Theoretical modeling of the resistance to gastric emptying and duodenogastric reflux due to pyloric motility alone, presuming antral and duodenal quiescence

Highlights

• The resistance offered by the pylorus to transpyloric flow was estimated.

• Wall shearing is highest near the mid-occlusion

• Friction is higher for higher frequency and occlusion.

• Flow is highly sensitive to frequency and occlusion.

• The frictional force is higher for Dilatants.

Abstract

A theoretical model of the pyloric channel, approximated as a two-dimensional tube with sinusoidal corrugation, is developed to estimate the degree of resistance offered by the pylorus to transpyloric flow (gastric emptying and duodenogastric reflux) in the viscous regime. Study indicates that the resistance of the channel depends on pressure gradient, flow behavior index and channel diameter. Flow is majorly determined by the extent of luminal opening; since they scale to fourth power of the diameter for Newtonian flow, with the exponent being higher for pseudoplastic and lesser in case of dilatants relative to Newtonian fluid. At zero pressure difference, across the channel, the closing pylorus drives the aborad propulsion of the contents at the intestinal end, and at the gastric end the flow is driven along the orad direction. While no transfer of contents occur at the centre of pylorus due to zero pressure gradients, it is essential to have a non-zero pressure difference to drive the flow through the channel. The extent of pressure difference is found to linearly relate to the transpyloric flow rate. The resistive function of the pyloric channel is observed at a higher occlusion where there is a development of higher pressure barrier that is sensitive to the flow behavior index, frequency, occlusion, and contraction length.

Introduction

The pylorus is a sphincter (a muscular tissue) that connects the stomach to the duodenum (Fisher and Cohen, 1973). It comprises of a band of smooth muscle fibers that is thick at the center and spreads across for a distance of approximately 5 cm in length; thus forming a controlled valve that has the ability to regulate the flow across the two compartments, that is, the stomach and the duodenum (Ramkumar and Schulze, 2005, Houghton et al., 1988). It plays an important role in digestion by allowing for the transfer of nutrient rich meal in controlled volumes. In postprandial state (after ingestion of meal), it permits only a sufficient amount of the meal to be allowed to empty into the duodenum (initial segment of the intestine); limited by the caloric load of the intestine’s ability to absorb (3 kcal/min). Motility patterns of the pylorus has a direct consequence to the physiology such as to empty (gastric emptying or GE) or reflux (duodenogastric reflux or DGR) (Mabrut and Collard, 2006, Muller-Lissner et al., 1981, Code et al., 1984). When the volumes of GE is affected, it leads to a slower emptying (gastroparesis) (Camilleri et al., 2018) or rapid emptying (dumping syndrome) (Berg and McCallum, 2016), similarly higher volumes of DGR can have a damaging effect on gastric mucosa leading to cancerous formation. In pyloric stenosis, one of the disorders of sphincter dysfunctions, the pylorus get narrowed, which as a consequence increases the resistance to transpyloric flow (Peters et al., 2014). Due to reduced flow of the nutrient rich gastric contents into the duodenum, the physiological processes of the nutrient absorption may get disturbed. Thus, as a consequence, motility dysfunctions may give rise to symptoms such as nausea, abdominal pain, vomiting and indigestion. In infants, it may lead to inadequate supply of nutrients resulting in malnutrition and weight loss. Since the pyloric segment plays a key role in regulating the digestion through control of gastric emptying and duodenogastric reflux, it therefore necessitates for understanding the behavior of pyloric channel to facilitate better treatment modalities for patients suffering from pyloric motility disorders.

Clinical questions arise as to how one can address the problem through surgery or mange the patient suffering from an impaired pyloric function (Avvari, 2019). Since the pylorus communicate with the adjacent segments, namely the antrum (distal stomach) and the duodenum, questions as to how the gastric emptying is regulated and to what extent these segments manifest is a challenge (Avvari, 2015, Avvari and Qi, 2019). One of the techniques is to explore the mechanics of gastric emptying due to pylorus only presuming no motility occurs in the antrum and duodenum, and further generation of pressure or the common cavity pressure resulting from fundic squeeze is neglected. This may enable to explore the contribution of the pyloric motility on the flow to some extent. The state of the art in the area of transpyloric flow is discussed in the following.

