Paul D. Docherty

A physiological Intensive Control Insulin-Nutrition-Glucose (ICING) model validated in critically ill patients

Intensive insulin therapy (IIT) and tight glycaemic control (TGC), particularly in intensive care unit (ICU), are the subjects of increasing and controversial debate in recent years. Model-based TGC has shown potential in delivering safe and tight glycaemic management, all the while limiting hypoglycaemia. A comprehensive, more physiologically relevant Intensive Control Insulin-Nutrition-Glucose (ICING) model is presented and validated using data from critically ill patients. Two existing glucose-insulin models are reviewed and formed the basis for the ICING model. Model limitations are discussed with respect to relevant physiology, pharmacodynamics and TGC practicality. Model identifiability issues are carefully considered for clinical settings. This article also contains significant reference to relevant physiology and clinical literature, as well as some references to the modeling efforts in this field. Identification of critical constant population parameters was performed in two stages, thus addressing model identifiability issues. Model predictive performance is the primary factor for optimizing population parameter values. The use of population values are necessary due to the limited clinical data available at the bedside in the clinical control scenario. Insulin sensitivity, S(I), the only dynamic, time-varying parameter, is identified hourly for each individual. All population parameters are justified physiologically and with respect to values reported in the clinical literature. A parameter sensitivity study confirms the validity of limiting time-varying parameters to S(I) only, as well as the choices for the population parameters. The ICING model achieves median fitting error of <1% over data from 173 patients (N=42,941 h in total) who received insulin while in the ICU and stayed for ≥ 72 h. Most importantly, the median per-patient 1-h ahead prediction error is a very low 2.80% [IQR 1.18, 6.41%]. It is significant that the 75th percentile prediction error is within the lower bound of typical glucometer measurement errors of 7-12%. These results confirm that the ICING model is suitable for developing model-based insulin therapies, and capable of delivering real-time model-based TGC with a very tight prediction error range. Finally, the detailed examination and discussion of issues surrounding model-based TGC and existing glucose-insulin models render this article a mini-review of the state of model-based TGC in critical care.

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

BackgroundDerivative 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.MethodsThe 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.ResultsThe 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.ConclusionsThus 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.

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.

DISTq: An Iterative Analysis of Glucose Data for Low-Cost, Real-Time and Accurate Estimation of Insulin Sensitivity

Insulin sensitivity (SI) estimation has numerous uses in medical and clinical situations. However, highresolution tests that are useful for clinical diagnosis and monitoring are often too intensive, long and costly for regular use. Simpler tests that mitigate these issues are not accurate enough for many clinical diagnostic or monitoring scenarios. The gap between these tests presents an opportunity for new approaches. The quick dynamic insulin sensitivity test (DISTq) utilises the model-based DIST test protocol and a series of population estimates to eliminate the need for insulin or C-peptide assays to enable a high resolution, low-intensity, real-time evaluation of SI. The method predicts patient specific insulin responses to the DIST test protocol with enough accuracy to yield a useful clinical insulin sensitivity metric for monitoring of diabetes therapy. The DISTq method replicated the findings of the fully sampled DIST test without the use of insulin or C-peptide assays. Correlations of the resulting SI values was R=0.91. The method was also compared to the euglycaemic hyperinsulinaemic clamp (EIC) in an in-silico Monte-Carlo analysis and showed a good ability to re-evaluate SIEIC (R=0.89), compared to the fully sampled DIST (R=0.98) Population-derived parameter estimates using a-posteriori population-based functions derived from DIST test data enables the simulation of insulin profiles that are sufficiently accurate to estimate SI to a relatively high precision. Thus, costly insulin and C-peptide assays are not necessary to obtain an accurate, but inexpensive, real-time estimate of insulin sensitivity. This estimate has enough resolution for SI prediction and monitoring of response to therapy. In borderline cases, re-evaluation of stored (frozen) blood samples for insulin and C-peptide would enable greater accuracy where necessary, enabling a hierarchy of tests in an economical fashion.

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.

Structural Identifiability and Practical Applicability of an Alveolar Recruitment Model for ARDS Patients

Patient-specific mathematical models of respiratory mechanics can offer substantial insight into patient state and pulmonary dynamics that are not directly measurable. Thus, they offer significant potential to evaluate and guide patient-specific lung protective ventilator strategies for acute respiratory distress syndrome (ARDS) patients. To assure bedside applicability, the model must be computationally efficient and identifiable from the limited available data, while also capturing dominant dynamics and trends observed in ARDS patients. In this study, an existing static recruitment model is enhanced by considering alveolar distension and implemented in a novel time-continuous dynamic respiratory mechanics model. The model was tested for structural identifiability and a hierarchical gradient descent approach was used to fit the model to low-flow test responses of 12 ARDS patients. Finally, a comprehensive practical identifiability analysis was performed to evaluate the impact of data quality on the model parameters. Identified parameter values were physiologically plausible and very accurately reproduced the measured pressure responses. Structural identifiability of the model was proven, but practical identifiability analysis of the results showed a lack of convexity on the error surface indicating that successful parameter identification is currently not assured in all test sets. Overall, the model presented is physiologically and clinically relevant, captures ARDS dynamics, and uses clinically descriptive parameters. The patient-specific models show the ability to capture pulmonary dynamics directly relevant to patient condition and clinical guidance. These characteristics currently cannot be directly measured or established without such a validated model.

