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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">A Survey of Insulin-Dependent Diabetes—Part II: Control Methods</title><author><name sortKey="Takahashi, Daisuke" sort="Takahashi, Daisuke" uniqKey="Takahashi D" first="Daisuke" last="Takahashi">Daisuke Takahashi</name><affiliation><nlm:aff id="I1">Department of Computer Science, The University of Alabama, Tuscaloosa, AL 35487, USA</nlm:aff></affiliation></author><author><name sortKey="Xiao, Yang" sort="Xiao, Yang" uniqKey="Xiao Y" first="Yang" last="Xiao">Yang Xiao</name><affiliation><nlm:aff id="I1">Department of Computer Science, The University of Alabama, Tuscaloosa, AL 35487, USA</nlm:aff></affiliation></author><author><name sortKey="Hu, Fei" sort="Hu, Fei" uniqKey="Hu F" first="Fei" last="Hu">Fei Hu</name><affiliation><nlm:aff id="I2">Computer Engineering Department, Rochester Institute of Technology, Rochester, NY 14623, USA</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">18566688</idno><idno type="pmc">2430031</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2430031</idno><idno type="RBID">PMC:2430031</idno><idno type="doi">10.1155/2008/739385</idno><date when="2008">2008</date><idno type="wicri:Area/Pmc/Corpus">000606</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000606</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">A Survey of Insulin-Dependent Diabetes—Part II: Control Methods</title><author><name sortKey="Takahashi, Daisuke" sort="Takahashi, Daisuke" uniqKey="Takahashi D" first="Daisuke" last="Takahashi">Daisuke Takahashi</name><affiliation><nlm:aff id="I1">Department of Computer Science, The University of Alabama, Tuscaloosa, AL 35487, USA</nlm:aff></affiliation></author><author><name sortKey="Xiao, Yang" sort="Xiao, Yang" uniqKey="Xiao Y" first="Yang" last="Xiao">Yang Xiao</name><affiliation><nlm:aff id="I1">Department of Computer Science, The University of Alabama, Tuscaloosa, AL 35487, USA</nlm:aff></affiliation></author><author><name sortKey="Hu, Fei" sort="Hu, Fei" uniqKey="Hu F" first="Fei" last="Hu">Fei Hu</name><affiliation><nlm:aff id="I2">Computer Engineering Department, Rochester Institute of Technology, Rochester, NY 14623, USA</nlm:aff></affiliation></author></analytic><series><title level="j">International Journal of Telemedicine and Applications</title><idno type="ISSN">1687-6415</idno><idno type="eISSN">1687-6423</idno><imprint><date when="2008">2008</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>We survey blood glucose control schemes for insulin-dependent diabetes therapies and systems. These schemes largely rely on mathematical models of the insulin-glucose relations, and these models are typically derived in an empirical or fundamental way. In an empirical way, the experimental insulin inputs and resulting blood-glucose outputs are used to generate a mathematical model, which includes a couple of equations approximating a very complex system. On the other hand, the insulin-glucose relation is also explained from the well-known facts of other biological mechanisms. Since these mechanisms are more or less related with each other, a mathematical model of the insulin-glucose system can be derived from these surrounding relations. This kind of method of the mathematical model derivation is called a fundamental method. Along with several mathematical models, researchers develop autonomous systems whether they involve medical devices or not to compensate metabolic disorders and these autonomous systems employ their own control methods. Basically, in insulin-dependent diabetes therapies, control methods are classified into three categories: open-loop, closed-loop, and partially closed-loop controls. The main difference among these methods is how much the systems are open to the outside people.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct></listBibl></div1></back></TEI><pmc article-type="review-article" xml:lang="EN"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Int J Telemed Appl</journal-id><journal-id journal-id-type="publisher-id">IJTA</journal-id><journal-title>International Journal of Telemedicine and Applications</journal-title><issn pub-type="ppub">1687-6415</issn><issn pub-type="epub">1687-6423</issn><publisher><publisher-name>Hindawi Publishing Corporation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">18566688</article-id><article-id pub-id-type="pmc">2430031</article-id><article-id pub-id-type="doi">10.1155/2008/739385</article-id><article-categories><subj-group subj-group-type="heading"><subject>Review Article</subject></subj-group></article-categories><title-group><article-title>A Survey of Insulin-Dependent Diabetes—Part II: Control Methods</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Takahashi</surname><given-names>Daisuke</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Xiao</surname><given-names>Yang</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref><xref ref-type="corresp" rid="cor1">*</xref></contrib><contrib contrib-type="author"><name><surname>Hu</surname><given-names>Fei</given-names></name><xref ref-type="aff" rid="I2"><sup>2</sup></xref></contrib></contrib-group><aff id="I1"><sup>1</sup>Department of Computer Science, The University of Alabama, Tuscaloosa, AL 35487, USA</aff><aff id="I2"><sup>2</sup>Computer Engineering Department, Rochester Institute of Technology, Rochester, NY 14623, USA</aff><author-notes><corresp id="cor1">*Yang Xiao: <email>yangxiao@ieee.org</email></corresp><fn fn-type="other"><p>Recommended by Jelena Misic</p></fn></author-notes><pub-date pub-type="ppub"><year>2008</year></pub-date><pub-date pub-type="epub"><day>12</day><month>6</month><year>2008</year></pub-date><volume>2008</volume><elocation-id>739385</elocation-id><history><date date-type="received"><day>26</day><month>12</month><year>2007</year></date><date date-type="accepted"><day>22</day><month>3</month><year>2008</year></date></history><permissions><copyright-statement>Copyright © 2008 Daisuke Takahashi et al.</copyright-statement><copyright-year>2008</copyright-year><license license-type="open-access"><p>This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</p></license></permissions><abstract><p>We survey blood glucose control schemes for insulin-dependent diabetes therapies and systems. These schemes largely rely on mathematical models of the insulin-glucose relations, and these models are typically derived in an empirical or fundamental way. In an empirical way, the experimental insulin inputs and resulting blood-glucose outputs are used to generate a mathematical model, which includes a couple of equations approximating a very complex system. On the other hand, the insulin-glucose relation is also explained from the well-known facts of other biological mechanisms. Since these mechanisms are more or less related with each other, a mathematical model of the insulin-glucose system can be derived from these surrounding relations. This kind of method of the mathematical model derivation is called a fundamental method. Along with several mathematical models, researchers develop autonomous systems whether they involve medical devices or not to compensate metabolic disorders and these autonomous systems employ their own control methods. Basically, in insulin-dependent diabetes therapies, control methods are classified into three categories: open-loop, closed-loop, and partially closed-loop controls. The main difference among these methods is how much the systems are open to the outside people.</p></abstract></article-meta></front><body><sec sec-type="section" id="sec1"><title>1. INTRODUCTION</title><p>Complexity of a human
biological system typically allows its relations to be expressed only in a
nonlinear way. Because of this complexity, it is not simple to achieve insulin-dependent
diabetic therapies autonomously. Diabetes mellitus is a metabolic disorder of
endogenous insulin allowing excessive amount of glucose to stay in blood. In
general, blood glucose is transformed into energy required by human activities,
such as, walking, and this transformation requires insulin functionality. However,
in diabetes mellitus, since a human body fully or partially lacks the insulin
functionality, unchanged glucose remains in blood. A condition of high blood
glucose profiles results in several complications, such as, eye, kidney, and
nerve damage, called hyperglycemia [<xref ref-type="bibr" rid="B46">1</xref>]. Thus, in order to avoid the
hyperglycemia, a continuous supply of exogenous insulin is required, and the
insulin-dependent diabetic therapy usually does this. On the contrary, too much
insulin supply may lead to a condition of low blood glucose profiles resulting
in drowsiness, mental malfunctioning, irritability, and loss of consciousness
[<xref ref-type="bibr" rid="B46">1</xref>]. This condition is called hypoglycemia and also dangerous to the diabetic.
