ES2540159B1 - Method for modeling blood glucose level by genetic programming - Google Patents

Abstract

Method for modeling the blood glucose level by genetic programming. # The invention consists of a method that, by applying evolutionary algorithms on random solutions and data taken from a patient with blood glucose, allows to establish a blood glucose level modeling to obtain a level modeling of glucose in future moments at the time of obtaining patient data. Patient data is at least glucose levels, intake and insulin fast and slow for a time interval. The evolutionary algorithm basically consists of applying genetic programming in its variant of evolutionary grammars or grammatical evolution. That is, apply custom grammars in BNF format, custom mapping processes and concrete error assessments to random solutions or previously generated models to obtain an expression that describes and predicts a patient's glucose levels. Among all patients, the method of the present invention is especially indicated for subjects with Diabetes Mellitus.

Description

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METHOD FOR THE MODELING OF THE GLUCEMY LEVEL BY GENETIC PROGRAMMING

OBJECT OF THE INVENTION

The present invention proposes to apply genetic programming to find a personalized model that describes and predicts a patient's glucose levels. Thus, the present invention describes a method that, from the historical data of a patient consisting of previous values of glucose, carbohydrates taken and injected insulins, obtains an expression that can be used to predict glucose values in the near future. .

The field of application of the present invention is the estimation of a patient's glucose from the measured data. Due to the nature of the invention, the glucose estimation of the present invention allows devices that operate according to the method of the present invention to predict a patient's glucose levels. Among all patients, the method of the present invention is especially indicated for subjects with Diabetes Mellitus.

BACKGROUND OF THE INVENTION

Diabetes Mellitus is a disease caused by a defect in the secretion or action of insulin, which is essential for the control of blood glucose levels.

In both cases the result is that the cells do not assimilate sugar and as a result, there is a rise in blood glucose levels or hyperglycemia. There are different types of diabetes depending on their nature. According to the ADA (American Diabetes Association) we can distinguish four types of DM:

• Type 1 Diabetes (T1DM): Cells do not produce insulin due to an autoimmune process. Currently this makes it necessary for the person to inject exogenous insulin, either by point injections or using an insulin pump.

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• Type 2 Diabetes (T2DM): It is the result of insulin resistance, where the cells fail to use insulin correctly. Sometimes it is combined with an absence, either partial or total insulin.

• Gestational Diabetes: Appears during pregnancy in one in ten pregnant women. Pregnancy is a change in metabolism, since the fetus uses the mother's energy to obtain food, oxygen and other resources. This causes a decrease in the secretion of insulin by the mother.

• Other types: such as cell problems, genetic defects that affect the action of insulin, caused by medications, genetic smdromes, etc.

In most cases, patients with a long course of the disease require the injection of exogenous insulin in several doses, or by an insulin pump. It is important to maintain good glycemic control to prevent both acute complications of diabetes (diabetic ketoacidosis and hypoglycemia, defined as a blood glucose value below 70mg = dl), as well as all multi-chronic complications associated with diabetic patients ( nephropaphy, retino pafia, microangiopafia and macroangiopafia).

In recent years it has been shown that strict control of the blood glucose level in critical patients improves their evolution and reduces medical costs. The control of glucose levels is a difficult task and it requires an effort by both parties, patients and their families. To maintain good blood glucose levels the patient must have some predictive ability to know what glucose level he would have if he ate a certain amount of food or if a certain amount of insulin of a certain type was injected. In fact, the ultimate goal is to avoid not only periods of hyperglycemia (glucose levels> 180 mg = dl) but also episodes of severe hypoglycemia (glucose levels <40mg = dl) that can lead the patient to death.

One of the aspects that makes blood glucose control difficult is the absence of a general model of response to both insulin and the various factors

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mentioned above, mainly due to the particularities of each patient.

The models present in the state of the art apply classical modeling techniques that result in the use of linear equations, defined profiles or models with a limited set of inputs.

Another type of techniques known in the state of the art and that have never been used to perform glucose estimation models are evolutionary techniques. Evolutionary techniques such as genetic programming (PG) have certain characteristics that make them especially useful for addressing problems of optimization and complex modeling. In the first place they are conceptually "simple" and so is their application. However, they have a well-defined and widely studied theoretical basis. Genetic programming has demonstrated its applicability to a multitude of real problems and is intrinsically parallel to working with a set of Moreover, evolutionary algorithms have great potential to incorporate knowledge about the domain in which they work and to incorporate other search mechanisms that are not necessarily evolutionary.

One of the best known applications of genetic programming is the symbolic regression and application of one of the variants of the PG, evolutionary grammar or English Grammatical Evolution (GE) allows us to obtain solutions to incorporate non-linear terms. GE evolutionary grammar is an evolutionary computation technique established in 1998 by the Conor Ryan group at the University of Limerick (Ireland). Genetic programming tries to find executable programs or functions that respond to reference data. The main advantage is that GE evolutionary grammar applies genetic operators to a complete chain, which simplifies the application of the search in different programming languages. It also has no memory problems, unlike basic genetic programming, where tree representation can lead to the known problem of bloating (an excessive growth of computer data structures in memory).

