An analysis of the complete strain field within Flexercell membranes

The purpose of the current investigation was to use finite element analysis to quantify the complete strain field for the membranes of the Flexercell^TM apparatus, a device extensively used to study the effects of mechanical loading on cultured cells. Four vacuum pressure simulations were run for the membrane for both the uniaxial and biaxial loading post, yielding the distribution of longitudinal (E_xx) and transverse (E_yy) strain for the uniaxial post, and the radial (E_rr) and the circumferential (E_θθ) strain for the biaxial post. The discrete values of each strain were evaluated at the center of the loading post as well as the region off of the post. Experimental measurements were made for both types of loading posts in order to validate our simulations. The biaxial post simulation was found to provide a central circular region of equal and constant E_rr and E_θθ in the membrane on the post. Likewise, the uniaxial post simulation provided a definitive region of constant E_xx for a central rectangular region on the post. For the uniaxial simulation, the region on the post resulted in small compressive E_yy, while the region off the post resulted in tensile E_yy. The biaxial simulation resulted in large tensile E_rr and E_θθ on the post, while the region off the post resulted in large E_rr and smaller E_θθ. Our simulations were reasonably consistent with the experimental measurements made for both types of loading posts. We believe that the results of this study will allow scientists to more accurately describe the response of cells to known strains on all portions of the membrane, thus increasing the range of known strain regions for investigation in the Flexercell^TM apparatus.     

Biaxial mechanical properties of the inferior vena cava in C57BL/6 and CB-17 SCID/bg mice

Multiple murine models have proven useful in studying the natural history of neovessel development in the tissue engineering of vascular grafts. Nevertheless, to better understand longitudinal changes in the biomechanics of such neovessels, we must first quantify native tissue structure and properties. In this paper, we present the first biaxial mechanical data for, and nonlinear constitutive modeling of, &QJ;the inferior vena cava from two models used in tissue engineering: wild-type C57BL/6 and immunodeficient CB-17 SCID/bg mice. Results show that inferior vena cava from the latter are significantly stiffer in the circumferential direction, both materially (as assessed by a stored energy function) and structurally (as assessed by the compliance), despite a lower intramural content of fibrillar collagen and similar wall thickness. Quantifying the natural history of neovessel development in different hosts could lead to increased insight into the mechanisms by which cells fashion and maintain extracellular matrix in order to match best the host stiffness while ensuring sufficient vascular integrity.     

The biaxial mechanical behaviour of abdominal aortic aneurysm intraluminal thrombus: Classification of morphology and the determination of layer and region specific properties

Intraluminal thrombus (ILT) is present in 75% of clinically-relevant abdominal aortic aneurysms (AAAs) yet, despite much research effort, its role in AAA biomechanics remains unclear. The aim of this work is to further evaluate the biomechanics of ILT and determine if different ILT morphologies have varying mechanical properties.     

Mechanical characterisation of porcine rectus sheath under uniaxial and biaxial tension

Incisional hernia development is a significant complication after laparoscopic abdominal surgery. Intra-abdominal pressure (IAP) is known to initiate the extrusion of intestines through the abdominal wall, but there is limited data on the mechanics of IAP generation and the structural properties of rectus sheath. This paper presents an explanation of the mechanics of IAP development, a study of the uniaxial and biaxial tensile properties of porcine rectus sheath, and a simple computational investigation of the tissue. Analysis using Laplace?s law showed a circumferential stress in the abdominal wall of approx. 1.1 MPa due to an IAP of 11 kPa, commonly seen during coughing. Uniaxial and biaxial tensile tests were conducted on samples of porcine rectus sheath to characterise the stress–stretch responses of the tissue. Under uniaxial tension, fibre direction samples failed on average at a stress of 4.5 MPa at a stretch of 1.07 while cross-fibre samples failed at a stress of 1.6 MPa under a stretch of 1.29. Under equi-biaxial tension, failure occurred at 1.6 MPa with the fibre direction stretching to only 1.02 while the cross-fibre direction stretched to 1.13. Uniaxial and biaxial stress–stretch plots are presented allowing detailed modelling of the tissue either in silico or in a surrogate material. An FeBio computational model of the tissue is presented using a combination of an Ogden and an exponential power law model to represent the matrix and fibres respectively. The structural properties of porcine rectus sheath have been characterised and add to the small set of human data in the literature with which it may be possible to develop methods to reduce the incidence of incisional hernia development.     

