Design and clinical pilot testing of the model-based dynamic insulin sensitivity and secretion test (DISST)

Optimization of identifying insulinaemic pharmacokinetic parameters using artificial neural network

BACKGROUND AND OBJECTIVE

The identification of insulinaemic pharmacokinetic parameters using the least-squares criterion approach is easily influenced by outlying data due to its sensitivity. Furthermore, the least-squares criterion has a tendency to overfit and produce incorrect results. Hence, this research proposes an alternative approach using the artificial neural network (ANN) with two hidden layers to optimize the identifying of insulinaemic pharmacokinetic parameters. The ANN is selected for its ability to avoid overfitting parameters and its faster speed in processing data.

METHODS

18 voluntarily participants were recruited from the Canterbury and Otago region of New Zealand to take part in a Dynamic Insulin Sensitivity and Secretion Test (DISST) clinical trial. A total of 46 DISST data were collected. However, due to ambiguous and inconsistency, 4 data had to be removed. Analysis was done using MATLAB 2020a.

RESULTS AND DISCUSSION

Results show that, with 42 gathered dataset, the ANN generates higher gains, ∅_P = 20.73 [12.21, 28.57] mU·L·mmol^-1·min^-1 and ∅_D = 60.42 [26.85, 131.38] mU·L·mmol^-1 as compared to the linear least square method, ∅_P = 19.67 [11.81, 28.02] mU·L·mmol^-1 ·min^-1 and ∅_D = 46.21 [7.25, 116.71] mU·L·mmol^-1. The average value of the insulin sensitivity (SI) of ANN is lower with, SI = 16 × 10^-4 L·mU^-1 ·min^-1 than the linear least square, SI = 17 × 10^-4 L·mU^-1 ·min^-1.

CONCLUSION

Although the ANN analysis provided a lower SI value, the results were more dependable than the linear least square model because the ANN approach yielded a better model fitting accuracy than the linear least square method with a lower residual error of less than 5%. With the implementation of this ANN architecture, it shows that ANN able to produce minimal error during optimization process particularly when dealing with outlying data. The findings may provide extra information to clinicians, allowing them to gain a better knowledge of the heterogenous aetiology of diabetes and therapeutic intervention options.

The Effects of Additional Local-Mixing Compartments in the DISST Model-Based Assessment of Insulin Sensitivity

BACKGROUND

The identification of insulin sensitivity in glycemic modelling can be heavily obstructed by the presence of outlying data or unmodelled effects. The effect of data indicative of local mixing is especially problematic with models assuming rapid mixing of compartments. Methods such as manual removal of data and outlier detection methods have been used to improve parameter ID in these cases, but modelling data with more compartments is another potential approach.

METHODS

This research compares a mixing model with local depot site compartments with an existing, clinically validated insulin sensitivity test model. The Levenberg-Marquardt (LM) parameter identification method was implemented alongside a modified version (aLM) capable of operator-independent omission of outlier data in accordance with the 3 standard deviation rule. Three cases were tested: LM where data points suspected to be affected by incomplete mixing at the depot site were removed, aLM, and LM with the more complex mixing model.

RESULTS

While insulin parameters identified in the mixing model differed greatly from those in the DISST model, there were strong Spearman correlations of approximately 0.93 for the insulin sensitivity values identified across all 3 methods. The 2 models also showed comparable identification stability in insulin sensitivity estimation through a Monte Carlo analysis. However, the mixing model required modifications to the identification process to improve convergence, and still failed to converge to feasible parameters on 5 of the 212 trials.

CONCLUSIONS

The mixing compartment model effectively captured the dynamics of mixing behavior, but with no significant improvement in insulin sensitivity identification.

The Impact of Exogenous Insulin Input on Calculating Hepatic Clearance Parameters

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.

Variability in Estimated Modelled Insulin Secretion

BACKGROUND

The ability to measure insulin secretion from pancreatic beta cells and monitor glucose-insulin physiology is vital to current health needs. C-peptide has been used successfully as a surrogate for plasma insulin concentration. Quantifying the expected variability of modelled insulin secretion will improve confidence in model estimates.

