A minimal model for glycemia control in critically ill patients

Arbitrary-order sliding mode-based robust control algorithm for the developing artificial pancreas mechanism

In Diabetes Mellitus, the pancreas remains incapable of insulin administration that leads to hyperglycaemia, an escalated glycaemic concentration, which may stimulate many complications. To circumvent this situation, a closed-loop control strategy is much needed for the exogenous insulin infusion in diabetic patients. This closed-loop structure is often termed as an artificial pancreas that is generally established by the employment of different feedback control strategies. In this work, the authors have proposed an arbitrary-order sliding mode control approach for development of the said mechanism. The term, arbitrary, is exercised in the sense of its applicability to any n-order controllable canonical system. The proposed control algorithm affirms the finite-time effective stabilisation of the glucose-insulin regulatory system, at the desired level, with the alleviation of sharp fluctuations. The novelty of this work lies in the sliding manifold that incorporates indirect non-linear terms. In addition, the necessary discontinuous terms are filtered-out once before its employment to the plant, i.e. diabetic patient. The robustness, in the presence of external disturbances, i.e. meal intake is confirmed via rigorous mathematical stability analysis. In addition, the effectiveness of the proposed control strategy is ascertained by comparing the results with the standard literature.

Toward Detecting Infection Incidence in People With Type 1 Diabetes Using Self-Recorded Data (Part 1): A Novel Framework for a Personalized Digital Infectious Disease Detection System

BACKGROUND

Type 1 diabetes is a chronic condition of blood glucose metabolic disorder caused by a lack of insulin secretion from pancreas cells. In people with type 1 diabetes, hyperglycemia often occurs upon infection incidences. Despite the fact that patients increasingly gather data about themselves, there are no solid findings that uncover the effect of infection incidences on key parameters of blood glucose dynamics to support the effort toward developing a digital infectious disease detection system.

OBJECTIVE

The study aims to retrospectively analyze the effect of infection incidence and pinpoint optimal parameters that can effectively be used as input variables for developing an infection detection algorithm and to provide a general framework regarding how a digital infectious disease detection system can be designed and developed using self-recorded data from people with type 1 diabetes as a secondary source of information.

METHODS

We retrospectively analyzed high precision self-recorded data of 10 patient-years captured within the longitudinal records of three people with type 1 diabetes. Obtaining such a rich and large data set from a large number of participants is extremely expensive and difficult to acquire, if not impossible. The data set incorporates blood glucose, insulin, carbohydrate, and self-reported events of infections. We investigated the temporal evolution and probability distribution of the key blood glucose parameters within a specified timeframe (weekly, daily, and hourly).

RESULTS

Our analysis demonstrated that upon infection incidence, there is a dramatic shift in the operating point of the individual blood glucose dynamics in all the timeframes (weekly, daily, and hourly), which clearly violates the usual norm of blood glucose dynamics. During regular or normal situations, higher insulin and reduced carbohydrate intake usually results in lower blood glucose levels. However, in all infection cases as opposed to the regular or normal days, blood glucose levels were elevated for a prolonged period despite higher insulin and reduced carbohydrates intake. For instance, compared with the preinfection and postinfection weeks, on average, blood glucose levels were elevated by 6.1% and 16%, insulin (bolus) was increased by 42% and 39.3%, and carbohydrate consumption was reduced by 19% and 28.1%, respectively.

CONCLUSIONS

We presented the effect of infection incidence on key parameters of blood glucose dynamics along with the necessary framework to exploit the information for realizing a digital infectious disease detection system. The results demonstrated that compared with regular or normal days, infection incidence substantially alters the norm of blood glucose dynamics, which are quite significant changes that could possibly be detected through personalized modeling, for example, prediction models and anomaly detection algorithms. Generally, we foresee that these findings can benefit the efforts toward building next generation digital infectious disease detection systems and provoke further thoughts in this challenging field.

