Models of subcutaneous insulin kinetics. A critical review

Improving the stability of insulin through effective chemical modifications: A Comprehensive review

Insulin, an essential peptide hormone, conjointly regulates blood glucose levels by its receptor and it is used as vital drug to treat diabetes. This therapeutic hormone may undergo different chemical modifications during industrial processes, pharmaceutical formulation, and through its endogenous storage in the pancreatic β-cells. Insulin is highly sensitive to environmental stresses and readily undergoes structural changes, being also able to unfold and aggregate in physiological conditions. Even; small changes altering the structural integrity of insulin may have significant impacts on its biological efficacy to its physiological and pharmacological activities. Insulin analogs have been engineered to achieve modified properties, such as improved stability, solubility, and pharmacokinetics, while preserving the molecular pharmacology of insulin. The casually or purposively strategies of chemical modifications of insulin occurred to improve its therapeutic and pharmaceutical properties. Knowing the effects of chemical modification, formation of aggregates, and nanoparticles on protein can be a new look at the production of protein analogues drugs and its application in living system. The project focused on effects of chemical modifications and nanoparticles on the structure, stability, aggregation and their results in effective drug delivery system, biological activity, and pharmacological properties of insulin. The future challenge in biotechnology and pharmacokinetic arises from the complexity of biopharmaceuticals, which are often molecular structures that require formulation and delivery strategies to ensure their efficacy and safety.

Digital Twins in Type 1 Diabetes: A Systematic Review

Digital twin is a new concept that is rapidly gaining recognition especially in the medical field. Indeed, being a virtual representation of real-world entities and processes, a digital twin can be used to accurately represent the patients' disease, clarify the treatment target, and realize personalized and precise therapies. However, despite being a revolutionary concept, the diffusion of digital twins in type 1 diabetes (T1D) is still limited. In this systematic review, we analyzed structure, operating conditions, and characteristics of digital twins being developed for T1D. Our search covered published documents until March 2024: 220 publications were identified, 37 of which were duplicated entries; in addition, 173 publications were removed after inspection of titles, abstracts, and keywords; and finally, 11 publications were fully reviewed, of which 8 were deemed eligible for inclusion. We found that all eight methodologies are not comprehensive multi-scale virtual replicas of the individual with T1D, but they all focus on describing glucose-insulin metabolism, aiming to simulate glucose concentration resultant from therapeutic interventions. In this review, we will compare and analyze different factors characterizing these digital twins, such as operating principles (mathematical model, twinning procedure, validation and assessment) and the key aspects for practical adoption (inclusion of physical activity, data required for twinning, open-source availability). We will conclude the paper listing which, in our opinion, are the current limitations and future directives of digital twins in T1D, hoping that this article can be helpful to researchers working on diabetes technologies to further develop the use of such an important instrument.

Safety of intranasal insulin administration in patients undergoing cardiovascular surgery: An open-label, nonrandomized, dose-escalation study

Objective

This study aimed to determine the maximum safe dose of intranasal insulin administration during cardiac surgery.

Methods

This open-label, Phase 1, single-center, dose-escalation clinical trial recruited patients scheduled to undergo elective cardiac surgery or major vascular surgery requiring cardiopulmonary bypass between February and September 2021. They were grouped into 5 dose-escalation cohorts and administered 0, 40, 80, 160, and 240 IU insulin (n = 6 in each group) via a metered nasal dispenser after the induction of general anesthesia. Blood samples were collected at 10-minute intervals for the first 60 minutes and at 30-minute intervals thereafter. Hypoglycemia was defined as a blood glucose level <70 mg/dL. Patient recruitment was terminated after hypoglycemia was observed in 2 patients in any of the groups.

Results

In total, 27 of 29 enrolled patients were administered intranasal insulin or saline. Hypoglycemia was not observed after the administration of intranasal insulin in the 0, 40, 80, or 160 IU groups; however, it was observed in 2 of 3 patients in the 240 IU group. The serum insulin concentration was elevated in the 160-IU group, but the C-peptide concentration was not elevated in any of the groups.

Conclusions

The administration of up to 160 IU intranasal insulin did not induce clinically significant hypoglycemia. However, 160 IU intranasal insulin should be administered cautiously because insulin can enter the systemic circulation in a dose-dependent manner.

In vivo variable and multi-day response from an insulin-releasing photoactivated depot

Previously we have demonstrated that light can be used to control the release of insulin in diabetic animals, followed by a reduction in blood glucose. This is accomplished using a photoactivated depot (PAD) of insulin injected into the skin, and irradiated by a small external LED light source. In this work for the first time we demonstrate dose-response, showing that we can vary insulin release and commensurate blood glucose reduction by varying the amount of light administered. In addition to demonstrating dose-response, we have shown multi-day depot response, with insulin being released on two different days from the same depot. The material used in these studies was CD-insulin, a form of insulin that has a highly non-polar cyclododecyl group attached, markedly reducing the solubility of the modified material, and allowing it to form a depot upon injection. Upon photolysis, the cyclododecyl group is removed, releasing fully native, soluble insulin. Variable response and multi-day response as demonstrated strongly support the potential utility of the PAD approach for the variable and extended release of therapeutic peptides.

