An Evolutionary Approach for Estimating the Blood Glucose by

Exploiting Interstitial Glucose Measurements

Ivanoe De Falco

, Antonio Della Cioppa

, Tomas Koutny

, Michal Krcma

Umberto Scafuri

and Ernesto Tarantino

ICAR, National Research Council of Italy, Via P. Castellino 111, Naples, Italy

NCLab, DIEM, University of Salerno, Via Giovanni Paolo II 132, Salerno, Italy

NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitni 8, Pilsen 306 14, Czech Republic

Diabetology Center at the Pilsen Hospital University, Alej Svobody 80, 323 00 Pilsen, Czech Republic

Keywords:

Blood Glucose Estimation, Interstitial Glucose, Evolutionary Algorithms.

Abstract:

The diabetes is correlated to a malfunction of the pancreas that produces very little or no insulin. A way

to improve the quality of life of people with diabetes is to implement an artiﬁcial pancreas able to inject an

insulin bolus when necessary. The aim of this paper is to devise a possibly step in constructing the fundamental

element of such an artiﬁcial pancreas - estimation of the blood glucose (BG) through interstitial glucose (IG)

measurements. In particular, a new methodology is presented to derive a mathematical relationship between

BG and IG by exploiting the ability of the evolutionary techniques in solving this regression task. An automatic

procedure is used to estimate the missing BG values within this database. To validate the discovered model a

comparison with other models is carried out during the experimental phase.

1 INTRODUCTION

Diabetes mellitus (DM) is a group of heterogeneous

disorders, which share the common trait of elevated

blood glucose level (BG). A number of medical risks

are associated with diabetes ranging from retinopathy,

neuropathy, and nephropathy or even more serious

complications such as the increased risk of heart dis-

ease and stroke (World Health Organization, 2013).

A large part of the world population is affected by

the diabetes that is a disease with no cure. Therefore,

a methodology able to help the sick persons is very

important not only to improve the patient’s quality of

life, but also to abate the costs of the treatment that

lasts for many years. To succeed in controlling BG,

we need to obtain as precise as possible BG-estimate

to establish the right amount of insulin to inject.

Several devices have been introduced to accom-

plish the task but most of them are invasive. Patients

are reluctant to invasive solution because of the asso-

ciated pain. Moreover, they usually provide measures

in intervals that ranges from about 15 minutes to a

couple of hours with no BG measurements taken dur-

ing the night. All this prevents to adequately take care

of the patient. Instead there is a wide availability of

easier-to-use Continuous Glucose Monitoring System

(CGMS) devices (Vashist, 2013) for the measurement

of the IG, i.e., the glucose in the subcutaneous tissue.

CMGS is minimally-invasive and can be pro-

grammed to take measures with a preﬁxed frequency

for a number of days, also during the night. Neverthe-

less, CGMS needs BG to calibrate - to transform the

measured electric current to glucose level. Patient has

to calibrate at least two times a day, when BG and IG

are steady. While the patient collects only a few BGs,

CGMS provides 288 measurements a day.

BG and IG can differ considerably due to physio-

logical reasons. Therefore, there is a need for efﬁcient

methodologies to derive a precise estimation of BG by

exploiting the large amount of available IG values.

Several studies (Rossetti et al., 2010) have proved

that the complexity of the relationship between glu-

cose dynamics in BG and IG is far too complex to be

captured in the simple calibration algorithms imple-

mented in CGMS devices available in the market, and

this affects the measurement accuracy. CGMS is a

low-power device that implies low computational ca-

pabilities. Although IG is not considered a perfect BG

indicator, nonetheless it is the only one to be available

with continuous and non-invasive measurements.

De Falco I., Della Cioppa A., Koutny T., Krcma M., Scafuri U. and Tarantino E.

An Evolutionar y Approach for Estimating the Blood Glucose by Exploiting Interstitial Glucose Measurements.

DOI: 10.5220/0006729706250632

In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (HEALTHINF 2018), pages 625-632

ISBN: 978-989-758-281-3

Some analytical models have been introduced in

the literature attempting to describe mathematical re-

lationship of IG and BG, as detailed in Section 2. All

these models represent a basic step to design and im-

plement an artiﬁcial pancreas, i.e., an artiﬁcial device

able to automatically drive insulin injections in case

of necessity. This device must be able to perform a

glycemic control by forecasting BG course through

the analysis of the IG signal.

