This article proposes a novel generalized Taylor expansion method of moments (TEMOM) scheme for solving the population balance equation. The proposed scheme can completely overcome the shortcoming of the existing TEMOM and substantially improve the accuracy for both integer and fractional moments. In the generalized TEMOM, the optimal number of equations is 2fC1, where f is an integer greater than zero. The existing TEMOM is a special case of the generalized TEMOM when f is 1. The generalized TEMOM was tested for aerosols undergoing Brownian coagulation in the continuum regime, and it was verified to achieve nearly the same accuracy as the quadrature method of moments (QMOM) with a fractional moment sequence, and higher accuracy than the QMOM with an integer moment sequence. Regarding accuracy and efficiency, the generalized TEMOM scheme was verified to be a competitive method for solving the population balance equation.
The aim of the present study was to investigate the protective effect of taurine on lipopolysaccharide (LPS)-induced liver injury and its mechanisms. Male rats were randomly divided into three groups: Normal saline, LPS model and taurine treatment. Experimental animals were treated with saline or taurine (dissolved in saline, 200 mg/kg/day) via intravenous injection. After 2 h, saline or LPS (0.5 mg/kg) was administrated via intraperitoneal injection. Markers of liver injury, pro-inflammatory cytokines and superoxide dismutase (SOD) activity were determined in plasma. Liver tissues were removed for morphological analysis and determination by western blot analysis. Taurine significantly reduced the elevation in the levels of LPS-induced aspartate transaminase and alanine transaminase and decreased the concentrations of LPS-induced inflammatory factors including tumor necrosis factor-α and interleukin-6. Taurine also increased the activity of SOD in serum and the expression of heme oxygenase-1 protein in liver tissue. Taurine pretreatment also reduced the elevated expression levels of LPS-induced cyclooxygenase-2, nuclear factor κB and extracellular regulated protein kinase. The results from the present study demonstrated that taurine alleviates LPS-induced liver injury. The beneficial role of taurine may be associated with its reduction of pro-inflammatory response and oxidative stress.
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