Coordination in circular and longitudinal muscle motions are of crucial importance in the motor function of gastrointestinal (GI) tract. Intestinal wall motions depend on myogenic-active properties of smooth muscles layers of intestinal wall, which i
s the ability to create active contractile forces in response to distension. Considering the stress in the circular and longitudinal smooth muscles as a sum of passive, depending on muscle deformations, and active, depending on muscle tone, components, and also assuming that the change in the muscle tone depends on the current stress-strain condition, the system of four ordinary differential equations (ODE) is obtained, which describes filling-emptying cycle of intestinal segment as a process of coordinated activities of circular and longitudinal muscles of intestinal wall. A general approach in formulating the modelling conditions is based on the previously described model restricted to the circularly distensible reservoir of constant length. Obtained results illustrate the character of coordinated activities of two orthogonal muscle layers, which are alternating phases of reciprocally and uniformly changing modalities such as stretching of the wall and muscle tone. The results also contribute to the existing understanding of the roles of Auerbachs and Meisners intermuscular and submucous neural plexuses in regulations of autonomous intestinal motility, as well as clarify functional mechanisms of the interstitial cells of Cajal (ICC) in triggering of smooth muscle contractions.
A notion of biologic system or just a system implies a functional wholeness of comprising system components. Positive and negative feedback are the examples of how the idea to unite anatomical elements in the whole functional structure was successful
ly used in practice to explain regulatory mechanisms in biology and medicine. There are numerous examples of functional and metabolic pathways which are not regulated by feedback loops and have a structure of reciprocal relationships. Expressed in the matrix form positive feedback, negative feedback, and reciprocal links represent three basis elements of a Lie algebra sl(2,R)of a special linear group SL(2,R). It is proposed that the mathematical group structure can be realized through the three regulatory elements playing a role of a functional basis of biologic systems. The structure of the basis elements endows the space of biological variables with indefinite metric. Metric structure resembles Minkowskis space-time (+, -, -) making the carrier spaces of biologic variables and the space of transformations inhomogeneous. It endows biologic systems with a rich functional structure, giving the regulatory elements special differentiating features to form steady autonomous subsystems reducible to one-dimensional components.