METHODS

Forty-three healthy adult males of Māori or Pacific peoples ancestry living in New Zealand participated in an frequently sampled, intravenous glucose tolerance test (FS-IVGTT) with an average age of 29 years and a BMI of 33 kg/m². A 2-compartment model framework and standardized kinetic parameters were used to estimate endogenous pancreatic insulin secretion from plasma C-peptide measurements. Monte Carlo analysis (N = 10 000) was then used to independently vary parameters within ±2 standard deviations of the mean of each variable and the 5th and 95th percentiles determined the bounds of the expected range of insulin secretion. Cumulative distribution functions (CDFs) were calculated for each subject for area under the curve (AUC) total, AUC Phase 1, and AUC Phase 2. Normalizing each AUC by the participant's median value over all N = 10 000 iterations quantifies the expected model-based variability in AUC.

RESULTS

Larger variation is found in subjects with a BMI > 30 kg/m², where the interquartile range is 34.3% compared to subjects with a BMI ≤ 30 kg/m² where the interquartile range is 24.7%.

CONCLUSIONS

Use of C-peptide measurements using a 2-compartment model and standardized kinetic parameters, one can expect ~±15% variation in modelled insulin secretion estimates. The variation should be considered when applying this insulin secretion estimation method to clinical diagnostic thresholds and interpretation of model-based analyses such as insulin sensitivity.

Determining Losses in Jet Injection Subcutaneous Insulin Delivery: A Model-Based Approach

OBJECTIVE

Accurate, safe glycemic management requires reliable delivery of insulin doses. Insulin can be delivered subcutaneously for action over a longer period of time. Needle-free jet injectors provide subcutaneous (SC) delivery without requiring needle use, but the volume of insulin absorbed varies due to losses associated with the delivery method. This study employs model-based methods to determine the expected proportion of active insulin present from a needle-free SC dose.

METHODS

Insulin, C-peptide, and glucose assay data from a frequently sampled insulin-modified oral glucose tolerance test trial with 2U SC insulin delivery, paired with a well-validated metabolic model, predict metabolic outcomes for N = 7 healthy adults. Subject-specific nonlinear hepatic clearance profiles are modeled over time using third-order basis splines with knots located at assay times. Hepatic clearance profiles are constrained within a physiological rate of change, and relative to plasma glucose profiles. Insulin loss proportions yielding optimal insulin predictions are then identified, quantifying delivery losses.

RESULTS

Optimal parameter identification suggests losses of up to 22% of the nominal 2U SC dose. The degree of loss varies between subjects and between trials on the same subject. Insulin fit accuracy improves where loss greater than 5% is identified, relative to where delivery loss is not modeled.

CONCLUSIONS

Modeling shows needle-free SC jet injection of a nominal dose of insulin does not necessarily provide metabolic action equivalent to total dose, and this availability significantly varies between trials. By quantifying and accounting for variability of jet injection insulin doses, better glycemic management outcomes using SC jet injection may be achieved.

Estimating Increased EGP During Stress Response in Critically Ill Patients

BACKGROUND

Stress-induced hyperglycemia is frequently experienced by critically ill patients and the use of glycemic control (GC) has been shown to improve patient outcomes. For model-based approaches to GC, it is important to understand and quantify model parameter assumptions. This study explores endogenous glucose production (EGP) and the use of a population-based parameter value in the intensive care unit context.

METHOD

Hourly insulin sensitivity (SI) was fit to clinical data from 145 patients on the Specialized Relative Insulin and Nutrition Titration GC protocol for at least 24 hours. Constraint of SI at a lower bound was used to explore likely EGP variability due to stress response. Minimum EGP was estimated during times when the model SI was constrained, and time and duration of events were examined.

RESULTS

Constrained events occur for 1.6% of patient hours. About 70% of constrained events occur in the first 12 hours and most events (~80%) occur when there is no exogenous nutrition given. Enhanced EGP values ranged from 1.16 mmol/min (current population value) to 2.75 mmol/min, with most being below 1.5 mmol/min (21% increase).

CONCLUSION

The frequency of constrained events is low and the current population value of 1.16 mmol/min is sufficient for more than 98% of patient hours, however, some patients experience significantly raised EGP probably due to an extreme stress response early in patient stay.