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Therefore, we propose to apply PG to find a personalized model that describes and predicts a patient's glucose levels. Our method will take the historical data of a patient consisting of previous values of glucose carbohydrates taken and insulin injected and from them you will get an expression that can be used to predict glucose values in the near future.

Through the models of the state of the art it is not possible to know an estimation of blood glucose in patients either generically or personalized to the patient. This implies that it is currently not possible to apply appropriate treatments to patients with diabetes. Although there are many jobs that use control models, to date the problem of modeling has not been addressed with evolutionary computation techniques. This solution has not been addressed to date due to its complexity through the use of classical techniques.

DESCRIPTION OF THE INVENTION

The present invention proposes a new technique that involves obtaining the particularized patient model using genetic programming "GP" ("Genetic Programming"). The "GP" genetic programming eliminates barriers related to the construction of the model, such as linearity or limitation in the input parameters. By applying the "GP" genetic programming in the manner disclosed by the present invention, it is possible Find a custom model that describes and predicts a patient's glucose levels. The method of the present invention takes the historical data of a patient consisting of previous values of glucose carbohydrates taken and insulin injected and, from them, obtains an expression that can be used to predict glucose values in the near future.

A first aspect of the invention is a method for modeling the level of blood glucose that allows to predict the glucose of an individual. The method comprises the following steps:

i) obtain from an individual data that includes, for a period of time k, at least:

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or glucose levels Gl; or levels of CH intake;

or levels of insulin injected with rapid effect IS and insulin injected with slow effect IL;

ii) apply an Evolutionary Algorithm to a set of solutions and to the data previously obtained;

iii) calculate a glucose prediction function GL for a later time (k + 1) at time k, such that:

GUk + 1) = f (Gi, CH, lS, lL).

Step ii) additionally comprises carrying out the following sub-steps:

a) generate the set of solutions with random N-solutions where each solution is formed by a string of characters (chromosome);

b) calculate N-expressions GLk for k = 1, ..., N obtained by decoding the set of random N-solutions by applying a BNF grammar and a mapping function;

c) calculate the error Ek that entails: calculate ek as the difference between the data obtained from the patient and the N-expressions GLk; and, apply a fitness function to each of the previously calculated errors ek; such that an associated error Ek is obtained for each GLk expression;

d) select N-1 solutions resulting from: taking the N-solutions and separating the solution with the lowest error Ek from the N-solutions; face the N-1 solutions taken two by two, selecting the solution with the lowest error Ek;

e) cross the previous N-1 solutions using a crossover probability algorithm;

f) mutate a character of the previous N-1 solutions using a mutation probability algorithm;

g) add the least error solution Ek set aside in step d) to the previous N-1 solutions;

h) Repeat steps c) to g) until a predefined stop condition is met.

The crossover probability algorithm comprises:

i) take the N-1 solutions two at a time;

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ii) establish a probability of crossing between 0 and 1;

iii) generate a random number between 0 and 1;

iv) if the random number generated is greater than the probability of crossing, there is no crossing;

v) if the random number generated is less than or equal to the probability of crossover, part of one solution is crossed with part of the other solution in such a way that the length of the character string is maintained.

On the other hand, the mutation probability algorithm comprises:

i) take the N-1 solutions one at a time;

ii) establish a probability of mutation between 0 and 1;

iii) generate a random number between 0 and 1;

iv) if the random number generated is greater than the probability of mutation, there is no mutation;

v) if the random number generated is less than or equal to the probability of mutation, one or more characters of the character string are mutated so that the length of the character string is maintained.

Additionally, the predefined stop condition is at least one of the following

terms:

• maximum number of iterations;

• convergence: does not improve in a number "p" of iterations;

• be close to an optimal theoretician.

On the other hand, the fitness function is one of the following functions (see table 2):

• square millimeters F1 (Least Squares);

• average error F2 (Average Error);

• maximum error F3 (Maximum Error);

• mean square error F4 (RSME);

• mean absolute deviation F5 (MAD).

 Objective

 Fitness Function

 Least Squares

 = ELi

 Average Error

 K = w ZL «i

 Maximum Error

 F3 = max (ek), 1 <k <N

 RSME

 II M it * i-1- ft to

 MAD

 p _ 1 y ^ N efc x Z ^ k = 1 GL (k)

Table 2.- Fitness functions.

The prediction of the glucose previously calculated is obtained from four input data taken from the patient. However, the number of input data can be variable up to a total of twenty-five input variables. Thus, the starting solution GL (k + 1) would be extended until it has an expression like the following:

GL (k + 1) = f (P, E, k, SI, IG, PG, CI, M, IC, IP, DI, OC, TI, FV, VI, PC, TE, FA, G (), C (), IS (),

10 IL (), F (), E (), Z)

where the operator • represents any current or previous moment in time and where f is a function that is calculated using a BNF grammar comprising the following form:

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<f> :: = <f><OP> <f>

| (<f> <OP> <f>)

| <PREOP> (<f>)

| <V>

20 | <Z>

<OP> :: = +

| -

I *

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| /

<PREOP> :: = SIN

COS

EXP

SO

LOG

ABS

LN

Tanh

COSH

SENH

DERIVADA_CON_RESPECTO_AL_TIMPO DERIVADA_CUADRADO_CON_RESPECTO_AL_TIMPO DERIVADA_TERCERA_CON_RESPECTO_AL_TIEMPO <V> :: = <P>

