Modular Closed-Loop Control of Diabetes

Abstract

Modularity plays a key role in many engineering systems, allowing for plug-and-play integration of components, enhancing flexibility and adaptability, and facilitating standardization. In the control of diabetes, i.e., the so-called “artificial pancreas,” modularity allows for the step-wise introduction of (and regulatory approval for) algorithmic components, starting with subsystems for assured patient safety and followed by higher layer components that serve to modify the patient’s basal rate in real time. In this paper, we introduce a three-layer modular architecture for the control of diabetes, consisting in a sensor/pump interface module (IM), a continuous safety module (CSM), and a real-time control module (RTCM), which separates the functions of insulin recommendation (postmeal insulin for mitigating hyperglycemia) and safety (prevention of hypoglycemia). In addition, we provide details of instances of all three layers of the architecture: the APS© serving as the IM, the safety supervision module (SSM) serving as the CSM, and the range correction module (RCM) serving as the RTCM. We evaluate the performance of the integrated system via in silico preclinical trials, demonstrating 1) the ability of the SSM to reduce the incidence of hypoglycemia under nonideal operating conditions and 2) the ability of the RCM to reduce glycemic variability.

I. Introduction

PATIENTS with type 1 diabetes mellitus have an insufficient supply of insulin, a hormone produced by the beta cells of the pancreas that allows glucose to be used as a fuel by the liver, muscle, and adipose cells of the body. When insulin is deficient or absent, a complex set of disorders arises, characterized by a common final element of hyperglycemia. Intensive treatment with insulin injections to maintain nearly normal levels of glycemia markedly reduces chronic complications [1]–[3], but may risk symptomatic hypoglycemia and potentially life-threatening severe hypoglycemia. Thus, hypoglycemia has been identified as the primary barrier to intensive diabetes management [4], [5]. Insulin-dependent patients face a life long optimization problem: to maintain strict glycemic control without increasing their risk for hypoglycemia. The struggle for tight glycemic control often results in large blood glucose (BG) fluctuations over time. This process is influenced by many external factors, including the timing and amount of insulin injected, food eaten, physical activity, etc. In other words, BG fluctuations in diabetes are the measurable result of the action of a complex dynamical system, subjected to many internal and external influences.

A. Historical Development of the Artificial Pancreas (AP)

The feasibility of external regulation of BG via intravenous (i.v.) glucose measurement and i.v. infusion of glucose and insulin to maintain normoglycemia is well established. Systems, such as glucose-controlled insulin infusion systems, commercialized as the “Biostator,” have been used in the hospital setting [6]–[11]. These systems were based on variants of the proportional derivative (PD) control strategy: injected insulin is proportional to the difference between a fixed target and the measured plasma glucose, as well as to the glucose rate of change. Other types of controllers for the i.v.–i.v. route have also been designed [12]–[16]. Intravenous closed-loop control, however, remains cumbersome and unsuited for outpatient use. An alternative to extracorporeal i.v. control is presented by implantable i.v.– intra-peritoneal (i.p.) systems employing i.v. sampling and intraperitoneal (i.p.) insulin delivery [17], [18].

Recent advances in compartmental models of glucose-insulin kinetics had encouraged the design of model-based closed-loop artificial pancreas systems [19], including the design of model-predictive control (MPC) systems that counteract the inherent delays of the system [20], [21]. The introduction of minimally invasive subcutaneous (s.c.) continuous glucose monitoring (CGM) devices has also encouraged the development of AP systems, including systems based on 1) s.c. sensing and i.p. insulin delivery [22] and 2) s.c. sensing and s.c. insulin delivery that avoid the need to surgically implant component devices through the use of continuous subcutaneous insulin infusion (CSII) pumps [23], [24]. In September 2006, the juvenile diabetes research foundation (JDRF) initiated the artificial pancreas project and funded a consortium of university centers to develop new algorithms and platforms enabling commercially viable s.c.–s.c. systems [25]. So far, encouraging pilot results have been reported using proportional-integral-derivative control [26], [27], MPC strategies [28]–[32], and fuzzy logic-based strategies [33].

B. Modular Control of Diabetes

In this paper, we promote a path of incremental developments for the control of BG, which, through the introduction of a modular architecture for closed-loop control, will sequentially bring elements of closed-loop control into clinical practice. Modular design is a well-defined concept that has been transferred across engineering disciplines, offering a number of advantages relating to 1) design flexibility and 2) incremental testing, regulatory approval, and deployment.

1) Design Flexibility

Algorithmic modules can be used either separately or within an integrated system, depending on patients’ or physicians’ preferences. Through the specification of a common software application interface (API) or a common hardware infrastructure, such as the universal serial bus, modularity allows plug-and-play composition of systems accommodating different types of BG sensors, different sensing modalities, different types of insulin delivery methods, different types of user interaction, and supplementary pharmaceuticals. Modularity allows components to be disabled, removed, modified, and/or replaced, accommodating rapidly changing and new technology, e.g., new sensors, insulin delivery methods. Clearly, standardization plays a key role in facilitating modular design, as has been the case in common device communication protocols. Controller and safety interfaces will be valuable assets to the development and deployment of the AP.

2) Incremental Testing, Regulatory Approval, and Deployment

Modularity allows for standardization of system functionality, layering, systematic design, and testing, thereby allowing for testing of modules in parallel or consecutive studies, ultimately simplifying the process of obtaining regulatory approval and clinical acceptance of system features. In addition, modularity helps to define clear functional boundaries between algorithmic subcomponents, allowing for claims to intellectual property to be set in community-accepted terms, encouraging the integration of new capabilities and new industrial partnerships.

The modular architecture developed in this paper, illustrated in Fig. 1, is proposed as a standard for the design of closed-loop artificial pancreas systems that control diabetes via the s.c.–s.c. route. Extending our prior study on “control to range” algorithms [34], we lay down a general framework that could apply to any type of closed-loop system, with specific recommendations for the data passed between modules. The proposed architecture separates the functions of 1) plug-and-play composition of hardware and software components, 2) supervisory control for safety, and 3) closed-loop insulin recommendation, leading to the specification of three main “layers” responsible for 1) hardware/software integration, i.e., the sensor/pump interface module (IM), 2) safety supervision, i.e., the continuous safety module (CSM), and 3) real-time control, i.e., the real-time control module (RTCM). Through the IM, the CSM and RTCM are called periodically, receiving new CGM and insulin pump data, updating internal state variables, and then providing appropriate outputs. The RTCM, which may be informed of meals and other inputs by the patient, produces an insulin recommendation $u_s^o(k)$ (U/h), expressed as a rate of insulin delivery relative to the patient’s basal rate u_b (k) (U/h), to be applied over the next sampling interval. Since $u_s^o(k)$ is relative to the patient’s basal rate, it can be thought of as a “basal rate” correction, which may be either positive or negative depending on the patient’s state. After receiving the insulin recommendation from the RTCM, the CSM determines whether the recommendation is safe and ultimately passes a final approved rate of insulin delivery u_a (k) (U/h) to the IM, possibly requiring the patient to confirm the recommendation and/or automatically modifying the recommendation in an effort to avoid hypoglycemia.

