WO2020127936A1

WO2020127936A1 - Method for estimating glycemia and/or controlling an insulin injection device

Info

Publication number: WO2020127936A1
Application number: PCT/EP2019/086622
Authority: WO
Inventors: Claude MOOG; Nicolas MAGDELAINE; Lucy CHAILLOUS; Mourad AÏT-AHMED
Original assignee: Université de Nantes; Centre Hospitalier Universitaire De Nantes; Centre National De La Recherche Scientifique; École Centrale De Nantes
Priority date: 2018-12-21
Filing date: 2019-12-20
Publication date: 2020-06-25
Also published as: WO2020127936A9

Abstract

A computer-implemented method for calculating insulin dosage of a user, comprising iteratively (n) performing the steps of: determining a time interval (Ts); receiving a blood glucose level xl(nTs) corresponding to said time interval (Ts); computing an insulin dose to be injected ud(nTs) in a next time interval; wherein the computation of the insulin dose to be injected ud(nTs) comprises at least: evaluating a first insulin dose q1(nTs), said first insulin dose being a function of the difference between the received blood glucose level xl(nTs) and a predefined blood glucose level target (xlref); evaluating a second insulin dose q2(nTs) based on an estimated value of the insulin dose still active in the body IOB(nTs) of the user; evaluating a third insulin dose q3(nTs), said third insulin dose being a function of a quantity of carbohydrates on board COB(nTs) of the user.

Description

METHOD FOR ESTIMATING GLYCEMIA AND/OR CONTROLLING AN

INSULIN INJECTION DEVICE

FIELD OF INVENTION

The present invention relates to the field of instrumentation with relation to pancreas insufficiency, especially diabetes, more specifically type-I diabetes. In particular, the invention proposes a new method and a new system for implementing a novel control strategy for regulating glycemia daily, weekly and annually, while ensuring positivity of the control and avoiding hypoglycemic episodes, without the need for patients to manually enter a bolus at each meal.

BACKGROUND OF INVENTION

Insulin was discovered almost 100 years ago. Until today, it is the only treatment for type- 1 diabetes. This treatment consists in multiple daily insulin injections. Basal-bolus schemes are widely used. Bolus Advisors are designed to help patient to compute bolus doses.

Same food, same injection, at same time of the day was an option for type-1 diabetes treatment but it was not very satisfactory. Functional insulin therapy is an educational program that helps patient to compute insulin injections. It defines tools as the insulin sensitivity factor (ISF) and the carbo to insulin ratio (CIR). These tools, empirically estimated from clinical protocols are used to compute insulin boluses depending on Blood Glucose (BG) level, Blood Glucose target, carbohydrates in the meal (CHO) in the meal and previous boluses.

The definitions of these tools are the following:

ISF, also known as correction factor (CF), is the Blood Glucose drop caused by one unit of rapid-acting insulin;

CIR, is the amount of CHO that compensates the glycemic drop caused by one unit of rapid-acting insulin. ISF and CIR allow to compute meal and correction boluses:

the Correction Bolus UBG, depending on the patient’ s CF, BG level and BG target is:

BGlevel ^— BGtarget

UBG = _ (i)

- the Meal Bolus Ucaft depends on the patient’s CIR and the amount of carbohydrates CHO in the meal:

CHO

^Ucarb OR ⁽²⁾

These tools are used in everyday life by diabetic patients to compute the insulin bolus given by: 7B_O1 UBG + f/Carb

(3)

Nevertheless, patients have difficulties in computing the correct insulin doses because:

CF might vary with the time of the day, physical activity, stress or illness;

CIR varies according to meal composition.

Hence, every meal turns into a stressful math problem for most type-1 diabetics. Nowadays, glucometers and insulin pump include a Bolus Wizard. Physicians inform these calculators with individualized values of CIR, CF or Blood Glucose Target according to the time of the day. Thus, diabetic patients only have to enter the estimated amount of CHO to obtain insulin dose recommendations.

However, one of the most common error is over-correcting a post-meal rise in Blood Glucose. It occurs when the amount of insulin that is still active in the body is not properly taken into account. This amount is called Insulin-On-Board (IOB). Most Bolus Wizard include the IOB to avoid hypoglycemia. The bolus is computed as: f/Bol = UBG + C/Carb - IOB (4) IOB is a function of the Duration of Insulin Action (DIA) and the number of previous boluses. IOB is computed in different ways according to the different Bolus Wizards. Nonetheless, incorrect estimation of DIA induces mismatch in the IOB and insulin injection. As a consequence, hypoglycemia occurs when DIA is underestimated while overestimation of DIA leads to hyperglycemia. Determination of individualized DIA remains a critical point.

Since the past 50 years, closed-loop control of Blood Glucose in type-1 diabetes, the so- called artificial pancreas (AP), remains a challenge. In 1977, the Biostator was the first realization of an artificial pancreas. Many families of controllers were designed, among which are the Proportional-Integrate-Derivative (PID), PID with insulin feedback, Biohormonals, sliding modes, fuzzy-logic and model-predictive controllers (MPC). The latter became popular because they included constraints on the control and safety algorithms. Nowadays, closed-loop clinical trials are conducted for inpatients and outpatients. Nevertheless, ambulatory autonomous artificial pancreas systems are not available because many improvements are needed. Among them, for MPC control algorithms: the prediction horizon has to be extended;

the accuracy of predictions given by the model has to be improved;

the individualization of the controller requires an engineering expert work. Some techniques still exist for evaluating the insulin to be injected in a hybrid closed- loop with a bolus set manually. But the existing techniques are based on a predefined bolus which is set manually by consideration of a level of CHO. The level of CHO is given at the beginning of a meal.

Consequently, there is still a need to provide a method and a system, acting as an autonomous artificial pancreas, for dynamically evaluating an insulin dose to be injected, based on an automatic evaluation of carbohydrates level, without the need for patients to manually enter a bolus at each meal, and ensuring positivity of the control while avoiding hypoglycemic episodes. SUMMARY

According to one aspect, the invention relates to a method for estimating glycemia and/or for controlling an insulin injection device of a user, comprising iteratively performing the steps of:

- determining a time interval ;

receiving a blood glucose level xi(nT_s) corresponding to said time interval; computing an insulin dose u_d(nT_s ) to be injected in a next time interval;

wherein the computation of the insulin dose u_d(nT_s) to be injected in a next time interval comprises at least:

- evaluating a first quantity of insulin dose qi(nT_s), said first quantity of insulin dose being a function of a comparison between the received blood glucose level xl(nTs) and a predefined blood glucose target xlref;

evaluating a second quantity of insulin dose q₂ (nT_s) based on an estimated value of the insulin dose still active in the body of the user;

- evaluating a third quantity of insulin dose q₃(nT_s), said third quantity being a function of a quantity of carbohydrates on board of the user.

Here, T_s is the duration of the time interval, also called the sampling time.

The first quantity of insulin dose qi(nT_s) will be called in the following text first insulin dose qi(nT_s). The second quantity of insulin dose q₂(nT_s) will be called in the following text second insulin dose q₂ (nT_s) . The third quantity of insulin dose q₃(nT_s) will be called in the following text third insulin dose q₃(nT_s).

