Method for controlling blood glucose and artificial pancreas system for carrying out the method

Abstract

The invention relates to a method for controlling glucose in a flexible-structure bihormonal artificial pancreas that manages optional meal and / or exercise alerts by means of coordinated control actions, comprising: measuring a plasma glucose signal; calculating an incremental plasma glucose measurement (y); defining a model for incremental plasma glucose; defining a carbohydrate ingestion as dependent on a carbohydrate content estimated by the patient; defining an expected postprandial incremental plasma glucose y*(s) according to an insulin bolus that has been administered; defining a corrected incremental plasma glucose y̅(s), a corrected insulin infusion ū(s) and a corrected carbohydrate ingestion d̅(s); defining a virtual control action μ(s), divided between regulatory actions μ r and counterregulatory actions μ cr ; and calculating the control actions using a 2-DOF feedback controller with a prefilter having a nominal value F r (s).

Description

[0001] METHOD FOR GLYCEMIC CONTROL AND ARTIFICIAL PANCREAS SYSTEM TO PERFORM SAID METHOD

[0002] DESCRIPTION

[0003] OBJECT OF THE INVENTION

[0004] The present invention falls within the technological field of glucose control. Specifically, the invention relates to regulatory control actions, through the administration of insulin, and counterregulatory control actions, through the administration of glucagon and / or rescue carbohydrates, to control glucose levels more effectively.

[0005] An object of the present invention is to provide a method for glucose control that is capable of managing optional meal and exercise reminders by means of a flexible structure bi-hormonal control system.

[0006] A second object of the present invention is to provide a flexible bihormonal artificial pancreas for the delivery of insulin, glucagon and / or rescue carbohydrates in a coordinated manner.

[0007] BACKGROUND OF THE INVENTION

[0008] Type 1 diabetes mellitus (T1DM) is an autoimmune disorder that destroys pancreatic β cells, resulting in the inability to secrete insulin. This hormone plays a crucial role in glucose homeostasis, as it is responsible for reducing plasma glucose concentrations.

[0009] As a result, people with T1DM tend to suffer from prolonged high blood glucose levels (hyperglycemia), which leads to serious long-term health problems such as cardiovascular disease, kidney disease, retinopathy, and neuropathy. This is why exogenous insulin administration is necessary.

[0010] Artificial pancreas (AP) systems have emerged as a technological treatment for T1DM, improving glycemic control compared to traditional treatments. However, diurnal control remains a challenge because mealtimes and exercise induce substantial fluctuations in glucose levels. Current hybrid AP systems rely on mealtime boluses with tailored carbohydrates to compensate for meal-induced glucose increases. In open-loop treatments, patients already have to deal with the burden of estimating carbohydrates and alerting the system (meal alert).

[0011] Therefore, some patients may not perceive the usefulness of the PA, discouraging its continuation. Therefore, a PA system should be able to achieve acceptable performance without the burden of meal reminders. A complete system without a meal reminder (fully automated), however, may not be suitable for all patients. Some patients with extensive experience in carbohydrate estimation may prefer to assume, at least occasionally, the burden of the meal reminder to reinforce postprandial control.

[0012] However, meal reminders, as a compensatory action, can interact with the feedback action in a PA designed to operate fully automated without such a reminder, resulting in excessive insulin administration and, consequently, hypoglycemia (abnormally low glucose levels). Therefore, PA systems must incorporate mechanisms that allow the user to receive meal reminders without increasing the risk of hypoglycemia.

[0013] Exercise is the other major disturbance that challenges the performance of the BP system. Although very intense exercise events can cause hyperglycemia (abnormally high glucose levels), light to moderate aerobic exercise, the most common physical activity practiced by non-athletes, lowers glucose levels. Current hybrid systems require users to plan their exercise to reduce insulin infusion hours before the start.

[0014] To eliminate exercise warnings, the BP system must have counterregulatory control actions that elevate glucose levels. Carbohydrate supplementation is the most practical option for treating mild exercise-related hypoglycemia. However, individuals concerned about weight gain may prefer subcutaneous glucagon administration as a non-caloric treatment for hypoglycemia. Bihormonal BP systems, with automatic insulin and glucagon delivery, have effectively reduced the duration of exercise-induced hypoglycemia in clinical trials.

[0015] Less physically active individuals with a low tendency to hypoglycemia may find the additional cost of bihormonal BP systems for timely glucagon administration unjustifiable. Low-dose self-administered glucagon with a pen may be a more appropriate option for these patients for safe and effective mitigation of non-severe hypoglycemia.

[0016] From the above analysis, the following three characteristic features are recommended in a PA system:

[0017] 1) effectively compensate for meals without food reminders,

[0018] 2) allow patients to notify of meals if they wish without compromising the performance of the feedback controller, and

[0019] 3) provide a counterregulatory control action to manage hypoglycemia mitigation, such as in unannounced exercise events.

