complexity of a human 
 biological system typically allows its relations to be expressed only in a 
 nonlinear way . because of this complexity
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 .
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 
 .
thus , the insulin - dependent diabetic therapy must concern both hyperglycemia 
 and hypoglycemia by providing an appropriate amount of exogenous insulin timely . at the beginning of the insulin - dependent 
 diabetic therapy
,   it is required to obtain an approximation of the insulin - glucose 
 relation .
two methods are taken in this process , namely , empirical and 
 fundamental methods .
arguably , this process is most time consuming . based on mathematical equations representing 
 the insulin - glucose mechanism ,
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 .
this paper is the second part of our 
 survey of insulin - dependent diabetes .
our first paper , 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 . the rest of the paper is organized as 
 follows . in section 2 , we briefly summarize diabetes mellitus for the sake of 
 induction to the topic . in section 3 , we explain empirical and fundamental 
 schemes to derive mathematical models of the insulin - glucose dynamics . from sections 
 4 through 6
, we explore the control strategies , especially for the insulin - glucose 
 dynamics . in these sections , we provide several applications based on the 
 controls .
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 . 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 . in the united states ,
currently 
 it costs 136 billion dollars annually to take care of 12 million diabetes patients [ 4 , 5 ] . in general , diabetes is considered as a condition that disproportionately 
 affects developed countries .
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 [ 6 , 7 ] . 
 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 .
diabetes eventually causes cardiovascular 
 disease , chronic renal failure , retinal damage , nerve damage , and microvascular damage . besides
, according to characteristics of 
 diabetes , it is typically classified into two types , namely , type 1 and type 2 
 diabetes . in short , in type 1 diabetes , from the malfunction of the 
 pancreas resulting from the destruction of the  cells of the islets of 
 langerhans , a supply of endogenous insulin completely stops .
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 . as mentioned before
this is caused by the malfunction of the 
 pancreas destroying the  cells which are responsible for the endogenous 
 insulin supply .
it is considered a reason why the destruction of the  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  cells .
type 1 diabetes is sometimes called childhood , juvenile or 
 insulin - dependent diabetes although it does not only emerge during a childhood 
 . 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 . although in type 
 2 diabetes , endogenous insulin still can facilitate its functionality , it is 
 largely degraded and can not sufficiently change blood glucose into energy . 

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 .
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 .
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 .
type 2 diabetes is also called non - insulin - dependent , obesity - related , 
 or adult - onset diabetes .
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 ,
to procure the mathematical models of 
 the human insulin - glucose system , several approaches are taken by researchers . in 
 these approaches ,
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 .
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 . 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 .
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 . in the fundamental methods , a 
 mathematical representation of the human internal system which
this system 
 behavior includes kinetics and material transport . according to 
 investigating the internal system ,
a lot of data from the literature can be 
 used to determine the system parameters .
in particular , in constructing a fundamental diabetes model , the 
 authors in   applied the insulin - release data of the  cells of the pancreas 
 from a number of examinations to a mathematical representation .
there 
 are several classes of solutions to this problem , ranging in complexity , prerequisite 
 knowledge , and feedback . 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 
 .
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 .
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 . according to this 
 mathematical model , an intravenous insulin delivery system
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
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 .
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 [ 1518 ] .
the system to deliver insulin mechanically in order to regulate the glycemic 
 profile is called the  closed - loop  system . as shown in figure 1
, the 
 closed - loop system completes its operating cycle within the system and no 
 external interaction to diabetic patients 
 is required [ 19 , 20 ] . 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 .
so far , along with the glucose sensor , the 
 closed - loop system also employs an insulin pump which continuously 
 infuses insulin via a subcutaneous root .
basically , insulin delivery is controlled by these implanted blood glucose sensors and an insulin pump 
 attached to a patient 's body [ 19 , 2123 ] . 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 .
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 . 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 . 

pole assignment is a standard control 
 systems technique for designing an infinite impulse response filter [ 19 , 24 ] . 

