CHAPTER FOUR -...

Technologies in the control of patients with diabetes Mellitus – Master Projects

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CHAPTER FOUR:

MODELING & CONTROL STRATEGIES 4.1 Introduction The blood-glucose control is one of the most difficult control problems to be solved in

biomedical engineering. One of the main reasons is that patients are extremely diverse

in their dynamics and in addition their characteristics are time varying. Due to the

inexistence of an outer control loop, replacing the partially or totally deficient blood-

glucose-control system of the human body, patients are regulating their glucose level

manually. Based on the measured glucose levels (obtained from extracted blood

samples), they decide on their own what is the necessary insulin dosage to be injected.

Although this process is supervised by doctors (diabetologists), mishandled situations

often appear. Hyperglycemia and hypoglycemia are both dangerous cases, but on short

term the latter is more dangerous, leading for example to coma. Therefore, 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.

To design an appropriate control, an adequate model is necessary. In the last 50 years

several models appeared. The mostly used and also the simplest one proved to be the

minimal model of Bergman, other more general, but more complicated models have

been studied, and used in number of implementations [20, 21, 22].

The control methods are generally categorized in three categories: open-loop control,

closed-loop control, and partial closed-loop control methods [8]. The rest of this chapter

will give more detailed explanations about existing insulin-glucose models, the control

loops, and control algorithms developed in blood glucose level control to achieve

normoglycemia in diabetic and critical care patients.

A Model predictive controller (MPC) developed during the master course, and a

Glucose-Insulin dynamics simulator under development, based on proportional-integral-

derivative (PID) controller, are given in more details in Appendix A.1 and A.2

4.2 Modeling the Human Insulin-Glucose System Glucose-Insulin models can be loosely grouped as being either empirical or

physiological [22,23]. The physiological model represents fundamental glucoregulatory

processes by deriving mathematical equations from knowledge about the human

internal functions - kinetics and material transport - which are already familiar enough.

The empirical methods largely depend on the input-output data from experiments.

Once having the model, the therapeutic strategy is designed. The therapy is expected to

follow the endogenous insulin functionality in decreasing the excessive glucose

production; by systematic exogenous insulin administration.

- Minimal model

A three compartment model, developed by Bergman in 1979, and termed the “minimal”

model, uses three equations representing plasma glucose, plasma insulin, and a remote


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insulin compartment [18]. Its main intention was to gain a better understanding of the

insulin action to clear glucose from circulation (see figure 4.1).

The remote insulin compartment filters the effect of administrated insulin, helping to

capture the dynamic lag that is present between insulin administration and resulting

decreases in plasma glucose. In addition, the “minimal” included a bilinear Glucose-

Insulin term within the plasma glucose equation capable of describing the increased

glucose absorption observed for equivalent insulin infusions at varying plasma glucose

concentrations. While the bilinear term in the “minimal” model constitutes nonlinearity,

the nonlinear model is amenable to controller synthesis.

Figure 4.1 Schematic representation of Bergman’s minimal model.

The model output is summarized in two main parameters, insulin sensitivity and glucose

effectiveness. Insulin sensitivity is a measure of the sensitivity of glucose clearance to

insulin concentrations and glucose effectiveness represents the ability to clear excess

glucose independently of insulin action. These parameters have ever since been

extensively used to assess the metabolic status of individual patients both in research

and clinic. In the minimal model, the complexity of the glucose-insulin interaction was

handled by using insulin concentrations as known fixed input while modeling

parameters related to glucose concentrations. The model was fitted to individual data.

- Closed-loop glucose-insulin models

In order to study the feasibility of therapy administration, many patients models have

been used, including the Bergman’s minimal model and models derived from it.

However, these models share the drawback that each one focuses on a separate entity,

usually glucose or insulin. As these models only represent one part of the glucose-

insulin system and require the other part as independent variable, they cannot be used

for simulation.

So, several studies have been developed to adapt and improve parameter estimation of

glucose effectiveness and insulin sensitivity in the model. Hovorka et al. [20] extended

the “minimal” model to include three subcompartments for both insulin and glucose,

representative of absorption, distribution, and elimination of the two compounds,

respectively, along with an insulin action subsystem characterizing insulin effects on

glucose absorption, elimination, and production.