<A>

# {k}

<SI>

<IG>

<PG>

<CI>

<M>

<IC>

<IP>

<DI>

<OC>

<TI>

<FV>

<VI>

<PC>

<TE>

<FA>

# {G [k- <J>]}

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| # {C [k- <J>]}

| # {IS [k- <J>]}

| # {IL [k- <J>]}

| # {F [k- <J>]}

l # {E [k- <J>]}

| # <Z>

<P> :: = "the weight of the individual in kg.";

<E> :: = "age of the individual in years";

<SI> :: = "glycemic units that lower 1 unit of insulin in mg / dl";

<IG> :: = "glycemic intake index" (that of glucose is 1, and may be higher or lower;)

<PG> :: = <D>. <D>

<CI> :: = <D>. <D>

<M> :: = 0

<IC> :: = 5

<IP> :: = 0

<DI> :: = 2

<OC> :: = 3

<TI> :: = 12

<FV> :: = 0.2

<VI> :: = 0.8

<PC> :: = 0.6

<FTSI> :: = + <D>. <D>

| - <D>. <D>

<J> :: = 0 | 1 | 2 | 3

I ■■■

| "instants of time" (for example: 96 ^ 24 hours at 15-minute intervals = 96 instants of time. In the case of using another prediction horizon or another sampling period, this rule would have to be modified)

<Z> :: = <D>. <D>

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<D> :: = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

where the different input parameters are:

P: current weight in kg;

A: current age in years; k: current instant;

FSI: insulin sensitivity or mg / dl that lowers blood glucose per unit of insulin;

IG: is the glycemic index;

PG: protein / fat units: amount of food that provides 100Kcal in the form of fat and / or protein, is measured in units;

CI: carbohydrate / insulin ratio;

M: menstruation, Yes = 1 or not = 0;

IC: Circulating insulin, insulin units;

IP: interval between the beginning of the infusion of prandial insulin and the beginning of the intake, in 15-minute intervals;

DI: duration of the last intake in 15 minute intervals;

OC: order in which food is consumed; (natural number corresponding to a row in a table of possible ordinations)

TI: time since the last intake in 15 minute intervals;

FV: absorption variability factor, value between 0 and 1;

VI: insulin variability, value between 0 and 1;

PC: preparation of the food (fried, roasted, condiments ..), value between 0 and 1;

FTSI: transient insulin sensitivity factor, will be determined by the effect of different types of diseases that the patient has and by the drugs he takes

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the patient, which increase or decrease glucose, and the effect of insulin. We define it as a value that goes from -1 to 1;

Z: is a constant; as for historical:

G () is the blood glucose history (or part of it);

C () is the history of carbohydrates;

IS () is short-acting insulin;

IL () is long-acting insulin;

F () is the physical exercise; Y,

E () is the stress level.

Regarding the mapping function indicated above, this includes the following expression:

Choice ^ = (CIV) MOD (# of choicesf)

where Choicei is the selected election for non-terminal i, CIV is the codon we are decoding, MOD is the module function and (# of choices ^ is the number of possible options for the rule in terminal i.

So far the method of the present invention is described when we start from scratch. That is, there is no previous model of the present invention applied to the patient. If there is an earlier model, method of the present invention, between steps i) and ii), optionally it included assessing whether or not the function GL (= model) of glucose prediction is correct.

In another aspect of the present invention, the present invention comprises a computer program for the execution of a method for modeling blood glucose level glucose prediction according to any one of the embodiments described above or in the "description of a or various forms of realization of the invention ”.

In another aspect of the present invention, the present invention comprises a storage medium containing a computer program for the execution of a

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method for modeling the blood glucose level the prediction of glucose according to any one of the embodiments described above or in the section "description of one or more embodiments of the invention".

The last aspect of the present invention is comprised of a computer system in which the computer program described above is loaded.

BRIEF DESCRIPTION OF THE FIGURES

Figure 1.- Represents a flow chart to calculate the glucose prediction model.

Figure 2.- Represents a flow chart to calculate the glucose prediction model in a web implementation.

Figure 3.- It is the example of grammar in BNF designed for symbolic regression.

Figure 4.- It is a first example of BNF grammar.

Figure 5.- It is a second example of BNF grammar.

Figure 6.- It is a third example of BNF grammar.

Figure 7.- It is a fourth example of BNF grammar.

DESCRIPTION OF ONE OR VARIOUS FORMS OF REALIZATION OF THE

INVENTION

Next, a description is made of one or several embodiments of the invention that, in a non-limiting way, help to better understand the present invention.

Figure 1 shows a flow chart of the method according to the present invention. First, data collection 1 is carried out during a period of

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given time k, for example seven days. The data collected are at least GL glucose levels, CH intake levels and IS rapid and IL slow effect insulin levels. Subsequently, 2 is evaluated if the model (= GL function) is correct (if a model already exists previously). If yes, it continues to collect data. Otherwise, an evolutionary algorithm 3 is applied, basically consisting of customizing a grammar in BNF format 4 by applying a mapping function 5. As a result of the application of the evolutionary algorithm 3, a new model characterized by the function 6:

GL (k + 1) = f (Gl, CH, IS, IL)

It depends on the data collected that are at least GL, CH, IS and IL.