According to one aspect, the invention relates to a computer-implemented method for calculating insulin dosage, comprising iteratively (n) performing the steps of:

determining a time interval T_s;

- receiving a measured blood glucose level xi(nT_s) corresponding to said time interval T_s;

computing an insulin dose to be injected u_d(nT_s) in a next time interval; wherein the computation of the insulin dose to be injected u_d(nT_s) comprises at least: evaluating a first insulin dose qi(nT_s), said first insulin dose being a function of a comparison between the received blood glucose level xi(nT_s) and a predefined blood glucose level target (xiref);

evaluating a second insulin dose q₂(nT_s) based on an estimated value of the insulin dose still active in the body of the user IOB(nT_s);

evaluating a third insulin dose q₃(nT_s), said third insulin dose being a function of a quantity of carbohydrates on board of the user COB(nT_s).

- determining a time interval T_s;

receiving a measured blood glucose level xi(nT_s) corresponding to said time interval T_s;

computing an insulin dose to be injected u_d(nT_s) in a next time interval; wherein the computation of the insulin dose to be injected u_d(nT_s) comprises at least:

- evaluating a first insulin dose qi(nT_s), said first insulin dose being a function of an insulin sensitivity factor and the difference between the received blood glucose level xi(nT_s) and a predefined blood glucose level target (xnef);

- evaluating a second insulin dose q₂(nT_s) based on an estimated value of the insulin dose still active in the body IOB(nT_s) of the user being function of a specific insulin response time, a plasma compartment insulin rate and a subcutaneous compartment insulin rate;

- evaluating a third insulin dose q₃(nT_s), said third insulin dose being a function of a quantity of carbohydrates on board COB(nT_s) of the user and a Carbo- to-Insulin Ratio;

- obtaining the insulin dose to be injected u_d(nT_s) in the next time interval as a function of at least the first insulin dose qi(nT_s), the second insulin dose

qi

q₂(nT_s), the third insulin dose q₃(nT_s) and a constant basal dose— Ts.

Q2

This present method advantageously allows to avoid hypoglycemia by insulin injection only (artificial pancreas) and to avoid glucagon injection or meal bolus. Furthermore, the present invention allows to estimate non-measurable variable such as the quantity of carbohydrates on board (COB) and the insulin dose still active in the body of the user, also called insulin on board (IOB).

The expression“receiving a blood glucose level xi(nT_s)” refers to a value xi(nT_s) which has been measured, for example thank to a sensor configured to measure the blood glucose level of a user. Such a sensor may be part of a more general for delivering insulin, said system comprising, in addition to the sensor, a processor and a memory comprising instructions to operate the method of the invention, as well as an insulin injection device.

Within the meaning of the invention, said first insulin dose qi(nT_s) corresponds to the insulin dose needed to reach at steady state the blood glucose target without considering previous insulin injections, nor meal, nor any disturbance.

Still within the meaning of the invention, a quantity of carbohydrates on board (COB) of a user is the quantity of carbohydrates from preceding meals which are still active, i.e. the quantity of carbohydrates that has been ingested minus the quantity of carbohydrates that has been digested. Hence, said third insulin dose of insulin dose corresponds to the insulin dose intended to compensate the glycemic raise due to the meal digestion.

In the following description, the insulin dose still active in the body refers, as known by the person skilled in the art, to the Insulin On Board (IOB). Moreover, the term“dose” refers to a quantity of insulin (in units) that is the product of a delivery rate (also called infusion rate) with a period of time (mainly the sampling time Ts), for example in minutes.

One advantage of the method is that it ensures a closed-loop control of the insulin dose to be injected, without the need for a bolus to be entered manually.

According to one embodiment, the evaluation of the third insulin dose q₃(nT_s) comprises the evaluation of a first quantity Ci(nT_s) of carbohydrates on board in the duodenum and/or a second quantity C2(nT_s) of carbohydrates on board in the stomach.

An accurate model is thus obtained, capable of taking into account two different flow rates of carbohydrates on board, which is advantageous since the flow rate of carbohydrates on board depends on the organ in which they transit. In addition to the evaluation of the first quantity Ci(nT_s) of carbohydrates on board in the duodenum and/or the second quantity C2(nT_s) of carbohydrates on board in the stomach, the evaluation of the third insulin dose can also comprise the evaluation of a quantity of carbohydrates on board in any other compartment of the digestive system, such as the jejunum.

According to one embodiment, the third insulin dose is a linear function of the first quantity Ci(nT_s) of carbohydrates on board in the duodenum and/or a linear function of the second quantity C2(nT_s) of carbohydrates on board in the stomach.

In this way, the model can compute quickly the insulin dose to be injected in a next time interval, thus optimizing the closed-loop control.

According to one embodiment, the first quantity Ci(nT_s) of carbohydrates on board in the duodenum is evaluated by using a first model comprising an estimation of a first carbohydrate flow .w(nTs) in the duodenum and by applying a predefined time constant q₅ to said first carbohydrate flow. In a particular embodiment, the first quantity Ci(nT_s) is equal to the product of said time constant 0₅ with said first carbohydrate flow X4(nT_s).

According to one embodiment, the second quantity C2(nT_s) of carbohydrates on board in the stomach is evaluated by using a second model comprising an estimation of a second carbohydrate flow X5(nT_s) in the stomach and by applying the predefined time constant q₅ to said second carbohydrate flow.

In a particular embodiment, the first quantity Ci(nT_s) is equal to the product of said time constant 0₅ with said first carbohydrate flow X5(nT_s).

One advantage is that constants of the model can be set automatically by a computer. In particular, simulations can be implemented to evaluate the models and define the best constants.

According to one embodiment, the insulin dose to be injected comprises a first term Q_t(nT_s), said first term Q_t(nT_s) being a linear function of the sum of the first, the second and the third insulin dose to be injected (q^nT , q₂(nT_s), q₃(nT_s))and a tuning factor k_d, said tuning factor being positive and inferior or equal to 1 and being configured to tune the duration of the injection to a predefined reference duration.

In particular, in order to have the properties of the closed-loop explained in the following section“Detailed description”, the tuning factor kd must be chosen such that k_d = 1— e^~kTs where k (being positive) is the tuning factor in the analog controller.

In this way, a control law is defined with a tuning factor that can be set according to different internal and external conditions. Simulations can be used to evaluate or to test different values of the tuning factor in order to define a realistic one. According to a particular embodiment, said tuning factor k_d is a multiplicative coefficient of said first term Q_t(nT_s)

According to a particular embodiment, the second insulin dose is subtracted to the first and the third quantities for evaluating the insulin dose Q_t(nT_s). In this way, Q_t(nT_s ) is expressed according to the following analytical formula: Q_t(_.nT_s) = q-_tinT_s) - q₂(nT_s) + q₃(nT_s)

Indeed, the first insulin dose q^nT_s) is the quantity of insulin to be injected due to hyperglycemia only and is therefore added to a constant insulin injection dose. The second insulin dose q₂(nT_s) is the quantity of insulin on board already in the body from the previous injections and which is still available, which is therefore subtracted from the constant insulin injection dose. Finally, third insulin dose q₃(nT_s) is the quantity of insulin to injected due to the carbohydrates on board COB which are still in the process of digestion from previous meals and is added to the constant insulin injection dose.

According to one embodiment, the computation of the insulin dose to be injected comprises a second term summed with the first term, said second term being calculated by determining at least one specific infusion rate of a predefined user profile. Otherwise said, the computation of the insulin dose u_d[n ] = u_d(nT_s), delivered in the next time interval, comprises a constant insulin injection dose such as basal dose Unas x T_s (where UBas is the basal infusion rate) and a variable insulin injection dose u_d [n] = ¾(hG₅) which is computed according to the method of the invention. In this way, the insulin dose ud[n] is referred as a“computed global insulin injection dose”, and is expressed according to the following analytical formula:

In this way, the control law can take into account the specific insulin needs of the user.