Coupled Diffusion-Binding-Deformation Modelling for Phase-Transition Microneedles-Based Drug Delivery

Phase-transition microneedles (PTMNs)-based transdermal drug delivery (TDD) is gaining popularity due to its non-invasiveness and ability to deliver a wide range of drugs. PTMNs absorb interstitial skin fluid (ISF) and transport drugs from microneedle (MNs) domain to the skin without polymer dissolution. To establish PTMNs for practical use, one needs to understand and optimise the key parameters governing drug transport mechanisms to achieve controlled drug delivery. In addressing this point, we have developed a coupled diffusion-binding-deformation model to understand the effect of physicochemical parameters (e.g., swelling capacity, drug binding) of MN and skin mechanical properties on overall drug transport behaviour. The contact mechanics at the MN and skin interface is introduced to account for the resistive force exerted by the deformed skin to MN swelling. The model is validated with the reported data of in vitro insulin delivery using polyvinyl alcohol (PVA) MN. The drug binding parameters are estimated from the fitting of the cumulative release of insulin within 6 hours of MN insertion. To predict the in vivo data of insulin delivery using the PVA MN, one-compartment model of drug pharmacokinetics is incorporated. It is shown in the paper that the model is able to predict the final insulin concentration in blood and in good agreement with the reported experimental data. The proposed model is concluded to be a tool for the predictive design and development of PTMNs-based TDD systems.

New model of glucose-insulin regulation characterizes effects of physical activity and facilitates personalized treatment evaluation in children and adults with type 1 diabetes

Accurate treatment adjustment to physical activity (PA) remains a challenging problem in type 1 diabetes (T1D) management. Exercise-driven effects on glucose metabolism depend strongly on duration and intensity of the activity, and are highly variable between patients. In-silico evaluation can support the development of improved treatment strategies, and can facilitate personalized treatment optimization. This requires models of the glucose-insulin system that capture relevant exercise-related processes. We developed a model of glucose-insulin regulation that describes changes in glucose metabolism for aerobic moderate- to high-intensity PA of short and prolonged duration. In particular, we incorporated the insulin-independent increase in glucose uptake and production, including glycogen depletion, and the prolonged rise in insulin sensitivity. The model further includes meal absorption and insulin kinetics, allowing simulation of everyday scenarios. The model accurately predicts glucose dynamics for varying PA scenarios in a range of independent validation data sets, and full-day simulations with PA of different timing, duration and intensity agree with clinical observations. We personalized the model on data from a multi-day free-living study of children with T1D by adjusting a small number of model parameters to each child. To assess the use of the personalized models for individual treatment evaluation, we compared subject-specific treatment options for PA management in replay simulations of the recorded data with altered meal, insulin and PA inputs.

A methodical survey of mathematical model-based control techniques based on open and closed loop control approach for diabetes management

Disturbance of blood sugar level is controlled through well-known biomechanical feedback loops: high levels of glucose in blood facilitate to release insulin from the pancreas which accelerates the absorption rate of cellular glucose. Low glucose levels encourage to release pancreatic glucagon which induces glycogen breakdown to glucose in the liver. These bio-control systems do not function properly in diabetic patients. Though the control of disease seems intuitively easy, in real life, due to many differences in structure by diet and fasting, exercise, medications, patient’s profile and other stressors, it is not that easy. The mathematical models of the glucose-insulin regulatory system follow the patient’s physiological conditions which make it difficult to identify and estimate all the model parameters. In this paper, we have given a systematic literature review on mathematical models of the diabetic patients, and various kinds of disease control techniques through the development of open and closed loop insulin deliver command system and optimization of exogenous insulin rate. It demonstrates the open and closed loop type model-based control strategies underlying the assumptions of the concerned models. The combination of mathematical model with control strategies such as genetic algorithm (GA), neural network (NN), sliding mode controller (SMC), model predictive controller (MPC), and fuzzy logic control (FLC) has been considered, which provides an overview of this area, highlighting the control profile over the diabetic model with promising clinical results, outlining key challenges, and identifying needs for the future research. Also, the significance of these control algorithms has been discussed in the presence of the noises, the controller’s robustness and various other disturbances. It provides substantial information on diabetes management through various control techniques.

Modeling of Pharmacokinetic Profiles of Insulin Aspart and Biphasic Insulin Aspart 30 / 70

The study includes modeling and simulation of insulin aspart pharmacokinetics (PK). The authors used PK data of biosimilar insulins - insulin aspart and biphasic insulin aspart 30/70 - to develop a predictive population PK model for the insulins. The model was built via Monolix software taking into account the weight-based dosing and the dose and body weight effects on the parameters. The model-based simulations were performed using the R package mlxR for various administered doses and various ratios of insulin aspart forms for a better understanding of the insulin behavior. The optimal model was a one-compartment model with a combination of zero- and first-order absorptions with absorption lag for the soluble form of insulin aspart and first-order absorption for the insulin aspart protamine suspension. The assumption of identical behavior of two insulins at the distribution and elimination phases was made. The developed PK model was fitted successfully to the experimental dataand all fitted parameters displayed a moderate coefficient of variation. The PK model allows us to predict PK profiles for various doses and formulations of insulin aspart and can be used to improve the accuracy, safety and ethics of novel clinical trials of insulin. This article is protected by copyright. All rights reserved.

Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with β-cells and the other with no β-cell component to determine their capability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1–4, depending on the diabetes severity of each group, with severity increasing from group 1–4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no β-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with β-cells required more parameters to match the data and we fitted the β-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of 1.2, and a difference in BIC of 0.12 for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1–3 ranging from 2.10 to 4.05. Our results suggest that the model without β-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes.

Simulation-Based Evaluation of Treatment Adjustment to Exercise in Type 1 Diabetes

Regular exercise is beneficial and recommended for people with type 1 diabetes, but increased glucose demand and changes in insulin sensitivity require treatment adjustments to prevent exercise-induced hypoglycemia. Several different adjustment strategies based on insulin bolus reductions and additional carbohydrate intake have been proposed, but large inter- and intraindividual variability and studies using different exercise duration, intensity, and timing impede a direct comparison of their effects. In this study, we use a mathematical model of the glucoregulatory system and implement published guidelines and strategies in-silico to provide a direct comparison on a single 'typical' person on a standard day with three meals. We augment this day by a broad range of exercise scenarios combining different intensity and duration of the exercise session, and different timing with respect to adjacent meals. We compare the resulting blood glucose trajectories and use summary measures to evaluate the time-in-range and risk scores for hypo- and hyperglycemic events for each simulation scenario, and to determine factors that impede prevention of hypoglycemia events. Our simulations suggest that the considered strategies and guidelines successfully minimize the risk for acute hypoglycemia. At the same time, all adjustments substantially increase the risk of late-onset hypoglycemia compared to no adjustment in many cases. We also find that timing between exercise and meals and additional carbohydrate intake during exercise can lead to non-intuitive behavior due to superposition of meal- and exercise-related glucose dynamics. Increased insulin sensitivity appears as a major driver of non-acute hypoglycemic events. Overall, our results indicate that further treatment adjustment might be required both immediately following exercise and up to several hours later, but that the intricate interplay between different dynamics makes it difficult to provide generic recommendations. However, our simulation scenarios extend substantially beyond the original scope of each model component and proper model validation is warranted before applying our in-silico results in a clinical setting.

Pharmacokinetics, tissue distribution and excretion of a novel long-acting human insulin analogue - recombinant insulin LysArg in rats

As a novel long-acting recombinant human insulin analogue, it is necessary to carry out the preclinical research for insulin LysArg. The purpose of this study was to characterise the pharmacokinetic, tissue distribution and excretion of insulin LysArg and provide a reference for its development. Three methods were used to measure the content of insulin LysArg in biological samples after a single subcutaneous administration in rats, including radioassay, radioassay after precipitation with TCA and separation by HPLC. After Subcutaneous administration of recombinant insulin LysArg 1, 2, 4 U/kg in rats, it showed both C_max and AUC_0-t were positively correlated with the dose. In the meanwhile, after a single subcutaneous administration of recombinant insulin LysArg at 2 U/kg in rats, the amount of radioactivity in most organs was highest at 1.5 h and then decreased gradually, no accumulation was found. The highest level of insulin LysArg was observed in the kidney. Like other macromolecules, insulin LysArg was mainly excreted from urine. The study fully illustrated the pharmacokinetic pattern of insulin LysArg, provided valuable informations to support its further development about safety and toxicology.

Modeling Subcutaneous Absorption of Long-Acting Insulin Glargine in Type 1 Diabetes

OBJECTIVE

Subcutaneous (sc) administration of long-acting insulin analogs is often employed in multiple daily injection (MDI) therapy of type 1 diabetes (T1D) to cover patient's basal insulin needs. Among these, insulin glargine 100 U/mL (Gla-100) and 300 U/mL (Gla-300) are formulations indicated for once daily sc administration in MDI therapy of T1D. A few semi-mechanistic models of sc absorption of insulin glargine have been proposed in the literature, but were not quantitatively assessed on a large dataset. The aim of this paper is to propose a model of sc absorption of insulin glargine able to describe the data and provide precise model parameters estimates with a clear physiological interpretation.

METHODS

Three candidate models were identified on a total of 47 and 77 insulin profiles of T1D subjects receiving a single or repeated sc administration of Gla-100 or Gla-300, respectively. Model comparison and selection were performed on the basis of their ability to describe the data and numerical identifiability.

