Distribution-based sub-population selection (DSPS): A method for in-silico reproduction of clinical trials outcomes

Diabetes presents a significant challenge to healthcare due to the short- and long-term complications associated with poor blood sugar control. Computer simulation platforms have emerged as promising tools for advancing diabetes therapy by simulating patient responses to treatments in a virtual environment. The University of Virginia Virtual Lab (UVLab) is a new simulation platform engineered to mimic the metabolic behavior of individuals with type 2 diabetes (T2D) using a mathematical model of glucose homeostasis in T2D and a large population of 6062 virtual subjects. This work proposes a statistical method - the Distribution-based sub-population selection (DSPS) method - for selecting subsets of virtual subjects from this large initial pool, ensuring that the selected group possesses the desired characteristics necessary to reproduce and predict the outcomes of a clinical trial. DSPS formulates the sub-population selection as a linear programming problem, identifying the largest virtual cohort to closely resemble the statistical properties (moments) of key outcomes from real-world clinical trials. The method was applied to the insulin degludec arm of a 26-week phase 3 clinical trial, evaluating the efficacy and safety of insulin degludec and liraglutide combination therapy. DSPS selected a sub-population that mirrored clinical trial data across key metrics, including glycemic efficacy, insulin dosages, and cumulative hypoglycemia events, with a relative sum of square errors of 0.33 and a percentage error of 1.07 %. This approach bridges the gap between large population simulation platforms and clinical trials, enabling the selection of virtual sub-populations with specific properties required for targeted studies.

Tailoring the Padova Type 2 Diabetes Simulator for Treatment Guidance in Target Populations

OBJECTIVE

The Padova type 2 diabetes (T2D) simulator (T2DS) has been recently proposed to optimize T2D treatments including novel long-acting insulins. It consists of a physiological model and an in silico population describing glucose dynamics, derived from early-stage T2D subjects studied with sophisticated tracer-based experimental techniques. This limits T2DS domain of validity to this specific sub-population. Conversely, running simulations in insulin-naïve or advanced T2D subjects, would be more valuable. However, it is rarely possible or cost-effective to run complex experiments in such populations. Therefore, we propose a method for tuning the T2DS to any desired T2D sub-population using published clinical data. As case study, we extended the T2DS to insulin-naïve T2D subjects, who need to start insulin therapy to compensate the reduced insulin function.

METHODS

T2DS model was identified based on literature data of the target population. The estimated parameters were used to generate a virtual cohort of insulin-naïve T2D subjects (inC1). A model of basal insulin degludec (IDeg) was also incorporated into the T2DS to enable basal insulin therapy. The resulting tailored T2DS was assessed by simulating IDeg therapy initiation and comparing simulated vs. clinical trial outcomes. For further validation, this procedure was reiterated to generate a new cohort of insulin-naïve T2D (inC2) assuming inC1 as target population.

RESULTS

No statistically significant differences were found when comparing fasting plasma glucose and IDeg dose, neither in clinical data vs. inC1, nor inC1 vs. inC2.

CONCLUSIONS

The tuned T2DS allowed reproducing the main findings of clinical studies in insulin-naïve T2D subjects.

SIGNIFICANCE

The proposed methodology makes the Padova T2DS usable for supporting treatment guidance in target T2D populations.

Developing the UVA/Padova Type 1 Diabetes Simulator: Modeling, Validation, Refinements, and Utility

Arguably, diabetes mellitus is one of the best quantified human conditions. In the past 50 years, the metabolic monitoring technologies progressed from occasional assessment of average glycemia via HbA1c, through episodic blood glucose readings, to continuous glucose monitoring (CGM) producing data points every few minutes. The high-temporal resolution of CGM data enabled increasingly intensive treatments, from decision support assisting insulin injection or oral medication, to automated closed-loop control, known as the "artificial pancreas." Throughout this progress, mathematical models and computer simulation of the human metabolic system became indispensable for the technological progress of diabetes treatment, enabling every step, from assessment of insulin sensitivity via the now classic Minimal Model of Glucose Kinetics, to in silico trials replacing animal experiments, to automated insulin delivery algorithms. In this review, we follow these developments, beginning with the Minimal Model, which evolved through the years to become large and comprehensive and trigger a paradigm change in the design of diabetes optimization strategies: in 2007, we introduced a sophisticated model of glucose-insulin dynamics and a computer simulator equipped with a "population" of N = 300 in silico "subjects" with type 1 diabetes. In January 2008, in an unprecedented decision, the Food and Drug Administration (FDA) accepted this simulator as a substitute to animal trials for the pre-clinical testing of insulin treatment strategies. This opened the field for rapid and cost-effective development and pre-clinical testing of new treatment approaches, which continues today. Meanwhile, animal experiments for the purpose of designing new insulin treatment algorithms have been abandoned.