According to another embodiment, other terms may be summed in order to calculate the insulin dose to be injected. In particular, in one embodiment, at least one term may be introduced by a user. In this case, the control law may be a hybrid closed-loop, where some terms are automatically determined by a computation step and at least one other term is introduced manually.

Input data for a hybrid closed-loop may be:

- a bolus uhyb(nTs)

and/or a CHO amount

- and/or an information about disturbance such as physical exercise, illness etc.

This information would be taken into account in different ways:

- insulin on board would be increased by the insulin quantity of ubyb(nTs)

- the CHO amount would generate a bolus (computed with the CIR) and a variable reference trajectory

disturbance could have an incidence on the basal rate Usas or on the tuning parameter kd (in numerical realization) or k (in an analogic realization).

According to one embodiment,

sensitivity factor and xiref is a predefined blood glucose level target;

- the second insulin dose q₂(nT_s) is equal to 9₃ {x₂(nT_s) + x₃ (nT_s)), where 03 is a specific insulin response time, where x₂ = (x₂— being the constant basal infusion

delivery rate, xi and X3 being the plasma and subcutaneous compartment insulin rates [U/min] (above the basal rate);

- the third insulin dose q₃(nT_s ) is equal to (Ci(nT_s)+C2(nT_s))*04/02, where 04 is a specific carbohydrates sensitivity factor so that Q2/Q4 is the Carbo-to-Insulin Ratio, called CIR.

This embodiment advantageously allows to avoid hyperglycemia thanks to the use of the variables: 1/02(02 being the specific insulin sensitivity factor), Q4/Q2 (the inverse of the

01

Carbo-to-Insulin Ratio), 03 (the specific insulin response time) and— (the constant

Q2

infusion delivery rate). According to one embodiment, a state observer allows evaluating at least one of the following variables:

- an estimated blood glucose level at a given point in time, said estimated blood glucose level being a function of the estimated blood glucose level at a previous moment, the plasma insulin rate at a previous moment, the estimated carbohydrate flow in the duodenum at a previous moment and the measured blood glucose level at a previous moment;

- an estimated plasma insulin rate (above the basal rate) at a given point in time, said plasma insulin rate being a function of the plasma insulin rate at a previous moment, the subcutaneous compartment insulin rate at a previous moment and the measured blood glucose level at a previous moment;

- an estimated subcutaneous compartment insulin rate (above the basal rate) at a given point in time, said estimated subcutaneous compartment insulin rate being a function of the subcutaneous compartment insulin rate at a previous moment, the quantity of insulin previously injected at a previous moment and the measured blood glucose level at a previous moment;

- an estimated carbohydrate flow in the duodenum at a given point in time, said estimated carbohydrate flow in the duodenum being a function of the estimated carbohydrate flow in the duodenum at a previous moment, the estimated carbohydrate flow in the stomach at a moment and the measured blood glucose level at a moment; - an estimated carbohydrate flow in the stomach at a given point in time, said estimated carbohydrate flow in the stomach being a function of the estimated carbohydrate flow in the stomach at a previous moment, an estimated glucose disturbance at a previous moment and the measured blood glucose level at a previous moment;

- an estimated disturbance at a given point in time, said estimated glucose disturbance being a function of the estimated disturbance at a previous moment and the measured blood glucose level at a previous moment.

According to one embodiment, a state observer allows evaluating at least one of the following variables:

- an estimated blood glucose level x [n] at a given point in time [n], said estimated blood glucose level x_t [n] being a function of the estimated blood glucose level x [n - 1] at a previous moment [n-1], the estimated plasma insulin rate x₂ [n - 1] at a previous moment [n-1], the estimated carbohydrate flow in the duodenum x₄[n - 1] at a previous moment [n-1] and the measured blood glucose level x₁ [n - 1] at a previous moment [n-1];

- an estimated plasma insulin rate x₂ [n] at a given point in time [n], said plasma insulin rate (¾ [n]) being a function of the estimated plasma insulin rate x₂ [n - 1] at a previous moment [n-1], the estimated subcutaneous compartment insulin rate ¾ [n - 1] at a previous moment [n-1] and the measured blood glucose level x n - 1] at a previous moment [n-1];

- an estimated subcutaneous compartment insulin rate ¾ [n] at a given point in time [n], said estimated subcutaneous compartment insulin rate x₃ [n] being a function of the subcutaneous compartment insulin rate x₃ [n - 1] at a previous moment [n- 1], the quantity of insulin above the basal dose previously injected u_d [n - 1] at a previous moment [n-1] and the measured blood glucose level x n— 1] at a previous moment [n-1];

- an estimated carbohydrate flow in the duodenum x₄ [n] at a given point in time [n], said estimated carbohydrate flow in the duodenum x₄[n] being a function of the estimated carbohydrate flow in the duodenum x₄[n - 1] at a previous moment [n- 1], the estimated carbohydrate flow in the stomach x₅[n - 1] at a previous moment [n-1] and the measured blood glucose level x_t [n - 1] at a previous moment [n-1];

- an estimated carbohydrate flow in the stomach x₅ [n] at a given point in time ([n]), said estimated carbohydrate flow in the stomach x₅ [n] being a function of the estimated carbohydrate flow in the stomach x₅ [n - 1] at a previous moment [n-1], an estimated glucose disturbance r[n— 1] at a previous moment [n-1] and the measured blood glucose level x_t [n - 1] at a moment [n-1];

- an estimated glucose disturbance f[n] at a given point in time [n], said estimated glucose disturbance [n] being a function of the estimated glucose disturbance f [n - 1] at a previous moment [n-1] and an estimated blood glucose level x₁ [n - 1] at a previous moment [n-1].

The given point in time [n] may be equivalently written as nT_s and the previous moment [n-1] as (n-l)Ts.

According to one embodiment, the state observer allows evaluating at least one of the following variables by solving the following system:

where T_s is the duration of the predefined time interval, Li, Li , L3, L4 and Ls are coefficients of a predefined vector ensuring the convergence of the estimation of the state towards the state, and the variable r(t) corresponds to the disturbance which is at the origin of the deviation of the glycemia.

According to one embodiment, the method comprises performing iteratively the steps of: receiving a blood glucose level xi(nT_s) corresponding to a time interval; computing an insulin dose to be injected in the next time interval.

According to one embodiment, the method comprises the use of control law for regulating the insulin dose to be injected, said control law comprising a closed-loop where the positivity of the value of the blood glucose level with respect to a glycemia threshold (defined above hypoglycemia) is evaluated to drive said control law on each time interval.

One advantage is to avoid hypoglycemic episodes for a patient.

According to one embodiment, the control law comprises a measurement of the value of the blood glucose level to determine a condition of positiveness of a linear equation comprising the following terms: xi(nT_s), x (nT_s), X4(nT_s) on each time interval. In this way, a control for activating the injection of the insulin dose can be generated, avoiding hypoglycemic episodes.

According to one embodiment, the control law comprises a measurement of the value of the blood glucose level to determine a condition of positiveness of a linear equation comprising the following terms: xi(nT_s), x₂(nT_s), x₃ (nT_s), X4(nT_s) and X5(nT_s) on each time interval.

According to one embodiment, the received blood glucose level xi(nT_s) is obtained from an iterative measurement of a sensor for measuring the blood glucose level, and the insulin dose to be injected is transmitted to a communication interface in order to activate an actuator of the insulin injection device for injecting the insulin dose. One advantage is to provide an equipment which is driven by a method configured to inject optimized insulin doses.

