validated mathematical models can be used to describe patient-specific insulin and nutrition kinetics, and outcome glycemic state.^1-4 They also enable mathematical identification of patient-specific parameters from clinical data.^5,6 Intravenous glucose tolerance tests (IVGTTs) use insulin assay data to determine insulin sensitivity and insulin kinetics. These tests are primarily used for assessing the diagnosis and progression of type 2 diabetes, which is characterized by impaired insulin sensitivity and impaired β-cell function.^7-10 Metabolic tests additionally assess treatments such as diet,^11,12 drug efficacy,^13-15 and the dynamics of insulin resistance.¹⁶

The precision of metabolic models and tests is important for accurate prediction of subject-specific parameters and subsequent outcome assessment.^17,18 Derived metrics such as insulin sensitivity are used in care and incorporated in model-based glycemic control.¹⁹ Thus, test precision is important in achieving desired safety and control outcomes as well as in accurately assessing new therapeutics or treatment approaches.

While structural identifiability of a model assesses theoretical ability to identify a parameter value,^20,21 practical identifiability also considers the impact of noise and other factors in finding precise, specific values.^5,22 A highly identifiable model enables mathematically distinct and precise determination of subject-specific parameters from discrete data.⁵

Model complexity influences data requirements and identifiability. A complex model may describe additional physiological dynamics but may also require more frequent or invasive sampling.² Conversely, a simple model may have less intensive data requirements but fail to describe certain dynamics or encounter identification and prediction limitations due to having a more general representation of a system.^4,23 Model-based approaches seek to provide the most precise outcome possible for the lowest clinical intensity.

Identification of subject-specific model parameters is significantly impacted by factors such as measurement frequency, timing, and assay error.^5,23,24 However, the impact of insulin modification on the identifiability of glycemic model parameters has not yet been explicitly examined with clinical data. Insulin modification is not frequently applied in IVGTTs but potentially allows more dynamic information to be collected from a trial, improving parameter identification and thus accuracy of subject representation. Specifically, this study seeks to determine the impact of small intravenous insulin boluses on the identification of insulin kinetic parameters in clinical glycemic tests.

Methods

Data

Study data come from two IVGTTs: the insulin-modified Dynamic Insulin Sensitivity and Secretion Test (DISST) study²⁵ (Trial A) and a glucose tolerance study undertaken at the University of Auckland, Auckland, New Zealand (Trial B). Both trials received ethics approval from the New Zealand Health and Disability Ethics Committee (HDEC). Both trials collected plasma insulin, plasma glucose, and C-peptide assays over 30-40 minutes. Figure 1 shows test protocol and timing for both trials.

Figure 1.

IVGTT protocol timing, including sampling and intervention timing (minutes). Plasma samples were assayed for glucose, insulin, and C-peptide. IVGTT: intravenous glucose tolerance test.

In Trial A, a 10-g glucose bolus is delivered intravenously to subjects at t = 0, followed by a 1-U intravenous insulin bolus delivered 12-13 minutes later. Trial A’s cohort consists of 50 healthy males and females. Glucose concentration was measured with the YSI 2300 STAT PLUS Glucose and L-Lactate analyzer (YSI Incorporated, Yellow Springs, OH, USA), and insulin and C-peptide concentrations with the Roche Elecsys Insulin assay (Roche Diagnostics, Basel, Switzerland).

Trial B’s protocol includes a glucose bolus delivery of 0.3 g per kilogram of body mass up to a maximum of 30 g, with no insulin modification. Trial B’s cohort consists of 43 healthy adult males. Glucose concentration was measured with the HemoCue Glucose 201+ System analyzer (HemoCue AB, Ängelholm, Sweden) and insulin and C-peptide concentrations with the Roche Elecsys Insulin assay (Roche Diagnostics, Basel, Switzerland).

N = 10 subjects were randomly selected for analysis from each trial. Table 1 shows subject demographics for selected cohorts from both trials.

Table 1.

Subject Demographics for Both Trials.