this consists of a set of filter coefficients and a feedback loop in order to 
 maintain a stable blood glucose level . 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 .
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 , the 
 iir in relation to blood glucose level , the insulin - glucose system , is 
 determined by the following computation : 
 ( 1)iir(t)=kpg(t)+kddg(t)dt+kcwithkp = amnvp ,  kdkp=1l+1m+1n+ba , kc = d+cakp , where g is blood glucose level and d is the insulin infusion rate through 
 the intravenous ( iv ) route .
parameters a , b , and c can be 
 calculated from the relationship between plasma insulin i and blood glucose levels in a normal person , which are written as(2)i(t)=ag(t)+bdg(t)dt+c . moreover , other parameters n and l are from next equations which are the pharmacokinetics of insulin 
 infusion through the sc route:(3)dx(t)dt = iir(t)+lx(t),dy(t)dt = lx(t)(p+o)y(t),dz(t)dt = py(t)nz(t),i(t)=z(t)v , where x , y , and z represent the insulin level in the two subcutaneous compartments and in the 
 plasma , respectively .
figure 2 shows such an x / y / z 3-level model . at last ,
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 .
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 .
however , the combination of 
 the pole - assignment strategy and regular insulin generated much worse result .
a difficulty of the pole - assignment 
 strategy is to repeatedly evaluate model parameters in each computation of the 
 iir . 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 k , that is , gk , is 
 evaluated from the glucose levels of time period k  1 through k  h , that is , { gk1 ,  , gkh } , and the insulin doses of time 
 period k  1 through k  p , { idk1 , idkp } , as 
 well as some unknown parameters  , which can be written as [ 2528](4)gk = m(gk1,  ,gkh , idk1,idkp, ) ,   where p and h are time delays .
since this method evaluates the blood glucose 
 level of time period k from the 
 previous evaluations and insulin doses , it can efficiently eliminate unnecessary 
 re - evaluations of the model parameters . besides , according to glucose level gk , the next insulin dose is calculated as(5)j=(gkgk1)2ridk , such that i 
 dk can minimize value j , where r is a weighting 
 factor designed to control the amount of insulin dose .
implementation of self - tuning adaptive 
 control , shown in figure 3 , is quite similar to pole - assignment control , as it 
 uses the same system modeling equations in order to compute the insulin 
 infusion rate .
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 .
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 .
a model predictive control ( mpc ) , or 
 nonlinear predictive control ( nlpc ) algorithm attempts to  learn  what nominal 
 means in a system [ 19 , 20 ] , shown in figure 4 . 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 .
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 .
apparently , the insulin - glucose system is complicated , and the system is considered to be nonlinear 
 . in , 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 figure 5 .
basically nns approach the problem of blood glucose management without attempting to 
 explicitly describe the exact model of the blood glucose - insulin system [ 3133 ] .
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 .
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 .
in addition to the control variables , it also designs a cost 
 function in relation to the insulin - glucose model [ 19 , 30 ] . 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 .
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 . in the forming of the control strategy ,  
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 figure 6 . from the 
 model , the subcutaneous insulin absorption
is calculated in two steps : the 
 subcutaneous mi analogs infusion and utilization from the subcutaneous depot . 
 with respect to the glucose regulation , in order to model the system 
 mathematically ,   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 . in the second step , using numerical data from simulations of the mathematical patient 
 model , the paper   develops the nonlinear system by nns in order to make 
 future blood glucose predictions . to do this
, the paper   utilizes a 
 nonlinear autoregressive model ( narx ) because of its popularity and usefulness . 

,idknu)+ek , where g is a sequence of subcutaneous glucose 
 profiles , especially gk is 
 a future glucose prediction , i d is a 
 sequence of subcutaneous insulin infusion rates , ek is a noise , and ny and nu are both durations 
 of glucose utilization and insulin activation , respectively . at this point
, however , the 
 approximation of the nonlinear function f 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 .
thus , the paper 
 uses a function of radial basis function ( rbf ) networks , which are a subclass 
 of regularization networks , in order to represent the nonlinear function f : ( 7)f(x(t))=i=1nwih(xxi0),h(xxi0)=1((xxi0)2+)2 , where h is a continuous function of rr , || || , represents the 
 euclidean norm , xi are some proper center values selected from the data points , wi are some weight constants , and  is a parameter representing the dispersion [ 19 , 30 ] . also the regularized orthogonal least squares ( rolss ) algorithm is 
 used to determine rbf weights and centers in order for f(x(t ) ) to fit the data under some constraints . the third step to model
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(8)argminid  j=[j = n1np(ejtej)+j=0nc1idt(t+j)uidt(t+j ) ] , where i d = [ idk , idk1 ,  , idknc1 ] and nc , np , n1 , e , u are parameters of the controller for tuning .
there are three steps for the process of a fuzzy logic algorithm : 
 fuzzification , rules , and defuzzification.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.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.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 . 
 
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 .
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 .
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 . in the paper , 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 dose of drug is defined as  zero ,  
  little ,  
ten rules are defined such that : if ( rate is overlow ) , then ( dosage 
 is zero);if ( concentration is overhigh ) and 
 ( rate is low ) , then ( dosage is little);if ( concentration is overhigh ) and 
 ( rate is highest ) , then ( dosage is most);and so forth . 
 
if ( rate is overlow ) , then ( dosage 
 is zero ) ; if ( concentration is overhigh ) and 
 ( rate is low ) , then ( dosage is little ) ; if ( concentration is overhigh ) and 
 ( rate is highest ) , then ( dosage is most ) ;
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 , are made according to model - based 
 or algorithmic - based decision support systems , such as dias , aida , and t - iddm 
 .
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 . 