Insulin sensitivity in critically ill patients: are women more insulin resistant?

Background

Glycaemic control (GC) in intensive care unit is challenging due to significant inter- and intra-patient variability, leading to increased risk of hypoglycaemia. Recent work showed higher insulin resistance in female preterm neonates. This study aims to determine if there are differences in inter- and intra-patient metabolic variability between sexes in adults, to gain in insight into any differences in metabolic response to injury. Any significant difference would suggest GC and randomised trial design should consider sex differences to personalise care.

Methods

Insulin sensitivity (SI) levels and variability are identified from retrospective clinical data for men and women. Data are divided using 6-h blocks to capture metabolic evolution over time. In total, 91 male and 54 female patient GC episodes of minimum 24 h are analysed. Hypothesis testing is used to determine whether differences are significant (P < 0.05), and equivalence testing is used to assess whether these differences can be considered equivalent at a clinical level. Data are assessed for the raw cohort and in 100 Monte Carlo simulations analyses where the number of men and women are equal.

Results

Demographic data between females and males were all similar, including GC outcomes (safety from hypoglycaemia and high (> 50%) time in target band). Females had consistently significantly lower SI levels than males, and this difference was not clinically equivalent. However, metabolic variability between sexes was never significantly different and always clinically equivalent. Thus, inter-patient variability was significantly different between males and females, but intra-patient variability was equivalent.

Conclusion

Given equivalent intra-patient variability and significantly greater insulin resistance, females can receive the same benefit from safe, effective GC as males, but may require higher insulin doses to achieve the same glycaemia. Clinical trials should consider sex differences in protocol design and outcome analyses.

Insulin sensitivity in critically ill patients: are women more insulin resistant?

BACKGROUND

Glycaemic control (GC) in intensive care unit is challenging due to significant inter- and intra-patient variability, leading to increased risk of hypoglycaemia. Recent work showed higher insulin resistance in female preterm neonates. This study aims to determine if there are differences in inter- and intra-patient metabolic variability between sexes in adults, to gain in insight into any differences in metabolic response to injury. Any significant difference would suggest GC and randomised trial design should consider sex differences to personalise care.

METHODS

Insulin sensitivity (SI) levels and variability are identified from retrospective clinical data for men and women. Data are divided using 6-h blocks to capture metabolic evolution over time. In total, 91 male and 54 female patient GC episodes of minimum 24 h are analysed. Hypothesis testing is used to determine whether differences are significant (P < 0.05), and equivalence testing is used to assess whether these differences can be considered equivalent at a clinical level. Data are assessed for the raw cohort and in 100 Monte Carlo simulations analyses where the number of men and women are equal.

RESULTS

Demographic data between females and males were all similar, including GC outcomes (safety from hypoglycaemia and high (> 50%) time in target band). Females had consistently significantly lower SI levels than males, and this difference was not clinically equivalent. However, metabolic variability between sexes was never significantly different and always clinically equivalent. Thus, inter-patient variability was significantly different between males and females, but intra-patient variability was equivalent.

CONCLUSION

Given equivalent intra-patient variability and significantly greater insulin resistance, females can receive the same benefit from safe, effective GC as males, but may require higher insulin doses to achieve the same glycaemia. Clinical trials should consider sex differences in protocol design and outcome analyses.

A subcutaneous insulin pharmacokinetic model for insulin Detemir

BACKGROUND AND OBJECTIVE

Type 2 diabetes (T2D) is rapidly increasing in incidence and has significant social and economic costs. Given the increasing cost of complications, even relatively short delays in the onset of T2D can significantly reduce long-term complications and costs. Equally, recent studies have shown the onset of T2D can be delayed by use of long-acting insulin, despite the risk and concomitant low adherence. Thus, there is a strong potential motivation to develop models of long-acting insulin analogues to enable safe, effective use in model-based dosing systems. In particular, there are no current models of long-acting insulin Detemir and its unique action for model-based control. The objective of this work is to develop a first model of insulin Detemir and its unique action, and validate it against existing data in the literature.

