A continuum mechanics-based musculo-mechanical model for esophageal transport

MRI-MECH: mechanics-informed MRI to estimate esophageal health

Dynamic magnetic resonance imaging (MRI) is a popular medical imaging technique that generates image sequences of the flow of a contrast material inside tissues and organs. However, its application to imaging bolus movement through the esophagus has only been demonstrated in few feasibility studies and is relatively unexplored. In this work, we present a computational framework called mechanics-informed MRI (MRI-MECH) that enhances that capability, thereby increasing the applicability of dynamic MRI for diagnosing esophageal disorders. Pineapple juice was used as the swallowed contrast material for the dynamic MRI, and the MRI image sequence was used as input to the MRI-MECH. The MRI-MECH modeled the esophagus as a flexible one-dimensional tube, and the elastic tube walls followed a linear tube law. Flow through the esophagus was governed by one-dimensional mass and momentum conservation equations. These equations were solved using a physics-informed neural network. The physics-informed neural network minimized the difference between the measurements from the MRI and model predictions and ensured that the physics of the fluid flow problem was always followed. MRI-MECH calculated the fluid velocity and pressure during esophageal transit and estimated the mechanical health of the esophagus by calculating wall stiffness and active relaxation. Additionally, MRI-MECH predicted missing information about the lower esophageal sphincter during the emptying process, demonstrating its applicability to scenarios with missing data or poor image resolution. In addition to potentially improving clinical decisions based on quantitative estimates of the mechanical health of the esophagus, MRI-MECH can also be adapted for application to other medical imaging modalities to enhance their functionality.

A mechanics-based perspective on the pressure-cross-sectional area loop within the esophageal body

Introduction: Plotting the pressure-cross-sectional area (P-CSA) hysteresis loops within the esophagus during a contraction cycle can provide mechanistic insights into esophageal motor function. Pressure and cross-sectional area during secondary peristalsis can be obtained from the functional lumen imaging probe (FLIP). The pressure-cross-sectional area plots at a location within the esophageal body (but away from the sphincter) reveal a horizontal loop shape. The horizontal loop shape has phases that appear similar to those in cardiovascular analyses, whichinclude isometric and isotonic contractions followed by isometric and isotonic relaxations. The aim of this study is to explain the various phases of the pressurecross-sectional area hysteresis loops within the esophageal body. Materials and Methods: We simulate flow inside a FLIP device placed inside the esophagus lumen. We focus on three scenarios: long functional lumen imaging probe bag placed insidethe esophagus but not passing through the lower esophageal sphincter, long functional lumen imaging probe bag that crosses the lower esophageal sphincter, and a short functional lumen imaging probe bag placed in the esophagus body that does not pass through the lower esophageal sphincter. Results and Discussion: Horizontal P-CSA area loop pattern is robust and is reproduced in all three cases with only small differences. The results indicate that the horizontal loop pattern is primarily a product of mechanical conditions rather than any inherently different function of the muscle itself. Thus, the distinct phases of the loop can be explained solely based on mechanics.

Virtual disease landscape using mechanics-informed machine learning: Application to esophageal disorders

Esophageal disorders are related to the mechanical properties and function of the esophageal wall. Therefore, to understand the underlying fundamental mechanisms behind various esophageal disorders, it is crucial to map mechanical behavior of the esophageal wall in terms of mechanics-based parameters corresponding to altered bolus transit and increased intrabolus pressure. We present a hybrid framework that combines fluid mechanics and machine learning to identify the underlying physics of various esophageal disorders (motility disorders, eosinophilic esophagitis, reflux disease, scleroderma esophagus) and maps them onto a parameter space which we call the virtual disease landscape (VDL). A one-dimensional inverse model processes the output from an esophageal diagnostic device called the functional lumen imaging probe (FLIP) to estimate the mechanical "health" of the esophagus by predicting a set of mechanics-based parameters such as esophageal wall stiffness, muscle contraction pattern and active relaxation of esophageal wall. The mechanics-based parameters were then used to train a neural network that consists of a variational autoencoder that generated a latent space and a side network that predicted mechanical work metrics for estimating esophagogastric junction motility. The latent vectors along with a set of discrete mechanics-based parameters define the VDL and formed clusters corresponding to specific esophageal disorders. The VDL not only distinguishes among disorders but also displayed disease progression over time. Finally, we demonstrated the clinical applicability of this framework for estimating the effectiveness of a treatment and tracking patients' condition after a treatment.