Identifier	Age (years)	Mass (kg)	Height (cm)	Body mass index (BMI; kg m⁻²)
A1	31	87	181	26.6
A2	34	62	171	21.3
A3	45	59	164	22.0
A4	29	72	184	21.4
A5	60	66	160	25.9
A6	50	89	186	25.7
A7	36	78	171	26.6
A8	24	84	180	26.1
A9	60	65	161	25.1
A10	60	67	157	27.2
B1	38	125	180	36.4
B2	24	92	180	31.9
B3	27	104	178	32.0
B4	22	83	179	26.8
B5	19	83	180	26.0
B6	24	79	172	26.9
B7	36	109	183	34.3
B8	28	121	185	35.2
B9	34	129	187	34.3
B10	27	110	184	32.2

Model

A clinically well-validated three-compartment model^1,26,27 describes subject metabolic dynamics over time to enable identification of subject-specific parameters. Compartments include plasma glucose, G [mg/dl]; plasma insulin, I [mU/l]; and interstitial insulin, Q [mU/l]. Plasma insulin concentration is the compartment of interest for identifying insulin kinetics from insulin assay data and is defined:¹

\overset{\cdot}{I} = - n_{K} I - n_{L} \frac{I}{1 + α_{I} I} - \frac{n_{I}}{V_{I}} (I - Q) + U_{e n} \frac{1 - x_{L}}{V_{I}} + \frac{U_{e x}}{V_{I}}

(1)

The interstitial insulin compartment is defined:

\overset{\cdot}{Q} = \frac{n_{I}}{V_{Q}} (I - Q) - n_{C} Q

(2)

Table 2 describes the parameters in Equations (1) and (2), where the well-accepted van Cauter model²⁸ is used to determine $U_{e n}$ from C-peptide assays, as well as C-peptide kinetic parameters assumed to match those for insulin, $n_{K}$ and $n_{I}$ .²⁹

Table 2.

Parameters for Plasma Insulin Compartment Equation (1).

Term		Value	Unit	Ref.
$n_{K}$	Renal insulin clearance	(calculated)	min⁻¹	Van Cauter et al; Lotz et al^28,29
$α_{I}$	Saturation of liver clearance	$0.0017$	l·mU⁻¹	Lin et al¹
$n_{I}$	Trans-endothelial insulin diffusion	(calculated)	l·min⁻¹	Van Cauter et al; Lotz et al^28,29
$U_{e n}$	Endogenous (pancreatic) insulin secretion	(identified, time-varying)	mU·min⁻¹	Van Cauter et al²⁸
$U_{e x}$	Exogenous (injected) insulin addition	(trial dependent)	mU	Figure 1
$V_{I}$	Plasma insulin volume of distribution	$4.0$	l	Lin et al¹
$n_{L}$	Hepatic insulin clearance	(identified)	min⁻¹	–
$x_{L}$	First-pass hepatic insulin clearance (fractional)	(identified)		–
$V_{Q}$	Interstitial insulin volume of distribution	$1.2 * V_{I}$	l	Krebs et al; Van Cauter et al^11,28
$n_{C}$	Peripheral degradation of insulin	$n_{I} / V_{Q}$	min⁻¹	Krebs et al; Lotz et al^11,30

Identification

Equation (1) is used to simulate each subject’s plasma insulin appearance, I. C-peptide assays are used to estimate endogenous insulin secretion, $U_{e n}$ , over the course of the simulation.²⁸ A selected pair of hepatic clearance parameter values $(n_{L}, x_{L})$ allows simulation of I. The accuracy of these parameter values is assessed by comparing the simulation to assay data.

A grid search over a range of parameter values yields an error surface and identifies optimal clearance values for each subject. Values of $n_{L}$ from -0.100 to 0.775 min^-1 and of $x_{L}$ from 0.075 to 0.950, both in intervals of 0.025, were used, covering the physiological range^29,31-33 and including surrounding non-physiological values. Non-physiological values indicate and capture identifiability problems.

For each $(n_{L}, x_{L})$ pair simulated, the mean squared error relative to the measured insulin assay data is calculated. These error values provide an error surface over the $(n_{L}, x_{L})$ ranges and identify the optimal parameter pair producing the lowest error. A high-resolution grid search is less efficient but ensures there is no impact of method or mathematics on results.