[0020] Many methods have been proposed to eliminate food alerts, but none have mechanisms to reduce interactions with the feedback action in case the patient alerts about food.

[0021] Regarding compensation for unplanned exercise, most glucagon-insulin systems lack carbohydrate suggestion modules and vice versa.

[0022] The few strategies that can work with glucagon and carbohydrates to mitigate hypoglycemia require food prompts.

[0023] However, as explained, a coordinated bihormonal BP system without food warnings that would allow patients to warn of meals if they prefer and decide the counterregulatory action between glucagon and carbohydrates has not been found in the art.

[0024] DESCRIPTION OF THE INVENTION

[0025] The method of the invention is a glycemic control method for a flexible bihormonal artificial pancreas. The method allows for the management of optional food and exercise cues through the use of a coordinated control action.

[0026] The system coordinates a regulatory control action (insulin) and a counterregulatory control action (glucagon and / or carbohydrates).

[0027] As explained above, the method of the invention handles unannounced meals, although the user may announce the meal if desired thanks to a non-interactive feedback-feedforward scheme that reduces interactions between feedback control and compensation control.

[0028] In addition to insulin, the system offers counterregulatory control to address hypoglycemic events induced, for example, by unannounced exercise events. Users can choose whether to administer this counterregulatory action as an automatic glucagon infusion via a pump, patient-administered glucagon suggestions via a pen, or carbohydrate intake suggestions.

[0029] The method of the invention can therefore handle meals (with or without a warning depending on user preference) and unwarned exercise events, offering in in silico studies parameters that are within the ranges recommended in clinical guidelines. The most significant change in performance corresponds to whether the patient chooses to warn about the meal or not. As expected, by warning about meals, the controller improves the % time in hyperglycemia compared to the unwarned operation without a noticeable deterioration of hypoglycemia-related parameters.

[0030] Furthermore, it must be considered that, in in silico studies, there are no relevant differences in the performance parameters between the use of glucagon or carbohydrates as a counterregulatory action, since, by design, they theoretically provide the same control effort, with the administration of glucagon having the advantage of a non-caloric intake and capable of being administered automatically by a pump.

[0031] The present invention provides near-optimal postprandial glucose control with and without meal or exercise reminders. Optimal control is defined as a method that minimizes the peak blood glucose level after a meal while simultaneously avoiding glucose levels below a prescribed threshold under nominal conditions, i.e., a predefined hypoglycemic limit (e.g., 70 mg / dL).

[0032] A feedback controller provides feedback control that achieves near-optimal postprandial glucose control when mealtimes are not prompted. The optional meal prompt is then managed by a non-interactive feedback-compensation scheme that inhibits insulin infusion after a pre-meal bolus of an optionally prompted meal, preventing excessive insulin administration and maintaining performance.

[0033] The proposed solution defines a novel control strategy designed to operate with and without meal or exercise prompts, achieving near-optimal postprandial glucose control under nominal conditions. The strategy includes pre-meal boluses in an insulin delivery control designed to achieve near-optimal postprandial glucose in the absence of a meal prompt, thus achieving optimized coordination between feedback control and compensatory actions. At the same time, it allows for calculating whether counterregulatory control action is necessary, for example, due to exercise events.

[0034] It should be noted that the optimal open-loop policy consists of administering an insulin bolus before mealtime, i.e., an impulsive compensatory control action, which cannot be generated by feedback, since feedback control cannot be implemented until the output is affected by the perturbation. This leads to the conclusion that the best performance achievable with feedback is obtained by administering an optimally sized bolus at the time the output is affected by the perturbation.

[0035] The expected postprandial variation in the CGM (y*), caused by the patient's advised meal intake and the associated administered bolus, is calculated based on meal and insulin models. This expected trajectory is used to calculate a correction term for the control action provided by the feedback controller, avoiding interactions between feedback and compensation actions that could lead to excessive insulin administration. As a result, the corrected feedback control action after a advised meal only regulates the deviation from the expected trajectory during the postprandial period due to the meal bolus.

[0036] Thus, the method of the invention is designed for near-optimal glycemic control with and without meal and / or exercise prompts and is configured as a near-optimal feedback controller designed to operate without meal prompts and a feedback-compensation coordination strategy for adapting meal boluses to optionally prompted meals. At the same time, the method of the invention allows for calculating counter-regulatory control actions when necessary.

[0037] The method comprises the step of measuring a plasma glucose signal (G(t)) by means of a continuous glucose monitor (CGM), represented by its Laplace transform (G(s)). From now on, any signal can be represented by its time domain (t) or Laplace domain (s), related by the Laplace transform. An incremental plasma glucose measurement (y) is introduced, which is calculated as: y(t) = G(t) - G bwhere G b It is a basal glucose value resulting from the application of a basal insulin infusion (or b )

[0038] So, an incremental insulin infusion is defined by: where (u T ) is the total insulin infusion.