An Electronic Health Record-Integrated Computerized Intravenous Insulin Infusion Protocol: Clinical Outcomes and in Silico Adjustment

BACKGROUND

We aimed to describe the outcome of a computerized intravenous insulin infusion (CII) protocol integrated to the electronic health record (EHR) system and to improve the CII protocol in silico using the EHR-based predictors of the outcome.

METHODS

Clinical outcomes of the patients who underwent the CII protocol between July 2016 and February 2017 and their matched controls were evaluated. In the CII protocol group (n=91), multivariable binary logistic regression analysis models were used to determine the independent associates with a delayed response (taking ≥6.0 hours for entering a glucose range of 70 to 180 mg/dL). The CII protocol was adjusted in silico according to the EHR-based parameters obtained in the first 3 hours of CII.

RESULTS

Use of the CII protocol was associated with fewer subjects with hypoglycemia alert values (P=0.003), earlier (P=0.002), and more stable (P=0.017) achievement of a glucose range of 70 to 180 mg/dL. Initial glucose level (P=0.001), change in glucose during the first 2 hours (P=0.026), and change in insulin infusion rate during the first 3 hours (P=0.029) were independently associated with delayed responses. Increasing the insulin infusion rate temporarily according to these parameters in silico significantly reduced delayed responses (P<0.0001) without hypoglycemia, especially in refractory patients.

CONCLUSION

Our CII protocol enabled faster and more stable glycemic control than conventional care with minimized risk of hypoglycemia. An EHR-based adjustment was simulated to reduce delayed responses without increased incidence of hypoglycemia.

Next-generation, personalised, model-based critical care medicine: a state-of-the art review of in silico virtual patient models, methods, and cohorts, and how to validation them

Critical care, like many healthcare areas, is under a dual assault from significantly increasing demographic and economic pressures. Intensive care unit (ICU) patients are highly variable in response to treatment, and increasingly aging populations mean ICUs are under increasing demand and their cohorts are increasingly ill. Equally, patient expectations are growing, while the economic ability to deliver care to all is declining. Better, more productive care is thus the big challenge. One means to that end is personalised care designed to manage the significant inter- and intra-patient variability that makes the ICU patient difficult. Thus, moving from current "one size fits all" protocolised care to adaptive, model-based "one method fits all" personalised care could deliver the required step change in the quality, and simultaneously the productivity and cost, of care. Computer models of human physiology are a unique tool to personalise care, as they can couple clinical data with mathematical methods to create subject-specific models and virtual patients to design new, personalised and more optimal protocols, as well as to guide care in real-time. They rely on identifying time varying patient-specific parameters in the model that capture inter- and intra-patient variability, the difference between patients and the evolution of patient condition. Properly validated, virtual patients represent the real patients, and can be used in silico to test different protocols or interventions, or in real-time to guide care. Hence, the underlying models and methods create the foundation for next generation care, as well as a tool for safely and rapidly developing personalised treatment protocols over large virtual cohorts using virtual trials. This review examines the models and methods used to create virtual patients. Specifically, it presents the models types and structures used and the data required. It then covers how to validate the resulting virtual patients and trials, and how these virtual trials can help design and optimise clinical trial. Links between these models and higher order, more complex physiome models are also discussed. In each section, it explores the progress reported up to date, especially on core ICU therapies in glycemic, circulatory and mechanical ventilation management, where high cost and frequency of occurrence provide a significant opportunity for model-based methods to have measurable clinical and economic impact. The outcomes are readily generalised to other areas of medical care.