Highly identifiable cases produce error surfaces with a distinct local optimum in a physiological range of parameter values.^5,6,34,35 Poorly identifiable cases have a larger region of parameter pairs whose simulation errors are close or equal to the optimum. To assess the uniqueness of an identified optimum, all parameter pairs around the optimum are located whose model errors are within the variance expected from 5% assay error.^36,37

To assess parameter equivalence due to assay error, a Monte Carlo analysis (N = 1000) is performed for each subject to determine how 5% assay error^36,37 influences model error. For each Monte Carlo trial, each insulin assay sample is multiplied by a normally distributed random variable with a mean of 1 and a standard deviation of 5%, thus adding variability equivalent to assay error. Additionally, insulin simulations are generated for each $(n_{L}, x_{L})$ pair on the 35 × 35 value parameter grid. Each simulation is compared to the N = 1000 modified data vectors by calculating the mean squared errors, generating 100 × 35 × 35 errors in total. One standard deviation of these errors, $σ_{e r r}$ , represents expected model simulation error due to 5% assay error over the physiological parameter range. This process is illustrated in Figure 2.

Figure 2.

Flowchart illustrating the Monte Carlo process used to determine $σ_{e r r}$ , the quantity of model simulation error expected from 5% measurement error on insulin assays.

A subject’s identifiable optimal parameter region is thus defined as the set of all $(n_{L}, x_{L})$ pairs whose simulation errors are within $σ_{e r r}$ of the optimum pair’s error. A large region indicates a poorly identifiable case, where identified parameter values may vary excessively even for moderate insulin assay errors.

Analyses

The optimal parameter regions for Trial A and Trial B subjects are compared to assess the impact of differences in trial design in the use of insulin modification. These differences quantify the identifiability of the insulin pharmacokinetic parameter values. The resulting errors can further impact the resulting identification of insulin sensitivity and other clinical diagnostic parameters. Insulin kinetic parameters $(n_{L}, x_{L})$ may also have their own clinical diagnostic value in some cases, and error should thus be minimized by design if possible.

Results

Figure 3 shows typical examples of model-identified and simulated insulin profiles for Trials A and B at the optimal parameter values. With no exogenous insulin bolus (Trial B), insulin profiles are relatively flatter with only pancreatic secretion. The addition of a relatively small 1 U insulin bolus yields a more dynamic insulin response.

Figure 3.

Sample of optimal insulin simulations from both trials, with corresponding glucose and C-peptide data. Subject A1 (left) displays a dynamic insulin response to exogenous insulin. Subject B2 (right) displays a relatively flat endogenous insulin profile.

Error surfaces for each subject are shown in Figure 4, where subject-specific optimal parameter regions are displayed in green. The optimal ranges of either parameter for each subject are additionally illustrated in Figure 5. The relative sizes of optimal parameter regions and accuracy of optimal insulin fits are provided in Table 3.

Figure 4.

Error surfaces for each subject in Trials A and B. Each optimal parameter region (green) contains errors within $σ_{e r r}$ of minimum error. Red shaded area represents physiological parameter range.^29,31-33 Yellow regions contain errors within 3* $σ_{e r r}$ of minimum error. Contours are logarithmically spaced at multiples of the lowest error of 1, 2.2, 4.6, 10.0, and so on.

Figure 5.

Optimal parameter ranges for each subject. Red shaded area represents physiological parameter ranges.^29,31-33

Table 3.

Optimal Parameter Regions Sizes and Mean Absolute Percentage Error of Optimal Insulin Fit for Each Subject.

