**4.4 Intestinal peristalsis**

Contractions of the intestine are a mix of elementary contractions such as stationary (SW), antegrade (APW), or retrograde propagating wave (RPW). A literature survey of the motility patterns indicate frequency of 15–18 wave min<sup>−</sup><sup>1</sup> , velocity of propagation of 0.1–0.4 cm s<sup>−</sup><sup>1</sup> , and higher propensity to develop

propagating contraction in the intestine in comparison to stationary contraction [44]. Retroperistalsis have been linked to the reflux of duodenal contents and trigger the development of DGR diseases. Standing contractions are the non-propagating contractions they are confined over a particular segment (12 waves min<sup>−</sup><sup>1</sup> ). They are known to be involved in the mixing process. Contractions appearing on one side of the channel are known as sleeve contractions. It involves longitudinal muscle for generating contraction [45] and help in mixing and churning of luminal contents [46]. Pendular movements are the longitudinal contraction of the muscles, which develops motility patterns involving to-and-fro motions of segmental shortening and extension. In physiology, the contractions occur as a mixture of the basic contractions, as discussed above. It is a well-known fact that upon nutrient infusion of duodenum, the duodenal motility patterns changes from propulsive to a segmental contraction that traveled only for a short span. Such contractions form segmental contractions or cluster contractions, which can be stationary or non-stationary [47].

#### **4.5 Flow due to circular muscle contractions**

Flow due to circular contraction were investigated by the author by approximating the flow for a Newtonian liquid meal with viscosity 1000 cP and density 1000 g cc<sup>−</sup><sup>1</sup> inside the APD segment [44]. The rationale for choosing such an assumption was—(1) for a liquid meal intake the meal mixes with gastric and duodeno-biliary-pancreatic secretions giving a mixture that is also a liquid; (2) the rheology of the contents present inside the duodenum is not yet known; therefore, a Newtonian approximation was made; (3) modeling a semi-solid meal increases the complexity, therefore, a liquid meal was considered to simplify the development of the APD segment. Further, the APD segment was assumed to be a rigid wall to simplify the flow model.

There is a formation of recirculation eddies near the occlusion zone (with velocities reaching its peak at its center) and occurrence of a local transport at the pyloric region (arising due to the pressure difference across it) (**Figure 4**). Results indicate that a retrograde moving wave cause pressurization at the head region of the wave in comparison to the tail region. As a result of this behavior, a steep pressure rise is developed to cause flow in the direction that is downward the steep. It was also found that this wave generates a pressure difference across the pylorus, that is, higher pressure on the antrum side in comparison to a lower pressure on proximal duodenum thereby causing reflux.

To understand the impact of variations in the intestinal peristalsis, the author performed a parametric study by varying the geometry and wave parameters of the contraction. Based on literature, a hypothetical range was considered for these parameters presuming that this range falls within the physiological regime.

The study demonstrated that higher degrees of occlusion and higher velocity for the propagatory contractions have a profound effect on the flow rate across the channel (**Table 1**). Although, for APWs, the emptying rate increases with occurrence of multiple waves, they also induce reflux when occurring in four numbers spread across the duodenum and centered at 8 cm away from pylorus. The effect of multiplicity in the RPW shows an increasing trend in reflux. In general, it can be interpreted that the APW type contractions lead to emptying while RPW lead to reflux.

Standing contractions (SW type) of closing type were found to be reflux inducing. However, they occur at less than one-tenth of a magnitude for variations in distance, wavelength, and degree of occlusion in comparison to the APW and the RPW contractions. They also show an increasing level of reflux with increasing values of parameters except for distance. When multiple standing waves occur they result in significant increase in the reflux.

**55**

**Figure 4.**

*and colors indicate the magnitude.*

**Contraction type**

*standing wave.*

*RPW, and SW type of contractions.*

**Table 1.**

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

On overall comparison of the reflux levels caused by the elementary contractions, it is clear that the SW of higher frequency and the RPW of higher occlusion (70%), higher velocity and occurring in multiple numbers dominate the list of

*Flow due retrograde wave traveling toward the pylorus. Arrows indicate velocity vector over the local region* 

The APW and RPW contraction show mixing at higher intensity that is typically of the order of hundreds that is ten times those of SW. Variations in distance and wavelengths of the APW and RPW type contractions show similar levels of mixing (**Table 2**). Contractions cause higher degree of mixing with increasing occlusions and are highly sensitive to the velocity, wherein a change from 1 to 4 cm s<sup>−</sup><sup>1</sup>