According to one embodiment, the method further comprises a step of controlling an insulin injection device.

According to another aspect, the invention relates to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method of the invention. According to another aspect, the invention relates to a system for delivering insulin, the system comprising:

a sensor for measuring the blood glucose level xl(t) of a user,

a processor and a memory comprising instructions to operate the method of the invention;

an insulin injection device.

According to one embodiment, the system comprises at least one observer module using a calculator for evaluating the states and estimating any disturbance from the measure of the glucose level (delivered by the sensor) and the values of past injected insulin (delivered by the insulin pump), a controller using the estimated state (provided by the state observer) and a calculator generating a set point and a computed insulin dose to be injected in the next time interval.

In this way, an equipment is provided for delivering insulin doses to a patient which can work automatically, without the need to define a bolus at each meal. According to one embodiment, the system comprises an observer module configured to evaluate the following parameters of the system:

_r(t).

As the disturbance is estimated, the control -law can use the explicit estimate of the disturbance instead of the estimate of the COB.

BRIEF DESCRIPTION OF THE FIGURES

Figure 1 compares the injection and the glycemia response with three different strategies according to different embodiments of the invention.

Figure 2 compares the evolution of the glycemia and of the control derived from the control law according to one embodiment of the invention in two different cases. The first case (n,p) is the same than (c,f) in Figure 1. The second case (o,q) uses the measurement of xi and the known input u (insulin injection). In this case no information about the meal is provided to the controller. Both cases use the same stretching gain k. Figure 3 illustrates a model of the dawn phenomenon and an example of a DBC regulator action.

Figure 4 illustrates a model of a subtractive disturbance by an energy consumption corresponding to a negative meal and an example of a DBC regulator action. Figure 5 illustrates another model of a subtractive disturbance by an increase of the insulin sensitivity of a patient and an example of a DBC regulator action.

Figure 6 illustrates one embodiment of the system of the invention.

Figure 7 illustrates the DBC on the UY A/Padova Simulator.

DETAILED DESCRIPTION

This invention proposes a method, a computer program and a system implementing a control law of the state feedback, derived from functional insulin therapy, in order to automatically:

- detect the meal (or any disturbance affecting blood glucose level) and estimate the carbohydrate load (respectively the equivalent carbohydrate load) and

- generate a bolus during a meal, without the need for a bolus to be entered manually and

- regulate glycemia daily, weekly and/or annually between the meal, while ensuring positivity of the injection and positivity of the glycemia with respect to a threshold defined above hypoglycemia.

The method aims to determine a dose of insulin to be injected, taking into account a level of insulin on board and a level of carbohydrates on board. A state observer detects the meal (or any disturbance affecting blood glucose level) and estimates the equivalent carbohydrate load. The control law of the state feedback computes basal-boluses inj ections, provides predictions on glucose dynamics using a long-term model, guarantees positivity of the control, and makes it possible to avoid hypoglycemic episodes.

The system of the invention also offers the advantage that it is easy to set-up. According to the invention, the tuning of the control law is individualized simply using a patient’s own standard parameters such as for example the correction factor and the duration of insulin action. Thanks to the use of the patient’s own parameters, the tuning is readily understandable to physicians, pump manufacturers, and patients themselves. In this section, a long-term model of the glucose-insulin dynamics is presented. This model is used to assess the properties of the present invention. It is established that the Insulin on Board and the Carbohydrates on board can both be computed as a combination of the states.

Long-term model of the glucose-insulin dynamics The model is:

xi is the BG, xi and Xi are the plasma and subcutaneous compartment insulin rates [U/min], respectively XA is the carbohydrate flow in the duodenum [g/min] and X5 is the carbohydrate flow in the stomach [g/min] r(t) is the carbohydrate flow of the meal and u(t) is the insulin infusion rate [U/min] Notice that all the states Xi represent physiological entities, therefore all are positive variables. ft is the net balance between the endogenous glucose production and the insulin independent glucose consumption, ft is the ISF and ft is a specific insulin response time, notably the time constant of the insulin subsystem related to the Duration of Insulin Action (DIA). ft is the Carbohydrates sensitivity and ft is the time constant of the digestion subsystem related to the Duration of Carbohydrates Action (DC A). 01

The function u(t) is written as u(t) = Unas + fi , where Unas =— is the constant infusion

delivery rate that allows maintaining a balance of blood glucose when fasting, better known as the patient’s specific basal rate, and where u represents any bolus injection (in terms of short-term variations of the infusion rate). Thus, X2 and x? can be written as:

The model results in the form of the following equations:

The model comprises the definition of constants qi, 6½, ft, ft, ft. These constants may be set in function of a predefined user profile (age, gender, etc.), antecedents, or other contextual characteristics. According to an embodiment, the constants are set automatically by entering configuration parameters through a user interface.

Insulin on Board (ΊOB)

IOB allows to evaluate the future glycemic drop in the absence of future bolus and future meals (or any other disturbance). A physiological definition of Insulin on Board is either: the units of insulin from previous boluses that are still active in the body, or the amount of insulin in the subcutaneous and the plasma compartments after boluses. According to the first definition, the state representation and the input fi, the IOB can be written as:

Now, merging Equations (11) and (12):

ΰ - ₂ = q₃ (¾ + ¾) (16)

Considering that no bolus was made before t = 0, one gets ¾(^Q) = 0 and ,¾₂ (0) = 0. Then with (15) and (16):

which agrees with the second physiological definition.

The Duration of Insulin Action (DIA) is the duration between the time where a bolus has been injected and the time where the remaining amount of this injection is 5% of the original injection. Equivalently when the amount of ύ is Uo Unit at t=0, the DIA is found solving IOB(DIA) = 0.05 Uo. Solving (11) and (12) for u = Uo5(t) yields:

and

#3 [min]

DIA [h] =

12.66 Carbohydrates on board (COB)

COB allows to evaluate the future glycemic rise in the absence of future meals (or distrubance) and insulin injection. The residuals active carbohydrates, i.e. the carbohydrates on board COB, represent the quantity [g] of carbohydrate of the previous meals which is still active. In other words, the COB is representing the quantity of carbohydrates that will be influent on blood glucose level, i.e. the quantity of carbohydrates that has been ingested minus the quantity of carbohydrates that has already been digested.

The quantity of carbohydrates on board COB(nTs) of a user is obtained by considering the quantities of carbohydrates (Ci) _[i;N] estimated in different compartments of said user. For example, the total COB quantity may be computed by the estimation of a quantity of carbohydrates Ci in the duodenum, a quantity of carbohydrates C2 in the stomach and/ or any quantity of carbohydrates in any other compartments of digestive system, such as the jejunum. In consequence, COB may be written:

COB (t) =

J f (G(T)— c₄(t))άt (18)

o

Considering the previous system (13) and (14), one gets:

And thus :

COB (t) = q₅ f (x₅ + x₄)dr = 0_s(x_s(t) + x₄(t)) (20)

Jo

Where 05 is a predefined time constant and xs and X4 some carbohydrate flow in the different compartments.

The duration of CHO action, named DCA, may be obtained by similar considerations dealing with IOB, when measuring the duration after which the COB is equal to 5%.

The DCA may be written with the following equation:

This result may be demonstrated with the equations (13) and (14) and by drawing the carbohydrates action curves with different values of 05.