Identifier	Area of optimal parameter region (percentage of phys. region area)	$x_{L}$ range	$n_{L}$ range [min⁻¹]	Mean absolute % error of optimal insulin fit
A1	1.5%	0.62-0.69	0.20-0.23	5.3%
A2	3.7%	0.54-0.64	0.25-0.30	11.7%
A3	1.3%	0.71-0.77	0.16-0.19	7.0%
A4	1.3%	0.66-0.71	0.18-0.21	5.6%
A5	2.0%	0.58-0.65	0.15-0.19	4.7%
A6	2.6%	0.52-0.60	0.20-0.24	3.8%
A7	1.9%	0.59-0.66	0.19-0.22	6.6%
A8	1.3%	0.67-0.73	0.18-0.21	1.0%
A9	2.1%	0.66-0.74	0.12-0.16	5.6%
A10	1.7%	0.59-0.66	0.14-0.17	8.7%
Mean (Trial A)	1.9%	0.07	0.04	6.0%
B1	12.3%	0.42-0.63	0.05-0.18	3.0%
B2	8.6%	0.59-0.73	0.13-0.28	3.1%
B3	7.9%	0.48-0.64	0.07-0.20	2.1%
B4	4.4%	0.50-0.60	0.15-0.24	3.3%
B5	10.5%	0.68-0.80	0.06-0.21	5.9%
B6	3.9%	0.52-0.61	0.11-0.19	2.7%
B7	22.3%	0.44-0.65	0.08-0.26	4.2%
B8	5.0%	0.24-0.36	0.07-0.14	4.6%
B9	12.8%	0.49-0.68	0.06-0.21	4.8%
B10	3.8%	0.42-0.51	0.13-0.20	3.1%
Mean (Trial B)	9.1%	0.14	0.12	3.7%

Sizes of optimal parameter regions are provided as both A) area as a percentage of the physiological parameter region^29,31-33 (evaluating at a denser grid resolution of 0.005), and B) ranges of each parameter across optimal region.

In Figures 3 and 4 and Table 3, Trial A has smaller regions more concentrated in physiologically accepted ranges. The optimal parameter ranges for both parameters from Trial A were significantly smaller than the those from Trial B (Wilcoxon rank-sum/Mann-Whitney U test P value < .001). These results suggest insulin modification provides a tighter range of physiologically acceptable identified parameter values and is thus a more identifiable case.

Discussion

Outcomes

A significant parameter trade-off between $x_{L}$ and $n_{L}$ is observed in Trial B’s error surfaces. This trade-off represents an inability to distinguish between input ( $1 - x_{L}$ ) and output ( $n_{L}$ ) rates of the insulin clearance in Equation (1) when the insulin bolus is not present. With the flat insulin profiles in Trial B (Figure 2), a proportional increase or decrease to both simulated input and output rates has little effect on the value of the model prediction. This trade-off is clear in the error surfaces (Figure 3), whose regions extend along a line of increasing $x_{L}$ and decreasing $n_{L}$ . Trial A limits this trade-off, as only specific parameter values provide an accurate dynamic response to the insulin bolus. Thus, the parameters describing these dynamics are more uniquely identifiable when an exogenous bolus is present, an effect well described mathematically.⁵

Trials A and B vary in the size of the glucose bolus delivered. Trial B includes a glucose bolus up to three times greater than Trial A. Subjects in Trial B thus have a stronger pancreatic trigger for insulin secretion, and a stronger endogenous insulin response could be expected. However, improved identification is observed in Trial A, despite the weaker endogenous insulin response. Improved identification is thus caused by the addition of exogenous insulin changing the insulin profile, and the magnitude of the insulin profile is not a factor. Overall, this suggests that the exogenous insulin bolus aids differentiation of general and first-pass hepatic clearance during parameter identification, where endogenously secreted insulin is influenced by both, and exogenous insulin does not undergo a first-pass hepatic cut.

These results suggest exogenous insulin boluses should be included in glycemic test protocol design if precision of modelled kinetics is a priority. The addition of even a single unit of insulin provides dynamic information which improves identification of insulin kinetics parameters. However, there is a small risk of hypoglycemia despite the small bolus size in Trial A.³⁸ While 1 U is a relatively small dose, subject-specific insulin sensitivity and resulting susceptibility to hypoglycemia should be assessed. Equally, the original DISST study included lean subjects with high insulin sensitivity and any hypoglycemia was light (blood glucose concentration > 54 mg/dl), posing minimal risk.²⁵ The DISST pilot study saw measurable insulin dynamics with 0.5 U boluses.³⁰

Limitations

Simulation error may be caused by model dynamics not accurately fitting observed dynamics in these patients. However, the model is very well-validated in clinical use in ICU,^1,19,39,40 in insulin sensitivity testing^25,31,41 and in assessing insulin kinetics,⁴⁰ including as virtual patients.^18,26 The clinical validity of the model provides certainty as to its representation of clearance dynamics.