[0039] Furthermore, incremental plasma glucose (y) is defined taking into account a carbohydrate intake (d), insulin infusion (u), glucagon administration (v) and rescue carbohydrate administration (w), defined by: where u(t) ≥ -u b , v(t) ≥ 0 and w(t) ≥ 0.

[0040] Carbohydrate delivery (w) could be further processed by a quantifier to provide an amount that the patient can easily administer manually. Glucagon delivery can also be quantified when the patient is prompted to use a pen for easy manual administration. Alternatively, a quantified glucagon signal can also be delivered automatically by a pump, rather than a continuous glucagon signal.

[0041] In the context of the invention G u , G v , G w , G d are linear time-invariant transfer functions that correlate, respectively, insulin, glucagon, rescue carbohydrate, and meal carbohydrate intake with glucose, and could be defined by multiple models known in the art, subject to the restriction that G u (s) / G u (s) and G u (s) / Gw (s) must be feasible, that is, the order of the numerator must be less than or equal to the order of the denominator.

[0042] Preferably, G models u , G v , G w , G d They are defined by the following structure: where are transfer functions in the form: where l u , l v , l w yl u are parameters that represent delays, s on parameters obtained previously and j is a index representing a patient.

[0043] A carbohydrate intake is defined as: where M* is the carbohydrate content estimated and reported by the patient.

[0044] Then, an expected postprandial incremental plasma glucose (y*) is defined as: y*(s) = G u (s) • u'(s) + G d(s) • d*(s) where u*(s) is the insulin bolus administered associated with the patient's manual meal notice.

[0045] Preferably, the insulin bolus u*(s) is calculated using a compensation controller C(s) as:

[0046] So, a corrected incremental plasma glucose a corrected insulin infusion u(s) and a corrected carbohydrate intake are defined as:

[0047] Using corrected insulin infusion a virtual control action can be defined as: so that

[0048] This newly obtained virtual control action is then divided into a regulatory action and a counterregulatory action. further dividing the counterregulatory action as where represents the counterregulatory effect implemented through the glucagon infusion and represents the counterregulatory effect implemented through carbohydrate suggestions, so that: Regulatory and counterregulatory actions are calculated as: where is a function that defines the change between regulatory actions and counter-regulatory (switching signal), for example, or a filtering of such as a moving average filter with a given sample window, yy is an adjustable factor, and where k cr is a previously obtained controller gain, and is defined as: calculating as a 2-DOF feedback controller with a nominal value prefilter as: and where F(s) is a central linear controller designed to stabilize the system. and that attenuates the disturbance and, in a preferred embodiment, could be calculated as a disturbance observer based control.

[0049] Preferably, the central controller F(s) is defined as: and the filters could be low-pass filters, more specifically, they could be defined as: where k, k r , there r are previously calculated parameters and r(s) is a nominal or target incremental glucose value with respect to G b .

[0050] This method also includes a step of distributing the counterregulatory action between the administration of glucagon and rescue carbohydrates in the form of: where is an adjustable parameter between 0 and 1.

[0051] In some embodiments, it may change over time, in some conditions where one counterregulatory action is more favorable than the other. For example, rescue carbohydrates are preferable to glucagon when the insulin intake is high (such as after a large insulin bolus), or when the cumulative glucagon administration is too large, to avoid side effects such as nausea, or due to user preference.

[0052] Then, the control actions to be applied are calculated as

[0053] The method of the invention may further comprise a step of implementing a correction to the regulatory and counter-regulatory actions to increase safety when applying the resulting control actions, such that: where o-(t) is the function that defines the switch between regulatory and counterregulatory actions, as explained above .

[0054] Furthermore, the method of the invention could further comprise a step of implementing a correction to avoid the administration of glucagon as compensation action.

[0055] In that case, It is divided between feedback actions and compensation such as:

[0056] Then it is calculated as:

[0057] As explained above, the control action for rescue carbohydrates could be discretized to deliver specific doses of a quantification level (q w ). In this case, the discretized control action could be calculated by: where [•] indicates the nearest integer operator, is a minimum threshold of accumulated carbohydrates to trigger a suggestion, where is a predicted glucose value over a given time horizon are thresholds for predicted glucose and measured glucose, respectively, that triggers the HypoFlag. A prediction for G( / c) could be calculated as: being <5 G ( / c) a discretized filtered glucose derivative, i.e. the discretization of: where is a previously determined time constant, and where BW is the user's body weight (kg), is a sampling period and it is a slack. Preferably, the threshold is equal to 60 mg / dl and the threshold is equal to 54 mg / dl. In addition, the time horizon t H It could be in the range of 5 to 300 min, preferably with a value of 60 min.