Fig. 1.

Modular architecture for closed-loop control of diabetes.

Aside from the specification of the general architecture (above), the primary contributions of this manuscript are 1) the detailed descriptions of instances interface, continuous safety, and RTCM (cf., Sections II–IV, respectively) and 2) a comprehensive in silico evaluation of the resulting fully integrated system, illustrating the relative impacts of the continuous safety and RTCM. In Section VI, we conclude the paper with a brief discussion of current and future developments for the integrated modular control to range system.

II. IM Instance: Artificial Pancreas System (APS)©

The sensor/pump interface layer of the modular architecture serves as the primary interface between the closed-loop computational algorithms of the upper layers of the architecture and the component devices providing sensing and actuation. The APS [35] is intended to provide a hardware/software interface. The APS, which is intended to support the evaluation of AP control algorithms in clinical research center (CRC) studies, consists of 1) low-level technical interfaces between component devices, 2) a generic API that allows for quick integration of closed-loop control algorithms, and 3) a set of human–machine interfaces (HMIs). Specifically, the APS enables four-way communication between a mathematical control algorithm, a CSII pump, a CGM measurement device, and the medical staff attending the AP clinical study.

Interestingly, the APS itself is implemented in a modular fashion, consisting of three main HMIs: 1) a main interface, which presents all the information to the physician and oversees the closed-loop controller, 2) an interface for the CGM device, which controls the sensor, logs all communication with the device, and transfers frequent glucose readings to the main interface, and 3) an interface for the CSII pump, which controls the pump, logs all communication with the pump, and exchanges data with the main interface. The APS streamlines communication between the AP devices, the user, and the control algorithm, and also provides safety interlocks and alarms. The modular structure of the APS permits plug-and-play composition of component devices (i.e., the CGM sensor and CSII pump) with various algorithmic modules. Thus, with the APS in place it is possible to test new system configurations without introducing major changes to the hardware/software core. From a regulatory perspective, the APS facilitates step-wise validation of various system components. For example, if an investigator wishes to evaluate a new closed-loop system in which the only change from a previously validated system is the RTCM, the new validation effort may focus on the characteristics and implementation of the new RTCM itself. The APS ensures data-path continuity throughout the rest of the system as before.

The APS has been accepted by the Food and Drug Administration (FDA) (MAF-1625) as a clinical system for use in CRC studies of closed-loop control algorithms. It is widely adopted within the JDRF AP Consortium, as well as within the European AP@home project. The APS is the only platform that has the capacity to support two CGM devices (DexCom Seven Plus, Abbott Freestyle Navigator), three CSII pumps (Insulet Omnipod, Animas OneTouch Ping, Roche Spirit Combo). The developers of the APS continue to support the integration of new devices.

III. CSM Instance: Safety Supervision Module (SSM)

Here, we present details of a CSM known as the SSM, designed to continuously monitor the patient’s state and to authorize insulin recommendations that come to it, either from the patient (in safety-augmented CSII therapy) or, as presented here, from the real-time control layer operating above it, intervening when needed to prevent hypoglycemia. The SSM uses all available glucose and insulin data (explicitly accounting for active insulin) in estimating the risk of hypoglycemia using the risk scale proposed in [36]. The SSM will either involve the patient in approving insulin recommendations or will automatically modify the insulin recommendation through the application of insulin-on-board (IOB) constraints [37], as well as the “power brakes” method of gradually attenuating the patient’s basal rate [38], which avoids completely shutting-off insulin (unless hypoglycemia is imminent). The SSM also issues appropriate warnings using a traffic-light abstraction indicating the risk of extreme hypoglycemic or hyperglycemic excursions. In particular, if hypoglycemia is inevitable despite the IOB constraints and power brakes, the system will display a hypoglycemia “red light,” indicating that external intervention with rescue carbohydrates is needed. Similarly, if the risk of hyperglycemia is sufficiently high, the system will display a hyperglycemia “red light,” which, given a properly functioning RTCM, is most likely an indication of a pump failure.

A. Data Coordination and State Estimation

The data coordination and state estimation blocks within the SSM are responsible for collating all available CGM and CSII data (made available by the IM) and estimating the state variables that are used within its safety supervision algorithm, particularly the BG and IOB states of the patient. In the following, let t (min) denotes the current time and k denotes the current discrete control update cycle.

1) Filtered, Slope-Corrected Glucose Measure Ĝ(k)

Based on the history of CGM samples received up to the current time the data coordination and state estimation blocks of the SSM compute a BG estimate Ĝ(k) (mg/dL) for the current control update cycle k. The estimate is computed as

$$Ĝ(k)=\overline{G}(k)+17·Ġ(k)$$

where Ḡ(k) (mg/dL) is the unweighted average of CGM samples received in (t − 10, t] and Ġ(k) (mg/dL/min) is the slope of the least-squares linear fit of all CGM samples received in (t − 30, t]. The 17-min slope correction serves to compensate for the diffusion lag between plasma glucose concentration and glucose concentration in interstitial tissues.

2) IOB [37]

Based on the history of insulin delivery up to the current time, the data coordination and estimation blocks assess the current amount of active correction insulin “on-board” Î_c (k)(U). The assessment makes use of the vector J_c (k) of correction (not meal related) insulin (U) delivered in the preceding 5-min intervals over the last 8 h, up to stage k. Insulin that would be delivered as the patient’s basal rate is not included in the vector J_c (k). Correction IOB amounts are computed for 4-, 6-, and 8-h insulin action curves and are computed as follows:

$${Î}_c^d(k)=\sum _{\tau =1,2,\dots }{\xi }^d(\tau )·{\{J_c(k)\}}_{\tau }$$

where 1) d ∈ {4, 6, 8}, 2) the notation {J_c (k)}_τ refers to the τth element of the vector J_c (k), i.e., the amount of correction insulin delivered in the τth most recent 5-min interval, and 3) ξ^d (τ) is the fraction of {J_c (k)}_τ that is still active according to the d-h action curve being used. The assessment of correction IOB is made as follows:

$${Î}_c(k)=\{\begin{array}{cc}{Î}_c^4(k),\hfill & Ĝ(k)>140\hfill \\ {\alpha }_1{Î}_c^4(k)+(1-{\alpha }_1){Î}_c^6(k),\hfill & Ĝ(k)\in (120,140]\hfill \\ {\alpha }_2{Î}_c^6(k)+(1-{\alpha }_2){Î}_c^8(k),\hfill & Ĝ(k)\in (100,120]\hfill \\ {Î}_c^8(k),\hfill & Ĝ(k)\le 100\hfill \end{array}$$

where α₁ = (Ĝ(k) − 120)/20 and α₂ = (Ĝ(k) − 100)/20. Thus, the assessment of correction IOB is the most conservative (i.e., the longest insulin action curve) when estimated BG is below 100 (mg/dL). The insulin action curves ξ⁴, ξ⁶, and ξ⁸ are all adapted from [39].