Normative values of intra-bolus pressure and esophageal compliance based on 4D high-resolution impedance manometry

BACKGROUND

This study aimed to quantify normative values of phase-specific intra-bolus pressure (IBP) and esophageal distensibility using 4D analysis of high-resolution-impedance manometry (HRIM).

METHODS

HRIM studies of supine swallows from 34 normal controls were analyzed with respect to the four phases of bolus transit: (1) accommodation, (2) compartmentalization, (3) peristalsis/esophageal emptying, and (4) ampullary emptying. Phase-specific IBP, bolus volume, and distensibility index (DI) in the esophageal body and esophagogastric junction (EGJ) during phases 1-3 were extracted.

RESULTS

The median (5-95th/IQR) IBP values were as follows: phase 1: 4.0 (-2.0-10.4/1.9-5.8) mmHg, phase 2: 5.7 (0.2-14.1/3.6-8.9) mmHg, and phase 3: 11.2 (2.9-19.4/7.7-15.1) mmHg. The median bolus volume calculated by integrating impedance planimetry cross-sectional areas was 4.1 ml during the compartmentalization phase. The EGJ-DI at max EGJ diameter during phase 2 and 3 was 2.8 (1.1-9.5/1.8-3.7) mm² /mmHg and 6.0 (3.2-20.3/5.1-7.8) mm² /mmHg, respectively. The phase 3 EGJ-DI values (6.0 (3.2-20.3/5.1-7.8) mm² /mmHg) were similar to those calculated using functional lumen imaging probe (FLIP) at the 60 ml volume on the same subjects (5.8 [3.5-7.2/5.0-6.4] mm² /mmHg).

CONCLUSIONS AND INFERENCES

4D-HRIM provides a standardized methodology to track the nadir impedance and provide measurements of IBP during maximal distention across phases 1-3 of bolus transit. Median IBP and delta IBP were different across the phases, supporting the need to define IBP by phase. Additionally, the EGJ-DI calculated during phase 3 was similar to the 60-ml EGJ-DI from FLIP in the same subjects suggesting that 4D-HRIM can quantify EGJ opening during primary peristalsis.

On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method's performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretization combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta functions). Earlier work with this methodology suggested that such coarse structural meshes can yield improved accuracy for shear-dominated cases and, further, found that accuracy improves when the structural mesh spacing is increased. However, these results were limited to simple test cases that did not include substantial pressure loading on the structure. This study investigates the effect of varying the relative mesh widths of the Lagrangian and Eulerian discretizations in a broader range of tests. Our results indicate that kernels satisfying a commonly imposed even-odd condition require higher resolution to achieve similar accuracy as kernels that do not satisfy this condition. We also find that narrower kernels are more robust, in the sense that they yield results that are less sensitive to relative changes in the Eulerian and Lagrangian mesh spacings, and that structural meshes that are substantially coarser than the Cartesian grid can yield high accuracy for shear-dominated cases but not for cases with large normal forces. We verify our results in a large-scale FSI model of a bovine pericardial bioprosthetic heart valve in a pulse duplicator.

Myotomy technique and esophageal contractility impact blown-out myotomy formation in achalasia: an in silico investigation