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To increase the biological relevance of the model, Cobelli et al. [19] included a

component for up-regulating plasma glucose concentrations, glucagon. In addition, the

insulin subsystem consisted of five physiologically interacting compartments (plasma,

liver, interstitial, stored pancreatic, and easily released pancreatic insulin), though the

latter two are unnecessary in the type I diabetic patient. Rather than incorporate

traditional Michaelis-Menton kinetics, this model used hyperbolic tangent functions to

describe the saturating biological behaviors such as hepatic glucose production. Other

physiological based models seek to describe glucose and insulin concentrations not only

in the plasma and liver but in metabolically relevant tissues (i.e. brain).

A combination organ-hormonal Glucose-Insulin model was developed by Guyton and

updated by Sorensen et al. [21] (see figure 4.2), and further employed by Parker et al.

[22]. Insulin and glucose were treated separately with coupled metabolic effects using

hyperbolic relationships similar to Cobelli. The model was extended to account for the

effects of metabolically important body organs on system-wide alternations in plasma

glucose concentrations. It is important to note that the parameters in these models

structures (Sorensen, Cobelli, and Parker) are not identifiable for individual patients,

making patient- specific adaptation of the entire model infeasible. While parameter

sensitivity analysis could identify key parameters affecting closed-loop controller

performance, the model nonlinearities hinder controller development, limiting the

potential use of such models in the controller algorithms (though the model is

informative in computer simulations).

Figure 4.2: Compartmental diagram of the glucose or insulin system in a diabetic patient [21].

Given the biological complexity of the Glucose-Insulin relationship, some researchers

have instead developed empirical models to relate administrated insulin dose to plasma

glucose response. These model structures developed a functional relationship (linear or

nonlinear) between insulin and glucose based on collected, patient-specific data. While

these relations make no attempt to correspond with the underlying physiology, such

models directly address patient-to-patient variability as the data-derived model will be

specific to individual patient dynamics. While intra-patient variability remains an issue,

empirical models are often more amenable to real-time parameter updating due to their

structure (e.g. low equation dimension, linear in the parameters, etc.).


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Parker in 1999 developed a first-order Volterra time series model for describing the

Glucose-Insulin relationship. Such a structure uses past inputs over the model memory

weighted by model coefficients to predict the effect of administered insulin on future

plasma glucose concentrations. Data for coefficient estimation would be attained

through tailored-input sequence studies (bolus inputs of insulin) with subsequent

measurements of plasma glucose levels. Proper inputs tailoring reduces system data

requirements and allows explicit evaluation of model coefficients. The model was later

extended to include both second and third-order coefficients because the steady state

predictions from Sorensen model (the estimated patient in these studies) depict a third-

order insulin-glucose relationship. Improvements in the model predictions were

attained, but at the cost of additional data requirements and model nonlinearity [23].

Other empirical modeling approaches used nonlinear neural networks models for blood

glucose, probabilistic models of Glucose-Insulin metabolism with parameter

distributions, fuzzy models [24], and autoregressive models using past glucose

measurements to predict future glucose values [25].

While complex nonlinear empirical models can often describe patient data with high

accuracy, the selection of model structure impacts parameter identifiability, data

requirements, and controller synthesis. Hence, the model application should be

evaluated a priori; determine if the function of the model purely descriptive or the

model will be utilized in model-based controller synthesis. The selected model structure

must satisfy the entire set of needs for the given application.

- Drug effect models

With the exception of models for insulin therapy, only few drug-disease models have

been published so far. However, the minimal model has been extensively used to

analyze drug effects. This was typically done by correlating a summary parameter of

drug exposure (concentration at a certain point in time, maximal concentration or area

under the concentration-time curve) to a minimal model parameter. The authors in [26]

presented a minimal model-derived approach that could reproduce a dose-dependent

effect of GLP-1 on insulin secretion. The model was based on observations in healthy

volunteers and required the input of data obtained by an IVGTT. The parameters

affected by the drug were determined by plotting drug plasma concentrations at a time

point close to tmax against individual parameter estimates. Significant covariate

regression relationships were included in the model. Models like this are valuable tools

for descriptive data analysis. However, as the time aspect is not taken into account and

dynamic control mechanisms are not reflected by this approach, it cannot be used for

predictive purposes.

- Models incorporating disease progression

An interesting new approach trying to elucidate the mechanisms leading to the

development of diabetes was proposed by Topp et al. [27]. The model adds the

dynamics of β-cell mass as a third major factor determining glycemic control besides

glucose and insulin kinetics. Starting from a single-compartment minimal modeling

approach, a component representing a slow, glucose-dependent change in β-cell mass

was added. Under the assumption that a gradual increase in plasma glucose causes an

increase in β-cell mass (compensation), while a large increase in glucose causes a


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decrease in β-cell mass (pancreatic exhaustion), three distinct pathways of β-cell failure

leading to hyperglycemia and diabetes were described by the model.