The ﬁrst contribution of the paper is the introduc-

tion of an innovative methodology to put out new

BG values without performing additional measure-

ments. This methodology allows increasing the num-

ber of the BG values contained in the database which

is a critical problem when searching for a prediction

model. The second contribution consists in exploit-

ing such a modiﬁed database to symbolically derive

a law able to describe BG values by starting from IG

measurements. These estimation problems are known

as regression problems. Considered the complexity,

we exploit the capability of the Genetic Programming

(GP) (Koza, 1992) in tackling regression problems

to ﬁnd an effective approximation of relationship be-

tween IG and BG values. The experiments are carried

out over a real-world database containing both BG

and IG measurements for several subjects suffering

from Type 1 DM, i.e., the case in which the pancreas

fails to produce insulin. The scope is to extract an

explicit relationship, i.e., a mathematical expression,

between BG and IG values that could be the core of

the knowledge base of an artiﬁcial pancreas.

The paper is structured as follows. In Sect. 2 a

short description of the related work is given. Section

3 outlines the methodology employed, along with an

innovative procedure to enrich the original database

presenting too many missing BG values in Sect. 3.1,

and the genetic-based regression model in Sect. 3.2.

A discussion on the achieved results and a comparison

with other models is reported in Sect. 4. Conclusions

and future work are exposed in Sect. 5.

2 RELATED WORK

Several models have been devised to ﬁnd a reciprocal

relationship between BG and IG values.

The ﬁrst, and most widely used, model attempting to

relate BG and IG was proposed by Steil and Rebrin

(Rebrin et al., 1999). It is represented by the follow-

ing equation:

di(t)

· i(t) = b(t) (1)

where b(t) and i(t) are the BG and the IG at time t,

and the parameters g and τ represent the steady-state

gain and the IG equilibration time constant, respec-

tively. An important task is the estimation of the best

possible values for g and τ so that the precision of the

model can be improved.

Makroglou et al. (Makroglou et al., 2006) pre-

sented an overview of several mathematical mod-

els aimed at describing the glucose-insulin regulatory

system with reference to DM. The described models

ranged from ordinary differential equations to partial

differential equations, to delay differential equations

to the integro-differential ones.

Per

ez-Gand

ıa (P

erez-Gand

ıa et al., 2010) em-

ployed an artiﬁcial neural network for the prediction

of the blood glucose concentration. The accuracy of

the tool was estimated by using the root mean square

error and the prediction delay.

Del Favero et al. (Del Favero et al., 2014) pro-

posed a model that tries to improve that by Steil and

Rebrin. Basically, they supposed that the value of g

is equal to 1, and added a way to calibrate the model

so that a true IG, represented by i

(t), can be restored.

This calibration is expressed by the equation:

(t) =

i(t) − β − γ · ∆t(t)

;∆t(t) = t −tcal (2)

where α, β, and γ are calibration parameters, and their

values must be recomputed each time the CGMS is

calibrated.

Koutny (Koutny, 2014) struggled to improve the

devised model of glucose dynamics to reduce its cal-

culation error, especially with rapid changes of BG

and IG, e.g., due to short-action insulin. This model

heavily relies on biological considerations, as for in-

stance the importance of capillaries and the fact they

have different permeabilities in different compart-

ments. By means of the proposed model tested on

hyperglycemic-clamp data, he succeeded in attaining

an improved model to compute the BG levels.

All the analytic models introduced presents the

problem of estimation of several parameters. This

estimation is usually performed by exploiting math-

ematical, biological or physiological considerations

or, in some cases, by performing an a-posteriori man-

ual tuning. Despite its importance, only in the last

years some attempts have been carried out to automat-

ically extrapolate the parameter estimation by means

of techniques able to deal with this optimization prob-

lem such as the evolutionary methods. Two of these

attempts are reported in the following.

Koutny (Koutny, 2016) combined the analytic

method proposed in 2014 with meta-Differential Evo-

lution (DE) (Price and Storn, 1997). Namely, starting

from a continuously measured level of IG for human

Type-1 diabetic patients, he computed a continuous

BG level. He used six different scenarios to ensure

robust validation of the calculation, and made use of

DE to evaluate the parameters for his model. All the

six scenarios, even the simplest ones, performed bet-

ter than CGMS in estimating BG values.

De Falco et al. (De Falco et al., 2017) proposed

a GP tool to estimate the BG values starting from

the easily available IG values. A relationship under

a form of an explicit mathematical expression was

excerpted. The experimentation was carried out on

a real-world database containing subjects suffering

from Type 1 diabetes. The comparison against state-

of-the-art models attested the effectiveness of the pro-

posed evolutionary approach.

