A tutorial on biomedical process control

A tutorial on biomedical process control

Frank Doyle, Lois Jovanovic, Dale Seborg, Robert S.Parker, B. Wayne Bequette, Annah M. Jeffrey, Xiaohua

Xia, Ian K. Craig, Thomas McAvoy *

Received 13 February 2006; received in revised form 15 January 2007;accepted 16 January 2007

Abstract

This paper presents a tutorial on five typical applicationswithin the area of biomedical process control. The specific appli-cations discussed include: control of insulin administration fortreating diabetes mellitus, dynamic modeling for anti-cancerchemotherapy regimen design, modeling and control of drug infu-sion in critical care, structured treatment interruptions: a controlmathematical approach to AIDS protocol design, and dynamicmodeling and control of the anticoagulant drug heparin. Theobjective of the tutorial is to illustrate the rich and importantset of problems within the biomedical area that process controlengineers can contribute to solving. Solution to these problemscan have a significant medical as well as economic impact.

Keywords: Model based control; Dynamic modeling; Optimization; Con-straints; Parameter estimation; Drug delivery; Pharmacokinetics; Anti-coagulation; Chemotherapy; Diabetes; HIV/AIDS therapy; Critical care

1. Introduction

The application of dynamic modeling and advancedcontrol techniques in the process industries has increasedsignificantly over the last two decades. Model predictivecontrol received a key boost from Shell’s publication oftheir dynamic matrix control methodology [1]. An impor-tant driver for the use of model based control was the eco-

nomic benefits that it achieved. Although the application ofadvanced control continues to increase in the processindustries, the field is beginning to show signs of maturing.As a result researchers are looking at new applicationareas, for example in the bioprocess area and applicationsto more complex systems, such as those involving liquidand solid phases. One excellent area to which advancedprocess control can be applied is the biomedical area. Bio-medical process control is rich with interesting and chal-lenging problems. When a physician administers a drughe/she is basically acting as a control engineer. The physi-cian’s goal is to achieve a therapeutic objective, and theirmanipulated variable is typically the drug delivery schedulethat they prescribe.

To facilitate process control researchers considering thebiomedical process control area, this paper gives a tutorialon this subject. In the tutorial five typical biomedical con-trol applications written by five different groups ofauthors are discussed. These five applications were not cho-

sen to give complete coverage of the field of biomedical pro-

cess control. Rather they were chosen as specific examples

of the types of biomedical control research that are being

carried out today. Each section of the tutorial is self con-tained and it contains literature references to the problemaddresses. The specific application areas addressedinvolve:

Control of insulin for treating diabetes mellitus byFrank Doyle Lois Jovanovic and Dale SeborgModeling for anti-cancer chemotherapy design byRobert S. ParkerModeling and control of drug infusion in critical care byB. Wayne BequetteStructured treatment interruptions: A control mathe-matical approach to AIDS protocol design by AnnahM. Jeffrey, Xiaohua Xia, and Ian K. CraigModeling and control of the anticoagulant drug heparinby Thomas McAvoy

Model based control of biological systems requires thesame components as in other process control applicationdomains; sensing of key process variables, a process model

doi:10.1016/j.jprocont.2007.01.006

* Corresponding author.E-mail address: mcavoy@isr.umd.edu (T. McAvoy).

www.elsevier.com/locate/jprocont

Journal of Process Control 17 (2007) 571–594

and actuators with sufficient authority to influence thecontrolled variables. As always, plant understanding iskey. Biological systems in general are distributed parame-ter, stochastic, nonlinear, time varying dynamical systems.Process models are often derived from first principles bydomain experts, such as theoretical biologists. In somecases data driven models are used. Biological systems tendto exhibit multi-compartmental interactions that are usu-ally not well understood and as a result, the interactionscannot be accurately modeled mathematically. Controlengineers have to convert these models into a form thatis suitable for controller design. This conversion requiresa certain basic understanding of the process that can besomewhat difficult for engineers to obtain, but is well worththe effort.

