Strain-energy function and three-dimensional stress distribution in esophageal biomechanics

Characterization of the layer, direction and time-dependent mechanical behaviour of the human oesophagus and the effects of formalin preservation

The mechanical characterization of the oesophagus is essential for applications such as medical device design, surgical simulations and tissue engineering, as well as for investigating the organ's pathophysiology. However, the material response of the oesophagus has not been established ex vivo in regard to the more complex aspects of its mechanical behaviour using fresh, human tissue: as of yet, in the literature, only the hyperelastic response of the intact wall has been studied. Therefore, in this study, the layer-dependent, anisotropic, visco-hyperelastic behaviour of the human oesophagus was investigated through various mechanical tests. For this, cyclic tests, with increasing stretch levels, were conducted on the layers of the human oesophagus in the longitudinal and circumferential directions and at two different strain rates. Additionally, stress-relaxation tests on the oesophageal layers were carried out in both directions. Overall, the results show discrete properties in each layer and direction, highlighting the importance of treating the oesophagus as a multi-layered composite material with direction-dependent behaviour. Previously, the authors conducted layer-dependent cyclic experimentation on formalin-embalmed human oesophagi. A comparison between the fresh and embalmed tissue response was carried out and revealed surprising similarities in terms of anisotropy, strain-rate dependency, stress-softening and hysteresis, with the main difference between the two preservation states being the magnitude of these properties. As formalin fixation is known to notably affect the formation of cross-links between the collagen of biological materials, the differences may reveal the influence of cross-links on the mechanical behaviour of soft tissues.

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.

Viscoelastic Properties of Acellular Matrices of Porcine Esophageal Mucosa and Comparison with Acellular Matrices of Porcine Small Intestine Submucosa and Bovine Pericardium

The aim of this study was to compare the viscoelastic properties of a decellularized mesh from the porcine esophagus, prepared by our group, with two commercial acellular tissues derived from porcine small intestine submucosa and bovine pericardium for use in medical devices. The tissues' viscoelastic properties were characterized by creep tests in tension, applying the load in the direction of the fibers or the transverse direction, and also by dynamic-shear mechanical tests between parallel plates or in tension at frequencies between 0.1 and 35 Hz. All the tests were performed in triplicate at a constant temperature of 37 °C immersed in distilled water. The tissues' surface and cross-sectional microstructure were observed by scanning electron microscopy (SEM) to characterize the orientation of the fibers. The matrices of the porcine esophagus present an elastic modulus in the order of 60 MPa when loaded in the longitudinal direction while those of the porcine intestine submucosa and bovine pericardium have an elastic modulus below 5 MPa. Nevertheless, the shear modulus of bovine pericardium nearly triplicates that of the esophageal matrix. The viscoelasticity of decellularized esophageal mucosa is characterized by a fast change in the creep compliance with time. The slope of the creep curve in the double logarithmic plot is twice that of the control samples. These results are consistent with the microstructure observed under electron microscopy regarding the orientation of the fibers that make up the matrices.

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.

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.

The Role of Biaxial Loading on Smooth Muscle Contractility in the Nulliparous Murine Cervix

Throughout the estrus cycle, the extracellular matrix (ECM) and cervical smooth muscle cells (cSMC) coordinate to accomplish normal physiologic function in the non-pregnant cervix. While previous uniaxial experiments provide fundamental knowledge about cervical contractility and biomechanics, the specimen preparation is disruptive to native organ geometry and does not permit simultaneous assessment of circumferential and axial properties. Thus, a need remains to investigate cervical contractility and passive biomechanics within physiologic multiaxial loading. Biaxial inflation-extension experiments overcome these limitations by preserving geometry, ECM-cell interactions, and multiaxially loading the cervix. Utilizing in vivo pressure measurements and inflation-extension testing, this study presented methodology and examined maximum biaxial contractility and biomechanics in the nulliparous murine cervix. The study showed that increased pressure resulted in decreased contractile potential in the circumferential direction, however, axial contractility remained unaffected. Additionally, total change in axial stress ([Formula: see text]) increased significantly (p < 0.05) compared to circumferential stress ([Formula: see text]) with maximum contraction. However, passive stiffness was significantly greater (p < 0.01) in the circumferential direction. Overall, axial cSMC may have a critical function in maintaining cervical homeostasis during normal function. Potentially, a loss of axial contractility in the cervix during pregnancy may result in maladaptive remodeling such as cervical insufficiency.