We used in silico models to investigate the impact of the dimensions of myotomy, contraction pattern, the tone of the esophagogastric junction (EGJ), and musculature at the myotomy site on esophageal wall stresses potentially leading to the formation of a blown-out myotomy (BOM). We performed three sets of simulations with an in silico esophagus model, wherein the myotomy-influenced region was modeled as an elliptical section devoid of muscle fibers. These sets investigated the effects of the dimensions of myotomy, differing esophageal contraction types, and differing esophagogastric junction (EGJ) tone and wall stiffness at the myotomy affected region on esophageal wall stresses potentially leading to BOM. Longer myotomy was found to be accompanied by a higher bolus volume accumulated at the myotomy site. With respect to esophageal contractions, deformation at the myotomy site was greatest with propagated peristalsis, followed by combined peristalsis and spasm, and pan-esophageal pressurization. Stronger EGJ tone with respect to the wall stiffness at the myotomy site was found to aid in increasing deformation at the myotomy site. In addition, we found that an esophagus with a shorter myotomy performed better at emptying the bolus than that with a longer myotomy. Shorter myotomies decrease the chance of BOM formation. Propagated peristalsis with EGJ outflow obstruction has the highest chance of BOM formation. We also found that abnormal residual EGJ tone may be a co-factor in the development of BOM, whereas remnant muscle fibers at myotomy site reduce the risk of BOM formation.NEW & NOTEWORTHY Blown-out myotomy (BOM) is a complication observed after myotomy, which is performed to treat achalasia. In silico simulations were performed to identify the factors leading to BOM formation. We found that a short myotomy that is not transmural and has some structural architecture intact reduces the risk of BOM formation. In addition, we found that high esophagogastric junction tone due to fundoplication is found to increase the risk of BOM formation.

A fully resolved multiphysics model of gastric peristalsis and bolus emptying in the upper gastrointestinal tract

Over the past few decades, in silico modeling of organ systems has significantly furthered our understanding of their physiology and biomechanical function. In spite of the relative importance of the digestive system in normal functioning of the human body, there is a scarcity of high-fidelity models for the upper gastrointestinal tract including the esophagus and the stomach. In this work, we present a detailed numerical model of the upper gastrointestinal tract that not only accounts for the fiber architecture of the muscle walls, but also the multiphasic components they help transport during normal digestive function. Construction details for 3D models of representative stomach geometry are presented along with a simple strategy for assigning circular and longitudinal muscle fiber orientations for each layer. We developed a fully resolved model of the stomach to simulate gastric peristalsis by systematically activating muscle fibers embedded in the stomach. Following this, for the first time, we simulate gravity-driven bolus emptying into the stomach due to density differences between ingested contents and fluid contents of the stomach. Finally, we present a case of retrograde flow of fluid from the stomach into the esophagus, resembling the phenomenon of acid reflux. This detailed computational model of the upper gastrointestinal tract provides a foundation for future models to investigate the biomechanics of acid reflux and probe various strategies for gastric bypass surgeries to address the growing problem of obesity.

Pump efficacy in a two-dimensional, fluid-structure interaction model of a chain of contracting lymphangions

The transport of lymph through the lymphatic vasculature is the mechanism for returning excess interstitial fluid to the circulatory system, and it is essential for fluid homeostasis. Collecting lymphatic vessels comprise a significant portion of the lymphatic vasculature and are divided by valves into contractile segments known as lymphangions. Despite its importance, lymphatic transport in collecting vessels is not well understood. We present a computational model to study lymph flow through chains of valved, contracting lymphangions. We used the Navier-Stokes equations to model the fluid flow and the immersed boundary method to handle the two-way, fluid-structure interaction in 2D, non-axisymmetric simulations. We used our model to evaluate the effects of chain length, contraction style, and adverse axial pressure difference (AAPD) on cycle-mean flow rates (CMFRs). In the model, longer lymphangion chains generally yield larger CMFRs, and they fail to generate positive CMFRs at higher AAPDs than shorter chains. Simultaneously contracting pumps generate the largest CMFRs at nearly every AAPD and for every chain length. Due to the contraction timing and valve dynamics, non-simultaneous pumps generate lower CMFRs than the simultaneous pumps; the discrepancy diminishes as the AAPD increases. Valve dynamics vary with the contraction style and exhibit hysteretic opening and closing behaviors. Our model provides insight into how contraction propagation affects flow rates and transport through a lymphangion chain.

