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  • 1. Ambrosi, D.
    et al.
    Ateshian, G. A.
    Arruda, E. M.
    Cowin, S. C.
    Dumais, J.
    Goriely, A.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Humphrey, J. D.
    Kemkemer, R.
    Kuhl, E.
    Olberding, J. E.
    Taber, L. A.
    Garikipati, K.
    Perspectives on biological growth and remodeling2011In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 59, no 4, p. 863-883Article, review/survey (Refereed)
    Abstract [en]

    The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

  • 2. Auer, M.
    et al.
    Regitnig, P.
    Stollberger, R.
    Ebner, F.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    A methodology to study the morphologic changes in lesions during in vitro angioplasty using MRI and image processing2008In: Medical Image Analysis, ISSN 1361-8415, E-ISSN 1361-8423, Vol. 12, no 2, p. 163-173Article in journal (Refereed)
    Abstract [en]

    The assessment of morphologic changes in atherosclerotic lesions during interventional procedures such as transluminal balloon angioplasty is an issue of highest clinical importance. We propose a methodology that allows realistic 3D morphomechanical modeling of the vessel, the plaque and the lumen at different stages of in vitro angioplasty. We elaborate on a novel device designed to guide angioplasty under controlled experimental conditions. The device allows to reproduce in vivo conditions as good as possible, i.e. axial in situ pre-stretch, 100 mmHg intraluminal pressure, 37 degrees C Tyrode solution, balloon inflation without external constraints using a high-pressure syringe and contrast medium. With a standard 1.5 T MR-system we accomplish multi-spectral images at different stages of the angioplasty experiment. After MR image acquisition the specimen is used for histopathological analysis and biomechanical tests. A segmentation process is used to generate NURBS-based 3D geometric models of the individual vessel and plaque components at different balloon pressures. Tissue components are segmented automatically using generalized gradient vector flow active contours. We investigated 10 human femoral arteries. The effects of balloon compression on the individual artery components is particularly described for two obstructed arteries with an intact collagenous cap, a pronounced lipid pool and with calcification. In both arteries we observe a significant increase in lumen area after angioplasty. Dissection between intima and media and reduction of the lipid pool are primary mechanisms of dilatation. This methodology provides a basis for studying plaque biomechanics under supra-physiological loading conditions. It has the potential to improve and validate finite element models of atherosclerotic plaques which may allow a better prediction of angioplasty procedures.

  • 3. Auer, M.
    et al.
    Stollberger, R.
    Regitnig, P.
    Ebner, F.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    3-D reconstruction of tissue components for atherosclerotic human arteries using ex vivo high-resolution MRI2006In: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 25, no 3, p. 345-357Article in journal (Refereed)
    Abstract [en]

    Automatic computer-based methods are well suited for the image analysis of the different components in atherosclerotic plaques. Although several groups work on such analysis some of the methods used are oversimplified and require improvements when used within a computational framework for predicting meaningful stress and strain distributions in the heterogeneous arterial wall under various loading conditions. Based on high-resolution magnetic resonance imaging of excised atherosclerotic human arteries and a series of two-dimensional (2-D) contours we present a segmentation tool that permits a three-dimensional (3-D) reconstruction of the most important tissue components of atherosclerotic arteries. The underlying principle of the proposed approach is a model-based snake algorithm for identifying 2-D contours, which uses information about the plaque composition and geometric data of the tissue layers. Validation of the computer-generated tissue boundaries is performed with 100 MR images, which are compared with the results of a manual segmentation performed by four experts. Based on the Hausdorff distance and the average distance for computer-to-expert differences and the interexpert differences for the outer boundary of the adventitia, the adventitia-media, media-intima, intima-lumen and calcification boundaries are less than 1 pixel (0.234 mm). The percentage statistic shows similar results to the modified Williams index in terms of accuracy. Except for the identification of lipid-rich regions the proposed algorithm is automatic. The nonuniform rational B-spline-based computer-generated 3-D models of the individual tissue components provide a basis for clinical and computational analysis.

  • 4. Auer, M.
    et al.
    Stollberger, R.
    Regitnig, P.
    Ebner, F.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    In Vitro Angioplasty of Atherosclerotic Human Femoral Arteries: Analysis of the Geometrical Changes in the Individual Tissues Using MRI and Image Processing2010In: Annals of Biomedical Engineering, ISSN 0090-6964, E-ISSN 1573-9686, Vol. 38, no 4, p. 1276-1287Article in journal (Refereed)
    Abstract [en]

    Existing atherosclerotic plaque imaging techniques such as intravascular ultrasound, multidetector computed tomography, optical coherence tomography, and high-resolution magnetic resonance imaging (hrMRI) require computerized methods to separate and analyze the plaque morphology. In this work, we perform in vitro balloon angioplasty experiments with 10 human femoral arteries using hrMRI and image processing. The vessel segments contain low-grade to high-grade lesions with very different plaque compositions. The experiments are designed to mimic the in vivo situation. We use a semi-automatic image processing tool to extract the three-dimensional (3D) geometries of the tissue components at four characteristic stages of the angioplasty procedure. The obtained geometries are then used to determine geometrical and mechanical indices in order to characterize, classify, and analyze the atherosclerotic plaques by their specific geometrical changes. During inflation, three vessels ruptured via helical crack propagation. The adventitia, media, and intima did not preserve their area/volume during inflation; the area changes of the lipid pool during inflation were significant. The characterization of changes in individual 3D tissue geometries, together with tissue-specific mechanical properties, may serve as a basis for refined finite element (FE) modeling, which is key to better understand stress evolution in various atherosclerotic plaque configurations.