3 THE METHODOLOGY

The methodology proposed within this paper can be

summarized in two basic steps: i) the deﬁnition of

a novel automatic procedure to enrich the database

with estimated BG values by exploiting an evolution-

ary optimizer for the calculation of the model param-

eters; ii) the use of an appropriate evolutionary tech-

nique, i.e., a GP algorithm, for solving the regression

model and extracting an explicit symbolic model.

3.1 Database Enrichment

The poor availability of BG values with respect to the

IG ones is one of the major problem in excerpting a

reciprocal and effective mathematical relationship be-

tween them. To overcome this problem we devise a

new procedure able to estimate a number of missing

BG values within the database used to solve the re-

lated regression problem.

Since the Steil-Rebrin model (Rebrin et al., 1999)

is still one of the most widely used to establish a rela-

tion between BG and IG, we have employed it to esti-

mate the missing BG values. To proceed in this direc-

tion, it is necessary to estimate the model parameters

of Eq. (1), i.e., the steady-state gain g and the equili-

bration constant τ, so to enhance the model precision.

Following the approach of Koutny in (Koutny, 2016),

this estimation is performed by using as optimizer an

evolutionary algorithm, namely the DE. Such an al-

gorithm works on a population of potential candidate

solutions representing the model parameters. Start-

ing from a population of randomly chosen parameter

values, the population evolves by performing recom-

bination and mutation of the current solutions through

speciﬁc evolutionary operators. The details related

to these operators can be found in (Price and Storn,

6.4

4.7

Figure 1: An exemplary tree-structured solution in GP.

1997). During the evolution the quality of the cur-

rent parameters is evaluated through a ﬁtness func-

tion. This function computes the mean square error

between the BG values estimated through the Steil-

Rebrin model endowed with the current parameters

and the available measured BG values of the original

database. The evolutionary procedure is applied it-

eratively until a ﬁtness of desired quality is achieved

or a ﬁxed number of iteration is performed. By ex-

ploiting the calculated parameter values at the end of

the evolution, we are able to estimate the BG values in

correspondence of all the IG values for which they are

missing. In this way a complete correspondence be-

tween all the IG and BG values is available. Naturally

the measured values in the original database are left

unchanged. The so-modiﬁed database is then used for

solving the symbolic regression problem. By consid-

ering that the number of estimated BG values in this

enriched database are much higher than those truly

measured, it will be necessary to introduce a correc-

tion factor to avoid a bias in the model extraction. The

detail of this correction factor will be reported in the

experimental section.

3.2 The General GP Framework

Genetic Programming (GP) is a heuristic methodol-

ogy well suited for optimization purposes (De Falco

et al., 2005; De Falco et al., 2006), and has its roots

in the implementation in a computer of mechanisms

borrowed from the natural evolution process that hap-

pens in populations.

Given a problem, GP works on a set, referred to as

population, of its solutions. Each solution, called in-

dividual, is a program represented under a tree struc-

ture form. The inner nodes in any individual denote

elementary functions, while the leaf nodes contain

terminals, i.e., either variables of the problem or con-

stant values. By reading a starting tree in pre-order

the corresponding program is got. An example is out-

lined in Fig. 1 in which the tree represents the in-order

expression 6.4 − (4.7 ∗ y) + x.

In GP the quality of each individual in solving the

Table 1: The set of the elementary functions along with the

related symbols.

Symbol Description

+ Addition

- Subtraction

* Multiplication

/ Protected division (is 1 if the denominator is 0)

sqrt Square root

pow Power

given problem is evaluated by means of a ﬁtness func-

tion Φ that should be tailored to the speciﬁc prob-

lem. The population of solutions evolve iteratively

from one generation to the next one by applying evo-

lutionary operators with the aim to improve the ﬁt-

ness function. This evolution ends when a ﬁxed maxi-

mum number of generations g

max

is reached A general

pseudo-code describing GP is reported the following:

• randomly generate an initial population with P in-

dividuals;

• evaluate the quality of each individual with the

help of the appropriate ﬁtness function;

• at each generation create a new population by re-

peating the steps below:

– randomly choose an evolutionary operator; i.

e., crossover, mutation, and copy;

– select as many individuals as needed by the op-

erator chosen in the current population;

– let the selected individuals undergo the operator

so as to generate a new individual;

– insert this latter into the new population being

created;

– assess the quality of the new individual through

the ﬁtness function;

• keep on creating a new population at each gener-

ation until reaching a preset g

max

The quality of the solutions achieved by GP, in terms

of ﬁtness function values, typically improves as the

number of generations increases. For a detailed de-

scription of the three operators the interested reader

can refer to (Koza, 1992).

