Zhichan decoction induces differentiation of dopaminergic neurons in Parkinson's disease rats after neural stem cell transplantation

The goal of this study was to increase the dopamine content and reduce dopaminergic metabolites in the brain of Parkinson’s disease rats. Using high-performance liquid chromatography, we found that dopamine and dopaminergic metabolite（dihydroxyphenylacetic acid and homovanillic acid） content in the midbrain of Parkinson’s disease rats was increased after neural stem cell transplantation ＋ Zhichan decoction, compared with neural stem cell transplantation alone. Our genetic algorithm results show that dihydroxyphenylacetic acid and homovanillic acid levels achieve global optimization. Neural stem cell transplantation ＋ Zhichan decoction increased dihydroxyphenylacetic acid levels up to 10-fold, while transplantation alone resulted in a 3-fold increment. Homovanillic acid levels showed no apparent change. Our experimental findings show that after neural stem cell transplantation in Parkinson’s disease rats, Zhichan decoction can promote differentiation of neural stem cells into dopaminergic neurons.

Numerical Discretization-Based Kernel Type Estimation Methods for Ordinary Differential Equation Models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation（ODE） models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method（kernel smoothing or local polynomial fitting） in the first stage, and a numerical discretization method（Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method） in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.