Interstitial insulin kinetic parameters for a 2-compartment insulin model with saturable clearance

Glucose-insulin system models are commonly used for identifying insulin sensitivity. With physiological, 2-compartment insulin kinetics models, accurate kinetic parameter values are required for reliable estimates of insulin sensitivity. This study uses data from 6 published microdialysis studies to determine the most appropriate parameter values for the transcapillary diffusion rate (n(I)) and cellular insulin clearance rate (n(C)). The 6 studies (12 data sets) used microdialysis techniques to simultaneously obtain interstitial and plasma insulin concentrations. The reported plasma insulin concentrations were used as input and interstitial insulin concentrations were simulated with the interstitial insulin kinetics sub-model. These simulated results were then compared to the reported interstitial measurements and the most appropriate set of parameter values was determined across the 12 data sets by combining the results. Interstitial insulin kinetic parameters values n(I)=n(C)=0.0060 min⁻¹ were shown to be the most appropriate. These parameter values are associated with an effective, interstitial insulin half-life, t(½)=58 min, within the range of 25-130 min reported by others.

[Glucose variability in intensive care unit]

Hyperglycemia is significantly associated with increased mortality in critically ill patients and then, strict control of blood glucose (BG) concentration is important. Lowering of BG levels with intensive insulin therapy (IIT) was recommended in order to improve patient outcomes. But recently, some recent prospective trials failed to confirm the initial data, showing conflicting results (significantly increased mortality with IIT, more hypoglycemic episodes). So there is no consensus about efficiency and safety of IIT. Significant associations between glucose variability and mortality have been confirmed by several recent studies. A difference in variability of BG control could explain why the effect of IIT varied from beneficial to harmful. Managing and decreasing this BG variability could be an important goal of BG control in critically ill patients. Clinicians have to consider definitions, physiopathology and impacts of glucose variability, in order to improve patient outcomes.

Physiological modeling, tight glycemic control, and the ICU clinician: what are models and how can they affect practice?

Critically ill patients are highly variable in their response to care and treatment. This variability and the search for improved outcomes have led to a significant increase in the use of protocolized care to reduce variability in care. However, protocolized care does not address the variability of outcome due to inter- and intra-patient variability, both in physiological state, and the response to disease and treatment. This lack of patient-specificity defines the opportunity for patient-specific approaches to diagnosis, care, and patient management, which are complementary to, and fit within, protocolized approaches.Computational models of human physiology offer the potential, with clinical data, to create patient-specific models that capture a patient's physiological status. Such models can provide new insights into patient condition by turning a series of sometimes confusing clinical data into a clear physiological picture. More directly, they can track patient-specific conditions and thus provide new means of diagnosis and opportunities for optimising therapy.This article presents the concept of model-based therapeutics, the use of computational models in clinical medicine and critical care in specific, as well as its potential clinical advantages, in a format designed for the clinical perspective. The review is presented in terms of a series of questions and answers. These aspects directly address questions concerning what makes a model, how it is made patient-specific, what it can be used for, its limitations and, importantly, what constitutes sufficient validation.To provide a concrete foundation, the concepts are presented broadly, but the details are given in terms of a specific case example. Specifically, tight glycemic control (TGC) is an area where inter- and intra-patient variability can dominate the quality of care control and care received from any given protocol. The overall review clearly shows the concept and significant clinical potential of using computational models in critical care medicine.

Identification of intraday metabolic profiles during closed-loop glucose control in individuals with type 1 diabetes

BACKGROUND

Algorithms for closed-loop insulin delivery can be designed and tuned empirically; however, a metabolic model that is predictive of clinical study results can potentially accelerate the process.

METHODS

Using data from a previously conducted closed-loop insulin delivery study, existing models of meal carbohydrate appearance, insulin pharmacokinetics, and the effect on glucose metabolism were identified for each of the 10 subjects studied. Insulin's effects to increase glucose uptake and decrease endogenous glucose production were described by the Bergman minimal model, and compartmental models were used to describe the pharmacokinetics of subcutaneous insulin absorption and glucose appearance following meals. The composite model, comprised of only five equations and eight parameters, was identified with and without intraday variance in insulin sensitivity (S(I)), glucose effectiveness at zero insulin (GEZI), and endogenous glucose production (EGP) at zero insulin.