3.2.1 GP for Regression

Since we wish to tackle a regression task, the popu-

lation will be constituted by a set of regression mod-

els. Each such model is encoded as a ‘formula’, repre-

sented as a tree whose nodes can include either func-

tions or terminals. The complete set of the functions

employed within this paper is outlined in Table 1.

The terminal set consists of the set of the indepen-

dent variables of the problem, plus the Const symbol

that denotes a constant value. This latter is always

used in relation to a problem variable, and its value

is randomly selected in a range suited to the speciﬁc

variable involved.

Aiming at obtaining a (sub)–optimal regression

model, a division of the database items into either

two or three sets takes typically place for learning pur-

poses. Due to the limited amount of measured items

in the available database, we have opted for a two-set

division, namely train and test sets. Learning is car-

ried out over the items of the train set with the goal

to attain a model useful to approximate the dependent

variable values as a function of the values of the in-

dependent problem variables. The quality of the best

model (in terms of best ﬁtness value over the train set)

provided by GP at the end of the execution is eval-

uated over the test set, whose items had been never

previously displayed to the GP algorithm.

To numerically assess the quality of each regres-

sion model S achieved during the GP execution, we

have employed the Root Mean Square Error (RMSE)

as ﬁtness function Φ, i.e:

Φ(S) =

∑

i=1

calc

(i) − y(i))

(3)

where y

calc

(i) represents output value for the i–th item

of the database by the model S under examination,

whereas y(i) is the value of the dependent variable for

the same i–th item. With this choice the regression

problem becomes a minimization problem.

4 EXPERIMENTAL RESULTS

The Database. From the Diabetology Center at the

Pilsen Hospital University, we received anonymized

datasets of Type 1 diabetic patients. We transformed

the datasets into a database. The database comprises

5 different patients. Each patient comprises several

time segments. Time segment is a period for which

the patient wore CGMS. There are 9, 30, 31, 38 and

38 time segments per patient, respectively. In total,

there are 146 time segments, which contain 342 BGs

and 36256 IGs.

The Findings. On the database, we apply the

methodology described in 3.1 to estimate the missing

BG values. This procedure necessitates of the estima-

tion of the parameters of the Steil-Rebrin model. The

estimation performed by means of the DE algorithm

has resulted in the following values for the parame-

ters: g = 0.98 and τ = 0.02. These values have been

used to enrich the dataset with the missing BG val-

ues. As already said, the truly measured BG are left

unchanged. The enriched dataset has been employed

to assess whether or not a general behavior, able to

suitably describe all of the involved subjects, can be

identiﬁed. If it were possible, this would result in an

unique model without the necessity to personalize it

as a function of the subject. The eventual existence

of a single model would simplify also the knowledge

base for the artiﬁcial pancreas.

To perform all the reported experiments GPTIPS

(Searson, 2009), a tool executing GP and running in

the MATLAB environment, has been used. The GP

parameters have been set at the following values: P=

500, g

max

= 500, tourn size = 30, p mutate = 0.1,

p cross = 0.9, and p copy = 0.02 after a preliminary

tuning phase. To simplify the results the maximum

tree depth and the maximum number of the tree nodes

have been set equal to 4 and 8 respectively.

We have assigned the ﬁrst 70% of its items to

the train set (25,370 items) and the remaining 30%

of items to the test set. Then we have executed the

tool for 10 times. The reason is that GP is a nonde-

terministic algorithm whose results depends on a ran-

dom integer value that should be assigned as seed to a

random number generator. Different seeds can yield

different results. Therefore, GPTIPS has been run 10

times over the dataset. The run reaching the lowest

RMSE value over the test has been taken into account

because its associated ﬁnal model has the highest abil-

ity to correctly compute unseen data.

Furthermore, the GP considers for the indepen-

dent variable IG a time interval of 30 minutes before

and 30 minutes after around a selected time t that is

the time at which the dependent variable BG has to

be computed. Considered that the IG values are taken

with a ∆t = 5 minutes, the values considered with re-

spect to IG at time t, i.e., i(t), ranges from i(t − ∆t) to

i(t −6∆t) for the past, and from i(t + ∆t) to i(t +6∆t)

for the future total of 14 independent variables, yield-

ing for GPTIPS 13 possible terminals, plus the const

node. In addition to these 13 variables, the dataset

contains also the estimated BG values b

(t) and the

measured BG values b

(t).