Strategies to Refine Gastric Stimulation and Pacing Protocols: Experimental and Modeling Approaches

Gastric pacing and stimulation strategies were first proposed in the 1960s to treat motility disorders. However, there has been relatively limited clinical translation of these techniques. Experimental investigations have been critical in advancing our understanding of the control mechanisms that innervate gut function. In this review, we will discuss the use of pacing to modulate the rhythmic slow wave conduction patterns generated by interstitial cells of Cajal in the gastric musculature. In addition, the use of gastric high-frequency stimulation methods that target nerves in the stomach to either inhibit or enhance stomach function will be discussed. Pacing and stimulation protocols to modulate gastric activity, effective parameters and limitations in the existing studies are summarized. Mathematical models are useful to understand complex and dynamic systems. A review of existing mathematical models and techniques that aim to help refine pacing and stimulation protocols are provided. Finally, some future directions and challenges that should be investigated are discussed.

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

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 three-dimensional (3D) immersed boundary (IB) simulations of peristaltic pumping in tube walls made of hyperelastic material. The major dynamics observed in the 3D simulations were also displayed by our one-dimensional (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 work done 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.

Neuromechanical wave resonance in jellyfish swimming

For organisms to have robust locomotion, their neuromuscular organization must adapt to constantly changing environments. In jellyfish, swimming robustness emerges when marginal pacemakers fire action potentials throughout the bell's motor nerve net, which signals the musculature to contract. The speed of the muscle activation wave is dictated by the passage times of the action potentials. However, passive elastic material properties also influence the emergent kinematics, with time scales independent of neuromuscular organization. In this multimodal study, we examine the interplay between these two time scales during turning. A three-dimensional computational fluid-structure interaction model of a jellyfish was developed to determine the resulting emergent kinematics, using bidirectional muscular activation waves to actuate the bell rim. Activation wave speeds near the material wave speed yielded successful turns, with a 76-fold difference in turning rate between the best and worst performers. Hyperextension of the margin occurred only at activation wave speeds near the material wave speed, suggesting resonance. This hyperextension resulted in a 34-fold asymmetry in the circulation of the vortex ring between the inside and outside of the turn. Experimental recording of the activation speed confirmed that jellyfish actuate within this range, and flow visualization using particle image velocimetry validated the corresponding fluid dynamics of the numerical model. This suggests that neuromechanical wave resonance plays an important role in the robustness of an organism's locomotory system and presents an undiscovered constraint on the evolution of flexible organisms. Understanding these dynamics is essential for developing actuators in soft body robotics and bioengineered pumps.

Mechanics informed fluoroscopy of esophageal transport

Fluoroscopy is a radiographic procedure for evaluating esophageal disorders such as achalasia, dysphasia and gastroesophageal reflux disease. It performs dynamic imaging of the swallowing process and provides anatomical detail and a qualitative idea of how well swallowed fluid is transported through the esophagus. In this work, we present a method called mechanics informed fluoroscopy (FluoroMech) that derives patient-specific quantitative information about esophageal function. FluoroMech uses a convolutional neural network to perform segmentation of image sequences generated from the fluoroscopy, and the segmented images become input to a one-dimensional model that predicts the flow rate and pressure distribution in fluid transported through the esophagus. We have extended this model to identify and estimate potential physiomarkers such as esophageal wall stiffness and active relaxation ahead of the peristaltic wave in the esophageal musculature. FluoroMech requires minimal computational time and hence can potentially be applied clinically in the diagnosis of esophageal disorders.

A deep-learning-based unsupervised model on esophageal manometry using variational autoencoder

High-resolution manometry (HRM) is the primary method for diagnosing esophageal motility disorders and its interpretation and classification are based on variables (features) from data of each swallow. Modeling and learning the semantics directly from raw swallow data could not only help automate the feature extraction, but also alleviate the bias from pre-defined features. With more than 32-thousand raw swallow data, a generative model using the approach of variational auto-encoder (VAE) was developed, which, to our knowledge, is the first deep-learning-based unsupervised model on raw esophageal manometry data. The VAE model was reformulated to include different types of loss motivated by domain knowledge and tuned with different hyper-parameters. Training of the VAE model was found sensitive on the learning rate and hence the evidence lower bound objective (ELBO) was further scaled by the data dimension. Case studies showed that the dimensionality of latent space have a big impact on the learned semantics. In particular, cases with 4-dimensional latent variables were found to encode various physiologically meaningful contraction patterns, including strength, propagation pattern as well as sphincter relaxation. Cases with so-called hybrid L2 loss seemed to better capture the coherence of contraction/relaxation transition. Discriminating capability was further evaluated using simple linear discriminative analysis (LDA) on predicting swallow type and swallow pressurization, which yields clustering patterns consistent with clinical impression. The current work on modeling and understanding swallow-level data will guide the development of study-level models for automatic diagnosis as the next stage.