B. Safety Supervision Algorithm

As specified in Section I-B, when the SSM is invoked it receives an insulin recommendation $u_s^o(k)$ (U/h) from the RTCM, which is understood to be relative to the patient’s basal rate u_b (k) (U/h) at stage k. (Thus, without the SSM the insulin pump would be commanded to deliver ${[u_s^o(k)+u_b(k)]}^{+}$ (U/h) for the next 5-min interval, where [u]⁺ = max{0, u}.) The main elements of the SSM’s safety supervision algorithm are illustrated in Fig. 2.

Fig. 2.

SSM safety supervision algorithm.

1) Insulin Request Classifier

The first step of the SSM safety supervision algorithm is to determine whether the RTCM-recommended rate $u_s^o(k)$ should actually be acknowledged by the patient as a bolus that should accompanied by additional carbohydrates. The recommendation is classified this way if all three of the following conditions are met:

1. the recommendation amounts to more than basal rate or more than one unit of insulin (whichever is larger), i.e., if

   $$u_s^o(k)/12>\text{max}\{u_b(k)/12,1\}$$

   where the constant 12 used here and throughout this section accounts for the 12 samples per hour associated with a 5-min sampling interval,
2. the recommendation is expected to cause BG to drop below 112.5 (mg/dL), i.e., if

   $$Ĝ(k)-[u_s^o(k)/12+{Î}_c(k)]·{\theta }_{\text{cor}r}(k)<G_{\text{thresh}}$$

   where θ_corr(k) is the patient’s correction factor (mg/dL/U) at stage k and G_thresh = 112.5 (mg/dL), and
3. more than 16 g of additional carbohydrates must be ingested to avoid BG dropping below 112.5 (mg/dL):

   $$[{Î}_c(k)+u_s^o(k)/12-\frac{{[Ĝ(k)-G_{\text{targ}}]}^{+}}{{\theta }_{\text{corr}}(k)}]·{\theta }_{\text{carb}}(k)>m_{CHO}$$

   where θ_carb(k) is the patient’s carbohydrate ratio (g/U) at stage k, m_CHO = 16 (g), and G_targ = 112.5 (mg/dL).

If all three conditions are met, then $u_s^o(k)/12$ (U) is presented to the user through a graphical user interface as a potentially unsafe bolus, and the user is asked to enter an approved bolus amount which is then passed on as the output of the SSM as a total rate of insulin delivery for the next 5-min interval: $u_a(k)=u_s^o(k)+u_b(k)$ (U/h). If any of the three conditions above are not met, then the RTCM recommendation $u_s^o(k)$ is passed on to the “correction filter” later.

2) Correction Filter

Whenever the RTCM recommendation is not classified as a bolus as above, the SSM subjects the recommendation to a filtering process designed to prevent excursions into hypoglycemia, comprising of two main parts: brakes and IOB constraints.

Power Brakes

The power brakes algorithm presented here is adapted from [38] and uses CGM data to continually assess the risk of hypoglycemia for the patient and, when a risk of hypoglycemia is detected, compute an attenuation factor to be applied to the insulin rate command before it is sent to the pump. A key component of the power brakes is that the attenuation action is adjusted smoothly as a function of CGM data. The process involves the computation of an attenuation factor:

$$\varphi (\rho (k))=\frac{1}{1+\rho (k)}$$

where ρ(k) quantifies the patient’s risk of hypoglycemia, described later. The attenuation factor is used to compute a power brake-approved insulin amount U_a,brake(k) (U) based on the patient’s basal rate and RTCM recommendation:

$$U_{a,\text{brake}}(k)=\varphi (\rho (k))·{[(u_s^o(k)+u_b(k))/12]}^{+}.$$

The risk factor ρ(k) is adapted from the BG symmetrization function introduced in [40] and is computed as follows:

$$\rho (k)=\{\begin{array}{cc}0,\hfill & Ğ(k)\ge 112.5\hfill \\ 10[a{(\mathit{\text{ln}}({(Ğ(k))}^b-c)]}^2,\hfill & Ğ(k)\in (20,112.5)\hfill \\ 100,\hfill & Ğ(k)\le 20\hfill \end{array}$$

where a = 1.509, b = 1.084, and c = 5.381, and

$$Ğ(k)=.5·(G^{*}(k)+Ĝ(k))$$

is a corrected estimate of BG that reflects the impact of correction IOB through

$$G^{*}(k)=Ĝ(k)-{[{Î}_c(k)]}^{+}·{\theta }_{\text{corr}}(k).$$

As discussed in [38], the degree of attenuation varies smoothly as a function of ρ(k).

IOB constraints

The correction filter also places limits on allowable correction insulin using the notion of IOB constraints [37]. Here, the constraint is computed based on an estimate of the current amount of correction insulin I_G(k) (U) required to return the patient to a BG concentration of 112.5 (mg/dL):

$$I_G(k)=\frac{Ĝ(k)-G_{\text{targ}}}{{\theta }_{\text{corr}}(k)}$$

where G_targ = 112.5 (mg/dL). The maximum allowable correction bolus U_max(k) (U) is then computed as

$$U_{\text{max}}(k)={[I_G(k)-{Î}_c(k)]}^{+}.$$

The IOB-constraint approved insulin amount U_a,IOB(k) (U) is based on the patient’s basal rate and RTCM recommendation:

$$U_{a,\mathrm{I}\mathrm{O}\mathrm{B}}(k)={[\text{min}\{U_{\text{max}}(k),u_s^o(k)/12\}+u_b(k)/12]}^{+}.$$

Integrated Correction Filter Action

The final, approved amount of insulin allowed by the SSM when the correction filter is invoked is

$$U_a(k)=\{\begin{array}{cc}\text{min}\{U_{a,\text{brake}}(k),U_{a,\mathrm{I}\mathrm{O}\mathrm{B}}(k)\},\hfill & Ġ(k)<0\hfill \\ \text{min}\{U_{a,\mathrm{I}\mathrm{O}\mathrm{B}}(k),{[(u_s^o(k)+u_b(k))/12]}^{+}\}\hfill & Ġ(k)\ge 0\hfill \end{array}$$

which is then passed on as the output of the SSM as a total rate insulin delivery for the next 5-min interval: u_a (k) = 12 · U_a (k) (U/h).

3) Other Elements of the SSM

In addition to the insulin request classifier and correction filter (discussed in the sections earlier), the SSM has a number of other safety features: fault mode contingencies and hypo-/hyperglycemia status lights. We only outline these features here because they do not lend themselves to in silico evaluation (with currently available simulators) and their impact is perceived mainly in actual humansubject trials, where, for example, the risk of hypoglycemia may trigger (by clinical protocol) the administration of “rescue carbs.”

Hypoglycemia Red/Yellow/Green Status Lights: The SSM algorithm provides a visual indication of the risk of hypoglycemia using a “traffic light” status indicator [38], as follows:

1. Red Hypoglycemia Indication: The hypoglycemia status signal is set to RED under either of the following conditions: a) if the insulin request classifier classifies an RTCM request as a bolus requiring the intake of additional carbohydrates or b) if the 10-min linear extrapolation of the last 20 min of CGM data drops below a threshold of 70 (mg/dL).

