Passive mechanical properties of porcine left circumflex artery and its mathematical description

Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability

The calibration of hyperelastic constitutive models of soft tissue and tissue surrogates is often treated as an exercise in curve-fitting to the average experimental response, and many of the complicating factors such as experimental boundary conditions and data variability are ignored. In this work, we focus on three questions that arise in this area: the ramifications of ignoring the experimental boundary conditions, the use of local optimizers, and the role of data variability. Using data from a uniaxial extension experiment on a tissue surrogate, we study how these three factors affect the calibration of isotropic hyperelastic constitutive models. Our results show that even with the simplest of constitutive models, it is necessary to look beyond a "good fit" to the average.

Characterization of the mechanical behavior of the optic nerve sheath and its role in spaceflight-induced ophthalmic changes

Visual impairment and intracranial pressure (VIIP) syndrome is characterized by a number of permanent ophthalmic changes, including loss of visual function. It occurs in some astronauts during long-duration spaceflight missions. Thus, understanding the pathophysiology of VIIP is currently a major priority in space medicine research. It is hypothesized that maladaptive remodeling of the optic nerve sheath (ONS), in response to microgravity-induced elevations in intracranial pressure (ICP), contributes to VIIP. However, little is known about ONS biomechanics. In this study, we developed a custom mechanical testing system that allowed for unconfined lengthening, twisting, and circumferential distension of the porcine ONS during inflation and axial loading. Data were fit to a four-fiber family constitutive equation to extract material and structural parameters. Inflation testing showed a characteristic "cross-over point" in the pressure-diameter curves under different axial loads in all samples that were tested; the cross-over pressure was [Formula: see text] mmHg ([Formula: see text]). Large sample-to-sample variations were observed in the circumferential strain, while only modest variations were observed in the circumferential stress. Multiphoton microscopy revealed that the collagen fibers of the ONS were primarily oriented axially when the tissue was loaded. The existence of this cross-over behavior is expected to be neuroprotective, as it would avoid optic nerve compression during routine changes in gaze angle, so long as ICP was within the normal range. Including these observations into computational models of VIIP will help provide insight into the pathophysiology of VIIP and could help identify risk factors and potential interventions.

Residual shear deformations in the coronary artery

Quantifying arterial residual deformations is critical for understanding the stresses and strains within the arterial wall during physiological and pathophysiological conditions. This study presents novel findings on residual shear deformations in the left anterior descending coronary artery. Residual shear deformations are most evident when thin, long axial strips are cut from the artery. These strips deform into helical configurations when placed in isotonic solution. A residual shear angle is introduced as a parameter to quantify the residual shear deformations. Furthermore, a stress analysis is performed to study the effects of residual shear deformations on the intramural shear stress distribution of an artery subjected to pressure, axial stretch, and torsion using numerical simulation. The results from the stress analyses suggest that residual shear deformations can significantly modulate the intramural shear stress across the arterial wall.

A STRUCTURE-MOTIVATED MODEL OF THE PASSIVE MECHANICAL RESPONSE OF THE PRIMARY PORCINE RENAL ARTERY

The primary renal arteries transport up to one fourth of cardiac output to the kidneys for blood plasma ultrafiltration, with a functional dependence on the vessel geometry, composition and mechanical properties. Despite the critical physiological function of the renal artery, the few biomechanical studies that have focused on this vessel are either uniaxial or only partially describe its bi-axial mechanical behavior. In this study, we quantify the passive mechanical response of the primary porcine renal artery through bi-axial mechanical testing that probes the pressure-deformed diameter and pressure-axial force relationships at various longitudinal extensions, including the in-vivo axial stretch ratio. Mechanical data are used to parameterize and validate a structure-motivated constitutive model of the arterial wall. Together, experimental data and theoretical predictions of the stress distribution within the arterial wall provide a comprehensive description of the passive mechanical response of the porcine renal artery.

