**4. Mechanics of small intestinal digestion: mixing, transport, and absorption**

#### **4.1 Basic mechanics**

#### *4.1.1 Law of Laplace*

We discuss the basic principles of mechanics as applied to the small intestine. The small intestine, as we know, is a muscular conduit having two types of muscle layers—circular and longitudinal muscles. When muscles undergo contraction (reduction in the length of the muscles) they happen to either close the lumen (circular contraction) or shorten the segment (longitudinal contraction). From mechanics point of view, such contraction develops forces by virtue of muscular activity. By applying basic principles of mechanics, we can deduce as to how the muscular contraction results in the generation of pressure forces and flows inside the lumen. In general, whenever the tissue undergoes contraction, we explain the principle that the reduction is caused by generation of forces per unit area or stress. Parameters of interest are the percentage reduction in the length or strain that is caused by the stress. So, there exists some relation between the stress and the strain of the material under consideration. This leads us to assess the elasticity of the material or modulus of elasticity that measures the ability of the material to resistance deformation when a stress is applied to it. The nature of resistance or wall stiffness can be visualized by referring to the stress vs. strain plots obtained by allowing the material to deform under various strains and measuring the stress. The stress-strain plot provides details relevant to the mechanical properties of the tissue.

For simple geometry such as intestine approximated as a uniform and circular cylinder, the relation between the stress and luminal pressure under the assumption of thin wall is given by Laplace's law. It says that, under equilibrium condition, the tensile stress developed in wall is proportional to the intraluminal pressure and the radius of the intestinal tube. Suggesting that if the pressure inside the intestine is increased by gas formation (fermentation), for a non-significant change in the radius to wall thickness, then there would be a corresponding increase in the tensile force of the wall.

#### *4.1.2 Flow through the channel*

Transport of fluid across narrow constriction can be better appreciated by considering a familiar example of flow through a cylindrical pipe, also referred to as the Hagen-Poiseuille flow. Applying a relatively higher pressure force at left end of the tube, in comparison to the right end, causes the fluid to move down the pressure gradient only if it has overcome the viscous resistance. In case of viscous flow, the fluid eventually gains inertia and reaches a steady state when the axial velocity profile is parabolic. Let us assume a straight channel that is static (i.e., no contractions), with occlusion at the center and applied pressure at the ends as if they were generated by the APD contractions. In steady state, the flow rate can be derived as *Q* = *πr*<sup>4</sup> *P*/(8 μl), which relates the rate of flow at the outlet to the pressure difference applied to the channel. Suggesting that, the flow rate is highly sensitive to the fourth power of the channel radius and inversely proportional to the channel length.

#### *4.1.3 Longitudinal shortening*

Using high-frequency ultrasound, Nicosia et al. were able to calculate the percentage reduction in the length of the longitudinal muscles [18]. As discussed in the later section, using the principle of mass conservation, the authors were able

**53**

**4.4 Intestinal peristalsis**

velocity of propagation of 0.1–0.4 cm s<sup>−</sup><sup>1</sup>

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

**4.2 Modeling small intestinal contractions**

**4.3 Pyloric contraction**

showing distinct patterns of activity every 90–120 min<sup>−</sup><sup>1</sup>

to quantify local longitudinal shortening as the ratio of longitudinal length after contraction relative to the initial length as inversely related to the ratio of cross-sectional area of the muscle after contraction relative to the initial area; L/L\* = 1/(A/A\*).

Unlike the gastric contractions, the small intestine motility patterns are not regular. In preprandial state, the small intestine enter into the interdigestive phase

motor complex or MMC) which include (1) a period of quiescence with no contractions (Phase I), (2) a long period of unsynchronized contractions (Phase II), and (3) a burst of strong and regular contractions (Phase III) [19]. Of these, phase III plays an important role in sweeping the undigested food particles (left over debris) and bacteria out of the small intestine and into the large intestine. However, after meal ingestion (postprandial), the small intestine switches to a more synchronized motility patterns.

Pylorus plays a key role in mediating the flow across the stomach and the duodenum. It does by developing higher resistance to flow through closing of the lumen. They typically open and close the lumen at intervals of 20 s [20]. Flow through the channel is driven by generating a pressure gradient across the two ends of the channel and depends on luminal diameter, degree of opening, length of canal; thus, regulating gastric emptying (GE) or duodenogastric reflux (DGR) [21–26]. Both antegrade and retrograde flow have been reported in the literature to be normal; however, when the quantity of flow in the reverse direction leads to increased volume of reflux, then it leads to DGR disease. The flow is found to be pulsatile in nature [27–34]. The pylorus exhibits both tonic and phasic contractions

contraction [35]. In postprandial state, pylorus opens and closes with mean diameter 5.4 ± 1.0 mm [21]. Out of 193 pyloric closure events, 133 occurred in 2 s of the antral and duodenal contraction in a study carried out in patients. The pylorus was reported to be in closed position for 55.5% of 154 isolated duodenal contractions