2. Yellow Hypoglycemia Indication: The hypoglycemia status signal is set to YELLOW if the condition for RED above is not true and the action of the correction filter approves less insulin than the suggested amount or the computed risk of hypoglycemia exists, i.e., if $u_a(k)<u_s^o(k)+u_b(k)$ or ρ(k) > 0.

3. Green Hypoglycemia Indication: The hypoglycemia status signal is set to GREEN if the conditions for RED and YELLOW above are not true.

Hyperglycemia Red/Yellow/Green Status Lights: The SSM algorithm is also responsible for determining hyperglycemia status light levels [38], as follows:

1. Red Hyperglycemia Indication: The hypoglycemia status signal is set to RED if all of the following conditions are met: a) the mean over 60 min of the CGM data is above 200 mg/dL, b) a 15-min linear extrapolation of the last 60 min of CGM data is increasing at a rate that exceeds .5 mg/dL/min, and c) Î_c (k) is greater than 2 U. The threshold values are set in such a way that RED corresponds in all likelihood to a failure of the insulin pump.

2. Yellow Hyperglycemia Indication: The hyperglycemia status signal is set to YELLOW if the condition for RED above is not true and if Î_c (k) + U_a (k) is greater than a threshold value of 2 U.

3. Green Hyperglycemia Indication: The hyperglycemia status signal is set to GREEN if the conditions for RED and YELLOW above are not true.

SSM Response to CGM Anomalies: The current clinical implementation of the SSM is built to withstand various anomalous conditions such as prolonged loss of contact with the CGM device. Generally, the methods for responding to these conditions and others (such as CGM calibration events, hypoglycemia treatments, and others) are beyond the scope of this study. However, to give a sense of how these conditions are handled, we note that if there is no CGM data for more than 10 min of operation, then the following rule for computing the approved insulin bolus for the current control interval applies:

$$u_a(k)=\{\begin{array}{cc}{u}_b(k),\hfill & \text{if}CG{M}_{\text{last}}\ge 100(\mathrm{m}\mathrm{g}/\mathrm{d}\mathrm{L})\hfill \\ 0,\hfill & \text{otherwise}\hfill \end{array}$$

where CGM_last is the value of the most recent CGM sample. Thus, in the absence of recent CGM data, the SSM approves the patient’s current basal rate as long as the most recent CGM reading was above 100 (mg/dL). Otherwise, zero insulin is approved.

IV. RTCM Instance: Open-Loop Informed LMPC Range Correction Module (RCM)

Here, we present the details of an RTCM, designed for control to range, known as the RCM. As an RTCM, the main responsibility of the RCM is to make appropriate adjustments to a patient’s nominal conventional therapy (basal and bolus insulin delivery) to maintain a normal glycemic range. The overall strategy employed by the RCM presented here is unconstrained MPC superimposed onto conventional therapy.

A. MPC Over Conventional Therapy

In recent years, MPC has emerged as one of the most promising approaches to glucose control (cf. [20], [41], [42], [43], [44], [45], [46]) owing to its ability to account for the anticipated impact of meals and insulin in the face of significant sensor and actuation delay. The main components of MPC are: the model, the cost function, and the constraints. The model is needed in order to predict 1) future states and outputs of the system as a function of the current state, 2) future values of the manipulated variables, and 3) future values of measurable or predictable disturbances (if known). The model can be linear or nonlinear; continuous time or discrete time; state space or input output; and black box, gray box or white box. The cost function measures the quality of closed-loop control. The rationale behind MPC is rather simple: 1) at each control cycle the sequence of future input moves optimizing the cost function subject to the constraints is computed; 2) only the first control move is applied, and 3) at the next step, the procedure is repeated by translating the prediction and control horizons: an optimization is again performed and only the first input move is applied. A recent clinical trial [29] carried out using the MPC regulator described in [46] demonstrated excellent nocturnal performance, as witnessed by nearly 5-fold reduction in the number of nocturnal hypoglycemic episodes and increased percent of time spent in the euglycemic range. At the same time, however, the performance of the MPC algorithm before and after breakfast was generally inferior to the conventional therapy.

The drawbacks highlighted in [29] can be circumvented by a control scheme that combines feedforward (FF) action, inspired by conventional therapy, and feedback actions obtained via MPC. Conventional insulin therapy (feedforward action) administers a profile of “basal” insulin throughout the day and premeal boluses computed from the estimated meal amount. Associated with the feedforward action is a nominal glucose profile, representing the trajectory of BG following meals under conventional therapy. The feedback action of the RCM bases its actions on the difference between the CGM signal and this nominal profile. If the difference is zero, no closed-loop correction is applied and the patient is subject to the conventional therapy alone. Although in practice the difference will always be nonzero, a well-designed feedforward action will require small-size feedback corrections. The major advantage is the possibility of combining prompt and rapid compensation of meals (through the feedforward premeal bolus) with a good capability to allow for model uncertainties and to adapt to unpredicted events, disturbances, and changes in patient’s dynamics.

1) Raw Linear MPC

The system is based on an approximate linear model of the insulin-glucose dynamics. The linear model is obtained from the linearization of the more complex nonlinear model described in [46] around a suitable working point. The nonlinear glucose metabolism model [46] can be represented in the following compact way:

$$\dot{\chi }(t)=f(t,\chi (t),I(t),\delta (t))$$

$$\eta (t)=g(\chi (t),\upsilon (t))$$

where χ ∈ R¹³ is the state vector, I ∈ R (U/h) represents administration of insulin, δ ∈ R (g/h) is the rate of carbohydrate ingestion, η ∈ R (mg/dL) is the measure of the s.c. glucose concentration, υ ∈ R is the measurement noise, while f(·, ·, ·, ·) and g(·, ·) are derived from the model equations. The deterministic part of the nonlinear model is linearized about the patient’s basal rate and discretized with sample time T_s to obtain

$$x(k+1)=A_{D}x(k)+B_{D}u(k)$$

$$y(k)=C_{D}x(k)$$

where k is the discrete time interval, A_D ∈ R^13×13, B_D ∈ R¹³, C_D ∈ R^1×13 are the state space matrices of the linearized model, x ∈ R¹³ is the state of the system, u represents deviation from the patient’s basal rate, and y represents deviation from the patient’s fasting BG level. Note that we do not include the meal disturbance δ in the linearized model because of the way meals are handled later. After model order reduction, the following input–output representation of the model is obtained:

$$y(k+1)=-a_{1}y(k)-\cdots -a_{n}y(k-n+1)+b_{1}u(k)+\cdots +b_{n}u(k-n+1)$$

where n ≤ 13 as a consequence of the model-order reduction. The final state-space (nonminimal) representation is obtained

$$x_{IO}(k+1)=A_{IO}{x}_{IO}(k)+B_{IO}u(k)$$

$$y(k)=C_{IO}{x}_{IO}(k)$$

with x_IO (k) = [y(k)′,…, y(k − n + 1)′, u(k − 1)′, …, u(k − n + 1)′]′ and the matrices A_IO, B_IO, C_IO defined accordingly.