[0058] The same methodology could be applied to the control action to administer glucagon as specific doses of a quantification level (q v). In this case, the specific control action is calculated by: where is a minimum threshold of accumulated glucagon to activate a suggestion, being a derivative of discretized filtered glucose, that is, the discretization of: where r s is a previously determined time constant and:

[0059] Preferably, when specific doses are used as control actions, the expected incremental postprandial plasma glucose could be calculated by adding the terms corresponding to these specific doses of counterregulatory actions, such as: where they are adjustable profits.

[0060] Preferably, They are designed to achieve an increase in the desired maximum output caused when the counter-regulatory action (v, w) is equal at the quantification level, obtaining as: where represents an inverse Laplace transform operator is the desired output variation due to the quantization level

[0061] Preferably, the expected incremental postprandial plasma glucose could be saturated resulting in: where the upper and lower thresholds are previously determined.

[0062] Optionally, the adjustable gain k, mentioned previously, is defined as k = 0.65 x 6 x (1 / Cfí 7 ).

[0063] Alternatively, the adjustable gain k is defined as: where is the inverse Laplace transform, yy mín and they are parameters adjustable, with M representing the expected worst-case meal size, and yy mínthe tolerable lower limit for the incremental postprandial glucose response to that meal

[0064] Optionally, M is defined as the meal size advised by the patient (M*) whenever an optional meal advice is given, yy min as the tolerable lower limit for the incremental postprandial glucose response to that meal M*, maintaining the calculated value of k over an adjustable time window from the time the meal was announced.

[0065] In some embodiments, the delivered insulin bolus (u*) is calculated from the patient's reported meal size (M*) as a bolus defined by u*(s) = C(s)M'(s) where C(s) is an offset controller that could be defined as: Alternatively, the compensation controller C(s) could follow a superbolo strategy defined as: being T σ> 0 a period of time where the pump is off.

[0066] The invention also relates to an artificial pancreas system incorporating the method for glycemic control as previously defined, comprising: a pump, for delivering an automated infusion of insulin, in accordance with a coordinated control action (or T ), and / or an automated glucagon infusion, in accordance with a coordinated control action (v, v); a continuous glucose monitor for detecting the plasma glucose signal (G(t)); and a first computing unit configured to perform the steps of the method of the invention.

[0067] Alternatively, the system could comprise a second pump to deliver the automated glucagon infusion.

[0068] In alternative embodiments, the artificial pancreas system comprises a display for reporting recommended control actions for the administration of glucagon and / or rescue carbohydrates. In these cases, the system could further comprise a pen device for the patient to administer the recommended dose of glucagon.

[0069] The invention also relates to a computer program adapted to carry out the steps of the defined method using the calculation unit of the artificial pancreas system, and to a computer-readable storage medium comprising said computer program.

[0070] DESCRIPTION OF THE DRAWINGS

[0071] To complement the description provided and to assist in a better understanding of the characteristics of the invention, in accordance with a preferred example of practical embodiment thereof, a set of drawings is attached as an integral part of said description in which, for illustrative and non-limiting purposes, the following has been represented: Figure 1.- shows a schematic representation of the control strategy followed by the method of the invention.

[0072] Figure 2.- shows a graph of the percentage of time where glucose is in a specific range

[0073] Figure 3.- shows the control actions calculated for the configurations of Figure 2 according to the method of the invention.

[0074] PREFERRED EMBODIMENTS OF THE INVENTION

[0075] To obtain parameters, patient-adapted control models based on an identification procedure are presented, resulting in personalized gains based on readily available clinically relevant patient parameters.

[0076] The interaction between glucose and insulin is a complex system, which can be represented by a high-dimensional nonlinear model. However, for control design purposes, simple models with few customized parameters are often used.

[0077] The proposed PA is validated with the cohort of 10 adults from the academic version of the UVa / Padova simulator in a challenging scenario with meals and exercise events.

[0078] Figure 1 depicts the proposed fully autonomous coordinated artificial pancreas system. The core of the system comprises four basic components: the asymmetric coordinated control (A), the carbohydrate and glucagon recommendation module (B), the patient action adaptation module (C), and the central controller and prefilter (D). The asymmetric coordinated control distributes the output of the patient action adaptation module into an insulin infusion, u(t), and a counterregulatory control action that decreases and increases glucose levels, respectively. As a counterregulatory control action, the user can configure the controller to provide an automatic glucagon infusion (v(t)), a suggestion of a quantified glucagon dose (v(t)) to be administered, e.g., by a pen, or a carbohydrate intake suggestion as obtained by the carbohydrate and glucagon recommendation module. The central controller was designed to operate without meal prompts, but the system can also handle prompted meals via the patient action adaptation module. This module also adapts the central controller's output when the user manually administers a quantified counterregulatory action, such as carbohydrate intake or glucagon injection.