Minimal and Maximal Models to Quantitate Glucose Metabolism: Tools to Measure, to Simulate and to Run in Silico Clinical Trials

Several models have been proposed to describe the glucose system at whole-body, organ/tissue and cellular level, designed to measure non-accessible parameters (minimal models), to simulate system behavior and run in silico clinical trials (maximal models). Here, we will review the authors' work, by putting it into a concise historical background. We will discuss first the parametric portrait provided by the oral minimal models-building on the classical intravenous glucose tolerance test minimal models-to measure otherwise non-accessible key parameters like insulin sensitivity and beta-cell responsivity from a physiological oral test, the mixed meal or the oral glucose tolerance tests, and what can be gained by adding a tracer to the oral glucose dose. These models were used in various pathophysiological studies, which we will briefly review. A deeper understanding of insulin sensitivity can be gained by measuring insulin action in the skeletal muscle. This requires the use of isotopic tracers: both the classical multiple-tracer dilution and the positron emission tomography techniques are discussed, which quantitate the effect of insulin on the individual steps of glucose metabolism, that is, bidirectional transport plasma-interstitium, and phosphorylation. Finally, we will present a cellular model of insulin secretion that, using a multiscale modeling approach, highlights the relations between minimal model indices and subcellular secretory events. In terms of maximal models, we will move from a parametric to a flux portrait of the system by discussing the triple tracer meal protocol implemented with the tracer-to-tracee clamp technique. This allows to arrive at quasi-model independent measurement of glucose rate of appearance (Ra), endogenous glucose production (EGP), and glucose rate of disappearance (Rd). Both the fast absorbing simple carbs and the slow absorbing complex carbs are discussed. This rich data base has allowed us to build the UVA/Padova Type 1 diabetes and the Padova Type 2 diabetes large scale simulators. In particular, the UVA/Padova Type 1 simulator proved to be a very useful tool to safely and effectively test in silico closed-loop control algorithms for an artificial pancreas (AP). This was the first and unique simulator of the glucose system accepted by the U.S. Food and Drug Administration as a substitute to animal trials for in silico testing AP algorithms. Recent uses of the simulator have looked at glucose sensors for non-adjunctive use and new insulin molecules.

A simulator with realistic and challenging scenarios for virtual T1D patients undergoing CSII and MDI therapy

In silico simulations have become essential for the development of diabetes treatments. However, currently available simulators are not challenging enough and often suffer from limitations in insulin and meal absorption variability, which is unable to realistically reflect the dynamics of people with type 1 diabetes (T1D). Additionally, T1D simulators are mainly designed for the testing of continuous subcutaneous insulin infusion (CSII) therapies. In this work, a simulator is presented that includes a generated virtual patient (VP) cohort and both fast- and long-acting Glargine-100 U/ml (Gla-100), Glargine-300 U/ml (Gla-300), and Degludec-100 U/ml (Deg-100) insulin models. Therefore, in addition to CSII therapies, multiple daily injections (MDI) therapies can also be tested. The Hovorka model and its published parameter probability distributions were used to generate cohorts of VPs that represent a T1D population. Valid patients are filtered through restrictions that guarantee that they are physiologically acceptable. To obtain more realistic scenarios, basal insulin profile patterns from the literature have been used to identify variability in insulin sensitivity. A library of mixed meals identified from real data has also been included. This work presents and validates a methodology for the creation of realistic VP cohorts that include physiological variability and a simulator that includes challenging and realistic scenarios for in silico testing. A cohort of 47 VPs has been generated and in silico simulations of both CSII and MDI therapies were performed in open-loop. The simulation outcome metrics were contrasted with literature results.

