GLYCAEMIA REGULATION PREDICTIVE CONTROL SYSTEMS

PERFORMANCES EVALUATION

A Comparative Study of Neural and Mathematical Models

Nathana¨el Cottin, Olivier Grunder and Abdellah ElMoudni

Laboratoire Syst`emes et Transports, Universit´e de Technologie de Belfort Montb´eliard, rue Thierry Mieg, Belfort, France

Keywords:

Diabetes, Glycaemia regulation, Insulin, NPC, Artiﬁcial neural network, Resilient propagation.

Abstract:

Type 1 blood glucose regulation remains a complex problem to simulate. Different blood glucose control

schemes for insulin-dependent diabetes therapies and systems have been proposed in the literature. This arti-

cle presents an adaptative predictive control system for glycaemia regulation based on feedforward Artiﬁcial

Neural Networks trained with the resilient propagation (RPROP) method. Experiments performed on a math-

ematical (theoretical) compensation model and our system aim to objectively compare the behaviour of each

approach when both exact and perturbated data are presented. These experiments, which make use of a virtual

patient, not only cover the ANN’s best conﬁguration and training parameters on exact training information,

they also demonstrate the accuracy of the neural approach when up to 20% perturbated data are supplied. As

a result of the experiments on perturbated data, the neural approach gives slightly better evaluations than the

theoretical model. This demonstrates the neural system’s ability to adapt to perturbated environments.

1 INTRODUCTION

Type 1 diabetics suffer from insulin-dependent dia-

betes chronic disorders. Their pancreatic β-cells do

not secrete sufﬁcient insulin, which mostly results in

hyperglycaemia states. Although many researches

have been conducted in the past decades, diabetics

still need practical daily solutions to help them reg-

ulate they blood glucose concentration (BGC).

This work is centered on the presentation of an

adaptive Neural Predictive Control (NPC) system

used to infer a particular patient’s blood glucose regu-

lation metabolism. This system is validated by means

of experimental comparisons against the theoretically

proven closed-loop control mathematical model pro-

posed by (Charpentier et al., 2005) used for blood

glucose regulation. Not only exact raw information

is used to evaluate accuracy of the experimented sys-

tems, up to 20% perturbated raw and test information

allows to verify the adaptability of our NPC approach.

Compared with other works, the proposed system

is designed to adapt to numerous blood glucose reg-

ulation techniques by means of pluggable modules

while conforming to a common regulation process.

This article is organized as follows: next section

presents some related works on closed-loop control

using mathematical models and Artiﬁcial Neural Net-

works (ANN) to position the context of this paper.

Section 3 introduces a Global Predictive Control Sys-

tem (GPCS) used for blood glucose regulation and its

derived systems which model the theoretical and neu-

ral approaches to be compared. Next section focuses

on practical experiments results based on a virtual pa-

tient with both exact and perturbated data. Conclu-

sions draw the beneﬁts and drawbacks of each ap-

proach and present some future works.

2 PREDICTIVE CONTROL

SYSTEMS ARCHITECTURES

2.1 Global PCS

Regulating glycaemia aims to fulﬁll patients with ei-

ther extra glucose or external insulin measurements.

Regulation is handled by a Global Predictive Control

System (GPCS) which takes the following parameters

into account:

• Some patient’s physical information, such as his

age and weight (i.e. miscellaneous parameters);

• A meal identiﬁer, used by the internal regulation

525

Cottin N., Grunder O. and ElMoudni A..

GLYCAEMIA REGULATION PREDICTIVE CONTROL SYSTEMS PERFORMANCES EVALUATION - A Comparative Study of Neural and Mathematical

Models.

DOI: 10.5220/0003138805250528

In Proceedings of the International Conference on Health Informatics (HEALTHINF-2011), pages 525-528

ISBN: 978-989-8425-34-8

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

module to perform initial tasks, before the regula-

tion process starts;

• The glycaemia value before taking the meal (i.e.

pre-meal glycaemia);

• The amount of carbohydrates the patient wishes

to ingest (i.e. initial meal carbohydrates);

• The expected glycaemia value the patient needs

to reach after having ingested the meal carbohy-

drates, assuming that short-term insulin has fully

taken effect (i.e. expected post-meal glycaemia).

As a result, the system estimates the ﬁnal gly-

caemia (i.e. evaluated post-meal glycaemia) as close

as possible to the patient’s expected glycaemia value.

It jointly suggests a (possibly null) short-term insulin

measurement to absorb the meal carbohydrates (in

case of hyperglycaemia) and the total amount of car-

bohydrates the patient should ingest. In case an in-

sulin measurement is predicted, this amount of carbo-

hydrates equals the initial meal carbohydrates value.

This makes sure that extra carbohydrates and insulin

measurements are mutually exclusive results.

2.2 Specializations

To operate glycaemia regulation, the global system

can be specialized in two PCS classes:

• Theoretical PCS (TPCS) which directly imple-

ment mathematical models for glycaemia regula-

tion, without any regulation control loop;

• Commanded PCS (CPCS) which operate by

means of an internal control-command compen-

sation loop to suggest insulin and carbohydrates.