In order to derive the control law, the following quadratic discrete-time cost function is considered J(x_IO (k), u(·))

$$=\sum _{i=0}^{N-1}({\Vert y(k+i)\Vert }_{Q_D}^2+{\Vert u(k+i)\Vert }_{R_D}^2)$$

where N is the prediction horizon and Q_D ≥ 0, R_D > 0.

The evolution of the system can be rewritten in a compact way as follows:

$$Y(k)={𝒜}_c{x}_{IO}(k)+{ℬ}_{c}U(k)$$

where Y (k) = [y(k + 1), y(k + 2), …, y(k + N − 1), y(k + N)], U(k) = [u(k)′, u(k + 1)′, …, u(k + N − 1)′]′ and 𝒜_c, ℬ_c, are derived using the discrete time Lagrange formula

$$x_{IO}(k+i)=A_{IO}^{i}xm(k)+\sum _{j=0}^{i-1}{A}_{IO}^{i-j-1}{B}_{IO}u(k+j).$$

In this way, the cost function becomes

$$\overline{J}(x(k),u(·))=Y(k)\prime 𝒬Y(k)+U(k)\prime ℛU(k)$$

where 𝒬 and ℛ are block-diagonal matrices that contain the matrices Q_D and R_D, respectively. The solution of the unconstrained optimization problem is

$$U^o(k)=-K_{x}x(k)$$

where

$$K_x={({ℬ}_c^T𝒬{ℬ}_c+ℛ)}^{-1}{ℬ}_c^T𝒬{𝒜}_c.$$

Finally, following the receding horizon approach the control law is given by

$$u_s^o(k)=[\begin{array}{c}\begin{array}{cccc}I\hfill & 0\hfill & \dots \hfill & 0\hfill \end{array}\hfill \end{array}]U^o(k).$$

To account for pump saturation, only a saturated value will be passed to the CSM module system. Similarly, $u_s^o(k)$ will be clipped to ensure that the final recommendation is nonnegative.

2) MPC Relative to the Patient’s Nominal Profile

The closed-loop regulator of the RCM bases its actions on the difference between the CGM signal and the patient’s nominal BG profile. Specifically, the measured output, insulin input, and meal input can be described by

$$y(k)=CGM(k)-G_{\mathrm{C}\mathrm{T}}(k)$$

$$u(k)=I(k)-u_{\mathrm{C}\mathrm{T}}(k)$$

where CGM(k) is the filtered measurement from the CGM device at stage k, G_CT(k) is the nominal glucose profile that represents the expected consequence of the conventional insulin therapy, I(k) is the average rate of total insulin delivery over the kth sampling interval, and u_CT(k) is the patient’s conventional insulin therapy (U/h) for the corresponding sampling interval. The filtered signal CGM(k) is obtained by passing the unweighted average of CGM samples received in [(k − 1)T_s; kT_s] through a first-order discrete-time filter with pole ϕ. The nominal glucose profile is computed as

$$G_{\mathrm{C}\mathrm{T}}(k)=\{\begin{array}{cc}\overline{G}(k),\hfill & 2\mathrm{h}-\text{interval},\text{starting}30\text{min after meal}\hfill \\ 130,\hfill & \text{otherwise}\hfill \end{array}$$

where Ḡ(k) is the expected consequence of the joint administration of meal and associated insulin bolus, approximated as

$$\overline{G}(k)=\text{min}\{\text{max}\{130,CGM(k)\},180\}.$$

Thus, Ḡ(k) can be regarded as a set-point for CGM(k) after a meal: as long as CGM(k) stays in the range [130, 180] (mg/dL) no further correction is required, while intervention is needed when CGM(k) goes out of the range. The signal u_CT(k) represents the rate of insulin delivery that would have resulted from conventional therapy (i.e., the patient’s basal rate profile and premeal boluses) in the kth sampling interval, multiplied by 0.9 to ensure conservativeness. Meal insulin is delivered as a feedforward premeal bolus, calculated according to the patient’s carbohydrate ratio. Thus, the meal input is not represented in the linearized system.

B. Individualization

Interindividual variability is one of the most complex factors to consider in the development of an AP. In this respect, a key contribution to the entire body of artificial pancreas research is the development of a dynamic simulator of Type 1 diabetic patients, equipped with 100 adult patients, 100 adolescents, and 100 children. This simulator was accepted by the Food and Drug Administration as a substitute of animal trials in order to obtain the approval for clinical trials in humans [47], [48]. Simulation experiments have shown that a fixed controller applied to the population results in disparate performance when applied to different patients: hence the need for an individualization of the control algorithm. A first possibility is to identify accurate individual models from experimental data [44], [49], [50]. However, this approach might be infeasible for the following reasons. First, an additional preliminary experiment would have to be performed to collect individual data for identifying the patient’s model. Apart from the issue of increased costs, there is the need to guarantee that the data are “sufficiently exciting” [50], in the sense that model parameters are practically identifiable. Indeed, meal events and premeal boluses are typically synchronized giving rise to almost collinear input signals. Although one may resort to ad hoc experiments where inputs are desynchronized, e.g., by splitting and anticipating/delaying premeal boluses (as studied in simulation [50]), this would pose further technical and ethical constraints. If ad hoc experiments are not possible, one could explore the use of advanced identification techniques that are less sensitive to poor data excitation than classical prediction error methods. This is indeed an open and challenging research topic, but so far only preliminary results are available [51].

An alternative, pursued in this paper, is to perform control design using the same model (A_D, B_D, C_D), derived via linearization of the nonlinear model of the average virtual patient) for all patients, individualizing only the cost function. The goal is to perform individual tuning using biometric and clinical parameters that are easily accessible or measurable, such as body weight (kg), total daily insulin (U), basal insulin delivery rate (U/h), insulin to carbohydrate ratio (U/gCHO), etc.

In the cost function, the possible tuning knobs are the prediction horizon and the weights Q_D and R_D. The choice of the prediction horizon should be linked to the time constant of the system. The available clinical parameters do not reflect such kind of dynamic information, and the optimal control law is affected just by the ratio Q_D / R_D. Hence, one can let R_D = 1 without any loss of generality. Fixing ϕ = 0.3, R_D = 1, T_s = 5 (min), and N = 24, the only parameter to be tuned is the scalar Q_D = q. The goal is to perform individual tuning of q using biometric and clinical parameters that are easily accessible or measurable, such as body weight (kg), total daily insulin (U), basal insulin delivery rate (U/h), insulin to carbohydrate ratio (U/gCHO), etc. To accomplish this goal, it is necessary to go through the following steps.

1. Choose a performance index that measures the quality of glycemic regulation in a specific clinical scenario.

2. Given a population of (in silico) patients find for each subject the optimal weight q^o.

3. Perform regression analysis to derive a function that produces an approximation ${\hat{q}}_{*}^o$ to q^o based on a subset of patient parameters derived from the screening questionnaire and/or metabolic tests.

