References
P. K. Klimov, Functional Relationships in the Digestive System [in Russian], Leningrad (1976).
A. Bortoff, “Myogenic control of intestinal motility,” Physiol. Rev.,56, No. 2, 418–434 (1976).
G. M. Frigo and S. Lecchini, “An improved method for studying the peristaltic reflex in the isolated colon,” Brit. J. Pharm.,39, 346–356 (1970).
J. J. Galligan, M. Costa, and J. B. Furness, “Gastrointestinal myoelectric activity in conscious guinea-pigs,” Am. J. Physiol.,249, No. 1, G92-G99 (1985).
A. D. Nozdrachev, Physiology of Vegetative Nervous Systems [in Russian], Leningrad (1983).
J. D. Wood, “Neurophysiology of Auerbach's plexus and control of intestinal motility,” Physiol. Rev.,213, No. 1, 275–286 (1975).
G. D. Hirst, M. E. Holman, and H. C. McKirdy, “Two descending nerve pathways activated by distension of guinea-pig small intestine,” J. Physiol.,244, No. 1, 113–127 (1975).
A. D. Nozdrachev, “Functional organization of myenteric plexus ganglia,” Fiziol. Zh. SSSR,63, No. 2, 268–276 (1977).
R. N. Miftakhov, “Nonlinear electromechanical waves in a cylindrical biomembrane,” in: Biomechanics of Soft Tissue [in Russian], Kazan' (1987), pp. 26–63.
R. N. Miftakhov, “Nonlinear transient wave deformation processes in soft biomembrane,” in: Biomechanics of Soft Tissue [in Russian], Kazan', (1987), pp. 64–74.
R. N. Miftakhov and I. S. Adamovich, “Simulation of cholinergic synapse,” in: Advances of Biomechanics in Medicine and Surgery [in Russian], Riga (1988), pp. 18–28.
R. N. Miftakhov, “Numerical analysis of electrical excitation and response of smooth-muscle fiber,” in: Mechanics of Biological Continua [in Russian], Kazan' (1986), pp. 68–80.
R. N. Miftakhov, “The effect of a change in the ionic composition of the medium on the propagation of excitation and the mechanical reaction of a smooth muscle,” in: Mechanics of Biological Continua [in Russian], Kazan' (1986), pp. 81–101.
G. Vantrappen, “The migrating myoelectric complex,” in: Motility of the Digestive Tract, New York (1982), pp. 157–167.
R. Hasselbrack and J. E. Thomas, “Control of intestinal rhythmic contractions by a duodenal pacemaker,” Am. J. Physiol.,201, No. 5, 955–960 (1961).
E. Bülbring, G. Burnstock, and M. E. Holman, “Excitation and conduction in the smooth muscle of the isolatedtaenia coli of the guinea-pig,” J. Physiol.,142, No. 3, 420–437 (1958).
A. Bortoff and E. Ghalib, “Temporal relationship between electrical and mechanical activity of longitudinal and circular muscle during intestinal peristalsis,” Digestive Diseases,17, No. 4, 317–325 (1972).
A. Crema, G. M. Frigo, and S. Lecchini, “A pharmacological analysis of the peristaltic reflex in the isolated colon of the guinea-pig or cat,” Brit. J. Pharm.,39, 334–345 (1970).
A. Bortoff, “Myogenic control of intestinal motility,” Physiol. Rev.,56, No. 2, 418–434 (1976).
H. L. Duthie, B. H. Brown, B. Robertson-Dunn, and others, “Electrical activity in the gastroduodenal area: slow waves in the proximal duodenum, a comparison of the man and dog,” Digestive Diseases,17, 344–351 (1972).
Physiology of Digestion [in Russian], Leningrad (1974).
T. Nagai and C. L. Prosser, “Electrical parameters of smooth muscle cells,” Am. J. Physiol.,204, No. 5, 915–924 (1963).
M. Kobayashi, C. L. Prosser, and T. Nagai, “Electrical properties of intestinal muscle as measured intracellularly and extracellularly,” Am. J. Physiol.,213, No. 4, 275–286 (1967).
A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol.,117, No. 4, 500–544 (1952).
H. Kuriyama and F. Mekata, “Biophysical properties of the longitudinal smooth muscle of the guinea-pig rectum,” J. Physiol.,212, No. 3, 667–683 (1971).
H. W. Kosterlitz and R. J. Lydon, “Impulse transmission in the myenteric plexus-longitudinal muscle preparation of the guinea-pig ileum,” Brit. J. Pharm.,43, No. 1, 74–85 (1971).
V. N. Ustinov, “Biopotentials of smooth muscle and contraction activity of the duodenum,” Fiziol. Zh. SSSR,61, No. 7, 1060–1067 (1975).