Modeling Between-Subject Variability in Subcutaneous Absorption of a Long-Acting Insulin Glargine 100 U/mL by a Nonlinear Mixed Effects Approach

Subcutaneous insulin absorption is well-known to vary significantly both between and within subjects (BSV and WSV, respectively). This variability considerably obstacles the establishing of a reproducible and effective insulin therapy. Some models exist to describe the subcutaneous kinetics of both fast and long-acting insulin analogues; however, none of them account for the BSV. The aim of this study is to develop a nonlinear mixed effects model able to describe the BSV observed in the subcutaneous absorption of a long-acting insulin glargine 100 U/mL. Four stochastic models of the BSV were added to a previously validated model of subcutaneous absorption of insulin glargine 100 U/mL. These were assessed on a database of 47 subjects with type 1 diabetes. The best model was selected based on residual analysis, precision of the estimates and parsimony criteria. The selected model provided good fit of individual data, precise population parameter estimates and allowed quantifying the BSV of the insulin glargine 100 U/mL pharmacokinetics. Future model development will include the description of the WSV of long- acting insulin absorption.

Modeling Intraperitoneal Insulin Absorption in Patients with Type 1 Diabetes

Standard insulin therapy to treat type 1 diabetes (T1D) consists of exogenous insulin administration through the subcutaneous (SC) tissue. Despite recent advances in insulin formulations, the SC route still suffers from delays and large inter/intra-subject variability that limiting optimal glucose control. Intraperitoneal (IP) insulin administration, despite its higher invasiveness, was shown to represent a valid alternative to the SC one. To date, no mathematical model describing the absorption and distribution of insulin after IP administration is available. Here, we aim to fill this gap by using data from eight patients with T1D, treated by implanted IP pump, studied in a hospitalized setting, with frequent measurements of plasma insulin and glucose concentration. A battery of models describing insulin kinetics after IP administration were tested. Model comparison and selection were performed based on model ability to predict the data, precision of parameters and parsimony criteria. The selected model assumed that the insulin absorption from the IP space was described by a linear, two-compartment model, coupled with a two-compartment model of whole-body insulin kinetics with hepatic insulin extraction controlled by hepatic insulin. Future developments include model incorporation into the UVa/Padova T1D Simulator for testing open- and closed-loop therapies with IP insulin administration.

Using Iterative Learning for Insulin Dosage Optimization in Multiple-Daily-Injections Therapy for People With Type 1 Diabetes

OBJECTIVE

In this work, we design iterative algorithms for the delivery of long-acting (basal) and rapid-acting (bolus) insulin, respectively, for people with type 1 diabetes (T1D) on multiple-daily-injections (MDIs) therapy using feedback from self-monitoring of blood glucose (SMBG) measurements.

METHODS

Iterative learning control (ILC) updates basal therapy consisting of one long-acting insulin injection per day, while run-to-run (R2R) adapts meal bolus therapy via the update of the mealtime-specific insulin-to-carbohydrate ratio (CR). Updates are due weekly and are based upon sparse SMBG measurements.

RESULTS

Upon termination of the 20 weeks long in-silico trial, in a scenario characterized by meal carbohydrate (CHO) normally distributed with mean μ = [50, 75, 75] grams and standard deviation σ = [5, 7, 7] grams, our strategy produced statistically significant improvements in time in range (70--180) [mg/dl], from 66.9(33.1) % to 93.6(6.7) %, p = 0.02.

CONCLUSIONS

Iterative learning shows potential to improve glycemic regulation over time by driving blood glucose closer to the recommended glycemic targets.

SIGNIFICANCE

Decision support systems (DSSs) and automated therapy advisors such as the one proposed here are expected to improve glycemic outcomes reducing the burden on patients on MDI therapy.

Titration of Long-Acting Insulin Using Continuous Glucose Monitoring and Smart Insulin Pens in Type 1 Diabetes: A Model-Based Carbohydrate-Free Approach

OBJECTIVE

Multiple daily injections (MDI) therapy is the most common treatment for type 1 diabetes (T1D), consisting of long-acting insulin to cover fasting conditions and rapid-acting insulin to cover meals. Titration of long-acting insulin is needed to achieve satisfactory glycemia but is challenging due to inter-and intra-individual metabolic variability. In this work, a novel titration algorithm for long-acting insulin leveraging continuous glucose monitoring (CGM) and smart insulin pens (SIP) data is proposed.

