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Alimentary |
1 Division of Neuroscience, John Curtin School of Medical Research, Canberra, ACT, 0200, Australia
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(Received 25 October 2005;
accepted after revision 14 December 2005;
first published online 15 December 2005)
Corresponding author F. R. Edwards: Division of Neuroscience, John Curtin School of Medical Research, Canberra, ACT, 0200, Australia. Email: frank.edwards{at}anu.edu.au
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Introduction |
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This paper explores what electrical parameters might give rise to the slow anal and more rapid circumferential conduction velocities of slow waves in the antrum. The approach taken was to incorporate the electrical models, which have been derived to explain the generation of slow waves in the circular layer of the guinea-pig antrum (Edwards & Hirst, 2003) and pacemaker potentials in ICCMY (Edwards & Hirst, 2005), into the multidimensional cable structures making up the ICCMY network and the longitudinal and circular muscle layers which form the wall of the antrum.
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Electrical simulations
Equivalent electrical circuit. The muscular wall of the antrum consists of two layers of smooth muscle, the longitudinal and circular layers, which are both electrically connected to the intervening layer of ICCMY. The nature of the electrical connections between the three layers has been determined experimentally in a previous study (Cousins et al. 2003).
Longitudinal muscle layer
In this study a segment of longitudinal muscle 2 mm long and 600 µm wide was represented as the series connexion of 20 isopotential compartments, each 100 µm long (see Methods in Cousins et al. 2003). Small isopotential sheets of longitudinal muscle with attached networks of ICCMY have been simulated previously (Edwards & Hirst, 2005). The equivalent electrical circuit for a single short, isopotential segment of longitudinal muscle (Fig. 1A; rightmost compartment) has previously been determined (Cousins et al. 2003) and the values for the background membrane conductance (gLM, 110 nS) and the membrane capacitance (CLM, 20 nF) of the longitudinal muscle segment used in this simulation are rounded versions of those shown in Fig. 1 of Edwards & Hirst (2005).
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A compartment representing an isopotential sheet of ICCMY network was connected to each longitudinal muscle compartment (Fig. 1A, central compartment) by a conductance with the value 300 nS (Cousins et al. 2003). Pacemaker potentials were simulated largely as previously described (Edwards & Hirst, 2005). Values for the background membrane conductance (gMY, 80 nS) and the membrane capacitance (CMY, 4 nF) of the ICCMY compartment were again rounded versions of those used before (Edwards & Hirst, 2005). Initial calculations showed that the electrical description of the primary component of the pacemaker potential generated by ICCMY (Edwards & Hirst, 2005) was unable to provide an adequate description on which to base the propagation of pacemaker potentials through the ICCMY network. Except in the case of Fig. 3, the model for the primary component, gPrim(t) (Fig. 1A), was altered, with the principal change being to introduce a voltage-dependent delay between conducted depolarization and initiation of the primary component. This follows the observation on murine intestinal ICCMY that the onset of the autonomous inward current, which corresponds to the primary component in guinea-pig gastric antrum in terms of duration and sensitivity to extracellular calcium ion concentration, is invariably preceded by a small but finite delay after the onset of depolarization (Goto et al. 2004). A single step chemical reaction was proposed to convert a precursor reagent into a messenger product as shown in eqn (1), and gPrim(t) was proposed to vary directly with the concentration of the product.
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| (1) |
, and the steady state inactivation, N, varied with membrane potential as shown in Fig. 1C. The time constant for activation, 
A, had the value 60 ms at all values of membrane potential as shown in Fig. 1C. That for inactivation, N, was voltage dependent and is also shown in Fig. 1C. The following eqns (2) were used to calculate A and N, which together with KPF and KPB yielded the time course of [product].