While Topp focused on the deterioration of glycemic control in untreated individuals,

Frey in [28] developed a model to study the long-term effect of gliclazide on FPG in

type 2 diabetic patients. A population PK-PD model incorporating an empirical linear

model for disease progression was used to quantify the effect of gliclazide over time

based on repeated FPG determinations. With this model it was possible to estimate a

mean rate of disease progression and the associated variability.

4.3 Control Methods The most prevalent feature of most control systems is that they form a loop. It is

because of this completed loop (often called the ‘feedback loop,’ though there are also

‘feedforward’ paths) that control algorithms work at all. Indeed, a controller without

sufficient knowledge of the state of the system it controls could not be expected to work

very well. If no sufficient knowledge is provided, this would be “opening the loop,” and

hampering the control of the plane.

The body’s method of regulating diabetes is a highly integrated control system

involving a complex suite of sensors and actuators at several levels from molecular and

cellular through the endocrine organ system. Patients who suffer from diabetes have

trouble with some part of this glycemic control system, to the effect that their blood

glucose levels are poorly controlled. They require intervention to aid in the control

effort. By attacking this as a ‘controls’ problem, an engineering solution might be such

an intervention.

- Open-loop control

Open-loop control methods are usually designed to follow predefined therapy without

feedback from system; does not employ any glucose sensors. The control loop can be

closed by the physician and the diabetic when interacting on the system. Thus, called

the programmed insulin infusion system [29] because of its incomplete openness.

One type of this method 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 non diabetic, 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

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. Another system was developed by Siemens and the Finsen Institute;

a programmed insulin infusion system that employed a moderately complex delivery

algorithm from another approach [29]. The system is capable of manually inserting

small pin connectors into the control unit in order to control the insulin delivery rate.

The infusion rate follows an exponential curve, and the insulin infusion rate is updated

every 30 minutes.


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- Partially-closed-loop Control

Current clinical approaches are best characterized as partially-closed-loop, heuristic,

adaptive control. They are adaptive because patients will typically receive check-ups

from their doctors in order to alter treatment regimens over time. The control loop is

only partially-closed for two reasons [25]. The first is because of the removal between

the adaptation algorithm (doctor) and the imperfect data (patient blood-glucose

measurements). Both inaccuracy of data and poor communication of that data impact

the sensor effectiveness. The second ‘loop-opener’ is patient inability or unwillingness

to properly actuate their treatments (insulin, exercise, etc.). The ways to tighten the

control loop in the face of these troubles are three: better education of patients, better

monitoring, and development of better heuristics to assist dosing decisions.

Figure 4.3: partially closed loop control, Grey blocks represent loop defects.

There has been an enormous amount of work (by every clinician treating diabetes,

everywhere) in developing heuristic methods for treating diabetes, and these methods

have been tested and refined via clinical studies. The ‘rule of 1800’ and the ‘rule of

1500’ are examples of such heuristic techniques that physicians use to prescribe insulin

regimens to their patients based upon how their blood-glucose is affected by insulin

doses. These techniques, while clearly not accounting for inter-patient variability, are

terribly hampered in attempts to account for intra-patient changes by the relatively-poor

feedback that is consistently present between patient and doctor. Communication theory

(Nyquist Sampling Theorem) relates the accuracy with which we can reconstruct a

signal based upon our sampling rate. A simple back-of-the-envelope calculation tells us

that we will not have a faithful reconstruction of the patient’s blood-glucose levels by

sampling at the typical four measurements per day. This is not to imply that these

heuristics do not help patients: it has been shown in the Diabetes Complication and

Control Trial (DCCT) [30] that intensive insulin therapy (IIT) significantly reduces the

risks associated with chronic hyperglycemia. However, the increased time and money

costs associated with IIT motivate further study.

Other partially-closed-loop systems that have been developed are the model-based

Diabetes Advisory System (DIAS) [32], and the Automated Insulin Dosage Advisor

(AIDA) [31]. Model-based systems begin their treatment by abstracting the human as a

set of compartments that interact via certain rules. In the case of diabetes care, a

common, simple model involves identifying a differential equation that governs the

relationship between insulin concentration in the blood and gluconeogenesis rates in the

liver.