Tension to passively cinch the mitral annulus through coronary sinus access: an ex vivo study in ovine model

INTRODUCTION

The transcatheter mitral valve repair (TMVR) technique utilizes a stent to cinch a segment of the mitral annulus (MA) and reduces mitral regurgitation. The cinching mechanism results in reduction of the septal-lateral distance. However, the mechanism has not been characterized completely. In this study, a method was developed to quantify the relation between cinching tension and MA area in an ex vivo ovine model.

METHOD

The cinching tension was measured from a suture inserted within the coronary sinus (CS) vessel with one end tied to the distal end of the vessel and the other end exited to the CS ostium where it was attached to a force transducer on a linear stage. The cinching tension, MA area, septal-lateral (S-L) and commissure-commissure (C-C) diameters and leakage was simultaneously measured in normal and dilated condition, under a hydrostatic left ventricular pressure of 90 mm Hg.

RESULTS

The MA area was increased up to 22.8% after MA dilation. A mean tension of 2.1 ± 0.5 N reduced the MA area by 21.3 ± 5.6% and S-L diameter by 24.2 ± 5.3%. Thus, leakage was improved by 51.7 ± 16.2% following restoration of normal MA geometry.

CONCLUSION

The cinching tension generated by the suture acts as a compensation force in MA reduction, implying the maximum tension needed to be generated by annuloplasty device to restore normal annular size. The relationship between cinching tension and the corresponding MA geometry will contribute to the development of future TMVR devices and understanding of myocardial contraction function.

Experimental investigation and constitutive modeling of the 3D histomechanical properties of vein tissue

Numerous studies have provided material models of arterial walls, but limited information is available on the pseudo-elastic response of vein walls and their underlying microstructure, and only few constitutive formulations have been proposed heretofore. Accordingly, we identified the histomechanics of healthy porcine jugular veins by applying an integrated approach of inflation/extension tests and histomorphometric evaluation. Several alternate phenomenological and microstructure-based strain-energy functions (SEF) were attempted to mimic the material response. Evaluation of their descriptive/predictive capacities showed that the exponential Fung-type SEF alone or in tandem with the neo-Hookean term did not capture the deformational response at high pressures. This problem was solved to a degree with the neo-Hookean and two-fiber (diagonally arranged) family SEF, but altogether the least reliable fit was generated. Fitting precision was much improved with the four-fiber (diagonally, circumferentially, longitudinally arranged) family model, as the inability of neo-Hookean function with force data was alleviated by use of the longitudinal-fiber family. Implementation of a quadratic term as a descriptor of low-pressure anisotropy facilitated the simulation of low-pressure and force data, and the four-fiber families simulated more faithfully than the two-fiber families the physiologic and high-pressure response. Importantly, this SEF was consistent with vein angioarchitecture, namely the occurrence of extensive elastin fibers along the longitudinal axis and few orthogonal fibers attached to them and of three collagen sets with circumferential, longitudinal, and diagonal arrangement, respectively. Our findings help to establish the relationship between vein microstructure and its biomechanical response, yet additional observations are obligatory prior to endeavoring generalizations to other veins.

A passive strain-energy function for elastic and muscular arteries: correlation of material parameters with histological data

A plethora of phenomenological and structure-motivated constitutive models have thus far been used as pseudoelastic descriptors in arterial biomechanics, but their parameters have not been explicitly correlated with histology. This study associated biaxial histological data with strain-energy function (SEF) parameters derived from uniaxial tension data of arteries from different topographical sites (carotid artery vs. thoracic aorta vs. femoral artery). A two-term SEF fitted the passive stress-strain data of healthy porcine tissue, justified by the biphasic response characterizing elastin-rich tissues. Selection of a quadratic (orthotropic) over the neo-Hookean (isotropic) term was dictated by the directional dissimilarities in low-stress mechanical response, consistent with our histological data indicating orthotropic symmetry for unstressed elastin. Use of the exponential term was dictated by mechanical dissimilarities at high stresses and variations in unstressed collagen composition and orientation. Accurate fits were attained; topographical variations and anisotropy in material parameters were accounted by respective variations in histomorphometrical data.