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| (2) |
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| (3) |
The model for the messenger-dependent unitary conductance, gPlat(t), was implemented with the parameters previously described (Edwards & Hirst, 2005) except that the maximum rate of production of the intermediate reagent, KF[precursor], was reduced from 0.168 mM s–1 to 0.086 mM s–1 and m was reduced from 0.25 s to 0.15 s. These refinements improved the accuracy of the wave propagation simulations without reducing the performance of the isopotential equivalent short segment model used previously (Edwards & Hirst, 2005). The value used for the conductance connecting adjacent compartments of ICCMY (gICC, Fig. 1B) was 2800 µS. Since there is no appearance of directional asymmetry in the antral ICCMY network (Hennig et al. 2004) and the conduction velocity of pacemaker potentials in the circumferential and anal direction did not differ significantly (Hirst et al. 2006), the ICCMY compartments were assumed to be equally well connected in the oro-anal direction and in the circumferential direction as shown in Fig. 1B (gICC). The conductance connecting one longitudinal muscle compartment axially to the next in the oro-anal direction (Fig. 1B, gLLA) was set to 5764 µS. Cousins et al. (1993) obtained a mean value of 631 µm for the axial length constant of longitudinal muscle layer in guinea-pig ileum. The values chosen for connexion of ICCMY compartments and longitudinal muscle compartments in the oro-anal direction allowed simulation of this estimate of passive electrical length constant and also of the propagation velocity of pacemaker and follower potentials in the anal direction. The transverse length constant for guinea-pig ileal longitudinal muscle was 59 µm (Cousins et al. 1993). As length constant varies inversely with the square root of the internal resistance of the equivalent cable (Jack et al. 1983), the transverse connecting conductance (Fig. 1B, gLLT) was made 50.4 µS.
Circular muscle equivalent cable
Conduction of slow waves in the circumferential direction proceeded at 13.9 mm s–1 in intact tissue (Hirst et al. 2006). Experiments on preparations of antrum where the longitudinal muscle layer and accompanying ICCMY network had been removed, except for a band near the greater curvature, showed that normal slow waves persisted throughout the circular muscle layer. Circumferential conduction velocity in the region devoid of ICCMY was 14.7 mm s–1 which was not significantly different from that in intact tissue (Hirst et al. 2006). Therefore, to model circumferential electrical propagation in the antrum, a segment of a circular muscle bundle 9.6 mm long was represented as the series connexion of 16 isopotential compartments, each 600 µm long and 100 µm wide (see Methods in Cousins et al. 2003). The passive length constant of a bundle of antral circular muscle is about 3 mm (Hirst et al. 2006) so a chain of 16 compartments represented about three length electrical constants. The equivalent electrical circuit for a single short, isopotential segment of circular muscle bundle (Fig. 1A; leftmost compartment) has previously been determined (Edwards & Hirst, 2003) and the values for the background membrane conductance (gCM, 500 nS) and membrane capacitance (CCM, 80 nF) used in this simulation are rounded versions of those used previously (Edwards & Hirst, 2005). The model for messenger-dependent unitary conductance, gReg(t), was implemented with the parameters previously described (Edwards & Hirst, 2005) except that the maximum rate of production of the intermediate reagent, KF[precursor], was doubled from 0.0196 mM s–1 to 0.0392 mM s–1. While this modification increased the peak amplitude of the simulated slow wave to a value near the upper end of the observed range, it also increased the onset rate to a value close to that seen in physiological experiments. Onset rate had not been a critical measure in the case of a single compartment; however, simulations indicated that conduction velocity varied with the initial rate of depolarization which determined the time taken for a neighbouring compartment to reach regenerative threshold. Therefore a better match of this characteristic was important in this multi-compartment model. This increase in KF[precursor] permitted successful simulation of slow wave propagation velocity (see Fig. 4); the onset latency of the regenerative component of the slow wave was well simulated following this adjustment. The conductance connecting one isopotential compartment axially with the adjacent compartment in the same circular muscle bundle (Fig. 1B, gCCA) was set to 11.9 µS to model the passive electrical length constant in the axial direction along the bundle (3 mm; Hirst et al. 2006). As circular muscle bundles were found to be poorly connected to adjacent bundles with failures of conduction every few bundles (Hirst et al. 2006), the value of gCCT (Fig. 1B) was set to zero.