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AIDA uses a model-based method of dosing insulin via prediction/verification cycles,

with significant heuristics in model assessment and initial conditions. Retrospective

tests have been effective for individual patients, but only 80% of patients had reliably-

predicted, meal-effected glucose levels within an RMS error of 34.5 mg/dl over 5-6

days. Qualitatively, the model requires 17 parameters, but assumes 15 of these to be

fixed, allowing variation only in the remaining two.

DIAS, in contrast, has no heuristic components: it is completely model-driven and uses

a complex Bayesian network of glucose-insulin interactions as a framework. It then

requires blood glucose measurements (finger-prick reports), carbohydrate intake, and

past insulin injection information to devise a current dose proposal/treatment regimen.

While results of blinded studies have been positive for the ability of the DIAS to

outperform doctors in lowering HbA1c over a set period of time, the results are not

statistically significant. Indeed, though the complication of the model makes it more

malleable to inter- and intra-patient variability, it also makes the entire system

vulnerable to error, and raises startup calibration issues.

Further, in both AIDA and DIAS, the variations allowed are typically only adjusted

from patient to patient, and not intra-patient (over time). Due to complexity and

measurement inability, neither can readily adapt its model structure nor patient

parameters to reflect intra-patient changes. This adds doubt to their abilities for broad-

population glycemic control applications.

So, while AIDA and DIAS address some of the cost and communication issues, they

still require adjustment as well as patient attention, accuracy, and ability to self-

medicate. Many clinicians feel that the error bars on their work are largely due to

imperfect follow-through by the patient, or the patient’s inability to dose insulin

(especially among certain patient populations such as adolescents and the elderly).

Indeed, other innovations such as the insulin pump are helping to reduce these types of

errors. However, once the loop of control is broken there is clear agreement in

Medicine, and solid theoretical support in Engineering, that the open loop versions will

never work as well as their similarly-constructed but closed-loop counterparts (basic

control theory). Hence, much research has been done to develop systems that take the

patient out of the loop.

- Closed-Loop Control Models

Some solutions have taken the patient out of the loop; closed-loop system completes its

operating cycle within the system and no external interaction to diabetic patients is

required [8,25], by integrating an automatic sensor, an algorithm, and a therapy delivery

actuator into a single device. This section presents several closed-loop control

algorithms and their results. Figure 4.4 below shows the basic structure of the closed

loop system.


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Figure 4.4 Block diagram of a glucose feedback control system

(SC denotes subcutaneous glucose measurement, as per the current technology).

4.4 Closed loop Control strategies A wide range of control algorithms have been in use [9,33], reaching the same control

problem from different approaches, ranging from classical strategies, to modern

algorithms, further to advanced ones. This section presents several closed-loop control

algorithms and their results.

4.4.1 Classical Control

- Proportional Integral derivative, PID-controller

First generations controllers, the most famous of which is the Biostator, regulated

plasma glucose through the co-administration of glucose and insulin. These controllers

employed numerical derivatives of patient glucose measurements to quickly respond to

changes in blood glucose and can be classified as nonlinear proportional-derivative

(PD) controllers. Other groups have employed more traditional proportional-derivative

(PD) or proportional-integral-derivative (PID) controllers in managing diabetes.

Controllers with derivative components may be highly noise sensitive, however,

requiring signal filtering to aid blood glucose regulation. Integral control provides

reference tracking, however, the integral component also may result in the over

administration of insulin during meal disturbance rejection resulting in post-prandial

undershoot and hypoglycemia. Thus, parameter tuning is essential for controller

stability and performance, while supervisory controls are required to ensure insulin

dosing levels remain within safety constraints. Note, the handling of constraints is a key

concern in the classical feedback control structures, motivating the development of

model-based controller designs.

A number of classical feedback controllers have been employed in the clinic, including

a PID controller by Medtronic (2004) and PD approaches by Shimoda (1997), Matsuo

(2003), and Gin (2003) [9,33]. The Medtronic results demonstrated an ability to regulate

plasma glucose concentrations from a hyperglycemic state with a subcutaneous glucose

sensor and external insulin delivery pump. Results from Shimoda demonstrated similar

controller performance between intravenously administered insulin and fast-acting,

subcutaneously administered lispro insulin. These results also demonstrated the

feasibility of subcutaneous delivery for ambulatory diabetic control. Renard (2003) and

Matsuo (2003) have also investigated intraperitoneal insulin delivery with intravenous

glucose sensing using PD control, demonstrating improved controller performance over

subcutaneously administered insulin.[33]


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The PID algorithm has the following mathematical representation:

+++= ∫

t

D

I

cdt

dedtteteKutu

0

0 )(1

)()( ττ

where, again, e = r -y is the error (difference between the setpoint and measured output;

e.g., difference between the desired and measured glucose concentration), u is the

manipulated input (e.g., insulin infusion rate), and u0 is the bias or steady-state

manipulated input (e.g., basal insulin infusion rate). The term PID indicates that the

control action (manipulated input value) is composed of three functions of the error:

One is directly proportional to the error, the second is proportional to the integral of the

error, and the third is proportional to the derivative of the error (de/dt). The three tuning

parameters are Kc, the proportional gain, TI, the integral time, and TD, the derivative

time.