METHODS

This study develops a detailed compartment model for insulin Detemir. Model specific parameters are identified using data from a range of published clinical studies on the pharmacokinetic of insulin Detemir. Model validity and robustness are assessed by identifying the model for each study and using average identified parameters over several dose sizes and study cohorts. Comparisons to peak concentration, time of peak concentration and overall error versus measured plasma concentrations are used to assess model accuracy and validity.

RESULTS

Almost all studies and cohorts fit literature data to within one standard deviation of error, even when using averaged identified model parameters. However, there appears to be a noticeable dose dependent dynamic not included in this first model, nor reported in the literature studies.

CONCLUSIONS

A first model of insulin Detemir including its unique albumin binding kinetics is derived and provisionally validated against clinical pharmacokinetic data. The pharmacokinetic curves are suitable for model-based control and general enough for use. While there are limitations in the studies used for validation that prevent a more complete understanding, the results provide an effective first model and justify the design and implementation of further, more precise human trials.

The Need to Calculate Target Glucose Levels When Measuring Changes in Insulin Sensitivity During Interventions for Individuals With Type 2 Diabetes

BACKGROUND

Physiological models that are used with dynamic test data to assess insulin sensitivity (SI) assume that the metabolic target glucose concentration ( G_TARGET) is equal to fasting glucose concentration ( G₀). However, recent research has implied that irregularities in G₀ in diabetes may cause erroneous SI values. This study quantifies the magnitude of these errors.

METHODS

A clinically validated insulin/glucose model was used to calculate SI with the standard fasting assumption (SFA) G₀ = G_TARGET. Then G_TARGET was treated as a variable in a second analysis (VGT). The outcomes were contrasted across twelve participants with established type 2 diabetes mellitus that were recruited to take part in a 24-week dietary intervention. Participants underwent three insulin-modified intravenous glucose tolerance tests (IM-IVGTT) at 0, 12, and 24 weeks.

RESULTS

SI_VGT had a median value of 3.36×10^-4 L·mU^-1·min^-1 (IQR: 2.30 - 4.95×10^-4) and were significantly lower ( P < .05) than the median SI_SFA (6.38×10^-4 L·mU^-1·min^-1, IQR: 4.87 - 9.39×10^-4). The VGT approach generally yielded lower SI values in line with expected participant physiology and more effectively tracked changes in participant state over the 24-week trial. Calculated G_TARGET values were significantly lower than G₀ values (median G_TARGET = 5.48 vs G₀ = 7.16 mmol·L^-1 P < .001) and were notably higher in individuals with longer term diabetes.

CONCLUSIONS

Typical modeling approaches can overestimate SI when G_TARGET does not equal G₀. Hence, calculating G_TARGET may enable more precise SI measurements in individuals with type 2 diabetes, and could imply a dysfunction in diabetic metabolism.

Levels and Diagnostic Value of Model-based Insulin Sensitivity in Sepsis: A Preliminary Study

Background and Aims:

Currently, there is a lack of real-time metric with high sensitivity and specificity to diagnose sepsis. Insulin sensitivity (SI) may be determined in real-time using mathematical glucose-insulin models; however, its effectiveness as a diagnostic test of sepsis is unknown. Our aims were to determine the levels and diagnostic value of model-based SI for identification of sepsis in critically ill patients.

Materials and Methods:

In this retrospective, cohort study, we analyzed SI levels in septic (n = 18) and nonseptic (n = 20) patients at 1 (baseline), 4, 8, 12, 16, 20, and 24 h of their Intensive Care Unit admission. Patients with diabetes mellitus Type I or Type II were excluded from the study. The SI levels were derived by fitting the blood glucose levels, insulin infusion and glucose input rates into the Intensive Control of Insulin-Nutrition-Glucose model.

Results:

The median SI levels were significantly lower in the sepsis than in the nonsepsis at all follow-up time points. The areas under the receiver operating characteristic curve of the model-based SI at baseline for discriminating sepsis from nonsepsis was 0.814 (95% confidence interval, 0.675–0.953). The optimal cutoff point of the SI test was 1.573 × 10⁻⁴ L/mu/min. At this cutoff point, the sensitivity was 77.8%, specificity was 75%, positive predictive value was 73.7%, and negative predictive value was 78.9%.