Thus, the insulin-dependent diabetic therapy must concern both hyperglycemia
and hypoglycemia by providing an appropriate amount of exogenous insulin timely.</p><p>At the beginning of the insulin-dependent
diabetic therapy, it is required to obtain an approximation of the insulin-glucose
relation. This relation is usually described in a number of mathematical
equations. Two methods are taken in this process, namely, empirical and
fundamental methods. Arguably, this process is most time consuming.</p><p>Based on mathematical equations representing
the insulin-glucose mechanism, therapies are systematically established. Broadly,
controlling the blood glucose levels is achieved by means of three strategies,
namely, open-loop, closed-loop, and partially closed-loop schemes. In general,
the fully and partially closed-loop schemes involves several medical devices
but the open-loop scheme does not. While in the closed-loop scheme, a system is
aimed to completely encompass the diabetic, open- and partially closed-loop
require the physician's contribution to complete the loops. Therefore, typically
any decisions of the insulin injections are made by a physician in open- and
partially closed-loop schemes. We explain these three strategies along with
applications in the later sections.</p><p>This paper is the second part of our
survey of insulin-dependent diabetes. Our first paper [<xref ref-type="bibr" rid="B45">2</xref>], the first part of
the survey, mostly spent its pages on the background of insulin-dependent
diabetes therapy, such as, description of type 1 and type 2 diabetes, the
insulin functionality, and medical devices involved in the insulin-dependent
therapy. In this paper, we survey blood glucose control schemes which lie on
the basics of the insulin-dependent diabetes therapies and systems.</p><p>The rest of the paper is organized as
follows. In <xref ref-type="sec" rid="sec2">Section 2</xref>, we briefly summarize diabetes mellitus for the sake of
induction to the topic. In <xref ref-type="sec" rid="sec3">Section 3</xref>, we explain empirical and fundamental
schemes to derive mathematical models of the insulin-glucose dynamics. From Sections
<xref ref-type="sec" rid="sec4">4</xref> through <xref ref-type="sec" rid="sec6">6</xref>, we explore the control strategies, especially for the insulin-glucose
dynamics. In these sections, we provide several applications based on the
controls. Finally, we conclude this survey in <xref ref-type="sec" rid="sec7">Section 7</xref>.</p></sec><sec sec-type="section" id="sec2"><title>2. TYPE 1 AND TYPE 2 DIABETES</title><p>The World Health Organization (WHO)
reported that there were currently nearly 180 million patients suffering from
diabetes allover the world, and the number of the diabetics would increase more
than 350 million people by 2030 [<xref ref-type="bibr" rid="B23">3</xref>]. From the same report, approximately 1.1
million people died from diabetes in 2005 and among this number, people under
70 years old account for a half [<xref ref-type="bibr" rid="B23">3</xref>]. In the United States, currently
it costs 136 billion dollars annually to take care of 12 million diabetes patients [<xref ref-type="bibr" rid="B20">4</xref>, <xref ref-type="bibr" rid="B24">5</xref>]. In general, diabetes is considered as a condition that disproportionately
affects developed countries.</p><p>Diabetes first emerged around 2000 B.C. while insulin and its functionality were discovered in 1921. Since the
discovery of insulin, insulin-dependent diabetes therapies mostly concern how
to delay the emergence of the complications in use of insulin supplement [<xref ref-type="bibr" rid="B15">6</xref>, <xref ref-type="bibr" rid="B16">7</xref>].
In short, diabetes is characterized in a condition that blood keeps high
glucose levels unchanged into energy resulting in several complications.
Although insulin is largely concerned with this reaction, diabetes fully or
partially lacks this functionality [<xref ref-type="bibr" rid="B6">8</xref>]. Diabetes eventually causes cardiovascular
disease, chronic renal failure, retinal damage, nerve damage, and microvascular damage.</p><p>Besides, according to characteristics of
diabetes, it is typically classified into two types, namely, type 1 and type 2
diabetes [<xref ref-type="bibr" rid="B6">8</xref>]. In short, in type 1 diabetes, from the malfunction of the
pancreas resulting from the destruction of the <italic>β</italic> cells of the Islets of
Langerhans, a supply of endogenous insulin completely stops. This requires
other sources of insulin supplementation. Otherwise, the diabetic eventually
falls into a condition of hyperglycemia. On the other hand, in type 2 diabetes,
the insulin functionality gradually weakens, but does not completely stops.
Since the diabetic more or less has the endogenous insulin supply, diabetes
therapies mostly focus on exercises or regimens consuming or suppressing
excessive glucose in blood. However, both type 1 diabetes and type 2 diabetes
are considered chronic and currently incurable.</p><p>As mentioned before, type 1 diabetes
completely stops the insulin supply. This is caused by the malfunction of the
pancreas destroying the <italic>β</italic> cells which are responsible for the endogenous
insulin supply. It is considered a reason why the destruction of the <italic>β</italic> cells
occurs is due to the immune system which should react an infection by viruses,
such as, the Coxsackie virus family or German measles but mistakenly destroys
the <italic>β</italic> cells [<xref ref-type="bibr" rid="B7">9</xref>]. Type 1 diabetes is sometimes called childhood, juvenile or
insulin-dependent diabetes although it does not only emerge during a childhood
[<xref ref-type="bibr" rid="B7">9</xref>].</p><p>On the other hand, type 2 diabetes does
not stop the endogenous insulin supply, but instead it is characterized in
insulin resistance, insulin deficiency, and hyperglycemia [<xref ref-type="bibr" rid="B8">10</xref>]. Although in type
2 diabetes, endogenous insulin still can facilitate its functionality, it is
largely degraded and cannot sufficiently change blood glucose into energy [<xref ref-type="bibr" rid="B13">11</xref>].
Thus, the amount of unchanged blood glucose will get larger resulting in
hyperglycemia, a condition of high blood glucose profiles, causing eye, kidney,
and nerve damage [<xref ref-type="bibr" rid="B14">12</xref>]. However, since in the early stage of type 2 diabetes,
the symptoms are not serious or noticeable, it is likely to miss its emergence
easily. This causes the diabetes more serious and critical. Type 2 diabetes is
sometimes inherited genetically, but in most of the cases it caused from
irregular life styles, such as, the lack of exercise, obesity or a sedentary
lifestyle [<xref ref-type="bibr" rid="B8">10</xref>]. Type 2 diabetes is also called non-insulin-dependent, obesity-related,
or adult-onset diabetes.</p><p>Currently, diabetes can be treated at
home by a patient himself or herself under the supervision of a physician.
During the earlier years of the diabetes treatment, logs and tables of insulin
injections and regimens were kept, and according to these records next insulin
injections and regimens as well as exercises are determined by a physician. Now,
microcontrollers and sensors enable autonomous insulin-dependent diabetes
therapies systematically adjusting the insulin supply. More precisely,
according to feedback from one or more blood glucose sensors, a rate of insulin
supply of an insulin pump is determined, which works like an “artificial
pancreas.” The advantages of an “artificial pancreas” are safe, automatic, and
nonintrusive. Several control schemes are developed in order to achieve the
optimal exogenous insulin supply suppressing the blood glucose levels within a
safe range of nominal. For more details about diabetes fundamentals, please
refer our first paper in [<xref ref-type="bibr" rid="B45">2</xref>].</p></sec><sec sec-type="section" id="sec3"><title>3. MODELING THE HUMAN INSULIN-GLUCOSE SYSTEM</title><p>To procure the mathematical models of
the human insulin-glucose system, several approaches are taken by researchers. In
these approaches, empirical and fundamental methods are preferably used by
them. These approaches aim to describe the insulin-glucose dynamics as a couple
of mathematical equations that should be easy to manipulate for the insulin
therapies and should fully describe the characteristics of the internal
insulin-glucose metabolism [<xref ref-type="bibr" rid="B17">13</xref>].</p><p>Basically, the empirical method uses a
model structure (formula or equation) which is determined theoretically with
several parameters. The behavior of this model structure is determined by only
the input-output data of the system from a number of experiments [<xref ref-type="bibr" rid="B17">13</xref>]. In this
method, capturing the system behavior or data is the most time-consuming
process. In an example of the linear structure of the insulin-glucose system, to
represent glucose effects, two parameters are used, and to represent insulin
effects, other two parameters are also used in order to close the model to the
actual system [<xref ref-type="bibr" rid="B17">13</xref>]. In addition to the input-output data, semiempirical method
utilizes other physiological factors, such as dynamic behavior and kinetics to
create a closer model of diabetic patients [<xref ref-type="bibr" rid="B17">13</xref>].</p><p>In the fundamental methods, a
mathematical representation of the human internal system which is already known
sufficiently by researchers constructs an insulin-glucose model. This system
behavior includes kinetics and material transport [<xref ref-type="bibr" rid="B17">13</xref>]. According to
investigating the internal system, a lot of data from the literature can be
