Structurally-motivated characterization of the passive pseudo-elastic response of esophagus and its layers

Estimation of the biaxial tensile behavior of ovine esophageal tissue using artificial neural networks

Diseases of the esophagus affect its function and often lead to replacement of long sections of the organ. Current healing methods involve the use of bioscaffolds processed from other animal models. Although the properties of these animal models are not exactly the same as those of the human esophagus, they nevertheless present a reasonable means of assessing the biomechanical properties of the esophageal tissue. Besides, sheep bear many similarities physiologically to humans and they also suffer from same diseases as humans. The morphology of their esophagus is also comparable to that of humans. Thus, in the study, an ovine esophagus was studied. Studies on the planar biaxial tests of the gross esophageal anatomy are limited. The composite nature of the gross anatomy of the esophagus makes the application of structure-based models such as Holzapfel-type models very difficult. In current studies the tissue is therefore often separated into specific layers with substantial collagen content. The effects of adipose tissue and other non-collagenous tissue often make the mechanical behavior of the esophagus widely diverse and unpredictable using deterministic structure-based models. Thus, it may be very difficult to predict its mechanical behavior. In the study, an NARX neural network was used to predict the stress-strain response of the gross anatomy of the ovine esophagus. The results show that the NARX model was able to achieve a correlation above 99.9% within a fitting error margin of 16%. Therefore, the use of artificial neural networks may provide a more accurate way of predicting the biaxial stress-strain response of the esophageal tissue, and lead to further improvements in the design and development of synthetic replacement materials for esophageal tissue.

Mechanical experimentation of the gastrointestinal tract: a systematic review

The gastrointestinal (GI) organs of the human body are responsible for transporting and extracting nutrients from food and drink, as well as excreting solid waste. Biomechanical experimentation of the GI organs provides insight into the mechanisms involved in their normal physiological functions, as well as understanding of how diseases can cause disruption to these. Additionally, experimental findings form the basis of all finite element (FE) modelling of these organs, which have a wide array of applications within medicine and engineering. This systematic review summarises the experimental studies that are currently in the literature (n = 247) and outlines the areas in which experimentation is lacking, highlighting what is still required in order to more fully understand the mechanical behaviour of the GI organs. These include (i) more human data, allowing for more accurate modelling for applications within medicine, (ii) an increase in time-dependent studies, and (iii) more sophisticated in vivo testing methods which allow for both the layer- and direction-dependent characterisation of the GI organs. The findings of this review can also be used to identify experimental data for the readers' own constitutive or FE modelling as the experimental studies have been grouped in terms of organ (oesophagus, stomach, small intestine, large intestine or rectum), test condition (ex vivo or in vivo), number of directions studied (isotropic or anisotropic), species family (human, porcine, feline etc.), tissue condition (intact wall or layer-dependent) and the type of test performed (biaxial tension, inflation-extension, distension (pressure-diameter), etc.). Furthermore, the studies that investigated the time-dependent (viscoelastic) behaviour of the tissues have been presented.

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.

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.

Experimental investigations of the human oesophagus: anisotropic properties of the embalmed mucosa-submucosa layer under large deformation

Mechanical characterisation of the layer-specific, viscoelastic properties of the human oesophagus is crucial in furthering the development of devices emerging in the field, such as robotic endoscopic biopsy devices, as well as in enhancing the realism, and therefore effectiveness, of surgical simulations. In this study, the viscoelastic and stress-softening behaviour of the passive human oesophagus was investigated through ex vivo cyclic mechanical tests. Due to restrictions placed on the laboratory as a result of COVID-19, only oesophagi from cadavers fixed in formalin were allowed for testing. Three oesophagi in total were separated into their two main layers and the mucosa-submucosa layer was investigated. A series of uniaxial tensile tests were conducted in the form of increasing stretch level cyclic tests at two different strain rates: 1% s[Formula: see text] and 10% s[Formula: see text]. Rectangular samples in both the longitudinal and circumferential directions were tested to observe any anisotropy. Histological analysis was also performed through a variety of staining methods. Overall, the longitudinal direction was found to be much stiffer than the circumferential direction. Stress-softening was observed in both directions, as well as permanent set and hysteresis. Strain rate-dependent behaviour was also apparent in the two directions, with an increase in strain rate resulting in an increase in stiffness. This strain rate dependency was more pronounced in the longitudinal direction than the circumferential direction. Finally, the results were discussed in regard to the histological content of the layer, and the behaviour was modelled and validated using a visco-hyperelastic matrix-fibre model.