[0079] The system design assumes the following simplified relationship between the incremental glucose u (mg / dl) with respect to the basal state, the incremental insulin infusion rate u (pmol / kg / min) with respect to the basal infusion u b , the glucagon infusion rate v (mg / kg / min) and the rescue carbohydrate delivery rate w (mg / kg / min): where d(s) corresponds to the oral carbohydrate intake (mg / kg / min) of size M modeled with an impulse signal, i.e., d(s) = M. The linear transfer functions with time delay G d (s), G u (s), G v (s), and G w (s) are described by where the superscript j indicates a patient-adapted gain. The control inputs are subject to the saturation constraints for all t. The dynamics in (2) presupposes three approximations to simplify the identification of the models:

[0080] 1) two compartments represent the input absorption (u, d, v, ow),

[0081] 2) one compartment simulates the effect of this input on glucose, and

[0082] 3) All models have an identical delay equal to 15 min.

[0083] Note that similar gain personalized models are conventional for diabetes control purposes.

[0084] The above model was identified for the 10 virtual adults in the UVa / Padova distribution version. The parameters of the control-oriented patient model corresponding to the virtual adults identified in the UVa / Padova simulator are shown in Table I.

[0085] Table I.

[0086] The presented control strategy should allow patients to notify of a meal, resulting in the delivery of an insulin bolus, if desired. However, doing so without informing the feedback controller can result in an insulin overdose. To avoid this situation, the central controller is informed about the meal through a non-interactive feedback-compensation scheme implemented in the patient action adaptation module. Let us define the variation from the expected output as where d*(s) = M* is the carbohydrate content of the advised meal (g), CIR is the carbohydrate to insulin ratio (g / U), BW is the body weight (kg), ve (0, 1) is an attenuation factor and the term (6000BV / ) -1 converts insulin units from U to pmol / kg. Subtracting (1) and (3) gives where . Now you can design the controller based on model (4), which already incorporates the compensatory actions performed by the patient. Note that, in the ideal case where the patient reports the exact meal size, resulting in the delivery of an insulin bolus of the appropriate size, the feedback controller will have no effect as long as the output follows the expected trajectory, thus avoiding unwanted interactions between feedback and compensatory actions.

[0087] Having more manipulated inputs than regulated outputs, as is the case with the MISO (multiple input single output) model (4), can be exploited to improve performance under different operating conditions and handle input saturation, but it also poses difficulties in the design procedure. To simplify this task and taking into account the nature of the different control actions, model (4) is conveniently rewritten as where It is considered a virtual control action that includes both regulatory and counterregulatory actions, defined by including the last two terms, which represent the counterregulatory effect implemented by glucagon infusion (v) or carbohydrate intake (w), provided by

[0088] The counterregulatory mode must be more aggressive to compensate for any drop in glucose levels that could have serious consequences for the patient. Let this be the result of the patient's action adaptation module. final control to distribute, is defined as which will be defined later. The following coordinated scheme is proposed with a controller gain increased by k cr ≥ 1 in counterregulatory mode.

[0089] Note that this definition satisfies the restriction for all t imposed by equation (6), unless saturations act. Furthermore, to comply

[0090] (8) and thus ensure the coordination of the two available counterregulatory actions, the following distribution is selected: where it can be adjusted, variably over time, to choose between glucagon or rescue carbohydrates.

[0091] The above coordination logic incorporates two mechanisms to minimize the consumption of counterregulatory actions. On the one hand, the switching is performed on a filtered signal or . This signal is calculated by applying a moving average filter with a three-sample window to the signal. This is to avoid unwanted activation of the counterregulatory mode due to the noise contained in the control action. Furthermore, the threshold for activating counterregulatory mode is shifted slightly by an adjustable factor y. This modification implies that there is a small dead zone - in which no counterregulatory actions are executed. min and max functions are used only to ensure the viability of the resulting control actions. Finally, taking as follows: defined above, the control signals that ensure closed-loop coordination can be calculated from (13) - (15) as A positive insulin pulse, i.e., an insulin bolus, is the optimal insulin infusion to limit the postprandial peak while minimizing glucose insufficiency. From the equivalent model (5), the following central controller can be derived: where They are strictly adequate filters with adjustable parameters k, k r , to , to r > 0. The control action (16) can be rewritten as: which shows that the output of the central controller is the contribution of two terms: one resulting from the tracking error and the other being a correction term due to the compensation shares provided. Note that, in some cases, by For example, during a postprandial period following a pre-meal bolus, an overestimated y* may lead to counterregulatory control action, which is undesirable. To avoid this, both contributions are combined as follows:

[0092] Rescue carbohydrate suggestions should be provided as quantized, concrete doses rather than at a continuous rate. Therefore, the continuous signal w must be converted into quantized pulses. Let r s > 0 is the sampling period, then the recommended carbohydrate intake at sampling time k, denoted as ív( / c), is given by where indicates the nearest integer operator, q w is the quantification level and is the minimum threshold of accumulated carbohydrates to activate a suggestion. The z signal w (k) is an auxiliary variable defined by where r sIt is a previously determined time constant that depends on the rate of accumulated carbohydrates with clearance described by

[0093] HypoFlag is an alert that indicates the risk of hypoglycemia. It corresponds to the condition where is the current reading of the continuous glucose monitor is the 1-h advance glucose prediction calculated with where is a discretization of i.e., the glucose derivative filtered with a time constant low-pass filter

[0094] The above quantification scheme will trigger a carbohydrate recommendation, a multiple of q w mg, provided that ) reaches . In turn, the suggested carbohydrates will be subtracted from the cumulative signal to compensate for the excess. To reduce the delay of the accumulation process, is set below qw . A A consequence of the quantization delay is that the controller may trigger a suggestion too late when the continuous equivalent w( / c) would be close to 0. The HypoFlag condition in (19) is set to reduce the risk of these late suggestions. In addition, it includes a forgetting factor and is set to zero when it is sufficiently low. large enough to trigger a suggestion, but the HypoFlag condition is not met.

[0095] Unlike rescue carbohydrate ingestion, the glucagon infusion rate can be delivered automatically via a pump (a pump other than an insulin pump or a dual-chamber pump). The system can deliver glucagon continuously while also having quantified carbohydrate suggestions. However, some patients may prefer manual low-dose glucagon injections as a non-caloric alternative to recover from mild hypoglycemia without the need for an additional (or more complex) pump. The glucagon quantification strategy implements the equivalent equations of the carbohydrate quantification scheme by correspondingly replacing

[0096] The quantified counterregulatory action may differ from that calculated by the central controller. To inform the central controller of this situation, the non-interactive feedback-compensation scheme is modified by redefining the expected output variation in (3) as follows: where define the increase in desired maximum output caused when the counterregulatory action equals the corresponding quantification level. Therefore, these parameters can be derived from where indicates the inverse Laplace transform operator and indicates the variation in desired output due to q v oq w . In addition, to prevent the output from accidentally causing hyperglycemia or hypoglycemia, the signal y* is saturated as follows:

[0097] It should be noted that the variation of the modified expected output in (24) is a practical consideration for implementation purposes; the design of the central controller is still based on the factored model (5) derived from (4).

[0098] Table II.

[0099] Table II lists the controller parameters. The central controller's gain k was individualized for subject j according to the following formula: where g is a safety factor set at 0.7. The values ​​of a, a r and v in Table II were derived through simulations. As the counterregulatory gain k is adjusted crand the factor y was heuristic, an optimization-based strategy was initially employed to individualize these parameters. However, optimization-based fits are unfeasible for clinical trials; therefore, a population value was also evaluated by taking the median of the optimal values ​​for each parameter. No relevant differences were found in the simulations between the use of the optimal and population fits. Therefore, population parameters were selected for this work for simplicity. Regarding the quantification-related parameters, the quantification level of carbohydrates was set at the conventional dose in commercial gels, i.e., 15 g. Glucagon suggestions were quantified at 0.08 mg, as this quantification level resulted in safe and effective control in a recent clinical trial. The remaining quantification-related parameters in the table and the thresholds that define the HypoFlag condition, were fitted by simulations. It can be observed from Table II that v yq w Both were set at one-third of the corresponding quantification level.

[0100] Regarding the results obtained, six configurations of the proposed controller - hybrid system with glucagon, hybrid system with carbohydrate suggestions, the system without food reminder with glucagon and the system without food reminder with carbohydrate suggestions, where glucagon was considered to be administered as a suggestion or as a continuous infusion - were simulated for the 10 virtual adults included in an extended version of the UVa / Padova simulator.

