Acupuncture requires a long-term training to handle acupoints. Three techniques exist:
(1) development of a local mechanical stress field by needle motions (lifting--thrusting cycle or rotation) at acupoints;
(2) development of a local temperature field by directly applying a heating moxa (mugwort herb) stick on the skin or indirectly by applying this stick on the acupuncture needle (moxibustion) at acupoints;
(3) development of a local electrical field by applying a small electric current between a pair of acupuncture needles (electroacupuncture, or percutaneous electrical nerve stimulation [PENS]) at acupoints.
Acupuncture effects result from a set of signals sent from activated mastocytes at given acupoints to local nerve endings, capillaries, heart, and brain. Mastocytes are activation by a mechanical stress field (mechanotransduction), heating (thermotransduction), or a electrical field (electrotransduction). Whatever the operation mode, calcium entry in the mastocyte triggers degranulation and release of chemoattractants, neural stimulants, and endocrine substances. The process is sustained by recruitment of mastocytes (chemotaxis).
In the case of mechanotransduction, the mechanical stress is modeled by a compact-supported function. The mathematical model is a system of 5 parabolic partial differential equations. Its simplest form describes the evolution of the density of mastocytes and the chemoattractant concentration.
A mathematical analysis leads to a theorem for blow-up condition as well as an analytical solution useful for validation. Numerical simulations are also carried out using a finite element method (freeFEM$++$) with mesh adaptivity.