Simulation studies of circular muscle contraction, longitudinal muscle shortening, and their coordination in esophageal transport

A Review of In Vitro and In Silico Swallowing Simulators: Design and Applications

Swallowing is a primary and complex behaviour that transports food and drink from the oral cavity, through the pharynx and oesophagus, into the stomach at an appropriate rate and speed. To understand this sophisticated behaviour, a tremendous amount of research has been carried out by utilising the in vivo approach, which is often challenging to perform, poses a risk to the subjects if interventions are undertaken and are seldom able to control for confounding factors. In contrast, in silico (computational) and in vitro (instrumental) methods offer an alternate insight into the process of the human swallowing system. However, the appropriateness of the design and application of these methods have not been formally evaluated. The purpose of this review is to investigate and evaluate the state of the art of in vitro and in silico swallowing simulators, focusing on the evaluation of their mechanical or computational designs in comparison to the corresponding swallowing mechanisms during various phases of swallowing (oral phase, pharyngeal phase and esophageal phase). Additionally, the potential of the simulators is also discussed in various areas of applications, including the study of swallowing impairments, swallowing medications, food process design and dysphagia management. We also address current limitations and recommendations for the future development of existing simulators.

Purinergic inhibitory regulation of esophageal smooth muscle is mediated by P2Y receptors and ATP-dependent potassium channels in rats

Purines such as ATP are regulatory transmitters in motility of the gastrointestinal tract. The aims of this study were to propose functional roles of purinergic regulation of esophageal motility. An isolated segment of the rat esophagus was placed in an organ bath, and mechanical responses were recorded using a force transducer. Exogenous application of ATP (10-100 μM) evoked relaxation of the esophageal smooth muscle in a longitudinal direction under the condition of carbachol (1 μM) -induced precontraction. Pretreatment with a non-selective P2 receptor antagonist, suramin (500 μM), and a P2Y receptor antagonist, cibacron blue F3GA (200 μM), inhibited the ATP (100 μM) -induced relaxation, but a P2X receptor antagonist, pyridoxal phosphate-6-azophenyl-2,4-disulfonic acid (50 μM), did not affect it. A blocker of ATP-dependent potassium channels (KATP channels), glibenclamide (200 μM), inhibited the ATP-induced relaxation and application of an opener of KATP channels, nicorandil (50 μM), produced relaxation. The findings suggest that ATP is involved in inhibitory regulation of the longitudinal smooth muscle in the muscularis mucosae of the rat esophagus via activation of P2Y receptors and then opening of KATP channels.

A mechanics-based perspective on the function of the esophagogastric junction during functional luminal imaging probe manometry

The esophagogastric junction (EGJ) is located at the distal end of the esophagus and acts as a valve allowing swallowed food to enter the stomach and preventing acid reflux. Irregular weakening or stiffening of the EGJ muscles results in changes to its opening and closing patterns which can progress into esophageal disorders. Therefore, understanding the physics of the opening and closing cycle of the EGJ can provide mechanistic insights into its function and can help identify the underlying conditions that cause its dysfunction. Using clinical functional lumen imaging probe (FLIP) data, we plotted the pressure-cross-sectional area loops at the EGJ location and distinguished two major loop types-a pressure dominant loop and a tone dominant loop. In this study, we aimed to identify the key characteristics that define each loop type and determine what causes the inversion from one loop to another. To do so, the clinical observations are reproduced using 1D simulations of flow inside a FLIP device located in the esophagus, and the work done by the EGJ wall over time is calculated. This work is decomposed into active and passive components, which reveal the competing mechanisms that dictate the loop type. These mechanisms are esophageal stiffness, fluid viscosity, and the EGJ relaxation pattern.

Peristaltic regimes in esophageal transport

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.

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.

EFFECTS OF STATIONARY CONTRACTION OF THE SMALL INTESTINE ON DIGESTION

In this paper, effects of stationary contraction on mixing and transport of a non-Newtonian fluid in the small intestine are analyzed theoretically. A semi-analytical method is developed to solve the governing equations of fluids flow in the intestine using lubrication theory. Results indicate that the stationary contraction helps in conferring two functions – (1) shearing of the contents, and (2) bidirectional transport over a short distance. The flow resulting from contraction is symmetric and occurs in both the directions; however, they do not lead to a net flow rate in one direction. The amount of shearing developed during such flows is reflective of their mixing ability. The effort of such peristalsis is largely determined by the flow behavior index; where energy requirements of developing similar shearing forces are higher for dilatants and lower for pseudoplastics. Flow is sensitive to frequency of contraction, luminal occlusion and wavelength of the contraction.

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.