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When modelling conduction of slow waves in the circumferential direction, pacing of the ICCMY network was provided by a corporal circular muscle equivalent compartment (Fig. 6). The model used to describe the corpus was similar to that for a segment of antral circular muscle bundle (Edwards & Hirst, 2005) with the value for h, the rate of recovery from inactivation at hyperpolarized membrane potentials, reduced from 6 s to 3.8 s to allow generation of slow waves at the higher rate of discharge seen in the corpus (Hashitani et al. 2005). This modification allowed simulation of corporal slow waves which reflected the range of amplitudes and peak negative membrane potentials encountered in the corpus (Hashitani et al. 2005).
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Plots of passive length constants (Figs 3A, 4A, 5A and 6A) were determined by injecting a current into the most oral longitudinal muscle compartment (or circular muscle compartment in Fig. 6) after voltage-dependent mechanisms had been disabled, and measuring the voltage response in each other muscle compartment. The apparent length constant at a compartment was then calculated using the distance from the most oral compartment and the ratio between the steady state voltage response in the most oral compartment and the steady state voltage response in the compartment under test. Since the cables modelled were of finite length, the length constant calculated in this way increased as the anal end of the cable was approached due to reflection of current (Jack et al. 1983). Measurements of conduction velocity were made in regions of the cable models which were sufficiently proximal that the measured length constant was within 10% of its design value. The passive length constant plots have been included to underline that the speed measurements were carried out over regions of approximately uniform apparent length constant.
Simulations were carried out using MatLab 7.0.4.365 (R14) SP2 (The MathWorks, Natick, MA, USA). Stiff differential equation solver ode15s was used. Computations were carried out on an Intel Pentium 4-based desktop computer.
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Results |
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The approach taken in this study has been to link together 20 pacemaker compartments whose properties matched those determined experimentally when recording pacemaker potentials from ICCMY located in isolated short segments of antral wall (Cousins et al. 2003). To examine the constraints imposed on the conduction of pacemaker potentials through a network of ICCMY when several ICCMY and attached longitudinal muscle compartments were connected together, the first aspect considered was what conditions were required for pacemaker potentials to be initiated such that they swept in an anal direction with a conduction velocity of 3.5 mm s–1 (Hirst et al. 2006). The objective was to achieve a propagation velocity near the average value recorded in physiological experiments while adhering as closely as possible to the parameter values arrived at in previous models of individual isopotential compartments (Edwards & Hirst, 2003, 2005). In initial simulations, all ICCMY compartments were given the same membrane conductance parameters and initial conditions; similarly, all longitudinal muscle compartments were made identical. Thus, all cells discharged in tandem with theoretically zero phase difference in each case. In fact, the stochastic nature of the generation of unitary potentials in the ICCMY compartments resulted in small phase differences; however, these differences varied from wave to wave (Fig. 2A). Thus, on some occasions, a pacemaker potential would first arise in an orally located compartment and propagate in an anal direction (Fig. 2Bc). On other occasions, an anally located compartment would discharge the first pacemaker potential and this would propagate in an oral direction (Fig. 2Bb). Simultaneous occurrence of pacemaker potentials in well separated compartments was also seen (Fig. 2Ba). Therefore a constant direction of wave propagation was not maintained under these conditions. The physiological correlate of this behaviour has been observed in isolated preparations of antrum (Ward et al. 2004; Hirst et al. 2006). To impart a direction to propagation of pacemaker potentials along the strip of longitudinal muscle and associated ICCMY network, the primary conductance (Fig. 1A, gPrim(t)) in the ICCMY compartment at one end of the chain was allotted a voltage threshold marginally more negative (1 mV) than was the case in the other ICCMY compartments. Therefore this first compartment, in isolation, had a rate of discharge slightly faster than that of the other compartments and introduced only a minor inhomogeneity, meant to represent pacemaking input from the corpus, into one end of the equivalent cable. This resulted in pacemaker potentials that propagated consistently in a single direction (Fig. 2C). The model used to generate the data shown in Fig. 2 was adjusted to discharge spontaneous pacemaker potentials at close to 4 waves min–1, so that a small change in threshold produced a constant direction of propagation with little increase in overall discharge rate. Furthermore, the cable model used to generate Fig. 2 was made electrically shorter than those encountered in physiological experiments. This resulted in a slowed conduction velocity in order to emphasize propagation delays.