Transpyloric flow is considered to be governed by the motility of the fundus, antrum, pylorus and the duodenum (Houghton et al., 1988, Read and Houghton, 1989). Manometry studies of the pyloric channel supports the idea that fundus regulates the flow rate by the squeezing the segment (via tonic contractions of the smooth muscle fibers of the fundus) in setting up small pressure gradients across the pyloric channel to drive the flow (Indireshkumar et al., 2000). Whereas antrum is less considered in regulating the flow through the pyloric channel, it also exercises control over the flow through coordination with the proximal stomach, pylorus and the duodenum (Collins et al., 1991, Sun et al., 1998). The delivery of gastric content to the duodenum is primarily controlled by the opening and closing of the pyloric sphincter; flow rate being highly sensitive to luminal diameter, linearly relates to the transpyloric pressure difference and inversely relates to the viscosity of the fluid (Avvari, 2015, Avvari and Qi, 2019). The pylorus also helps facilitate the grinding of the food through closure as the antral wave approaches close to it; generating higher forces in the region sufficient enough to grind the food. Computer simulation of the stomach indicates that the pylorus also acts by filtering the meal selectively while emptying the gastric contents into the duodenum or “magenstrasse” (Pal et al., 2007). While the pylorus can independently open and close irrespective of the adjacent gastrointestinal segments (appears as isolated pyloric pressure waves or IPPW on intraluminal manometry), however, it is not sufficient to drive the transpyloric flow (Treacy et al., 1992). A non-zero pressure gradient is required to cause the fluid transport which may arise from the fundic, antral or duodenal motility. The pyloric sphincter also coordinates with the duodenal segment to regulate the flow. In silico studies demonstrate that the duodenal contractions travelling close to the pylorus, predominantly cause the reflux of the duodenal contents back into the stomach which could be a major contributor to the duodenogastric reflux (Avvari, 2015).

The natures of contraction in the pyloric region and the adjacent segments associated to it were well documented during 1960s through concurrent cineradiography and manometry. Pylorus is a sphincter (comprising of a thick layer of circular muscle fibers) which opens and closes the channel to regulate the flow through it (Ehrlein, 1988). Contraction of the pyloric segment is not independent; rather they coordinate with the neighboring segments of the intestine to perform the digestion. Numerous clinical studies corroborates with the idea that pylorus have the flexibility to undergo contraction independently (demonstrated by occurrence of isolated pyloric pressure waves or IPPW in pressure iso-contour map using manometry) or in unison with adjacent segment through feedback regulation. According to Carlson et al., pylorus closure is always observed with the terminal antral contraction, a striking feature that is known to cause retropulsion of the contents back into the stomach while the terminal antrum contracted forcefully (Carlson et al., 1966). In the study, the pylorus was found open in 28% of the observation. It is during this phase that the antrum relaxes and the pylorus begins to open to allow for the antegrade transport of the fluid. While at lower antral pressures, there were negligible transfer of chyme (bolus of food mixed with acidic contents of stomach) into the pylorus, at higher antral pressures there were bolus transit (confirmed using pH drop in the duodenum bulb) indicated in majority of the events (Rhodes et al., 1966). The activity of the pylorus in relation to antrum and duodenum were further explored in 22 normal subjects following a test meal of 500 ml of dilute orange juice using ultrasound (King et al., 1985). The sequence of motor activity in the antro-pyloric-duodenal regions that comprised of terminal antral contraction (TAC) and duodenal contraction (DC) were observed every 20 sec with certain overlap; with TAC preceding the DC. Observations of the pyloric activity by King et al. were in agreement with previous works which suggests that the pyloric closing is associated with TAC for most of the pyloric closure events and opening during events of antral relaxation.

Motor function of the pylorus is governed by the feedback mechanism which has been demonstrated to alter the rate of gastric emptying (Treacy et al., 1990). Studies using intraduodenal infusion of nutrients have shown to reduce the occurrence of antral pressure waves and an increase in the IPPW (Heddle et al., 1988). The inter-segmental dependence of the motility of antro-pyloro-duodenal segment and nutrient induced feedback regulatory mechanism has direct implication in deciding the rates of gastric emptying (Miller et al., 1981).

