**5.3 Effect of advancing LLS on flows**

Like the peristalsis waves (which are modeling as trains of periodic sinusoidal waves traversing the muscular tube at certain velocity), the LLS is modeled as a sinusoidal wave whose amplitude relates to the local shortening (*l/l0*) and propagates with the CC. As shown in **Figure 5**, LLS brings together the neighboring tissues through generation of a localized wave of shortening. As a result of this, the circular muscles become denser giving its advantage to compress the lumen at ease. We consider that the longitudinal contraction is in relative motion to the CC; hence, we define them as LLS of advancing type.

As the LLS traverse the intestine with CC, the intestinal wall undergoes deformation. Such change in the wall generates wall momentum which acts as a source of energy to push the fluid and develop flows. The details of the wall motions are provided in the form of a local wall velocity in **Figure 5**. Circular contractions are wall motions that appear as ripples traveling over the surface of water. As the circular muscles contract, the wall moves radially inward; however, as the wave moves at certain velocity they appear to close the head region of the wave leaving behind the tail end to relax or open (outward velocity vector; first panel in **Figure 5**). For advancing LLS, a wave of localized shortening occurs which travels at certain speed. During such activity, the surface of the intestinal wall appear to move forward but recoils back to its original position after the disturbance has traverse the segment. This generates a net forward velocity, as shown in second panel of **Figure 5**. Superimposing both the waves result in a summation of the two velocity vectors (third panel in **Figure 5**). We may summarize that the introduction of LLS results in an axial displacement of the wall and CC in radial displacement.

#### **Figure 5.**

*A cartoon diagram illustrating the circular (CC) and longitudinal contractions (LLS) in the intestinal wall. L is the length and R is the radius of the intestine. CC is characterized by the wavelength (*λ*) and the percentage occlusion of the lumen (pocc). Peak value of LLS is given by the peak l/l0 ratio which is spaced at a relative distance (*δ*) from the peak CC or the point of maximal occlusion.*

Considering no-slip condition (fluid particle at wall moves with the same velocity with which the wall moves), we also learn that there is an effective axial displacement of the fluid adjacent to wall and helps to drag the peripheral part of the food along with it (**Figure 6**).

Rheology plays an essential role in regulating the transport of the digesta from stomach to duodenum (gastric emptying) and duodenum (duodenogastric reflux). For a meal that is highly viscous, the mixing and transport can be a difficult task to be performed by the enteric system when compared to low viscous digesta. Since the mechanical processes taking part in intestine correlates to the rate at which absorption takes place and determines the serum glucose levels, the subject matter is of high relevance to satiety, indigestion, and other digestive disorders of the gut.

Let us estimate the flow regime of water, juice, and honey. We consider an intestinal geometry with diameter 2.5 cm (2.5–3 cm), and wave traveling at a characteristic velocity of 2.5 cm s<sup>−</sup><sup>1</sup> (2.5–5 cm s<sup>−</sup><sup>1</sup> ) for short and long wavelength of one and ten times the diameter. Assuming a fluid density of 1 g cc<sup>−</sup><sup>1</sup> and fluid viscosities of 1 cP (water), 0.65P (juice), and 33P (honey) and substituting into the formula (*Re = ρvD/μ*) we determine Reynolds number as 625, 9.615, and 0.189. As per the long wavelength approximation [54], we perform viscous scaling by a factor (=diameter/wavelength of the wave) to get an approximate Reynolds number. At one-tenth of scaling, the Reynolds number is found to be 62.5, 0.9615, and 0.0189. At higher Reynolds number, the inertial forces of the fluid are much higher than viscous resistance and as a result lead to turbulence flow. We speculate that a fast moving contraction of the intestine help in pushing the fluid to a higher extent that it leads to turbulence and upon interaction with air leads to borborygmus (a rumbling, growling or gurgling noise of the intestine). The studies of the bowel sounds (auscultation) were pioneered by Cannon in the early twentieth century. However, due to technical challenges, the method appears to be of some hope to clinicians in diagnosing GI disorders through bowel sound computational analysis (BSCA) [55]. At low *Re*, the flows are laminar and silent.

Flow details of the intestinal peristalsis have been recently reported in the literature [56]. When a wave of contraction propagates along the intestinal wall, they develop peripheral forces that can be directed radially inward, axially oriented,

**59**

**Figure 6.**

the region of contraction.