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Clearly the preceding approach could not provide an adequate description of physiological data with the simple description of pacemaker activity used previously. The simulation of ICCMY electrical activity shown in Fig. 3 used a model for the primary component (Fig. 1A, gPrim(t)) which responded rapidly to conducted depolarization (Edwards & Hirst, 2005). However, Goto et al. (2004) describe an autonomous inward current in isolated mouse intestinal ICCMY. When this current was activated it displayed an autonomous time course, lasting about 500 ms regardless of the duration of the initiating depolarization. Furthermore, the autonomous inward current displayed a brief, membrane potential-dependent delay of 20–200 ms following applied depolarization. The conduction velocity of pacemaker potentials is determined by the onset latency of the primary component once local voltage threshold is reached. Therefore, since the properties of the initial component of antral and intestinal ICCMY are very similar (Hirst & Edwards, 2001; Kito et al. 2002, 2005; Kito & Suzuki, 2003), the model previously used for the primary component of antral pacemaker potentials was altered to include a brief voltage-dependent delay between the arrival of conducted depolarization and the onset of the primary component (see Methods). The coupling conductance between adjacent ICCMY compartments was made 2800 µS and that between adjacent compartments of longitudinal muscle was made 5764 µS so as to match the estimated passive length constant (631 µm; Cousins et al. 1993). These selections yielded similar length constants for an isolated ICCMY equivalent cable (590 µm) and an isolated longitudinal muscle equivalent cable (720 µm) – values that are not accessible to experimental verification due to the limitations of dissection. The result of the computation is shown in Fig. 4. As in Fig. 3A, the passive length constant for the cross-connected cable pair is close to the design value of 631 µm (Fig. 4A, dotted line). However, using the altered model for gPrim(t), the propagation velocity between the second and twelfth compartments was 3.3 mm s–1 which was close to the average speed seen in the physiologically acquired records (3.5 mm s–1, Hirst et al. 2006).
Slow waves travel around the circumference of the antrum more quickly (14.7 mm s–1) than pacemaker potentials travel down the greater curvature (3.5 mm s–1, Hirst et al. 2006). However, the propagation speed of pacemaker potentials in the ICCMY network is similar in both circumferential and anal directions after removal of circular muscle sheet (3.5 mm s–1, Hirst et al. 2006). It seemed possible that the simple addition of a passive circular muscle current pathway in the circumferential orientation might alone be sufficient to account for the observed difference in propagation speed. Therefore it was of interest to see at what speed pacemaker potentials would propagate around the circumference of the stomach if sustaining the wave were due to the action of ICCMY in the absence of ICCIM. The model used to generate the data shown in Fig. 4 was altered in two ways. Firstly, the conductances connecting longitudinal muscle compartments were set to 50.4 µS to correspond to gLLT (Fig. 1B). This was necessary because the direction of follower potential conduction is in this case transverse to the axis of the longitudinal muscle cells. Since the ICCMY network is assumed to be isotropic, the conductance connecting ICCMY compartments remained unchanged (Fig. 1B, gICC). The propagation speed of pacemaker potentials was measured in this circumferentially orientated network before circular muscle compartments were added, to check that it was similar to that in the anal direction, as seen in the physiological records (Hirst et al. 2006). Pacemaker potentials propagated at 2.7 mm s–1 or about 18% slower than in the anal direction. The mean values for propagation velocities of follower potentials along and across the longitudinal muscle layer after removal of the circular layer were 3.7 mm s–1 and 3.2 mm s–1, a difference of 14% and in the same direction as the simulation (Hirst et al. 2006). The second alteration to the model was the connection of a circular muscle compartment to each ICCMY compartment, as is the case for intact antral tissue. The circular muscle compartments were each connected to the adjacent circular muscle compartment (Fig. 5B) via conductances of value 11.9 µS to give a passive length constant of 3 mm (see Methods) (Hirst et al. 2006). Furthermore, the circular muscle compartments were made passive by omitting gReg(t) (Fig. 1A) from each compartment. These modifications changed the measured length constant of the ICCMY network and attached longitudinal and circular muscle layers to about 200 µm (Fig. 