used to determine the system parameters. Usually the model averages studied
behaviors. In particular, in constructing a fundamental diabetes model, the
authors in [<xref ref-type="bibr" rid="B18">14</xref>] applied the insulin-release data of the <italic>β</italic> cells of the pancreas
from a number of examinations to a mathematical representation.</p></sec><sec sec-type="section" id="sec4"><title>4. OPEN-LOOP CONTROL MODELS</title><p>Arguably, the most complex component of blood glucose management is the control domain. There
are several classes of solutions to this problem, ranging in complexity, prerequisite
knowledge, and feedback.</p><p>The open-loop system for the insulin-dependent diabetes therapy does not employ any
glucose sensors. However, occasionally calling the “open-loop” system is not appropriate
and more precisely, the system should be called the “programmed” insulin
infusion system because of its incomplete openness. That is, the control loop
can be closed by the physician and the diabetic when interacting on the system
[<xref ref-type="bibr" rid="B26">15</xref>].</p><p>One example of the systems is one that was developed by Case-Western Reserve University, and
this system is considered to be one of the most intelligent programmed insulin
infusion products that deal with the noninsulin-dependent diabetics [<xref ref-type="bibr" rid="B26">15</xref>]. The
idea is that from an analysis of the insulin curve in the nondiabetic, it was
turned out that the curve approximately traces a combination of a double
exponential curve and a basal insulin infusion [<xref ref-type="bibr" rid="B26">15</xref>]. According to this
mathematical model, an intravenous insulin delivery system was designed such that
it followed the real pancreas functionality of the nondiabetic. The system
utilized a portable cart containing the control system, the insulin-pump, power
supplies, and insulin reservoir so that the patient could move around with the
devices. The insulin pump delivers low-concentration insulin and updates the
insulin delivery rate every 30 seconds. Because of its simplicity, the system
can be set up and operated by nurses [<xref ref-type="bibr" rid="B26">15</xref>].</p><p>This research revealed the diabetics had the blood glucose profile to be improved
considerably from a two-week examination, and, moreover, the improved
conditions remained even several days after the examination. On the other hand,
the researches of this programmed system so far did not indicate any
hypocglycemic condition yet [<xref ref-type="bibr" rid="B26">15</xref>].</p><p>In addition to the achievement of Case-Western Reserve University, Siemens and the Finsen
Institute also developed a programmed insulin infusion
system that employed a moderately complex delivery algorithm from another
approach. The system is capable of manually inserting small pin connectors into
the control unit in order to control the insulin delivery rate. Like a product
of Case-Western Reserve University, the infusion rate follows an exponential curve, and the
insulin infusion rate is updated every 30 minutes [<xref ref-type="bibr" rid="B26">15</xref>–<xref ref-type="bibr" rid="B29">18</xref>].</p></sec><sec sec-type="section" id="sec5"><title>5. CLOSED-LOOP CONTROL MODELS</title><p>The system to deliver insulin mechanically in order to regulate the glycemic
profile is called the “closed-loop” system [<xref ref-type="bibr" rid="B26">15</xref>]. As shown in <xref ref-type="fig" rid="fig1">Figure 1</xref>, the
closed-loop system completes its operating cycle within the system and no
external interaction to diabetic patients
is required [<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B5">20</xref>]. In other words, the closed-loop control uses the feedback
from the output. Typically, the closed-loop system for type 1 diabetes therapy utilizes the glucose sensor and schematically consists
of three phases: blood glucose measurements, insulin demand calculation, and
insulin injection. The closed-loop system repeats this sequence. So far, along with the glucose sensor, the
closed-loop system also employs an insulin pump which continuously
infuses insulin via a subcutaneous root.</p><p>Basically, insulin delivery is controlled by these implanted blood glucose sensors and an insulin pump
attached to a patient's body [<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B2">21</xref>–<xref ref-type="bibr" rid="B4">23</xref>]. In short, according to measurements
of glucose level from an implanted blood glucose sensor, an insulin pump
continuously infuses insulin into a patient's body. However, although implanted
blood glucose sensors benefit a lot for the diabetes therapy, establishing
reliable measurements of blood glucose is so difficult that many researches in
this field are still under way by many biomedical researchers [<xref ref-type="bibr" rid="B1">19</xref>]. <xref ref-type="fig" rid="fig1">Figure 1</xref> shows
a control flow of a closed-loop strategy.</p><p>Currently many forms of blood glucose sensors exist, such as fingerstick types, implantable types, or noninvasive
types. For example, in applying a fingerstick-type blood glucose sensor, blood
glucose levels are measured three to seven times a day and according to the
measurements, the amount of insulin supply by an insulin pump is updated
manually. However, since with the fingerstick-type sensors, measurements are
carried out by patients themselves on regular basis, managing patient lifestyle
by themselves is rather troublesome. Meanwhile, when using an implantable blood
glucose sensor, glucose levels in blood are automatically monitored in a
certain amount of period.</p><p>In calculating the insulin infusion, many control models are developed by researchers until now: pole-assignment
strategy, self-tuning adaptive control, or nonlinear predictive control [<xref ref-type="bibr" rid="B1">19</xref>].
More details about these schemes are explained in the later subsections.</p><sec sec-type="subsection" id="subsec5.1"><title>5.1. Pole-assignment strategy</title><p>Pole assignment is a standard control
systems technique for designing an infinite impulse response filter [<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B41">24</xref>].
This consists of a set of filter coefficients and a feedback loop in order to
maintain a stable blood glucose level.</p><p>In general, the closed-loop schemes of the
insulin-dependent diabetes therapy utilize an insulin pump that automatically
supplies insulin into the human body subcutaneously [<xref ref-type="bibr" rid="B1">19</xref>]. Usually the glucose
levels are monitored by a needle-type glucose sensor through the subcutaneous (SC)
route, and the insulin infusion rate (IIR) is determined by continuous measurements
of the blood glucose level. For example, in pole-assignment strategy [<xref ref-type="bibr" rid="B2">21</xref>], the
IIR in relation to blood glucose level, the insulin-glucose system, is
determined by the following computation:
<disp-formula id="sd1"><label>(1)</label><mml:math id="M1"><mml:mrow><mml:mtable width="auto" columnalign="left"><mml:mtr><mml:mtd><mml:mtext>IIR</mml:mtext><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>with</mml:mtext></mml:mtd><mml:mtd></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>a</mml:mi><mml:mi>m</mml:mi><mml:mi>n</mml:mi><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mi>d</mml:mi><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mfrac><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></disp-formula> where <italic>G</italic> is blood glucose level and <italic>d</italic> is the insulin infusion rate through
the intravenous (IV) route. Parameters <italic>a</italic>, <italic>b</italic>, and <italic>c</italic> can be
calculated from the relationship between plasma insulin <italic>I</italic> and blood glucose levels in a normal person, which are written as<disp-formula id="sd2"><label>(2)</label><mml:math id="M2"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula> Moreover, other parameters <italic>n</italic> and <italic>l</italic> are from next equations which are the pharmacokinetics of insulin
infusion through the SC route:<disp-formula id="sd3"><label>(3)</label><mml:math id="M3"><mml:mrow><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mtext>IIR</mml:mtext><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:mi>l</mml:mi><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mi>l</mml:mi><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>o</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>Z</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mi>p</mml:mi><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mi>n</mml:mi><mml:mi>Z</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>Z</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>V</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></disp-formula> where <italic>X</italic>, <italic>Y</italic>, and <italic>Z</italic> represent the insulin level in the two subcutaneous compartments and in the
plasma, respectively. <xref ref-type="fig" rid="fig2">Figure 2</xref> shows such an <italic>X/Y/Z</italic> 3-level model.</p><p>At last, <italic>m</italic> is calculated as <italic>m</italic> = <italic>p</italic> + <italic>o</italic> [<xref ref-type="bibr" rid="B1">19</xref>].</p><p>This is a simplified approach, forgoing
adaptive control for ease of characterization and implementation. For most
situations, it will perform as desired, but if it encounters a situation that
it handles poorly, it will handle that situation poorly every time it occurs
again in the future.</p><p>Experiments showed that the combination
of the pole-assignment strategy and Lispro insulin generated a similar trend to
the use of the IV route with regular insulin [<xref ref-type="bibr" rid="B1">19</xref>]. However, the combination of