Comparison of biaxial mechanical properties of coronary sinus tissues from porcine, ovine and aged human species

Due to its proximity to the mitral valve, the coronary sinus (CS) vessel serves as a conduit for the deployment and implantation of the percutaneous transvenous mitral annuloplasty (PTMA) devices that can potentially reduce the mitral regurgitation. Because CS vessel is a venous tissue and seldom diseased, its mechanical properties have not been well studied. In this study, we performed a multi-axial mechanical test and histological analysis to characterize the mechanical and structural properties of the aged human, porcine and ovine CS tissues. The results showed that the aged human CS tissues exhibited much stiffer and highly anisotropic behaviors compared to the porcine and ovine. Both of the porcine and ovine CS vessel walls were thicker and mainly composed of striated muscle fibers (SMF), whereas the thinner aged human CS had higher collagen, less SMF, and more fragmented elastin fibers, which are possibly due to aging effects. We also observed that the anatomical features of porcine CS vessel might be not suitable for PTMA deployment. These differences between animal and human models raise questions for the validity of using animal models to investigate the biomechanics involved in the PTMA intervention. Therefore, caution must be taken in future studies of PTMA stents using animal models.

A linearized and incompressible constitutive model for arteries

In many biomechanical studies, blood vessels can be modeled as pseudoelastic orthotropic materials that are incompressible (volume-preserving) under physiological loading. To use a minimum number of elastic constants to describe the constitutive behavior of arteries, we adopt a generalized Hooke's law for the co-rotational Cauchy stress and a recently proposed logarithmic-exponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving deformations. Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret. In particular, the number of independent elastic constants reduces from ten to seven in the orthotropic model. As an illustratory study, we fit this model to measured data of porcine coronary arteries in inflation-stretch tests. Four parameters, n (material nonlinearity), Young's moduli E₁ (circumferential), E₂ (axial), and E₃ (radial) are necessary to fit the data. The advantages and limitations of this model are discussed.

Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue

The mechanical behavior of blood vessels is known to be viscoelastic rather than elastic. The functional role of viscoelasticity, however, has remained largely unclear. The hypothesis of this study is that viscoelasticity reduces the stresses and strains in the vessel wall, which may have a significant impact on the fatigue life of the blood vessel wall. To verify the hypothesis, the pulsatile stress in rabbit thoracic artery at physiological loading condition was investigated with a quasi-linear viscoelastic model, where the normalized stress relaxation function is assumed to be isotropic, while the stress-strain relationship is anisotropic and nonlinear. The artery was subjected to the same boundary condition, and the mechanical equilibrium equation was solved for both the viscoelastic and an elastic (which has a constant relaxation function) model. Numerical results show that, compared with purely elastic response, the viscoelastic property of arteries reduces the magnitudes and temporal variations of circumferential stress and strain. The radial wall movement is also reduced due to viscoelasticity. These findings imply that viscoelasticity may be beneficial for the fatigue life of blood vessels, which undergo millions of cyclic mechanical loadings each year of life.

A model for passive elastic properties of rat vena cava

A two-dimensional model for the elastic properties of vena cava abdominalis under orthotropic deformation is introduced and tested against the experimental data obtained from six specimen of rat venae cavae by pressurization experiments. The model is based on membrane approximation and suited for vessels where most of the elastic elements are oriented axially, while circumferential contraction is exerted by redirecting axial stress by some network of oblique fibers. For the experimental data considered in this paper, the ratio between axial and circumferential stress depends almost exclusively on the circumferential extension ratio. As a consequence, the mechanical system can be formally decomposed in a kinematic system reacting by axial contraction on circumferential extension without any loss or storage of energy, serially connected to a hyperelastic system acting only in axial direction. Both systems are modeled separately by equations obtained by a purely phenomenological approach with two parameters for each system. This leads to reasonable reproduction of the experimental data. Introducing a correction parameter, which takes into account that the model assumption on the decomposition does not hold exactly, we get better reproduction of data. However, this is paid for by loss of physical rigor and in particular by departing from the assumption of hyperelasticity.