Prestressing in finite deformation abdominal aortic aneurysm simulation

In abdominal aortic aneurysm (AAA) simulation the patient-specific geometry of the object of interest is very often reconstructed from in vivo medical imaging such as CT scans. Such geometries represent a deformed configuration stressed by typical in vivo conditions. However, commonly, such structures are considered stress-free in simulation. In this contribution we sketch and compare two methods to introduce a physically meaningful stress/strain state to the obtained geometry for simulations in the finite strain regime and demonstrate the necessity of such prestressing techniques. One method is based on an inverse design analysis to calculate a stress-free reference configuration. The other method developed here is based on a modified updated Lagrangian formulation. Formulation of both methods is provided. Applicability and accurateness of both approaches are compared and evaluated utilizing fully three-dimensional patient-specific AAA structures in the finite strain regime.     

Patient-Specific Artery Shrinkage and 3D Zero-Stress State in Multi-Component 3D FSI Models for Carotid Atherosclerotic Plaques Based on <i>In Vivo</i> MRI Data

Image-based computational models for atherosclerotic plaques have been developed to perform mechanical analysis to quantify critical flow and stress/strain conditions related to plaque rupture which often leads directly to heart attack or stroke. An important modeling issue is how to determine zero stress state from in vivo plaque geometries. This paper presents a method to quantify human carotid artery axial and inner circumferential shrinkages by using patient-specific ex vivo and in vivo MRI images. A shrink-stretch process based on patient-specific in vivo plaque morphology and shrinkage data was introduced to shrink the in vivo geometry first to find the zero-stress state (opening angle was ignored to reduce the complexity), and then stretch and pressurize to recover the in vivo plaque geometry with computed initial stress, strain, flow pressure and velocity conditions. Effects of the shrink-stretch process on plaque stress/strain distributions were demonstrated based on patient-specific data using 3D models with fluid-structure interactions (FSI). The average artery axial and inner circumferential shrinkages were 25% and 7.9%, respectively, based on a data set obtained from 10 patients. Maximum values of maximum principal stress and strain increased 349.8% and 249% respectively with 33% axial stretch. Influence of inner circumferential shrinkage (7.9%) was not very noticeable under 33% axial stretch, but became more noticeable under smaller axial stretch. Our results indicated that accurate knowledge of artery shrinkages and the shrink-stretch process will considerably improve the accuracy of computational predictions made based on results from those in vivo MRI-based FSI models.     

Dynamic material properties of the human sclera

As a result of trauma, approximately 30,000 people become blind in one eye every year in the United States. A common injury prediction tool is computational modeling, which requires accurate material properties to produce reliable results. Therefore, the purpose of this study was to determine the dynamic material properties of the human sclera. A high-rate pressurization system was used to create dynamic pressure to the point of rupture in 12 human eyes. Measurements were obtained for the internal pressure, the diameter of the globe, the thickness of the sclera, and the changing coordinates of the optical markers using high-rate video. A relationship between true stress and true strain was determined for the sclera tissue in two directions. It was found that the average maximum true stress was 13.89±4.81 MPa for both the equatorial and meridional directions, the average maximum true strain along the equator was 0.041±0.014, and the average maximum true strain along the meridian was 0.058±0.018. Results show a significant difference in the maximum strain in the equatorial and meridional directions (p=0.02). In comparing these data with previous studies, it is concluded that the human sclera is both anisotropic and viscoelastic. The dynamic material properties presented in this study can be used for advanced models of the human eye to help prevent eye injuries in the future.     

Inverse elastostatic stress analysis in pre-deformed biological structures: Demonstration using abdominal aortic aneurysms

In stress analysis of membrane-like biological structures, the geometry constructed from in vivo image, which often corresponds to a deformed state, is routinely taken as the initial stress-free geometry. In this paper, we show that this limitation can be completely removed using an inverse elastostatic approach, namely, a method for finding the initial geometry of an elastic body from a given deformed state. We demonstrate the utility of the inverse approach using a patient-specific abdominal aortic aneurysm model, and identify the scope of error in stress estimation in the conventional approach within a realistic range of material parameter variations.     