The collected data can be extended with one or several input variables until a model characterized by a function with the following expression is obtained:

GL (k + 1) = f (P, E, k, SI, IG, PG, CI, M, IC, IP, DI, OC, TI, FV, VI, PC, TE, FA, G (), C (), IS (),

il (), f (), e (), z)

where:

P: current weight in kg;

A: current age in years; k: current instant;

FSI: insulin sensitivity or mg / dl that lowers blood glucose per unit of insulin;

IG: is the glycemic index u;

PG: protein / fat units: amount of food that provides 100Kcal in the form of fat and / or protein, is measured in units;

CI: carbohydrate / insulin ratio;

M: menstruation (days since the last menstruation), Yes = 1 or not = 0;

IC: Circulating insulin, insulin units;

IP: interval between the beginning of the infusion of prandial insulin and the beginning of the intake, in 15-minute intervals;

DI: duration of the last intake in 15 minute intervals;

OC: order in which food is consumed; (natural number corresponding to one

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row in a table of possible ordinations)

TI: time since the last intake in 15 minute intervals;

FV: absorption variability factor, value between 0 and 1;

VI: insulin variability, value between 0 and 1;

PC: preparation of the food (fried, roasted, condiments ..), value between 0 and 1;

FTSI: transient insulin sensitivity factor, will be determined by the effect of different types of diseases that the patient has and by the drugs taken by the patient, which increase or decrease glucose, and the effect of insulin. We define it as a value that goes from -1 to 1;

Z: is a constant; as for historical:

G () is the blood glucose history (or part of it);

C () is the history of carbohydrates;

IS () is short-acting insulin;

IL () is long-acting insulin;

F () is the physical exercise; Y,

E () is the stress level.

Figure 2 shows a flow chart where the method of the present invention is implemented within a computer system comprising a database 7 and a web application 8, through which, a patient 9 can enter 11 into the database 7 data corresponding to glucose levels measured by a continuous glucose meter 10. The computer system additionally comprises computational means 15 such as memories, microprocessors, input / output units. The computational means 15 are in charge of storing the grammar and processing the evolutionary algorithm to obtain the mathematical model or expression for GL (k + 1) 6 with which to obtain the prediction of glucose 13. The computational models 15 can be extended with computational means optional 15 'that would serve to predict glucose 14 and indicate insulin boluses in a future time (for example 2 hours) combining the GL function (k + 1) with the "instantaneous" glucose data, expected intake, physical exercise and insulin regulated 12.

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Next, it is detailed how the evolutionary algorithm is applied to model the level of glycemia in individuals by means of Genetic Programming, and especially in subjects with Diabetes Mellitus.

1. Evolutionary Approach

The objective of the present invention is to find an expression that models the glucose level of a diabetic patient. This expression must be obtained, at least, from previous glucose, carbohydrate and insulin data stored in a system or database. Therefore, we are facing a problem similar to the problem of symbolic regression. Symbolic regression tries to obtain mathematical expressions that reproduce a discrete set of data.

Genetic Programming (PG) has proven effective in a large number of symbolic regression problems, although it has some limitations, which often come from the mode of representation such as "bloating." Another point to consider is that in Genetic Programming (PG), evolution occurs in the phenotype of the individual and not in its representation (genotype) During the last years, variants of genetic programming, evolutionary grammar have appeared to propose different approaches to evolution. Evolutionary (GE) allows the generation of computer programs in an arbitrary language.This is achieved through the use of grammar to specify the rules for obtaining programs.Specifically, the present invention uses grammar expressed in the form of BNF (Backus Naur form ).

In contrast to the genetic algorithms, which work with representation of solutions, the Evolutionary Grammar GE works (evolves) with a genetic code that determines the production process of the solution. The process of code translation is determined by the Grammar represented as BNF.

BNF is a technical notation to express context-free grammar. A representation in BNF can be any specification of a complete language or

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a subset of a problem oriented language. A BNF specification is a set of derivation rules, expressed in the form:

<s ^ bolus> :: = <expression>

The rules are composed of terminal and non-terminal sequences. The symbols that appear on the left are non-terminal, while the terminals never appear on the left side. In this case, it can be affirmed that <symbol ^ is non-terminal and, although it is not a complete BNF specification, it can also be affirmed for the present invention that <expression> will be a non-terminal since they always appear between the pair <>. Therefore, in this case, the non-terminal <symbol> will be replaced by an expression. The replacement operation is represented with ":: =". The rest of the grammar must indicate the different possibilities.

A grammar is represented by a 4-tuple {N, T, P, S}, where N is the set of non-terminals, T is the set of terminals, P are the production rules for the assignment of elements from N to T , and S is a start symbol that should appear in N. The options within a production rule are separated by the symbol "|".

Figure 3 represents an example of grammar in BNF designed for symbolic regression. The code that represents an expression will consist of elements of a set of T terminals. These have been combined with the rules of grammar as explained below.

In addition the grammar can be adapted to skew the search of the evolutionary process because there is a finite number of options of production rules, which limits the search space.