Biomechanical constitutive modeling of the gastrointestinal tissues: a systematic review

The gastrointestinal (GI) tract is a continuous channel through the body that consists of the esophagus, the stomach, the small intestine, the large intestine, and the rectum. Its primary functions are to move the intake of food for digestion before storing and ultimately expulsion of feces. The mechanical behavior of GI tissues thus plays a crucial role for GI function in health and disease. The mechanical properties are characterized by a biomechanical constitutive model, which is a mathematical representation of the relation between load and deformation in a tissue. Hence, validated biomechanical constitutive models are essential to characterize and simulate the mechanical behavior of the GI tract. Here, a systematic review of these constitutive models is provided. This review is limited to studies where a model of the strain energy function is proposed to characterize the stress-strain relation of a GI tissue. Several needs are identified for more advanced modeling including: 1) Microstructural models that provide actual structure-function relations; 2) Validation of coupled electro-mechanical models accounting for active muscle contractions; 3) Human data to develop and validate models. The findings from this review provide guidelines for using existing constitutive models as well as perspective and directions for future studies.

Experimental investigations of the human oesophagus: anisotropic properties of the embalmed muscular layer under large deformation

The oesophagus is a primarily mechanical organ whose material characterisation would aid in the investigation of its pathophysiology, help in the field of tissue engineering, and improve surgical simulations and the design of medical devices. However, the layer-dependent, anisotropic properties of the organ have not been investigated using human tissue, particularly in regard to its viscoelastic and stress-softening behaviour. Restrictions caused by the COVID-19 pandemic meant that fresh human tissue was not available for dissection. Therefore, in this study, the layer-specific material properties of the human oesophagus were investigated through ex vivo experimentation of the embalmed muscularis propria layer. For this, a series of uniaxial tension cyclic tests with increasing stretch levels were conducted at two different strain rates. The muscular layers from three different cadaveric specimens were tested in both the longitudinal and circumferential directions. The results displayed highly nonlinear and anisotropic behaviour, with both time- and history-dependent stress-softening. The longitudinal direction was found to be stiffer than the circumferential direction at both strain rates. Strain rate-dependent behaviour was apparent, with an increase in strain rate resulting in an increase in stiffness in both directions. Histological analysis was carried out via various staining methods; the results of which were discussed with regard to the experimentally observed stress-stretch response. Finally, the behaviour of the muscularis propria was simulated using a matrix-fibre model able to capture the various mechanical phenomena exhibited, the fibre orientation of which was driven by the histological findings of the study.

3D biomechanical properties of the layered esophagus: Fung-type SEF and new constitutive model

BACKGROUND AND PURPOSE

Most current studies on the passive biomechanical properties of esophageal tissues directly use the exponential strain energy function (SEF) to fit and calculate the constants of the constitutive equation. In the context of the extensive application of exponential SEF, in-depth research on the exponential SEF is still lacking. The purpose of this study is to combine the exponential function with the polynomial SEF to obtain the most suitable constitutive equation to describe the three-dimensional passive behavior of the esophagus.

METHODS

fresh pig esophagus with a length of 13 cm in the middle position was selected as esophageal samples. The esophageal sample was separated into muscular layer and mucosal layer with surgical scissors. Stretch-inflation mechanical tests of the intact esophagus, esophageal muscular, and esophageal mucosa were carried out on a triaxial test machine. The external radius, axial force, and internal pressure were recorded simultaneously. The seven-parameter Fung-type SEF and several new SEFs combining polynomials and exponents were used to fit the experimental data curves.