While direct imaging and manometry studies provide details relevant of the antro-pyloro-duodenal motility and the inter-dependency between the adjacent segments to the pyloric sphincter, it does not provide clues relevant to emptying patterns, emptying rate and volume of emptying. It is however known that pyloric channel introduces a period of occlusion to flow resulting in an intermittent flow or pulsatile flow occurring for a duration of 2–5 s (Keinke et al., 1984). Flow across the channel show an alternate sequence of emptying and reflux episodes; where the DGR episodes occur just before the closure of pylorus (Hausken et al., 1992). Direct imaging of the gastric emptying and quantification of the flow rate became possible with combined of doppler effect with B-mode imaging. Using Doppler imaging, Hausken et al. determined the volume of flows through the channel as follows – 1) volumes of gastric emptying had an average of 4.3 ml which occurred for a duration of 0.69 s, and 2) volumes duodenogastric reflux showed an average of 8.3 ml occurring over a time interval for 1.4 s on average (Hausken et al., 2001). For flows occurring at more than 1 sec, the flow rates range from 2.1 to 5.22 ml/min which are majorly reflux events. Marciani et al. found that the viscous meal and nutrient meal had an effect of slowing the gastric emptying in health individuals (Marciani et al., 2001). For low viscous meal (0.06 Pa.s) and high viscous meal (29.5 Pa.s), the emptying rate reported a mean of 6.1 ml/min and 4.7 ml/min respectively for control (or non-nutrient meals) and 4.1 ml/min and 3.3 ml/min for nutrient meal respectively. At higher caloric load, the rate of gastric emptying remains nearly the same for initial 30 min in contrast to lower caloric load where the rate of gastric emptying is reported to be much faster (Mazzawi et al., 2019).

Although numerous clinical studies have been performed, hitherto, the mechanism involved in the regulation of transpyloric flow is not clear. The challenge is the inability to capture simultaneous recordings of luminal pressures at the antro-pyloro-duodenal (APD) segment, wall movement resulting from muscular contractions, nature of meal distribution during APD wall motion, and patterns of the luminal flow.

Recent studies involving computer modeling have provided details of the flows resulting from the APD motility. Flow through the channel is regulated by the pyloric sphincter; a group of circular smooth muscle fiber that controls the opening and closing of the pyloric channel. Assuming the pyloric channel as having a sinusoidal constriction, lubrication theory suggests that the axisymmetric flow through the channel follows a linear relationship for the pressure drop versus the flow rate (Li and Brasseur, 1993). Computer simulation of the APD segment was also performed to investigate the flow and mixing in the duodenum for cases of open and close pylorus, however, the degree of resistance to flow was not evaluated in the study (Dillard et al., 2007). The jet flow was found to be affected by the narrowing of the lumen providing qualitative details on the flow obstruction by closing of the channel. While the authors have analyzed for flow regime characterized by Re greater than 1 (1 to 333), it falls outside of the physiological regime in postprandial, since the Re ≪1. For example, assuming radial velocity of the pyloric wall at 0.1 cm/s (pyloric closing and opening at 3 cycles/sec at maximum diameter of 1 cm) for fluid of density equal to water (1gm/cm³) and viscosity of 1000cP (assuming 1000 time viscosity of water at 20 °C), the Reynolds number is calculated to be 0.01. For fluid viscosity at 10 times the water at 20 °C, the Reynolds number is 1 which is referred to as the low Re flows. Whereas the results of Dillard et al. may be applicable in preprandial state with liquid meal of viscosity equal to those of water, the simulation results do not capture the physiological flows.

