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.

Monte Carlo analysis of a new model-based method for insulin sensitivity testing.

Insulin resistance (IR), or low insulin sensitivity, is a major risk factor in the pathogenesis of type 2 diabetes and cardiovascular disease. A simple, high resolution assessment of IR would enable earlier diagnosis and more accurate monitoring of intervention effects. Current assessments are either too intensive for clinical settings (Euglycaemic Clamp, IVGTT) or have too low resolution (HOMA, fasting glucose/insulin). Based on high correlation of a model-based measure of insulin sensitivity and the clamp, a novel, clinically useful test protocol is designed with: physiological dosing, short duration (<1 h), simple protocol, low cost and high repeatability. Accuracy and repeatability are assessed with Monte Carlo analysis on a virtual clamp cohort (N=146). Insulin sensitivity as measured by this test has a coefficient of variation (CV) of CV(SI)=4.5% (90% CI: 3.8-5.7%), slightly higher than clamp ISI (CV(ISI)=3.3% (90% CI: 3.0-4.0%)) and significantly lower than HOMA (CV(HOMA)=10.0% (90% CI: 9.1-10.8%)). Correlation to glucose and unit normalised ISI is r=0.98 (90% CI: 0.97-0.98). The proposed protocol is simple, cost effective, repeatable and highly correlated to the gold-standard clamp.

Transient and steady-state euglycemic clamp validation of a model for glycemic control and insulin sensitivity testing.

BACKGROUND: There is an urgent need for a simple and accurate measure of insulin sensitivity to diagnose insulin resistance in the general population and quantify changes due to clinical intervention. A new physiological control model of glucose and insulin metabolism is validated with the euglycemic-hyperinsulinemic clamp during steady and transient states. METHODS: The data consist of n = 60 (15 lean, 15 overweight, 15 obese, and 15 morbidly obese) euglycemic-hyperinsulinemic clamp trials performed on normoglycemic insulin-resistant individuals. The glucose and insulin model is fitted using an integral-based method. Correlations between clamp-derived insulin sensitivity index (ISI) and the model's insulin sensitivity parameter (SI) are obtained during steady and transient states. Results are compared with log-homeostasis model assessment (HOMA), a widely used fasting surrogate for insulin sensitivity. RESULTS: Correlation between model-based insulin sensitivity, SI, and ISIG (ISI normalized by steady-state glucose) is r = 0.99 (n = 60) at steady state and r = 0.97 at transient state, respectively. Correlations did not significantly change across subgroups, with narrow 95% confidence intervals. Log-HOMA correlations are r=-0.72 to SI and r=-0.71 to ISIG for the overall population but are significantly lower in the subgroups, with wide 95% confidence intervals. CONCLUSIONS: The model-based insulin sensitivity parameter, SI, highly correlates to ISIG in all subgroups, even when only considering a transient state. The high correlation of SI offers the potential for a short, simple yet highly correlated, model-based assessment of insulin sensitivity that is not currently available.

Separate modal analysis for tumor detection with a digital image elasto tomography (DIET) breast cancer screening system.

PURPOSE: It is estimated that every year, 1 × 10(6) women are diagnosed with breast cancer, and more than 410,000 die annually worldwide. Digital Image Elasto Tomography (DIET) is a new noninvasive breast cancer screening modality that induces mechanical vibrations in the breast and images its surface motion with digital cameras to detect changes in stiffness. This research develops a new automated approach for diagnosing breast cancer using DIET based on a modal analysis model. METHODS: The first and second natural frequency of silicone phantom breasts is analyzed. Separate modal analysis is performed for each region of the phantom to estimate the modal parameters using imaged motion data over several input frequencies. Statistical methods are used to assess the likelihood of a frequency shift, which can indicate tumor location. Phantoms with 5, 10, and 20 mm stiff inclusions are tested, as well as a homogeneous (healthy) phantom. Inclusions are located at four locations with different depth. RESULTS: The second natural frequency proves to be a reliable metric with the potential to clearly distinguish lesion like inclusions of different stiffness, as well as providing an approximate location for the tumor like inclusions. The 10 and 20 mm inclusions are always detected regardless of depth. The 5 mm inclusions are only detected near the surface. The homogeneous phantom always yields a negative result, as expected. CONCLUSIONS: Detection is based on a statistical likelihood analysis to determine the presence of significantly different frequency response over the phantom, which is a novel approach to this problem. The overall results show promise and justify proof of concept trials with human subjects.