Four-dimensional impedance manometry derived from esophageal high-resolution impedance-manometry studies: a novel analysis paradigm

BACKGROUND

This study aimed to introduce a novel analysis paradigm, referred to as 4-dimensional (4D) manometry based on biophysical analysis; 4D manometry enables the visualization of luminal geometry of the esophagus and esophagogastric junction (EGJ) using high-resolution-impedance-manometry (HRIM) data.

METHODS

HRIM studies from two asymptomatic controls and one type-I achalasia patient were analyzed. Concomitant fluoroscopy images from one control subject were used to validate the calculated temporal-spatial luminal radius and time-history of intraluminal bolus volume and movement. EGJ analysis computed diameter threshold for emptying, emptying time, flow rate, and distensibility index (DI), which were compared with bolus flow time (BFT) analysis.

RESULTS

For normal control, calculated volumes for 5 ml swallows were 4.1 ml-6.7 ml; for 30 ml swallows 21.3 ml-21.8 ml. With type-I achalasia, >4 ml of intraesophageal bolus residual was present both pre- and post-swallow. The four phases of bolus transit were clearly illustrated on the time-history of bolus movement, correlating well with the fluoroscopic images. In the control subjects, the EGJ diameter threshold for emptying was 8 mm for 5 ml swallows and 10 mm for 30 ml swallows; emptying time was 1.2-2.2 s for 5 ml swallows (BFT was 0.3-3 s) and 3.25-3.75 s for 30 ml swallows; DI was 2.4-3.4 mm²/mmHg for 5 ml swallows and 4.2-4.6 mm²/mmHg for 30 ml swallows.

CONCLUSIONS

The 4D manometry system facilitates a comprehensive characterization of dynamic esophageal bolus transit with concurrent luminal morphology and pressure from conventional HRIM measurements. Calculations of flow rate and wall distensibility provide novel measures of EGJ functionality.

Stabilization approaches for the hyperelastic immersed boundary method for problems of large-deformation incompressible elasticity

The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses Lagrangian coordinates to describe the structural deformations, stresses, and resultant forces. Integral transforms with Dirac delta function kernels connect the Eulerian and Lagrangian frames. The fluid and the structure are both typically treated as incompressible materials. Upon discretization, however, the incompressibility of the structure is only maintained approximately. To obtain an immersed method for incompressible hyperelastic structures that is robust under large structural deformations, we introduce a volumetric energy in the solid region that stabilizes the formulation and improves the accuracy of the numerical scheme. This formulation augments the discrete Lagrange multiplier for the incompressibility constraint, thereby improving the original method's accuracy. This volumetric energy is incorporated by decomposing the strain energy into isochoric and dilatational components, as in standard solid mechanics formulations of nearly incompressible elasticity. We study the performance of the stabilized method using several quasi-static solid mechanics benchmarks, a dynamic fluid-structure interaction benchmark, and a detailed three-dimensional model of esophageal transport. The accuracy achieved by the stabilized immersed formulation is comparable to that of a stabilized finite element method for incompressible elasticity using similar numbers of structural degrees of freedom.