The findings of this study are limited by the amount of data available and a limited set of subjects. While differences between Trials A and B may be due to selection error, other larger analyses show similar identifiability issues in insulin kinetic models.^23,42-46 The consistency of identifiability results, even with a very small insulin bolus, strongly suggests the insulin modification and its change in the observed dynamics causes the improvement in identification, matching prior analyses.⁵ However, differences between cohorts in age, ethnicity, sex, and BMI should be noted, and further research should repeat this study with one consistent cohort. While the limited number of subjects per trial could be seen as a limitation of these results, Figures 3–4 and Table 3 show the differences in identifiability are consistent and clear. Equally, the addition of further subjects to from these and other trials would not contribute further information to this analysis. Thus, the number of subjects is large enough to demonstrate the identifiability issue and its consistency across all subjects between trials.

The two cohorts can differ in body weight and BMI, which can affect some kinetics parameters, such as volume of distribution. This model has been very well validated with constant volume parameters.^25,30 Furthermore, the identification of the hepatic clearance parameters is dependent on the shape, not the value, of the insulin curve. The effect of changing volume parameters with weight would be to translate the insulin curve up and down without altering the dynamics captured by the $n_{L}$ and $x_{L}$ parameters. A consistent exchange between I and Q compartment volumes is observed in Equations (1) and (2). Thus, it can be concluded that this difference in identifiability is primarily due to insulin modification rather than a significant disparity in distribution volume from differences in cohort demographics.

There are timing differences in the Trial A and B protocols (Figure 1). Trial B has more measurements around the peak of the endogenous response, which should more completely capture the peak and improve identification. However, this improvement is not observed in the results, and improved identification is achieved in Trial A despite the less frequently sampled protocol. This outcome matches results in work by Docherty et al⁵ on the timing of measurements and identifiability, and thus this difference does not impact the results presented here, as Trial B has a superset of the measurements of Trial A.

Analyzing separate trial cohorts introduces potential error due to inter-trial subject variability. Subjects with a strong first-phase endogenous insulin response likely have inherently more identifiable kinetics than those with weaker first-phase response due to stronger clearance dynamics being evident in the sampled insulin assay data. However, the significant improvement in identification in Trial A outweighs this smaller individual variation. Subjects with strong first phase insulin responses are also not typically the targets of diabetes research and diagnostic metabolic tests. Thus, the consistent results over 20 subjects suggest a benefit from the small added insulin bolus regardless of variability in first-phase response.

The model has several fixed parameters and limited samples, both of which may limit the robustness of identified values. However, the model has been proven to accurately describe dynamics to the limit the model defines them in both clinical use for glycemic control^25,41,47,48 and has demonstrated excellent accuracy in identifying insulin sensitivity and other metabolic characteristics. Regarding sampling rates, extra assays with a dense sampling grid are shown to not always improve identification,⁵ where this work by Docherty et al showed subjecting a subject to extra samples may be unnecessary as sparser sampling is sufficient for robust identification. Thus, the sampling protocols employed here should be appropriate for this analysis using this model, based on our prior experiences.^5,29,41

Implications

While the model used in this study is well-validated in clinical use and research, its predictions and outcomes are only as accurate as the data analyzed. Determining subject-specific clearance responses requires data that display the response dynamics described by the model. If these response dynamics are not strongly observable in the data, the relevant parameters cannot be expected to be accurately identified. The addition of an insulin bolus clarifies differing dynamics of general and first-pass hepatic insulin clearances, thus improving identification of both these rate parameters and subsequent model parameters such as insulin sensitivity.