figure 7 shows 
 a control flow of a partial closed - loop scheme . 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 .
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 .
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 . 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 
 .
basically , this four - dimensional space optimization is intrinsic . besides , occasionally a clinician 
 provides him / her with a feedforward strategy from the patient 's lifestyle .
the insulin regiment prescribed by a 
 doctor , to be administered manually , constitutes partially closed - loop control 
 [ 19 , 24 ] .
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 .
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 .
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 , g , a remote insulin compartment , x , and an insulin compartment , i [ 4 , 36 , 37 ] .
basically , the bergman 
 model has a very simple form and is represented as follows:(9)dg(t)dt=(p1+x(t))g(t)+p1gb , dx(t)dt=p2x(t)+p3(i(t)ib),di(t)dt=(g(t)h)tni(t ) , where g(t ) 
 represents plasma glucose and i(t ) represents plasma insulin at certain 
 time t , which are initialized at t = 0 .
x(t ) represents the 
 effect of insulin causing net glucose disappearance , for example , the remote 
 insulin concentration .
gb represents a base value of plasma 
 glucose and likewise , ib represents a base value of plasma insulin . moreover , p1 is a parameter representing glucose 
 effectiveness , p2 fractionally represents 
 the insulin - dependent increase rates and p3 fractionally represents 
 the net remote insulin disappearance rates .
h 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  insulin secretion .
furthermore , 
 insulin is removed from the plasma insulin space at rate of n. the bergman model is used for 
 efficiently predicting the certain diabetes patient system dynamics .
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 [ 4 , 38 ] .
basically , aida is used for estimating effects of 
 insulin injections and regimens in type 1 diabetic therapy .
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 [ 19 , 38 ] . to model the insulin - glucose dynamics , 

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 [ 38 , 39 ] .
figure 9 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 .
moreover , the aida model applies a 
 process of insulin absorption derived by berger and rodbard to its pharmacokinetics 
 of the model .
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 . 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 . at last , this nonlinear dynamic model of 
 aida consists of four differentials , 11 algebraic equations and 17 parameters . 
 from the data , the model will be constructed while simulations are performed 
 for each therapeutic choice to optimize the following cost function:(10)j(g)=0t(g(t)g0)2dt , where g0 describes a set point .
the diabetes advisory system ( dias ) is a nonlinear model of the blood 
 glucose - insulin system based upon real - life parameters , versus simply bg 
 measurements .
it incorporates qualitative and quantitative input from the 
 user , including bg levels , meals , and past insulin injections .
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 figure 10 .
besides , 
 dias has three different modes , for example , the learning mode , the prediction 
 mode , and the advisory mode . in figure 10 , 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 [ 42 , 43 ] .
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 . in addition , this flow of carbohydrate is redrawn more precisely by using 
 difference equations , which are shown in figure 11 . 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 figure 11
, 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 [ 42 , 43 ] . 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 [ 42 , 43 ] . 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 figure 11 [ 42 , 43 ] .
the  +  and    symbols in figure 11 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 ) [ 42 , 43 ] .
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 [ 42 , 43 ] .
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 ) .
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 . 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 [ 42 , 43 ] . for 
 instance ,   an example of a 
 prediction of blood glucose transition from , 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 .
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 [ 42 , 43 ] .
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 , 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 ,
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 [ 42 , 43 ] . 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 .
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 ) [ 19 , 44 , 45 ] . the system 
 architecture is shown in figure 12 . 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 .
in addition to the hospital 
 database , the pu also has a local database that enables patients to deal with 
 their own diabetics cases autonomously . on the other hand ,
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 .
data communication is made up 
 between the two devices . from the perspective of the decision support for the therapy , the rbr and cbrs
are designed 
 to resolve the following premises . 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 
 .
one goal of t - iddm is to refine the models to generate more precise 
 prediction of the insulin - glucose models from the limited inputs .
t - iddm provides the professionals with more systematical way to 
 plan the therapy for particular insulin - dependent diabetics . 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 . 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 .
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 .
a set of past 
 cases is narrowed for searching according to very high - level view of the cases 
 by a nave bayes strategy , and after that , in the proper retrieval step , 
 cases having the closest to the current situation are effectively chosen and 
 shown to the user . regarding the artificial insulin - glucose control system ,   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
the system works with batteries so that it 
 can be portable . 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 .
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 . 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 . 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 .
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 ) .
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 .
 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 . 
1. INTRODUCTION
2. TYPE 1 AND TYPE 2 DIABETES
3. MODELING THE HUMAN INSULIN-GLUCOSE  SYSTEM
4. OPEN-LOOP CONTROL MODELS
5. CLOSED-LOOP CONTROL MODELS
6. PARTIAL CLOSED-LOOP SCHEME
7. CONCLUSION