*Biomechanics of the Small Intestinal Contractions DOI: http://dx.doi.org/10.5772/intechopen.86539*

or inclined depending on the nature of contraction (CC and/or LLS) (**Figure 7**). As a result, the head region develops a higher pressure relative to the tail end. While at the tail end, development of low pressure field results from the retraction of the wall as if they were to open the channel. As a result the development of differential pressure forces across the segment, a pressure gradient which acts as a driving force to propel the luminal contents from a region of higher pressure to the lower pressure (retrograde flow). Flow due to advancing LLS is less prominent due to generation of low fluid velocity and low shear stress. Since they develop axial velocity at the wall, the advancing LLS, through viscous behavior, drags the neighboring fluid to move along with the wall creating a whirlpool-like motion in

*A snapshot of a simulation study indicating the wall velocity (blue line) along the radial direction (CC) and no shortening (LLS, red line) (first panel). Study involving LLS (approximated by sinusoidal waveform) without CC; the wall is pulled toward the point of peak LLS (second panel). Effect of CC and LLS on wall velocity.*

*Digestive System - Recent Advances*

along with it (**Figure 6**).

*distance (*δ*) from the peak CC or the point of maximal occlusion.*

**Figure 5.**

characteristic velocity of 2.5 cm s<sup>−</sup><sup>1</sup>

At low *Re*, the flows are laminar and silent.

Considering no-slip condition (fluid particle at wall moves with the same velocity with which the wall moves), we also learn that there is an effective axial displacement of the fluid adjacent to wall and helps to drag the peripheral part of the food

*A cartoon diagram illustrating the circular (CC) and longitudinal contractions (LLS) in the intestinal wall. L is the length and R is the radius of the intestine. CC is characterized by the wavelength (*λ*) and the percentage occlusion of the lumen (pocc). Peak value of LLS is given by the peak l/l0 ratio which is spaced at a relative* 

Rheology plays an essential role in regulating the transport of the digesta from stomach to duodenum (gastric emptying) and duodenum (duodenogastric reflux). For a meal that is highly viscous, the mixing and transport can be a difficult task to be performed by the enteric system when compared to low viscous digesta. Since the mechanical processes taking part in intestine correlates to the rate at which absorption takes place and determines the serum glucose levels, the subject matter is of high relevance to satiety, indigestion, and other digestive disorders of the gut. Let us estimate the flow regime of water, juice, and honey. We consider an intestinal geometry with diameter 2.5 cm (2.5–3 cm), and wave traveling at a

(2.5–5 cm s<sup>−</sup><sup>1</sup>

viscosities of 1 cP (water), 0.65P (juice), and 33P (honey) and substituting into the formula (*Re = ρvD/μ*) we determine Reynolds number as 625, 9.615, and 0.189. As per the long wavelength approximation [54], we perform viscous scaling by a factor (=diameter/wavelength of the wave) to get an approximate Reynolds number. At one-tenth of scaling, the Reynolds number is found to be 62.5, 0.9615, and 0.0189. At higher Reynolds number, the inertial forces of the fluid are much higher than viscous resistance and as a result lead to turbulence flow. We speculate that a fast moving contraction of the intestine help in pushing the fluid to a higher extent that it leads to turbulence and upon interaction with air leads to borborygmus (a rumbling, growling or gurgling noise of the intestine). The studies of the bowel sounds (auscultation) were pioneered by Cannon in the early twentieth century. However, due to technical challenges, the method appears to be of some hope to clinicians in diagnosing GI disorders through bowel sound computational analysis (BSCA) [55].

Flow details of the intestinal peristalsis have been recently reported in the literature [56]. When a wave of contraction propagates along the intestinal wall, they develop peripheral forces that can be directed radially inward, axially oriented,

of one and ten times the diameter. Assuming a fluid density of 1 g cc<sup>−</sup><sup>1</sup>

) for short and long wavelength

and fluid

**58**

#### **Figure 6.**

*A snapshot of a simulation study indicating the wall velocity (blue line) along the radial direction (CC) and no shortening (LLS, red line) (first panel). Study involving LLS (approximated by sinusoidal waveform) without CC; the wall is pulled toward the point of peak LLS (second panel). Effect of CC and LLS on wall velocity.*

or inclined depending on the nature of contraction (CC and/or LLS) (**Figure 7**). As a result, the head region develops a higher pressure relative to the tail end. While at the tail end, development of low pressure field results from the retraction of the wall as if they were to open the channel. As a result the development of differential pressure forces across the segment, a pressure gradient which acts as a driving force to propel the luminal contents from a region of higher pressure to the lower pressure (retrograde flow). Flow due to advancing LLS is less prominent due to generation of low fluid velocity and low shear stress. Since they develop axial velocity at the wall, the advancing LLS, through viscous behavior, drags the neighboring fluid to move along with the wall creating a whirlpool-like motion in the region of contraction.