The Observer

The method of the invention allows evaluating the COB automatically, trough X4 and xs, without a need for the patient to announce the meal time or to enter the carbohydrate load.

The invention deals with a control law design which intends to compute a bolus at each time interval in order to generate an adapted insulin injection without any action of the user for setting the bolus at each meal. In that way, the invention includes a state observer that detects the meal (or any disturbance affecting blood glucose level) and estimates the carbohydrate load (respectively the equivalent carbohydrate load) without any information about the meal (neither announcement nor carbohydrate load). This state observer evaluates the states xi, x₂, x₃, X4 and xs of the model and allows to compute the IOB and the COB, both being a combination of the states (see (17) and (20)).

In one embodiment, a state observer is used for the implementation of the method of the invention. The state observer comprises at least one processor for evaluating the states of the system with a minimum information so as to ensure a closed-loop operation for computing the insulin dose to be injected periodically. The minimum information comprises at least the blood glucose level xi.

An unknown entry state observer allows estimating the state of the system (its internal variables), in an autonomous loop i.e. without having the meal input r(t). The state is estimated by considering the glucose measurement y(t)= xi(t) and the injection u(t) calculated by the control-law. In one embodiment, the only two variables y(t) and u(t) are known by the state observer that delivers the state estimates which are used by the controller. In one embodiment, the disturbance r(t) which is at the origin of the deviation of the glycemia, mainly the carbohydrate load of the meal, is estimated together with the state of the system.

In the case of a disturbance that is not due to a meal, the estimation of the disturbance corresponds to an equivalent amount of carbohydrates causing the measured effect. This equivalent quantity may be negative value in the case of a hypoglycemic disturbance (physical effort).

The state observer may be considered as a copy of the model of the system to which is added an output injection ensuring the convergence of the estimation of the state X(t) and the estimation of the disturbance f(t) towards the real state of the system X(t) = (xi, x₂, x₃, X4 X5)^T and towards the exogenous (meal) or endogenous (physical effort, hormonal phenomenon such as the dawn effect, etc.) disturbance r(t).

Noting x = (X r)^T the increased state of the disturbance r, le model may be written as:

^'m = A. x(ΐ) + B. U(t)

1/(0 = C. (t)

And more particularly given by the following system:

y(t) = i i it)

Noting O = [C CA CA² . .]^T the“observability matrix”, it may be demonstrated that this matrix is a matrix of full rank and the following vector is observable :

The state observer may be a Luenberger observer:

j¾ ₌ A. x(ί) + B. U(t)— L (Y _(t)— no) i?(t) = c.m

where L (V(t)- Y(t)^ is the output injection. L is a vector computed for ensuring the convergence of the estimation error toward zero. u(t) represents an insulin infusion rate and ύ represents any bolus injection (in terms of short-term variations of the infusion rate). ud(nTs) or ud[n] represents a quantity (i.e. dose) of insulin to be injected on the next time interval. Consequently, ud(nTs) is obtained by computing an integral of u(t) over a time interval [t, t + Ts]

The equations of the state observer in the discrete case by applying a Euler approximation of the derivative term may be written:

x[n ] is used as an equivalent notation of x(nT_s).

r[n] is used as an equivalent notation f(nT_s).

u_d = u_d - U_Bas x T_s =

u(t)dt represents the injection above the basal dose over a time interval.

x_t [n] = y[n\ represents the blood glucose measurement at the time nT_s. In one example, the state observer is configured with an algorithm that may implement the method of the invention.

The Control Law

According to this invention, a new control law called‘Dynamic Bolus Calculator’, named DBC, is introduced. In one embodiment, the DBC is based on the following correction bolus formula:

UB ]— ¾G + Uc arb ^~ IOB (4) where Ucaft = CHO/CIR Using the COB instead of CHO we obtain:

G— G_ref COB

UBOI +—— - IOB (19)

CF CIR

According to one embodiment, the computed global insulin injection rate u(t) comprises a constant insulin injection rate such as basal rate Unas and a variable insulin injection rate u_k(t) which is the specific bolus injection computed by the control-law.

The global injection rate u(t) will be the state feedback u_k(t) modulating the constant insulin injection rate Unas. In consequence, the invention deals with a control law u(t) which may be expressed as a sum of a correction rate term u_k(t) and a constant rate term Unas. The following relationship may be written:

In consequence, the model may be written as the following system to solve:

i_/(t) * i (t ) (22)

The correction rate u_k(t) is the dynamic version of the bolus used in functional insulin therapy where u_k is defined as u_k = k. U_Boi = ku When taking CF = 02 and CIR = Q2/Q4, the correction rate u_k ( t ) may be written as follow:

By defining the following expressions:

i(t) = Xl(t) - XI ref

X₄(t) = X4(t)

- x₅(t)= xs(t)

The correction rate u_k(t ) may be expressed as follow:

The state feedback u_k(t) defines a family ofDBC controllers, Dynamic Bolus Calculator, set by k[min^_1], with k positive, i.e. k > 0. An interesting property of this family of controllers is that the total quantity (i.e. dose) of injected insulin does not depend on k. The total dose, in absence of future meals or any disturbance, is equal to the given bolus (19) as it is involved by the following equation:

The k-gain allows increasing the duration to inject the total dose of insulin UB_OI and will increase the robustness of the closed loop. The k-gain allows setting the robustness with respect to modeling uncertainties and measurement noises.

The following equations may be written as a state feedback:

According to one embodiment, the device comprises a memory in which the model is set by the previous equations. This memory may store the different constants and parameters so that to implement the steps of the method according to the invention. The computation of the states of the system is realized periodically by a calculator in order to generate the value of the quantity (i.e. dose) of insulin to be injected. According to one embodiment, an interface allows adjusting some parameters such as the CIR value.

Input/state positivity

In this section, properties as stability and positivity of the closed-loop trajectories are addressed. It is proven that this feedback (27) generates a positive control, which ensures the positivity of, x_t that is x_x(t) > x_lref. In medical terms, this property is a guaranty of no hypoglycemic episodes.

The positivity of the trajectories may be controlled periodically by an algorithm implemented in the device of the invention. In one embodiment, the positivity of the control is respected with the method of the invention so that to ensure closed loop operation of the device delivering insulin.

According to Eq. (25), the closed-loop system reads as:

which is a stable system with some conditions on the eigenvalues of the matrix.

The positivity of the input/state trajectories, i.e.

ϋ _an(j

discussed through the notion of positively invariant sets, denoted PIS. These properties are valid in the case where 03 > 05. This case corresponds to the case where insulin acts more slowly than the meals, which is the most frequent case.

The eigenvalues of the matrix A are Ai=-k, l2=-1/03, l3=-1/03, l4=-1/05, As=-l/05.

The system is stable with k > 0.