Overall, improved parameter identification aids outcome test precision by providing a more physiologically accurate model. Accurate determination of subject-specific parameter values within a physiological range improves reliability of model predictions in clinical use to guide care.^17,44,49,50 In insulin sensitivity and metabolic testing, improved precision carries over to the insulin sensitivity metric and removes a source of variability in the error, as seen here in the wide range of $n_{L}$ and $x_{L}$ values found. Greater certainty implies greater diagnostic resolution and better precision in assessing the impact of new therapeutic approaches, where such intensive tests have often been used.^11-16 The model-based approach to metabolic tests is thus more relevant and accurate when an insulin bolus is included.

Conclusion

Comparison of two intravenous glucose tolerance tests has demonstrated the addition of a 1 U insulin bolus improves identification of general and first-pass hepatic clearance parameter values. Addition of this bolus reduced the region of optimal parameter values by a factor of 4.7 and provided more physiologically acceptable parameter values. Insulin modification is not commonly employed in IVGTTs, but even small insulin additions are shown to improve outcome test precision at minimal additional clinical cost and risk. Thus, future protocol design for model-based tests should consider adding an exogenous insulin bolus for these modelling benefits, especially where accuracy of glucose-insulin kinetics is a priority.

Footnotes

Abbreviations

BMI, body mass index; DISST, Dynamic Insulin Sensitivity and Secretion Test; IVGTT, intravenous glucose tolerance test.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are supported by New Zealand Science for Technological Innovation National Science Challenge [#CRS-53-2019] and MedTech Core [TEC #370571].

Funders of clinical trial A: Health Research Council of New Zealand (HRC).

Funders of clinical trial B: The Auckland Medical Research Foundation (AMRF), the Health Research Council of New Zealand (HRC) and the Maurice Wilkins Centre (MWC). TLM is supported by a Rutherford Discovery Fellowship.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

ORCID iDs

Alexander D. McHugh

Jennifer L. Knopp

Jennifer J. Ormsbee

References

Lin

Razak

Pretty

, et al. A physiological Intensive Control Insulin-Nutrition-Glucose (ICING) model validated in critically ill patients. Comput Methods Programs Biomed. 2011;102:192-205.

Hovorka

Canonico

Chassin

, et al. Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol Meas. 2004;25:905-920.

Kovatchev

Breton

Dalla Man

Cobelli

In silico preclinical trials: a proof of concept in closed-loop control of type 1 diabetes. J Diabetes Sci Technol. 2009;3:44-55.

Bergman

Bortolan

Cobelli

Toffolo

Identification of a minimal model of glucose disappearance for estimating insulin sensitivity. IFAC Proc. 1979;12:883-890.

Docherty

Chase

Lotz

Desaive

A graphical method for practical and informative identifiability analyses of physiological models: a case study of insulin kinetics and sensitivity. Biomed Eng OnLine. 2011;10:39.

Cobelli

DiStefano

JJ.

Parameter and structural identifiability concepts and ambiguities: a critical review and analysis. Am J Physiol-Regul Integr Comp Physiol. 1980;239:R7-24.

Zethelius

Hales

Lithell

Berne

Insulin resistance, impaired early insulin response, and insulin propeptides as predictors of the development of type 2 diabetes: a population-based, 7-year follow-up study in 70-year-old men. Diabetes Care. 2004;27:1433-1438.

McAuley

Williams

Mann

, et al. Intensive lifestyle changes are necessary to improve insulin sensitivity: a randomized controlled trial. Diabetes Care. 2002;25:445-452.

McLaughlin

Heterogeneity in the prevalence of risk factors for cardiovascular disease and type 2 diabetes mellitus in obese individuals: effect of differences in insulin sensitivity. Arch Intern Med. 2007;167:642.

10.

Hanley

AJG

Williams

Festa

Wagenknecht

D’Agostino

Haffner

. Liver markers and development of the metabolic syndrome: the insulin resistance atherosclerosis study. Diabetes. 2005;54:3140-3147.

11.

Krebs

Bell

Hall

, et al. Improvements in glucose metabolism and insulin sensitivity with a low-carbohydrate diet in obese patients with type 2 diabetes. J Am Coll Nutr. 2013;32:11-17.

12.

Te Morenga

Docherty

Williams

Mann

. The effect of a diet moderately high in protein and fiber on insulin sensitivity measured using the Dynamic Insulin Sensitivity and Secretion Test (DISST). Nutrients. 2017;9:1291.

