Peristaltic regimes in esophageal transport

Abstract

A FLIP device gives cross-sectional area along the length of the esophagus and one pressure measurement, both as a function of time. Deducing mechanical properties of the esophagus including wall material properties, contraction strength, and wall relaxation from these data are a challenging inverse problem. Knowing mechanical properties can change how clinical decisions are made because of its potential for in-vivo mechanistic insights. To obtain such information, we conducted a parametric study to identify peristaltic regimes by using a 1D model of peristaltic flow through an elastic tube closed on both ends and also applied it to interpret clinical data. The results gave insightful information about the effect of tube stiffness, fluid/bolus density and contraction strength on the resulting esophagus shape through quantitive representations of the peristaltic regimes. Our analysis also revealed the mechanics of the opening of the contraction area as a function of bolus flow resistance. Lastly, we concluded that peristaltic driven flow displays three modes of peristaltic geometries, but all physiologically relevant flows fall into two peristaltic regimes characterized by a tight contraction.

Keywords: Elastic tube flow; Esophagus; Fluid–structure interaction; Peristalsis; Reduced-order model.

Fig. 1

Tube geometries of the three physiologically relevant peristaltic regimes identified by Acharya et al. (2021). The shapes were captured from three different simulations at a single time instance in the contractile cycle

Fig. 2

A plot of the peristaltic activation function $\theta$ from Eq. (14) along the tube length at a time instant. Contraction occurs when $\theta <1$ and relaxation occurs when $\theta >1$

Fig. 3

The geometry corresponding to the reduced-order model

Fig. 4

Plotting the friction coefficient ${\psi }_{\mu }^{\prime }$ and non-dimensional area parameter $A_2^{″}$ to show their linear correlation

Fig. 5

The friction parameter ${\psi }_{\mu }^{\prime }$ plotted as a function of the non-dimensional contraction area parameter $A_c^{″}$

Fig. 6

The friction parameter ${\psi }_{\mu }^{\prime }$ was plotted as a function of the non-dimensional contraction area parameter $A_c^{″\prime }$

Fig. 7

Tube geometry of the three peristaltic regimes in a FLIP device when there is relaxation distal of contraction. The separation into three regimes was done based on the observations similar to those in Fig. 5

Fig. 8

Plot of the friction parameter ${\psi }_{\mu }^{\prime }$ as a function of $A_c^{″}$ with six highlighted cases with the same $\psi$ and ${\theta }_c$ and changing $\beta$. The value of $\beta$ in each case is written on the plot. The plot shows how in peristaltic regimes 1 and 2, friction parameter increases as fluid viscosity parameter increases $(\beta )$

Fig. 9

Plot of the friction parameter ${\psi }_{\mu }^{\prime }$ as a function of $A_c^{″\prime }$ alongside the line ${\psi }_{\mu }^{\prime }=1-A_c^{″\prime }-C$. This plot uses the output data from the simulations where there is no relaxation, ${\theta }_1=1.0$

Fig. 10

Plot of the actual cross-sectional area at location 2 as a function of the calculated cross-sectional area at location 2 from Eq. (42) for cases classified as peristaltic regime 3. This plot shows an approximate linear line of slope 1, meaning that the model and data match well

Fig. 11

Plot of the friction parameter ${\psi }_{\mu }^{\prime }$ as a function of $A_c^{″}$ with five highlighted cases with the same $\psi$ and ${\theta }_c$ and changing $\beta$. The value of $\beta$ in each case is written on the plot. The plot shows how in peristaltic regimes 3, friction parameter $({\psi }_{\mu }^{\prime })$ decreases as fluid viscosity parameter $(\beta )$ increases

Fig. 12

Plot of the friction parameter ${\psi }_{\mu }^{\prime }$ as a function of $A_c^{″\prime }$ with the two lines in Eqs. (35) and (39)

Fig. 13

Three plots of the friction parameter ${\psi }_{\mu }^{\prime }$ as a function of $A_c^{″\prime }$, each with a different set of highlighted simulations. Each set shares contractile cycle simulations with the same contraction strength and wall stiffness, with changing fluid resistance parameter

Fig. 14

Tube geometry at transition

Fig. 15

Esophagus wall shape of a control at a single time instance (Acharya et al. 2020; Lin et al. 2013; Carlson et al. 2016). The cross sectional data were captures using a FLIP device

Fig. 16

The friction parameter ${\psi }_{\mu }^{\prime }$ plotted as a function of the non-dimensional contraction area parameter $A_c^{″}$ for both simulation and clinical FLIP contractile cycles