2. Mapping process.

As mentioned above, the present invention applies an evolutionary algorithm to evolve genotypes, which are represented as a chain of

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integer values Each genotype maps the start symbol to terminal symbols by reading the codons, which, in this example of realization, are 8 bits long. The process is similar to the one explained in the previous section but, instead of making random choices, we will make the decisions by reading the genotype. Each codon is therefore an integer value of the genotype, which is processed by the following mapping function:

Choice ^ = (CIV) MOD (# of choicesf)

where Choicei is the selected election for the non-terminal i, CIV is the codon that is being decoded, MOD is the module function and (# of choices) is the number of possible options for the rule in terminal i.

The mapping function takes the integer value of the chromosome, calculates the module with respect to the number of possibilities of the rule and selects the option according to the result. Since the module function returns values between 0 and (# of choices) - 1, the first option corresponds to the first value, 0, the second to 1, and so on. Therefore, if a rule has only one possibility, it will always be selected.

In the present embodiment, the mapping process uses the grammar of Figure 3, designed to solve a problem of symbolic regression and glucose model problems, in the absence of particularizing the terminal set, which is described in the Next section An individual is made up of a series of genes (integer values). Each gene can take a value between 0 and 255 since the codons are 8 bits. Assume for example the following individual of 7 genes:

12 - 55 - 23 - 47 - 38 - 254 - 2

The start symbol is S = {expr}, so the expression of the solution will start with this non-terminal:

Solution = <expr>

To obtain the phenotype we apply the mapping function to the first gene (CIV = 12) using the rule of the first non-terminal of the expression. At this point only one

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non-terminal, <expr>, which corresponds to rule I of Figure 3. The number of options in that rule is three. Therefore, the mapping function applied is:

12 MOD 3 = 0

So the first option is selected, <expr> <op> <expr>, and the mapping process is continued. The option selected replaces the decoded non-terminals. As a result, the expression is, at this point:

Solution = <expr> <op> <expr>

The process will continue with the following gene, 55, which is used to decode the first non-terminal of the expression in its current state of development. Then the mapping is applied again, now to rule I:

55 MOD 3 = 1

The second option, <pre_op> (<expr>), is then selected. The expression becomes:

Solution = <pre op> (<expr>) <op> <expr>

The next gene, 23, becomes decoded. At this point in the process, the first non-terminal that appears in the expression is <pre_op>. Therefore, the mapping function can be applied to rule III, which has three possibilities:

23 MOD 3 = 2

When taking the value 2, the third option is selected, the terminal symbol Abs.

The expression becomes:

Solution = Abs (<expr>) <op> <expr> The following gene, 47, decodes <expr> with rule I:

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47 MOD 3 = 2

So the third option is selected, <var>. The expression becomes:

Solution = Abs (<var>) <op> <expi>

Gene 38 decodes <var> with rule IV:

38 MOD 2 = 0

This value selects the first option, the non-terminal X.

Solution = Abs (X) <op> <expi>

The non-terminal <op> is decoded with 254 and rule II:

254 MOD 4 = 2

This value selects the third option, the * terminal.

Solution = Abs (X) * <expi>

The following gene, 2, decodes <expr> with rule I:

2 MOD 3 = 2

This value selects the third option, the non-terminal <var>.

Solution = Abs (X) * <vai>

At this point the process of transformation from genotype to phenotype has depleted the codons. That is to say, all the genes or codons have been used but an expression with terminals in all its components has not been reached.

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The solution is to reuse the codons starting with the first one again. This represents a novelty regarding evolutionary algorithms other than Evolutionary Grammar, of the state of the art. In fact it is possible to reuse the codons several times. This technique is known as "wrapping" and simulates the phenomenon of gene overlapping that occurs in many organisms. Reusing codons is not a problem since in Evolutionary Grammar (GE), a codon always generates the same integer value and, if it applies to the same rule, it generates the same solution. However, if we use them with different rules we will obtain different parts of phenotypes. Thus, Evolutionary Grammar (GE) ensures that an individual genotype always produces the same phenotype. Therefore, the " wrapping ”is not a problem.

Thus, applying "wrapping", the process goes back, to the first gene, 12, which is used to decode <var> with rule IV:

12 MOD 2 = 0

This value selects the first option, the non-terminal X, giving rise to the definitive expression of the phenotype:

Solution = Abs (X) * X

The following section describes four grammar corresponding to four realization examples to represent different search spaces to obtain expressions that model blood glucose levels.

3. Description of the model.

For a model to be complete, that model, for glucose levels, should be based on observable factors as well as other features hidden and intrinsic to the patient's organism. The observable factors are those data that the patient has collected manually or an automatic device, while the unobservable ones must be inferred. For these reasons, the present invention proposes a model that considers all these factors, applying Grammar

Evolutionary (GE) to infer an expression that characterizes the behavior of glucose in diabetic patients.

3.1. Available data and general glucose model.

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The level of glucose at any given time depends on several factors, some of them intrinsic to the functioning of the organism. In the case of a diabetes patient, the most relevant are the level of glucose that was until the last measurement, the ingested carbohydrates and the injected insulin. These factors are included in the 10 data sets of our patients. It is important to note that these data are easy to collect for a real patient. The glucose value is measured with blood analyzers, carbohydrates are measured in units ingested from daily meals, and the amount of insulin as well as the type, are data that the patient obviously knows.