The method of the invention allows determining the conditions ensuring the positivity of the system. The input r(t) is positive by definition, r(t) being a rate of flow, the matrix B_r and C are both positives. Moreover, the states ₄ and x_s are not are controllable but are still positive values because of the following relationship: (30)

where: X₄₅ = (x₄ x₅)^T

Definition 1 : Given a dynamical system x = Ax, x e Mⁿ, and a trajectory x(t, xo), where xo is an initial condition, a non-empty set W <º Mⁿ is a positively invariant set if

V x₀ e W = x(t, x₀) e W Vt > 0 Definition 2: if M E M^rxn then W(M) denotes the polyhedron W(M) = {x e Mⁿ | Mx ³ 0}

The polyhedral set W(M) is a positively invariant set for the system of definition 1 if, and only if, there exists a Metzler matrix H such that: MA-HM = 0

It can be shown when Q3 > Q5 that a the largest polyhedral PIS for the system described by the equation (28) is W(M*) in W(I_5c5) where:

This result may be demonstrated by considering the following matrixes

W(M_cί½) is a PIS if and only if there exists a Metzler matrix H where H = (hij) so that:

The following egality is true: Mxi½ 4— HMxU_k = 0 when:

The 0j are defined as positive values and k > 0. The relations (31) have no solution. There is no Metzler matrix that verifies the relationship: Mxu_kA— HMxu_k = 0

Consequently, W(Mcί½) is not a PIS. The maximal polyhedral invariant set, called PIS, for the system (28) and (29) is included in W(Mc¾) and may be expressed as: il(M _{J23 )} n Ui ) midi Ί

Where:

W(M) is a positively invariant set, PIS, for the system according to the definition 1 if, and only if, there exists a Metzler matrix so that: MM— H M = 0

H is a Metzler matrix if, and only if, hij > 0

In consequence:

For any x E W(M)

The following relationship is verified

Both conditions x₅ > 0 and ws < 0 imply the following relationship: fi _l i_l + W2X2 + >3¾ + W4X4 > 0 (33)

Consequently,

>₅ = 0

We obtain:

With the condition hy > 0, it may be written:

Under the hypothesis Q3 > Q5, which indicates that insulin acts more slowly than the meal, H is a Metzler matrix if:

Applying the condition (33) with:

Consequently, H is Mezler if the following conditions are completed:

The matrix H is Metzler.

W(M°) is a PIS where:

W° = (n -q_$ 0 e Wi

The maximum PIS may be determined. For: e W(M°)

It can be written:

That imply the following inequalities: ³ 0

In such conditions, every trajectory initialized in the polyhedron W(M*) stay in said polyhedron. The invention gives the set of initial conditions depending on patient’s specific parameters such that no hypoglycemic episode occurs during the closed-loop in case of positive perturbation (i.e. meals). From a medical point of view, the positiveness of the input ensures that x_x > 0, i.e. guaranties the exclusion of hypoglycemia episodes.

Moreover, the positivity of the control is respected.

The following constraints at the beginning of the trajectory of the polyhedron should be respected:

The positivity of the initial states of x₂ and x₃ is an equivalent condition to the condition where the injection u(t) is larger or equal to the basal rate for a time long enough.

The positivity of the initial control is an equivalent condition to the condition where at the beginning of the closed loop, the cumulated effect of the insulin on board IOB and the carbohydrates on board COB will not decrease the glycemia below a reference value.

The fulfillment of the condition (35) on x₂ and x₄ yields that the closed-loop ensures no hypoglycemic episode in case of positive perturbation (i.e. meals). One advantage is to be independent from an operator action setting the value of the bolus at each meal. The control of the positiveness of the trajectories of the polyhedron allows providing an autonomous device generating an insulin dose to be injected.

In one embodiment, the device of the invention comprises at least a calculator and a memory for controlling the condition on the positiveness of the trajectories of the polyhedron, in particular the conditions on x₂ and x₄ values. The amount of Insulin-On-Board, IOB, is a function of the Duration of Insulin Action DIA and the number of previous boluses. IOB is computed in different ways according to the different Bolus Wizards.

The IOB represents the sum of insulin units of the previous bolus in the subcutaneous compartment and in the plasma compartment.

x₂ and x₃ are respectively the plasma and subcutaneous compartment insulin rates above the basal rate [U/min], it can be written that:

The quantity 03 ₂ represents the insulin units above the basal rate in the plasma.

Likewise, the COB represents the carbohydrates quantity in the stomach and the duodenum.

COB = 0₅ (x₄ + x )

= %¾ + %¾

— ffduo + Seat

x₄ being the rate (g/min) at the output of the duodenum and x₅ the rate at the output of the stomachs, we can be written: ffduo = ¾

The quantity Os ₄ represents the quantity in grams of carbohydrates in the duodenum.

The increasing of glycemia caused by the carbohydrates may be noted: ^²· x ISF.

CIR The method of the invention may be implemented automatically by setting at the beginning initial conditions related to a patient. In one embodiment, the initial conditions are set with an empty stomach with a basal rate, for example at the wake-up of the patient.

According to an embodiment, the total dose of insulin to be injected is independent of the parameter k.

The system (29) is transformed to its Jordan form, i.e. z(t) = T^~lATz(i) = Jz(i)

Where:

J is a Metzler matrix and the octant R³+ is a positive invariant.

The trajectories of the state z(t) may be computed by using the eigen modes decomposition.

A transition matrix T such that: x = Tz is:

The trajectories of the state (t) from the trajectories z(t):

The control (23) is computed with the system (36) as follow:

By computing the integral, the total dose of injected insulin may be computed:

Z3(0) may be expressed with (39) as

The total dose of the injected insulin is:

From the relationships (37) and (40), the control may be expressed as follow: u_k(t) = z_z(0)k(ke_{3 -} l†e ^M

As the control trajectory Eq. (37) is an exponential function depending on k, that allow us to stretch the trajectory ensuring that the same dose of insulin is administered for all k > 0. By setting k to approaching infinite value, the bolus is injected instantly, that means the control u_k becomes a Dirac. If k approaches to zero, the bolus will be injected during an infinite duration with an infinitesimally rate.

The Figure 1 represents a closed loop with state feedback in a nominal case; this means that the estimated parameters 0) are those of a virtual patient.

According to one embodiment, a mathematical model of the metabolism of a diabetic patient is used to define the virtual patient. This model allows testing in simulation different scenarios corresponding to different closed loop configurations.

Each virtual patient is defined by a set of parameters. These parameters are used to define a configuration of a model. With a wide range of parameters, it is then possible to configure different patient profiles of a model however, it is also possible to use different models of virtual patients.

In a first embodiment of the invention, a first model of the virtual patient that may be applied is defined in the publication: N. Magdelaine, L. Chaillous, I. Guilhem, J.-Y. Poirier, M. Krempf, C. Moog, E. Le Carpentier. "A Long-term Model of the Glucose- Insulin Dynamics of Type 1 Diabetes". IEEE Transactions on Bio-Medical Engineering, 62(6): 1546-1552, June 2015.

In a second embodiment of the invention, a second model of the virtual patient that may be applied is defined in the following publication: C. Dalla Man, R.A. Rizza, and C. Cobelli. Meal Simulation Model of the Glucose-Insulin System. IEEE Transactions on Bio-Medical Engineering, 54(10) : 1740 -1749, October 2007. This model is known as UVA/ Padova simulator. This model comprises a first modeling of a CGM sensor that allows considering the noise and the delays and a second modeling of the pump especially for quantifying the flow of the pump.

For instance, the parameters 0i, 02, 03, 04, and 0s of the virtual patient are identified on the first model from a set of standard data (insulin injections, blood level record, carbohydrate load).

Figure 1 compares the injection and the glycemia response with three different strategies. The first strategy (a,d) is in open-loop : the patient injects manually and precisely the needed dose. The second (b,e) uses the control law according to one embodiment of the invention to compute the injection ; the states xi, X2, X3, X4, xs are supposed known and the stretching factor k is set to 1. The third strategy (c,f) differs from the second strategy only by the value of k.

Figure 1 illustrates especially the evolution of the state in a closed loop during one day. The state may be observed with the unique following entries:

- u_k which is an input of the system corresponding to the level of insulin to be injected and;

- the states xi, X2, X3, X4, xs are supposed known (measured).