the pole-assignment strategy and regular insulin generated much worse result.</p></sec><sec sec-type="subsection" id="subsec5.2"><title>5.2. Self-tuning adaptive control</title><p>A difficulty of the pole-assignment
strategy is to repeatedly evaluate model parameters in each computation of the
IIR [<xref ref-type="bibr" rid="B1">19</xref>]. To avoid re-evaluations of the model parameters, the self-tuning
adaptive control closed-loop scheme employs a recursive assessment of the model
parameters so that the glucose level of time period <italic>k</italic>, that is, <italic>G</italic><sub><italic>k</italic></sub>, is
evaluated from the glucose levels of time period <italic>k</italic> − 1 through <italic>k</italic> − <italic>h</italic>, that is, {<italic>G</italic><sub><italic>k</italic>−1</sub>,…, <italic>G</italic><sub><italic>k</italic>−<italic>h</italic></sub>}, and the insulin doses of time
period <italic>k</italic> − 1 through <italic>k</italic> − <italic>p</italic>, {<italic>I</italic><italic>D</italic><sub><italic>k</italic>−1</sub>, <italic>I</italic><italic>D</italic><sub><italic>k</italic>−<italic>p</italic></sub>}, as
well as some unknown parameters Θ, which can be written as [<xref ref-type="bibr" rid="B9">25</xref>–<xref ref-type="bibr" rid="B12">28</xref>]<disp-formula id="sd4"><label>(4)</label><mml:math id="M4"><mml:mrow><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>M</mml:mi><mml:mrow><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo minsize="1em" maxsize="1em">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula> where <italic>p</italic> and <italic>h</italic> are time delays. Since this method evaluates the blood glucose
level of time period <italic>k</italic> from the
previous evaluations and insulin doses, it can efficiently eliminate unnecessary
re-evaluations of the model parameters.</p><p>Besides, according to glucose level <italic>G</italic><sub><italic>k</italic></sub>, the next insulin dose is calculated as<disp-formula id="sd5"><label>(5)</label><mml:math id="M5"><mml:mrow><mml:mi>J</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo minsize="1em" maxsize="1em">)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mi>r</mml:mi><mml:msub><mml:mrow><mml:mi>I</mml:mi><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula> such that <italic>I</italic><italic>D</italic><sub><italic>k</italic></sub> can minimize value <italic>J</italic>, where <italic>r</italic> is a weighting
factor designed to control the amount of insulin dose.</p><p>Implementation of self-tuning adaptive
control, shown in <xref ref-type="fig" rid="fig3">Figure 3</xref>, is quite similar to pole-assignment control, as it
uses the same system modeling equations in order to compute the insulin
infusion rate [<xref ref-type="bibr" rid="B1">19</xref>].</p><p>The primary difference between the two
methods is that another controller is used to constantly evaluate the system
model, and may “tune” or redesign the PD controller parameters as needed to
obtain more accurate results based upon minimum variance.</p><p>One advantage of this control scheme is
that it is comparatively easy for a physician to estimate the future trend of
blood glucose levels from a set of the past inputs, where the model can be used
to predict hypoglycemic or hyperglycemic events before they occur [<xref ref-type="bibr" rid="B17">13</xref>].</p></sec><sec sec-type="subsection" id="subsec5.3"><title>5.3. Model predictive control</title><p>A model predictive control (MPC), or
nonlinear predictive control (NLPC) algorithm attempts to “learn” what nominal
means in a system [<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B5">20</xref>], shown in <xref ref-type="fig" rid="fig4">Figure 4</xref>. In the case of blood glucose management,
a nonlinear MPC algorithm uses sensor data to track glycoregulatory system
parameters in order to predict the levels of required insulin infusions. It
then uses models of the human glucose metabolism to estimate the effects of the
insulin injection. An example of a model used is a nonlinear autoregressive
(NARX) model, where previous blood glucose (BG) levels and insulin dosage
levels are run through a nonlinear function, often obtained through neural
network learning.</p><p>Bayesian learning is applied using the
model-predicted effect of the insulin, and its actual measured effect. The
learning process adjusts system parameters in order to increase the accuracy of
its predictions as more iterations are performed. Using this method, the system
will become increasingly accurate, and will begin to “understand” how the
patient that it is calibrated to will react to insulin injections of varying
compositions and strengths.</p></sec><sec sec-type="subsection" id="subsec5.4"><title>5.4. Nonlinear predictive control (neural predictive control)</title><p>Apparently, the insulin-glucose system is complicated, and the system is considered to be nonlinear
[<xref ref-type="bibr" rid="B39">29</xref>]. In [<xref ref-type="bibr" rid="B38">30</xref>], in order to follow this nonlinearity, one method utilizes a
collaboration of a neural network (NN) and nonlinear model predictive control
(NPC) technique, that is, neural predictive control. More precisely, NNs and an
NPC are used to simulate the glucoregulatory system. A schematic diagram of the
neural predictive control is shown in <xref ref-type="fig" rid="fig5">Figure 5</xref>.</p><p>Basically NNs approach the problem of blood glucose management without attempting to
explicitly describe the exact model of the blood glucose-insulin system [<xref ref-type="bibr" rid="B42">31</xref>–<xref ref-type="bibr" rid="B44">33</xref>]. This is particularly useful in situations where patients have a disease
that complicates normal model description, or an abnormality exists which makes
prediction difficult using just measured parameters and sensor data.</p><p>Like other control strategies, the main goal of the neural predictive control is to
achieve regulation of the glucose profiles for the type 1 diabetics predicting
a future glucose curve from the nonlinear model with time delays, so it can
follow a similar curve to the metabolism of normal people. A feed forward
neural network employing backpropagation can be trained offline using
accumulated patient data, including daily blood glucose readings as well as
insulin dosages. A neural network will then be able to “learn” based upon
experience, much as a human brain learns. This will help it to predict
nonlinear behavior, even multiple orders removed, imperceptible to standard
data interpretation methods. This capability to be “intuitive” helps to drive a
system in which unknowns or immeasurable parameters are still accounted for,
and abnormalities are detected and intelligently handled.</p><p>The neural predictive control reveals several physiological variables to be
controlled. In addition to the control variables, it also designs a cost
function in relation to the insulin-glucose model [<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B38">30</xref>].</p><p>In the mechanism of the scheme, the neural predictive control makes consecutive
control actions toward the glucose metabolism altering the control variables,
so that the actions consequently minimize a designed cost function at each
sampling time. However, the alteration of the control variables also changes
the optimization problem at each sampling time. On the other hand, the model
and its parameters can be of no difference during a whole examination [<xref ref-type="bibr" rid="B1">19</xref>].</p><p>Fortunately, in order to regulate the glucose profile, the so-called monomeric insulin (MI)
analogs are currently available. These MI analogs have advantages that they are
able to be absorbed through the subcutaneous route three or four times faster
than human insulin resulting in that the rise of the plasma insulin
concentration grows faster. Besides, the MI analogs are more predicable than
human insulin due to its less variability [<xref ref-type="bibr" rid="B38">30</xref>].</p><p>In the forming of the control strategy, [<xref ref-type="bibr" rid="B38">30</xref>] first develops a mathematical model
of the insulin-glucose dynamics of the type 1 diabetics, which is mainly broken
down into three parts: the subcutaneous insulin absorption model, glucose
regulation model, and subcutaneous glucose model, shown in <xref ref-type="fig" rid="fig6">Figure 6</xref>. From the
model, the subcutaneous insulin absorption is calculated in two steps: the
subcutaneous MI analogs infusion and utilization from the subcutaneous depot [<xref ref-type="bibr" rid="B40">34</xref>].
With respect to the glucose regulation, in order to model the system
mathematically, [<xref ref-type="bibr" rid="B38">30</xref>] adopts a compartmental model in which there are single
compartments for glucose and glucagon, and three compartments for insulin
(liver and portal insulin, plasma insulin, and insulin in the interstitial
fluid). Also in the model, net hepatic glucose balance, renal glucose excretion,
and glucose utilization are simulated to generate numerical values. From the
glucose regulation model, the subcutaneous glucose model is generated by investigating
transfer rates between the plasma and subcutaneous compartments. Consequently,
the subcutaneous glucose model forms a linear, first-order system with the
transfer function [<xref ref-type="bibr" rid="B38">30</xref>].</p><p>In the second step, using numerical data from simulations of the mathematical patient
model, the paper [<xref ref-type="bibr" rid="B38">30</xref>] develops the nonlinear system by NNs in order to make
future blood glucose predictions. To do this, the paper [<xref ref-type="bibr" rid="B38">30</xref>] utilizes a
nonlinear autoregressive model (NARX) because of its popularity and usefulness.