Conclusions:

Model-based SI ruled in and ruled out sepsis with fairly high sensitivity and specificity in our critically ill nondiabetic patients. These findings can be used as a foundation for further, prospective investigation in this area.

The Effect of a Diet Moderately High in Protein and Fiber on Insulin Sensitivity Measured Using the Dynamic Insulin Sensitivity and Secretion Test (DISST)

Evidence shows that weight loss improves insulin sensitivity but few studies have examined the effect of macronutrient composition independently of weight loss on direct measures of insulin sensitivity. We randomised 89 overweight or obese women to either a standard diet (StdD), that was intended to be low in fat and relatively high in carbohydrate (n = 42) or to a relatively high protein (up to 30% of energy), relatively high fibre (>30 g/day) diet (HPHFib) (n = 47) for 10 weeks. Advice regarding strict adherence to energy intake goals was not given. Insulin sensitivity and secretion was assessed by a novel method—the Dynamic Insulin Sensitivity and Secretion Test (DISST). Although there were significant improvements in body composition and most cardiometabolic risk factors on HPHFib, insulin sensitivity was reduced by 19.3% (95% CI: 31.8%, 4.5%; p = 0.013) in comparison with StdD. We conclude that the reduction in insulin sensitivity after a diet relatively high in both protein and fibre, despite cardiometabolic improvements, suggests insulin sensitivity may reflect metabolic adaptations to dietary composition for maintenance of glucose homeostasis, rather than impaired metabolism.

Untangling glycaemia and mortality in critical care

Background

Hyperglycaemia is associated with adverse outcomes in the intensive care unit, and initial studies suggested outcome benefits of glycaemic control (GC). However, subsequent studies often failed to replicate these results, and they were often unable to achieve consistent, safe control, raising questions about the benefit or harm of GC as well as the nature of the association of glycaemia with mortality and clinical outcomes. In this study, we evaluated if non-survivors are harder to control than survivors and determined if glycaemic outcome is a function of patient condition and eventual outcome or of the glycaemic control provided.

Methods

Clinically validated, model-based, hour-to-hour insulin sensitivity (SI) and its hour-to-hour variability (%ΔSI) were identified over the first 72 h of therapy in 145 patients (119 survivors, 26 non-survivors). In hypothesis testing, we compared distributions of SI and %ΔSI in 6-hourly blocks for survivors and non-survivors. In equivalence testing, we assessed if differences in these distributions, based on blood glucose measurement error, were clinically significant.

Results

SI level was never equivalent between survivors and non-survivors (95% CI of percentage difference in medians outside ±12%). Non-survivors had higher SI, ranging from 9% to 47% higher overall in 6-h blocks, and this difference became statistically significant as glycaemic control progressed. %ΔSI was equivalent between survivors and non-survivors for all 6-hourly blocks (95% CI of difference in medians within ±12%) and decreased in general over time as glycaemic control progressed.

Conclusions

Whereas non-survivors had higher SI levels, variability was equivalent to that of survivors over the first 72 h. These results indicate survivors and non-survivors are equally controllable, given an effective glycaemic control protocol, suggesting that glycaemia level and variability, and thus the association between glycaemia and outcome, are essentially determined by the control provided rather than by underlying patient or metabolic condition.

Electronic supplementary material

The online version of this article (doi:10.1186/s13054-017-1725-y) contains supplementary material, which is available to authorized users.

Incorporating bolus and infusion pharmacokinetics into the ICING insulin model

The ICING model has been successfully used to guide clinical decisions on insulin administration in critical illness. However, insulin pharmacokinetics in the ICING model can be improved to better describe both intravenous (IV) bolus and infusion insulin administration. Patient data from 217 Dynamic Insulin Sensitivity and Secretion Tests (DISST) and 36 Intravenous Glucose Tolerance Tests (IVGTT) from independent dietary intervention studies was used to fit model parameters to a model structure that conforms to known behaviour. The DISST tests measured both endogenous and exogenous IV insulin bolus responses, while the IVGTT measured exogenous IV insulin infusion dynamics. Unidentifiable parameters were given physiologically justified values, with knowledge on relative insulin clearance rates used to constrain parameter values. The resulting whole-cohort description was able to simultaneously describe both IV bolus and infusion dynamics, and improves ICING model descriptive capability. Improved infusion dynamics will allow better description of subcutaneous insulin, the insulin administration route favoured in outpatient care of diabetes.