**Figure 7.** *Effect of simultaneous circular and longitudinal contractions on flow.*

The advancing LLS and CC lead to the generation of pressure field and shear stress of similar trend. Local variations in the pressure along the axis indicate a linear variation in the non-contraction region and a nonlinear variation in the contraction region; zero at the center and boundaries—inlet and outlet of the intestinal segment. The pressure peaks at an offset from the center and shows symmetry about the axis for a contraction wave at the mid-segment. The wall shear stress shows a peak at the center of the contraction region and reduces to lower value at the either end of the wave and remains constant throughout the non-contraction region. Axial variations in the pressure and wall shear stress are similar for fluid of pseudo-plastic, Newtonian, and dilatants type. The study also reports that the pressure developed is higher for shear thickening fluids in comparison to shear-thinning fluid (**Table 4**). In a similar manner, wall shearing is highest for the dilatants. Shear stress in the lumen is highest at the wall and reduces linearly to the lowest value


**61**

*Biomechanics of the Small Intestinal Contractions DOI: http://dx.doi.org/10.5772/intechopen.86539*

**6.1 Mixing**

with formation of eddies.

**6.2 Transport**

the contents, flow rate, and peak velocity significantly.

**6. Physiological relevance of intestinal motility**

manage the patient suffering from motility disorders.

at the center. At region where the shearing is higher there is a more stirring of the fluid. CC and LLS coordination is found to affect the luminal pressure, shearing of

Using imaginary tracers, the author was able to determine particle trajectories due to the peristalsis—CC and LLS [56]. Two kinds of flows were observed; one resulting in axial displacement of the fluid and other causing circulation of the fluids (eddies). The radial displacement brought the fluid from the core region to the periphery and vice versa; thus allowing for flushing of the fluid proximal to the mucosa. However, the particles were displaced when the wave traverses the segment. Particle motion is highly dependent on the type of intestinal motility. Positioning of the tracers at various depths of the lumen showed different trajectory and followed the wall; particles close to the wall tend to follow the wall, while those near the axis exhibited near circulation. The authors report that the radial dimension of the whorls is found to be higher when the particles were positioned close to the wall and least at the center. Suggesting that, the contractions are more effective near the wall since the particles experience most of the wall momentum and least at the center of the lumen. Such a behavior is indicative of the mixing of the contents; given that the shearing is effective near the wall

When contraction traverses at 50% occlusion, there is a higher tendency for the particles to undergo circulation; favoring mixing [56]. However, at 80% occlusion, the particles tend to under more of axial displacement and less of a radial displacement with no circulation; favoring transport. Particles positioned near the center were found to travel a longer distance in comparison to those near the wall. Such behavior reminds us the parabolic velocity profile in case of pressure driven flows in pipe. Previous studies corroborates with the understanding that the flows in occlusion regions tend to show a parabolic profile [44]. Rheological effects of the particle displacement suggest that the eccentricity of the particle trajectory for Newtonian fluid is more and undergoes a near complete circulation. Particle trajectory for dilatants showed formation of a complete circulation. For fluid having flow behavior index less than 1.0, following observations were made (1) particles tend to travel with higher velocity over longer distance and (2) particles showed more of a radial predominance. There were no significant changes in the flow developed by introducing the LLS; however, due to additional momentum along the axial direction they tend to suppress the radial displacement of the tracer leading to a more translocation. The transport has been linked to malabsorption of the nutrients and electrolyte concentration. Alternations in the intestinal transit can disturb the equilibrium of osmolality and intestinal absorption leading to diarrhea or constipation [57]. Knowledge of the intestinal transit of bolus is essential when design the drug. Orally administered drugs have to be tuned to the environmental conditions of the small intestine so that drug bioavailability can be maximized. Since the physical properties of the meal, such as viscosity can greatly influence the transport behavior, clinical preparation of the food can be administered to help

**Table 4.**

*Effect of contractility and rheology (normalized values) on flow; based on semi-analytical method.*

at the center. At region where the shearing is higher there is a more stirring of the fluid. CC and LLS coordination is found to affect the luminal pressure, shearing of the contents, flow rate, and peak velocity significantly.
