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The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system, using Monte Carlo (MC) algorithm with importance sampling. However, conventional MC algorithm has some difficulties when applied to inverse potentials. We propose to use effective potential and extrapolation method to solve the problem. We present examples from the hydrogen system.

BackgroundThe glenohumeral joint is subjected to opposing forces when the direction of shoulder motion is changed, accelerating and decelerating to make the movements. The influence of motion velocity or acceleration on translation of the humeral head has not been evaluated although direction and distance of humeral head translation has been analyzed in real time in normal shoulders. We hypothesized that, in a normal shoulder, the humeral head does not deviate significantly or suddenly during active shoulder rotation regardless of motion velocity. The purpose of this study was to clarify normal intraarticular kinematics of humeral head position and translation during axial shoulder rotation with the arm by the side of the body at different rotational velocities using cine magnetic resonance imaging (MRI).MethodsBoth shoulders of ten healthy adults (mean age group between 27.80 ± 6.05 years) were used in this study. Prior to MRI scan, dynamic glenohumeral stability was confirmed by physical examination. The glenohumeral joint was scanned during active shoulder rotation at three angular velocities (low, medium and high velocities), with the arm by the side of the body by real-time cine MRI while recording with the help of a video camera. Translation of the humeral head and rotation angles on MR imaging and video camera were measured to match shoulder rotational positions.ResultsThere were no statistical differences of the humeral head position and translation among three rotation velocities (p > 0.05). Translation of the humeral head was distributed from 1.44 ± 2.45 mm anteriorly to 0.65 ± 1.84 mm posteriorly at low velocity, from 0.74 ± 1.92 mm anteriorly to 0.75 ± 2.17 mm posteriorly at medium velocity, and from 2.62 ± 2.19 anteriorly to 1.17 ± 1.44 mm posteriorly at high velocity.ConclusionsTranslation of the humeral head was shown to undergo no significant change throughout the ranges of internal and external rotation, or among different rotational velocities in dynamic stability of the glenohumeral joint.

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