The basic motor function of the colon is to mix and knead its contents, propel them slowly in the caudad direction, hold them in the distal colon until defecation, and provide a strong propulsive force during defecation. Infrequently, it also produces mass movements in the proximal colon. These motor functions are achieved in most species by three different types of contractions: the individual phasic contractions that include the short- and long-duration contractions, organized groups of contractions that include the migrating and nonmigrating motor complexes, and special propulsive contractions (giant migrating contractions). The spatial and temporal patterns of all of these contractions are controlled by myogenic, neural, and chemical control mechanisms. The individual phasic contractions are highly disorganized in time and space in the colon. For this reason, they are effective in mixing and kneading and slow distal propulsion. The underlying cause of the disorganization of short duration contractions is the irregularity in the frequency and waveshape of colonic electrical control activity and its phase unlocking throughout the colon. The individual contractions in many species occur in cyclic bursts called contractile states. At least in some species, these contractile states exhibit mostly caudad and sometimes orad migration. However, there are also nonmigrating or randomly migrating contractile states in the colon. These two patterns of contractile states are called colonic migrating motor complexes and colonic nonmigrating motor complexes, respectively. The giant migrating contractions provide the strong propulsive force for defecation and mass movements. The neural control of colonic contractions is organized at three levels--enteric, autonomic, and central. The enteric nervous system contains cholinergic and peptidergic neurons and plays a major role in the control of colonic contractions. The autonomic nerves, the vagi, pelvic, lumbar colonic, hypogastric, and splanchnic nerves, seem to continuously monitor the state of the colon and provide a modulatory input when necessary. These nerves play a major role in the reflexive control of colonic motor function. The voluntary input from the central nervous system coordinates the motor activity of the colon, rectum, anal canal and sphincters for orderly evacuation of feces during defecation. The role of acetylcholine, nonadrenaline, and the yet to be completely identified nonadrenergic, noncholinergic neurotransmitter, possibly VIP, in the control of contractions is fairly well established. Besides these, there are several other peptides and chemicals that are localized in the colonic wall; their physiological roles remain unknown. Colonic motor activity has been studied in several disease states. The findings have not always been consistent.(ABSTRACT TRUNCATED AT 400 WORDS)

Physiology and pathophysiology of colonic motor activity (2).

A set of van der Pol oscillators is arranged in a network in which each oscillator is coupled to each other oscillator. Through the selection of coupling coefficients, the network is made to appear as a ring and as a chain of coupled oscillators. Each oscillator is provided with amplitude, frequency, and offset parameters which have analytically indeterminable effects on the output waves. These systems are simulated on the digital computer in order to study the amplitude, frequency, offset, and phase relationships of the waves versus parameter changes. Based on the simulations, systems of coupled oscillators are configured so that they exhibit stable patterns of signals which can be used to model the central pattern generator (CPG) of living organisms. Using a simple biped as an example locomotory system, the CPG model generates control signals for simulated walking and jumping maneuvers. It is shown that with parameter adjustments, as guided by the simulations, the model can be made to generate kinematic trajectories which closely resemble those for the human walking gait. Further-more, minor tuning of these parameters along with some algebraic sign changes of coupling coefficients can effect a transition in the trajectories to those of a two-legged hopping gait. The generalized CPG model is shown to be versatile enough that it can also generate various n-legged gaits and spinal undulatory motions, as in the swimming motions of a fish.

Modeling of a Neural Pattern Generator with Coupled nonlinear Oscillators

The results of an investigation of the structure and stability of various oscillatory modes of an inductance coupled ring of the van der Pol oscillators, using a nonlinear mode analysis, are presented. It has been demonstrated that all single modes, both standing and traveling waves, are stable, but that simultaneous two and three modes are not stable. Experiments have been performed using four- and five-oscillator rings and the results obtained agree well with the theory.

Mode analysis of a ring of a large number of mutually coupled van der Pol oscillators

Self-Sustained Oscillations in a Ring Array of Coupled Lossless Transmission Lines

Coupled oscillators in a ring are studied using perturbation and numerical methods. Stability of waves with nearest neighbor weak coupling is shown for a class of simple oscillators. Linkens' [23] model for colorectal activity is analyzed and several stable modes are found. Stability of waves with general (non nearest neighbor coupling) is determined and comparisons to the nearest neighbor case are made. Approximate solutions to a ring with inhomogeneities are compared with numerical simulations.

The behavior of rings of coupled oscillators.

Measurement of the colorectal myoelectrical activity in humans has revealed three basic patterns of behavior, comprising a lower frequency oscillation of about 0.05 Hz, a higher frequency of about 0.12 Hz and periods of zero activity. To simulate these myoelectrical patterns, the concept of linked relaxation oscillators is extended in this paper using three different mathematical model structures. In the three models two of the activity patterns are obtained as two stable limit cycle solutions produced by symmetrically coupling together two relaxation oscillators. The first model comprises a ring of interconnected oscillators which produces a third stable solution representing the higher frequency of oscillation. Summation of adjacent oscillator outputs reproduces the zero activity when the oscillators are in antiphase. By addition of an extra coefficient into the basic relaxation oscillator equation for the second model, the zero state becomes a stable condition and the three patterns are obtained without the necessity of a ring structure. The third model requires an in-situ change in a parameter value for the lower and higher frequencies to decay away to the zero activity condition.

Herbert L. Duthie

Papers

Mathematical Modeling of the Colorectal Myoelectrical Activity in Humans