1) Performance Index

While there are well-established measures of performance for individuals [52], it is of paramount importance to choose a performance metric for control system design that guarantees satisfactory performance for the entire population of patients. This motivated the introduction of the so-called control variability grid analysis (CVGA) [53], which associates to each patient a point in a plane, as in Fig. 3. The two coordinates correspond, via a nonlinear transformation, to the minimal G_MIN and maximal G_MAX glucose value reached in a specific simulation scenario; the glucose concentrations in the 2-h time period following meal consumption are not considered in the computation of the maximum. The lower left corner is associated with ideal glycemic control while high x-values correspond to hypoglycemic episodes and high y-values to hyperglycemic episodes. The plane is partitioned into nine regions corresponding to different levels of glycemic control quality, from A (best) to E (worst). In this way, the results from a real or simulated trial can be visualized by plotting the population of in silico patients as a cloud of points onto the CVGA and summarized by counting the percentage of points in the nine regions. Of course, a good controller will bring as many patients as possible in the A and B regions.

Fig. 3.

CV GA with level lines labeled according to performance index. The dots represent virtual patients while the red line is the so-called calibration curve for the patient #100. The scenario refers to the virtual protocol discussed in Section V-A. The numbers of patients in the regions A, B, C, and D are reported at the top of the plot.

The performance index is given by the distance in the infinity norm from the lower left corner of the CVGA. In this way the points with the same cost are on the level lines depicted in Fig. 3. Assuming that the cost range is [0, 60], then the performance index is given by

$$C={\Vert \left[\begin{array}{c}{X}_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}\hfill \\ Y_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}\hfill \end{array}\right]\Vert }_{\infty }=\text{max}\{X_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}},Y_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}\}$$

where the coordinates X_CVGA and Y_CVGA are defined as

$$X_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}=\text{max}(\text{min}(110-G_{\text{MIN}},60),0)$$

$$Y_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}=\text{max}(\text{min}(p(G_{\text{MAX}}),60),0)$$

and

$$p(x)=2.683·{10}^{-6}{x}^3-2.210·{10}^{-3}{x}^2+0.7540x-59.77$$

is the unique cubic function that interpolates the points (110,0), (180,20), (300,40), and (400,60).

2) Calibration of an In Silico Patient

The goal is to identify the optimal value of the parameter q for each virtual patient. To do this, different values of q are considered. Then, for each value of q a virtual experiment is performed with the in silico simulator (including virtual insulin sensor and synthetic measurement noise), resulting in a point on the CVGA grid. Let Γ(q) denote a curve, referred to here as calibration curve, that represents the locus of CVGA points associated with all possible values of q:

$$\mathrm{\Gamma }(q)≔\{(x,y)|x=X_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}(q),y=Y_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}(q),q\in R^{+}\}.$$

In general, an increase of the weight q implies a greater control effort, that is, a larger quantity of insulin with a consequent decrease of the glucose profile. Therefore, the calibration curve develops as shown in red in Fig. 3, from upper left to lower right. Assuming that Γ(q) is such that Y_CVGA(q) is monotonically decreasing in q and X_CVGA(q) is monotonically increasing in q, the (global) minimum of C(q) = max{X_CVGA(q), Y_CVGA(q)} is achieved at the intersection between the calibration curve and the main diagonal (see Fig. 3). The optimal weight q^o, therefore, is calculated by solving the following nonlinear equation:

$$X_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}(q^o)=Y_{\mathrm{C}\mathrm{V}\mathrm{G}\mathrm{A}}(q^o).$$

This equation can be solved with a bisection algorithm that requires an in silico simulation for each evaluated q.

3) Regression Analysis

Unfortunately, the calibration procedure described earlier cannot be applied to real patients either in clinical experiments or in simulation. Tuning based on clinical experimentation would require testing closed-loop control with unsafe values of q and tuning based on simulation presumes the ability to match real individual patients to in silico patients. A more feasible approach is to use clinical parameters obtained from the screening questionnaire and/or metabolic tests. For the virtual patients both the clinical parameters and the optimal weight q^o are known and can therefore be used to learn a relationship that predicts the optimal weight q^o as a function of clinical parameter. The choice adopted here is to consider a set of parameters obtained from the questionnaire so as to avoid expensive metabolic tests. Using a stepwise regression method, the insulin to carbohydrate ratio and the basal insulin rate of the individual have been selected as the most appropriate parameters.

In order to derive a simple tuning rule for the weight q, consider the following model for the 100 virtual patients:

$$q^o(i)=\phi {(i)}^T\vartheta +\epsilon (i),i=1,\dots ,100$$

where q^o (i) is the optimal weight for the ith virtual patient, φ(i) is the vector of log-transformed clinical parameters (basal insulin rate and carbohydrate ratio) for the ith virtual patient, ϑ is the parameter vector to be estimated, and ε(i) is an error term. The clinical parameters have been log-transformed:

$$\phi (i)=[1\text{log}{\theta }_{u_b}\text{log}{\theta }_{\text{carb}}]$$

where the first regressor introduces a constant term in the regression, θ_ub is the patient’s daily average basal rate, and θ_carb is the patient’s average carbohydrate ratio. The least square estimate is given by

$${\vartheta }^{LS}={(\sum _{i=1}^{100}\phi (i)\phi {(i)}^T)}^{-1}\sum _{i=1}^{100}\phi (i)q^o(i).$$

Then, the optimal weight $q_{*}^o$ of a (possibly real) patient whose clinical parameters are φ_* is approximated as

$${\hat{q}}_{*}^o={\phi }_{*}^T{\vartheta }^{LS}$$

In order to act conservatively and reduce the probability of hypoglycemic events, a reduction factor α < 0 is applied to the parameter ${\hat{q}}_{*}^o$.

V. Preclinical In Silico Preclinical Trials: Evaluation of the SSM+RCM Modular System

Here, the algorithmic components of Sections III and IV are evaluated in a 22-h virtual clinical protocol, comparing baseline performance of conventional therapy (modeled as basal rate plus premeal boluses) to 1) the performance of SSM-augmented conventional therapy, where the patient’s basal rate can be attenuated by the SSM, and 2) the performance of SSM+RCM-augmented conventional therapy, where meal boluses are computed in a conventional fashion but the patient’s basal rate can be adjusted (positively or negatively) by the RCM as supervised by the SSM.

A. In Silico Experimental Design: Virtual Protocol

The virtual protocol begins with the patient in basal steady state at 10:00 am. A lunch comprising 70 (g) of carbohydrate is taken at 12:00 pm (noon), and a dinner meal of 70 (g) of carbohydrate is taken at 7:00 pm. A snack with 20 (g) of carbohydrate is administered at 10:30 pm, treated as a meal with attendant premeal bolus. The patient is discharged at 8:00 am the next day. From 10:00 am to 2:00 pm the patient is controlled with her/his prescribed conventional strategy, while after 2:00 pm the selected closed loop control strategies are used. In order to eliminate the potential transient effect of the transition from conventional therapy to closed-loop regulation, the outcome metrics are computed beginning at 4:00 pm, 2 h after the onset of closed-loop control.

Simulations of 100 adult patients with four different scenarios presenting deviations from the nominal insulin or meal therapy are implemented to evaluate the characteristics of the different strategies.