RESULTS

The most parsimonious model is linear two-compartment and accounts for the insulin distribution between the two compartments after sc administration through parameter k. Between the two formulations, we report a lower fraction of insulin in the first versus second compartment (k = 86% versus 94% in Gla-100 versus Gla-300, p < 0.05), a lower dissolution rate from the first to the second compartment ([Formula: see text] versus 0.0008 min^-1 in Gla-100 versus Gla-300, p << 0.001), and a similar rate of insulin absorption from the second compartment to plasma ([Formula: see text] versus 0.0016 min^-1 in Gla-100 versus Gla-300, p = NS), in accordance with the mechanisms of insulin glargine protraction.

CONCLUSIONS

The proposed model is able to both accurately describe plasma insulin data after sc administration and precisely estimate physiologically plausible parameters.

SIGNIFICANCE

The model can be incorporated in simulation platforms potentially usable for optimizing basal insulin treatment strategies.

Modeling the acute effects of exercise on insulin kinetics in type 1 diabetes

Our objective is to develop a physiology-based model of insulin kinetics to understand how exercise alters insulin concentrations in those with type 1 diabetes (T1D). We reveal the relationship between the insulin absorption rate ([Formula: see text]) from subcutaneous tissue, the insulin delivery rate ([Formula: see text]) to skeletal muscle, and two physiological parameters that characterize the tissue: the perfusion rate (Q) and the capillary permeability surface area (PS), both of which increase during exercise because of capillary recruitment. We compare model predictions to experimental observations from two pump-wearing T1D cohorts [resting subjects ([Formula: see text]) and exercising subjects ([Formula: see text])] who were each given a mixed-meal tolerance test and a bolus of insulin. Using independently measured values of Q and PS from literature, the model predicts that during exercise insulin concentration increases by 30% in plasma and by 60% in skeletal muscle. Predictions reasonably agree with experimental observations from the two cohorts, without the need for parameter estimation by curve fitting. The insulin kinetics model suggests that the increase in surface area associated with exercise-induced capillary recruitment significantly increases [Formula: see text] and [Formula: see text], which explains why insulin concentrations in plasma and skeletal muscle increase during exercise, ultimately enhancing insulin-dependent glucose uptake. Preventing hypoglycemia is of paramount importance in determining the proper insulin dose during exercise. The presented model provides mechanistic insight into how exercise affects insulin kinetics, which could be useful in guiding the design of decision support systems and artificial pancreas control algorithms.

Modeling of Diabetes and Its Clinical Impact

Understanding all aspects of diabetes treatment is hindered by the complexity of this chronic disease and its multifaceted complications and comorbidities, including social and financial impacts. In vivo studies as well as clinical trials provided invaluable information for unraveling not only metabolic processes but also risk estimations of, for example, complications. These approaches are often time- and cost-consuming and have frequently been supported by simulation models. Simulation models provide the opportunity to investigate diabetes treatment from additional viewpoints and with alternative objectives. This review presents selected models focusing either on metabolic processes or risk estimations and financial outcomes to provide a basic insight into this complex subject. It also discusses opportunities and challenges of modeling diabetes.

Open-loop glucose control: Automatic IOB-based super-bolus feature for commercial insulin pumps

BACKGROUND AND OBJECTIVE

Although there has been significant progress towards closed-loop type 1 diabetes mellitus (T1DM) treatments, most diabetic patients still treat this metabolic disorder in an open-loop manner, based on insulin pump therapy (basal and bolus insulin infusion). This paper presents a method for automatic insulin bolus shaping based on insulin-on-board (IOB) as an alternative to conventional bolus dosing.

METHODS

The methodology presented allows the pump to generate the so-called super-bolus (SB) employing a two-compartment IOB dynamic model. The extra amount of insulin to boost the bolus and the basal cutoff time are computed using the duration of insulin action (DIA). In this way, the pump automatically re-establishes basal insulin when IOB reaches its basal level. Thus, detrimental transients caused by manual or a-priori computations are avoided.

RESULTS

The potential of this method is illustrated via in-silico trials over a 30 patients cohort in single meal and single day scenarios. In the first ones, improvements were found (standard treatment vs. automatic SB) both in percentage time in euglycemia (75g meal: 81.9 ± 15.59 vs. 89.51 ± 11.95, ρ ≃ 0; 100g meal: 75.12 ± 18.23 vs. 85.46 ± 14.96, ρ ≃ 0) and time in hypoglecymia (75g meal: 5.92 ± 14.48 vs. 0.97 ± 4.15, ρ=0.008; 100g meal: 9.5 ± 17.02 vs. 1.85 ± 7.05, ρ=0.014). In a single day scenario, considering intra-patient variability, the time in hypoglycemia was reduced (9.57 ± 14.48 vs. 4.21 ± 6.18, ρ=0.028) and improved the time in euglycemia (79.46 ± 17.46 vs. 86.29 ± 11.73, ρ=0.007).

CONCLUSIONS

The automatic IOB-based SB has the potential of a better performance in comparison with the standard treatment, particularly for high glycemic index meals with high carbohydrate content. Both glucose excursion and time spent in hypoglycemia were reduced.