In Equation (3) y(i) represents the measured BG

value in the i–th item of the set, and y

calc

(i) is its esti-

mate through the use of the IG values.

As explained in Section 3.1, to avoid bias in the

model extraction a ﬁtness function with a correction

factor p

has been devised. To this aim a global ﬁtness

function RMSE

ALL

arranged as the sum of two sub-

ﬁtness functions appropriately weighted by an appro-

priate correction factor p

is introduced. In formula

this function can be expressed as follows:

RMSE

ALL

= (1 − p

) · RMSE

+ p

· RMSE

(4)

where RMSE

is the error evaluated on the estimated

values while RMSE

is the error computed on the

Table 2: RMSE

values obtained by the different methods.

GP GP IGBG IGBG S-R

opt

S-R

opt

Train Test Train Test Train Test

9.65 10.15 17.17 18.27 14.71 13.82

measured values.

The correction factor is given by p

= n

where

is the number of the estimated values and n

is the

total number of values in the dataset. The choice for

the correction factor in Eq. 4 is due to the fact that the

number of measured values is about 1% with respect

to the number of estimated values. Therefore, consid-

ered that RMSE

weights much more than RMSE

in order to avoid bias toward the estimated values we

have decided to assign to the correction factors values

inversely proportional to the weights of the respective

sub-ﬁtness functions.

Throughout our experiments, we compare our GP-

based method endowed the new methodology to esti-

mate the missing BG values against a GP approach

which makes use of the measured IG values as if

they were the exact measured values of the BG. This

method is denoted as IGBG. The last comparison is

performed with the state-of-the art Steil-Rebrin model

(Rebrin et al., 1999) with the parameters optimized

through DE. Hereinafter this model is named S-R

opt

The best model found for the global database is:

b(t) =1.16 · i(t + ∆t)) − 0.00369 · i(t − 6∆t)−

0.141 · i(t −∆t) +

(10.6 · (i(t) + (i(t) − ∆t))

i(t + 3∆t)

− 20.6

where i is the measured IG and b is the computed BG.

The obtained model uses ﬁve out of the thirteen

inputs, namely the IG values at times t, t − ∆t, t −

6∆t, t + ∆t and t + 3∆t. This conﬁrms the statement

in (Boyne et al., 2003; Steil et al., 2000) that delays

of up to 13 minutes take place between IG and BG.

From a quantitative viewpoint, Table 2 shows the

RMSE

of the different models over train and test

sets. Of course, for the IGBG method there is no

learning. Our method has the best performance with

respect to the other models, and obtains an RMSE

value equal to 9.65 over the train set, and to 10.15

over the test set. This is a very good result, because

this means that the difference between a BG value es-

timated by this model and the real BG value is about

10 mg/dl in a typical range between 50 and 400. This

relatively small RMSE

ensures that the use of the

above model can be of great help in assessing whether

the subject is in a normal state, or is undergoing a hy-

perglycemic or a hypoglycemic episode.

Figure 2 shows how well the BG values estimated

by the computed model ﬁt the BG measured data over

both train and test sets. As a general comment, ﬁtting

is very satisfactory also over test set data, never shown

0 200 400 600 800 1000

100

150

200

250

300

Time [Δt ticks, Δt = 5min]

Glucose [mg/ml]

Measured Blood Glocose

Computed Blood Glucose

35900 36000 36100 36200

100

150

200

250

300

Time [Δt ticks, Δt = 5min]

Glucose [mg/ml]

Measured Blood Glocose

Computed Blood Glucose

Figure 2: The estimate of the values through GP. Top: ﬁrst 2 segments on train set. Bottom: last 4 segments on test set.

to the system during learning, BG peaks are very of-

ten caught in terms of both time and magnitude.

The frequency of relative errors for the three in-

vestigated models is reported in Table 3. As it can be

appreciated from the table, for our model 87.74% of

the items has a relative error lower than 10%, which is

an excellent result. Moreover, more than 95% of the

items has an error lower than 20%, which is also good

with respect to ISO 15197:2003 and 15197:2013 ac-

curacy standards for blood glucose meters. The table

also evidences that these results are much better than

those achieved when IG is used as the real value of

BG, and better also than S-R

opt

model for the items

with relative errors lower than 10% and 20%. S-R

opt

model has slightly better values than GP for a relative

error lower than 5% while the results are the same

for the other relative errors. This means that the pro-

posed GP-based approach can actually help in better

estimating BG.