Silicone breast phantoms for elastographic imaging evaluation.

PURPOSE: Breast cancer is a major public health issue for women, and early detection significantly increases survival rate. Currently, there is increased research interest in elastographic soft-tissue imaging techniques based on the correlation between pathology and mechanical stiffness. Anthropomorphic breast phantoms are critical for ex vivo validation of emerging elastographic technologies. This research develops heterogeneous breast phantoms for use in testing elastographic imaging modalities. METHODS: Mechanical property estimation of eight different elastomers is performed to determine storage moduli (E') and damping ratios (ζ) using a dynamic mechanical analyzer. Dynamic compression testing was carried out isothermally at room temperature over a range of 4-50 Hz. Silicone compositions with physiologically realistic storage modulus were chosen for mimicking skin adipose, cancerous tumors, and pectoral muscles and 13 anthropomorphic breast phantoms were constructed for ex vivo trials of digital image elastotomography (DIET) breast cancer screening system. A simpler fabrication was used to assess the possibility of multiple tumor detection using magnetic resonance elastography (MRE). RESULTS: Silicone materials with ranges of storage moduli (E') from 2 to 570 kPa and damping ratios (ζ) from 0.03 to 0.56 were identified. The resulting phantoms were tested in two different elastographic breast cancer diagnostic modalities. A significant contrast was successfully identified between healthy tissues and cancerous tumors both in MRE and DIET. CONCLUSIONS: The phantoms presented promise aid to researchers in elastographic imaging modalities for breast cancer detection and provide a foundation for silicone based phantom materials for mimicking soft tissues of other human organs.

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.

Independent cohort cross-validation of the real-time DISTq estimation of insulin sensitivity.

Insulin sensitivity (SI) is useful in the diagnosis, screening and treatment of diabetes. However, most current tests cannot provide an accurate, immediate or real-time estimate. The DISTq method does not require insulin or C-peptide assays like most SI tests, thus enabling real-time, low-cost SI estimation. The method uses a posteriori parameter estimations in the absence of insulin or C-peptide assays to simulate accurate, patient-specific, insulin concentrations that enable SI identification. Mathematical functions for the a posteriori parameter estimates were generated using data from 46 fully sampled DIST tests (glucose, insulin and C-peptide). SI values found using the DISTq from the 46 test pilot cohort and a second independent 218 test cohort correlated R=0.890 and R=0.825, respectively, to the fully sampled (including insulin and C-peptide assays) DIST SI metrics. When the a posteriori insulin estimation functions were derived using the second cohort, correlations for the pilot and second cohorts reduced to 0.765 and 0.818, respectively. These results show accurate SI estimation is possible in the absence of insulin or C-peptide assays using the proposed method. Such estimates may only need to be generated once and then used repeatedly in the future for isolated cohorts. The reduced correlation using the second cohort was due to this cohort's bias towards low SI insulin resistant subjects, limiting the data set's ability to generalise over a wider range. All the correlations remain high enough for the DISTq to be a useful test for a number of clinical applications. The unique real-time results can be generated within minutes of testing as no insulin and C-peptide assays are required and may enable new clinical applications.

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.

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 three-compartment model of the C-peptide-insulin dynamic during the DIST test.

