MODELLING OF HUMAN V AND KIDNEY SYSTEMS ISUAL

Abstract

Modelling of a system is a very useful tool for proper understanding and analysis. Of late, modelling of human systems has gained its importance as well as popularity owing to more and more interaction amongcst medical profess ionals, and physicists, mathematicians and engineers. Almost all the human systems can be quantitatively studied by proper modelling. In the present work, attention is focussed on two systems only} visual system and kidney system. The choice of the systems has been made due to their utmost importance. HUMAN VISUAL SYSTEM The process of phototransduction is modelled as a two stage process ia, diffusion phenomenon followed by inhibition stage. A distributed parameter model for diffusion stage responsible for bleaching of pigments is developed. The model is analogous to an R.C. cable model of transmission line. In this case,a finite length (of pigment layers) has been taken. Frequency response of the diffusion stage shows a very interesting phenomenon. The response is not monophasic and has oscillations at low frequency. The transient response of model is calculated for the impulse and step inputs and compared with the results given by Rushton. The response of the model given here is fast as compared to the response of the model given by Rushton. The model developed is more realistic as it is based upon the actual phenomenon of bleaching. ii The second stage is the inhibition stage. The magnitude response of the inhibition stage is obtained from the experi mental amplitude data divided by the theoretical magnitude response of the diffusion stage. The theoretical magnitude response of the inhibition stage shows a rising trend for lower frequencies and decreasing trend for higher frequencies. This is the response of the actual inhibiting process. From the magnitude response of the inhibiting stage, a transfer function is obtained to represent the inhibition stage. The parameters of the transfer function are estimated so as to fit the data of its magnitude response. Parameters are calcu lated for different adaptation levels. The plots for slope and order of the model show a linear behaviour with the adaptation level in the log scale. A transfer function for the complete process of phototransduction is obtained. A network is proposed to realize the second stage. The proposed model accounts for the high and low frequency flicker responses. The behaviour of the model at high and low frequencies is controlled by the non-linear neutral process. The functional elements of the model are known components of the retina. Due to phototransduction of the light signal, electrical signal is generated in the receptor .The receptor layer signal is processed by the neurons in the retina before reaching the optic nerve. A simple neuronal network model is proposed for this process. It is then modified by the environ mental imputs to function as a. Visual pattern processor. Here the dependence of the transfer weight of the synapses on iii axon-transfer factor and dendrite transfer factor is consi dered. The simulation tests are carried out for the different type of patterns. HUMAN KIDNEY SYSTEM A five compartment model is proposed for the human kidney system. A method is given to reduce the order of the model. Results of the reduced order model are compared with the original model. The model is analyzed for the clearance of solute by hemodialysis. The results show that the clearance of low molecular weight solute is possible by this process. Model is further analyzed for clearance of solute by diffusion and hemofiltration as simultaneous process. In this case,it is found that the clearance of solute of low and middle molecular weight is possible. The treatment time is less as compared to hemodialysis process. The process of hemodialysis is not an optimal one. It is desired to reduce the treatment time with minimum operating cost, keeping the C.S.F. pressure within desired limits. An optimal feedback control policy is developed considering the dialysate flow and blood flow rates as the controlled parameters. A quadratic performance index is assumed . With the implemen tation of this policy,the requirement of dialysate fluid is reduced and the treatment time is less. The C.S.F. pressure remains within limits. If the clearance of middle molecule is required, then the process of simultaneous hemodialysis and hemofiltration is used. Another optimal policy is developed considering dialysate flow, blood flow, and the hemofiltration iv rates as the controlled parameters. This policy reduces the requirement of dialysate fluid and sterile fluid to replace the body water loss and the treatment time.- The C.S.F. pressure is within the desired limits. These policies are very useful for the home dialysis system since the cost of treatment is minimum. In hospitals, the treatment time is important as compared to cost of dialysate. Another policy is developed, for the minimum treatment time. Idapunov's direct method is used for the development of this policy. The reduction in treatment time is at the cost of dialysate fluid requirement. Another time optimal policy is developed taking hemodia lysis and hemofiltration as simultaneous processes. The policy is obtained using blood flow, dialysate flow, and hemofiltration rates as the controlled parameters. In this case ,the treatment time is minimum as compared to treatment time for feed back policy. The C.S.F. pressure is within limits.