Characterizing heterogeneous properties of cerebral aneurysms with unknown stress-free geometry: a precursor to in vivo identification

Mechanical characterization of dissected and dilated human ascending aorta using Fung-type hyperelastic models with pre-identified initial tangent moduli for low-stress distensibility

Ascending aortic dissection (AD) is a potentially fatal vascular disease associated with degradation and fragmentation of the elastic fibers in the aortic media, increasing low-stress distensibility, and a dilated aorta may lead to dissection. In this study, a Fung-type hyperelastic model was formulated incorporating the initial tangent moduli (ITM) of stress-strain curves as an index of low-stress distensibility. ITM were correlated with the material constants by linearizing incompressible stress-strain relationships at zero strain. For uniaxial loading tests, the robustness of the material constants was examined in the stress ranges of 0-200, 0-180, and 0-160 kPa and to the ITM values of 100%, 95%, and 90%. Examination revealed stable changes in the material constants of 80% of the specimens. For equibiaxial stretch tests, the material constants were determined for each curve of the isotropic and anisotropic deformation groups by pre-identifying the ITM and minimizing fitting errors using isotropic or anisotropic models. The errors for all groups were <6% using a transversely isotropic model, and <10% for an orthotropic model. Comparisons with experimental curves showed that Fung-type models described both the ITM and significant stiffening at high stress levels. The mechanical characteristics of the aorta in the stage prior/posterior to dissection is such that while hardening occurs under both low- and high-stress levels with an increase in collagen content as an aging response, softening occurs under low-stress conditions due to histological abnormalities such as elastin deficiency and fragmentation. Numerical simulations using Fung-type models implied that elastic fiber degeneration and fragmentation in AD tissues reduced not only the low-stress stiffness but also the elastic stiffness with superimposed shear. The latter stiffness was modulated by the stiffening at high stress levels in tensile deformation behavior and normal-strain state under physiological loading conditions, and therefore provides further insight into wall rupture.

Estimating aortic thoracic aneurysm rupture risk using tension-strain data in physiological pressure range: an in vitro study

Previous studies have shown that the rupture properties of an ascending thoracic aortic aneurysm (ATAA) are strongly correlated with the pre-rupture response features. In this work, we present a two-step machine learning method to predict where the rupture is likely to occur in ATAA and what safety reserve the structure may have. The study was carried out using ATAA specimens from 15 patients who underwent surgical intervention. Through inflation test, full-field deformation data and post-rupture images were collected, from which the wall tension and surface strain distributions were computed. The tension-strain data in the pressure range of 9-18 kPa were fitted to a third-order polynomial to characterize the response properties. It is hypothesized that the region where rupture is prone to initiate is associated with a high level of tension buildup. A machine learning method is devised to predict the peak risk region. The predicted regions were found to match the actual rupture sites in 13 samples out of the total 15. In the second step, another machine learning model is utilized to predict the tissue's rupture strength in the peak risk region. Results suggest that the ATAA rupture risk can be reasonably predicted using tension-strain response in the physiological range. This may open a pathway for evaluating the ATAA rupture propensity using information of in vivo response.

Prediction of local strength of ascending thoracic aortic aneurysms

Knowledges of both local stress and strength are needed for a reliable evaluation of the rupture risk for ascending thoracic aortic aneurysm (ATAA). In this study, machine learning is applied to predict the local strength of ATAA tissues based on tension-strain data collected through in vitro inflation tests on tissue samples. Inputs to machine learning models are tension, strain, slope, and curvature values at two points on the low strain region of the tension-strain curve. The models are trained using data from locations where the tissue ruptured, and subsequently applied to data from intact sites to predict the local rupture strength. The predicted strengths are compared with the known strength at rupture sites as well as the highest tension the tissues experienced at the intact sites. A local rupture index, which is the ratio of the end tension to the predicted rupture strength, is computed. The 'hot spots' of the rupture index are found to match the rupture sites better than those of the peak tension. The study suggests that the strength of ATAA tissue could be reliably predicted from early phase response features defined in this work.