Dynamic insulin sensitivity (SI) tests often utilise model-based parameter estimation. This research analyses the impact of expanding the typically used two-compartment model of insulin and C-peptide kinetics to incorporate a hepatic third compartment. The proposed model requires only four C-peptide assays to simulate endogenous insulin production (uen), greatly reducing the cost and clinical burden. Sixteen subjects participated in 46 dynamic insulin sensitivity tests (DIST). Population kinetic parameters are identified for the new compartment. Results are assessed by model error versus measured data and repeatability of the identified SI. The median C-peptide error was 0% (IQR: -7.3, 6.7)%. Median insulin error was 7% (IQR: -28.7, 6.3)%. Strong correlation (r=0.92) existed between the SI values of the new model and those from the original two-compartment model. Repeatability in SI was similar between models (new model inter/intra-dose variability 3.6/12.3% original model -8.5/11.3%). When frequent C-peptide samples may be available, the added hepatic compartment does not offer significant diagnostic, repeatability improvement over the two-compartment model. However, a novel and successful three-compartment modelling strategy was developed which provided accurate estimation of endogenous insulin production and the subsequent SI identification from sparse C-peptide data.

The identification of insulin saturation effects during the dynamic insulin sensitivity test.

BACKGROUND: Many insulin sensitivity (SI) tests identify a sensitivity metric that is proportional to the total available insulin and measured glucose disposal despite general acceptance that insulin action is saturable. Accounting for insulin action saturation may aid inter-participant and/or inter-test comparisons of insulin efficiency, and model-based glycaemic regulation. METHOD: Eighteen subjects participated in 46 dynamic insulin sensitivity tests (DIST, low-dose 40-50 minute insulin-modified IVGTT). The data was used to identify and compare SI metrics from three models: a proportional model (SI(L)), a saturable model (SI(S )and Q50) and a model similar to the Minimal Model (SG and SI(G)). The three models are compared using inter-trial parameter repeatability, and fit to data. RESULTS: The single variable proportional model produced the metric with least intra-subject variation: 13.8% vs 40.1%/55.6%, (SI(S)/I50) for the saturable model and 15.8%/88.2% (SI(G)/SG) for the third model. The average plasma insulin concentration at half maximum action (I50) was 139.3 mU·L⁻¹, which is comparable to studies which use more robust stepped EIC protocols. CONCLUSIONS: The saturation model and method presented enables a reasonable estimation of an overall patient-specific saturation threshold, which is a unique result for a test of such low dose and duration. The detection of previously published population trends and significant bias above noise suggests that the model and method successfully detects actual saturation signals. Furthermore, the saturation model allowed closer fits to the clinical data than the other models, and the saturation parameter showed a moderate distinction between NGT and IFG-T2DM subgroups. However, the proposed model did not provide metrics of sufficient resolution to enable confidence in the method for either SI metric comparisons across dynamic tests or for glycamic control.

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

BACKGROUND: Insulin resistance is a significant risk factor in the pathogenesis of type 2 diabetes. This article presents pilot study results of the dynamic insulin sensitivity and secretion test (DISST), a high-resolution, low-intensity test to diagnose insulin sensitivity (IS) and characterize pancreatic insulin secretion in response to a (small) glucose challenge. This pilot study examines the effect of glucose and insulin dose on the DISST, and tests its repeatability. METHODS: DISST tests were performed on 16 subjects randomly allocated to low (5 g glucose, 0.5 U insulin), medium (10 g glucose, 1 U insulin) and high dose (20 g glucose, 2 U insulin) protocols. Two or three tests were performed on each subject a few days apart. RESULTS: Average variability in IS between low and medium dose was 10.3% (p=.50) and between medium and high dose 6.0% (p=.87). Geometric mean variability between tests was 6.0% (multiplicative standard deviation (MSD) 4.9%). Geometric mean variability in first phase endogenous insulin response was 6.8% (MSD 2.2%). Results were most consistent in subjects with low IS. CONCLUSIONS: These findings suggest that DISST may be an easily performed dynamic test to quantify IS with high resolution, especially among those with reduced IS.