Most process variables in biological systems can only bemeasured online, if at all, under clinically controlled condi-tions such as in a hospital. In many cases measurements areonly available at discrete intervals with long associateddead-times. Sensor accuracy has the potential to hindereffective control of the process variables. For example, inSection 4 of this paper, the currently available (off-line)assays cannot detect viral loads below 50 copies per mLof plasma (20 for ultra sensitive assays). Drugs are oftenthe only actuators available to manipulate controlled vari-ables in biological systems. For accurate control a goodactuator model is also required as the control signal usedis the drug efficacy and not the number of pills. This meansthat, the dosage to end point efficacy relationship has to beclearly defined for each drug. In cases where more than onedrug is used to treat the same condition, then considerationhas to be made for issues such as drug–drug interactions aswell as the combined efficacy. Lastly design of drug dosingregimens should be done using clinically driven criteria.

Although the five application areas discussed in thispaper are diverse they have a number of elements in com-mon. They all involve the use of dynamic models and theydeal with problems whose solution will yield significanteconomic benefits as well as improved quality of lifethrough better therapy. All five problems involve the useof advanced control, particularly model based and optimi-zation based control. Further dynamic models for most ofthe biomedical applications discussed show a great deal ofvariability from patient to patient and methods to deal withthis variability have to be incorporated into the solution toeach problem. Clearly, there are some problems in the bio-medical area that lend themselves to data based modeling.The fact that this tutorial does not consider these problemsshould not be interpreted as indicating their lack ofimportance.

The biomedical process control area is one that hasgreat growth potential, and one for which the tools usedby process control engineers directly apply. However, thebiomedical control field has its difficulties as well. Oneobvious difficulty involves the safety of any proposednew strategy for delivering a drug. If there is any questionabout the safety of a new drug policy then the policy will

not be used. There is the issue of the medical and engineer-ing communities being open to what the other communityhas to offer. It is important for both engineers and physi-cians to find collaborators with whom they are able towork effectively. There is also a communication issue sinceengineers and physicians tend to use different terminologyand come at problems from different perspectives. Forexample engineers talk about lumped parameter systemsand physicians use the term compartment models. In spiteof these difficulties, the biomedical process control holdstremendous promise. The area is rich with interesting,important and challenging problems, and it is hoped thatthis tutorial paper will stimulate process control engineersto look further into it.

Reference

[1] C.R. Cutler, B.L. Ramaker, Dynamic matrix control – a computercontrol algorithm, Joint Automatic Control Conf., San Francisco, CA,1980.

doi:10.1016/j.jprocont.2007.01.012

I. Glucose control strategies for treating type 1 diabetes

mellitus

Frank Doyle a, Lois Jovanovic a, Dale Seborg b

a Department of Chemical Engineering, University of

California, Santa Barbara, CA 93106, United Statesb Sansum Diabetes Research Institute, Santa, Barbara CA,

United States

1. Introduction

Type 1 diabetes mellitus is a disease characterized bycomplete pancreatic b-cell insufficiency. The only treatmentis with subcutaneous or intravenous insulin injections, tra-ditionally administered in an open-loop manner. Withoutinsulin treatment, these patients die. Insulin was discoveredin 1921, and although now it has been purified and manu-factured by recombinant DNA technology, one still mustindividualize the treatment to mimic normal physiologyin order to prevent the complications of hyper- and hypo-glycemia (elevated glucose levels, and low glucose levels,respectively). The literature documents [1–3] the strongcorrelation between hyperglycemic excursions and theincrease the risk of complications. The Diabetes Controland Complications trial [1] was the landmark study of1440 type 1 diabetic people randomized into two treatmentwings: intensive insulin delivery and standard care. Thosepeople who had mean blood glucose concentrations below110 mg/dl (glycosylated hemoglobin levels less than 6.0%)had no increase risk for retinopathy, nephropathy andperipheral vascular disease. Those patients who had ele-

572 F. Doyle et al. / Journal of Process Control 17 (2007) 571–594