The CPCS overall regulation principle is depicted

by ﬁgure 1. A CPCS relies on two key components:

• A predictor, which estimates a glycaemia positive

or negative deviation given carbohydrates and in-

sulin values. It may also take into account some

patient’s miscellanous information to produce a

satisfactory glycaemia prediction;

• An adaptive controller, which modiﬁes the cur-

rent insulin or carbohydrates values based on a

predicted glycaemia. The controller also deter-

mines the control loop stop condition.

The controller uses initial meal carbohydrates

once. This value is then replaced with the regulated

value (although the controller may have keep this ini-

tial value in case it regulates insulin).

3 EXPERIMENTS

This study compares the behaviour and the quality of

the compensation results of an NPC CPCS (i.e. neural

CPCS) against a TPCS. The TPCS is assumed to pro-

vide exact results: a vitual patient, that strictly con-

forms to the mathematical model implemented in the

TPCS, is used to train the neural CPCS.

Then, some perturbations using a normal distribu-

tion are added both on training and test data. This

implies that the TPCS produces errors compared with

the exact data (without perturbations).

Experimentsaredriven on a virtualpatient on both ex-

act and perturbated raw information. This virtual pa-

tient behaves like the theoretical compensation model

proposed by (Charpentier et al., 2005) in case of ex-

act raw information. Use of this virtual patient allows

to determine the neural approach accuracy against the

theoretical model. Indeed, two PCS are compared:

• A theoretical PCS (TPCS), which implements the

mathematical compensation model of the virtual

patient. This PCS provides exact results when ex-

act source raw information is used, which means

that no deviation is produced;

• A neural CPCS, which integrates a neural predic-

tor based on a n− n− 1 (n refers to the number of

inputs of this predictor, conforming to ﬁgure 1)

feedforward ANN (Mhaskar, 2005). Input and

hidden layers use the sigmoid activation function

and the output layer uses the hyperbolic tangent

activation function (to represent a signed devia-

tion). This neural CPCS approximates compensa-

tion values based on the function the ANN infers.

Deviations between PCS suggestions and exact

expected compensation values are expressed as fol-

lows:

• Carbohydrates deviations are expressed in grams;

• Short-term insulin deviations are expressed by a

number of unitary doses.

3.1 Neural CPCS Training

The neural predictor of the neural CPCS is trained

from known raw information using supervised train-

ing techniques. This set of raw information is ran-

domly generated, though conforming to the mathe-

matical model of (Charpentier et al., 2005).

A raw information item is basically composed of

the GPCS inputs and outputs values. However, the

ﬁnal post-meal glycaemia value does not correspond

to the neural PCS estimated glycaemia but refers to a

physical measurement (performed by the patient him-

self or by a medical assistant).

HEALTHINF 2011 - International Conference on Health Informatics

526

Meal

carbohydrates

Miscellaneous

parameters

(age, weight, ...)

Insulin

Carbohydrates (incl.

extra carbohydrates)

Controller

Predicted

glycaemia

Predictor

Initial

glycaemia

Final glycaemia

Predicted

glycaemia

Expected

glycaemia

Carbohydrates

Insulin

Figure 1: CPCS regulation principle.

Experiments indicate that the best conﬁguration

for the ANN is obtained for 100 training data and

3000 training epochs. Other experiments (not men-

tioned here) prove that using more than 200 training

information does not signiﬁcantly lower the average

and maximum deviations indices. On the contrary,

a regression phenomenon is observed (i.e. the car-

bohydrates and short-term insulin deviations become

larger when more than 200 training information items

are used).

Given a meal identiﬁer, the corresponding ANN

is trained with the selected raw information items,

whose meal identiﬁer matches the given identi-

ﬁer. The “resilient propagation” training algorithm

(RPROP) with default parameter values suggested

by (Riedmiller and Braun, 1993) is used.

One could have experimented with “well-chosen”

raw information (i.e. deterministic raw information)

which cover a wide range of values and provide all

compensation cases, but this would have two main

drawbacks:

• The experimental results would be slanted as the

ANN would give insigniﬁant deviation values;

• This case is deﬁnitely unrealistic: a patient will

never cover the whole range of possible val-

ues for all parameters (i.e. pre-glycaemia, post-

glycaemia and meal carbohydrates in particular).

3.2 Results Review on Exact Data

The results of this comparison are gathered in table 1.

This table indicates average and maximum regulation

glucose and compensation short-term insulin devia-

tions from exact measurements provided by the math-

ematical model. The neural PCS is trained with ran-

domized exact information.

This table demonstrates that 100 training informa-

tion items lead to the lowest short-term insulin aver-

age and maximum deviations (of 0.05 and 0.17 re-

spectively). The maximum carbohydrates deviation

of 1g is not signiﬁcant and does not reﬂect upon the

Table 1: Neural CPCS deviations from expected compensa-

tions using exact training data and 3000 epochs.

