SD Rat Liver Polydatin Concentration Control Based On Sliding Mode with High-gain Observer

Abstract

In this paper, we use the sliding mode control based on high gain observer to control the concentration of Polydatin in the liver of SD rates. Through data processing and with the help of the nlinfit function in MATLAB, we take a fitting analysis by using the Polydatin distribution data in SD rats’ liver tissues and achieve a very good fitting effect. Based on the fitting function that have got, we take the sliding mode control to design observer and controller for controlling the output and creating MATLAB / Simulink simulation program. The mathematical model that we made is clear and accurate, from which, we can easily observe and analyze the input-output curves, estimate effectively the results, achieve our purpose that control the output by controlling the input. Simulation results show that the control algorithm have certain robustness and can achieve a good result to the external disturbance and parameter uncertainty. Introduction Modern pharmacological studies show that the Polydatin can improve microcirculation, inhibit the release of lysosomal enzymes, lower blood pressure, anti-lipid peroxidation, anti-platelet aggregation, anti-platelet aggregation, cure cough and asthma, anti-bacterial, anti-viral and so on [1-3]. The polydatin injections can be used to treat myocardial ischemia, cerebral ischemia, shock and other cardiovascular cerebrovascular diseases, to reduce tissue and organ damages caused by a variety of factors [4, 5]. Taking effect in cells, Polydatin provides a theoretical guidance for developing new drugs and studying shock mechanism [6, 7]. Sliding mode control is a special control strategy, with a simple algorithm, have a advantage of insensitivity to parameter changes and disturbances, no system online identification, physical implementation simplicity, robustness and high reliability [8], it is widely used in a various of control systems in engineering practice, especially for the deterministic control system that can establish a accurate mathematical model. This control method makes the system state slide along the sliding surface by switching the control parameters, it also makes the system uncertain when it is affected by the proactive move parameters and external interference. It is the feature that makes the sliding mode control method attention of scholars [9, 10]. International Conference on Biological Sciences and Technology (BST 2016) © 2016. The authors Published by Atlantis Press 85 Data [7] SD rats were intravenously injected with a single dose administration of 20mg/Kg Polydatin, the data of drug distribution in liver tissue are as following Table1. Table 1. The data of drug distribution in liver tissue Time(min) Liver tissue drug concentration (μ/g)) 10 1.74±0.46 40 0.38±0.02 60 0.27±0.13 120 0.15±0.09 240 0.11±0.02 Establishing Two-compartment Model [11, 12] Establishing Pharmacokinetic Model The amount of drugs x1(t) in absorption chamber (such as blood) satisfies the following differential formula (1): 1 1 1 1 0 ( ) ( ), (0) dx t k x t x mc dt    (1) In formula (1), k1 is the ratio of drug's rate(the amount of the drugs reduces in per unit time in the absorption chamber), from absorption chamber (or blood) to central chamber (such as liver), and the amount of drug in absorption chamber. mc0 is the total amount of drugs, m is the mass of SD rats,c0 is the ratio. The amount of drugs in Central chamber (such as liver) satisfies the differential formula (2): ) ( ) ( ) ( 1 2 1 1 1 t y k t x k dt t dy   , 0 ) 0 ( 1  y (2) In formula (2), k2 is the ratio of drug's rate (the amount of drugs reduces in per unit time in the central chamber), from the central chamber to vitro, and the amount of drugs in the central compartment. We solve the above formula (2) initial results by using MATLAB, the results are as follows formula (3). 1 1 0 0 1 2 1 1 1 2 ( ) ( ) ( ) k t k t k t x t mc e mc k y t e e k k           (3) Note c(t)=y1(t)/m1, among them, m1 is the mass of the liver, bringing c(t) into the formula (3), we can obtain as follows formula(4):