It should be noted that, while the PID equation is relatively straightforward, there are a

number of additional features required in any commercial implementation of the

algorithm. When the controller is switched from manual to automatic mode it is

important that “bumpless transfer” occur, that is, the manipulated input does not

immediately change at the time of the switch. Also, an “anti-reset windup” feature must

be included so that the integral term does not “windup” when the manipulated input hits

a constraint.

Figure 4.5 below shows the results obtained using a PID controller, with the Bergman

modified Model [34]. The results show that the controller keeps the glucose inside the

given boundaries in both scenarios.

Figure 4.5: Testing the tuned PID controller. Meal test, with breakfast, lunch, dinner and snack. The first

graph show the meal rates. initial values for the meal rates are chosen to be between 5-10 mg/dL

Appendix A.2 shows more details about the simulator, Simple Diabetes Simulator

(ASDS) based on PID controller that has been developed to study the dynamics of

glucose-insulin in Diabetic patients.

- Pole assignment control strategy

Pole-assignment strategies have also been attempted. These methods begin with a

differential equation mediated, compartmental model glucose-insulin interactions, and


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cast control as a filtering problem. After identifying and plugging in the parameters for

the differential equations, these methods ‘place poles’ in the s-plane to compute

algorithmically the required insulin dose given a set of glucose measurements. While

such filters are physically easy to implement, and control well-understood systems well,

they face the same trouble as the PID controllers in that the parameters are difficult to

attain, and change over time. Because of the tremendous sensitivity of these algorithms

to inter- and intra-patient variations, the problem of glycemic control has turned its

focus to adaptive algorithms.

4.4.2 Modern Control

- Adaptive controllers

Adaptive filtering is a well-developed field that includes several basic topologies that

allow not only outputs of the filter to be changed over time, but also the method by

which those outputs are generated; the filter continuously monitors its own success

through a defined metric, and is equipped with the capability of altering its own

processing scheme to better meet the success criterion. There are two basic ways in

which adaptation has been used to address glycemic control: model-parameter

estimation and simultaneous model and model-parameter estimation. Both of these are

variations of “plant identification”, and both have been integrated into a system that

uses the ‘current’ plant model to predict glucose levels based on current and past insulin

injections, and assigns an insulin regimen to deal with this [9,25].

- Neuro-Fuzzy Controller and expert systems

The field of fuzzy logic and fuzzy systems theory is based on the notion that some

input-output relationships are not “crisp.” Consider a process where a particular

manipulated input change may result in possibly three different magnitudes of changes

in an output: low, medium, and high. Fuzzy logic would provide some smoothing to

indicate that the output might be a mix of low and medium, for example.

Often biological systems are nonlinear, difficult, or impossible to model

mathematically. However, fuzzy logic is empirically-based and model free, thus opens

doors for control systems that would normally be deemed unfeasible for automation.

Furthermore, fuzzy logic is very robust and does not need precise and noise-free inputs

to generate usable outputs. Finally, it can easily be modified and fine tuned during

operation [9].

Expert systems are basically rule-based, with rules provided by “experts” with

knowledge of the system at hand. These types of models are often used as protocols for

insulin delivery in critical care, for example. Here, the clinician would specify rules,

such as, if the glucose value is between X and Y, then deliver Z units of insulin. This

type of strategy can often be implemented in a fuzzy logic-based framework.

ANNs evolved from a physiological description of the function of neurons and neural

networks in animals. An ANN is now more generally used to provide a nonlinear

relationship between inputs and outputs. An ANN is first “trained” by providing known

input and output data and optimizing parameters in the ANN to provide a best fit to the


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data. Verification is performed by testing the performance on input–output data that

were not used for training [25].

Basically NNs approach the problem of blood glucose management without attempting

to explicitly describe the exact model of the blood glucose-insulin system. 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 [36].

