Expansion of the lumen develops in the region of relaxation (Figure 2a(ii)) and fluid immediately downstream of the contraction increases in velocity. The pressure on the lumen in the contraction area and the intra-luminal pressure downstream of the contraction both increase (Figure 2b(ii)). A high-pressure zone is created in the right half of the contraction due to the antegrade movement of the peristaltic wave.
The addition of muscle relaxation downstream of the contraction therefore causes the walls to expand. The area of high pressure to the right of the contraction is similar to the case with the DI. For 0.1 Pa.s (Figure 4b), the length of the contracted region on the left side of the peristaltic wave is now shorter in the upstream longitudinal direction.
For 3 Pa.s (Figure 4d), the top wall contraction is mildly reduced, but the axial length of the contracted region is comparable to the base case. The leading edge of the DI relaxation (marked by line A) arrives first, followed by the top of the DI (line B), the neutral center of the wave (line C), the peak contraction (line D) and the end of the contraction (line E) . This is primarily due to the increasing importance of DI at low viscosities in generating pressure.
So there is a high local pressure gradient in the outer radial half of the colon.
Effect of Degree of Contraction of Tube (lumen occlusion)
As in Figure 5, we superimpose vertical dashed lines representing the times when parts of the peristaltic wave cross this position. At 20% occlusion, the relaxation time for the system is short enough for the walls to relax back to their natural state before the arrival of the next wave. Therefore, the transport velocity is approximately zero before the leading edge of the next wave arrives.
There is a reduction of the positive current peak by 45% and a reduction of the retrograde current peak by 40%. For the 60% occlusion, there is increased retrograde flow before the arrival of the leading edge of the wave. The peak retrograde current increases by 25%, but further lags behind the peak contraction that occurs two-thirds of the way between D and E.
The maximum retrograde flow increases by another 20% and lags further behind the maximum contraction that occurs just after the trailing edge of the wave has passed (point E). The maximum retrograde flow increases by 85% and coincides with the trailing edge of the wave at point E. The displacement of the peak antegrade transport behind the peak relaxation depends not only on the viscosity (as observed in the previous section) but also on the degree of occlusion also.
Therefore at very high occlusion and high viscosity the maximum transport occurs immediately before the neutral part of the wave. There is therefore an exponential increase in transport with increasing closure rate for the 1 Pa.s case, such that transport increases twentyfold for a fourfold reduction in the open contraction area. At higher viscosity (10 Pa.s) transport also increases with closure rate, so there is a fivefold increase in transport when the open shrinkage area is halved.
In normal intestinal function, a range of different wave amplitudes is typically measured across the entire length of the colon, but the role that low- and high-amplitude waves play in mixing and transport is not yet clear. The length of the upstream contracted region behind the wave is much greater for larger contractions. This suggests that the timescale for the memory stored in the system will also depend on the degree of contraction of the lumen.
Length of Peristaltic Wave
A mild pressure gradient is seen in the longitudinal direction extending to the right side of the DI and all the way to the downstream end of our colonic segment. Compared to the 4 cm wave, the peak wall pressures are strongly localized to the right of the contraction. There is a mild reduction in peak retrograde velocities and the retrograde flow extends a shorter distance to the left from the contraction area.
Again, as in Figure 5 , we superimpose vertical dashed lines representing the times when characteristic parts of the peristaltic wave cross this position. The base case initially showed some retrograde flow before the arrival of the DI part of the wave. The reduction in retrograde flow then decreases faster in the wake of the contraction than for the base case.
Therefore, we observe a marked decrease in net volumetric transport when the peristaltic wave length decreases from 8 cm to 2 cm. Furthermore, they do not appear to play a role in mixing the contents due to the loss of the recirculation zone at these lengths. It appears to allow efficient transport for a compact content area as well as reduced muscle work, even for partial occlusion of the lumen.
Faecal viscosity controls both the degree of localization of the fluid flow and the magnitude of the radial variation in pressure. This has implications for the interpretation of measurements from manometric sensors within the colon as the pressure recorded will depend on both viscosity and the radial position of the sensor. The degree of occlusion of the lumen was also found to strongly influence the rate of transport.
The timescale for the memory of the coupled fluid-wall system depends on both viscosity and confinement rate. Decreased peristaltic wavelength leads to decreased transport velocity as the recirculation zone disappears for waves that are much shorter than the diameter of the lumen. Dr Dinning is supported by NHMRC grant #630502 and the Flinders Medical Center Clinicians' Special Purpose Fund, Australia.
The vertical lines represent: (A) onset of DI; (B) peak DI; (C) neutral part of the wave between DI and contraction; (D) peak contraction; and (E) the end of the wave. The vertical lines represent: (A) onset of DI; (B) peak DI; (C) neutral part of the wave between DI and.