METHODS

The algorithm is based on a glucoregulatory model that describes insulin and meal effects on blood glucose fluctuations. The model is individualized on patient's data and used to extract the theoretical glucose curve in fasting conditions; the individualization step does not require any carbohydrate records. A cost function is employed to search for the optimal long-acting insulin dose to achieve the desired glycemic target in the fasting state. The algorithm was tested in two virtual studies performed within a validated T1D simulation platform, deploying different levels of metabolic variability (nominal and variance). The performance of the method was compared to that achieved with two published titration algorithms based on self-measured blood glucose (SMBG) records. The sensitivity of the algorithm to carbohydrate records was also analyzed.

RESULTS

The proposed method outperformed SMBG-based methods in terms of reduction of exposure to hypoglycemia, especially during the night period (0 am-6 am). In the variance scenario, during the night, an improvement in the time in the target glycemic range (70-180 mg/dL) from 69.0% to 86.4% and a decrease in the time in hypoglycemia (<70 mg/dL) from 10.7% to 2.6% was observed. Robustness analysis showed that the method performance is non-sensitive to carbohydrate records.

CONCLUSION

The use of CGM and SIP in people with T1D using MDI therapy has the potential to inform smart insulin titration algorithms that improve glycemic control. Clinical studies in real-world settings are warranted to further test the proposed titration algorithm.

SIGNIFICANCE

This algorithm is a step towards a decision support system that improves glycemic control and potentially the quality of life, in a population of individuals with T1D who cannot benefit from the artificial pancreas system.

The Padova Type 2 Diabetes Simulator from Triple-Tracer Single-Meal Studies: In Silico Trials Also Possible in Rare but Not-So-Rare Individuals

Background:In silico trials in type 2 diabetes (T2D) would be useful for testing diabetes treatments and accelerating the development of new antidiabetic drugs. In this study, we present a T2D simulator able to reproduce the variability observed in a T2D population. The simulator also allows to safely experiment on virtual subjects with severe (and possibly rare) pathological conditions. Methods: A meal simulation model of glucose, insulin, and C-peptide systems, made of 15 differential equations and 39 parameters, has been identified using a system decomposition and forcing function Bayesian strategy on data of 51 T2D subjects undergoing a single triple-tracer mixed meal. One hundred T2D in silico subjects have been generated from the joint distribution of estimated model parameters. A case study is presented to illustrate the simulator use for testing a virtual drug (improving insulin action and secretion) in a subpopulation of rare, extremely impaired, T2D subjects. Results: The model well fitted T2D data and parameters were estimated with precision. Simulated plasma glucose, insulin, and C-peptide well matched the data (e.g., median [25^th-75^th percentile] glucose area under the curves of 6.9 [6.1-8.5] 10⁴ mg/dL·min in silico vs. 7.0 [5.6-8.2] 10⁴ mg/dL·min in vivo). The potential use of the simulator was shown in a case study, in which the (virtual) antidiabetic drug dose was optimized for very insulin-resistant T2D subjects. Conclusions: We have developed a T2D simulator that captures the behavior of T2D population during a meal, both in terms of average and intersubject variability. The simulator represents a cost-effective way to test new antidiabetic drugs, before moving to human trials.

A Model-Based Insulin Dose Optimization Algorithm for People With Type 1 Diabetes on Multiple Daily Injections Therapy

OBJECTIVE

Multiple daily injections (MDI) therapy is the most common treatment for type 1 diabetes (T1D) including basal insulin doses to keep glucose levels constant during fasting conditions and bolus insulin doses with meals. Optimal insulin dosing is critical to achieving satisfactory glycemia but is challenging due to inter- and intra-individual variability. Here, we present a novel model-based iterative algorithm that optimizes insulin doses using previous-day glucose, insulin, and meal data.

METHODS

Our algorithm employs a maximum-a-posteriori method to estimate parameters of a model describing the effects of changes in basal-bolus insulin doses. Then, parameter estimates, their confidence intervals, and the goodness of fit, are combined to generate new recommendations. We assessed our algorithm in three ways. First, a clinical data set of 150 days (15 participants) were used to evaluate the proposed model and the estimation method. Second, 60-day simulations were performed to demonstrate the efficacy of the algorithm. Third, a sample 6-day clinical experiment is presented and discussed.

RESULTS

The model fitted the clinical data well with a root-mean-square-error of 1.75 mmol/L. Simulation results showed an improvement in the time in target (3.9-10 mmol/L) from 64% to 77% and a decrease in the time in hypoglycemia (< 3.9 mmol/L) from 8.1% to 3.8%. The clinical experiment demonstrated the feasibility of the algorithm.