1. Scenario 1: The ingested amount of glucose and the parameter values are exactly the ones considered in the protocol. In all scenarios, the control strategies have access to nominal information only. For the other scenarios later we report only variables that differ from nominal values.

2. Scenario 2: For all 100 patients the ingested amount of glucose is the nominal one multiplied by a random factor uniformly distributed in [0.5, 1.5].

3. Scenario 3: A ± 25% variation is randomly applied to the insulin sensitivity (e.g., parameters K_p3 and V_mx, see [54]) of each in silico patient. The decision between increase or decrease is randomly taken for each patient with equal probability.

4. Scenario 4: A 25% increase of basal insulin rate is introduced.

The three control strategies are as follows.

1. FF: basal insulin with feedforward premeal insulin boluses, individually tailored to the patient’s nominal carbohydrate ratio. This strategy is intended as a reasonable representation of conventional CSII therapy and is the “open-loop” strategy that the in silico patients use prior to commencement of closed-loop operation (later) at 2:00 pm. Note that in Scenario 1 meal size estimate are correct; however, this is not the case in Scenario 2.

2. +SSM: conventional (FF) therapy augmented with the SSM CSM of Section III guarding against hypoglycemic episodes. For this in silico evaluation, all boluses “caught” by the insulin request classifier are accepted.

3. +RCM (fully integrated system): conventional (FF) therapy augmented with both the SSM CSM and the RCM RTCM of Section IV performing closed-loop regulation. For this in silico evaluation, the parameter α is set to achieve a 20% reduction of q.

In total, 1200 simulations have been run, corresponding to 26 400 h of simulated trial.

B. Results

The outcome metrics evaluated from the simulation results are presented in Table I. The euglycemic target range is defined as the interval [70, 180] (mg/dL), while the tight target range is [80, 140] (mg/dL). Ahypoglycemic event is defined as a glucose measurement below 70 mg/dL. In the table, “mean of glucose” refers to the average value of BG level across all subjects. “Intersubject variability of glucose” refers to the square root of the average across subjects of the within subject variance of BG in the time span between 4 pm and 8 am (the next day). All five metrics are evaluated 1) overall, i.e., from 4:00 pm (2 h after commencement of closed-loop operation) to 8:00 am the next day, 2) in the recovery period after dinner, i.e., from 7:00 pm to midnight, and 3) in the night time regime, i.e., from midnight to 8:00 am.

Table I.

Simulation results

		Scenario 1			Scenario 2			Scenario 3			Scenario 4
		overall	dinner	night	overall	dinner	night	overall	dinner	night	overall	dinner	night
% Time in Target [70 – 180] (mg/dL)	FF	95.3	83.2	95.7	91.5	79.9	92.1	80.7	73.7	80.9	85.9	88.2	83.7
	+SSM	94.0	82.9	94.1	89.9	80.0	90.0	79.7	73.2	79.8	96.9	85.2	96.9
	+RCM	95.9	85.2	95.9	94.8	83.1	94.9	94.4	82.1	94.0	96.6	85.7	96.5
% Time in Tight Target [80 – 140] (mg/dL)	FF	69.3	42.1	72.3	66.4	45.0	68.1	47.3	37.7	47.4	70.2	58.1	68.5
	+SSM	56.4	41.2	55.5	57.3	44.3	56.3	45.1	36.1	45.5	81.1	50.2	83.0
	+RCM	72.7	51.8	70.2	75.8	55.2	73.7	67.4	49.8	65.7	82.4	54.2	82.1
% Time in Hypo [< 70] (mg/dL)	FF	0.0	0.0	0.0	0.0	0.0	0.0	1.9	0.4	2.2	13.1	3.4	15.3
	+SSM	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	+RCM	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.1	0.0	0.1
Mean of Glucose	FF	135	151	134	136	153	135	140	154	139	102	129	99.7
	+SSM	142	152	142	144	155	145	153	159	153	124	145	123
	+RCM	135	146	137	134	148	136	137	148	139	126	143	127
Inter-subject Variability of Glucose	FF	18.4	21.7	17.0	28.8	34.9	26.2	40.9	40.3	44.3	23.2	23.9	24.4
	+SSM	18.2	21.5	16.9	27.7	33.7	25.2	35.3	36.3	37.1	18.8	21.8	17.8
	+RCM	16.7	19.9	15.4	23.9	30.8	20.2	23.1	28.8	19.7	17.1	20.1	16.1

The results are also illustrated in Figs. 4–9. In Fig. 4, average BG and 2.5% and 97.5% percentiles are plotted for Scenario 3, comparing FF with the fully integrated system (+RCM). In Fig. 5, the boxplots of plasma glucose are plotted for the four scenarios subject to the three glucose control strategies. In order to summarize and compare the strategies, overall percent times in euglycemic (tight) target ranges are reported in Fig. 6 (see Fig. 7) for the four scenarios. An assessment of individual glycemic regulation is provided in the next two figures that report the CVGA plots that compare FF with: SSM (see Fig. 8) and the fully integrated system (+RCM) (see Fig. 9).

Fig. 4.

Median (continuous line) and the 2.5% (dashed) and 97.5% (dashed) percentiles of the glucose time series are plotted for Scenario 3 (insulin sensitivity perturbation) subject to either FF (thin, red line) or +RCM (heavy, blue line) control strategy. Target (70–180 mg/dL) and tight target (80–140 mg/dL) limits are shown in black (solid and dotted, respectively). The variability reduction due to the +RCM system (i.e., FF with both the RCM and SSM) is apparent, along with the system’s ability to prevent hypoglycemic episodes. (In the 10:00 am–2:00 pm time frame the in silico patients use conventional (FF) therapy, and, then, at 2:00 pm they switch as appropriate to the closed-loop +RCM strategy.) The outcome metrics reported in Table I are computed beginning 2 h after closed-loop control, i.e., at 4:00 pm (green line).

Fig. 9.

CVGA plot for 100 virtual patients under the +SSM and +RCM strategies. As observed in Fig. 8, the SSM effectively prevents hypoglycemia. Here, it can be seen that, in all scenarios, the RCM increases the number of patients in region A (optimal regulation). This is achieved without jeopardizing safety as only one patient is subject to hypoglycemia in Scenario 4.

Fig. 5.

Boxplots of plasma glucose in the four scenarios. In nominal conditions (Scenario 1) the three control strategies, FF, +SSM, +RCM, show similar performance. In the perturbed scenarios, variability increases under the FF strategy, with substantial risk of hypoglycemia in Scenarios 3 and 4. Safety is restored by the SSM module at the cost of an increase of glucose levels, especially in Scenario 3. A further improvement is introduced by the addition of the closed-loop action of the RCM module in the fully integrated strategy, reducing variability in all nonnominal scenarios.

Fig. 6.

Performance of the FF, +SSM, and +RCM control strategies as measured by the time in target range of 70–180 (mg/dL). Note that in Scenario 4 FF performance is improved with the addition of the SSM, and a further improvement over both FF and SSM is observed in Scenarios 2–4 after the inclusion of RCM.