The form is described as<disp-formula id="sd6"><label>(6)</label><mml:math id="M6"><mml:mrow><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo minsize="1em" maxsize="1em">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi></mml:mi></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>I</mml:mi><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>I</mml:mi><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo minsize="1em" maxsize="1em">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></disp-formula> where <italic>G</italic> is a sequence of subcutaneous glucose
profiles, especially <italic>G</italic><sub><italic>k</italic></sub> is
a future glucose prediction, <italic>ID</italic> is a
sequence of subcutaneous insulin infusion rates, <italic>e</italic><sub><italic>k</italic></sub> is a noise, and <italic>n</italic><sub><italic>y</italic></sub> and <italic>n</italic><sub><italic>u</italic></sub> are both durations
of glucose utilization and insulin activation, respectively.</p><p>At this point, however, the
approximation of the nonlinear function <italic>f</italic> is a hard task. A reason why to approximate the nonlinear function is difficult
is that the function is required to be made up from finite data although there
are usually infinite solutions for it. To resolve this difficulty,
approximation based on regularization techniques is used because it was proved
that regularization principles consequently can derive networks with one layer
of hidden units, that is, regularization networks [<xref ref-type="bibr" rid="B38">30</xref>]. Thus, the paper [<xref ref-type="bibr" rid="B38">30</xref>]
uses a function of radial basis function (RBF) networks, which are a subclass
of regularization networks, in order to represent the nonlinear function <italic>f</italic> :<disp-formula id="sd7"><label>(7)</label><mml:math id="M7"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mi>f</mml:mi><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo minsize="1em" maxsize="1em">)</mml:mo></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mstyle><mml:mrow><mml:munderover><mml:mrow><mml:mstyle displaystyle="true"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow></mml:mstyle></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:mrow><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mi>H</mml:mi><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:mo minsize="1em" maxsize="1em">∥</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo minsize="1em" maxsize="1em">∥</mml:mo><mml:mo minsize="1em" maxsize="1em">)</mml:mo></mml:mrow></mml:mrow></mml:mstyle><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>H</mml:mi><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:mrow><mml:mo minsize="1em" maxsize="1em">∥</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo minsize="1em" maxsize="1em">∥</mml:mo></mml:mrow><mml:mo minsize="1em" maxsize="1em">)</mml:mo></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mo minsize="1.25em" maxsize="1.25em">(</mml:mo><mml:msup><mml:mrow><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:msubsup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo minsize="1em" maxsize="1em">)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>β</mml:mi><mml:mo minsize="1.25em" maxsize="1.25em">)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></disp-formula> where <italic>H</italic> is a continuous function of <bold>R</bold><sup>+</sup>→<bold>R</bold>, || ||, represents the
Euclidean norm, <italic>x</italic><sub><italic>i</italic></sub><sup>0</sup> are some proper center values selected from the data points, <italic>w</italic><sub><italic>i</italic></sub> are some weight constants, and <italic>β</italic> is a parameter representing the dispersion [<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B38">30</xref>]. Also the regularized orthogonal least squares (ROLSs) algorithm is
used to determine RBF weights and centers in order for <italic>f</italic>(<italic>x</italic>(<italic>t</italic>)) to fit the data under some constraints [<xref ref-type="bibr" rid="B1">19</xref>].</p><p>The third step to model the control
scheme is to design an NPC [<xref ref-type="bibr" rid="B38">30</xref>]. To do this, the moving horizon approach is
used to obtain the control law. Thus, eventually controlling the glucose
profiles is turned into resolving the minimization problem where a sequence of
subcutaneous insulin infusions must sufficiently minimize the problem below<disp-formula id="sd8"><label>(8)</label><mml:math id="M8"><mml:mrow><mml:mi>arg</mml:mi><mml:mo></mml:mo><mml:munder><mml:mrow><mml:mi>min</mml:mi><mml:mo></mml:mo></mml:mrow><mml:mrow><mml:mi>I</mml:mi><mml:mi>D</mml:mi></mml:mrow></mml:munder><mml:mtext> </mml:mtext><mml:mi>J</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo minsize="1.75em" maxsize="1.75em">[</mml:mo><mml:mrow><mml:mstyle><mml:mrow><mml:munderover><mml:mrow><mml:mstyle displaystyle="true"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow></mml:mstyle></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munderover><mml:mrow><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:msubsup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msubsup><mml:mi>Γ</mml:mi><mml:msub><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo minsize="1em" maxsize="1em">)</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:mrow></mml:mstyle><mml:mstyle><mml:mrow><mml:munderover><mml:mrow><mml:mstyle displaystyle="true"><mml:mrow><mml:mo>∑</mml:mo></mml:mrow></mml:mstyle></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mrow><mml:mi>Δ</mml:mi><mml:mi>I</mml:mi><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mrow><mml:mi>Γ</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi></mml:mrow></mml:msub><mml:mi>Δ</mml:mi><mml:mi>I</mml:mi><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:mrow><mml:mo minsize="1.75em" maxsize="1.75em">]</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula> where <italic>I</italic><italic>D</italic> = [<italic>I</italic><italic>D</italic><sub><italic>k</italic></sub>, <italic>I</italic><italic>D</italic><sub><italic>k</italic>−1</sub>,…, <italic>I</italic><italic>D</italic><sub><italic>k</italic>−<italic>N</italic><sub><italic>c</italic></sub>−1</sub>]<sup><italic>T</italic></sup> and <italic>N</italic><sub><italic>c</italic></sub>, <italic>N</italic><sub><italic>p</italic></sub>, <italic>N</italic><sub>1</sub>, Γ<sub><italic>e</italic></sub>, Γ<sub><italic>u</italic></sub> are parameters of the controller for tuning.</p></sec><sec sec-type="subsection" id="subsec5.5"><title>5.5. Fuzzy control scheme</title><p>A fuzzy control scheme is studied in
[<xref ref-type="bibr" rid="B47">35</xref>]. There are three steps for the process of a fuzzy logic algorithm:
fuzzification, rules, and defuzzification.<list list-type="order"><list-item><p>Fuzzification: the input of a
controller is an exact number, like the concentration of glucose is 100 mg/dl.
What the fuzzification do is to fuzzy the concentration such as low
concentration, high concentration, and proper concentration. Every exact number
has the weight of all these low concentration, high concentration, and proper
concentration.</p></list-item><list-item><p>Rules: after defining the fuzzy
concept of input, rules are made to decide what the output should be: more
drug, a little drug, or no drug.</p></list-item><list-item><p>Defuzzification: after the rule,
the output of fuzzy concept is obtained, for example, more of 0.8 and little of
0.2. But the output which is the object model's input must be an exact number,
that needs to be defuzzification. By defuzzification, the output gets an exact
number.</p></list-item></list></p><p>In the paper [<xref ref-type="bibr" rid="B47">35</xref>], it is assumed that
there are two different inputs of the concentration of glucose and the change
rate of concentration, and one output of the dose of drug. “overlow,” “good,”
“high,” and “overhigh” are defined for the concentration. The rate is
“overlow,” “low,” “high,” and “highest.” The dose of drug is defined as “zero,”
“little,” “norm,” “more,” and “most.” Ten rules are defined such that [<xref ref-type="bibr" rid="B47">35</xref>]:<list list-type="order"><list-item><p>if (rate is overlow), then (dosage
is zero);</p></list-item><list-item><p>if (concentration is overhigh) and
(rate is low), then (dosage is little);</p></list-item><list-item><p>if (concentration is overhigh) and
(rate is highest), then (dosage is most);</p></list-item><list-item><p>and so forth.</p></list-item></list></p></sec></sec><sec sec-type="section" id="sec6"><title>6. PARTIAL CLOSED-LOOP SCHEME</title><p>In a partially closed-loop scheme of the
insulin-dependent diabetes therapy, measurements are conducted three to seven
times per day, and insulin injections are also performed three to four times
under the supervision of a physician. These decisions, for example, the number
and type of insulin injections, insulin dosage [<xref ref-type="bibr" rid="B1">19</xref>], are made according to model-based
or algorithmic-based decision support systems, such as DIAS, AIDA, and T-IDDM
[<xref ref-type="bibr" rid="B1">19</xref>]. Insulin injections are usually performed by using the subcutaneous (SC)
route due to its management and safety. Also there is an alternative route for
insulin delivery that is ideal for control, the intravenous (IV) route.
However, this route is not ideal for the management and safety. <xref ref-type="fig" rid="fig7">Figure 7</xref> shows
a control flow of a partial closed-loop scheme.</p><p>While in the closed-loop systems, the blood glucose levels are automatically monitored by an
implantable sensor and according to the measurements, insulin infusions are
carried out in the use of an insulin pump or three or four times of the insulin
injections, in the partial closed-loop, the metabolic controls partly rely on the
physician's evaluations of the measurements of the blood glucose levels, the
amount of insulin injections and physical exercises as well as glycosuria and
ketonuria [<xref ref-type="bibr" rid="B1">19</xref>]. Moreover, as other metrics of the evaluation, medium period
indicators, such as glycated hemoglobin (HbA1c), are captured, where the blood
glucose levels of the past 60 days can be seen. These data are recorded by the patients
everyday. In other words, the partial closed-loop scheme is made out of a
collaboration of the feedforward and feedback controls, and usually feedforward controls are made by clinicians who determine it
from the patient's lifestyles. However, these evaluations largely rely on doctor's
experiences.</p><p>From the objective of the insulin therapy that aims to reconstruct the
artificial insulin metabolisms in relation to the levels of blood glucose in
the body, it is typically an optimization problem that is viewed from four dimensions:
the number of injections, time of injection, insulin type, and insulin dosage
[<xref ref-type="bibr" rid="B1">19</xref>]. Basically, this four-dimensional space optimization is intrinsic.</p><p>Besides, occasionally a clinician
provides him/her with a feedforward strategy from the patient's lifestyle.</p><sec sec-type="subsection" id="subsec6.1"><title>6.1. Physician prescribed regiment</title><p>The insulin regiment prescribed by a
doctor, to be administered manually, constitutes partially closed-loop control
[<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B41">24</xref>]. A physician will dictate an insulin administration routine to a
patient, variant upon a patient's lifestyle. Patients under such a system
monitor their blood glucose level several times a day, administering insulin
based upon prescribed tables according to their schedule and BG level. <xref ref-type="fig" rid="fig8">Figure 8</xref>shows the procedure.</p><p>This is the method that has
traditionally been used by insulin-dependent diabetics, but it performs poorly
compared to other methods. Partially, closed-loop control is far from real time
and only updates its control routine at scheduled physician visits.