A Pointwise Method for Identifying Biomechanical Heterogeneity of the Human Gallbladder

Identifying the heterogeneous biomechanical property of human gallbladder (GB) walls from non-invasive measurements can have clinical significance in patient-specific modeling and acalculous biliary pain diagnosis. In this article, a pointwise method was proposed to measure the heterogeneity of ten samples of human GB during refilling. Three different points, two on the equator of GB body 90° apart and one on the apex of GB fundus, were chosen to represent the typical regions of interest. The stretches at these points were estimated from ultrasound images of the GB during the bile emptying phase based on an analytical model. The model was validated against the experimental data of a lamb GB. The material parameters at the different points were determined inversely by making use of a structure-based anisotropic constitutive model. This anisotropic model yielded much better accuracy when compared to a number of phenomenologically-based constitutive laws, as demonstrated by its significantly reduced least-square errors in stress curve fitting. The results confirmed that the human GB wall material was heterogeneous, particularly toward the apex region. Our study also suggested that non-uniform wall thickness of the GB was important in determining the material parameters, in particular, on the parameters associated with the properties of the matrix and the longitudinal fibers—the difference could be as large as 20–30% compared to that of the uniform thickness model.

Characteristics of thoracic aortic aneurysm rupture in vitro

Ascending thoracic aortic aneurysms (ATAAs) are focal dilatations in the aorta that are prone to rupture or dissection. To accurately evaluate the rupture risk, one must know the local mechanical conditions at the rupture site and understand how rupture is triggered in a layered fibrous media. A challenge facing experimental studies of ATAA rupture is that the ATAA tissue is highly heterogeneous; experimental protocols that operate under the premise of tissue homogeneity will have difficulty delineating the location conditions. In this work, we employed a previously established pointwise identification method to characterize wall stress, strain, and property distributions to a sub-millimeter resolution. Based on the acquired field data, we obtained the local mechanical properties at the rupture site in nine ATAA tissue samples. The rupture stress, ultimate strain, energy density, and the toughness of the tested samples were also reported. Our results show that the direction of the rupture is aligned with the direction of maximum stiffness, indicating that higher stiffness is not always related to higher strength. It was also found that the rupture generally occurs at a location of highest stored energy. As a higher stiffness and higher strain energy indicate a larger recruitment of collagen fibers in the tissue at the location and along the direction of rupture, the recruitment of collagen fibers in the deformation of the tissue is probably essential in ATAA rupture.

STATEMENT OF SIGNIFICANCE

A major challenge in the experimental study of aneurysm properties is that the tissues are heterogeneous. When the specimens are not reasonably homogeneous, traditional tests that work under the premise of tissue homogeneity cannot reliably delineate the local conditions at the rupture site. In this work, we investigated the local characteristics of rupture of human ascending aortic aneurysm tissue. We identified the stress, strain, and elastic properties to a submillimeter resolution. Based on the field values, we determined the local conditions - elastic properties, direction of maximum stiffness, stress, strain, energy consumption - at the rupture site. It was found that the tissues consistently cleave in the direction of the maximum stiffness, and generally occurs at the location of highest energy. Since a higher stiffness and higher strain energy indicate a larger recruitment of collagen fibers in the tissue at the location and along the direction of rupture, the work suggests that the recruitment of collagen fibers in the deformation of the tissue is probably essential in aneurysm rupture.

Digital image correlation-based point-wise inverse characterization of heterogeneous material properties of gallbladder in vitro

Continuing advances in mechanobiology reveal more and more that many cell types, especially those responsible for establishing, maintaining, remodelling or repairing extracellular matrix, are extremely sensitive to their local mechanical environment. Indeed, it appears that they fashion the extracellular matrix so as to promote a ‘mechanical homeostasis’. A natural corollary, therefore, is that cells will try to offset complexities in geometry and applied loads with heterogeneous material properties in order to render their local environment mechanobiologically favourable. There is a pressing need, therefore, for hybrid experimental–computational methods in biomechanics that can quantify such heterogeneities. In this paper, we present an approach that combines experimental information on full-field surface geometry and deformations with a membrane-based point-wise inverse method to infer full-field mechanical properties for soft tissues that exhibit nonlinear behaviours under finite deformations. To illustrate the potential utility of this new approach, we present the first quantification of regional mechanical properties of an excised but intact gallbladder, a thin-walled, sac-like organ that plays a fundamental role in normal digestion. The gallbladder was inflated to a maximum local stretch of 120% in eight pressure increments; at each pressure pause, the entire three-dimensional surface was optically extracted, and from which the surface strains were computed. Wall stresses in each state were predicted from the deformed geometry and the applied pressure using an inverse elastostatic method. The elastic properties of the gallbladder tissue were then characterized locally using point-wise stress–strain data. The gallbladder was found to be highly heterogeneous, with drastically different stiffness between the hepatic and the serosal sides. The identified material model was validated through forward finite-element analysis; both the configurations and the local stress–strain patterns were well reproduced.