Fig. 7.

Performance of the FF, +SSM, and +RCM control strategies as measured by the time in the “tight” target range of 80–140 (mg/dL). Comparing FF to +SSM in Scenarios 1–3 the hypoglycemia-reducing tendency of the SSM actually leads to a reduction of the time spent in the tight target range. However, with the addition of the RCM, the fully integrated system improves over FF in all scenarios.

Fig. 8.

CVGA plot for 100 virtual patients under the FF and +SSM strategies. Note that in nominal conditions (Scenario 1) both strategies control the patients well. However, in the nonnominal Scenarios 2–4, the FF strategy fails to avoid low-glucose values. In particular, in Scenario 3 (Scenario 4) there are ten (31) patients suffering from hypoglycemic events. On the contrary, SSM is very effective in preventing hypoglycemia in that no hypo event occurs in any scenario.

C. Discussion of Results

1) Nominal versus Nonnominal Open-Loop Performance

It appears that conventional FF therapy (basal insulin plus premeal boluses) is well tailored to individual patients under nominal conditions. In fact, in Scenario 1, all FF performance measures are more than satisfactory. For instance, the overall time in the euglycemic target range exceeds 91% and no hypoglycemic episodes are observed. Moreover, in Scenario 1, the improvements achieved by adding the SSM and RCM modules are marginal. This is not surprising as the major benefit of safety and closed-loop functionalities lies in the rejection of disturbances and in the mitigation of perturbations with respect to nominal operating conditions. As a matter of fact, the performance of the FF strategy degrades in (nonnominal) Scenarios 2–4. In particular, Scenarios 3 and 4 are critical in terms of both time in target and time in hypoglycemia.

2) Prevention of Hypoglycemia

The FF strategy fails to prevent hypoglycemia in Scenario 3 (with more than 1.3% time below 70 (mg/dL)) and, especially, in Scenario 4 (with more than 9% time in hypoglycemia, largely due to inadequate nocturnal regulation). The SSM module (+SSM) does remarkably well as it achieves complete prevention (0% time in hypo in all scenarios). This comes at the expense of regulation performance measured as time in either the euglycemic or tight target ranges. In order to recover performance, the RCM module (+RCM) is less conservative but without any substantial increase of the risk of hypoglycemia (0% time in hypoglycemia in Scenarios 1–3 and less than 0.5% in Scenario 4).

3) Glycemic Variability Reduction Effect of the RCM

It is interesting to note that in Scenarios 2–4 the fully integrated system (+RCM) brings a substantial reduction of glucose variability as measured by the square root of the average of within-subject variances (see the variability of glucose index in Table I), compared to the feedforward strategy FF. In fact, a first reduction is obtained by SSM, whose performance is further improved by the RCM. In particular, a dramatic reduction is observed in Scenario 3: in passing from FF to +SSM and then to +RCM, night time variability decreases from 44 to 36 and then 17 mg/dL. Variability reduction is important as it reflects the ability of SSM and RCM to compensate for the uncertainties that characterize the nonnominal Scenarios 2–4.

4) Effects of SSM and RCM on Mean Glucose

The inclusion of the SSM module increases the glucose mean with respect to conventional therapy alone. This effect is a natural consequence of the reduction of insulin delivery motivated by the prevention of hypoglycemic episodes. On the other hand, the addition of the RCM module decreases the glucose mean. Indeed, in the first three scenarios the overall glucose mean returns close to the nominal one (around 140 mg/dL), showing that closed-loop control can effectively manage incomplete knowledge without shifting glucose profiles upwards with respect to FF. The relative role of the SSM and RCM modules is clear: SSM guarantees prevention of hypo episodes at the cost of an upward shift of glucose profile, while the inclusion of RCM recovers nominal performance. Scenario 4 deserves a specific comment: in conventional (FF) therapy there is a dangerous decrease of the glucose mean as witnessed by the frequent hypoglycemic episodes (for the FF strategy overall time in hypoglycemia is above 9% and night time in hypo is 15%). In Scenario 4, there is no significant reduction of glucose mean passing from +SSM to +RCM because the glucose mean associated with SSM is already low and cannot be modified without increasing the risk of hypoglycemia.

5) Time in Euglycemic Target Range 70–180 (mg/dL)

In Scenarios 3 and 4, there is a substantial degradation of FF performance (passing from 91% in Scenario 1 to 80% and 87% in Scenarios 3 and 4). In Scenarios 1–3, the SSM guards safety without introducing any appreciable performance degradation, while a substantial benefit is observed in the last scenario, where time out of target is largely due to hypoglycemic episodes. In particular, the SSM (+SSM) recovers a 93% time in target, which is as good as the best nominal performance. Also the RCM module (+RCM) performs remarkably well as it guarantees a time in target between 90% and 92% in all scenarios. Consider, for instance, Scenario 3, where the +SSM strategy achieves zero hypoglycemia but time in target remains equal to that of FF therapy alone (about 80%). The addition of the RCM module (+RCM) brings time in target to a very satisfactory 90%.

6) Time in Tight Target Range 80–140 (mg/dL)

Some of the comments made above for percent time in the euglycemic target range also apply to the time spent in the tight target range. In particular, the SSM (+SSM) does very well in Scenario 4, where the addition of the RCM can hardly introduce further improvement. At the same time, it is worth noting that the percent time spent in the tight target range is the most sensitive indicator with respect to conservativeness entailed by SSM. Indeed, the price for guaranteeing safety is clearly seen in Scenarios 1 and 2 where, compared to FF, the time spent in tight target range decreases from 59% to 50% and from 58% to 51%, respectively. It is remarkable that the RCM restores excellent values in all scenarios (never less than 58%, see Scenario 3).

Overall, the comments above can be summarized as follows: 1) In an ideal world, characterized by nominal conditions and no lack of information, conventional (FF) therapy is effective, but it fails to guarantee safety and performance in realistic nonnominal scenarios. 2) The SSM module is very effective in preventing hypoglycemic episodes, but this comes at the expense of some conservativeness (upwards shift of glucose profiles), which is relaxed by the addition of RCM. 3) A major benefit of the RCM (and marginally of the SSM) is the reduction of variability of BG with respect to conventional (FF) therapy. 4) In the nonnominal scenarios, the RCM module is very effective in recovering nominal performance, as measured by percent time spent in both the euglycemic and tight target ranges.

VI. Conclusion

In this study, we have introduced a modular architecture for the control of diabetes, consisting in a sensor/pump IM, a CSM, and RTCM, collectively providing the diabetes technology research community a convenient framework for plug-and-play composition of systems for clinical experimentation. In providing details of instances of all three layers of the architecture, i.e., with the APS© serving as the IM, with the SSM serving as the CSM, and with the RCM serving as the RTCM, we have illustrated a fully integrated closed-loop system. In silico preclinical testing of the SSM+RCM system demonstrates the role of the SSM in mitigating the risk of hypoglycemia when employed in a conventional therapy setting, as well as the role of the RCM in reducing glycemic variability while not introducing additional hypoglycemic risk. Clinical evaluation of the fully integrated system is currently underway.