Modeling Subcutaneous Absorption of Fast-Acting Insulin in Type 1 Diabetes

OBJECTIVE

Subcutaneous (sc) administration of fast-acting insulin analogues is the key in conventional therapy of type 1 diabetes (T1D). A model of sc insulin absorption would be helpful for optimizing insulin therapy and test new open- and closed-loop treatment strategies in in silico platforms. Some models have been published in the literature, but none was assessed on a frequently-sampled large dataset of T1D subjects. The aim here is to propose a model of sc absorption of fast-acting insulin, which is able to describe the data and precisely estimate model parameters with a clear physiological interpretation.

METHODS

Three candidate models were identified on 116 T1D subjects, who underwent a single sc injection of fast-acting insulin and were compared on the basis of their ability to describe the data and their numerical identifiability.

RESULTS

A linear two-compartment model including a subject-specific delay in sc insulin absorption is proposed. On average, a delay of 7.6 min in insulin appearance in the first compartment is detected, then the insulin is slowly absorbed into plasma (in 23% of the subjects) with a rate of 0.0034 min-1, while the remaining diffuses into the second compartment, with a rate constant of 0.028 min-1, and then finally absorbed into plasma with a rate constant of 0.014 min-1.

CONCLUSION

Among the three tested models, the one proposed here is the only one able to both accurately describe plasma insulin data after a single sc injection and precisely estimate physiologically plausible parameters. The model needs to be further tested in case of variable sc insulin delivery and/or multiple insulin doses.

SIGNIFICANCE

Results are expected to help the development of new open- and closed-loop insulin treatment strategies.

Choosing an optimal input for an intravenous glucose tolerance test to aid parameter identification

OBJECTIVE

The minimal model is used to estimate insulin sensitivity in patients with diabetes, following an intravenous glucose tolerance test (IVGTT). Issues have been reported regarding parameter estimation, including correlation between insulin sensitivity and action parameters. The objective was to reduce these issues, by modifying the input of glucose in the test.

METHODS

Data were available for 24 volunteers following an IVGTT and glucose clamp test. Correlation between parameters was explored using likelihood heatmaps. An integrated glucose-insulin model was used to simulate glucose and insulin concentrations following new glucose inputs. The improved input for the test was selected by finding the minimum inverse of the determinant of the Fisher information matrix.

KEY FINDINGS

When the minimal model was fitted to the IVGTT data, there was clear correlation between the insulin parameters. With the glucose clamp, all parameters were correlated and badly estimated. The modified input, a bolus dose followed by constant infusion, resulted in improvement in parameter estimation and reduction in parameter correlation.

CONCLUSIONS

It is possible to reduce the issues with parameter estimation in the minimal model by modifying the glucose input, leading to a simplified test deign and a reduction in the total amount of glucose infused.

Modeling Pharmacokinetic Profiles of Insulin Regimens to Enhance Understanding of Subcutaneous Insulin Regimens

Insulin pharmacokinetics following subcutaneous administration were modeled, simulated, and displayed through an interactive and user‐friendly interface to illustrate the time course of administered insulins frequently prescribed, providing a simple tool for clinicians through a straightforward visualization of insulin regimens. Pharmacokinetic data of insulin formulations with different onset and duration of action from several clinical studies, including insulin glargine, regular insulin, neutral protamine Hagedorn (NPH), insulin lispro, and premixed preparations of NPH with regular insulin (Mix 70/30), and insulin lispro protamine suspension with insulin lispro (Mix 50/50, Mix 75/25), were used to develop a predictive population pharmacokinetic model of insulins with consideration of factors such as insulin formulation, weight‐based dosing, body‐weight effect on volume of distribution, and administration time relative to meals, on the insulin time‐action profile. The model‐predicted insulin profile of each insulin was validated and confirmed to be comparable to observed data via an external validation method. Model‐based simulations of clinically relevant insulin‐dosing scenarios to cater to specific initial patient and prescribing conditions were then implemented with differential equations using the R statistical program (version 3.2.2). The R package Shiny was subsequently applied to build a web browser interface to execute and visualize the model simulation outputs. The application of insulin pharmacokinetic modeling enabled informative visualization of insulin time‐action profiles and provided an efficient and intuitive educational tool to quickly convey and interactively explore many insulin time‐action profiles to ease the understanding of insulin formulations in clinical practice.

Physiology-Invariant Meal Detection for Type 1 Diabetes

BACKGROUND

Fully automated artificial pancreas systems require meal detectors to supplement blood glucose level regulation, where false meal detections can cause unnecessary insulin delivery with potentially fatal consequences, and missed detections may cause the patient to experience extreme hyperglycemia. Most existing meal detectors monitor various measures of glucose rate-of-change to detect meals where varying physiology and meal content complicate balancing detector sensitivity versus specificity.

METHODS

We developed a novel meal detector based on a minimal glucose-insulin metabolism model and show that the detector is, by design, invariant to patient-specific physiological parameters in the minimal model. Our physiological parameter-invariant (PAIN) detector achieves a near-constant false alarm rate across all individuals and is evaluated against three other major existing meal detectors on a clinical type 1 diabetes data set.