[0101] The scenario included 14 days with 3 meals per day, randomized in carbohydrate content and time: 37.0 [30.0, 45.0] g (median [25th percentile, 75th percentile]) at 8:05 [7:45, 8:15] h, 53.0 [36.0, 58.0] g at 13:05 [12:50, 13:15] h, and 75.5 [53.0, 90.0] g at 19:50 [19:35, 20:10] h. In addition, 8 aerobic exercise sessions were randomly scheduled at 19:17 [14:40, 22:10] h on alternate days, starting from the first day, with a duration of 55.0 [50.0, 60.0] min and an intensity of 48.5 [47.5, 53.0] % of the maximum oxygen volume. The effect of exercise on glucose was implemented by increasing insulin sensitivity.Finally, controller configurations were tested for noise (Dexcom25 built-in sensor model) and the following sources of variability, which were implemented in the academic version of the simulator: nominal values ​​of the meal absorption rate and carbohydrate bioavailability parameters from the meal absorption model varied by meal with a uniform distribution of ±30% and ±10%, respectively; nominal values ​​of parameters describing insulin pharmacokinetics varied according to a uniform distribution of ±30% for each meal; circadian variation in insulin sensitivity was represented as a 24-h period sinusoid shift with random amplitude following a uniform ±30% and random phase; and misestimation of the carbohydrate content of the meal was implemented.It is worth noting that, for the controller configuration with carbohydrate and glucagon suggestions, the user follows the recommendation (i.e., takes the carbohydrates or administers glucagon) simultaneously with the suggestion. Even more ideally, this assumption is considered in other studies in the literature. The performance of the controller configurations was assessed using the percentage of time in range, below range, or above range, and daily insulin, glucagon, and carbohydrate intake.

[0102] Figure 2 shows a graph of the percentage of time glucose is within a specific range. The lower and upper bounds represent the 25th and 75th percentiles, respectively, and the thick black horizontal lines correspond to the median. The crosses represent the means. The upper and lower whisker ends represent the largest and smallest values, respectively, no more than (at most) 1.5 times the interquartile range. Black dots beyond the whisker correspond to outliers.

[0103] Prescribed and unannounced meals are considered. In addition, glucagon administered continuously via a pump (glucagon) and quantified glucagon suggestions via a pen (glucagon suggestion) are evaluated. Carbohydrates are always quantified and suggested to the patient for manual intake (carbohydrate suggestion).

[0104] All controller configurations can handle both meal and unprompted exercise events, as shown in Figure 2, with mean values ​​within their respective ranges. Hypoglycemic episodes are rare across all configurations. Only subjects 3 and 6 had episodes with a CGM <54 mg / dL, although their time in this range was below 0.70%. Six subjects had episodes with a CGM <70, but these were clinically acceptable. The patient with the longest time in hypoglycemia (subject 3) was only 1.6% below 70 mg / dL. The reduction in time in hypoglycemia is achieved without excessive counterregulatory control actions.

[0105] Figure 3 shows the control actions calculated for the configurations of Figure 2 according to the method of the invention.

[0106] In the glucagon setting, the required daily dose is less than 1 mg, as shown in Figure 3, a threshold where subjects typically experience nausea. The required daily dose in the carbohydrate setting is similar to that of other controllers in the literature evaluated in equivalent synthetic settings.

Claims

CLAIMS 1. A method for glucose control in a flexible bihormonal artificial pancreas capable of managing optional food and exercise notifications through a coordinated control action, the method comprising the steps of: - measure a plasma glucose signal (G(t)) using a continuous glucose monitor (CGM); - calculate an incremental plasma glucose measurement by: where G b is a basal glucose value; - define a model for incremental plasma glucose (y), taking into account a carbohydrate intake (d), an incremental insulin infusion (u) with respect to a basal infusion u b , a glucagon administration (v) and a rescue carbohydrate administration (w), such as: linear time-invariant transfer functions, which correlate carbohydrate intake (d), incremental insulin infusion (u), glucagon administration (v), and rescue carbohydrate administration (w) with incremental plasma glucose (y), and are subject to the restriction that the order of the numerator does not exceed the order of the denominator; - define a carbohydrate intake as: where M* is a carbohydrate content estimated and reported by a patient; - define an expected incremental postprandial plasma glucose as: where is the administered insulin bolus associated with the manual warning of patient food; - define a corrected incremental plasma glucose , a corrected insulin infusion ü(s) and a corrected carbohydrate intake as: - define a virtual control action / ¿(s) as: such that: - split the control action between regulatory and counterregulatory control actions - distribute the counterregulatory action as where represents the counterregulatory effect implemented through the Glucagon infusion represents the counterregulatory effect implemented through carbohydrate intake, so that: - calculate regulatory and counterregulatory actions such as: where σ(t) is a function defining a shift between regulatory and counterregulatory actions, yy is an adjustable factor, and where k cr is a previously obtained controller gain, and is defined as: calculating as a 2-DOF feedback controller with a nominal value prefilter as: and where K(s) is a central linear controller designed to stabilize the system and attenuates the disturbance ¿(s), - calculate the counterregulatory actions in the form of: where is an adjustable parameter; and - calculate control actions such as:

2. Method according to claim 1, wherein the G models u , G v , G w , G d are obtained as: where are transfer functions in the form: where l u , l v , l w yl u are parameters that represent delays, s onparameters obtained previously and j is a index representing a patient.