- Model Predictive Control (MPC)

MPC was developed primarily in the petrochemical industry, in both the United States

and France, in the 1960s and 1970s. The key challenges were large-scale, constrained

processes with many manipulated inputs and measured outputs. Here, a model is used to

predict the effect of current and future control moves (insulin infusion rates) on the

future outputs (glucose concentration). An optimizer finds the best set of current and

future control moves to maintain the desired outputs over this future prediction horizon.

The optimization-based approach of MPC enables constraints to be satisfied, but is quite

intuitive to process operators and engineers alike. MPC structures are ideal for avoiding

controller undershoot in meal rejection. The undershoot results from over administration

of insulin as the controller attempts to minimize predicted deviations from a basal

plasma glucose reference. A dynamic trajectory, such as a gradually decreasing

reference trajectory, in rejecting hyperglycemia serves to reduce this undershoot. As

hypoglycemia is more life-threatening, a more aggressive trajectory to basal glucose

should be employed when low blood glucose levels manifest. Alternative approaches to

a dynamic reference trajectory include designing either an asymmetric or priority

weighted objective function to more severely penalize hypoglycemia; this can reduce

hypoglycemia following a meal disturbance in simulation. It may also be necessary to

adapt the reference trajectory based on different patient conditions (i.e. fasting or

exercise), however, it may be easier to incorporate patient variability through parameter

updates rather than altering the reference trajectory.

MPC has been used in a number of artificial pancreas applications [22,34,35,36]. A

MPC with feedforward loop for controlling the blood glucose level based on

subcutaneous measurements, and using Bergman model has been developed during the

master course “Predictive Control”, the figure 4.6 below show the results obtained

during the work, and indicating that the controller is working nicely to maintain the

Glucose level with the constraints in the presence of meal and sensor disturbance.


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0 2 4 6 8 10 12 14 16 18 20 22 24

0

50

100

u(t)[mU/m

in ]

time (h)

u(t)

Constraints

0 2 4 6 8 10 12 14 16 18 20 22 24

50

100

150

200

time (h)

z(t) [m

g/dL]

z(t)

Setpoint

Figure 4.6: Insulin input and output with process and measurement noise, the controller

Applies acceptable control actions u(t) to maintain the BG within safe range

NMPC algorithms directly incorporate dosing and model constraints within the control

structure. Model-based NMPC has been evaluated in simulation using the Bergman,

Sorensen, Volterra, and Hovorka models in controllers’ synthesis and regulating plasma

glucose concentrations from a simulated patient. The Hovorka model has also been used

in clinical trials for maintaining normoglycemia during fasting conditions[35].

More details on the MPC strategy are given in Appendix A.1 that discuss a MPC

scheme designed during one of the master courses

- Run-to-run, learning, and repetitive control

Run-to-run control has been applied to several traditional batch processes in the

chemical industry. The 24-h cycle of eating meals, measuring blood glucose

concentrations, and delivering the correct insulin bolus, with the goal of achieving the

optimal blood glucose profile, can be viewed in the same spirit as traditional batch

processes such as emulsion polymerization [33].

Run-to-run controller adaptation uses patient data collected over a predefined period

that is used to update patient parameters over the following control period. Such

technique was applied in a limited clinical trial where Zisser et al [37] demonstrated the

applicability of run-to-run control in managing insulin administration for meal

management.

4.4.3 Post-modern control No model perfectly describes the behavior of a system, so it is important to design

controllers that can tolerate a certain degree of uncertainty (model error) while

remaining stable and satisfying desired performance characteristics.

The frequency response methods of Bode considered uncertainty using the notion of

gain and phase margins. In the 1980s and 1990s, rigorous techniques were developed to

explicitly consider the effect of model uncertainty for multivariable systems, and to

simultaneously consider the impact of model uncertainty on the stability and


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performance of feedback systems. These modern technique include H∞ control, H2/H∞

control, µ-synthesis, Linear Parameter Varying (LPV) technique.

The H∞ control framework is well suited for glucose regulation, due to the ability to

tune the controller for robustness to uncertainty while mathematically guaranteeing a

certain degree of performance. In this case, it is important for a closed–loop controller

to tolerate patient variability and dynamic uncertainty while rapidly rejecting meal

disturbances and tracking the constant glucose reference. The controller allowed custom

tuning to trade – off these potentially conflicting [38].