> **% Occlusion (↑)**

**Velocity (cm s<sup>−</sup><sup>1</sup>**

**or frequency (↑)**

**)** 

lead to a ten-fold increase in Imixing. Further, it was seen that multiple waves can cause significant rise in mixing. However, the standing contractions show negligible mixing that are typically of the order of tens and are highly sensitive to frequency and multiple waves. While Imixing shows extent of mixing in the whole duodenum,

APW Negligible Negligible ↑ ↑ ↑ RPW Negligible Negligible ↑ ↑ ↑ SW\* ↓ ↑ ↑ ↑ ↑ *\*For SW, frequency is considered. APW, antegrade propagating wave; RPW, retrograde propagating wave; and SW,* 

*Effects of duodenal pumping on transpyloric flow rate (GE or DGR) studied for various parameters of APW,* 

**Wavelength (↑)**

can

**Multiple waves (↑)**

reflux inducing contractions of the duodenum.

**Distance (↑)**

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

#### **Figure 4.**

*Digestive System - Recent Advances*

**4.5 Flow due to circular muscle contractions**

1000 g cc<sup>−</sup><sup>1</sup>

simplify the flow model.

duodenum thereby causing reflux.

result in significant increase in the reflux.

propagating contraction in the intestine in comparison to stationary contraction [44]. Retroperistalsis have been linked to the reflux of duodenal contents and trigger the development of DGR diseases. Standing contractions are the non-propagating

are known to be involved in the mixing process. Contractions appearing on one side of the channel are known as sleeve contractions. It involves longitudinal muscle for generating contraction [45] and help in mixing and churning of luminal contents [46]. Pendular movements are the longitudinal contraction of the muscles, which develops motility patterns involving to-and-fro motions of segmental shortening and extension. In physiology, the contractions occur as a mixture of the basic contractions, as discussed above. It is a well-known fact that upon nutrient infusion of duodenum, the duodenal motility patterns changes from propulsive to a segmental contraction that traveled only for a short span. Such contractions form segmental contractions or cluster contractions, which can be stationary or non-stationary [47].

Flow due to circular contraction were investigated by the author by approximating the flow for a Newtonian liquid meal with viscosity 1000 cP and density

assumption was—(1) for a liquid meal intake the meal mixes with gastric and duodeno-biliary-pancreatic secretions giving a mixture that is also a liquid; (2) the rheology of the contents present inside the duodenum is not yet known; therefore, a Newtonian approximation was made; (3) modeling a semi-solid meal increases the complexity, therefore, a liquid meal was considered to simplify the development of the APD segment. Further, the APD segment was assumed to be a rigid wall to

inside the APD segment [44]. The rationale for choosing such an

There is a formation of recirculation eddies near the occlusion zone (with velocities reaching its peak at its center) and occurrence of a local transport at the pyloric region (arising due to the pressure difference across it) (**Figure 4**). Results indicate that a retrograde moving wave cause pressurization at the head region of the wave in comparison to the tail region. As a result of this behavior, a steep pressure rise is developed to cause flow in the direction that is downward the steep. It was also found that this wave generates a pressure difference across the pylorus, that is, higher pressure on the antrum side in comparison to a lower pressure on proximal

To understand the impact of variations in the intestinal peristalsis, the author performed a parametric study by varying the geometry and wave parameters of the contraction. Based on literature, a hypothetical range was considered for these

The study demonstrated that higher degrees of occlusion and higher velocity for the propagatory contractions have a profound effect on the flow rate across the channel (**Table 1**). Although, for APWs, the emptying rate increases with occurrence of multiple waves, they also induce reflux when occurring in four numbers spread across the duodenum and centered at 8 cm away from pylorus. The effect of multiplicity in the RPW shows an increasing trend in reflux. In general, it can be interpreted that the APW type contractions lead to emptying while RPW lead to reflux. Standing contractions (SW type) of closing type were found to be reflux inducing. However, they occur at less than one-tenth of a magnitude for variations in distance, wavelength, and degree of occlusion in comparison to the APW and the RPW contractions. They also show an increasing level of reflux with increasing values of parameters except for distance. When multiple standing waves occur they

parameters presuming that this range falls within the physiological regime.

). They

contractions they are confined over a particular segment (12 waves min<sup>−</sup><sup>1</sup>

**54**

*Flow due retrograde wave traveling toward the pylorus. Arrows indicate velocity vector over the local region and colors indicate the magnitude.*

On overall comparison of the reflux levels caused by the elementary contractions, it is clear that the SW of higher frequency and the RPW of higher occlusion (70%), higher velocity and occurring in multiple numbers dominate the list of reflux inducing contractions of the duodenum.