between subsequent pyloric pressure events with each flow lasting for 3.5 ± 0.1 s with volumes of 0.3 ± 0.01 ml being release during the stroke. They occur 2.8 ± 0.7 s before pyloric pressure event, and 2.3 ± 0.5 s before antral wall motion [39]. Mealdependent effects of pyloric motility using clinical trials of intravenous injection of 20% dextrose solution indicated causation of pyloric contraction, suppression of antral contraction, and duodenal phase-3-like motility [40]. The duration and intensity of phasic and tonic contraction of the pylorus showed direct correlation with caloric content of dextrose solution been infused into duodenum. Increase in caloric content caused increase in isolated pyloric pressure waves and basal pyloric pressure [41]. Duodenal infusion of saline shows no change in motility patterns of APD; whereas, triglyceride and fatty acid infusion suppresses antral contractions, but enhances pyloric phasic and tonic activity and delays gastric emptying [42, 43].

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>

, and higher propensity to develop

[35–38], which develops a pressure of 10.8 ± 4.5 mmHg at 1–4 min<sup>−</sup><sup>1</sup>

recorded. In porcine flow, pulses happen at 11.2 ± 0.4 min<sup>−</sup><sup>1</sup>

(also known as Migrating

rates of phasic

,

frequency and occur

*Digestive System - Recent Advances*

*4.1.2 Flow through the channel*

*4.1.3 Longitudinal shortening*

**absorption**

**4.1 Basic mechanics**

*4.1.1 Law of Laplace*

**4. Mechanics of small intestinal digestion: mixing, transport, and** 

We discuss the basic principles of mechanics as applied to the small intestine. The small intestine, as we know, is a muscular conduit having two types of muscle layers—circular and longitudinal muscles. When muscles undergo contraction (reduction in the length of the muscles) they happen to either close the lumen (circular contraction) or shorten the segment (longitudinal contraction). From mechanics point of view, such contraction develops forces by virtue of muscular activity. By applying basic principles of mechanics, we can deduce as to how the muscular contraction results in the generation of pressure forces and flows inside the lumen. In general, whenever the tissue undergoes contraction, we explain the principle that the reduction is caused by generation of forces per unit area or stress. Parameters of interest are the percentage reduction in the length or strain that is caused by the stress. So, there exists some relation between the stress and the strain of the material under consideration. This leads us to assess the elasticity of the material or modulus of elasticity that measures the ability of the material to resistance deformation when a stress is applied to it. The nature of resistance or wall stiffness can be visualized by referring to the stress vs. strain plots obtained by allowing the material to deform under various strains and measuring the stress. The stress-strain plot provides details relevant to the mechanical properties of the tissue. For simple geometry such as intestine approximated as a uniform and circular cylinder, the relation between the stress and luminal pressure under the assumption of thin wall is given by Laplace's law. It says that, under equilibrium condition, the tensile stress developed in wall is proportional to the intraluminal pressure and the radius of the intestinal tube. Suggesting that if the pressure inside the intestine is increased by gas formation (fermentation), for a non-significant change in the radius to wall thickness, then there would be a corresponding increase in the tensile force of the wall.

Transport of fluid across narrow constriction can be better appreciated by considering a familiar example of flow through a cylindrical pipe, also referred to as the Hagen-Poiseuille flow. Applying a relatively higher pressure force at left end of the tube, in comparison to the right end, causes the fluid to move down the pressure gradient only if it has overcome the viscous resistance. In case of viscous flow, the fluid eventually gains inertia and reaches a steady state when the axial velocity profile is parabolic. Let us assume a straight channel that is static (i.e., no contractions), with occlusion at the center and applied pressure at the ends as if they were generated by the APD contractions. In steady state, the flow rate can be derived as *Q* = *πr*<sup>4</sup> *P*/(8 μl), which relates the rate of flow at the outlet to the pressure difference applied to the channel. Suggesting that, the flow rate is highly sensitive to the fourth power of the channel radius and inversely proportional to the channel length.

Using high-frequency ultrasound, Nicosia et al. were able to calculate the percentage reduction in the length of the longitudinal muscles [18]. As discussed in the later section, using the principle of mass conservation, the authors were able

**52**

to quantify local longitudinal shortening as the ratio of longitudinal length after contraction relative to the initial length as inversely related to the ratio of cross-sectional area of the muscle after contraction relative to the initial area; L/L\* = 1/(A/A\*).

## **4.2 Modeling small intestinal contractions**

Unlike the gastric contractions, the small intestine motility patterns are not regular. In preprandial state, the small intestine enter into the interdigestive phase showing distinct patterns of activity every 90–120 min<sup>−</sup><sup>1</sup> (also known as Migrating motor complex or MMC) which include (1) a period of quiescence with no contractions (Phase I), (2) a long period of unsynchronized contractions (Phase II), and (3) a burst of strong and regular contractions (Phase III) [19]. Of these, phase III plays an important role in sweeping the undigested food particles (left over debris) and bacteria out of the small intestine and into the large intestine. However, after meal ingestion (postprandial), the small intestine switches to a more synchronized motility patterns.