In summery, an ideal controller for diabetic patient would limit insulin infusions,

minimize hypoglycemia events, and be robust to patient variability and signal failure. It

would adapt to the needs of the patient throughout the day, operating effectively during

fasting, meal consumption, and daily activity. The underlying control algorithm for

diabetic patients need not be excessively complex; a linear control may be sufficient for

diabetic patient regulation in simulation. However, the supervisory controls for patient

safety are inherently more complex that the underlying patient model. Like many

control applications, model parsimony and model accuracy must be balanced in the

synthesis of a diabetic patient control system. When integrated with a supervisory

control layer, the level of model detail required remains an open issue.

4.4 Challenges in developing the artificial pancreas An important consideration in diabetic patient glucose control is whether fast

convergence to a desired plasma glucose concentration is the physiologically ideal

result. Algorithms are typically designed to minimize deviations from basal glucose

concentrations with minimal concern on the total insulin delivered. However, the

normal glucose response of the pancreas in “meal disturbance” rejection has a slower,

biphasic characteristic similar to a combination of feedforward and feedback control.

Though this same profile can be generated with higher order models or advanced

control structures. Insulin has an effect on multiple other subsystems, and while these

interactions will have already been altered due to the diabetic state of the patient, it may

to preferential to mimic the natural insulin release of the body. Additional clinical

studies with extended data collection are required to determine whether controller action

should follow the insulin response generated by a healthy pancreas.

The route of glucose administration and type of insulin must also be considered for

glucose control as different pathways and insulin formulations resulting in differing

plasma glucose dynamics. Most glucose-insulin models assume intravenous insulin

administration, meaning insulin is immediately available in plasma. While such delivery

schemes are implementable in the critical care units, ambulatory diabetics rely on

subcutaneous injections for their daily insulin needs, introducing lag between insulin

administration and glucose response. While fast acting insulin formulations have

alleviated some of the time delay associated with subcutaneous injections, the dynamics

of subcutaneous delivery would still impact closed-loop controller synthesis. While

investigations into novel oral delivery systems continue, the bulk of the literature has

focused on modeling insulin effects from subcutaneous injections.

The above models structures operate under the assumption that plasma glucose

concentration measurements are readily available. Such measurements can be obtained

in critical care management through the intravenous insertion of a catheter. However,


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catheter measurements are invasive and require a bed-ridden patient; this is not

conducive to ambulatory diabetic lifestyles. Sensors for outpatient diabetics typically

measures patient glucose concentrations in subcutaneous or interstitial tissues,

necessitating additional considerations, such as sensor measurements lagging plasma

concentration and signal noise, that complicate closed-loop controller formulation. In

addition, sensor dynamics must also be considered during control formulation,

specifically time constant and time delays resulting from sensor measurements.

Inclusion of this information is critical for control design, and dynamic information

regarding specific sensors can typically be obtained from the manufacturer, though

definitions for these parameters vary between manufacturers.

The Glucocentric models might not be the ideal structures to use for controlling diabetic

patients, McGarry in 2002, discussed the need for a more lipocentric point of view.

Studies have shown that free fatty acids, a key metabolite in the glucose-insulin

interaction, can inhibit insulin-modulated uptake of glucose into the liver and peripheral

tissues. Other studies have demonstrated that plasma glucose and insulin have lipolytic

and anti-lipolitic effects, respectively, highlighting the interplay between the three

compounds. Additionally, skeletal muscle relies primarily on free fatty acid for its

energy needs when the body is at rest. Despite the interaction of free fatty acids with

glucose and insulin, the primary controller disturbance “meal” test considers only the

consumed carbohydrates. Many authors advocate feedforward controller predictions

result when an inaccurate glucose intake is provided. Similarly, a meal with large lipid

content would dramatically alter model predictions unless the glucose-insulin

relationship was altered to include lipid effects. Incorporation of free fatty acid effects

into the Bergman “minimal” model should allow for improved plasma glucose control

as well as more realistic representation for the classical meal rejection test case.

Figure 4.7: Convergence toward Automation in Diabetes treatment, from Roche/Disetronic

4.5 Telematic Control systems

4.5.1 Teleheath systems in Diabetes Diabetes has in many cases an asymptomatic nature. The time frame between sustained

hyperglycemia and observable complications can be extended, thus making a long-term

monitoring of secondary prevention an essential part of appropriate diabetes care. The

regular practices such as eating regularly every day, exercising, insulin administration,

monitoring blood glucose levels and blood pressure, and observing proper foot care


46

have become necessary for patients with diabetes. These practices are often perceived

by patients as a very heavy load. However, the result of a patient without enough self-

care is the inability to attain continuous glycemic control and an increased risk of the

complications.