13.

Lee

Murphy

McCall

, et al. Nadolol reduces insulin sensitivity in liver cirrhosis: a randomized double-blind crossover trial. Diabetes Metab Res Rev. 2017;33:e2859.

14.

Pretty

Chase

Le Compte

Lin

Shaw

Impact of metoprolol on insulin sensitivity in the ICU. IFAC Proc. 2011;44:1763-1767.

15.

Gudbjörnsdóttir

Fowelin

Elam

, et al. The effect of metoprolol treatment on insulin sensitivity and diurnal plasma hormone levels in hypertensive subjects. Eur J Clin Invest. 2003;27:29-35.

16.

Cobelli

Pacini

Toffolo

Sacca

Estimation of insulin sensitivity and glucose clearance from minimal model: new insights from labeled IVGTT. Am J Physiol-Endocrinol Metab. 1986;250:E591- E598.

17.

Chase

Benyo

Desaive

Glycemic control in the intensive care unit: a control systems perspective. Annu Rev Control. 2019;48:359-368.

18.

Chase

Suhaimi

Penning

, et al. Validation of a model-based virtual trials method for tight glycemic control in intensive care. Biomed Eng OnLine. 2010;9:84.

19.

Stewart

Pretty

Tomlinson

, et al. Safety, efficacy and clinical generalization of the STAR protocol: a retrospective analysis. Ann Intensive Care 2016;6:24.

20.

Audoly

Bellu

D’Angio

Saccomani

Cobelli

Global identifiability of nonlinear models of biological systems. IEEE Trans Biomed Eng. 2001;48:55-65.

21.

Bellu

Saccomani

Audoly

D’Angiò

DAISY: a new software tool to test global identifiability of biological and physiological systems. Comput Methods Programs Biomed. 2007;88:52-61.

22.

Raue

Kreutz

Maiwald

, et al. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics. 2009;25:1923-1929.

23.

Pillonetto

Sparacino

Magni

Bellazzi

Cobelli

Minimal model S_I =0 problem in NIDDM subjects: nonzero Bayesian estimates with credible confidence intervals. Am J Physiol-Endocrinol Metab. 2002;282:E564-E573.

24.

Erichsen

Agbaje

Luzio

Owens

Hovorka

Population and individual minimal modeling of the frequently sampled insulin-modified intravenous glucose tolerance test. Metabolism. 2004;53:1349-1354.

25.

McAuley

Berkeley

Docherty

, et al. The dynamic insulin sensitivity and secretion test—a novel measure of insulin sensitivity. Metabolism. 2011;60:1748-1756.

26.

Dickson

Thomas

Pretty

Stewart

Shaw

Chase

JG.

Evaluation of a plasma insulin model for glycaemic control in intensive care. Annu Int Conf IEEE Eng Med Biol Soc. 2015;2015: 4009-4012.

27.

Docherty

Chase

Lotz

, et al. Evaluation of the performances and costs of a spectrum of dynamic insulin sensitivity test protocols. Presentation at: UKACC International Conference on Control 2010; January 2010; Coventry, UK.

28.

Van Cauter

Mestrez

Sturis

Polonsky

. Estimation of insulin secretion rates from C-peptide levels. Comparison of individual and standard kinetic parameters for C-peptide clearance. Diabetes. 1992;41:368-377.

29.

Lotz

Chase

McAuley

, et al. Monte Carlo analysis of a new model-based method for insulin sensitivity testing. Comput Methods Programs Biomed. 2008;89:215-225.

30.

Lotz

Chase

McAuley

, et al. Design and clinical pilot testing of the model-based dynamic insulin sensitivity and secretion test (DISST). J Diabetes Sci Technol. 2010;4:1408-1423.

31.

Lotz

Chase

McAuley

, et al. Transient and steady-state euglycemic clamp validation of a model for glycemic control and insulin sensitivity testing. Diabetes Technol Ther. 2006;8:338-346.

32.

Sherwin

Kramer

Tobin

, et al. A model of the kinetics of insulin in man. J Clin Invest. 1974;53:1481-1492.