Instability of Incompatible Bilayered Soft Tissues and the Role of Interface Conditions

Mechanical stability analysis is instructive in explaining biological processes like morphogenesis, organogenesis, and pathogenesis of soft tissues. Consideration of the layered, residually stressed structure of tissues, requires accounting for the joint effects of interface conditions and layer incompatibility. This paper is concerned with the influence of imposed rate (incremental) interface conditions (RICs) on critical loads in soft tissues, within the context of linear bifurcation analysis. Aiming at simplicity, we analyze a model of bilayered isotropic hyperelastic (neo-Hookean) spherical shells with residual stresses generated by “shrink-fitting” two perfectly bonded layers with radial interfacial incompatibility. This setting allows a comparison between available, seemingly equivalent, interface conditions commonly used in the literature of layered media stability. We analytically determine the circumstances under which the interface conditions are equivalent or not, and numerically demonstrate significant differences between interface conditions with increasing level of layer incompatibility. Differences of more than tenfold in buckling and 30% in inflation instability critical loads are recorded using the different RICs. Contrasting instability characteristics are also revealed using the different RICs in the presence of incompatibility: inflation instability can occur before pressure maximum, and spontaneous instability may be excluded for thin shells. These findings are relevant to the growing body of stability studies of layered and residually stressed tissues. The impact of interface conditions on critical thresholds is significant in studies that use concepts of instability to draw conclusions about the normal development and the pathologies of tissues like arteries, esophagus, airways, and the brain.

Esophageal Biomechanics Revisited: A Tale of Tenacity, Anastomoses, and Suture Bite Lengths in Swine

BACKGROUND

Anastomotic tension has repeatedly been associated with anastomotic leakages after esophagectomy for cancer or esophageal atresia repair. We therefore aimed to determine which anastomotic technique would come as close as possible to the native esophagus in sustaining traction forces. Constant traction for several minutes at esophageal remnants and large suture bites are also considered relevant in long-gap esophageal atresia repair.

METHODS

Porcine esophagi were subjected to linear traction using a motorized horizontal test stand. We compared breaking strengths of native esophagi to simple continuous, simple interrupted, stapled, and barbed suture anastomoses. We also investigated the effects of suture bite length and phases of constant traction on breaking strengths and powered all experiments to at least 80% using exploratory investigations (n = 5 per group).

RESULTS

Continuous suture anastomoses had a breaking strength comparable to native esophagi (Δ = -5.25 Newton, 95% confidence interval: -10.69 to 0.19 Newton, p = 0.058) and outperformed all other investigated anastomoses (Δ ≥14.01 Newton, p ≤ 0.02). Breaking strength correlated with suture bite length (R = 0.905) and predicted breaking strength for the simple stitch (adjusted R² = 0.812, p < 0.0001), but not for anastomoses. Phases of incrementally increasing constant traction resulted in higher breaking strengths (Δ = 13.36 Newton, 95% confidence interval: 9.93 to 16.79 Newton, p < 0.0001) and higher length gain (Δ = 1.06 cm, 95% confidence interval: 0.65 to 1.48 cm, p < 0.0001) compared with controls.

CONCLUSIONS

Only simple continuous anastomoses achieved the linear breaking strength of native tissue. Our study provides important insights in tolerance to traction forces, but its results have to be corroborated in living animals as anastomotic leakages are multifactorial processes.

Constitutive modeling of the passive inflation-extension behavior of the swine colon

In the present work, we propose the first structural constitutive model of the passive mechanical behavior of the swine colon that is validated against physiological inflation-extension tests, and accounts for residual strains. Sections from the spiral colon and the descending colon were considered to investigate potential regional variability. We found that the proposed constitutive model accurately captures the passive inflation-extension behavior of both regions of the swine colon (coefficient of determination R²=0.94±0.02). The model revealed that the circumferential muscle layer does not provide significant mechanical support under passive conditions and the circumferential load is actually carried by the submucosa layer. The stress analysis permitted by the model showed that the colon tissue can distend up to 30% radially without significant increase in the wall stresses suggesting a highly compliant behavior of the tissue. This is in-line with the requirement for the tissue to easily accommodate variable quantities of fecal matter. The analysis also showed that the descending colon is significantly more compliant than the spiral colon, which is relevant to the storage function of the descending colon. Histological analysis showed that the swine colon possesses a four-layer structure similar to the human colon, where the longitudinal muscle layer is organized into bands called taeniae, a typical feature of the human colon. The model and the estimated parameters can be used in a Finite Element framework to conduct simulations with realistic geometry of the swine colon. The resulting computational model will provide a foundation for virtual assessment of safe and effective devices for the treatment of colonic diseases.

