@Article{CiCP-18-831,
author = {Marc Thiriet, Yannick Deleuze and Tony Wen-Hann Sheu},
title = {A Biological Model of Acupuncture and Its Derived Mathematical Modeling and Simulations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {18},
number = {4},
pages = {831--849},
abstract = {<p style="text-align: justify;">(<strong>Aims</strong>) Acupuncture was employed since 2 millenaries, but the underlying
mechanisms are not globally handled. The present study is aimed at proposing an
explanation by pointing out involved processes and a convincing modeling to demonstrate
its efficiency when carried out by trained practitioners.<br/>(<strong>Method</strong>) In the absence of global knowledge of any mechanism explaining the
acupuncture process, a biological model is first developed, based on stimulation in a
given domain around the needle tip of a proper mastocyte population by a mechanical
stress, electrical, electromagnetic, or heat field. Whatever the type of mechanical or
physical stimuli, mastocytes degranulate. Released messengers either facilitate the
transfer of main mediators, or target their cognate receptors of local nerve terminals or
after being conveyed by blood their receptors on cerebral cells. Signaling to the brain
is fast by nervous impulses and delayed by circulating messengers that nevertheless
distribute preferentially in the brain region of interest due to hyperemia. The process
is self-sustained due to mastocyte chemotaxis from the nearby dense microcirculatory
circuit and surrounding mastocyte pools, which are inadequate for acupuncture, but
serve as a signal relay. A simple mathematical model is solved analytically. Numerical
simulations are also carried out using the finite element method with mesh adaptivity.<br/>(<strong>Results</strong>) The analytical solution of the simple mathematical model demonstrates
the conditions filled by a mastocyte population to operate efficiently. A theorem gives
the blow-up condition. This analytical solution serves for validation of numerical experiments.
Numerical simulations show that when the needle is positioned in the
periphery of the acupoint or outside it, the response is too weak. This explains why a&nbsp;long training is necessary as the needle implantation requires a precision with a magnitude
of the order of 1 mm.<br/>(<strong>Conclusion</strong>) The acupoint must contain a highly concentrated population of mastocytes
(e.g., very-high–amplitude, small-width Gaussian distribution) to get an initial
proper response. Permanent signaling is provided by chemotaxis and continuous recruitment
of mastocytes. Therefore, the density and distribution of mastocytes are
crucial factors for efficient acupuncture as well as availability of circulating and neighboring
pools of mastocytes.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.121214.250515s},
url = {http://global-sci.org/intro/article_detail/cicp/11051.html}
}