In vivo determination of elastic properties of the human aorta based on 4D ultrasound data

Computational analysis of the biomechanics of the vascular system aims at a better understanding of its physiology and pathophysiology. To be of clinical use, however, these models and thus their predictions, have to be patient specific regarding geometry, boundary conditions and material. In this paper we present an approach to determine individual material properties of human aortae based on a new type of in vivo full field displacement data acquired by dimensional time resolved three dimensional ultrasound (4D-US) imaging. We developed a nested iterative Finite Element Updating method to solve two coupled inverse problems: The prestrains that are present in the imaged diastolic configuration of the aortic wall are determined. The solution of this problem is integrated in an iterative method to identify the nonlinear hyperelastic anisotropic material response of the aorta to physiologic deformation states. The method was applied to 4D-US data sets of the abdominal aorta of five healthy volunteers and verified by a numerical experiment. This non-invasive in vivo technique can be regarded as a first step to determine patient individual material properties of the human aorta.

Physical factors effecting cerebral aneurysm pathophysiology

Many factors that are either blood-, wall-, or hemodynamics-borne have been associated with the initiation, growth, and rupture of intracranial aneurysms. The distribution of cerebral aneurysms around the bifurcations of the circle of Willis has provided the impetus for numerous studies trying to link hemodynamic factors (flow impingement, pressure, and/or wall shear stress) to aneurysm pathophysiology. The focus of this review is to provide a broad overview of such hemodynamic associations as well as the subsumed aspects of vascular anatomy and wall structure. Hemodynamic factors seem to be correlated to the distribution of aneurysms on the intracranial arterial tree and complex, slow flow patterns seem to be associated with aneurysm growth and rupture. However, both the prevalence of aneurysms in the general population and the incidence of ruptures in the aneurysm population are extremely low. This suggests that hemodynamic factors and purely mechanical explanations by themselves may serve as necessary, but never as necessary and sufficient conditions of this disease's causation. The ultimate cause is not yet known, but it is likely an additive or multiplicative effect of a handful of biochemical and biomechanical factors.

On the prospect of patient-specific biomechanics without patient-specific properties of tissues

This paper presents main theses of two keynote lectures delivered at Euromech Colloquium "Advanced experimental approaches and inverse problems in tissue biomechanics" held in Saint Etienne in June 2012. We are witnessing an advent of patient-specific biomechanics that will bring in the future personalized treatments to sufferers all over the world. It is the current task of biomechanists to devise methods for clinically-relevant patient-specific modeling. One of the obstacles standing before the biomechanics community is the difficulty in obtaining patient-specific properties of tissues to be used in biomechanical models. We postulate that focusing on reformulating computational mechanics problems in such a way that the results are weakly sensitive to the variation in mechanical properties of simulated continua is more likely to bear fruit in near future. We consider two types of problems: (i) displacement-zero traction problems whose solutions in displacements are weakly sensitive to mechanical properties of the considered continuum; and (ii) problems that are approximately statically determinate and therefore their solutions in stresses are also weakly sensitive to mechanical properties of constituents. We demonstrate that the kinematically loaded biomechanical models of the first type are applicable in the field of image-guided surgery where the current, intraoperative configuration of a soft organ is of critical importance. We show that sac-like membranes, which are prototypes of many thin-walled biological organs, are approximately statically determinate and therefore useful solutions for wall stress can be obtained without the knowledge of the wall's properties. We demonstrate the clinical applicability and effectiveness of the proposed methods using examples from modeling neurosurgery and intracranial aneurysms.

A shell-based inverse approach of stress analysis in intracranial aneurysms

Predicting pressure induced wall stress in intracranial aneurysms continues to be of interest for aneurysm safety assessment. In quasi-static analysis, there are two distinct approaches that one may take, the forward approach and the inverse approach. The inverse approach starts from a deformed configuration and thus is naturally suited to image-based, patient-specific analysis. Early studies by the authors' team suggested that the inverse approach, in the context of estimating the wall stress in cerebral aneurysms, depends weakly on the material description. In this article, we present a population study to further demonstrate the inverse method, in particular, the remarkable feature of insensitivity to material properties. Twenty-six aneurysm models derived from patient-specific images were employed in the study. Wall stresses were predicted in both the inverse and forward approaches using three material models. Results showed that, while forward computation yielded up to ~100% stress difference between some materials, the inverse solutions stayed close across materials. The inverse method, in addition to being methodologically accurate in dealing with pre-deformations, has the added convenience of insensitivity to uncertainties in wall tissue properties. New insight into the stress-geometry relation was also discussed.