The necessity of identifying the basal glucose set-point in the IVGTT for patients with Type 2 Diabetes

Background

The model-based dynamic insulin sensitivity and secretion test (DISST) uses fasting glucose (G₀) as the basal glucose (G_B) concentration when assessing insulin sensitivity (SI). However, this model was developed in a healthy, normoglycaemic cohort. We sought to determine the suitability the DISST model has for individuals with established type 2 diabetes (T2D).

Methods

14 participants with established T2D were recruited to take part in a dietary intervention study. Insulin-modified intravenous glucose tolerance tests (IM-IVGTT) were undertaken at week 0, 12 and 24 and were used with DISST model to identify G_B. A total of 36 tests were conducted across 12 participants throughout the study. Measured G₀ and identified G_B values were compared using a Kolmogorov-Smirnov (KS) and signed rank (RS) test for the cohort.

Results

There were significant differences between the G₀ and identified G_B values in this cohort (p_rs and p_ks < 0.0001), although both values were well correlated (R = 0.70). The residual plot demonstrates that the modified model captures the behaviour of the participants more accurately than the original model.

Conclusions

This analysis has shown that G_B is an important variable for modelling the glycaemic behaviour in T2D. These findings suggest that the original DISST model, while appropriate for normoglycaemic cohorts, needs to model basal glucose level as a variable for assessing individuals with established T2D.

Use of the DISST model to estimate the HOMA and Matsuda indexes using only a basal insulin assay

It is hypothesized that early detection of reduced insulin sensitivity (SI) could prompt intervention that may reduce the considerable financial strain type 2 diabetes mellitus (T2DM) places on global health care. Reduction of the cost of already inexpensive SI metrics such as the Matsuda and HOMA indexes would enable more widespread, economically feasible use of these metrics for screening. The goal of this research was to determine a means of reducing the number of insulin samples and therefore the cost required to provide an accurate Matsuda Index value. The Dynamic Insulin Sensitivity and Secretion Test (DISST) model was used with the glucose and basal insulin measurements from an Oral Glucose Tolerance Test (OGTT) to predict patient insulin responses. The insulin response to the OGTT was determined via population based regression analysis that incorporated the 60-minute glucose and basal insulin values. The proposed method derived accurate and precise Matsuda Indices as compared to the fully sampled Matsuda (R = .95) using only the basal assay insulin-level data and 4 glucose measurements. Using a model employing the basal insulin also allows for determination of the 1-day HOMA value. The DISST model was successfully modified to allow for the accurate prediction an individual's insulin response to the OGTT. In turn, this enabled highly accurate and precise estimation of a Matsuda Index using only the glucose and basal insulin assays. As insulin assays account for the majority of the cost of the Matsuda Index, this model offers a significant reduction in assay cost.

A novel hierarchal-based approach to measure insulin sensitivity and secretion in at-risk populations

The pathogenesis of type 2 diabetes is characterized by insulin resistance and insulin secretory dysfunction. Few existing metabolic tests measure both characteristics, and no such tests are inexpensive enough to enable widespread use. A hierarchical approach uses 2 down-sampled tests in the dynamic insulin sensitivity and secretion test (DISST) family to first determine insulin sensitivity (SI) using 4 glucose measurements. Second the insulin secretion is determined for only participants with reduced SI using 3 C-peptide measurements from the original test. The hierarchical approach is assessed via its ability to classify 214 individual test responses of 71 females with an elevated risk of type 2 diabetes into 5 bins with equivalence to the fully sampled DISST. Using an arbitrary SI cut-off, 102 test responses were reassayed for C-peptide and unique insulin secretion characteristics estimated. The hierarchical approach correctly classified 84.5% of the test responses and 94.4% of the responses of individuals with increased fasting glucose. The hierarchical approach is a low-cost methodology for measuring key characteristics of type 2 diabetes. Thus the approach could provide an economical approach to studying the pathogenesis of type 2 diabetes, or in early risk screening. As the higher cost test uses the same clinical protocol as the low-cost test, the cost of the additional information is limited to the assay cost of C-peptide, and no additional procedures or callbacks are required.