Improvements in Glucose Metabolism and Insulin Sensitivity with a Low-Carbohydrate Diet in Obese Patients with Type 2 Diabetes

Objective: The optimal diet for weight loss in type 2 diabetes remains controversial. This study examined a low-carbohydrate, high-fat diet with detailed physiological assessments of insulin sensitivity, glycemic control, and risk factors for cardiovascular disease. Methods: Fourteen obese patients (body mass index [BMI] 40.6 ± 4.9 kg/m2) with type 2 diabetes were recruited for an “Atkins”-type low-carbohydrate diet. Measurements were made at 0, 12, and 24 weeks of weight, insulin sensitivity, HbA1c, lipids, and blood pressure. Results: Twelve completers lost a mean of 9.7 ± 1.8 kg over 24 weeks attributable to a major reduction in carbohydrates and resultant reduction in total energy intake. Glycemic control significantly improved (HbA1c −1.1 ± 0.25%) with reductions in hypoglycemic medication. Fasting glucose, homeostasis model assessment (HOMA), and area under the curve (AUC) glucose (intravenous glucose tolerance test [IVGTT]) were significantly reduced by week 12 ( p < 0.05). There were nonsignificant improvements in insulin sensitivity (SI) at week 12 ( p = 0.19) and week 24 ( p = 0.31). Systolic blood pressure was reduced (mean −10.0 mmHg between weeks 0 and 24, p = 0.13). Mean high-density lipoprotein (HDL), low-density lipoprotein (LDL), and total cholesterol all increased. The ratio of total: HDL cholesterol and triglycerides was reduced. Conclusion: A low-carbohydrate diet was well tolerated and achieved weight loss over 24 weeks in subjects with diabetes. Glycemic control improved with a reduction in requirements for hypoglycemic agents.

Iterative integral parameter identification of a respiratory mechanics model

BackgroundPatient-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.MethodsAn 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.ResultsThe 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.ConclusionThese 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.

Time-Varying Respiratory System Elastance: A Physiological Model for Patients Who Are Spontaneously Breathing

Background Respiratory mechanics models can aid in optimising patient-specific mechanical ventilation (MV), but the applications are limited to fully sedated MV patients who have little or no spontaneously breathing efforts. This research presents a time-varying elastance (Edrs) model that can be used in spontaneously breathing patients to determine their respiratory mechanics. Methods A time-varying respiratory elastance model is developed with a negative elastic component (Edemand), to describe the driving pressure generated during a patient initiated breathing cycle. Data from 22 patients who are partially mechanically ventilated using Pressure Support (PS) and Neurally Adjusted Ventilatory Assist (NAVA) are used to investigate the physiology relevance of the time-varying elastance model and its clinical potential. Edrs of every breathing cycle for each patient at different ventilation modes are presented for comparison. Results At the start of every breathing cycle initiated by patient, Edrs is < 0. This negativity is attributed from the Edemand due to a positive lung volume intake at through negative pressure in the lung compartment. The mapping of Edrs trajectories was able to give unique information to patients’ breathing variability under different ventilation modes. The area under the curve of Edrs (AUCEdrs) for most patients is > 25 cmH2Os/l and thus can be used as an acute respiratory distress syndrome (ARDS) severity indicator. Conclusion The Edrs model captures unique dynamic respiratory mechanics for spontaneously breathing patients with respiratory failure. The model is fully general and is applicable to both fully controlled and partially assisted MV modes.

Non-identifiability of the Rayleigh damping material model in magnetic resonance elastography

Magnetic Resonance Elastography (MRE) is an emerging imaging modality for quantifying soft tissue elasticity deduced from displacement measurements within the tissue obtained by phase sensitive Magnetic Resonance Imaging (MRI) techniques. MRE has potential to detect a range of pathologies, diseases and cancer formations, especially tumors. The mechanical model commonly used in MRE is linear viscoelasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a subspace-based nonlinear inversion (SNLI) algorithm to reconstruct viscoelastic properties, energy attenuation mechanisms and concomitant damping behavior of the tissue-simulating phantoms. This research performs a thorough evaluation of the RD model in MRE focusing on unique identification of RD parameters, μI and ρI. Results show the non-identifiability of the RD model at a single input frequency based on a structural analysis with a series of supporting experimental phantom results. The estimated real shear modulus values (μR) were substantially correct in characterising various material types and correlated well with the expected stiffness contrast of the physical phantoms. However, estimated RD parameters displayed consistent poor reconstruction accuracy leading to unpredictable trends in parameter behaviour. To overcome this issue, two alternative approaches were developed: (1) simultaneous multi-frequency inversion; and (2) parametric-based reconstruction. Overall, the RD model estimates the real shear shear modulus (μR) well, but identifying damping parameters (μI and ρI) is not possible without an alternative approach.