Viscoelastic characterization of peripapillary sclera: material properties by quadrant in rabbit and monkey eyes

In this report we characterize the viscoelastic material properties of peripapillary sclera from the four quadrants surrounding the optic nerve head in both rabbit and monkey eyes. Scleral tensile specimens harvested from each quadrant were subjected to uniaxial stress relaxation and tensile ramp to failure tests. Linear viscoelastic theory, coupled with a spectral reduced relaxation function, was employed to characterize the viscoelastic properties of the tissues. We detected no differences in the stress-strain curves of specimens from the four quadrants surrounding the optic nerve head (ONH) below a strain of 4 percent in either the rabbit or monkey. While the peripapillary sclera from monkey eyes is significantly stiffer (both instantaneously and in equilibrium) and relaxes more slowly than that from rabbits, we detected no differences in the viscoelastic material properties (tested at strains of 0-1 percent) of sclera from the four quadrants surrounding the ONH within either species group.     

Material properties of the cornea and sclera: a modelling approach to test experimental analysis

Material properties of cornea and sclera are important for maintaining the shape of the eye and the requisite surface curvatures for optics. They also need to withstand the forces of external and internal musculature and fluctuations in intraocular pressure (IOP). These properties are difficult to measure and variable results have been reported. A previously published experimental procedure, from which the material properties of the eyeball coats were obtained, has been modelled in this paper using Finite Element Analysis, in order to test the accuracy of the experiment. Material parameters were calculated from the model and the resulting relationships between stress and strain for the cornea and sclera compared to their experimentally obtained counterparts. The comparison between model and experiment was close for the sclera but more varied for the cornea. The pressure vessel model can be applied for measuring the material properties of the sclera but is less accurate for the cornea.     

Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.     

The influence of fiber dispersion on the mechanical response of aortic tissues in health and disease: a computational study

Changes in the structural components of aortic tissues have been shown to play a significant role in the pathogenesis of aortic degeneration. Therefore, reliable stress analyses require a suitable and meaningful constitutive model that captures micro-structural changes. As recent data show, in-plane and out-of-plane collagen fiber dispersions vary significantly between healthy and aneurysmatic aortic walls. The aim of this study is to computationally investigate the influence of fiber dispersion on the mechanical response of aortic tissues in health and disease. In particular, the influence of three different fiber dispersions is studied: (i) non-rotationally symmetric dispersion, the most realistic assumption for aortic tissues; (ii) transversely isotropic dispersion, a special case; (iii) perfectly aligned fibers (no dispersion in either plane), another special case. Explicit expressions for the stress and elasticity tensors as needed for the implementation in a finite element code are provided. Three representative numerical examples are studied: planar biaxial extension, inflation of residually stressed and pre-stretched aortic segments and inflation of an idealized abdominal aortic aneurysm (AAA) geometry. For the AAA geometry the case of isotropic dispersion is additionally analyzed. Documented structural and mechanical parameters are taken from human aortas (healthy media/adventitia and AAA). The influence of fiber dispersions upon magnitudes and distributions of stresses and deformations are presented and analyzed. Stresses vary significantly, especially in the AAA case, where material stiffening is significantly influenced by fiber dispersion. The results highlight the need to incorporate the structural differences into finite element simulations to obtain more accurate stress predictions. Additionally, results show the capability of one constitutive model to represent different scenarios of aortic micro-structures allowing future studies of collagen reorientation during disease progression.     

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear,anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress–strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model?s nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean±95% confidence interval) of the disc?s nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc?s full nonlinear response in multiple loading scenarios.     