4.5.2 Developed Platforms The advantage of using the telehealth systems for diabetic patients which use

standardized communication platforms for health data transmitted between patients and

care givers has been widely recognized. Telehealth systems not only provide patients

with a new method of self-management of the measurement data and self-management

information, but also reduce caregivers’ duties of caring for and monitoring patients

because they can easily obtain the historical data of the patients.

Most current telehealth research for diabetes use modems, telephone lines, or the

Internet to transmit patients’ measurement data and self-management information to

their health care provider or hospital. Blood glucose levels and blood pressure are the

most common measurement data for telehealth systems for diabetic patients.

Piette et al. [39] used the Automated Telephone Disease Management (ATDM) system

with telephone nurse follow-up for improving diabetes treatment processes and

outcomes in Department of Veterans Affairs (VA) clinics in the United Sates. ATDM

systems use specialized computer technology to deliver messages and collect

information from patients using either their telephone’s touch-tone keypad or voice-

recognition software. Biweekly, patients receive the calls whitch lasted 5-8 min for

ATDM assessment, and a nurse educator’s follow-up that was based on their ATDM

assessment reports. During ATDM assessment, patients used their touch-tone keypad

reporting their self-monitored blood glucose (SMBG) results, other self-care activities,

perceived glycemic control, symptoms, and use of guideline-recommended medical

care.

Gómez et al. [40] proposed the DIABTel telemedicine system as an intensive

management tool for patients with diabetes. DIABTel is a telemedicine service that

offers a doctor-patient integrated approach, complementing the daily care of diabetic

patients. The DIABTel telemedicine system consists of two main components: the

medical workstation, a PC-based system that is used by physicians and nurses in

diabetes day centre units of hospitals, and the patient unit, a palmtop-computer that is

used by patients during their daily living. The patient unit can be set to transmit data

through a direct phone call to the DIABTel server or through a TCP/IP connection via

any internet service provider. In the study, patients were asked to send their self-

management data and/or messages to doctors at least once every 2 weeks. The self-

management data includes blood glucose results, insulin changes, diet modifications

and additional events. When new data is received, doctors have to analyze it and

provide feed-back within the next 24 hours.

Bellazzi et al. [41] proposed a Telematic Management of Insulin-Dependent Diabetes

Mellitus (T-IDDM) project that used similar architecture of Gómez’s study to manage

patients with Type 1 diabetes, figure 4.8 below shows the architecture of the T-IDDM

system.


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Figure 4.8: T-IDDM system architecture [41]

In the systems proposed by Montori et al. [42], diabetic patients monitor their blood

glucose every day, and transmit the recorded blood glucose data using a modem to the

centralized server to the health care provider at least every two weeks. Glucose analysis

software on this server assists the nurse to interpret the data. The health care provider

reviews each transmission and calls the patient to discuss the information transmitted

and make treatment changes as needed.

Mougiakakou et al. [43] proposed a system for tele-monitoring and tele-management of

Type 1 diabetic patients. This system consists of two main parts: the Patient Unit (PU)

and the Patient Management Unit (PMU). In the PU, information related with glucose

levels, insulin intake, diet, and physical activity are integrated into a monitoring unit,

either manually or automatically, and are transmitted through telecommunication

networks to the PMU. The PMU consists of a database module, a data analysis module,

and an insulin advisory module, that can be accessed by both care-giver and patients.

The data analysis module of the PMU supports tools for medical experts and diabetic

patients to identify the regularity in the occurrence of an episode at a certain time of the

day, the trend patterns of long-term variation, and predict medical event risk factors

related with the long-term complications of diabetes mellitus.

Jansá et al. [44] used telephone lines to transmit measurement results. The patient

connects the GlucoBeep (a telematic communication system) to the glucose meter and

places its loudspeaker on the telephone microphone. All the glycaemia values are sent

electronically, the server also invites the patient to leave a 1-min vocal message about

insulin doses and events. All of the data are encoded and stored in the server and are

unloaded by the diabetes team. All patients were asked to perform at least three glucose

tests per day on average.

Jansá et al. [44] used telephone lines to transmit measurement results. The patient

connects the GlucoBeep (a telematic communication system) to the glucose meter and

places its loudspeaker on the telephone microphone. All the glycaemia values are sent

electronically, the server also invites the patient to leave a 1-min vocal message about

insulin doses and events. All of the data are encoded and stored in the server and are

unloaded by the diabetes team. All patients were asked to perform at least three glucose

tests per day on average.

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