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the ‘computational dissection’ of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress–strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.     

Soft ellipsoid potential for biaxial molecules

A soft ellipsoid contact pair potential model for biaxial molecules is proposed considering the configuration dependent energy anisotropy explicitly alongwith their geometrical aspects. Analytic expressions of forces and torques for this coarse-grained potential are provided to make it convenient for molecular dynamics simulation study. Additionally, some molecular dynamics simulations are performed to generate biaxial smectic and nematic liquid crystal phases.     

Biaxial biomechanical properties of the nonpregnant murine cervix and uterus

From a biomechanical perspective, female reproductive health is an understudied area of research. There is an incomplete understanding of the complex function and interaction between the cervix and uterus. This, in part, is due to the limited research into multiaxial biomechanical functions and geometry of these organs. Knowledge of the biomechanical function and interaction between these organs may elucidate etiologies of conditions such as preterm birth. Therefore, the objective of this study was to quantify the multiaxial biomechanical properties of the murine cervix and uterus using a biaxial testing set-up. To accomplish this, an inflation-extension testing protocol (n = 15) was leveraged to quantify biaxial biomechanical properties while preserving native matrix interactions and geometry. Ultrasound imaging and histology (n = 10) were performed to evaluate regional geometry and microstructure, respectively. Histological analysis identified a statistically significant greater collagen content and significantly smaller smooth muscle content in the cervix as compared to the uterus. No statistically significant differences in elastic fibers were identified. Analysis of bilinear fits revealed a significantly stiffer response from the circumferentially orientated ECM fibers compared to axially orientated fibers in both organs. Bilinear fits and a two-fiber family constitutive model showed that the cervix was significantly less distensible than the uterus. We submit that the regional biaxial information reported in this study aids in establishing an appropriate reference configuration for mathematical models of the uterine-cervical complex. Thus, may aid future work to elucidate the biomechanical mechanisms leading to cervical or uterine conditions.     

Biaxial mechanical testing of posterior sclera using high-resolution ultrasound speckle tracking for strain measurements

This study aimed to characterize the mechanical responses of the sclera, the white outer coat of the eye, under equal-biaxial loading with unrestricted shear. An ultrasound speckle tracking technique was used to measure tissue deformation through sample thickness, expanding the capabilities of surface strain techniques. Eight porcine scleral samples were tested within 72 h postmortem  . High resolution ultrasound scans of scleral cross-sections along the two loading axes were acquired at 25 consecutive biaxial load levels. An additional repeat of the biaxial loading cycle was performed to measure a third normal strain emulating a strain gage rosette for calculating the in-plane shear. The repeatability of the strain measurements during identical biaxial ramps was evaluated. A correlation-based ultrasound speckle tracking algorithm was used to compute the displacement field and determine the distributive strains in the sample cross-sections. A Fung type constitutive model including a shear term was used to determine the material constants of each individual specimen by fitting the model parameters to the experimental stress–strain data. A non-linear stress–strain response was observed in all samples. The meridian direction had significantly larger strains than that of the circumferential direction during equal-biaxial loadings (P's<0.05$P\text{'}s<0.05$). The stiffness along the two directions was also significantly different (P=0.02) but highly correlated (R²=0.8). These results showed that the mechanical properties of the porcine sclera were nonlinear and anisotropic under biaxial loading. This work has also demonstrated the feasibility of using ultrasound speckle tracking for strain measurements during mechanical testing.