RESULTS

Substantial intraday variation in SI, GEZI and EGP was observed in 7 of 10 subjects (root mean square error in model fit greater than 25 mg/dl with fixed parameters and nadir and/or peak glucose levels differing more than 25 mg/dl from model predictions). With intraday variation in these three parameters, plasma glucose and insulin were well fit by the model (R(2) = 0.933 +/- 0.00971 [mean +/- standard error of the mean] ranging from 0.879-0.974 for glucose; R(2) = 0.879 +/- 0.0151, range 0.819-0.972 for insulin). Once subject parameters were identified, the original study could be reconstructed using only the initial glucose value and basal insulin rate at the time closed loop was initiated together with meal carbohydrate information (glucose, R(2) = 0.900 +/- 0.015; insulin delivery, R(2) = 0.640 +/- 0.034; and insulin concentration, R(2) = 0.717 +/- 0.041).

CONCLUSION

Metabolic models used in developing and comparing closed-loop insulin delivery algorithms will need to explicitly describe intraday variation in metabolic parameters, but the model itself need not be comprised by a large number of compartments or differential equations.

Nonlinear modeling of the dynamic effects of infused insulin on glucose: comparison of compartmental with Volterra models

This paper presents the results of a computational study that compares simulated compartmental (differential equation) and Volterra models of the dynamic effects of insulin on blood glucose concentration in humans. In the first approach, we employ the widely accepted "minimal model" and an augmented form of it, which incorporates the effect of insulin secretion by the pancreas, in order to represent the actual closed-loop operating conditions of the system, and in the second modeling approach, we employ the general class of Volterra-type models that are estimated from input-output data. We demonstrate both the equivalence between the two approaches analytically and the feasibility of obtaining accurate Volterra models from insulin-glucose data generated from the compartmental models. The results corroborate the proposition that it may be preferable to obtain data-driven (i.e., inductive) models in a more general and realistic operating context, without resorting to the restrictive prior assumptions and simplifications regarding model structure and/or experimental protocols (e.g., glucose tolerance tests) that are necessary for the compartmental models proposed previously. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions-a risk that is avoided when we let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models, as our simulation results suggest.

Computational study of an augmented minimal model for glycaemia control

In this paper we introduce a new model structure for the metabolic effects of intravenous insulin on blood glucose in man and derive its parameter values from the widely used model of Sorensen. The proposed model attempts to combine the advantages of the existing comprehensive and minimal models. Validation of the new model is done through deriving equivalent nonparametric nonlinear models in the form of Principal Dynamic Modes. We show that the new structure can represent the insulin-glucose dynamics of healthy subjects as well as Type 1 and Type 2 diabetics, with appropriate adjustment in its parameters.

Glycemia prediction in critically ill patients using an adaptive modeling approach

BACKGROUND

Strict blood glucose control by applying nurse-driven protocols is common nowadays in intensive care units (ICUs). Implementation of a predictive control system can potentially reduce the workload for medical staff but requires a model for accurately predicting the glycemia signal within a certain time horizon.

METHODS

GlucoDay (A. Menarini Diagnostics, Italy) data coming from 19 critically ill patients (from a surgical ICU) are used to estimate the initial ICU "minimal" model (based on data of the first 24 hours) and to reestimate the model as new measurements are obtained. The reestimation is performed every hour or every 4 hours. For both approaches the optimal size of the data set for each reestimation is determined.

RESULTS

The prediction error that is obtained when applying the 1-hour reestimation strategy is significantly smaller than when the model is reestimated only every 4 hours (p < 0.001). The optimal size of the data set to be considered in each reestimation process of the ICU minimal model is found to be 4 hours. The obtained average "mean percentage error" is 7.6% (SD 3.1%) and 14.6% (SD 7.0%) when the model is reestimated every hour and 4 hours, respectively.

CONCLUSIONS

Implementation of the ICU minimal model in the appropriate reestimation process results in clinically acceptable prediction errors. Therefore, the model is able to predict glycemia trends of patients admitted to the surgical ICU and can potentially be used in a predictive control system.