Immersed Methods for Fluid-Structure Interaction

Fluid-structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid-structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid-structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

Migration resistance of esophageal stents: The role of stent design

OBJECTIVE

Stenting is one of the major treatments for malignant esophageal cancer. However, stent migration compromises clinical outcomes. A flared end design of the stent diminishes its migration. The goal of this work is to quantitatively characterize stent migration to develop new strategies for better clinical outcomes.

METHODS

An esophageal stent with flared ends and a straight counterpart were virtually deployed in an esophagus with asymmetric stricture using the finite element method. The resulted esophagus shape, wall stress, and migration resistance force of the stent were quantified and compared.

RESULTS

The lumen gain for both the flared stent and the straight one exhibited no significant difference. The flared stent induced a significantly larger contact force and thus a larger stress onto the esophagus wall. In addition, more migration resistance force was required to pull the flared stent through the esophagus. This force was inversely related to the occurrence rate of stent migration. A doubled strut diameter also increased the migration resistance force by approximately 56%. An increased friction coefficient from 0.1 to 0.3 also boosted the migration resistance force by approximately 39%.

SUMMARY

The mechanical advantage of the flared stent was unveiled by the significantly increased contact force, which provided the anchoring effect to resist stent migration. Both the strut diameter and friction coefficient positively correlated with the migration resistance force, and thus the occurrence of stent migration.

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.

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

In this work, we extend our previous esophageal transport model using an immersed boundary (IB) method with discrete fiber-based structural model, to one using a continuum mechanics-based model that is approximated based on finite elements (IB-FE). To deal with the leakage of flow when the Lagrangian mesh becomes coarser than the fluid mesh, we employ adaptive interaction quadrature points to deal with Lagrangian-Eulerian interaction equations based on a previous work (Griffith and Luo [1]). In particular, we introduce a new anisotropic adaptive interaction quadrature rule. The new rule permits us to vary the interaction quadrature points not only at each time-step and element but also at different orientations per element. This helps to avoid the leakage issue without sacrificing the computational efficiency and accuracy in dealing with the interaction equations. For the material model, we extend our previous fiber-based model to a continuum-based model. We present formulations for general fiber-reinforced material models in the IB-FE framework. The new material model can handle non-linear elasticity and fiber-matrix interactions, and thus permits us to consider more realistic material behavior of biological tissues. To validate our method, we first study a case in which a three-dimensional short tube is dilated. Results on the pressure-displacement relationship and the stress distribution matches very well with those obtained from the implicit FE method. We remark that in our IB-FE case, the three-dimensional tube undergoes a very large deformation and the Lagrangian mesh-size becomes about 6 times of Eulerian mesh-size in the circumferential orientation. To validate the performance of the method in handling fiber-matrix material models, we perform a second study on dilating a long fiber-reinforced tube. Errors are small when we compare numerical solutions with analytical solutions. The technique is then applied to the problem of esophageal transport. We use two fiber-reinforced models for the esophageal tissue: a bi-linear model and an exponential model. We present three cases on esophageal transport that differ in the material model and the muscle fiber architecture. The overall transport features are consistent with those observed from the previous model. We remark that the continuum-based model can handle more realistic and complicated material behavior. This is demonstrated in our third case where a spatially varying fiber architecture is included based on experimental study. We find that this unique muscle fiber architecture could generate a so-called pressure transition zone, which is a luminal pressure pattern that is of clinical interest. This suggests an important role of muscle fiber architecture in esophageal transport.

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.

Simulation studies of the role of esophageal mucosa in bolus transport

Based on a fully coupled computational model for esophageal transport, we analyzed the role of the mucosa (including the submucosa) in esophageal bolus transport and how bolus transport is affected by mucosal stiffness. Two groups of studies were conducted using a computational model. In the first group, a base case that represents normal esophageal transport and two hypothetical cases were simulated: (1) esophageal mucosa replaced by muscle and (2) esophagus without mucosa. For the base case, the geometric configuration of the esophageal wall was examined and the mechanical role of mucosa was analyzed. For the hypothetical cases, the pressure field and transport features were examined. In the second group of studies, cases with mucosa of varying stiffness were simulated. Overall transport characteristics were examined, and both pressure and geometry were analyzed. Results show that a compliant mucosa helped accommodate the incoming bolus and lubricate the moving bolus. Bolus transport was marginally achieved without mucosa or with mucosa replaced by muscle. A stiff mucosa greatly impaired bolus transport due to the lowered esophageal distensibility and increased luminal pressure. We conclude that mucosa is essential for normal esophageal transport function. Mechanically stiffened mucosa reduces the distensibility of the esophagus by obstructing luminal opening and bolus transport. Mucosal stiffening may be relevant in diseases characterized by reduced esophageal distensibility, elevated intrabolus pressure, and/or hypertensive muscle contraction such as eosinophilic esophagitis and jackhammer esophagus.