RESULTS

The stretch-inflation test data and the morphometric parameters at the zero-stress state of the layered esophagus were obtained. The new SEF with polynomial and exponential combination is more suitable to describe describing the three-dimensional passive biomechanical properties of esophageal tissue. Among them, New-Fung13 SEF is more suitable for describing the passive biomechanical properties of intact esophageal tissue, Sokolis-Fung13 SEF is more suitable for the esophageal muscle layer, and New-Fung10 SEF is more suitable for the esophageal mucosa. The constitutive parameters of the optimal constitutive model for each layer of the esophagus were obtained.

Variation of Passive Biomechanical Properties of the Small Intestine along Its Length: Microstructure-Based Characterization

Multiaxial testing of the small intestinal wall is critical for understanding its biomechanical properties and defining material models, but limited data and material models are available. The aim of the present study was to develop a microstructure-based material model for the small intestine and test whether there was a significant variation in the passive biomechanical properties along the length of the organ. Rat tissue was cut into eight segments that underwent inflation/extension testing, and their nonlinearly hyper-elastic and anisotropic response was characterized by a fiber-reinforced model. Extensive parametric analysis showed a non-significant contribution to the model of the isotropic matrix and circumferential-fiber family, leading also to severe over-parameterization. Such issues were not apparent with the reduced neo-Hookean and (axial and diagonal)-fiber family model, that provided equally accurate fitting results. Absence from the model of either the axial or diagonal-fiber families led to ill representations of the force- and pressure-diameter data, respectively. The primary direction of anisotropy, designated by the estimated orientation angle of diagonal-fiber families, was about 35° to the axial direction, corroborating prior microscopic observations of submucosal collagen-fiber orientation. The estimated model parameters varied across and within the duodenum, jejunum, and ileum, corroborating histologically assessed segmental differences in layer thicknesses.

The Macro- and Micro-Mechanics of the Colon and Rectum II: Theoretical and Computational Methods

Abnormal colorectal biomechanics and mechanotransduction associate with an array of gastrointestinal diseases, including inflammatory bowel disease, irritable bowel syndrome, diverticula disease, anorectal disorders, ileus, and chronic constipation. Visceral pain, principally evoked from mechanical distension, has a unique biomechanical component that plays a critical role in mechanotransduction, the process of encoding mechanical stimuli to the colorectum by sensory afferents. To fully understand the underlying mechanisms of visceral mechanical neural encoding demands focused attention on the macro- and micro-mechanics of colon tissue. Motivated by biomechanical experiments on the colon and rectum, increasing efforts focus on developing constitutive frameworks to interpret and predict the anisotropic and nonlinear biomechanical behaviors of the multilayered colorectum. We will review the current literature on computational modeling of the colon and rectum as well as the mechanical neural encoding by stretch sensitive afferent endings, and then highlight our recent advances in these areas. Current models provide insight into organ- and tissue-level biomechanics as well as the stretch-sensitive afferent endings of colorectal tissues yet an important challenge in modeling theory remains. The research community has not connected the biomechanical models to those of mechanosensitive nerve endings to create a cohesive multiscale framework for predicting mechanotransduction from organ-level biomechanics.