Material properties and effect of preconditioning of human sclera,optic nerve,and optic nerve sheath

The optic nerve (ON) is a recently recognized tractional load on the eye during larger horizontal eye rotations. In order to understand the mechanical behavior of the eye during adduction, it is necessary to characterize material properties of the sclera, ON, and in particular its sheath. We performed tensile loading of specimens taken from fresh postmortem human eyes to characterize the range of variation in their biomechanical properties and determine the effect of preconditioning. We fitted reduced polynomial hyperelastic models to represent the nonlinear tensile behavior of the anterior, equatorial, posterior, and peripapillary sclera, as well as the ON and its sheath. For comparison, we analyzed tangent moduli in low and high strain regions to represent stiffness. Scleral stiffness generally decreased from anterior to posterior ocular regions. The ON had the lowest tangent modulus, but was surrounded by a much stiffer sheath. The low-strain hyperelastic behaviors of adjacent anatomical regions of the ON, ON sheath, and posterior sclera were similar as appropriate to avoid discontinuities at their boundaries. Regional stiffnesses within individual eyes were moderately correlated, implying that mechanical properties in one region of an eye do not reliably reflect properties of another region of that eye, and that potentially pathological combinations could occur in an eye if regional properties are discrepant. Preconditioning modestly stiffened ocular tissues, except peripapillary sclera that softened. The nonlinear mechanical behavior of posterior ocular tissues permits their stresses to match closely at low strains, although progressively increasing strain causes particularly great stress in the peripapillary region.

     

Study on the Constitutive Model for Jointed Rock Mass

A new elasto-plastic constitutive model for jointed rock mass, which can consider the persistence ratio in different visual angle and anisotropic increase of plastic strain, is proposed. The proposed the yield strength criterion, which is anisotropic, is not only related to friction angle and cohesion of jointed rock masses at the visual angle but also related to the intersection angle between the visual angle and the directions of the principal stresses. Some numerical examples are given to analyze and verify the proposed constitutive model. The results show the proposed constitutive model has high precision to calculate displacement, stress and plastic strain and can be applied in engineering analysis.     

Investigation of the influence of external factors on the conformational dynamics of rhodopsin-like receptors by means of molecular dynamics simulation

Abstract

The study reports about the influence of binding of orthosteric ligands on the conformational dynamics of β-2-adrenoreceptor. Using molecular dynamics (MD) simulation, we found that there was a little fraction of active states of the receptor in its apo (ligand-free) ensemble. Analysis of MD trajectories indicated that such spontaneous activation of the receptor is accompanied by the motion in intracellular part of its alpha-helices. Thus, receptor’s constitutive activity directly results from its conformational dynamics. On the other hand, the binding of a full agonist resulted in a significant shift of the initial equilibrium towards its active state. Finally, the binding of the inverse agonist stabilized the receptor in its inactive state. It is likely that the binding of inverse agonists might be a universal way of constitutive activity inhibition in vivo. Our results indicate that ligand binding redistribute pre-existing conformational degrees of freedom (in accordance to the Monod–Wyman–Changeux Model) of the receptor rather than cause induced fit in it. Therefore, the ensemble of biologically relevant receptor conformations is encoded in its spatial structure, and individual conformations from that ensemble might be used by the cell in conformity with the physiological behavior.     

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.     

The reaction-limited kinetics of membrane-to-surface adhesion and detachment

Biological adhesion is frequently mediated by specific membrane proteins (adhesion molecules). Starting with the notion of adhesion molecules, we present a simple model of the physics of membrane-to-surface attachment and detachment. This model consists of coupling the equations for deformation of an elastic membrane with equations for the chemical kinetics of the adhesion molecules. We propose a set of constitutive laws relating bond stress to bond strain and also relating the chemical rate constants of the adhesion molecules to bond strain. We derive an exact formula for the critical tension. We also describe a fast and accurate finite difference algorithm for generating numerical solutions of our model. Using this algorithm, we are able to compute the transient behaviour during the initial phases of adhesion and detachment as well as the steady-state geometry of adhesion and the velocity of the contact. An unexpected consequence of our model is the predicted occurrence of states in which adhesion cannot be reversed by application of tension. Such states occur only if the adhesion molecules have certain constitutive properties (catch-bonds). We discuss the rational for such catch-bonds and their possible biological significance. Finally, by analysis of numerical solutions, we derive an accurate and general expression for the steady-state velocity of attachment and detachment. As applications of the theory, we discuss data on the rolling velocity of granulocytes in post-capillary venules and data on lectin-mediated adhesion of red cells.     