Clinical validation of the quick dynamic insulin sensitivity test

The quick dynamic insulin sensitivity test (DISTq) can yield an insulin sensitivity result immediately after a 30-min clinical protocol. The test uses intravenous boluses of 10 g glucose and 1 U insulin at t = 1 and 11 min, respectively, and measures glucose levels in samples taken at t = 0, 10, 20, and 30 min. The low clinical cost of the protocol is enabled via robust model formulation and a series of population-derived relationships that estimate insulin pharmacokinetics as a function of insulin sensitivity (SI). Fifty individuals underwent the gold standard euglycaemic clamp (EIC) and DISTq within an eight-day period. SI values from the EIC and two DISTq variants (four-sample DISTq and two-sample DISTq30) were compared with correlation, Bland-Altman and receiver operator curve analyses. DISTq and DISTq30 correlated well with the EIC [R = 0.76 and 0.75, and receiver operator curve c-index = 0.84 and 0.85, respectively]. The median differences between EIC and DISTq/DISTq30 SI values were 13% and 22%, respectively. The DISTq estimation method predicted individual insulin responses without specific insulin assays with relative accuracy and thus high equivalence to EIC SI values was achieved. DISTq produced very inexpensive, relatively accurate immediate results, and can thus enable a number of applications that are impossible with established SI tests.

Iterative integral parameter identification of a respiratory mechanics model

BACKGROUND

Patient-specific respiratory mechanics models can support the evaluation of optimal lung protective ventilator settings during ventilation therapy. Clinical application requires that the individual's model parameter values must be identified with information available at the bedside. Multiple linear regression or gradient-based parameter identification methods are highly sensitive to noise and initial parameter estimates. Thus, they are difficult to apply at the bedside to support therapeutic decisions.

METHODS

An iterative integral parameter identification method is applied to a second order respiratory mechanics model. The method is compared to the commonly used regression methods and error-mapping approaches using simulated and clinical data. The clinical potential of the method was evaluated on data from 13 Acute Respiratory Distress Syndrome (ARDS) patients.

RESULTS

The iterative integral method converged to error minima 350 times faster than the Simplex Search Method using simulation data sets and 50 times faster using clinical data sets. Established regression methods reported erroneous results due to sensitivity to noise. In contrast, the iterative integral method was effective independent of initial parameter estimations, and converged successfully in each case tested.

CONCLUSION

These investigations reveal that the iterative integral method is beneficial with respect to computing time, operator independence and robustness, and thus applicable at the bedside for this clinical application.

Characterisation of the iterative integral parameter identification method

Parameter identification methods are used to find optimal parameter values to fit models to measured data. The single integral method was defined as a simple and robust parameter identification method. However, the method did not necessarily converge to optimum parameter values. Thus, the iterative integral method (IIM) was developed. IIM will be compared to a proprietary nonlinear-least-squares-based Levenberg-Marquardt parameter identification algorithm using a range of reasonable starting values. Performance is assessed by the rate and accuracy of convergence for an exemplar two parameters insulin pharmacokinetic model, where true values are known a priori. IIM successfully converged to within 1% of the true values in all cases with a median time of 1.23 s (IQR 0.82-1.55 s; range 0.61-3.91 s). The nonlinear-least-squares method failed to converge in 22% of the cases and had a median (successful) convergence time of 3.29 s (IQR 2.04-4.89 s; range 0.42-44.9 s). IIM is a stable and relatively quick parameter identification method that can be applied in a broad variety of model configurations. In contrast to most established methods, IIM is not susceptible to local minima and is thus, starting point and operator independent.

