A statistical virtual patient population for the glucoregulatory system in type 1 diabetes with integrated exercise model

Abstract

Purpose: We introduce two validated single (SH) and dual hormone (DH) mathematical models that represent an in-silico virtual patient population (VPP) for type 1 diabetes (T1D). The VPP can be used to evaluate automated insulin and glucagon delivery algorithms, so-called artificial pancreas (AP) algorithms that are currently being used to help people with T1D better manage their glucose levels. We present validation results comparing these virtual patients with true clinical patients undergoing AP control and demonstrate that the virtual patients behave similarly to people with T1D.

Methods: A single hormone virtual patient population (SH-VPP) was created that is comprised of eight differential equations that describe insulin kinetics, insulin dynamics and carbohydrate absorption. The parameters in this model that represent insulin sensitivity were statistically sampled from a normal distribution to create a population of virtual patients with different levels of insulin sensitivity. A dual hormone virtual patient population (DH-VPP) extended this SH-VPP by incorporating additional equations to represent glucagon kinetics and glucagon dynamics. The DH-VPP is comprised of thirteen differential equations and a parameter representing glucagon sensitivity, which was statistically sampled from a normal distribution to create virtual patients with different levels of glucagon sensitivity. We evaluated the SH-VPP and DH-VPP on a clinical data set of 20 people with T1D who participated in a 3.5-day outpatient AP study. Twenty virtual patients were matched with the 20 clinical patients by total daily insulin requirements and body weight. The identical meals given during the AP study were given to the virtual patients and the identical AP control algorithm that was used to control the glucose of the virtual patients was used on the clinical patients. We compared percent time in target range (70-180 mg/dL), time in hypoglycemia (<70 mg/dL) and time in hyperglycemia (>180 mg/dL) for both the virtual patients and the actual patients.

Results: The subjects in the SH-VPP performed similarly vs. the actual patients (time in range: 78.1 ± 5.1% vs. 74.3 ± 8.1%, p = 0.11; time in hypoglycemia: 3.4 ± 1.3% vs. 2.8 ± 1.7%, p = 0.23). The subjects in the DH-VPP also performed similarly vs. the actual patients (time in range: 75.6 ± 5.5% vs. 71.9 ± 10.9%, p = 0.13; time in hypoglycemia: 0.9 ± 0.8% vs. 1.3 ± 1%, p = 0.19). While the VPPs tended to over-estimate the time in range relative to actual patients, the difference was not statistically significant.

Conclusions: We have verified that a SH-VPP and a DH-VPP performed comparably with actual patients undergoing AP control using an identical control algorithm. The SH-VPP and DH-VPP may be used as a simulator for pre-evaluation of T1D control algorithms.

Fig 1. Block diagram of the glucoregulatory model.

Fig 2. Estimated TDIR across Sc values.

Sc of 0.4 was selected as the insulin sensitivity modifier for people with T1D for generating VPPs of people with an average weight of 76.3 kg.

Fig 3. Histogram of the TDIR values of the clinical patients (left), SH-VPP (middle) and DH-VPP (right).

Fig 4. Simulated vs. actual glucose and insulin profiles of one representative subject in single-hormone trial.

Both experiments were initialized at 8:00 am. Carbs are shown with circles. Filled circles show the start of exercise. Higher resolution data from this study is shown in Fig A in S1 File.

Fig 5. Simulated vs. actual glucose, insulin and glucagon profiles of one representative subject in dual-hormone trial.

Both experiments were initialized at 8:00 am. Carbs are shown with circles. Filled circles show the start of exercise. Higher resolution data from this study is shown in Fig B in S1 File.