Liquid in the gastroesophageal segment promotes reflux, but compliance does not: a mathematical modeling study

Abstract

The mechanical force relationships that distinguish normal from chronic reflux at sphincter opening are poorly understood and difficult to measure in vivo. Our aim was to apply physics-based computer simulations to determine mechanical pathogenesis of gastroesophageal reflux. A mathematical model of the gastroesophageal segment (GES) was developed, incorporating the primary anatomical and physiomechanical elements that drive GES opening and reflux. In vivo data were used to quantify muscle stiffness, sphincter tone, and gastric pressure. The liquid lining the mucosa was modeled as an "effective liquid film" between the mucosa and a manometric catheter. Newton's second law was solved mathematically, and the space-time details of opening and reflux were predicted for systematic variations in gastric pressure increase, film thickness, muscle stiffness, and tone. "Reflux" was defined as "2 ml of refluxate entering the esophagus within 1 s." GES opening and reflux were different events. Both were sensitive to changes in gastric pressure and sphincter tone. Reflux initiation was extremely sensitive to the liquid film thickness; the protective function of the sphincter was destroyed with only 0.4 mm of liquid in the GES. Compliance had no effect on reflux initiation, but affected reflux volume. The presence of abnormal levels of liquid within the collapsed GES can greatly increase the probability for reflux, suggesting a mechanical mechanism that may differentiate normal reflux from gastroesophageal reflux disease. Compliance does not affect the probability for reflux, but affects reflux volume once it occurs. Opening without reflux suggests the existence of "gastroesophageal pooling" in the distal esophagus, with clinical implications.

Fig. 1.

Schematic of the interaction between physiological and mechanical changes in the gastroesophageal sphincter associated with opening from below. A: resting state; B: relaxation; C: gastroesophageal segment (GES) opening; D: gastro-esophageal (GE) reflux. LES, lower esophageal sphincter; P_TONE, myogenic tone pressure; P_E, esophageal lumen pressure; P_T, thoracic cavity pressure; P_G, gastric pressure; P_A, abdominal cavity pressure.

Fig. 2.

Specification of the mathematical model of the GES with opening from below. The modeled GES is shown before opening (A) and after opening (B). An orthogonal coordinate system (η, ξ) was also used in the mathematical model (refer to appendix). C: the change in effective muscle stiffness through the GES as modeled. D: the mathematical model predicts the change in geometry of the midlayer of the muscularis propria and fluid flow during opening and reflux driven by the assumed pressure difference between the stomach and mediastinum relative to the external pressures shown here.

Fig. 3.

Separating the parameter combinations that distinguish GES “opening” from “no opening” (solid curves), and that separate “reflux” from “no reflux” (dashed curves) for specified effective film thickness, ɛ. For specified increase in P_G, the GES opens when the level of sphincter augmentation pressure (tone) is below the solid curve and refluxes when augmentation pressure is below the dashed curve for specified film thickness. If the parameter combinations place the GES between a pair of solid and dashed curves, the GES will open and liquid will enter the distal esophagus, but at a rate insufficient to satisfy the criterion for reflux.

Fig. 4.

Effect of liquid film thickness on the parameter combinations that define the boundary between reflux and no reflux. A: the sphincter augmentation pressure that is required to prevent reflux is plotted against the effective film thickness ɛ for fixed gastric pressure P_G increase (ΔP_G). B: ΔP_G that is required to trigger reflux is plotted against ɛ for fixed sphincter augmentation pressure. Transient LES relaxation (tLESR) is given by zero sphincter augmentation pressure. The simulations were carried out down to film thickness = 0.4 mm. The curves in A were extrapolated to smaller film thicknesses, and the curves in B were extended by using the extrapolated values.

Fig. 5.

Effect of liquid film thickness on the parameter combinations that define the boundary between opening and no opening. The values for the curves below film thickness of 0.2 mm are extrapolations, as explained in Fig. 4. This figure is to be compared with Fig. 4B, where we plot the increase in P_G required to trigger opening (as opposed to reflux in Fig. 4B) for fixed sphincter augmentation pressure. Note that, with a fully relaxed sphincter (tLESR), opening occurs for any rise in P_G at all liquid film thicknesses, whereas reflux is progressively suppressed at lower film thicknesses (Fig. 4B).

Fig. 6.

Tonic requirements to prevent reflux as a function of P_G rise for different fixed liquid film thicknesses.

Fig. 7.

Sensitivity of the initiation of reflux to changes in net GES muscle stiffness, and to changes in P_G, relative to baseline (baseline P_G = 5 mmHg above baseline intrathoracic pressure). μ_M, muscle stiffness coefficient.

Fig. 8.

A: sensitivity of maximum GES radius to changes in net GES muscle stiffness relative to normal subjects (curve A), and to changes in P_G relative to baseline (curve B). Maximum GES opening shows a strong sensitivity to both parameters. B: sensitivity of the volume of reflux after 1 s to changes in net GES muscle stiffness (μ_M) and to changes in P_G relative to baseline.