3. Method according to any one of claims 1 to 2, further comprising a step of implementing a correction to the regulatory and counter-regulatory actions in the form of: where σ is a function that defines the change between regulatory and counterregulatory actions and γ is an adjustable factor.

4. Method according to any one of claims 1 to 3, wherein a(t) is equal to or a moving average filter of with a sample window determined.

5. Method according to any one of claims 1 to 4, further comprising a step of implementing a correction to such as: defining feedback actions and compensation as: where r(s) is a nominal incremental glucose value with respect to G b .

6. Method according to any one of claims 1 to 5, wherein the controller K(s) is defined as: and the filters are defined as: where are previously calculated parameters and r is a value nominal incremental glucose with respect to G b .

7. Method according to any one of claims 1 to 6, wherein It varies over time according to the conditions in which one counterregulatory action is more favorable than the other.

8. Method according to any one of claims 1 to 5, wherein the rescue carbohydrates are administered as specific doses of a quantification level (q w ) calculated by: and where is a minimum threshold of accumulated carbohydrates to activate a suggestion, where is a prediction for G(k) over a defined time horizon are predetermined thresholds for predicted glucose and measured glucose, respectively; and where: where BW is the user's body weight (kg), is a period of sampling and it is a slack.

9. Method according to claim 8, wherein the prediction for is calculated as: being a discretization of the filtered glucose derivative: where is a previously determined time constant.

10. Method according to any one of claims 1 to 9, wherein glucagon is administered as specific doses of a quantification level (q v ) calculated by: and where It is a minimum threshold of accumulated glucagon to trigger a suggestion where is a prediction for G( / c) over a defined time horizon s on predetermined thresholds for predicted glucose and measured glucose, respectively; and where: where BW is the user's body weight (kg), is a sampling period and is a slack.

11. Method according to claim 10, wherein the prediction for is calculated as: being a discretization of the filtered glucose derivative where is a previously determined time constant.

12. Method according to any of claims 8 to 11, wherein is 60 mg / dl, is 54 mg / dl and the time horizon is 60 min.

13. Method according to any of claims 8 to 12, wherein the expected postprandial incremental plasma glucose It is calculated by adding the terms corresponding to specific doses of counterregulatory actions, such as: where they are adjustable profits.

14. Method according to claim 13, wherein the adjustable gains s e determine the earnings needed to achieve a raise of the maximum desired output when the counterregulatory action (v, w) is equal at the level of quantification (q v , q w ), obtaining as: where represents an inverse Laplace transform operator and is the desired output variation due to the quantization level 15. Method according to any one of claims 1 to 14, wherein the expected postprandial incremental plasma glucose y*(s) is saturated as:

16. Method according to claim 15, wherein 180 is 70.

17. Method according to any one of claims 6 to 16, wherein an adjustable gain k of the controller K(s) is defined as 18. Method according to any of claims 6 to 16, wherein the adjustable gain k is defined as: where is the inverse Laplace transform, are parameters adjustable, representing the expected worst-case meal size, yy mín the tolerable lower limit for the incremental postprandial glucose response to that meal 19. Method according to claim 18, wherein M is defined as the size of the meal advised by the patient whenever a meal advice is given. optional food, yy min as the tolerable lower limit for the incremental postprandial glucose response to that meal M*, maintaining the calculated value of k over an adjustable time window from the time the meal was announced.

20. Method according to any one of claims 1 to 19, wherein the insulin bolus is administered as a result of an optional meal reminder, It is calculated from the meal size reported by the patient (M*) as a bolus defined by where C(s) is a compensation controller given by:

21. Method according to any of claims 1 to 19, wherein the administered insulin bolus is calculated from the advised meal size. by the patient as a superbolus defined by where C(s) is a compensation controller given by: being a period of time where the pump is off.

22. Artificial pancreas system for performing the method for controlling glycemia as defined in any of claims 1 to 21, comprising: a pump (3), for delivering insulin according to a coordinated control action an automated infusion of glucagon, according to a coordinated control action a continuous glucose monitor (2) to measure the plasma glucose signal a first computing unit (1) configured to carry out the steps of any of claims 1 to 21.

23. The artificial pancreas system according to claim 22, further comprising a second pump for delivering the automated glucagon infusion.

24. The artificial pancreas system according to any of claims 22 to 23, further comprising a display for notifying recommended control actions for the administration of glucagon and / or rescue carbohydrates.

25. The artificial pancreas system according to any of claims 22 to 24, further comprising a pen device for the patient to deliver the recommended glucagon control actions.

26. Computer program adapted to perform the steps of the method according to any of claims 1 to 21 using the defined calculation unit of the artificial pancreas system according to any of claims 22 to 25.

27. Computer-readable storage medium comprising the computer program according to claim 26.

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