The dynamic insulin sensitivity and secretion test--a novel measure of insulin sensitivity

The objective was to validate the methodology for the dynamic insulin sensitivity and secretion test (DISST) and to demonstrate its potential in clinical and research settings. One hundred twenty-three men and women had routine clinical and biochemical measurements, an oral glucose tolerance test, and a DISST. For the DISST, participants were cannulated for blood sampling and bolus administration. Blood samples were drawn at t = 0, 10, 15, 25, and 35 minutes for measurement of glucose, insulin, and C-peptide. A 10-g bolus of intravenous glucose at t = 5 minutes and 1 U of intravenous insulin immediately after the t = 15 minute sample were given. Fifty participants also had a hyperinsulinemic-euglycemic clamp. Relationships between DISST insulin sensitivity (SI) and the clamp, and both DISST SI and secretion and other metabolic variables were measured. A Bland-Altman plot showed little bias in the comparison of DISST with the clamp, with DISST underestimating the glucose clamp by 0.1·10(-2)·mg·L·kg(-1)·min(-1)·pmol(-1) (90% confidence interval, -0.2 to 0). The correlation between SI as measured by DISST and the clamp was 0.82; the c unit for the receiver operating characteristic curve analysis for the 2 tests was 0.96. Metabolic variables showed significant correlations with DISST SI and the second phase of insulin release. The DISST also appears able to distinguish different insulin secretion patterns in individuals with identical SI values. The DISST is a simple, dynamic test that compares favorably with the clamp in assessing SI and allows simultaneous assessment of insulin secretion. The DISST has the potential to provide even more information about the pathophysiology of diabetes than more complicated tests.

A spectrum of dynamic insulin sensitivity test protocols

BACKGROUND

Numerous tests have been developed to estimate insulin sensitivity (SI). However, most of the established tests are either too expensive for widespread application or do not yield reliable results. The dynamic insulin sensitivity and secretion test (DISST) uses assays of glucose, insulin, and C-peptide from nine samples to quantify SI and endogenous insulin secretion (UN) at a comparatively low cost. The quick dynamic insulin sensitivity test has shown that the DISST SI values are robust to significant assay omissions.

METHODS

Eight DISST-based variations of the nine-sample assay regimen are proposed to investigate the effects of assay omission within the DISST-based framework. SI and UN were identified using the fully-sampled DISST and data from 218 nine-sample tests undertaken in 74 female individuals with elevated diabetes risk. This same data was then used with appropriate assay omissions to identify SI and UN with the eight DISST-based assay variations.

RESULTS

Median intraprocedure proportional difference between SI values from fully-sampled DISST and the DISST-based variants was in the range of -17.9 to 7.8%. Correlations were in the range of r = 0.71 to 0.92 with the highest correlations between variants with the greatest commonality with the nine-sample DISST. Metrics of UN correlated relatively well between tests when C-peptide was assayed (r = 0.72 to 1) but were sometimes not well estimated when samples were not assayed for C-peptide (r = -0.14 to 0.75).

CONCLUSIONS

The DISST-based spectrum offers a series of tests with very distinct compromises of information yield, accuracy, assay cost, and clinical intensity. Thus, the spectrum of tests has the potential to enable researchers to better allocate funds by selecting an optimal test configuration for their particular application.

A graphical method for practical and informative identifiability analyses of physiological models: a case study of insulin kinetics and sensitivity

BACKGROUND

Derivative based a-priori structural identifiability analyses of mathematical models can offer valuable insight into the identifiability of model parameters. However, these analyses are only capable of a binary confirmation of the mathematical distinction of parameters and a positive outcome can begin to lose relevance when measurement error is introduced. This article presents an integral based method that allows the observation of the identifiability of models with two-parameters in the presence of assay error.

METHODS

The method measures the distinction of the integral formulations of the parameter coefficients at the proposed sampling times. It can thus predict the susceptibility of the parameters to the effects of measurement error. The method is tested in-silico with Monte Carlo analyses of a number of insulin sensitivity test applications.

RESULTS

The method successfully captured the analogous nature of identifiability observed in Monte Carlo analyses of a number of cases including protocol alterations, parameter changes and differences in participant behaviour. However, due to the numerical nature of the analyses, prediction was not perfect in all cases.

CONCLUSIONS

Thus although the current method has valuable and significant capabilities in terms of study or test protocol design, additional developments would further strengthen the predictive capability of the method. Finally, the method captures the experimental reality that sampling error and timing can negate assumed parameter identifiability and that identifiability is a continuous rather than discrete phenomenon.