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.

Nondestructive measurement of esophageal biaxial mechanical properties utilizing sonometry

Malignant esophageal pathology typically requires resection of the esophagus and reconstruction to restore foregut continuity. Reconstruction options are limited and morbid. The esophagus represents a useful target for tissue engineering strategies based on relative simplicity in comparison to other organs. The ideal tissue engineered conduit would have sufficient and ideally matched mechanical tolerances to native esophageal tissue. Current methods for mechanical testing of esophageal tissues both in vivo and ex vivo are typically destructive, alter tissue conformation, ignore anisotropy, or are not able to be performed in fluid media. The aim of this study was to investigate biomechanical properties of swine esophageal tissues through nondestructive testing utilizing sonometry ex vivo. This method allows for biomechanical determination of tissue properties, particularly longitudinal and circumferential moduli and strain energy functions. The relative contribution of mucosal-submucosal layers and muscular layers are compared to composite esophagi. Swine thoracic esophageal tissues (n  =  15) were tested by pressure loading using a continuous pressure pump system to generate stress. Preconditioning of tissue was performed by pressure loading with the pump system and pre-straining the tissue to in vivo length before data was recorded. Sonometry using piezocrystals was utilized to determine longitudinal and circumferential strain on five composite esophagi. Similarly, five mucosa-submucosal and five muscular layers from thoracic esophagi were tested independently. This work on esophageal tissues is consistent with reported uniaxial and biaxial mechanical testing and reported results using strain energy theory and also provides high resolution displacements, preserves native architectural structure and allows assessment of biomechanical properties in fluid media. This method may be of use to characterize mechanical properties of tissue engineered esophageal constructs.

Multiaxial mechanical response and constitutive modeling of esophageal tissues: Impact on esophageal tissue engineering

Congenital defects of the esophagus are relatively frequent, with 1 out of 2500 babies suffering from such a defect. A new method of treatment by implanting tissue engineered esophagi into newborns is currently being developed and tested using ovine esophagi. For the reconstruction of the biological function of native tissues with engineered esophagi, their cellular structure as well as their mechanical properties must be considered. Since very limited mechanical and structural data for the esophagus are available, the aim of this study was to investigate the multiaxial mechanical behavior of the ovine esophagus and the underlying microstructure. Therefore, uniaxial tensile, biaxial tensile and extension-inflation tests on esophagi were performed. The underlying microstructure was examined in stained histological sections through standard optical microscopy techniques. Moreover, the uniaxial ultimate tensile strength and residual deformations of the tissue were determined. Both the mucosa-submucosa and the muscle layers showed nonlinear and anisotropic mechanical behavior during uniaxial, biaxial and inflation testing. Cyclical inflation of the intact esophageal tube caused marked softening of the passive esophagi in the circumferential direction. The rupture strength of the mucosa-submucosa layer was much higher than that of the muscle layer. Overall, the ovine esophagus showed a heterogeneous and anisotropic behavior with different mechanical properties for the individual layers. The intact and layer-specific multiaxial properties were characterized using a well-known three-dimensional microstructurally based strain-energy function. This novel and complete set of data serves the basis for a better understanding of tissue remodeling in diseased esophagi and can be used to perform computer simulations of surgical interventions or medical-device applications.

Biomechanical behavior and histological organization of the three-layered passive esophagus as a function of topography

The zero-stress state of the mucosa-submucosa and two muscle esophageal layers has been delineated, but their multi-axial response has not, because muscle dissection may not leave tubular specimens intact for inflation/extension testing. The histomechanical behavior of the three-layered porcine esophagus was investigated in this study, through light microscopic examination and uniaxial tension, with two-dimensional strain measurement in pairs of orthogonally oriented specimens. The two-dimensional Fung-type strain–energy function described suitably the pseudo-elastic tissue response, affording faithful simulations to our data. Differences in the scleroprotein content and configuration were identified as a function of layer, topography, and orientation, substantiating the macromechanical differences found. In view of the failure and optimized material parameters, the mucosa-submucosa was stronger and stiffer than muscle, associating it with a higher collagen content. A notable topographical distribution was apparent, with data for the abdominal region differentiated from that for the cervical region, owing to the existence of inner muscle with a circumferential arrangement and of outer muscle with a longitudinal arrangement in the former region, and of both muscle layers with oblique arrangement in the latter region, with thoracic esophagus being a transition zone. Tissue from the mucosa-submucosa was stronger and stiffer longitudinally, relating with a preferential collagen reinforcement along that axis, but more extensible in the orthogonal axis.