RESULTS

In the clinical evaluation, the PAIN-based detector achieves an 86.9% sensitivity for an average false alarm rate of two alarms per day. In addition, for all false alarm rates, the PAIN-based detector performance is significantly better than three other existing meal detectors. In addition, the evaluation results show that the PAIN-based detector uniquely (as compared with the other meal detectors) has low variance in detection and false alarm rates across all patients, without patient-specific personalization.

CONCLUSIONS

The PAIN-based meal detector has demonstrated better detection performance than existing meal detectors, and it has the unique strength of achieving a consistent performance across a population with varying physiology without any individual-level parameter tuning or training.

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.

Pharmacokinetic Model of the Transport of Fast-Acting Insulin From the Subcutaneous and Intradermal Spaces to Blood

Pharmacokinetic (PK) models describing the transport of insulin from the injection site to blood assist clinical decision making and are part of in silico platforms for developing and testing of insulin delivery strategies for treatment of patients with diabetes. The ability of these models to accurately describe all facets of the in vivo insulin transport is therefore critical for their application. Here, we propose a new model of fast-acting insulin analogs transport from the subcutaneous and intradermal spaces to blood that can accommodate clinically observed biphasic appearance and delayed clearance of injected insulin, 2 phenomena that are not captured by existing PK models. To develop the model we compare 9 insulin transport PK models which describe hypothetical insulin delivery pathways potentially capable of approximating biphasic appearance of exogenous insulin. The models are tested with respect to their ability to describe clinical data from 10 healthy volunteers which received 1 subcutaneous and 2 intradermal insulin injections on 3 different occasions. The optimal model, selected based on information and posterior identifiability criteria, assumes that insulin is delivered at the administrative site and is then transported to the bloodstream via 2 independent routes (1) diffusion-like process to the blood and (2) combination of diffusion-like processes followed by an additional compartment before entering the blood. This optimal model accounts for biphasic appearance and delayed clearance of exogenous insulin. It agrees better with the clinical data as compared to commonly used models and is expected to improve the in silico development and testing of insulin treatment strategies, including artificial pancreas systems.

A therapy parameter-based model for predicting blood glucose concentrations in patients with type 1 diabetes

In this paper, the problem of predicting blood glucose concentrations (BG) for the treatment of patients with type 1 diabetes, is addressed. Predicting BG is of very high importance as most treatments, which consist in exogenous insulin injections, rely on the availability of BG predictions. Many models that can be used for predicting BG are available in the literature. However, it is widely admitted that it is almost impossible to perfectly model blood glucose dynamics while still being able to identify model parameters using only blood glucose measurements. The main contribution of this work is to propose a simple and identifiable linear dynamical model, which is based on the static prediction model of standard therapy. It is shown that the model parameters are intrinsically correlated with physician-set therapy parameters and that the reduction of the number of model parameters to identify leads to inferior data fits but to equivalent or slightly improved prediction capabilities compared to state-of-the-art models: a sign of an appropriate model structure and superior reliability. The validation of the proposed dynamic model is performed using data from the UVa simulator and real clinical data, and potential uses of the proposed model for state estimation and BG control are discussed.

Pharmacokinetics modeling of exogenous glucagon in type 1 diabetes mellitus patients

BACKGROUND

Insulin-induced hypoglycemia is as a critical barrier in the treatment of type 1 diabetes mellitus patients and may lead to unconsciousness, brain damage, or even death. Clinically, glucagon is used as a rescue drug to treat severe hypoglycemic episodes. More recently, in a bihormonal closed-loop glucose control, glucagon has been used subcutaneously along with insulin for protection against hypoglycemia. In this context, small doses of glucagon are frequently administered. The efficacy and safety of such systems, however, require precise information on the pharmacokinetics of the glucagon transport from the administrative site to the circulation, which is currently lacking. The goal of this work is to address this need by developing and validating a mathematical model of exogenous glucagon transport to the plasma.

MATERIALS AND METHODS

Eight pharmacokinetic models with various levels of complexity were fitted to nine clinical datasets. An optimal model was chosen in two consecutive steps. At Step 1, all models were screened for parameter identifiability (discarding the unidentifiable candidates). At Step 2, the remaining models are compared based on Bayesian information criterion.

RESULTS

At Step 1, two models were removed for higher parameter fractional SDs. Another three were discarded for location of their optimal parameters on the parameter search boundaries. At Step 2, an optimal model was selected based on the Bayesian information criterion. It has a simple linear structure, assuming that glucagon is injected into one compartment, from where it enters a pool for a slower release into a third, plasma compartment. In the first and third compartments, glucagon is cleared at a rate proportional to its concentration.

CONCLUSIONS

A linear kinetic model of glucagon intervention has been developed and validated. It is expected to provide guidance for glucagon delivery and the construction of preclinical simulation testing platforms.

Faster pharmacokinetics and increased patient acceptance of intradermal insulin delivery using a single hollow microneedle in children and adolescents with type 1 diabetes

OBJECTIVE

In an effort to improve compliance with insulin therapy and to accelerate insulin pharmacokinetics, we tested the hypothesis that intradermal insulin delivery using a hollow microneedle causes less pain and leads to faster onset and offset of insulin pharmacokinetics in children and adolescents with type 1 diabetes (T1DM) compared with a subcutaneous, insulin pump catheter.