An Immersed Interface Method for Discrete Surfaces

Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary (IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction (FSI) in such systems, but a difficulty of the IB formulation of these problems is that the pressure and viscous stress are generally discontinuous at fluid-solid interfaces. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method (IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to numerical methods that rely on smooth representations of the interface geometry. This paper introduces an immersed interface formulation that uses only a C 0 representation of the immersed interface, such as those provided by standard nodal Lagrangian finite element methods. Verification examples for models with prescribed interface motion demonstrate that the method sharply resolves stress discontinuities along immersed boundaries while avoiding the need for analytic information about the interface geometry. Our results also demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global second-order accuracy. Specifically, we demonstrate second-order global convergence rates along with nearly second-order local convergence in the Eulerian velocity field, and between first- and second-order global convergence rates along with approximately first-order local convergence for the Eulerian pressure field. We also demonstrate approximately second-order local convergence in the interfacial displacement and velocity along with first-order local convergence in the fluid traction along the interface. As a demonstration of the method's ability to tackle more complex geometries, the present approach is also used to simulate flow in a patient-averaged anatomical model of the inferior vena cava, which is the large vein that carries deoxygenated blood from the lower extremities back to the heart. Comparisons of the general hemodynamics and wall shear stress obtained by the present IIM and a body-fitted discretization approach show that the present method yields results that are in good agreement with those obtained by the body-fitted approach.

Studies of abnormalities of the lower esophageal sphincter during esophageal emptying based on a fully coupled bolus-esophageal-gastric model

The aim of this work was to develop a fully coupled bolus-esophageal-gastric model based on the immersed boundary-finite element method to study the process of esophageal emptying across the esophagogastric junction (EGJ). The model included an esophageal segment, an ellipsoid-shaped stomach, a bolus, and a simple model of the passive and active sphincteric functions of the lower esophageal sphincter (LES). We conducted three sets of case studies: (1) the effect of a non-relaxing LES; (2) the influence of the tissue anisotropy in the form of asymmetrical right- and left-sided compliance of the LES segment; and (3) the influence of LES and gastric wall stiffness on bulge formation of the distal esophageal wall. We found that a non-relaxing LES caused sustained high wall stress along the LES segment and obstruction of bolus emptying. From the simulations of tissue anisotropy, we found that the weaker side (i.e., more compliant) of the LES segment sustained greater deformation, greater wall shear stress, and a greater high-pressure load during bolus transit. In the third set of studies, we found that a right-sided bulge in the esophageal wall tends to develop during esophageal emptying when LES stiffness was decreased or gastric wall stiffness was increased. Hence, the bulge may be partly due to the asymmetric configuration of the gastric wall with respect to the esophageal tube. Together, the observations from these simulations provide insight into the genesis of epiphrenic diverticula, a complication observed with esophageal motility disorders. Future work, with additional layers of complexity to the model, will delve into the mechanics of gastroesophageal reflux and the effects of hiatus hernia on EGJ function.

Hybrid finite difference/finite element immersed boundary method

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach.

Could the peristaltic transition zone be caused by non-uniform esophageal muscle fiber architecture? A simulation study

BACKGROUND

Based on a fully coupled computational model of esophageal transport, we analyzed how varied esophageal muscle fiber architecture and/or dual contraction waves (CWs) affect bolus transport. Specifically, we studied the luminal pressure profile in those cases to better understand possible origins of the peristaltic transition zone.

METHODS

Two groups of studies were conducted using a computational model. The first studied esophageal transport with circumferential-longitudinal fiber architecture, helical fiber architecture and various combinations of the two. In the second group, cases with dual CWs and varied muscle fiber architecture were simulated. Overall transport characteristics were examined and the space-time profiles of luminal pressure were plotted and compared.

KEY RESULTS

Helical muscle fiber architecture featured reduced circumferential wall stress, greater esophageal distensibility, and greater axial shortening. Non-uniform fiber architecture featured a peristaltic pressure trough between two high-pressure segments. The distal pressure segment showed greater amplitude than the proximal segment, consistent with experimental data. Dual CWs also featured a pressure trough between two high-pressure segments. However, the minimum pressure in the region of overlap was much lower, and the amplitudes of the two high-pressure segments were similar.

CONCLUSIONS & INFERENCES

The efficacy of esophageal transport is greatly affected by muscle fiber architecture. The peristaltic transition zone may be attributable to non-uniform architecture of muscle fibers along the length of the esophagus and/or dual CWs. The difference in amplitude between the proximal and distal pressure segments may be attributable to non-uniform muscle fiber architecture.