Efficacy of acupuncture at ghost points combined with fluoxetine in treating depression:A randomized study

BACKGROUND Depression affects more than 350 million people worldwide.In China,4.2%(54 million people)of the total population suffers from depression.Psychotherapy has been shown to change cognition,improve personality,and enhance the ability to cope with difficulties and setbacks.While pharmacotherapy can reduce symptoms,it is also associated with adverse reactions and relapse after drug withdrawal.Therefore,there has been an increasing emphasis placed on the use of non-pharmacological therapies for depression.The hypothesis of this study was that acupuncture at ghost points combined with fluoxetine would be more effective than fluoxetine alone for the treatment of depression.AIM To investigate the efficacy of acupuncture at ghost points combined with fluoxetine for the treatment of patients with depression.METHODS This randomized controlled trial included patients with mild to moderate depression(n=160).Patients received either acupuncture at ghost points combined with fluoxetine(n=80)or fluoxetine alone(control group,n=80).Needles were retained in place for 30 min,5 times a week;three treatment cycles were administered.The Mann–Whitney U test was used to compare functional magnet resonance imaging parameters,Hamilton depression rating scale(HAMD)scores,and self-rating depression scale(SDS)scores between the acupuncture group and control group.RESULTS There were no significant differences in HAMD or SDS scores between the acupuncture group and control group,before or after 4 wk of treatment.The acupuncture group exhibited significantly lower HAMD and SDS scores than the control group after 8 wk of treatment(P<0.05).The acupuncture group had significantly lower fractional Amplitude of Low Frequency Fluctuations values for the left anterior wedge leaf,left posterior cingulate gyrus,left middle occipital gyrus,and left inferior occipital gyrus after 8 wk.The acupuncture group also had significantly higher values for the right inferior frontal gyrus,right insula,and right hippocampus(P<0.05).After 8 wk of treatment,the effective rates of the acupuncture and control groups were 51.25%and 36.25%,respectively(P<0.05).CONCLUSION The study results suggest that acupuncture at ghost points combined with fluoxetine is more effective than fluoxetine alone for the treatment of patients with mild to moderate depression.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology

We propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded domains.The technique is based on a smooth coordinate transformation,which maps an unbounded domain into a unit square.Arbitrary geometries are defined by suitable level-set functions.The equations are discretized by classical nine-point stencil on interior points,while boundary conditions and high order reconstructions are used to define the field variables at ghost-points,which are grid nodes external to the domain with a neighbor inside the domain.The linear system arising from such discretization is solved by a multigrid strategy.The approach is then applied to solve elasticity problems in volcanology for computing the displacement caused by pressure sources.The method is suitable to treat problems in which the geometry of the source often changes(explore the effects of different scenarios,or solve inverse problems in which the geometry itself is part of the unknown),since it does not require complex re-meshing when the geometry is modified.Several numerical tests are successfully performed,which asses the effectiveness of the present approach.