Pumping Patterns and Work Done During Peristalsis in Finite-Length Elastic Tubes

Abstract

Balloon dilation catheters are often used to quantify the physiological state of peristaltic activity in tubular organs and comment on their ability to propel fluid which is important for healthy human function. To fully understand this system's behavior, we analyzed the effect of a solitary peristaltic wave on a fluid-filled elastic tube with closed ends. A reduced order model that predicts the resulting tube wall deformations, flow velocities and pressure variations is presented. This simplified model is compared with detailed fluid-structure 3D immersed boundary simulations of peristaltic pumping in tube walls made of hyperelastic material. The major dynamics observed in the 3D simulations were also displayed by our 1D model under laminar flow conditions. Using the 1D model, several pumping regimes were investigated and presented in the form of a regime map that summarizes the system's response for a range of physiological conditions. Finally, the amount of workdone during a peristaltic event in this configuration was defined and quantified. The variation of elastic energy and work done during pumping was found to have a unique signature for each regime. An extension of the 1D model is applied to enhance patient data collected by the device and find the work done for a typical esophageal peristaltic wave. This detailed characterization of the system's behavior aids in better interpreting the clinical data obtained from dilation catheters. Additionally, the pumping capacity of the esophagus can be quantified for comparative studies between disease groups.

Pressure -- area loop based phenotypic classification and mechanics of esophagogastric junction physiology

“…We apply this function to the model in the intention of mimicking both the muscle contraction of the traveling wave which pushes fluid forward, as well as the contraction and relaxation of the EGJ muscles. Using an activation function to vary the reference area is often used in cases where the external activation pressure at a specific location varies sinusoidally with time [17,19,20,21].…”

“…The elastic tube is closed on both ends and the volume inside the tube remains constant such that there is no flow in or out of the tube [17,18]. Therefore…”

“…To determine the key parameters that dictate the loop type, we developed a 1D model of a flow inside a FLIP device placed in the esophagus. The model is similar to the one described by [17,18]. The mass and momentum conservation equations are…”

“…The constants ρ and µ are the fluid density and viscosity, respectively. These 1D forms of the continuity and the momentum conservation equations were derived in [19] and have been widely used to describe valveless pumping [17,20,21,18]. The last equation in this system expresses pressure in terms of the tube's cross-sectional area.…”

“…Here, ∆P is the difference between the pressure inside and outside the tube (∆P = P i − P o ), K e is tube stiffness, and A o is the undeformed reference area representing the cross-sectional area of the tube when ∆P = 0 [17,18]. Lastly, θ(x, t) is an activation term which changes the reference cross-sectional area of the tube wall.…”