While pylorus is known to be a primary regulator of flow, contraction in the neighboring segments (antrum and duodenum) can also affect the transpyloric flow rates by modulating the pressure gradient across the channel. Effect of antral contractions with the pyloric activity was analyzed for varying degree of antral and pyloric motility disorder using multiphase flow model to study extent of particle dissolution and reactions between components (Trusov et al., 2016, Kamaltdinov et al., 2018). The study demonstrates the significance of antral contractions in stomach evacuation or emptying of gastric particles. The particles of size larger than 1.7 mm tend to stay inside the antral compartment and do not evacuate into the bowel. Whereas particles with size of less than 0.2 mm can easily transit into the duodenum during events of pylorus opening (Trusov et al., 2016). Functional disorder of the antrum affects the particle transit into the duodenum significantly and to a lesser extent for functional disorder of the duodenum (Kamaltdinov et al., 2018). Flow of the small particles occurs as the contractile wave traverses from the middle of the antral segment aborally, where the pylorus is in open state. In another study, computer simulations for an anatomically realistic gastroduodenal model using lattice Boltzmann approach for flow simulation showed that the coordination between the contractions of the antrum and pylorus play a key role in determining the extent of gastric emptying and the bile reflex. Authors have analyzed the impairment in coordination by controlling the time of pyloric closure and the time lapse in pyloric closure relative to the onset of TAC (Ishida et al., 2019). Simulations demonstrated the age old concept of the TAC involvement in the flow regulation as follows – emptying occurs when the pyloric was opening during TAC (typically in the rage of 3–8 ml/min) and opening of the pylorus together with antral relaxation induced a dodenogastric reflux at a rate of 10–30 ml/min. Emptying was found maximum at a rate of 27 m/min for low viscous meal (μ = 4.2 × 10⁻³ Pa∙s) and minimum at 10 ml/min (for open pylorus) for higher viscous meal (μ = 1.3 Pa∙s).

While the literature provides details relevant to the particle transit and sieving action of the pylorus, it does not provides details of hydrodynamics resistance to flow in the pyloric channel; the details relevant to the extent to which the flow is suppressed in the pyloric channel relative to the motor activity in the antrum and the duodenum. The coordination between the contraction of the antrum, pylorus and the duodenum play a key role in regulating gastric emptying (Avvari, 2015). Two modes of APD coordination were reported in the literature which includes – only pyloric motility (opening and closing of the pyloric channel) in absence of gastric and duodenal motility, pyloric motility in presence of duodenal motility and gastric quiescence (Avvari, 2015).

Effect of duodenal contractions on transpyloric flow is of significance to understand the mechanism underlying the suppression of DGR, besides enhancing gastric emptying. Flow in the duodenum is a complex process and involves contribution of various parameters such as local longitudinal shortening (LLS) magnitude, LLS spacing, fluid viscosity, wavelength of the wave, and degree of luminal occlusion (Avvari, 2019). Computer model of the antropyloroduodenal segment in three-dimensional study of fluid flow demonstrate that certain contractions of the duodenum function as reflux causing contractions (RCC; contractions inducing DGR) of the duodenum (Avvari, 2015). By monitoring the pressure gradient and reflux rates, the RCCs contributing to major reflux were found which includes – closing type stationary wave, retrograde propagating wave and proximal contractions (both antegrade and retrograde propagating wave). This suggests that the duodenal contraction can modulate the pyloric resistance to flow.

Due to limitations in the clinical studies, the contribution of the pylorus in the causation of the gastric emptying is still ambiguous. It is still an open question as to how the pylorus facilitates emptying or reflux and what values of pressure gradients are required to drive the flow. Despite qualitative inferences, the quantitative detail of the flow is missing. Since the coordination of pylorus with antrum and duodenum is complex to study, one may objectively dissect the motor function of the pylorus.

In this study, using Newton’s law of motion for fluids, a theoretical model is developed for estimating the resistance of the pylorus for fluid of Newtonian and non-Newtonian type. Although literature in the area of flow through construction as in stenosed tube as in arteries (Nadeem et al., 2011, Ahmad et al., 2019) and peristalsis in biological systems such as blood vessels (Maiti and Misra, 2013, Misra and Maiti, 2012, Misra and Pandey, 2002, Misra and Pandey, 1995), esophagus (Misra and Maiti, 2012, Misra and Pandey, 2001), intestine (Avvari, 2019) is available, the consideration of wall movements is different for pylorus. The wavy nature of pyloric wall is of key interest to explore the transport phenomena in causation of the pathology such as the duodenogastric reflux. In compliance with the theoretical models as studied in literature using lubrication approximation, the effects of pyloric motor function on the transploric flow is studied for non-Newtonian fluid. Flow through the channel was investigated for pressure, flow rate, and, shear stress for variations in contractility and fluid rheology parameters are elaborated in results section, followed by discussion. In conclusion, key results were summarized that are involved in conferring resistance to flow.