Three different meals representing the breakfast at 8:00 am, the lunch at 12:00 and the diner at 20:00. In the first graph the level of CHO is indicated, showing the quantity of carbohydrates in the meal, respectively 50g, 70g, 80g.

The curve“a” represents the evolution of glycemia with bolus that is defined manually, the curve“b” represents the evolution of glycemia with the dynamic bolus calculator, DBC, with a tuning factor k set to 1. The curve“c” represents the evolution of glycemia with the dynamic bolus calculator with a tuning factor k set to 0, 1.

The level of insulin to be injected is showing in the figure bellow where the curves d, e and f respectively correspond to the previous a, b and c curves.

The curve d represents a manually injected insulin quantity at different times. The curves e and f represent the quantity of insulin injected with a dynamic bolus calculator coupled to an injection system. Figure 2 displays regulated glycemia and of insulin to be injected u(t) with:

- the glycemia regulation by means of a closed loop with a state feedback (measured states); curve n is the glycemia and curve p is the injection;

- the glycemia regulation by means of a closed loop with a state feedback with the state observer (estimated states); curve o is the glycemia and curve q is the injection.

The BG excursion with a state observer is almost equal, or practically equal, to the BG excursion with a state feedback. The BG excursion is almost equal to the curve in figure 1 calculated with a bolus. The control with a state observer stays close to the positive control, but the f½ is sometimes negative. Nevertheless, the global infusion i' Bas + ¾r stay always positive, superior to a minimal value, 0,53 U/h which may be compared to the basal flow rate: 0,73U/h.

The closed loop with a state feedback which is reconstructed ensures that the glycemia evolved until regaining the reference by the positive values and consequently ensures that no hypoglycemic episodes happens.

According to an embodiment of the invention, the tuning factor k may be set. An optimization of the calculation of the value of k may resulted from the following equations.

In the nominal case, the transfer in closed loop L is given by

L(s) = - F_k(sl - A)-¾

It may result from equations (25) and (26), the following relationship:

L= k/s

In the non-nominal case, it can be written:

Considering the previous state feedback, the target loop transfer ^ is given by:

L = -f i l - LG' B It could be written that:

Where Oj, are real positive values from patient parameters and q\ are the estimated one.

The setting of the tuning factor k may be done through a user interface for instance according to a predefined patient profile. According to one embodiment, it may be selected from a predefined list of values corresponding to predefined user profile.

In one embodiment, the method and the device of the invention are configured to detect the meal, the beginning, the duration of the meal and its equivalent carbohydrate load. According to one embodiment, the user may set a predefine scheme comprising meals planning. According to one embodiment, the method of the invention may comprise a step for evaluating some phenomena such as a dawn phenomenon. This phenomenon corresponds to an increase of carbohydrates during the night under the effect of hormones. This phenomenon may be modelled by introducing a perturbation in the blood glucose evolution during a predefined time window. Figure 3, graph 10 represents an example of a hyperglycemic anomaly (e.g. the dawn phenomenon) that is modelled by a predefined curve of blood glucose level during a predefined time window. The evolution of blood glucose level may be modelled by a linear function having a slope of 25 mg/dl/h, for example, between a first hour Hi and a second hour Hi. An initial condition may be set at initial hour Ho. This phenomenon may be corrected manually, for example by a predefined pattern of basal rate.

This phenomenon can also be corrected automatically by the DBC. The dawn phenomenon will be estimated through an equivalent CHO load and an adequate injection will be computed and injected.

According to one embodiment, the state observer detects any perturbation i.e. any change in the blood glucose evolution and estimates its equivalent carbohydrate load. Figure 3, graph 11 shows a real time bolus computation and injection due to the detection of the dawn phenomenon during the night, approximatively at 2h00.

The state observer automatically detects the end of the phenomenon and the control-law will evaluate in real time the appropriate bolus so that glycemia recovers goes to reference by positive values.

One advantage of the closed loop operation of the system is to regulate with a better accuracy the level of insulin to be injected.

According to one implementation, the method comprises the setting of the frequency measurements of glucose level. For instance, this period may be set each 5 min. In another embodiment, the method comprises evaluating the presence of subtractive disturbance such as when a patient has physical activity. In the example of figures 4 and 5, two models of a subtractive disturbance are represented.

In Figure 4, graph 12, the subtractive disturbance is modeled by an energy consumption corresponding to a negative meal bolus, for example - lOg. In this case, when the hypoglycemic disturbance is detected, a real time bolus (which in this case is negative) is computed and injected. This bolus is added to the basal rate to compute the global infusion rate.

In the example of Figure 5, the subtractive disturbance may be modeled by an increase of the insulin sensitivity of a patient. The insulin sensitivity may be modeled by modifying a parameter of the system such as a predefined constant. For instance, it could correspond to a modification of the CF (CF= Q2) and/or the DIA (“Duration of insulin Action”) parameter(s). A weighting coefficient may be applied for example during a time window for modifying the system. In the example of Figure 5, graph 14, a temporary increase in insulin sensitivity is modeled by applying a coefficient of 1.5 during 7 hours. Note that in case of hypoglycemic disturbance, the positivity of the control is no more guaranteed. But as the disturbance is detected as it occurs, the global infusion rate is reduced to limit at best the glycemic decrease. In one embodiment, the method comprises a step for evaluating a disturbance.

One advantage of the method of the invention is to define the COB in function of the state. This allows generating dynamically the bolus computed periodically. The robustness of the closed loop operation is especially ensured by the tuning factor k. Figure 7 shows simulations on UV A/Padova Simulator to assess the performances of the control-law. It challenges robustness against on simulation on a no-linear model, noise and delay introduced by the CGM device.

Figure 6 represents one embodiment of an injection system according to the invention. The injection system allows computing and delivering insulin to a patient. The system comprises:

- at least one sensor for measuring the blood glucose level xl(nTs) in the blood of a patient at each interval of time Ts;

- a state observer associated to the said sensor that comprises a first software layer for computing the following parameters:

Xi (nT_s), x₂ ( iT_s), x₃(nT_s), x₄(nT_s), x₅(nT_s), r(nT_s) the first software layer may be implemented by at least a memory and a calculator for estimating the said parameters with the following inputs: the blood glucose level xl(nTs) and the level of insulin dose of the previous injection

¾((n - 1) T_s);

a second software layer implementing the regulating method according to the invention,

the second software layer may be implemented by at least a memory and a calculator for estimating the insulin dose to be injected taking account of conditions provided by a control law.

an injection device that introduces a dose ud(nTs) at each loop of the regulating method.

According to one embodiment, the state observer may comprise the sensor. In such a case, the state observer is a smart sensor comprising a sensor and a calculator implementing the first software layer. According to one embodiment shown in Figure 6, the state observer evaluates the following parameters of the system: the carbohydrates on board in the duodenum Cl and/or the carbohydrates on board in the stomach C2.

According to one embodiment, the first and second software layers may be ensured by the same components (memory, calculator, etc.).

