A Biological Model of Acupuncture and Its Derived Mathematical Modeling and Simulations (Communications in Computational Physics, 2020)
(Aims) Acupuncture was employed since 2 millenaries, but the underlyingmechanisms are not globally handled. The present study is aimed at proposing anexplanation by pointing out involved processes and a convincing modeling to demonstrateits efficiency when carried out by trained practitioners.(Method) In the absence of global knowledge of any mechanism explaining theacupuncture process, a biological model is first developed, based on stimulation in agiven domain around the needle tip of a proper mastocyte population by a mechanicalstress, electrical, electromagnetic, or heat field. Whatever the type of mechanical orphysical stimuli, mastocytes degranulate. Released messengers either facilitate thetransfer of main mediators, or target their cognate receptors of local nerve terminals orafter being conveyed by blood their receptors on cerebral cells. Signaling to the brainis fast by nervous impulses and delayed by circulating messengers that neverthelessdistribute preferentially in the brain region of interest due to hyperemia. The processis self-sustained due to mastocyte chemotaxis from the nearby dense microcirculatorycircuit and surrounding mastocyte pools, which are inadequate for acupuncture, butserve as a signal relay. A simple mathematical model is solved analytically. Numericalsimulations are also carried out using the finite element method with mesh adaptivity.(Results) The analytical solution of the simple mathematical model demonstratesthe conditions filled by a mastocyte population to operate efficiently. A theorem givesthe blow-up condition. This analytical solution serves for validation of numerical experiments.Numerical simulations show that when the needle is positioned in theperiphery of the acupoint or outside it, the response is too weak. This explains why a long training is necessary as the needle implantation requires a precision with a magnitudeof the order of 1 mm.(Conclusion) The acupoint must contain a highly concentrated population of mastocytes(e.g., very-high–amplitude, small-width Gaussian distribution) to get an initialproper response. Permanent signaling is provided by chemotaxis and continuous recruitmentof mastocytes. Therefore, the density and distribution of mastocytes arecrucial factors for efficient acupuncture as well as availability of circulating and neighboringpools of mastocytes.