Furthermore, lifestyle events such as eating, sleeping, or working out must be
accounted for by the patient in their interpretation of insulin tables,
introducing the very real danger of human error.</p></sec><sec sec-type="subsection" id="subsec6.2"><title>6.2. The Bergman model</title><p>The Bergman model is one of the virtual
diabetes patient models represented in the literature. In the Bergman model,
the certain dynamics of the diabetes patient system can be represented as
mathematical equations by employing three-order model: a glucose compartment, <italic>G</italic>, a remote insulin compartment, <italic>X</italic>, and an insulin compartment, <italic>I</italic> [<xref ref-type="bibr" rid="B20">4</xref>, <xref ref-type="bibr" rid="B21">36</xref>, <xref ref-type="bibr" rid="B22">37</xref>]. Basically, the Bergman
model has a very simple form and is represented as follows:<disp-formula id="sd9"><label>(9)</label><mml:math id="M9"><mml:mrow><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo minsize="1em" maxsize="1em">)</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo minsize="1em" maxsize="1em">)</mml:mo><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mtd><mml:mtd><mml:mo>=</mml:mo><mml:mi>γ</mml:mi><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:mi>h</mml:mi><mml:mo minsize="1em" maxsize="1em">)</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mi>n</mml:mi><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></disp-formula> where <italic>G</italic>(<italic>t</italic>)
represents plasma glucose and <italic>I</italic>(<italic>t</italic>) represents plasma insulin at certain
time <italic>t</italic>, which are initialized at <italic>t</italic> = 0. <italic>X</italic>(<italic>t</italic>) represents the
effect of insulin causing net glucose disappearance, for example, the remote
insulin concentration. <italic>G</italic><sub><italic>b</italic></sub> represents a base value of plasma
glucose and likewise, <italic>I</italic><sub><italic>b</italic></sub> represents a base value of plasma insulin.</p><p>Moreover, <italic>p</italic><sub>1</sub> is a parameter representing glucose
effectiveness, <italic>p</italic><sub>2</sub> fractionally represents
the insulin-dependent increase rates and <italic>p</italic><sub>3</sub> fractionally represents
the net remote insulin disappearance rates. <italic>h</italic> is a threshold where the plasma glucose levels are expected not to exceed. When
the plasma glucose levels exceed the threshold, the second-phase of insulin
secretion will be performed with additional <italic>γ</italic> insulin secretion. Furthermore,
insulin is removed from the plasma insulin space at rate of <italic>n</italic>.</p><p>The Bergman model is used for
efficiently predicting the certain diabetes patient system dynamics.</p></sec><sec sec-type="subsection" id="subsec6.3"><title>6.3. Automated insulin dosage advisor</title><p>The automated insulin dosage advisor (AIDA) is a virtual diabetes patient model that was originally designed for the
educational purpose so as to help patients and clinicians learn effective
glycemic control [<xref ref-type="bibr" rid="B20">4</xref>, <xref ref-type="bibr" rid="B33">38</xref>]. Basically, AIDA is used for estimating effects of
insulin injections and regimens in type 1 diabetic therapy [<xref ref-type="bibr" rid="B32">39</xref>]. More precisely,
AIDA is a simulation program that models the insulin-glucose dynamics based on
the physiological rules around metabolism of a single glucose compartment [<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B33">38</xref>].</p><p>To model the insulin-glucose dynamics,
AIDA prepares a single glucose pool (compartment) of extracellular glucose.
Metabolism around the glucose compartment is carried out such that delivering
glucose into the compartment is conducted both by being absorbed by the
intestine and by being produced by the liver (gluconeogenesis). On the other
hand, removing glucose out of the compartment is carried out by
insulin-independent and insulin-dependent glucose utilization. More precisely,
by the insulin-independent glucose utilization, glucose is carried from the
compartment into red blood cells, the central nervous system and viscera,
whereas by the insulin-dependent glucose utilization, glucose is carried from
the compartment into the liver and periphery. To hepatic and peripheral glucose
utilization, AIDA is designed to have a capability of adding different insulin
sensitivities by modeling them separately. Besides, the renal threshold is
defined in order to model renal glucose losses [<xref ref-type="bibr" rid="B33">38</xref>, <xref ref-type="bibr" rid="B32">39</xref>]. <xref ref-type="fig" rid="fig9">Figure 9</xref> shows a
variation of the net hepatic glucose balance in terms of the changes of the
amount of the active insulin and blood glucose (BG) levels in the form of
nomograms.</p><p>Moreover, the AIDA model applies a
process of insulin absorption derived by Berger and Rodbard to its pharmacokinetics
of the model [<xref ref-type="bibr" rid="B34">40</xref>].</p><p>In addition, insulin is separated into
two compartments where one is for plasma insulin and the other is “active”
insulin. On the basis of a physiological model, “active” insulin controls
metabolism. On the other hand, hepatic degradation produces insulin from plasma
insulin [<xref ref-type="bibr" rid="B32">39</xref>].</p><p>In the use of AIDA, by comparing home-monitored
blood glucose levels to a typical behavior of blood glucose of a patient, for
example, the model day, metabolic problems are identified. According to
particular metabolic problems, AIDA can generate several possible solutions,
and among these possible solutions, one best solution will be selected
according to a nonlinear dynamic model of the insulin-glucose system.</p><p>At last, this nonlinear dynamic model of
AIDA consists of four differentials, 11 algebraic equations and 17 parameters [<xref ref-type="bibr" rid="B25">41</xref>].
From the data, the model will be constructed while simulations are performed
for each therapeutic choice to optimize the following cost function:<disp-formula id="sd10"><label>(10)</label><mml:math id="M10"><mml:mrow><mml:mi>J</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mstyle><mml:mrow><mml:msubsup><mml:mrow><mml:mstyle displaystyle="true"><mml:mrow><mml:mo>∫</mml:mo></mml:mrow></mml:mstyle></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:msup><mml:mrow><mml:mo minsize="1em" maxsize="1em">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo minsize="1em" maxsize="1em">)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula> where <italic>G</italic><sub>0</sub> describes a set point [<xref ref-type="bibr" rid="B1">19</xref>].</p></sec><sec sec-type="subsection" id="subsec6.4"><title>6.4. Diabetes advisory system</title><p>The diabetes advisory system (DIAS) is a nonlinear model of the blood
glucose-insulin system based upon real-life parameters, versus simply BG
measurements [<xref ref-type="bibr" rid="B2">21</xref>]. It incorporates qualitative and quantitative input from the
user, including BG levels, meals, and past insulin injections.</p><p>The system uses a discrete-time finite-state model of the system based upon user
input. The system uses what it understands about the system as a whole,
including dormant compartmentalized insulin, predigested carbohydrates, and
current BG levels to compute a Bayesian estimate of future BG levels. It uses
all known information in order to compute the value of the optimal dosage such
that it minimizes an associated cost function (i.e., hypoglycemia is far more
“costly” than hyperglycemia, due to its possibility of severe damage). Over
iterations, it will adjust its system model parameters to better account for
patient specific reactions it detects. For example, in DIAS, the flow of the
physiological calculation of carbohydrate is drawn by <xref ref-type="fig" rid="fig10">Figure 10</xref> [<xref ref-type="bibr" rid="B31">42</xref>]. Besides,
DIAS has three different modes, for example, the learning mode, the prediction
mode, and the advisory mode.</p><p>In <xref ref-type="fig" rid="fig10">Figure 10</xref>, there are two associated state variables, for example, CHO and BG,
and both of them record how much carbohydrate content exists in the gut
compartment and the blood compartment, respectively [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>]. For example, in
this model, carbohydrate content is, at first, taken in from meals and
delivered to the gut and the blood compartment. During the delivery to the
blood, some of carbohydrate content is absorbed by the gut and only the rest of
it is delivered to the blood and transformed into the main energy.</p><p>In addition, this flow of carbohydrate is redrawn more precisely by using
difference equations, which are shown in <xref ref-type="fig" rid="fig11">Figure 11</xref>. In this redrawn model, the
amount of carbohydrate content in both the gut (CHO) and blood (BG) compartment
is updated in every hour such that both increase and decrease of carbohydrate
content are kept track of in each compartment. In <xref ref-type="fig" rid="fig11">Figure 11</xref>, the GUT-ABS
process variable represents how much glucose is absorbed by the gut, and the
rest of glucose remains in the gut and is recorded in the CHO state variable.