Development of a clinical type 1 diabetes metabolic system model and in silico simulation tool.

OBJECTIVES: The goal of this study was to develop a system model of type 1 diabetes for the purpose of in silico simulation for the prediction of long-term glycemic control outcomes. METHODS: The system model was created and identified on a physiological cohort of virtual type 1 diabetes patients (n = 40). Integral-based identification was used to develop (n = 40) insulin sensitivity profiles. RESULTS: The n = 40 insulin sensitivity profiles provide a driving input for virtual patient trials using the models developed. The identified models have a median (90% range) absolute percentage error of 1.33% (0.08-7.20%). The median (90% range) absolute error was 0.12 mmol/liter (0.01-0.56 mmol/liter). The model and integral-based identification of SI captured all patient dynamics with low error, which would lead to more physiological behavior simulation. CONCLUSIONS: A simulation tool incorporating n = 40 virtual patient data sets to predict long-term glycemic control outcomes from clinical interventions was developed based on a physiological type 1 diabetes metabolic system model. The overall goal is to utilize this model and insulin sensitivity profiles to develop and optimize self-monitoring blood glucose and multiple daily injection therapy.

A subcutaneous insulin pharmacokinetic model for computer simulation in a diabetes decision support role: model structure and parameter identification.

OBJECTIVE: The goal of this study was to develop a unified physiological subcutaneous (SC) insulin absorption model for computer simulation in a clinical diabetes decision support role. The model must model the plasma insulin appearance of a wide range of current insulins, especially monomer insulin and insulin glargine, utilizing common chemical states and transport rates, where appropriate. METHODS: A compartmental model was developed with 13 patient-specific model parameters covering six diverse insulin types [rapid-acting, regular, neutral protamine Hagedorn (NPH), lente, ultralente, and glargine insulin]. Model parameters were identified using 37 sets of mean plasma insulin time-course data from an extensive literature review via nonlinear optimization methods. RESULTS: All fitted parameters have a coefficient of variation <100% (median 51.3%, 95th percentile 3.6-60.6%) and can be considered a posteriori identifiable. CONCLUSION: A model is presented to describe SC injected insulin appearance in plasma in a diabetes decision support role. Clinically current insulin types (monomeric insulin, regular insulin, NPH, insulin, and glargine) and older insulin types (lente and ultralente) are included in a unified framework that accounts for nonlinear concentration and dose dependency. Future work requires clinical validation using published pharmacokinetic studies.

A subcutaneous insulin pharmacokinetic model for computer simulation in a diabetes decision support role: validation and simulation.

OBJECTIVE: The goal of this study was to validate a previously derived and identified physiological subcutaneous (SC) insulin absorption model for computer simulation in a clinical diabetes decision support role using published pharmacokinetic summary measures. METHODS: Validation was performed using maximal plasma insulin concentration (C(max)) and time to maximal concentration (t(max) pharmacokinetic summary measures. Values were either reported or estimated from 37 pharmacokinetic studies over six modeled insulin types. A validation comparison was made to equivalent pharmacokinetic summary measures calculated from model generated curves fitted to respective plasma insulin concentration data. The validation result was a measure of goodness of fit. Validation for each reported study was classified into one of four cases. RESULTS: Of 37 model fits, 22 were validated on both the C(max) and the t(max) summary measures. Another 6 model fits were partially validated on one measure only due to lack of reporting on the second measure with errors to reported or estimated ranges of <12%. Another 7 studies could not be validated on either measure because of inadequate reported clinical data. Finally, 2 separate model fits to data from the same study failed the validation with 90 and 71% error on t(max) only, which was likely caused by protocol-based error. No model fit failed the validation on both measures. CONCLUSIONS: A previously derived and identified model was clinically validated for six insulin types using C(max) and t(max) summary measures from published pharmacokinetic studies. Hence, this article presents a clinically valid model that accounts for multiple nonlinear effects and six different types of SC insulin in a computationally modest form suitable for use in clinical decision support.