Table 3: The frequency of relative errors: cumulative prob-

ability of lower than or equal to relative error.

Relative error GP IGBG S-R

opt

≤5% 59.43% 41.51% 60.38

≤10% 87.74% 72.64% 83.02

≤15% 90.57% 84.91% 90.57

≤20% 95.28% 90.57% 92.45

≤25% 98.11% 93.40% 98.11

≤30% 98.11% 96.23% 98.11

≤35% 98.11% 96.23% 98.11

≤40% 100.0% 98.11% 100.0

≤45% 100.0% 98.11% 100.0

≤50% 100.0% 100.0% 100.0

Figure 3 shows the results in terms of the Clarke

Error Grid analysis (Clarke et al., 1987), that is widely

used in the studies about diabetes. Basically, the 2D-

estimate space is subdivided into ﬁve zones labeled

from A to E. The higher the number of points falling

in zones A and B, the better the estimate. Points

Figure 3: Clarke grid analysis. Left: train set. Right: test set.

falling in the other zones represent different types of

situations that should be avoided. As it can be seen,

almost all of the points lie in the zones A and B, and

this holds true not only for the train set but for the

test set too, which is a hint of a very good estimate.

Numerically, the percentage of points falling in the

different zones is reported in Table 4 for the test set,

and this for all the models. For GP we report also the

results over the train set, and for IGBG the results are

related to the whole database.

Figure 4 reports the same diagram on all the

dataset. For GP the zones A and B contain more than

99% of the points in test set (ISO 15197:2013 require-

ment), which is very good and is superior to IGBG,

and slightly outperforms also the S-R

opt

method. Also

the absence of points related to situations C and E is

an excellent outcome of the proposed model. As a

comparison, GP has a lower number of points lying

in the zone D than IGBG and the S-R

opt

models. This

is a very important outcome because zone D points

out a possible risky inadequacy for hypoglycemia or

hyperglycemia identiﬁcation.

Summarizing, the results obtained seem to imply

that a unique model extracted by using GP can ﬁt

all of the subjects involved in this study, and the ar-

tiﬁcial pancreas for all of them could be based on

evolutionary-devised models.

5 CONCLUSIONS

The main problem for a regression model in ﬁnding

a relationship between variables is the absence of a

sufﬁcient number of value of the variables to be cor-

Figure 4: Clarke grid analysis on the whole dataset.

related. This situation is usual in the ﬁeld of diabetes

research where the easily available number of IG val-

ues contrast with the low number of corresponding

number of BG values. Within this paper, to overcome

the problem we have devised an evolutionary proce-

dure to enrich the database made up of many miss-

ing BG values by exploiting the Steil-Rebrin model

and the DE technique to estimate these missing BG

values. Afterward, a GP algorithm has been used to

excerpt an explicit relationship between BG and IG

values under the form of a mathematical expression.

This model has been compared both against a GP

approach which makes use of the measured IG val-

Table 4: The Percentage of Points Falling in the Different Zones of the Clarke Error Grid.

Zone GP Train GP Test IGBG Train IGBC Test S-R

opt

Train S-R

opt

Test

A 98.73% 95.28% 94.49% 90.57% 97.46% 93.40%

B 0.85% 4.72% 4.24% 8.49% 1.69% 6.60 %

A + B 99.58% 100% 98.73% 99.06% 99.15% 100%

C 0.00 % 0.00% 0,00% 0.0% 0% 0%

D 0.42% 0% 1.27% 0.94% 0.85% 0%

E 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

ues as if they were the exact measured values of

the BG, and against the state-of-the-art Steil-Rebrin

model with optimized parameters. The results have

shown its superiority in terms of lower RMSE, and

of better ﬁtting in the Clarke Error Grid. The ﬁnd-

ings obtained seem to imply that a unique model can

ﬁt all of the subjects involved in this study, and the

artiﬁcial pancreas for all of them could be based on

evolutionary-devised model.

Future work implies the use of evolutionary-

devised model in a clinical trial to estimate the BG

values of the involved subjects, so as to further test its

effectiveness. In the positive case, this model could

be added to an under-development artiﬁcial pancreas

device for a real experimentation.

ACKNOWLEDGEMENTS

This publication was partially supported by the

project LO1506 of the Czech Ministry of Education,

Youth and Sports.

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