Besides, the RENAL-CL process variable represents how much glucose is removed, the
INS-INDEP-UTIL process variable represents how much glucose is used
independently of insulin, the INS-DEP-UTIL, on the other hand, represents the
amount of glucose to be used for insulin-glucose dynamics, and the GLU-PROD
process variable represents the amount of glucose produced by the liver [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>].</p><p>In DIAS, there are also two input variables, for example, MEAL and INS-INJ, where
the MEAL input variable is carbohydrate intakes at given time from each meal,
and the INS-INJ input variable represents the amount of the external insulin
injection [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>].</p><p>Furthermore, to adjust individual physiological differences, two other parameters are
employed, for example, INS-SENS and NPH-MAX, where the INS-SENS parameter
stands for the insulin sensitivity that affects the active insulin (ACT-INS)
variable, and the NPH-MAX parameter represents the time when NPH insulin
achieves the maximum absorption or concentration, shown in <xref ref-type="fig" rid="fig11">Figure 11</xref> [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>].</p><p>The “+” and “−” symbols in <xref ref-type="fig" rid="fig11">Figure 11</xref> represent fluctuation of carbohydrate on the CHO and BG state variables. For
example, the CHO state variable at HOUR 1 can be written as an equation such
that CHO (HOUR 1) = CHO (HOUR 0) – GUT-ABS (HOUR 0) + MEAL (HOUR 1) [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>].</p><p>The transition among the states in a graph of difference equations in DIAS is
defined by causal probabilities. More precisely, the graph representation of
difference equations of DIAS is defined by a causal probabilistic network (CPN)
or a Bayesian network using the HUGIN approach [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>]. For example, the
transition probability of the amount of carbohydrate absorbed by the gut given
the carbohydrate content in the gastrointestinal tract is P(GUT-ABS ∣ CHO) [<xref ref-type="bibr" rid="B31">42</xref>].</p><p>As previously mentioned, there are three modes in DIAS to conduct a calculation of
the optimal insulin dosage (the decision support system): the learning mode,
the prediction mode, and the advisory mode.</p><p>At first, the learning mode is used to generate the two adjustable parameters, for
example, the insulin sensitivity (INS-SENS) and time-to-peak absorption of NPH
(NPH), from the collection of standard data, such as the amount of blood
glucose, insulin injection, and carbohydrate content in the meals [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>]. For
instance, an example of a
prediction of blood glucose transition from [<xref ref-type="bibr" rid="B31">42</xref>], from the measurements of blood glucose, the mixture of short-acting
insulin and intermediate-acting insulin
and the carbohydrate intake, the transition of blood glucose is
predicted as a straight line.</p><p>Secondly, the objective of the prediction mode is to predict the resulting blood glucose
concentration from given an intake of carbohydrate and insulin injection as
well as two adjustable parameters estimated in the learning mode [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>]. There
is a risk of hypoglycemia around lunch time, the ratio of the insulin mixture
is manually changed in the morning to handle the condition. As an
example of the objective of the
prediction mode of DIAS given from [<xref ref-type="bibr" rid="B31">42</xref>], there is a risk of hypoglycemia around lunch time, the ratio of the insulin
mixture is manually changed in the morning to handle the condition. In
DIAS, this mode calculates an effect of a manually modified insulin therapy.</p><p>At last, the advisory mode, which is considered as a special version of the
prediction mode, is used to generate possible insulin therapies that avoid the
overall risk of an excess or shortage of blood glucose by minimizing an utility
measure. In the advisory mode, the manual changes of the insulin regimen
conducted in the prediction mode, such as switching to a different mixture of
insulin, are automatically replaced to an optimal way by the system. For example, a replaced version of an optimal insulin injection procedure is used
by the advisory mode, where the mode recommends reducing the amount of NPH
insulin from 10 to 6 U before dinner resulting in avoiding hypoglycemia during
bedtime [<xref ref-type="bibr" rid="B31">42</xref>, <xref ref-type="bibr" rid="B30">43</xref>]. As an example of a result calculated by the DIAS advisory mode, DIAS further
generates an optimal solution of an insulin therapy automatically to avoid the overall risk of an excess or shortage
of blood glucose by minimizing a utility measure.</p></sec><sec sec-type="subsection" id="subsec6.5"><title>6.5. Telematic management of insulin-dependent diabetes mellitus</title><p>The EU developed telematic management of insulin dependent diabates mellitus
(T-IDDM) which was a telemedicine system that supported clinician's decision-making
for providing insulin for the insulin-dependent diabetics. Basically the system
consist of two modules, for example, a patient unit (PU) and a medical unit
(MU), and two decision support elements, for example, a rule-based reasoner
(RBR) and a case-based retrieval system (CBRS) [<xref ref-type="bibr" rid="B1">19</xref>, <xref ref-type="bibr" rid="B35">44</xref>, <xref ref-type="bibr" rid="B36">45</xref>]. The system
architecture is shown in <xref ref-type="fig" rid="fig12">Figure 12</xref>.</p><p>With the system, the PU is basically responsible for monitoring changes of the blood
glucose concentration in patients, and the physiological data are transferred
to the hospital database via the Internet. Both manual and automatic
measurements and data transfers are allowed. In addition to the hospital
database, the PU also has a local database that enables patients to deal with
their own diabetics cases autonomously [<xref ref-type="bibr" rid="B35">44</xref>].</p><p>On the other hand, the MU is responsible for supporting the clinician's sides of
functionality. Thus the MU can visualize incoming data from patients, analyze
them, and generate optimal insulin treatments for particular patients.
Basically, the MU is a web-based application made up of collaborating five
servers: a database server, temporal abstraction server, data analysis server,
decision support system, and web server [<xref ref-type="bibr" rid="B35">44</xref>]. Data communication is made up
between the two devices.</p><p>From the perspective of the decision support for the therapy, the RBR and CBRS are designed
to resolve the following premises.</p><p>At first, the insulin-glucose dynamics is very complicated that only highly
parameterized nonlinear models can be applied to it although it is usual to
have no more than three or four blood glucose tests per day in the
insulin-dependent diabetes therapy, which is not enough to model the dynamics.
