Date Published: July 25, 2019
Publisher: Public Library of Science
Author(s): Navid Resalat, Joseph El Youssef, Nichole Tyler, Jessica Castle, Peter G. Jacobs, Pasquale Palumbo.
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.
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.
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.
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.
Mathematical models of the glucoregulatory system have been used within in-silico virtual patient simulations for many years [1, 2]. The FDA-approved UVA/Padova simulator, which was developed in 2008 (known as S2008 simulator), was one of the first simulators to model glucose-insulin metabolism. In the S2008 simulator, 100 virtual adults, 100 virtual adolescents, and 100 virtual children were generated by randomly drawing samples from the joint distribution of the parameters of the model . At first, the 100 virtual adults were produced from a given nominal insulin sensitivity value and then the virtual children and adolescents were generated with higher and lower insulin sensitivity values. Since 2008, many studies have used the 2008 version of the UVA/Padova simulator for open loop [1, 4] and AP [5, 6] computer analyses. In 2013, due to hypoglycemia underestimation of the S2008 simulator, three new features were integrated. Dalla Man et al.  incorporated the non-linear effect of insulin action for glucose levels below a threshold. In addition, they added the glucagon kinetics and dynamics models to simulate the counter-regulatory behavior of glucagon for glucose levels below a threshold. They also modified the insulin-to-carb ratio as well as the correction factor for better representation of postprandial glucose excursions. The new simulator was named the S2013 simulator. Visentin et al.  validated the S2013 simulator with a database consisting of two sets of 24 glucose profiles recorded during one open loop study and one AP study across type 1 diabetes. Each glucose profile was controlled for 22 hours with two meal intakes. In both control trials, the variations of the meal intakes were negligible at each meal event across the patients. To validate the S2013 simulator, actual insulin profiles were given to the 100 virtual adults and the closest virtual adults were selected whose clinical outcomes were similar to the patients. Finally, the performance of the selected virtual adults were compared with the patients in terms of percent time spent in hyper- and hypoglycemia along with low and high blood glucose indices. They found better clinical consistency with the S2013, however unlike the S2008 simulator, the S2013 simulator overestimated the percent time spent in hypoglycemia significantly . Later in 2016, to validate the S2013 simulator across type 1 diabetes and to better model time spent in hypoglycemia, Visentin et al.  fit the simulator to the actual dataset recorded from 47 people with T1D using a Bayesian approach. They found that the insulin sensitivity was around 30% less than the nominal values, showing that the insulin sensitivity of the S2013 simulator should be further modified to represent people with type 1 diabetes. While the S2013 simulator has been used by various research institutions to validate AP algorithms prior to running clinical studies, it is no longer commercially available and there is a need in the field for alternative VPPs to validate AP control algorithms. The Cambridge single-hormone simulator is another simulator developed for type 1 diabetes, which consists of 18 virtual patients . The simulator was validated with a clinical dataset during overnight periods. In 2013, Haidar et al.  used the Cambridge simulator and developed a single-hormone virtual patient population by fitting the glucoregulatory model to glucose data of 12 young people with type 1 diabetes using a Markov chain Monte Carlo sampling method. In this paper, the glucoregulatory model used is similar to the Cambridge glucoregulatory model, except the insulin kinetics model is different. Our preliminary testing on the virtual populations showed that the insulin kinetics model published in Hovorka et al.  better reflects the physiological characteristics of adults with T1D.
The SH-VPP and DH-VPP were generated based on glucoregulatory models consisting of insulin and glucagon kinetics and dynamics models and a glucose kinetics model. The SH-VPP was generated by statistically sampling the most sensitive inter-subject parameters of the insulin dynamics model. To generate the DH-VPP, the parameters of the insulin and glucagon dynamics models as well as one parameter in the glucose kinetics model were statistically sampled. Both VPPs were validated with experimental data.
Fig 3 show the histogram of the patients, SH-VPP and DH-VPP. The range of the TDIR values of SH-VPP started at 20 units and ended at 120 units. The peak of the histogram was around 40–45 units showing that the TDIR values of the SH-VPP were well-scaled regarding the average TDIR value shown in Table 1. A similar range is also observable in DH-VPP. The peak of the histogram occurred for TDIR values between 40–45 units, however the minimum TDIR spanned to smaller levels for several virtual patients simulating the situations where certain individuals with T1D may require less insulin.
In this paper, we described the design of two T1D virtual patient populations that can be used to evaluate single-hormone and dual-hormone control algorithms within automated drug delivery systems for helping people with T1D better manage their glucose levels. These virtual populations were validated against clinical data acquired from real-world patients with T1D . The results showed no significant difference between the performance outcome measures of the VPPs and the true patients when treated with an automated control algorithm intervention and when given identical meals. In this study, we were able to validate the VPP on a clinical data set whereby patients with T1D were matched with their in-silico virtual twin by TDIR and weight. Both real patients and virtual patients were given the same meals and exercise regimen while their glucose was controlled using the same control algorithm. It is important to emphasize that, while we used just one control algorithm to validate the VPPs, this does not mean that these VPPs are compatible with just a single control algorithm. Any control algorithm can now be used with the VPPs. We have simply used a single control algorithm to validate that when virtual patients and actual patients are given comparable amounts of insulin, glucagon, meals, and exercise, the glycemic outcome metrics between the virtual and actual patients are not statistically different.