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

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Abstract

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, SI, 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 SI 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.

Introduction

Since the landmark study in surgical intensive care unit (ICU) patients by Van Den Berghe et al. [1], which reduced mortality 18–45% using tight glycaemic control (TGC), the attitude towards tolerating hyperglycaemia in critically ill patients has changed. Hyperglycaemia worsens outcomes, increasing the risk of severe infection [2], myocardial infarction [3], and critical illnesses such as polyneuropathy and multiple organ failure [1]. However, repeating these results has been difficult, and thus the role of tight glyceamic control during critical illness and suitable glycaemic ranges have been under scrutiny in recent years [4], [5], [6], [7], [8], [9], [10], [11]. However, conclusions are varied with both success [1], [12], [13], [14], failure [15], and, primarily, no clear outcome [16], [17], [18], [19], [20], [21].

Although it is now becoming an unacceptable practice to allow excessive hyperglycaemia and its associated effects [8], [22], [23], [24], moderately elevated blood glucose levels are tolerated or recommended [11] because of the fear of hypoglycaemia and higher nursing effort frequently associated with TGC [8], [10], [25], [26]. Interestingly, some TGC studies that reported a mortality reduction also had reduced and relatively low hypoglycaemic rates [13], [14], whereas almost all other reports had increased and often excessive hypoglycaemia [15], [17]. Finally, model-based and model-derived TGC methods have shown the ability to provide very tight control with little or no hypoglycaemia [13], [27], [28], [29], [30].

Many studies have developed glucose–insulin models with varying degrees of complexity for a wide range of uses, primarily in research studies of insulin sensitivity [27], [31], [32], [33], [34], [35], [36]. A more comprehensive model review can be found in [28]. For a model to be successful in delivery of TGC, it needs to reflect observable physiology, as well as known biological mechanisms. In addition, it should be uniquely identifiable, and the type and number of parameters to be identified should reflect the clinically available data that will provide validation. Finally, the most important aspect for a model to be used in model-based TGC is its predictive ability, where most studies provide only fitting error as validation [29], [33], [36], [37].

This paper presents a more comprehensive model, ICING (Intensive Control Insulin-Nutrition-Glucose), for the use of glycaemic control particularly in the ICU. The model addresses several incomplete or implicit physiological aspects from prior models by Chase et al. [27] and Lotz et al. [38]. Model limitations are discussed with respect to physiology, pharmacodynamics and TGC practicality. Model identifiability issues are carefully considered for clinical settings. The ICING model is validated using clinical data from critically ill patients and assessed for both its fitting, and more critically for TGC, predictive performance. Finally, issues surrounding TGC and existing glucose–insulin models are extensively reviewed and discussed.

Section snippets

Glucose–insulin physiology model

Two clinically validated glucose–insulin physiology models set the basis of this study. Both models share the same basic structure of the Minimal Model [32]. The model from Chase et al. [27] was developed and validated for glycaemic level management in the ICU. This model captures the fundamental dynamics seen in critically ill patients, yet has a relatively simple mathematical structure enabling rapid identification of patient-specific parameters [39]. This model only requires measurements in

Model validation methods

Validation of the glucose–insulin model presented in Eqs. (9), (10), (11), (12), (13), (14) is performed using data from 173 patients (42,941 total hours) that were on the SPRINT TGC protocol [13] for 3 or more days, which also had a statistically significant hospital mortality reductions. These patients also had long enough stays to exhibit periods of both dynamic evolution and metabolic stability. The median APACHE II score for this cohort is 19 [IQR 16, 25] and the median age is 64 [IQR 49,

pG and EGPb – Stage 1

The per-patient median fitting and prediction errors over the ranges pG = 0.001–0.1 min−1 and EGPb = 0–3.5 mmol/min are shown in Fig. 1. Fig. 1a and c shows the median of all median hourly % errors for each patient. Fig. 1b and d shows the median range of the 90% confidence interval in hourly % error for each patient. Smaller (tighter) range means tighter distribution with less outliers. In general, lower fitting and prediction errors and error ranges are produced in the lower pG and lower EGPb

Discussion

The new ICING model presented in this study is an integration and improvement of two clinically validated glucose–insulin physiological models [27], [38]. This new model has more explicit physiological relevance without increasing the number of patient-specific parameters to be identified. In particular, the insulin kinetics is expressed with distinctive routes for insulin clearance and transport from plasma, which reflects biological mechanisms. A more realistic model for gastric glucose

Conclusions

A new, more comprehensive glucose–insulin model is presented and validated using data from critically ill patients. The model is capable of accurately capturing long term dynamics and evolution of a critically ill patient’s glucose–insulin response. Insulin sensitivity SI is the only parameter that is identified hourly for each individual. Its identification is guaranteed to be unique given the integral fitting method used in this study. Population constant parameters pG, EGPb and nI have been

Conflict of interest

The authors declare no conflict of interest with respect to this work.

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