CONCLUSION

Our algorithm has the potential to improve glycemic control in people with T1D using MDI.

SIGNIFICANCE

This work is a step forward towards a decision support system that improves their quality of life.

In Silico Head-to-Head Comparison of Insulin Glargine 300 U/mL and Insulin Degludec 100 U/mL in Type 1 Diabetes

Background: Second-generation long-acting insulin glargine 300 U/mL (Gla-300) and degludec 100 U/mL (Deg-100) provide novel basal insulin therapies for the treatment of type 1 diabetes (T1D). Both offer a flatter pharmacokinetic (PK) profile than the previous generation of long-acting insulins, thus improving glycemic control while reducing hypoglycemic events. This work describes an in silico head-to-head comparison of the two basal insulins on 24-h glucose profiles and was used to guide the design of a clinical trial. Materials and Methods: The Universities of Virginia (UVA)/Padova T1D simulator describes the intra-/interday variability of glucose-insulin dynamics and thus provides a robust bench-test for assessing glucose control for basal insulin therapies. A PK model describing subcutaneous absorption of Deg-100, in addition to the one already available for Gla-300, has been developed based on T1D clinical data and incorporated into the simulator. One hundred in silico T1D subjects received a basal insulin dose (Gla-300 or Deg-100) for 12 weeks (8 weeks uptitration, 4 weeks stable dosing) by morning or evening administration in a basal/bolus regimen. The virtual patients were uptitrated to their individual doses with two different titration rules. Results: The last 2-week simulated continuous glucose monitoring data were used to calculate various outcome metrics for both basal insulin treatments, with primary outcome being the percent time in glucose target (70-140 mg/dL). The simulations show no statistically significant difference for Gla-300 versus Deg-100 in the main endpoints. Conclusions: This work suggests comparable glucose control using either Gla-300 or Deg-100 and was used to guide the design of a clinical trial intended to compare second-generation long-acting insulin analogues.

Artificial Pancreas Control Strategies Used for Type 1 Diabetes Control and Treatment: A Comprehensive Analysis

This paper presents a comprehensive survey about the fundamental components of the artificial pancreas (AP) system including insulin administration and delivery, glucose measurement (GM), and control strategies/algorithms used for type 1 diabetes mellitus (T1DM) treatment and control. Our main focus is on the T1DM that emerges due to pancreas’s failure to produce sufficient insulin due to the loss of beta cells (β-cells). We discuss various insulin administration and delivery methods including physiological methods, open-loop, and closed-loop schemes. Furthermore, we report several factors such as hyperglycemia, hypoglycemia, and many other physical factors that need to be considered while infusing insulin in human body via AP systems. We discuss three prominent control algorithms including proportional-integral- derivative (PID), fuzzy logic, and model predictive, which have been clinically evaluated and have all shown promising results. In addition, linear and non-linear insulin infusion control schemes have been formally discussed. To the best of our knowledge, this is the first work which systematically covers recent developments in the AP components with a solid foundation for future studies in the T1DM field.

In Silico Cloning of Target Type 2 Diabetes Population for Treatments Development and Decision Support. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2020;2020:5111-5114. [PMID: 33019136 DOI: 10.1109/embc44109.2020.9175271]

Therapies for treatment of type 2 diabetes (T2D) involve a variety of medications, depending on the stage of T2D progression. It is now an accepted knowledge that in silico trials can help to accelerate drug development and support treatment optimization. A T2D simulator (T2DS), consisting of a model of the glucose-insulin system and an in silico population describing glucose-insulin dynamics in T2D subjects, has been recently developed based on early-stage T2D data, studied with sophisticated experimental techniques. This limits the domain of validity of the simulator to this specific sub-population of T2D. Here we proposed a method for tuning the T2DS to any desired T2D target population, e.g. insulin-naïve (i.e., not experienced with insulin) patients, without the need to resort to complex and expensive clinical studies. This will allow to use the T2DS for testing treatments in the target population. To illustrate the methodology, we used a case study: extending the T2DS to reproduce the behavior of insulin-naïve T2D subjects. The methodology described here can be extended to other stages of T2D, allowing an extensive in silico testing phase of different treatments before human trials.

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.