A Mathematical Model to Study the Mechanical Information Induced by Lifting-Thrusting Needle

Focusing on the mechanical effect of traditional Chinese acupuncture, this study builds a mathematical model that simulates the mechanical process of lifting-thrusting needle. Analytic and numerical solutions are obtained to explore the mechanical information (displacement, strain, stress, and energy) in the skin tissue. Our results show that (1) needle manipulation leads to tissue displacement and mechanical stress field, but the needle should be inserted into the right position (about π/ω cm around the acupoint, where ω is the angular frequency) and enough depth (about 2 cm in lower limbs) to achieve effective mechanical stimuli; (2) the tissue displacement decays with an increase of distance from the stimulus position, more rapidly at higher frequencies; (3) there is an inverse relationship between the area of the 'effective influence region' (where shear strain > 0.2) and the stimulus frequency, which means larger needle movement is needed at higher frequencies to achieve a better curative effect; (4) more energy is required to maintain high frequency manipulation. This study proposes a preliminary comprehension of the mechanical response around the needle during the acupuncture process.