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For the first example of realization, data were obtained with a measurement period between two consecutive 15 minutes over 24 hours. Table 1 shows the data set obtained for a patient "X1". In each row of table k the time is represented, where k = 1 is 00:00 AM, GL is the glucose level at that time, CH the units of ingested carbohydrates, IS the insulin of rapid effect injected and IL the one of slow effect.

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 k

 GL CH IS IL

 one

 209.1453 0 0 0

 2

 209.1453 0 0 0

 3

 205.79354 0 0 0

 4

 Q02.5G395 0 Q 0

 5

 199.43946 0 Q 0

 6

 196.41567 0 0 0

 7

 193.49677 0 0 0

 S

 190.69246 0 Q 0

 9

 188.01547 0 Q 0

 IQ

 185.47971 0 Q 0

 ii

 183.09885 0 Q 0

 12

 180.88533 0 0 0

 13

 178.84963 0 Q 0

 14

 176.9999 0 Q 0

 IS

 175.34167 0 Q 0

 16

 173.87786 0 0 0

 17

 172,608 0 0 0 0

 13

 171.53263 0 0 0

 19

 170.6451 0 Q 0

 twenty

 169.94031 0 Q 0

 twenty-one

 169.41076 0 0 0

 22

 169.04771 0 0 0

 2. 3

 168.84148 0 Q 0

 24

 168.78173 0 Q 0

 25

 168.85766 0 Q 0

 26

 169.05827 0 Q 0

 27

 169.37254 0 0 0

 2S

 169.78957 0 Q 0

 29

 170.29872 0 Q 0

 30

 170.88974 0 Q 0

 31

 171.55425 0 0 0

 32

 172.27976 0 3 12

 33

 173.05923 30 Q 0

 k

 GL CH IS IL k GL CH IS IL

 3. 4

 174.09018 0 0 0 6G 272.82541 0 0 0

 35

 176.68898 0 0 0 67 271.4209 0 0 0

 36

 184.17896 0 0 0 68 272.60383 0 0 0

 37

 195.61325 0 0 0 69 271.58261 0 0 0

 38

 209.11478 0 0 0 70 268 30335 0 0 0

 39

 223.51534 0 0 0 71 263 63006 0 4 0

 40

 237.54628 0 0 0 72 258.18738 0 0 0

 41

 247.25104 20 0 0 73 252.2917 30 0 0

 42

 250.72465 0 0 0 74 246.13977 0 0 0

 43

 251.90543 0 0 0 75 240.98451 0 0 0

 44

 255.86031 0 0 0 76 241.19843 0 0 0

 Four. Five

 262.91532 0 0 0 77 246.19998 0 0 0

 46

 271.63911 0 0 0 78 254.31449 0 0 0

 47

 277.89942 0 0 0 79 264.42406 0 0 0

 48

 278,70943 0 0 0 80 275 21267 0 0 0

 49

 275.38173 40 0 0 81 282 61864 0 0 0

 fifty

 269.9759 0 0 0 82 284.42698 0 0 0

 51

 264.80613 0 0 0 S3 282.33176 0 0 0

 52

 264.5835 0 0 0 84 277.80323 0 0 0

 53

 269.03811 0 0 0 85 271.88307 0 0 0

 54

 276.56921 0 0 0 86 265 29768 0 0 0

 55

 286.01609 0 0 0 87 258.54258 0 0 0

 56

 296.54932 0 0 0 88 251.94544 0 0 0

 57

 307.58483 0 0 0 89 245.71299 0 0 0

 58

 317.78442 0 0 0 90 239.91877 0 0 0

 59

 322.9634 0 0 0 91 234.68683 0 0 IS

 60

 322.05895 0 0 0 92 230.03136 0 0 0

 61

 317.01482 0 0 0 93 225.93797 0 0 0

 62

 309.34854 0 0 0 94 222.23379 0 0 0

 63

 300.16725 0 0 0 95 218.78458 0 0 0

 64

 290.26909 10 0 0 96 215.4919 0 0 0

 65

 280.21928 0 0 0 97 212.29133 0 0 0

Table 1.- Example of data taken for a patient "X1" for the values GL, CH, IS IL.

The proposed model provides us with the estimated glucose values, represented by GL. In each iteration, the estimated glucose is obtained using the previous estimated values, and the values of carbohydrates and insulin at that instant, formally:

GL (k + 1) = f (GL; CH; IS; IL); 1 <k <N (ec.1)

where Gt (k + 1) is the future estimated value for glucose, an instant after the current one, and the rest of the variables have the same interpretation as the one described above. In this way the Evolutionary Grammar (GE) engine should be able to decide the aspect of f. To guide the search we need a grammar that limits the search space and captures the dynamics of blood glucose levels. Below we detail the grammar used in the present invention.

3.2. BNF grammar for modeling glucose levels.

5

10

fifteen

twenty

25

30

Following the general model shown in (ec.1), four grammar have been designed where the estimated glucose depends solely on observable factors. The incorporation of knowledge of the problem into grammar improves the performance of the exploration. Thus ^ the grammar designed follow the advice of the doctors in the research team. According to its indications, the expected behavior of glucose can vary throughout the day, so that possible influences have been added in the form of time windows. In short, there are four grammar that mix the different observations.