Claims

1. A computer-implemented method for calculating insulin dosage, comprising iteratively (n) performing the steps of:

determining a time interval T_s;

- evaluating a first insulin dose qi(nT_s), said first insulin dose being a function of an insulin sensitivity factor and the difference between the received blood glucose level xi(nT_s) and a predefined blood glucose level target (xiref);

- evaluating a second insulin dose q₂ (nT_s) based on an estimated value of the insulin dose still active in the body IOB(nT_s) of the user being function of a specific insulin response time, a plasma compartment insulin rate and a subcutaneous compartment insulin rate;

- evaluating a third insulin dose q₃(nT_s), said third insulin dose being a function of a quantity of carbohydrates on board COB(nT_s) of the user and a Carbo-to-Insulin Ratio;

- obtaining the insulin dose to be injected u_d(nT_s) in the next time interval as a function of at least the first insulin dose qi(nT_s), the second insulin dose q₂(nT_s), the third insulin dose q₃(nT_s) and a constant basal dose

2. A method according to claim 1, wherein the evaluation of the third insulin dose q₃(nT_s) of insulin dose comprises the evaluation of a first quantity Ci(nT_s) of carbohydrates on board in the duodenum and/or a second quantity C2(nTs) of carbohydrates on board in the stomach.

3. A method according to claim 2, wherein the third insulin dose q₃(nT_s) of insulin dose is a linear function of the first quantity Ci(nT_s) of carbohydrates on board in the duodenum and/or a linear function of the second quantity C2(nT_s) of carbohydrates on board in the stomach.

4. A method according to claim 3, wherein:

- the first quantity Ci(nT_s) of carbohydrates on board in the duodenum is evaluated by using a first model comprising an estimation of a first carbohydrate flow X4(nT_s) in the duodenum and by applying a predefined time constant 05 to said first carbohydrate flow X4(nT_s); and/or - the second quantity C2(nT_s) of carbohydrates on board in the stomach is evaluated by a second model comprising an estimation of a second carbohydrate flow xs(nT_s) in the stomach and by applying the predefined time constant 05 to said second carbohydrate flow xsfnTs).

5. A method according to any one of claims 1 to 4, wherein the insulin dose to be injected comprises a first term Q_t(nT_s), said first term Q_t(nT_s) being a linear function of the sum of the first, the second and the third insulin dose of the insulin dose to be injected (q_x (nT_s), q₂ (nT_s), q₃ (nT_s)) and a tuning factor (kd), said tuning factor being positive and inferior or equal to 1 and being configured to tune the duration of the injection to a predefined reference duration.

6. A method according to any one of claims 1 to 5, wherein the computation of the insulin dose to be injected comprises a second term summed with the first term Q_t(nT_s), said second term being calculated by determining at least one specific infusion rate of a predefined user profile.

7. A method according to any one of claims 2 to 6, wherein:

Xi(nT_s)-x₁ .

- the first insulin dose qi(nT_s) is equal to - - -— , where 02 is the specific

insulin sensitivity factor and xiref is a predefined blood glucose level target;

- the second insulin dose is equal to 0₃(x₂ (nT_s) + x₃(nT_s))„ where 03 is the specific insulin response time, where x₂ and x₃ are function of the plasma and subcutaneous compartment insulin rates; - the third insulin dose q₃(nT_s) is equal to (Ci(nT_s)+C2(nT_s))*04/02 where 04 is a specific carbohydrates sensitivity factor so that Q2/Q4 is the Carbo-to- Insulin Ratio.

8. A method according to claim 7, wherein a state observer allows evaluating at least one of the following variables:

- an estimated blood glucose level n] at a given point in time nT_s, said estimated blood glucose level x n] being a function of the estimated blood glucose level x [n - 1] at a previous moment (n-l)T_s, the estimated plasma insulin rate x₂[n— 1] at a previous moment (n-l)T_s, the estimated carbohydrate flow in the duodenum x₄[n - 1] at a previous moment (n-l)T_s and the measured blood glucose level x n - 1] at a previous moment (n- 1)T_S;

- an estimated plasma insulin rate x₂ [n ] at a given point in time nT_s, said plasma insulin rate ¾ W being a function of the estimated plasma insulin rate x₂ iⁿ 1] at a previous moment (n-l)T_s, the estimated subcutaneous compartment insulin rate x₃[n - 1] at a previous moment (n-l)T_s and the measured blood glucose level x₄ [n - 1] at a previous moment (n-l)T_s;

- an estimated subcutaneous compartment insulin rate ¾ [n] at a given point in time nT_s, said estimated subcutaneous compartment insulin rate x₃ [n] being a function of the subcutaneous compartment insulin rate x₃ [n - 1] at a previous moment (n-l)T_s, the quantity of insulin above the basal dose previously injected fi_d[n - 1] at a previous moment (n-l)T_s and the measured blood glucose level x₄ [n - 1] at a previous moment (n-l)T_s;

- an estimated carbohydrate flow in the duodenum x₄[n] at a given point in time nT_s, said estimated carbohydrate flow in the duodenum x₄[n] being a function of the estimated carbohydrate flow in the duodenum x₄[n - 1] at a previous moment (n-l)T_s, the estimated carbohydrate flow in the stomach x₅ [n - 1] at a previous moment (n-l)T_s and the measured blood glucose level x_t [n - 1] at a previous moment (n-l)T_s;

- an estimated carbohydrate flow in the stomach x₅ [n] at a given point in time nT_s, said estimated carbohydrate flow in the stomach x₅ [n] being a function of the estimated carbohydrate flow in the stomach x₅[n - 1] at a previous moment (n-l)T_s, an estimated glucose disturbance r[n - 1] at a previous moment (n-l)T_s and the measured blood glucose level x n - 1] at a moment (n-l)T_s;

- an estimated glucose disturbance r[n] at a given point in time nT_s, said estimated glucose disturbance f[n] being a function of the estimated glucose disturbance f[n - 1] at a previous moment (n-l)T_s and an estimated blood glucose level x n - 1] at a previous moment (n-l)T_s.

9. A method according to claim 8, wherein the state observer allows evaluating the following variables by solving the following system:

where Li, L2, L3, L4 and Ls are coefficients of a predefined vector ensuring the convergence of the estimation of the state towards the state, and the variable r(t) corresponds to a disturbance which is at the origin of the deviation of the glycemia.

10. A method according to any one of claims 1 to 9, comprising iteratively n performing the steps of:

receiving a blood glucose level xi(nT_s) corresponding to the time interval

Ts;

computing an insulin dose to be injected in the next time interval.

11. A method according to claim 10, using a control law for regulating the insulin dose to be injected, said control law comprising a closed-loop where the positivity of the value of the blood glucose level xi(nT_s) is evaluated to drive said control law on each time interval T_s.

12. A method according to claim 11, wherein the control law comprises a measurement of the value of the blood glucose level xi(nT_s) to determine a condition of positivity of a linear equation comprising the following terms: xi(nT_s), x₂(nT_s ), X4(nT_s) on each time interval T_s.

13. A method according to any one of claims 1 to 12, wherein the received blood glucose level xi(nT_s) is computed from an iterative measurement of a sensor for measuring the blood glucose level, and the insulin to be injected is transmitted to a communication interface in order to activate an actuator of the insulin injection device for injecting the insulin dose.

14. A method according to any one of claims 1 to 13, further comprising a step of controlling an insulin injection device.

15. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method of any one of claims 1 to 14.

16. A system for delivering insulin, the system comprising:

a sensor for measuring the blood glucose level xi(t) of a user, a processor and a memory comprising instructions to operate the method according to any one of claims 1 to 14;

an insulin injection device.

17. A system according to claim 16, wherein the system comprises:

a processor and a memory comprising instructions to operate the method according to any one of claims 7 to 14;

an observer module configured to evaluate the following parameters of the system:

Xi(nT_s), x₂ (nT_s ), x₃(nT_s), x₄(nT_s), x₅(nT_s),†(nT_s).