The APW and RPW contraction show mixing at higher intensity that is typically of the order of hundreds that is ten times those of SW. Variations in distance and wavelengths of the APW and RPW type contractions show similar levels of mixing (**Table 2**). Contractions cause higher degree of mixing with increasing occlusions and are highly sensitive to the velocity, wherein a change from 1 to 4 cm s<sup>−</sup><sup>1</sup> can lead to a ten-fold increase in Imixing. Further, it was seen that multiple waves can cause significant rise in mixing. However, the standing contractions show negligible mixing that are typically of the order of tens and are highly sensitive to frequency and multiple waves. While Imixing shows extent of mixing in the whole duodenum,


*\*For SW, frequency is considered. APW, antegrade propagating wave; RPW, retrograde propagating wave; and SW, standing wave.*

#### **Table 1.**

*Effects of duodenal pumping on transpyloric flow rate (GE or DGR) studied for various parameters of APW, RPW, and SW type of contractions.*


**Table 2.**

*Effect of APD contractions on intensity of mixing.*


**Table 3.**

*Effect of APD contractions on volume of mixing.*

we also wanted to quantify the region over which the mixing or the volume of mixing is significant (computed as the volume of duodenum that has mixing index above 1.005). Changes in distance and wavelength of the peristaltic waves showed no major change in volume of mixing; however, it was sensitive to occlusion to some extent and highly sensitive to velocity and multiple waves. Standing contractions, on the other hand, showed zero or negligible volumes of mixing, except for a frequency of 6 Hz where they showed some mixing (**Table 3**).

### **5. Significance of the longitudinal muscles**

#### **5.1 What is LLS?**

Contractions of the longitudinal muscles, when occurring over short range of the gut segment, are referred to as the local longitudinal shortening. In literature, longitudinal shortening have been investigated as if they are advancing with the contraction, which we define as the advancing LLS and those that are stationary or stationary LLS are rarely considered. During LLS, the longitudinal muscles contract to shorten the segment along the axial direction only.

#### **5.2 Learning from esophageal studies of LLS**

LLS studies of the intestinal segments have been rarely considered. In order to understand the mechanophysiology of the LLS in intestine, we resort to the LLS studies of the esophageal segment.

One of the classical studies of LLS was the study of esophageal peristalsis during feline. By using a widely spaced metal clips clamped to the esophageal mucosa (four tantalum wires that were imbedded in the outer esophageal wall), Dodds et al. [48] captured the longitudinal shortening of the esophageal segment which varies with their relative position. The study demonstrated the existence of a wave of local longitudinal shortening that moves in conjunction with the bolus. They also found that the relative displacements of the markers vary from one location to the other

**57**

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

length of the esophagus [53].

**5.3 Effect of advancing LLS on flows**

we define them as LLS of advancing type.

location suggesting that the LLS is effective over a given segment of the esophagus (especially the distal most esophagus). Subsequent studies, using widely spaced metal clips attached to the esophageal mucosa, support the contractive nature of the longitudinal muscles in the local regions of the esophageal wall during peristalsis [49–51]. Measuring local longitudinal shortening was, however, a challenge using the mucosal clip studies; given the large spacing of 3–10 cm. Nicosia et al. provided a more accurate method of determining the LLS and their coordination with CC using the high-frequency ultrasound transducer [18]. By employing the principle of law of mass conservation, the changes in the cross-sectional area with the temporal variation in local longitudinal shortening was made; which were compared with the luminal pressure measured using high resolution manometry. Following relation was derived: cross-sectional area during rest phase/cross-sectional area during contraction = length of the segment during contracted state/length during rest. Key observations were as follows: (1) during luminal filling (with bolus entry), the esophagus distends reducing the effective thickness of the muscles, (2) the wave of longitudinal shortening was followed by the circular contraction, (3) contraction of the longitudinal muscles were found to nearly coincide with the peak luminal pressure, (4) longitudinal shortening overlaps the CC and occur prior to CC and ended after CC, and (5) lastly, the strength of LLS directly relates to the generation of higher luminal pressure. Further clinical studies by the investigators also indicate the prior contraction of the longitudinal muscle during onset of distal esophageal peristalasis [18, 49, 50]. Such fine coordination the contraction of two muscles fibers provides for a mechanical advantage of gathering the neighboring circular muscle fiber closer to ensure that the circular contraction occurs at ease [52]. The coordination of CC and LLS is managed by the enteric and central nervous system. The delay in the onset of contraction is due to the existence of a gradient of latency of contraction along the

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,

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.