RESEARCH DESIGN AND METHODS

In this repeated measures study, 16 children and adolescents with T1DM received Lispro insulin by microneedle and subcutaneous administration on separate days. Subjects rated the pain of insertion and infusion using a visual analog scale. Blood specimens were collected over 4 h to determine insulin and glucose concentrations.

RESULTS

Microneedle insertion pain was significantly lower compared with insertion of the subcutaneous catheter (p = 0.005). Insulin onset time was 22 min faster (p = 0.0004) and offset time was 34 min faster (p = 0.017) after hollow microneedle delivery compared with subcutaneous delivery.

CONCLUSIONS

In this study, intradermal insulin delivery using a single, hollow microneedle device resulted in less insertion pain and faster insulin onset and offset in children and adolescents with T1DM. A reduction in pain might improve compliance with insulin delivery. The faster onset and offset times of insulin action may enable closed-loop insulin therapy.

Glucose-insulin regulation model with subcutaneous insulin injection and evaluation using diabetic inpatients data

Closed-loop insulin delivery systems often implement glucose measurement and insulin administration in the subcutis. However some existing models for glucose-insulin system ignored the dynamics of subcutaneous glucose and subcutaneously-injected insulin. This paper reports a two-compartment model that includes glucose and insulin dynamics in subcutis, and its evaluation using patient data. Clinical information such as glucose level, insulin dosage, insulin injection time and meals of anonymous diabetes inpatients was collected. Measured glucose level of the diabetic inpatients agrees with that of computer simulation. Due to the lack of glucose-insulin model with subcutaneously-injected insulin for type 2 diabetic patients, our model was compared with existing model for type 1 subjects. The new glucose-insulin model can mimic dynamics of glucose and insulin under the disturbance of insulin injections and meals. Model parameters were estimated using nonlinear least square method and their effect on pathology and physiology of diabetes were analyzed.

The impact of mathematical modeling on the understanding of diabetes and related complications

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.

Diabetes technology: markers, monitoring, assessment, and control of blood glucose fluctuations in diabetes

People with diabetes face a life-long optimization problem: to maintain strict glycemic control without increasing their risk for hypoglycemia. Since the discovery of insulin in 1921, the external regulation of diabetes by engineering means has became a hallmark of this optimization. Diabetes technology has progressed remarkably over the past 50 years-a progress that includes the development of markers for diabetes control, sophisticated monitoring techniques, mathematical models, assessment procedures, and control algorithms. Continuous glucose monitoring (CGM) was introduced in 1999 and has evolved from means for retroactive review of blood glucose profiles to versatile reliable devices, which monitor the course of glucose fluctuations in real time and provide interactive feedback to the patient. Technology integrating CGM with insulin pumps is now available, opening the field for automated closed-loop control, known as the artificial pancreas. Following a number of in-clinic trials, the quest for a wearable ambulatory artificial pancreas is under way, with a first prototype tested in outpatient setting during the past year. This paper discusses key milestones of diabetes technology development, focusing on the progress in the past 10 years and on the artificial pancreas-still not a cure, but arguably the most promising treatment of diabetes to date.

Mathematical model for glucose regulation in the whole-body system

The human body needs continuous and stable glucose supply for maintaining its biological functions. Stable glucose supply comes from the homeostatic regulation of the blood glucose level, which is controlled by various glucose consuming or producing organs. Therefore, it is important to understand the whole-body glucose regulation mechanism. In this article, we describe various mathematical models proposed for glucose regulation in the human body, and discuss the difficulty and limitation in reproducing real processes of glucose regulation.

Personalized blood glucose models for exercise, meal and insulin interventions in type 1 diabetic children

Modern healthcare is rapidly evolving towards a personalized, predictive, preventive and participatory approach of treatment to achieve better quality of life (QoL) in patients. Identification of personalized blood glucose (BG) prediction models incorporating the lifestyle interventions can help in devising optimal patient specific exercise, food, and insulin prescriptions, which in turn can prevent the risk of frequent hypoglycemic episodes and other diabetes complications. Hence, we propose a modeling methodology based on multi-input single-output time series models, to develop personalized BG models for 12 type 1 diabetic (T1D) children, using the clinical data from Diabetes Research in Children's Network. The multiple inputs needed to develop the proposed models were rate of perceived exertion (RPE) values (which quantify the exercise intensity), carbohydrate absorption dynamics, basal insulin infusion and bolus insulin absorption kinetics. Linear model classes like Box-Jenkins (1 patient), state space (1 patient) and process transfer function models (7 patients) of different orders were found to be the most suitable as the personalized models for 9 patients, whereas nonlinear Hammerstein-Wiener models of different orders were found to be the personalized models for 3 patients. Hence, inter-patient variability was captured by these models as each patient follows a different personalized model.