5A; continuous line). The propagation velocity between the second and twelfth compartments was found to fall to 1.6 mm s–1, much slower than the velocity, 14.7 mm s–1, measured from the physiological data (Hirst et al. 2006). Thus, adding the circular muscle pathway actually slowed the propagation speed from 2.7 mm s–1 to 1.6 mm s–1 rather than speeding it. This was because the circular muscle membrane provided additional pathways for the propagating current to flow to the extracellular environment as well as to adjacent ICCMY compartments. This speed reduction mirrored that found in the comparison between slow waves in intact antrum (2.5 mm s–1) and those after removal of the circular layer (3.5 mm s–1, Hirst et al. 2006). Therefore circumferential conduction of current via an added passive circular muscle pathway is unlikely to account for the rapid circumferential propagation of slow waves; it in fact would be expected to slow the radial conduction velocity.
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Discussion |
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When the model was set up using a chain of ICCMY with identical properties, pacemaker potentials originated at different points along the chain (Fig. 2). This behaviour is detected in physiological recordings from isolated regions of the antrum (Hennig et al. 2004; Ward et al. 2004; Hirst et al. 2006) but does not occur in the intact stomach (Szurszewski, 1981; Davenport, 1989). An anally directed progression of pacemaker potentials in the ICCMY network could be achieved by making more negative the activation potential of the initial component of the pacemaker potential of the most oral node in the ICCMY network. The alternative approach was to provide a stimulus at the oral end of the chain of ICCMY with a higher frequency of occurrence than that naturally generated by the ICCMY network. In the intact stomach such a stimulus is provided by the corpus which generates slow waves with a higher frequency of discharge than that of the isolated antrum (Hashitani et al. 2005). When attached to the corpus, the natural frequency is entrained to be the same as that of the corpus (Hashitani et al. 2005). A pacemaker potential initiated in the most orally located compartment proceeded strictly in an anal direction as the refractory characteristics of the primary and regenerative components prevented backfiring along the cable.
Pacemaker potentials propagate very slowly in an anal direction. Furthermore, after removal of the circular layer, their conduction velocities in the anal and circumferential directions are similar (Hirst et al. 2006). In such preparations, the ICCMY network is connected solely to the longitudinal muscle layer by a finite, predetermined resistance (Cousins et al. 2003). Previous studies on the longitudinal muscle layer have indicated that its passive electrical length constants are asymmetrical, more readily allowing current flow in an oro-anal direction (Cousins et al. 1993; see also Hirst et al. 2006), so giving rise to different conduction velocities of action potentials in the two directions (Stevens et al. 1999). The simplest explanation for the slow propagation of pacemaker potentials in the anal direction might be that the resistance between adjacent ICCMY was very high. This seems an unlikely explanation since dyes readily move though the ICCMY network (Dickens et al. 1999) and numerous gap junctions are found in the network (Jimenez et al. 1999). When this proposition was tested using a simulation it was found possible to slow the propagation velocity markedly by making the resistance between ICCMY very high. This meant that current flow for propagation occurred almost solely via the longitudinal muscle layer. However, given the asymmetry of longitudinal muscle passive length constants in the oro-anal and circumferential directions, the conduction velocity in the circumferential direction fell even more dramatically. Clearly this is not in accord with the finding that the conduction velocity of pacemaker potentials, in preparations containing only ICCMY and longitudinal muscle, is very similar in the longitudinal and circumferential directions (Hirst et al. 2006). An alternative explanation was sought. In their description of the electrical properties of murine intestinal ICCMY, Goto et al. (2004) found that the onset of the initial component of the pacemaker potential occurred after a brief but finite delay. Thus the electrical description of pacemaker activity was modified to incorporate this behaviour. When this was done, even though an appreciable part of the current necessary to allow propagation of pacemaker potentials continued to flow though the longitudinal layer, appropriate simulations of conduction velocity in the anal and circumferential directions could be achieved (Fig. 4).
