Energy-based bond graph modelling of biomolecular systems is extended to include chemoelectrical transduction thus enabling integrated thermodynamically compliant modelling of chemoelectrical systems in general and excitable membranes in particular. Our general approach is illustrated by recreating a well-known model of an excitable membrane. This model is used to investigate the energy consumed during a membrane action potential thus contributing to the current debate on the trade-off between the speed of an action potential event and energy consumption. The influx of is often taken as a proxy for energy consumption; in contrast, this study presents an energy-based model of action potentials. As the energy-based approach avoids the assumptions underlying the proxy approach it can be directly used to compute energy consumption in both healthy and diseased neurons. These results are illustrated by comparing the energy consumption of healthy and degenerative retinal ganglion cells using both simulated and in vitro data.

This study considers the problem of non-fragile reliable control synthesis for mathematical model of interaction between the sugarcane borer (Diatraea saccharalis) and its egg parasitoid Trichogramma galloi. In particular, the control could be substituted by periodic releases of a small population of natural enemies and hence it is important to propose the time-varying controller in sugarcane borer. The main aim of this study is to design a state feedback non-fragile (time-varying) reliable controller such that the states of the sugarcane borer system reach the equilibrium point within the desired period. A novel approach is proposed to deal with the uncertain matrices which appear in non-fragile reliable control. Finally, simulations based on sugarcane borer systems are conducted to illustrate the advantages and effectiveness of the proposed design technique. The result reveals that the proposed non-fragile control provides good performance in spite of periodic releases of a small population of natural enemies occurs.

Deep brain stimulation (DBS) is a clinical remedy to control tremor in Parkinson's disease. In DBS, one of the two main areas of basal ganglia (BG) is stimulated. This stimulation is produced with no feedback of the tremor and often causes a wide range of unpleasant side effects. Using a feedback signal from tremor, the stimulatory signal can be reduced or terminated to avoid extra stimulation and as a result decrease the side effects. To design a closed-loop controller for the non-linear BG model, a complete study of controllability and observability of this system is presented in this study. This study shows that the BG model is controllable and observable. The authors also propose the idea of stimulating the two BG areas simultaneously. A two-part controller is then designed: a feedback linearisation controller for subthalamic nucleus stimulation and a partial state feedback controller for globus pallidus internal stimulation. The controllers are designed to decrease three indicators: the hand tremor, the level of delivered stimulation signal in disease condition, and the ratio of the level of delivered stimulation signal in health condition to disease condition. Considering these three indicators, the simulation results show satisfactory performance.