Retrobulbar primitive neuroectodermal tumor in a squirrel monkey (Saimiri sciureus)

Background A 2.8‐year‐old female captive‐bred common squirrel monkey (Saimiri sciureus) showed exophthalmos of the right eye, and the eye was surgically enucleated. A tumor mass was found in the eye. Methods Formalin‐fixed tumor samples were examined histopathologically and immunohistochemically for diagnosis. Results The retrobulbar tumor mass adhered to the sclera and infiltrated the choroid. Histopathologically, tumor cells were pleomorphic, arranged in a sheet pattern, and mimicked primitive neuroectodermal cells. The tumor cells were strongly positive for precursor neuronal cell markers (beta III tubulin, neuron‐specific enolase, vimentin, nestin, doublecortin, oligo2, and S‐100), but negative for mature cell markers (cytokeratin, neurofilament, and glial fibrillary acidic protein) and a retinoblastoma marker (rhodopsin). Conclusions This is the first reported case for the retrobulbar location of primitive neuroectodermal tumor in non‐human primates.     

Oxygen tension in thein vivo cornea

The steady state distribution of oxygen tension in thein vivo cornea is estimated in the present study by using a nonlinear oxygen consumption rate equation of the Michaelis-Menten type. Such a rate expression is more accurate than the previous simplified versions in predicting the oxygen consumption rate. It is found that for an open eye with or without contact lens, the oxygen tensions predicted previously are in good agreement with these predicted in the present work. However, for a closed eye with or without contact lens, the previous predictions underestimate the oxygen tension.     

Stress-strain behavior for curved exponential strips

For the two-parameter (A, α) exponentially-stiffening constituitive relation, typical of many biological materials, it is shown that the uniaxial stress-strain behavior of an initially curved strip is significantly changed by the residual bending stresses. Closedform theoretical results depend on the thickness to radius ratio (h/R) and the relative strain level ε(h/R). The bending stresses tend to obscure accurate measurement ofA and α unless care is taken. However, it is shown that by changing co-ordinates to (dℝ/d∈, ℝ)-space, bothA and α can be recovered from the high stress data, and α alone can be recovered from the low stress data. This has practical application to the mechanics of cornea, sclera, and heart muscle.     

Identification of the material parameters of soft tissues in the compressed leg

Elastic compression is recommended in prophylaxis and the treatment of venous disorder of the human leg. However, the mechanisms of compression are not completely understood and the response of internal tissues to the external pressure is partially unknown. To address this later issue, a 3D FE model of a human leg is developed. The geometry is derived from 3D CT scans. The FE model is made up of soft tissues and rigid bones. An inverse method is applied to identify the properties of soft tissues which are modelled as hyperelastic, near-incompressible, homogeneous and isotropic materials. The principle is to calibrate the constitutive properties using CT scans carried out with and without the presence of a compression sock. The deformed geometry computed by the calibrated FE model is in agreement with the geometry deduced from the CT scans. The model also provides the internal pressure distribution, which may lead to medical exploitation in the future.     

Compression behavior of porcine spinal cord white matter

Spinal cord injury often results from a compressive load; however, the compression behavior of spinal cord white matter has not been clearly established. Quantifying the compression behavior is important for advancing our understanding of spinal cord injury mechanics and facilitating the use of finite element models to study injury. The objective of this study was to characterize the unconfined compression behavior of isolated white matter segments and determine the constitutive model which best captured the stress-strain behavior. Spinal cord white matter samples were harvested immediately following sacrifice from juvenile Yorkshire pigs (n=104). The samples were compressed to 40% strain at four strain rates (0.005, 0.05, 0.5, and 5.0/s) and allowed to relax for 60s. The effects of preload, peak strain, sample aspect ratio, and time post mortem on peak stress, and constitutive model parameters were also examined. Strain rate had a significant effect on peak stress (p<0.001). A first-order Ogden model best captured the loading response of spinal cord white matter (R(2)=0.99) and a viscoelastic material model combining a first-order Ogden model with a 3-term Prony series effectively captured the effect of strain rate and the relaxation response. This study showed spinal cord white matter to be less stiff than previously estimated by inverse finite element methods, which will have a significant effect on finite element model predictions of the magnitude and distribution of stresses and strains in the spinal cord. This study is the first to quantify the unconfined compression response of spinal cord white matter.