Slow waves conduct faster in a circumferential direction than do pacemaker potentials in an anal direction. Having found that the spread of pacemaker activity could be influenced by the electrical properties of the cells to which ICCMY were coupled, the effect of adding a circular muscle chain to the model was examined. It was found that since this layer had such a low input resistance, rather than increasing the circumferential conduction velocity of pacemaker potentials, the current drain actually reduced the circumferential conduction velocity (Fig. 5). As it had been found that ICCMY were not required for the circumferential spread of slow waves, the effect of introducing the regenerative component of the slow wave was examined.
Circumferential spread of the slow waves takes place within the circular muscle layer, outpacing circumferential spread of pacemaker potentials via the ICCMY network and associated longitudinal muscle layer. Presumably waves in ICCMY which lie far from the greater curvature are initiated by slow waves in the underlying circular muscle, although no physiological experiments have been conducted to examine this point. Hence, when the longitudinal muscle and the ICCMY network are removed from a sheet of circular muscle, except for a band near the greater curvature, normal slow waves persist throughout the circular muscle layer (Hirst et al. 2006). Likewise, anally directed progression of electrical activity appears to be carried mainly by the ICCMY network and associated longitudinal muscle layer. When the circular muscle layer is removed, pacemaker potentials continue to propagate through the remaining layers in an anal direction at an unchanged speed (Hirst et al. 2006). Moreover the poor and variable oro-anal connectivity between circular muscle bundles will prohibit extensive oro-anal conduction in the circular layer. A model comprising 16 circular muscle compartments, each isopotential, and together representing about three length constants of cable was chosen. With minor alterations to the parameters specified by Edwards & Hirst (2005) (see Methods) slow waves propagated along this equivalent circular muscle bundle at 14 mm s–1 which was close to 14.7 mm s–1, the speed measured in the tissue after removal of most of the ICCMY layer (Hirst et al. 2006). The predictive power of the model offered is limited by the accuracy of the kinetic models used for the primary and plateau components of the pacemaker potential in the ICCMY network and the regenerative potential in circular muscle compartments. The simplified reactions leading to increased discharge of unitary events may not be precise. Furthermore, some voltage-dependent membrane currents exist in both circular and longitudinal smooth muscle cells which have been treated as ohmic in these simulations. However, the model as described is able to mimic a suite of behaviours seen in physiological experiments on antral tissue. Extension of the model to incorporate other regions of stomach and neural contributions may lead to a more rapid understanding of the locus and genesis of gastric dysrhythmias and other clinical conditions.
In summary, pacemaker depolarizations originating in the gastric corpus conduct slowly in an anal direction presumably via the ICCMY network and associated longitudinal muscle layer, their propagation speed limited by the onset latency of the primary component of the antral pacemaker potential. Excitation of circular muscle bundles occurs at the region of largest ICCMY density, the greater curvature, and spreads rapidly around the stomach via small groups of adjacent circular muscle bundles. The amplitude and speed of the circumferential slow wave and associated contraction is maintained by ICCIM within the circular muscle bundles. The rapid circumferential spread of the slow wave forms a ring of contraction around the stomach which moves in an anal direction at about 3.5 mm s–1, propelling the gastric contents towards the gastro-duodenal junction.
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References |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Cousins HM, Edwards FR, Hirst GDS & Wendt IR (1993). Cholinergic neuromuscular transmission in the longitudinal muscle of the guinea-pig ileum. J Physiol 471, 61–86.
Davenport HW (1989). Gastrointestinal physiology, 1895–1975: motility. In Handbook of Physiology, Section 6, Gastrointestinal System, Part 1, pp. 1–101. American Physiological Society, Bethesda.
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