Y. Abe and T. Tomita, “Cable properties of smooth muscle,” J. Physiol.,196, No. 1, 87–100 (1968).
W. J. Snape Jr. and Swee-Teck Tan, “Role of sodium or calcium in electrical depolarization of feline colonic smooth muscle,” Am. J. Physiol.,243, No. 1, 66–72 (1985).
R. N. Miftakhov, “Reaction of smooth muscle to electrical stimulation by a train of impulses,” in: Strength and Stability of Membranes [in Russian], Kazan' (1986), pp. 110–122.
A. Bertuzzi, R. Mancinelli, G. Ronzoni, and S. Salinari, “A mathematical model of intestinal motor activity,” J. Biomech.,11, No. 1–2, 41–47 (1978).
M. Pescatori, F. Grasetti, G. Ronzoni, R. Mancinelli, A. Bertuzzi, and S. Salinari, “Peristalsis in distal colon of the rabbit: an analysis of mechanical events,” Am. J. Physiol.,236, No. 4, 464–472 (1979).
A. Bertuzzi, R. Mancinelli, M. Pescatori, and S. Salinari, “An analysis of the peristaltic reflex,” Biol. Cyber.,35, No. 4, 205–212 (1979).
A. Bertuzzi, S. Salinari, R. Mancinelli, and M. Pescatori, “Peristaltic transport of solid bolus,” J. Biomech.,16, No. 7, 464–469 (1983).
U. Yaji and I. Norio, “Biomechanical analysis of peristalsis. A simulation model of peristalsis for liquid contents,” Trans. Soc. Instrum. Contr. Eng.,21, No. 2, 172–176 (1985).
U. Yaji, “Autonomy and distribution of motion in small intestine,” Keisoku to Seige,26, No. 1, 75–77 (1987).
G. D. S. Hirst and H. C. McKirdy, “Synaptic potentials recorded from neurons of the submucous plexus of guinea-pig small intestine,” J. Physiol.,249, No. 2, 369–385 (1975).
M. E. Holman, G. D. S. Hirst, and I. Spence, “Preliminary studies of the neurons of Auerbach's plexus using intracellular microelectrodes,” Austr. J. Exper. Biol. Med. Sci.,50, Part 7, 795–801 (1972).
S. R. Kottegoda, “An analysis of possible nervous mechanisms involved in the peristaltic reflex,” J. Physiol.,200, No. 3, 687–712 (1969).
W. D. M. Paton and M. A. Zar, “The origin of acetylcholine released from guinea-pig intestine and longitudinal muscle strips,” J. Physiol.,194, No. 1, 13–33 (1968).
J. Christensen, J. R. Golover, E. O. Macagno, R. B. Singerman, and N. W. Weisbrodt, “Statistics of contractions at a point in the human duodenum,” Am. J. Physiol.,221, No. 6, 1818–1823 (1971).
I. R. Morris, P. H. Hammond, C. Darby, and I. Taylor, “Relationship between motility and myoelectrical activity in the canine small and large intestine studied by a common electrode,” in: Motility of the Digestive Tract, New York (1982), pp. 250–265.
P. C. Specht and A. Bortoff, “Propagation and electrical entrainment of intestinal slow waves,” Digestive Diseases,17, No. 4, 311–316 (1972).
C. Mendel, A. Pousse, A. Lambert, P. Sava, and J. F. Gremier, “Recording of canine intestinal chronic longitudinal movements,” in: Gastrointestinal Motility, New York (1980), pp. 323–330.
B. H. Brown, “Electrophysiological measurements from the smooth muscle of human gastrointestinal tract,” IEE Med. Electron. Monograph, No. 18-22, 1–26 (1976).
N. E. Diamant and A. Bortoff, “Nature of the intestinal slow-wave frequency gradient,” Am. J. Physiol.,216, No. 2, 301–307 (1969).
D. A. Linkens, “Colonic electrical activity and frequency multiplication in coupled non-linear oscillators,” J. Physiol.,276, No. 1, 37–38 (1978).
T. S. Nelsen and J. C. Becker, “Simulation of the electrical and mechanical gradient in the small intestine,” Am. J. Physiol.,214, No. 4, 749–767 (1968).
Additional information
Translated from Issledovaniya po Prikladnoi Matematike, No. 17, pp. 78–105, 1990.
Rights and permissions
About this article
Cite this article
Miftakhov, R.N. Mathematical modeling of the peristaltic reflex: A numerical experiment. J Math Sci 71, 2775–2789 (1994). https://doi.org/10.1007/BF02110585
Issue Date:
DOI: https://doi.org/10.1007/BF02110585