Optimal design of clinical tests for the identification of physiological models of type 1 diabetes in the presence of model mismatch

How to design a clinical test aimed at identifying in the safest, most precise and quickest way the subject-specific parameters of a detailed model of glucose homeostasis in type 1 diabetes is the topic of this article. Recently, standard techniques of model-based design of experiments (MBDoE) for parameter identification have been proposed to design clinical tests for the identification of the model parameters for a single type 1 diabetic individual. However, standard MBDoE is affected by some limitations. In particular, the existence of a structural mismatch between the responses of the subject and that of the model to be identified, together with initial uncertainty in the model parameters may lead to design clinical tests that are sub-optimal (scarcely informative) or even unsafe (the actual response of the subject might be hypoglycaemic or strongly hyperglycaemic). The integrated use of two advanced MBDoE techniques (online model-based redesign of experiments and backoff-based MBDoE) is proposed in this article as a way to effectively tackle the above issue. Online model-based experiment redesign is utilised to exploit the information embedded in the experimental data as soon as the data become available, and to adjust the clinical test accordingly whilst the test is running. Backoff-based MBDoE explicitly accounts for model parameter uncertainty, and allows one to plan a test that is both optimally informative and safe by design. The effectiveness and features of the proposed approach are assessed and critically discussed via a simulated case study based on state-of-the-art detailed models of glucose homeostasis. It is shown that the proposed approach based on advanced MBDoE techniques allows defining safe, informative and subject-tailored clinical tests for model identification, with limited experimental effort.

A computational model of the human glucose-insulin regulatory system

OBJECTIVE

A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. The proposed method for the estimation of parameters for a system of ordinary differential equations (ODEs) that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test (GTT) in physiological studies is presented. The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.

METHODS

Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals (SSR) function, which quantifies the difference between theoretical model predictions and GTT's experimental observations. Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.

RESULTS

Based on the Ackerman's published data, we estimated the key parameters by applying R-based iterative computer programs. As a result, the theoretically simulated curves perfectly matched the experimental data points. Our model showed that the estimated parameters, computed frequency and period values, were proven a good indicator of diabetes.

CONCLUSION

The present paper introduces a computational algorithm to biomedical problems, particularly to endocrinology and metabolism fields, which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier. The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.

Smart sensors and virtual physiology human approach as a basis of personalized therapies in diabetes mellitus

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient's information to the models.A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies.

Systems engineering medicine: engineering the inflammation response to infectious and traumatic challenges

The complexity of the systemic inflammatory response and the lack of a treatment breakthrough in the treatment of pathogenic infection demand that advanced tools be brought to bear in the treatment of severe sepsis and trauma. Systems medicine, the translational science counterpart to basic science's systems biology, is the interface at which these tools may be constructed. Rapid initial strides in improving sepsis treatment are possible through the use of phenomenological modelling and optimization tools for process understanding and device design. Higher impact, and more generalizable, treatment designs are based on mechanistic understanding developed through the use of physiologically based models, characterization of population variability, and the use of control-theoretic systems engineering concepts. In this review we introduce acute inflammation and sepsis as an example of just one area that is currently underserved by the systems medicine community, and, therefore, an area in which contributions of all types can be made.

Gaussian Process modelling of blood glucose response to free-living physical activity data in people with type 1 diabetes

Good blood glucose control is important to people with type 1 diabetes to prevent diabetes-related complications. Too much blood glucose (hyperglycaemia) causes long-term micro-vascular complications, while a severe drop in blood glucose (hypoglycaemia) can cause life-threatening coma. Finding the right balance between quantity and type of food intake, physical activity levels and insulin dosage, is a daily challenge. Increased physical activity levels often cause changes in blood glucose due to increased glucose uptake into tissues such as muscle. To date we have limited knowledge about the minute by minute effects of exercise on blood glucose levels, in part due to the difficulty in measuring glucose and physical activity levels continuously, in a free-living environment. By using a light and user-friendly armband we can record physical activity energy expenditure on a minute-by-minute basis. Simultaneously, by using a continuous glucose monitoring system we can record glucose concentrations. In this paper, Gaussian Processes are used to model the glucose excursions in response to physical activity data, to study its effect on glycaemic control.

MATHEMATICAL MODELS OF SUBCUTANEOUS INJECTION OF INSULIN ANALOGUES: A MINI-REVIEW

In the last three decades, several models relevant to the subcutaneous injection of insulin analogues have appeared in the literature. Most of them model the absorption of insulin analogues in the injection depot and then compute the plasma insulin concentration. The most recent systemic models directly simulate the plasma insulin dynamics. These models have been and/or can be applied to the technology of the insulin pump or to the coming closed-loop systems, also known as the artificial pancreas. In this paper, we selectively review these models in detail and at point out that these models provide key building blocks for some important endeavors into physiological questions of insulin secretion and action. For example, it is not clear at this time whether or not picomolar doses of insulin are found near the islets and there is no experimental method to assess this in vivo. This is of interest because picomolar concentrations of insulin have been found to be effective at blocking beta-cell death and increasing beta-cell growth in recent cell culture experiments.