Limit Cycle of a Single-Neuron System With Smooth Continuous and Binary-Value Activation Functions and Its Circuitry Design.

In this brief, we investigate the limit cycle of a single-neuron system with smooth continuous and binary-value activation functions and its circuit design. By transforming the system into Liénard-type and using Poincaré-Bendixson theorem as well as the symmetry of these systems, we obtain the existence conditions of limit cycle of the system. Then, by comparing the integral value of the differential of positive definite function along two assumed limit cycles, we prove that the system cannot produce two coexisting limit cycles, which means that the system has at most one limit cycle. In addition, according to the two specific functions, i.e., smooth continuous and binary-value activation functions of the system, we give the numerical simulation and realize the circuit design of the single-neuron system by using Multisim modeling, respectively. The waveform diagram and phase diagram of the numerical simulation and circuit simulation are obtained. By comparing the results of numerical and circuit simulation, the effectiveness of our mathematical analysis and the feasibility of circuit design are better illustrated.

Combined use of non-biological artificial liver treatments for patients with acute liver failure complicated by multiple organ dysfunction syndrome.

BACKGROUND: Acute liver failure (ALF) caused by viral and non-viral hepatitis is often accompanied with severe metabolic disorders, the accumulation of toxic substances and continuous release and accumulation of a large number of endogenous toxins and inflammatory mediators. The present study aimed to investigate the effects of various combined non-biological artificial liver treatments for patients with acute liver failure (ALF) complicated by multiple organ dysfunction syndrome (MODS). METHODS: Thirty-one patients with mid- or late-stage liver failure complicated by MODS (score 4) were randomly divided into three treatment groups: plasmapheresis (PE) combined with hemoperfusion (HP) and continuous venovenous hemodiafiltration (CVVHDF), PE+CVVHDF, and HP+CVVHDF, respectively. Heart rate (HR) before and after treatment, mean arterial pressure (MAP), respiratory index (PaO2/FiO2), hepatic function, platelet count, and blood coagulation were determined. RESULTS: Significant improvement was observed in HR, MAP, PaO2/FiO2, total bilirubin (TBIL) and alanine aminotransferase (ALT) levels after treatment (P<0.05). TBIL and ALT decreased more significantly after treatment in the PE+CVVHDF and PE+HP+CVVHDF groups (P<0.01). Prothrombin time (PT) and albumin were significantly improved only in the PE+CVVHDF and PE+HP+CVVHDF groups (P<0.05). TBIL decreased more significantly in the PE+HP+CVVHDF group than in the HP+CVVHDF and PE+CVVHDF groups (P<0.05). The survival rate of the patients was 58.1% (18/31), viral survival rate 36.4% (4/11), and non-viral survival rate 70% (14/20). CONCLUSION: Liver function was relatively improved after treatment, but PE+HP+CVVHDF was more efficient for the removal of toxic metabolites, especially bilirubin. The survival rate was significantly higher in the patients with non-viral liver failure than in those with viral liver failure.