Grammar 1

It is well known that carbohydrate intake raises glucose while injections lower it. For this reason in the first grammar carbohydrates always add while insulin always subtracts. It also allows you to use any previous value of glucose, carbohydrates or insulin when building the expression.

GL (k + 1) = fg (Gl (k-m)) + fch (CH (k-m)) - end (IS (k-m); IL (k-m)); 0 <m <k; (gr.1)

The concrete form of fg, fch and end is obtained by GE with Grammar 1, shown in Figure 4. The three terms <exprgluc>, <exprch> and <exprins> correspond to fgi, fch and end, respectively and are expressions that may use prefixes (operands) such as those in rule IX, variables for each of the terms or combinations thereof through rule VIII.

Grammar 2

This grammar is a particular case of the previous one that limits the historical values of glucose, carbohydrates and insulin to the current instant k and the previous k-1. The resulting model has the general expression:

Gl (k + 1) = fgl ((TL (k-m)) + fch (CH (k-m)) - end (IS (k-m); IL (k-m)); 0 <m <1; (gr. 2)

5

10

fifteen

twenty

25

30

Figure 5 shows the grammar used. You simply have to limit the indexes in rules III, V and VII to 00 and 01.

Grammar 3

To give more freedom to the search, the connective operations are left free, extending them to the basic arithmetic operations. The general expression of the model is (gr.3), where f is the function that connects the three subexpressions for glucose, carbohydrates and insulin.

Gl (k + 1) = f (fg (Gl (k - m)); fch (CH (k - m)); fn (IS (k - m); IL (k - m))); 0 <m <k; (gr.3)

Grammar 3 is in charge of defining this model, which presents a slight modification in rule I of grammar 1. It is to change the fixed operations + and - by the non-terminal <op> and continuation is defined in the rule VIII. Figure 6 shows grammar 3.

Grammar 4

The general model is similar to grammar 2 but adds freedom to function f that relates the subexpressions of glucose, carbohydrates and insulin.

Gl (k + 1) = f (fgl (Gl (k - m)); fch (CH (k - m)); fn (IS (k - m); IL (k. M))); 0 <m <1; (gr. 4)

For this, grammar 4 is similar to grammar 2 but giving freedom to the operations in rule I. The grammar is shown in Figure 7.

3.3. Evaluation fitness or aptitude (error ek)

If the grammar limits the search space of the Evolutionary Grammar GE, the mission of the "fitness" functions (also known as fitness) is to guide the evolution towards a good solution. To calculate the "fitness", first you get the

25

Time series of the complete glucose, GL, from the phenotype generated by the genotype of the individual and the grammar used. In this step the estimated glucose in k is fed back to estimate the glucose in the following k.

5 The error ek, defined as the absolute difference between the actual value, in the training set, and the estimated value for each k is measured below.

ek = \ GL (k) - Gl (k) \, l <k <N

10 Finally, the five different fitness functions are used, based on the error ek, shown in Table 2. The fitness functions contained in Table 2 are: F1 (square mm), F2 (average error), F3 (maximum error ), F4 (mean square error) and F5 (mean absolute deviation).

 Objective

 Fitness Function

 Least Squares

 Fi = ELi

 Average Error

 ^ = F EL *

 Maximum Error

 F3 = max (ek), 1 <k <N

 RSME

 MAD

 P _ 1 eh N 1 GL {k)

fifteen

Table 2.- Examples of fitness functions.

Claims (11)