33.

Ferrannini

Wahren

Faber

Felig

Binder

DeFronzo

RA.

Splanchnic and renal metabolism of insulin in human subjects: a dose-response study. Am J Physiol-Endocrinol Metab. 1983;244:E517-E527.

34.

Docherty

Chase

David

Characterisation of the iterative integral parameter identification method. Med Biol Eng Comput. 2012;50:127-134.

35.

Carson

Cobelli

Modelling Methodology for Physiology and Medicine. Newnes; 2013.

36.

Wallace

Levy

Matthews

DR.

An increase in insulin sensitivity and basal beta-cell function in diabetic subjects treated with pioglitazone in a placebo-controlled randomized study. Diabet Med. 2004;21:568-576.

37.

Roche. Data sheet - insulin immunoassay, elecsys 1010/2010/modular analytics E170. Technical report 12017547 122, 2004. Mannheim, Germany: Roche Diagnostics.

38.

Bekisz

Holder-Pearson

Chase

Desaive

In silico validation of a new model-based oral-subcutaneous insulin sensitivity testing through Monte Carlo sensitivity analyses. Biomed Signal Process Control. 2020;61:102030.

39.

Pri

Chase

Pretty

, et al. Evolution of insulin sensitivity and its variability in out-of-hospital cardiac arrest (OHCA) patients treated with hypothermia. Crit Care. 2014;18:586.

40.

Jamaludin

Docherty

Geoffrey Chase

Shaw

GM.

Impact of haemodialysis on insulin kinetics of acute kidney injury patients in critical care. J Med Biol Eng. 2015;35:125-133.

41.

Docherty

Chase

Lotz

, et al. DISTq: an iterative analysis of glucose data for low-cost, real-time and accurate estimation of insulin sensitivity. Open Med Inform J. 2009;3:65-76.

42.

Pillonetto

Sparacino

Cobelli

Numerical non-identifiability regions of the minimal model of glucose kinetics: superiority of Bayesian estimation. Math Biosci. 2003;184:53-67.

43.

Ljung

Glad

On global identifiability for arbitrary model parametrizations. Automatica. 1994;30:265-276.

44.

Toffolo

Campioni

Basu

Rizza

Cobelli

A minimal model of insulin secretion and kinetics to assess hepatic insulin extraction. Am J Physiol-Endocrinol Metab. 2006;290:E169-E176.

45.

Yang

Youn

Bergman

RN.

Modified protocols improve insulin sensitivity estimation using the minimal model. Am J Physiol-Endocrinol Metab. 1987;253:E595–E602.

46.

Haffner

D’Agostino

Festa

, et al. Low insulin sensitivity (Si = 0) in diabetic and nondiabetic subjects in the insulin resistance atherosclerosis study: is it associated with components of the metabolic syndrome and nontraditional risk factors? Diabetes Care. 2003;26:2796-2803.

47.

Docherty

Chase

Lotz

, et al. Independent cohort cross-validation of the real-time DISTq estimation of insulin sensitivity. Comput Methods Programs Biomed .2011;102:94-104.

48.

Davidson

Docherty

Chase

JG.

Use of the DISST model to estimate the HOMA and Matsuda indexes using only a basal insulin assay. J Diabetes Sci Technol. 2014;8:815-820.

49.

Hovorka

Kumareswaran

Harris

, et al. Overnight closed loop insulin delivery (artificial pancreas) in adults with type 1 diabetes: crossover randomised controlled studies. BMJ. 2011;342:d1855.

50.

Kovatchev

Renard

Cobelli

, et al. Safety of outpatient closed-loop control: first randomized crossover trials of a wearable artificial pancreas. Diabetes Care. 2014;37:1789-1796.

The Impact of Exogenous Insulin Input on Calculating Hepatic Clearance Parameters

Abstract

Objective:

Method:

Results:

Conclusions:

Keywords

Introduction

Methods

Data

Model

Identification

Analyses

Results

Discussion

Outcomes

Limitations

Implications

Conclusion

Footnotes

Abbreviations

Funding

Declaration of Conflicting Interests

ORCID iDs

References