Alterations with age in the biomechanical behavior of human ureteral wall: Microstructure-based modeling

The human ureters have not been thoroughly explored from the biomechanics perspective, despite the wealth of such data for other soft-tissue types. This study was motivated by the need to use relevant biomechanical data from human ureters and microstructure-based material formulations for simulations of ureteral peristalsis and stenting. Our starting choice was the four-fiber family model that has proven its validity as a descriptor of the multiaxial response of cardiovascular tissues. The degree of model complexity, required for rigorous fits to passive quasi-static pressure-diameter-force data at several axial stretches, was systematically investigated. Ureteral segments from sixteen human autopsy subjects were evaluated. A diagonal and axial family model allowed equally-good fits as the full model for all age groups and ureteral regions; considerably better than those allowed by the phenomenological Fung-type model whose root-mean-square error of fitting was three-fold greater. This reduced model mimicked the structure seen in histologic sections, namely plentiful diagonal collagen fibers in the lamina propria and axial fibers in the muscle and adventitia. The paucity of elastin fibers and mixed muscle orientation justified the use of isotropic muscle-dominated matrix with small neo-Hookean parameter values. The significantly thicker lamina propria in the lower than the upper ureter of young subjects (312 ± 27 vs. 232 ± 26 μm; mean ± standard error) corroborated the significant regional differences in diagonal-fiber family parameter values. The significant muscle thickening with age (upper ureter: 373 ± 48 vs. 527 ± 67 μm; middle: 388 ± 29 vs. 575 ± 69 μm; lower: 440 ± 21 vs. 602 ± 71 μm) corroborated the significant age-related increase in axial-fiber family parameter values.

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.

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.

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.

Effect of ovariectomy and Sideritis euboea extract administration on large artery mechanics, morphology, and structure in middle-aged rats

BACKGROUND

Arterial function is regulated by estrogen, but no consistent pattern of arterial mechanical remodeling in response to depleted estrogen levels is available.

OBJECTIVE

To examine long-term effects of ovariectomy (OVX) on the mechanical properties, morphology, and histological structure of the carotid artery in middle-aged rats and a potentially protective effect of Sideritis euboea extract (SID), commonly consumed as "mountain tea".

METHODS

10-month-old female Wistar rats were allocated into control (sham-operated), OVX, OVX+SID, and OVX+MALT (maltodextrin; excipient used for dilution of SID) groups. They were sacrificed after 6 months and their carotid arteries were submitted to inflation/extension tests and to dimensional and histological evaluation.

RESULTS

Remodeling in OVX rats was characterized by a decreased in situ axial extension ratio, along with increased opening angle, thickness, and area of the vessel wall and of its medial layer, but unchanged lumen diameter. Compositional changes involved increased elastin/collagen densities. Characterization by the "four-fiber" microstructure-motivated model revealed similar in situ biaxial response of carotid arteries in OVX and control rats.

CONCLUSIONS

Carotid artery remodeling in OVX rats was largely consistent with hypertensive remodeling, despite the minor arterial pressure changes found, and was not altered by administration of SID, despite previous evidence of its osteo-protective effect.

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.

A fully resolved active musculo-mechanical model for esophageal transport

Esophageal transport is a physiological process that mechanically transports an ingested food bolus from the pharynx to the stomach via the esophagus, a multilayered muscular tube. This process involves interactions between the bolus, the esophagus, and the neurally coordinated activation of the esophageal muscles. In this work, we use an immersed boundary (IB) approach to simulate peristaltic transport in the esophagus. The bolus is treated as a viscous fluid that is actively transported by the muscular esophagus, and the esophagus is modeled as an actively contracting, fiber-reinforced tube. Before considering the full model of the esophagus, however, we first consider a standard benchmark problem of flow past a cylinder. Next a simplified version of our model is verified by comparison to an analytic solution to the tube dilation problem. Finally, three different complex models of the multi-layered esophagus, which differ in their activation patterns and the layouts of the mucosal layers, are extensively tested. To our knowledge, these simulations are the first of their kind to incorporate the bolus, the multi-layered esophagus tube, and muscle activation into an integrated model. Consistent with experimental observations, our simulations capture the pressure peak generated by the muscle activation pulse that travels along the bolus tail. These fully resolved simulations provide new insights into roles of the mucosal layers during bolus transport. In addition, the information on pressure and the kinematics of the esophageal wall resulting from the coordination of muscle activation is provided, which may help relate clinical data from manometry and ultrasound images to the underlying esophageal motor function.