APPLICATION OF OPTIMIZATION TECHNIQUES TO BIOLOGICAL SYSTEMS

Abstract

Since last two decades, there has been a remarkable development in the field of systems theory, culminating in its application in almost all the systems including bio logical systems. The ease of analysis of biological systems through mathematical modelling has encouraged the engineers to extend the concept of systems theory in this field. The aim of the present work is to illustrate the appli cation of system techniques to the modelling and control of certain physiological systems. For this purpose, the patientartificial kidney system and the human respiratory system are analysed in this dissertation. Hemodialysis has been a widely accepted mode of therapy for the treatment of chronic kidney failure. Although there is no doubt about the clinical efficacy of the method, however, the planning of the hemodialysis therapy for individuals is done largely on emperical grounds. The physicians are not even aware, except in a general sense, how the various para meters of the dialyser operation effectively control the patient's dialysis. Despite satisfactory results, it is still far from an optimal procedure and is both time consuming and expensive. The work embodied in the first part of the ihesis deals -liwith the development of optimal control policies for hemo dialysis. This is done by considering a mathematical model of the patient coupled to an artificial kidney system. The body fluids are represented by three compartments with uniform mixing. It is assumed that all the cells may be lumped together as a cellular compartment. The blood plasma and inter stitial fluids are lumped together as extracellular compartment. The brain fluid compartment is added for simulating the carebral pressure transients. The model equations are obtained by applying material balance around different fluid compartments. A method is developed for the estimation of model parameters pertaining to the transfer of urea from intra-cellular to the extra cellular spaces and from extracellular space to cerebros pinal fluid are obtained using a parameter estimation technique. These parameters are evaluated for dogs of various sizes and a linear correlation is presented for these data, which are in reasonable agreement with data reported for humans. A computer simulation of hemodialysis, using the model and the parameters has been presented and the effect of various controlling variables on the dialysis are studied. It is desirable to remove the biological waste as fast as possible in order to minimize the treatment time. However, with increasing dialysis rates, the cerebrospinalfluid pressure undergoes large dynamic overshoots, causing much discomfort to the patient. The dialysis has to be so controlled that the treatment time is minimized and the discomfort to the patient avoided. An optimal policy for hemodialysis based upon three factors: 1) a 3-compartment distribution model for urea, 2) dialysis characteristics of artificial kidney and 3; a maximum CSF to plasma urea grad ient, has been developed. The rate of urea loss is optimized by varying both the dialysate flow and the flow of the patient's blood. The major finding is that the simultaneous variation of dialysate and blood flow can result in shorten ing of dialysis time without achieving high CSF to urea gradients. The policy can easily be implemented by clinicians and would result in considerable reduction in treatment time. The objective of minimizing the treatment time is achieved by devising a time optimal control policy for the above problem. Application of this policy reduces the treatment time to an overall minimum. However, the dialysate feed requirement increases substantially and unless the dialysis facility is to be utilized for two shifts, this policy probably can not be justified. To reduce the quantity of fresh dialysate, a new scheme utilizing recycling of the dialysate has been suggested. It has been found that by recycling a portion of the dialysate, the amount of fresh make-up needed could be reduced substantially and considerable reduction in treatment time affected. An optimal policy pertaining to blood flow and the flow of dialysate fresh make-up has been developed for this system. Although the reduction in -ivtreatment time with this scheme is not large, but when considered in conjunction with the daily operating schedule of a dialysis centre, the potential cost savings for the patient may be substantial. This scheme may be particularly suitable for home dialysis, since the use of smaller dialysate make-up rate, in a recycle system, will reduce the cost at the expense of a slightly longer dialysis. In the second part of the thesis, the techniques of mathematical optimization and parameter estimation are used either in designing external assistance or as a tool in diagnosing the disease of a patient. For this study, the human respiratory system is consi&red. An analysis of controlled ventilation has been carried out for patients, whose breathing is controlled by external means such as artificial ventilators. The basic design para meters of the ventilator are obtained based upon minimization of the average alveolar pressure subject to the maximum ventilatory work capacity of the patients. Optimal input pressure waveform is decided on the basis of average and peak alveolar pressures and the inspiratory time. A method is developed to estimate the paramters of a mathematical model of the pulmonary mechanical system. This • is accomplished by tuning the mathematical model to fit a a set of patient data by means of Extended Gauss Newton algorithm. The estimation procedure is applied to experimental -vdata obtained during shallow panting maneuvers from normal subjects and subjects with obstructive lung disease. Based upon the estimation of the physiological parameters associated with the model and other theoretical considerations, it has been shown that adiagnostic characterization of the patient can be made.