Due to the limitation of the measurements, some parameters are required to be
fixed in all cases whereas only a few parameters are free to be set up
according to each patient case. However, this limitation of setting parameters
must make the models and the quality of prediction inflexible and inaccurate
[<xref ref-type="bibr" rid="B1">19</xref>]. One goal of T-IDDM is to refine the models to generate more precise
prediction of the insulin-glucose models from the limited inputs.</p><p>Secondly, the insulin therapy largely usually depends on experiences of the
professionals. T-IDDM provides the professionals with more systematical way to
plan the therapy for particular insulin-dependent diabetics.</p><p>At last, the same metabolic behavior occasionally generates different results. For
example, either “honeymoon” effect or other troubles may cause the same number
of hypoglycemia over a month. However, this type of wrong diagnosis may fall
the diabetic into a critical situation. Therefore, in independence of metabolic
behaviors, T-IDDM should employ context that can generate different results
from the same metabolic behavior. Also the
introduction of context may reduce the search space from whole possible
solutions [<xref ref-type="bibr" rid="B1">19</xref>].</p><p>In the implementation of the RBR, to optimize the therapy, it runs four sequential
tasks each of which is connected to a set of rules through a forward chaining
mechanism. These four sequential tasks are the data analysis, problem
identification, suggestion selection, and therapy revision [<xref ref-type="bibr" rid="B35">44</xref>].</p><p>However, only the RBR is sometimes not enough to produce reliable suggestions of the
therapy for poorly controlled patients. Therefore, in consideration of that
situation, in addition to the RBR, T-IDDM employs the CBRS to improve the
system to be more accurate. The objective of the CBRS is to search a pool of
past cases for similar situations to the current condition and utilize them to
help the user make an optimal decision for the current condition [<xref ref-type="bibr" rid="B35">44</xref>]. This
case retrieval follows two steps. In the classification step, a set of past
cases is narrowed for searching according to very high-level view of the cases
by a Naïve Bayes strategy [<xref ref-type="bibr" rid="B37">46</xref>], and after that, in the proper retrieval step,
cases having the closest to the current situation are effectively chosen and
shown to the user [<xref ref-type="bibr" rid="B1">19</xref>].</p></sec><sec sec-type="subsection" id="subsec6.6"><title>6.6. Insulin-glucose system</title><p>Regarding the artificial insulin-glucose control system, [<xref ref-type="bibr" rid="B19">47</xref>] designs a fuzzy logic
reasoning system. There are mainly two modules (e.g., an analog signal conditioning
board and a microcontroller board) and other interface devices, such as a LCD
display, a sixteen button keypad, and alarm system, along with the operating
software to work the system. The software operates the system according to a
fuzzy logic reasoning method. In the system, an analog signal conditioning
board is responsible for generating electrical signals from vital parameters
monitored by several biomedical sensors. These parameters include sweating,
snoring, heart rate, and EEG. In the meantime, a microcontroller board
processes these electrical signals. The system works with batteries so that it
can be portable.</p><p>In the use of the system, several electrodes are placed on the particular segment
of the human body capturing the four physiological parameters. Basically, these
electrodes are connected to an analog signal conditioning board that amplifies
and filters the vital signs. Since a 10 bit A/D converter interfaces a
microcontroller board, the analog signals can be converted to the digital signals
with the sampling rate of 100 samples/s. The microcontroller invokes the fuzzy
logic reasoning algorithm that resides on the ROM of the system to process the
four parameters.</p></sec></sec><sec sec-type="section" id="sec7"><title>7. CONCLUSION</title><p>This survey mainly focuses discussions
on control methods for the insulin-dependent diabetes (type 1 diabetes). Three
control methods are introduced in this paper, namely, open-loop, fully, and
partially closed-loop control methods. In either of them, the objective of the control
methods is to suppress the blood glucose profiles to avoid a condition of
hyperglycemia. Because diabetes is a metabolic disorder which is characterized
as complete or partial lack of insulin functionality, therapies can be done by making
up for the lack of insulin supply by exogenous insulin replacement.</p><p>In the open-loop control method, the
insulin replacement is programmed such that the amount of the insulin supply
follows the non-diabetic insulin delivery. The open-loop control method usually
does not count on utilization of blood glucose sensors, but instead, a
transition of the insulin supply is captured by carefully examining the
nondiabetic in advance.</p><p>On the other hand, fully and partially
closed-loop controls typically rely on feedbacks from the blood glucose sensor
measurement. In the closed-loop control method, the system loop is fully closed
so that it does not require any assessment by physicians. It is only based on
feedbacks from one or more blood glucose sensors, and it usually requires
continuous glucose measurements. Thus from the measurements of blood glucose
profiles, a rate of the insulin supply by an insulin pump is adjusted so that
it can lead to neither conditions of hyperglycemia nor hypoglycemia. Examples
of the closed-loop control method are pole-assignment model, self-tuning
adaptive control, model predictive control, and nonlinear predictive control.</p><p>In addition to the blood glucose sensor
feedbacks, partially closed-loop control also relies on feedforwards by
physicians. In the partially closed-loop control method, the blood glucose
measurements are conducted three to seven times per day and insulin injections
are done three or four times per day. Although both the blood glucose samples and
insulin injections are discrete, these are compensated by physicians’ feedford
assessment of insulin requirements. Usually a calculation of the insulin supply
utilizes a flow chart or table which describes complex relations between blood
glucose reduction and insulin supply. Examples of the partially closed-loop control
method includes Bergman model, automated insulin dosage advisor (AIDA) and diabetes
advisory system (DIAS).</p><p>Currently, diabetes is considered
incurable. Hence challenges of the blood glucose control methods are to delay
the emergence of diabetic complications but not cure the patients from
diabetes. In practice, three control methods introduced in this survey
partially satisfy these requirements. However, our expectation is that the
progress of the technology will enable the construction an “artificial
pancreas” that follow the regular functionality of the actual pancreas, and
this new technology must lie on the current control technologies.</p></sec></body><back><ack><title>ACKNOWLEDGMENT</title><p>The work is partially supported by the US National Science Foundation (NSF) under Grants no.
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reasoning for monitoring hypoglycaemia in diabetic patients</article-title><conf-name>In: Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, vol. 3</conf-name><conf-date>October-November 1997</conf-date><conf-loc>Chicago, Ill, USA</conf-loc><fpage>1108</fpage><lpage>1111</lpage></citation></ref></ref-list></back><floats-wrap><fig id="fig1" position="float"><label>Figure 1</label><caption><p>A
control flow of closed-loop control models [<xref ref-type="bibr" rid="B1">19</xref>]. Entire loop of the control is
closed from outside by utilizing an insulin pump and in vivo blood glucose (BG)
sensors. Both insulin injections and glucose measurements are carried out
subcutaneously.</p></caption><graphic xlink:href="IJTA2008-739385.001"></graphic></fig><fig id="fig2" position="float"><label>Figure 2</label><caption><p>Three-level model of subcutaneous insulin absorption.</p></caption><graphic xlink:href="IJTA2008-739385.002"></graphic></fig><fig id="fig3" position="float"><label>Figure 3</label><caption><p>Self-Tuning adaptive control.</p></caption><graphic xlink:href="IJTA2008-739385.003"></graphic></fig><fig id="fig4" position="float"><label>Figure 4</label><caption><p>Model predictive closed-loop control.</p></caption><graphic xlink:href="IJTA2008-739385.004"></graphic></fig><fig id="fig5" position="float"><label>Figure 5</label><caption><p>Schematic
representation of neural prediction control proposed for the nonlinear
predictive control study of the glucose metabolism, which consists of an
amalgamation of a neural network and nonlinear predictive control technique.</p></caption><graphic xlink:href="IJTA2008-739385.005"></graphic></fig><fig id="fig6" position="float"><label>Figure 6</label><caption><p>Compartmental models of the glucose regulation system from [<xref ref-type="bibr" rid="B38">30</xref>]. Compartment <italic>g</italic>is plasma glucose; compartments <italic>u</italic><sub>11</sub>, <italic>u</italic><sub>12</sub>; and <italic>u</italic><sub>13</sub> are plasma insulin, liver
insulin, and interstitial insulin, respectively, and compartment <italic>u</italic><sub>2</sub> is plasma glucagon. External injections of glucose and insulin
are represented as <italic>I</italic><sub><italic>x</italic></sub> and <italic>I</italic><sub><italic>u</italic></sub>. NHGB stands
for the net hepatic glucose balance. Nonlinear functions are represented as <italic>F</italic><sub><italic>i</italic></sub> which depends on
variables <italic>a</italic>, <italic>b</italic>, <italic>c</italic>, and <italic>d</italic>.</p></caption><graphic xlink:href="IJTA2008-739385.006"></graphic></fig><fig id="fig7" position="float"><label>Figure 7</label><caption><p> A control flow of
partially closed-loop insulin therapy models from [<xref ref-type="bibr" rid="B1">19</xref>]. In general, in this
case, insulin dosages are supported by an expert system that generates an
optimal insulin dosage from a comparison between a model case and a prediction
of a future blood glucose transition.</p></caption><graphic xlink:href="IJTA2008-739385.007"></graphic></fig><fig id="fig8" position="float"><label>Figure 8</label><caption><p>Partially closed-loop control.</p></caption><graphic xlink:href="IJTA2008-739385.008"></graphic></fig><fig id="fig9" position="float"><label>Figure 9</label><caption><p>Variation
of the net hepatic glucose balance in terms of the changes of the amount of the
active insulin and blood glucose (BG) levels from [<xref ref-type="bibr" rid="B32">39</xref>]. The figure demonstrates
that the amount of the active insulin reduces the net hepatic glucose balance.
The transitions of the net hepatic glucose balance depend on a liver
sensitivity parameter <italic>S</italic><sub><italic>h</italic></sub>. A value of <italic>S</italic><sub><italic>h</italic></sub> is within the
range of 0 to 1.</p></caption><graphic xlink:href="IJTA2008-739385.009"></graphic></fig><fig id="fig10" position="float"><label>Figure 10</label><caption><p>The flow of the physiological calculation of
carbohydrate by the diabetes advisory
system (DIAS) from [<xref ref-type="bibr" rid="B31">42</xref>]. There are two state variables in the model. CHO
stands for the amount of carbohydrate in the gut compartment and BG stands for
that in the blood compartment. In the figure, the carbohydrate intake raises
the level of CHO and likewise, the gut absorption raises the level of BG. On the
other hand, the glucose utilization lowers the level of BG.</p></caption><graphic xlink:href="IJTA2008-739385.010"></graphic></fig><fig id="fig11" position="float"><label>Figure 11</label><caption><p>Another form of the insulin-glucose dynamics which is described by difference
equations from [<xref ref-type="bibr" rid="B31">42</xref>]. This figure shows that the amounts of carbohydrate in both
the gut and blood are calculated every hour. Basically, these calculations are
made depending upon absorptions and utilization. For example, the figure shows
the difference equations between hour 0 and hour 1.</p></caption><graphic xlink:href="IJTA2008-739385.011"></graphic></fig><fig id="fig12" position="float"><label>Figure 12</label><caption><p> The T-IDDM project architecture from [<xref ref-type="bibr" rid="B35">44</xref>].</p></caption><graphic xlink:href="IJTA2008-739385.012"></graphic></fig></floats-wrap></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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