The virtual esophagus: investigating esophageal functions in silico

Esophageal and gastroesophageal junction (GEJ) diseases are highly prevalent worldwide and are a significant socioeconomic burden. Recently, applications of multiscale mathematical models of the upper gastrointestinal tract have gained attention. These in silico investigations can contribute to the development of a virtual esophagus modeling framework as part of the larger GIome and Physiome initiatives. There are also other modeling investigations that have potential screening and treatment applications. These models incorporate detailed anatomical models of the esophagus and GEJ, tissue biomechanical properties and bolus transport, sensory properties, and, potentially, bioelectrical models of the neural and myogenic pathways of esophageal and GEJ functions. A next step is to improve the integration between the different components of the virtual esophagus, encoding standards, and simulation environments to perform more realistic simulations of normal and pathophysiological functions. Ultimately, the models will be validated and will provide predictive evaluations of the effects of novel endoscopic, surgical, and pharmaceutical treatment options and will facilitate the clinical translation of these treatments.

The Esophagiome: concept, status, and future perspectives

The term "Esophagiome" is meant to imply a holistic, multiscale treatment of esophageal function from cellular and muscle physiology to the mechanical responses that transport and mix fluid contents. The development and application of multiscale mathematical models of esophageal function are central to the Esophagiome concept. These model elements underlie the development of a "virtual esophagus" modeling framework to characterize and analyze function and disease by quantitatively contrasting normal and pathophysiological function. Functional models incorporate anatomical details with sensory-motor properties and functional responses, especially related to biomechanical functions, such as bolus transport and gastrointestinal fluid mixing. This brief review provides insight into Esophagiome research. Future advanced models can provide predictive evaluations of the therapeutic consequences of surgical and endoscopic treatments and will aim to facilitate clinical diagnostics and treatment.

Regulation and dysregulation of esophageal peristalsis by the integrated function of circular and longitudinal muscle layers in health and disease

Muscularis propria throughout the entire gastrointestinal tract including the esophagus is comprised of circular and longitudinal muscle layers. Based on the studies conducted in the colon and the small intestine, for more than a century, it has been debated whether the two muscle layers contract synchronously or reciprocally during the ascending contraction and descending relaxation of the peristaltic reflex. Recent studies in the esophagus and colon prove that the two muscle layers indeed contract and relax together in almost perfect synchrony during ascending contraction and descending relaxation of the peristaltic reflex, respectively. Studies in patients with various types of esophageal motor disorders reveal temporal disassociation between the circular and longitudinal muscle layers. We suggest that the discoordination between the two muscle layers plays a role in the genesis of esophageal symptoms, i.e., dysphagia and esophageal pain. Certain pathologies may selectively target one and not the other muscle layer, e.g., in eosinophilic esophagitis there is a selective dysfunction of the longitudinal muscle layer. In achalasia esophagus, swallows are accompanied by the strong contraction of the longitudinal muscle without circular muscle contraction. The possibility that the discoordination between two muscle layers plays a role in the genesis of esophageal symptoms, i.e., dysphagia and esophageal pain are discussed. The purpose of this review is to summarize the regulation and dysregulation of peristalsis by the coordinated and discoordinated function of circular and longitudinal muscle layers in health and diseased states.

Diabetes-induced mechanophysiological changes in the esophagus

Esophageal disorders are common in diabetes mellitus (DM) patients. DM induces mechanostructural remodeling in the esophagus of humans and animal models. The remodeling is related to esophageal sensorimotor abnormalities and to symptoms frequently encountered by DM patients. For example, gastroesophageal reflux disease (GERD) is a common disorder associated with DM. This review addresses diabetic remodeling of esophageal properties and function in light of the Esophagiome, a scientifically based modeling effort to describe the physiological dynamics of the normal, intact esophagus built upon interdisciplinary approaches with applications for esophageal disease. Unraveling the structural, biomechanical, and sensory remodeling of the esophagus in DM must be based on a multidisciplinary approach that can bridge the knowledge from a variety of scientific disciplines. The first focus of this review is DM-induced morphodynamic and biomechanical remodeling in the esophagus. Second, we review the sensorimotor dysfunction in DM and how it relates to esophageal remodeling. Finally, we discuss the clinical consequences of DM-induced esophageal remodeling, especially in relation to GERD. The ultimate aim is to increase the understanding of DM-induced remodeling of esophageal structure and sensorimotor function in order to assist clinicians to better understand the esophageal disorders induced by DM and to develop better treatments for those patients.