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

*Digestive System - Recent Advances*

**Distance (↑)**

*Effect of APD contractions on intensity of mixing.*

*Effect of APD contractions on volume of mixing.*

**Distance (↑)**

**Wavelength (↑)**

**Wavelength (↑)**

**% Occlusion (↑)**

> **% occlusion (↑)**

APW ↑ or ↓ ↓ ↑ ↑ ↑ or ↓ RPW Negligible ↑ ↑ ↑ ↑ SW ↓ ↑ ↑ ↑ ↑

APW Negligible Negligible ↑ ↑ ↑ RPW Negligible Negligible ↑ ↑ ↑ SW Negligible Negligible Negligible ↑ Negligible

**Velocity (cm s<sup>−</sup><sup>1</sup>**

**or frequency (↑)**

**Velocity (cm s<sup>−</sup><sup>1</sup>**

**or frequency (↑)**

**)** 

**)** 

**Multiple waves (↑)**

**Multiple waves (↑)**

**Contraction type**

**Contraction type**

**Table 2.**

**Table 3.**

we also wanted to quantify the region over which the mixing or the volume of mixing is significant (computed as the volume of duodenum that has mixing index above 1.005). Changes in distance and wavelength of the peristaltic waves showed no major change in volume of mixing; however, it was sensitive to occlusion to some extent and highly sensitive to velocity and multiple waves. Standing contractions, on the other hand, showed zero or negligible volumes of mixing, except for a

Contractions of the longitudinal muscles, when occurring over short range of the gut segment, are referred to as the local longitudinal shortening. In literature, longitudinal shortening have been investigated as if they are advancing with the contraction, which we define as the advancing LLS and those that are stationary or stationary LLS are rarely considered. During LLS, the longitudinal muscles contract

LLS studies of the intestinal segments have been rarely considered. In order to understand the mechanophysiology of the LLS in intestine, we resort to the LLS

One of the classical studies of LLS was the study of esophageal peristalsis during feline. By using a widely spaced metal clips clamped to the esophageal mucosa (four tantalum wires that were imbedded in the outer esophageal wall), Dodds et al. [48] captured the longitudinal shortening of the esophageal segment which varies with their relative position. The study demonstrated the existence of a wave of local longitudinal shortening that moves in conjunction with the bolus. They also found that the relative displacements of the markers vary from one location to the other

frequency of 6 Hz where they showed some mixing (**Table 3**).

**5. Significance of the longitudinal muscles**

to shorten the segment along the axial direction only.

**5.2 Learning from esophageal studies of LLS**

studies of the esophageal segment.

**5.1 What is LLS?**

**56**

location suggesting that the LLS is effective over a given segment of the esophagus (especially the distal most esophagus). Subsequent studies, using widely spaced metal clips attached to the esophageal mucosa, support the contractive nature of the longitudinal muscles in the local regions of the esophageal wall during peristalsis [49–51]. Measuring local longitudinal shortening was, however, a challenge using the mucosal clip studies; given the large spacing of 3–10 cm. Nicosia et al. provided a more accurate method of determining the LLS and their coordination with CC using the high-frequency ultrasound transducer [18]. By employing the principle of law of mass conservation, the changes in the cross-sectional area with the temporal variation in local longitudinal shortening was made; which were compared with the luminal pressure measured using high resolution manometry. Following relation was derived: cross-sectional area during rest phase/cross-sectional area during contraction = length of the segment during contracted state/length during rest. Key observations were as follows: (1) during luminal filling (with bolus entry), the esophagus distends reducing the effective thickness of the muscles, (2) the wave of longitudinal shortening was followed by the circular contraction, (3) contraction of the longitudinal muscles were found to nearly coincide with the peak luminal pressure, (4) longitudinal shortening overlaps the CC and occur prior to CC and ended after CC, and (5) lastly, the strength of LLS directly relates to the generation of higher luminal pressure. Further clinical studies by the investigators also indicate the prior contraction of the longitudinal muscle during onset of distal esophageal peristalasis [18, 49, 50]. Such fine coordination the contraction of two muscles fibers provides for a mechanical advantage of gathering the neighboring circular muscle fiber closer to ensure that the circular contraction occurs at ease [52]. The coordination of CC and LLS is managed by the enteric and central nervous system. The delay in the onset of contraction is due to the existence of a gradient of latency of contraction along the length of the esophagus [53].