5 10 fifteen twenty 25 30 1.- Method for modeling the blood glucose level through genetic programming comprising the following steps: i) obtain from an individual data that includes, for a period of time k, at least: or GL glucose levels; or levels of CH intake; or levels of insulin injected with rapid effect IS and insulin injected with slow effect IL; ii) apply an Evolutionary Algorithm to a set of solutions and to the data previously obtained; iii) calculate a glucose prediction function GL for a later time (k + 1) at time k, such that: GL (k +1) = / (GL, CH, IS, IL) characterized in that step ii) additionally comprises carrying out the following steps: a) generate the set of solutions with random N-solutions where each solution is formed by a string of characters (chromosome); b) calculate N-expressions GLk for k = 1, ..., N obtained by decoding the set of random N-solutions by applying a BNF grammar and a mapping function; c) calculate the error Ek that entails: calculate ek as the difference between the data obtained from the patient and the N-expressions GLk; and, apply a fitness function to each of the previously calculated errors ek; such that an associated error Ek is obtained for each GLk expression; d) select N-1 solutions resulting from: taking the N-solutions and separating the solution with the lowest error Ek from the N-solutions; face the N-1 solutions taken two by two, selecting the solution with the lowest error Ek; e) cross the previous N-1 solutions using a crossover probability algorithm; f) mutate a character of the previous N-1 solutions using a mutation probability algorithm; 5 10 fifteen twenty 25 30 g) add the least error solution Ek set aside in step d) to the previous N-1 solutions; h) Repeat steps c) to g) until a predefined stop condition is met. 2. - Method according to claim 1, characterized in that the algorithm of crossover probability includes: i) take the N-1 solutions two at a time; ii) establish a probability of crossing between 0 and 1; iii) generate a random number between 0 and 1; iv) if the random number generated is greater than the probability of crossing, there is no crossing; v) if the random number generated is less than or equal to the probability of crossover, part of one solution is crossed with part of the other solution in such a way that the length of the character string is maintained. 3. - Method according to claim 1, characterized in that the algorithm of probability of mutation includes: i) take the N-1 solutions one at a time; ii) establish a probability of mutation between 0 and 1; iii) generate a random number between 0 and 1; iv) if the random number generated is greater than the probability of mutation, there is no mutation; v) if the random number generated is less than or equal to the probability of mutation, a character in the character string is mutated so that the length of the character string is maintained. 4. - Method according to claim 1, characterized in that the predefined stop condition is at least one of the following conditions: • maximum number of iterations; • convergence: does not improve in a number "p" of iterations; • be close to an optimal theoretician. 5 10 fifteen twenty 25 30 5. - Method according to claim 1, characterized in that the fitness function is one of the following functions: • least squares; • average error; • maximum error; • mean square error; • mean absolute deviation. 6. - Method according to claim 1, characterized in that the solution GL (k + 1) has the following expression: GL (k + 1) = f (P, E, k, SI, IG, PG, CI, M, IC, IP, DI, OC, TI, FV, VI, PC, TE, FA, G (■), C (■), IS (■), IL (), F (), E (), Z) where the operator • represents any current or previous moment in time and where f is a function that is calculated using a BNF grammar comprising the following form: <f> :: = <f><OP> <f> | (<f> <OP> <f>) | <PREOP> (<f>) | <V> I <Z> <OP> :: = + | / <PREOP> :: = SIN | COS | EXP | SO | LOG | ABS | LN 5 10 fifteen twenty 25 30 Tanh COSH SENH DERIVADA_CON_RESPECTO_AL_TIMPO DERIVADA_CUADRADO_CON_RESPECTO_AL_TIMPO DERIVADA_TERCERA_CON_RESPECTO_AL_TIEMPO <V> :: = <P> <A> # {k} <SI> <IG> <PG> <CI> <M> <IC> <IP> <DI> <OC> <TI> <FV> <VI> <PC> <TE> <FA> # {G [k- <J>]} # {C [k- <J>]} # {IS [k- <J>]} # {IL [k- <J>]} # {F [k- <J>]} # {E [k- <J>]} # <Z> <P> :: = "the weight of the individual in kg."; <E> :: = "age of the individual in years"; 5 10 fifteen twenty 25 30 <SI> :: = "glycemic units that lower 1 unit of insulin in mg / dl"; <IG> :: = "glycemic intake index" (that of glucose is 1, and may be higher or lower;) <PG> :: = <D>. <D> <CI> :: = <D>. <D> <M> :: = 0 <IC> :: = 5 <IP> :: = 0 <DI> :: = 2 <OC> :: = 3 <TI> :: = 12 <FV> :: = 0.2 <VI> :: = 0.8 <PC> :: = 0.6 <FTSI> :: = + <D>. <D> | - <D>. <D> <J> :: = 0 | 1 | 2 | 3 I - | “Time instants” (for example: 96 ^ 24 hours at 15 minute intervals = 96 time instants. In the case of using another prediction horizon or another sampling period, this rule would have to be modified); <Z> :: = <D>. <D> <D> :: = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 5 10 fifteen twenty 25 30 | 8 | 9 where the different input parameters are: P: current weight in kg; A: current age in years; k: current instant; FSI: insulin sensitivity or mg / dl that lowers blood glucose per unit of insulin; IG: is the glycemic Index; PG: protelna / fat units: amount of food that provides 100Kcal in the form of fat and / or protelnas, is measured in units; CI: carbohydrate / insulin ratio; M: menstruation, YES = 1 or not = 0; IC: Circulating insulin, insulin units; IP: interval between the beginning of the infusion of prandial insulin and the beginning of the intake, in 15-minute intervals; DI: duration of the last intake in 15 minute intervals; OC: order in which food is consumed; (natural number corresponding to a row in a table of possible ordinations) TI: time since the last intake in 15 minute intervals; FV: absorption variability factor, value between 0 and 1; VI: insulin variability, value between 0 and 1; PC: preparation of the food (fried, roasted, condiments ..), value between 0 and 1; FTSI: transient insulin sensitivity factor: value from -1 to 1; Z: is a constant; as for historical: G () is the blood glucose history (or part of it); C () is the history of carbohydrates; IS () is short-acting insulin; IL () is long-acting insulin; F () is the physical exercise; Y, E () is the stress level. 7. - Method according to claim 1, characterized in that the mapping function comprises the following expression: Choicei = (CIV) MOD (# of choices where Choicei is the choice selected for non-terminal i, CIV is the codon we are decoding, MOD is the module function and (# of choices ^ is the number of 5 possible options for the rule in terminal i. 8. - Method according to claim 1, characterized in that the method, between steps i) and ii), optionally comprises evaluating the GL function of predicting glucose previously calculated when there is a previously calculated glucose model. 10 9. - Computer program characterized in that it comprises the execution of a defined method according to any one of claims 1 to 8. 10. Storage medium characterized in that it comprises a computer program defined according to claim 9. 11.- Computer system characterized in that said computer system loads the computer program defined in claim 9.