მათემატიკის დეპარტამენტის სამეცნიერო სემინარი თემაზე: "Modelling of acupuncture"

მომხსენებელი: პროფესორი    მ. ტირიე  (პიერ და მარი კიურის უნივერსიტეტი)
 

მოკლე ანოტაცია

Traditional Chinese medicine defines acupuncture points, or emph{acupoints}, for therapeutic objectives, more than 2500 years ago. An acupuncture needle is inserted into selected acupoints on the bodys surface, on which mechanical (needling with lifting--thrusting cycle or twisting), electrical (electro-needling), or other types (e.g., heat [moxibustion]) of physical stimulations are exerted, in particular to cause analgesia. Acupuncture can be assumed to be based on the chemical response especially of mastocytes at acupoints to the sensed mechanical stresses caused by needle motions. A self-sustained process is created via the recruitment of circulating mastocytes and excitation of regional pools of mastocytes. Chemical mediators are supposed to be quasi-instantaneously released by the mechanotransduction process that mainly relies on an sudden, rapid, and copious calcium entry in the mastocyte cytosol. This calcium wave that gush and pervade the mastocyte enables it to discharge chemoattractants, nerve messengers, cardiovascular stimulants, and endocrine messengers. On the other hand, the regeneration of granules content inside the mastocyte is delayed and slow. Following chemotaxis from regional pools and blood, newly arrived mastocytes at acupoints experience a degranulation triggered by the stress field.  The resulting self-sustained process enables the local elevation of vascular permeability for improved cardiac output and enhanced endocrine signaling, vasodilation associated with a resulting increase in blood flow (remote cardiac effect), endocrine signaling to central nervous system that supports a delayed and permanent response from neurons situated in a brain region characterized by hyperemia, which can receive set of action potentials during a long period.

The mathematical model of acupunture can be represented by the set of equations that incorporates 2~equation related to the populations of non-degranulated and degranulated mastocytes and 3~equations that describe the temporal evolution of concentrations of chemoattractant, liberated nerve stimulant ($s_n(t,x)$), and endocrine activator of some sites of the central nervous system, when convection (i.e., Stokes flow of extracellular water triggered by needle motions) in the extracellular matrix remains negligible.