Neural PCS Training data

deviations 50 100 200

Carbo- Average 0 0 0

hydrates Max 0 1 0

Insulin

Average 0.18 0.05 0.11

Max 0.56 0.17 0.37

accuracy of the measurements. The widest insulin

deviation obtained for 50 training data reﬂects the

lack of information to train from. Use of 200 train-

ing data provides still acceptable measurements (i.e.

below 0.5 doses) but a (well-known) regression phe-

nomenon starts to become visible.

3.3 Support for Perturbated Data

Previous experiments were based on exact raw infor-

mation to train the ANN and validate the neural PCS

behaviour. In order to ensure the validity of the neural

PCS in a “real” environment, we use perturbated raw

information for training to simulate devices measures

deviations, patients reading errors and instable sensi-

tivity to insulin deseases. Perturbations apply to pre-

meal and post-meal glycaemia as well as meal carbo-

hydrates on each raw information item. Each pertur-

bation follows to a normal distribution centered on 0

with a 20% deviation maximum and a 10% average

of the initial (i.e. exact) value. This means that each

initial (i.e. exact) value can be modiﬁed up to ±20%.

Table 2 gathers theoretical and neural PCS be-

haviours in the presence of perturbated information.

The set of representative initial (exact) values being

perturbated, the TPCS produces deviations from the

exact measurements. The neural CPCS uses pertur-

bated training information randomly generated. Each

deviation is calculated from the exact initial values.

As table 2 states, both theoretical and neural PCS

show they limits as some predicted measurements are

unacceptable. This is due to the fact that perturbations

GLYCAEMIA REGULATION PREDICTIVE CONTROL SYSTEMS PERFORMANCES EVALUATION - A

Comparative Study of Neural and Mathematical Models

527

Table 2: Deviations for theoretical and neural PCS from ex-

pected compensations (with original non perturbated data)

using perturbated training data and 3000 epochs.

TPCS and neural Th. Training data

CPCS deviations PCS 50 100 200

Carbo- Average 0 0 0 0

hydrates Max 2 4 4 4

Insulin

Average 1.12 1.10 0.95 1.10

Max 3.29 3.22 1.84 3.20

on initial values introduce a dynamic modiﬁcation of

the initial sensitivity to insulin which cannot be mod-

elled by the TPCS: the mathematical formulaes lead

to generate errors proportional to the deviation intro-

duced by the perturbation. On the contrary, the neural

CPCS, thanks to its neural predictor, demonstrates its

ability to suggest more acceptable evaluations.

Once again, the neural CPCS trained with 100

data seems to provide the best measurements: in this

case, the maximum insulin deviation is divided by

a factor of 1.8 between the TPCS and the neural

CPCS. The results of table 2 demonstrate that the neu-

ral CPCS suggests either comparable or more accu-

rate values than the TPCS. The neural CPCS is able

to genealize an average compensation function from

perturbated training data and give good approxima-

tions, whereas the TPCS is more rigid. The neural

CPCS ability to approximate the compensation func-

tion even when perturbated data are used is mostly

due to the training process tuning (in terms of num-

ber of training data and maximum number of epochs)

which reduces the noise generated by perturbations

on training data.

4 CONCLUSIONS

An adaptive GPCS has been proposed. Theoretical

and neural variants of this global system (TPCS and

neural CPCS, respectively) have been presented and

compared using both exact and up to 20% perturbated

data. Each datum is randomly generated, though con-

forming to the theoretical model proposed by (Char-

pentier et al., 2005). As a result, the neural approach

appeared to be accurate and adaptable to each pa-

tient’s reaction to insulin and glucose. This study

highlights that NPC techniques provide similar mea-

surement to empirical models and are able to handle

perturbations. The main drawback of NPC lies in the

amount of training data required to perform an ac-

ceptable training. This can be problematic when the

system does not have access to enough information.

Use of predetermined ANN based on a type 1 diabetes

database is investigated.

Compared with other type 1 diabetes closed-loop

control systems in the literature (Takahashi et al.,

2008), the Global PCS architecture is highly modu-

lar thanks to programming interfaces which allow to

deﬁne its effective behaviour.

Although this study demonstrated that the neu-

ral predictor provides acceptable glycaemia devia-

tions, complementary work is still necessary to eval-

uate other ANN conﬁgurations and activation func-

tions. The neural CPCS can be used “as is”. How-

ever, further testing is needed in case of meals recov-

ery (which occurs when a patient eats while the previ-

ous meal short-term insulin has not fully taken effect).

Long-term insulin regulation is currently left for fu-

ture works as the corresponding controlled and math-

ematical models are much more complex due to the

combined short-term and long-term insulin effects.

Future works will also concern the deﬁnition of train-

ing data selection heuristics. These heuristics will be

used to retain the most relevant training information

and leave unnecessary information out.

Finally, similar experiments could also be pro-

posed on systems which make use of Support Vector

Machine (SVN) techniques in place of ANN.

ACKNOWLEDGEMENTS

Jointly to the University of Technology of Belfort-

Montbeliard (UTBM), France, this work is supported

by the European Center for Diabetes Studies, Stras-

bourg, France and The ACTIMAGE Group, France.

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