  • 5. Balzani, D.
    et al.
    Holzapfel, Gerhard
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics. Graz University of Technology, Institute of Biomechanics, Center of Biomedical Engineering.
    Brinkhues, S.
    Modeling of damage in soft biological tissues and application to arterial walls2011In: Computational Plasticity XI - Fundamentals and Applications, 2011, p. 764-775Conference paper (Refereed)
    Abstract [en]

    A new material model is proposed for the description of stress-softening observed in cyclic tension tests performed on soft biological tissues. The modeling framework is based on the concept of internal variables introducing a scalar-valued variable for the representation of fiber damage. Remanent strains in fiber direction can be represented as a result of microscopic damage of the fiber crosslinks. Particular internal variables are defined able to capture the nature of soft biological tissues that no damage occurs in the physiological loading domain. A specific model is adjusted to experimental data taking into account the supra-physiological loading regime. For the description of the physiological domain polyconvex functions are used which also take into account fiber dispersion in a phenomenological approach. The applicability of the model in numerical simulations is shown by a representative example where the damage distribution in an arterial cross-section is analyzed.

  • 6. Balzani, D.
    et al.
    Neff, P.
    Schroeder, J.
    Holzapfel, Gerhard A.
    A polyconvex framework for soft biological tissues. Adjustment to experimental data2006In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 43, no 20, p. 6052-6070Article in journal (Refereed)
    Abstract [en]

    The main goal of this contribution is to provide a simple method for constructing transversely isotropic polyconvex functions suitable for the description of biological soft tissues. The advantage of our approach is that only a few parameters are necessary to approximate a variety of stress-strain curves and to satisfy the condition of a stress-free reference configuration a priori in the framework of polyconvexity. The proposed polyconvex stored energies are embedded into the concept of structural tensors and the representation theorems for isotropic tensor functions are utilized. As an example, the medial layer of a human abdominal aorta is investigated, modeled by some of the proposed polyconvex functions and compared with experimental data. Hereby, the economic fitting to experimental data, and hence the easy handling of the functions is shown.

  • 7. Balzani, Daniel
    et al.
    Brinkhues, Sarah
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Constitutive framework for the modeling of damage in collagenous soft tissues with application to arterial walls2012In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 213, p. 139-151Article in journal (Refereed)
    Abstract [en]

    In this paper a new material model is proposed for the description of stress-softening observed in cyclic tension tests of collagenous soft tissues such as arterial walls, for applied loads beyond the physiological level. The modeling framework makes use of terms known from continuum damage mechanics and the concept of internal variables introducing a scalar-valued variable for the representation of fiber damage. A principle is given for the construction of damage models able to reflect remanent strains as a result of microscopic damage in the reinforcing collagen fiber families. Particular internal variables are defined able to capture the nature of arterial tissues that no damage occurs in the physiological loading domain. By application of this principle, specific models are derived and fitted to experimental data. Finally, their applicability in numerical simulations is shown by some representative examples where the damage distribution in arterial cross-sections is analyzed.

  • 8. Bauer, M.
    et al.
    Mazza, E.
    Nava, A.
    Zeck, W.
    Eder, M.
    Bajka, M.
    Cacho, F.
    Lang, U.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.). Graz University of Technology, Austria.
    In vivo characterization of the mechanics of human uterine cervices2007In: Reproductive Biomechanics, Blackwell Publishing, 2007, p. 186-202Conference paper (Refereed)
    Abstract [en]

    The uterine cervix has to provide mechanical resistance to ensure a normal development of the fetus. This is guaranteed by the composition of its extracellular matrix, which functions as a fiber-reinforced composite. At term a complex remodeling process allows the cervical canal to open for birth. This remodeling is achieved by changes in the quality and quantity of collagen fibers and ground substance and their interplay, which influences the biomechanical behavior of the cervix but also contributes to pathologic conditions such as cervical incompetence (CI). We start by reviewing the anatomy and histological composition of the human cervix, and discuss its physiologic function and pathologic condition in pregnancy including biomechanical aspects. Established diagnostic methods on the cervix (palpation, endovaginal ultrasound) used in clinics as well as methods for assessment of cervical consistency (light-induced fluorescence, electrical current, and impedance) are discussed. We show the first clinical application of an aspiration device, which allows in vivo testing of the biomechanical properties of the cervix with the aim to establish the physiological biomechanical changes throughout gestation and to detect pregnant women at risk for CI. In a pilot study on nonpregnant cervices before and after hysterectomy we found no considerable difference in the biomechanical response between in vivo and ex vivo. An outlook on further clinical applications during pregnancy is presented.

  • 9. Bauer, Margit
    et al.
    Mazza, Edoardo
    Jabareen, Mahmood
    Sultan, Leila
    Bajka, Michael
    Lang, Uwe
    Zimmermann, Roland
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Assessment of the in vivo biomechanical properties of the human uterine cervix in pregnancy using the aspiration test A feasibility study2009In: European Journal of Obstetrics, Gynecology, and Reproductive Biology, ISSN 0301-2115, E-ISSN 1872-7654, Vol. 144, p. S77-S81Article in journal (Refereed)
    Abstract [en]

    Objective: To date no diagnostic tool is yet available to objectively assess the in vivo biomechanical properties of the uterine cervix during gestation. Methods: We show the first clinical application of an aspiration device to assess the in vivo biomechanical properties of the cervix in pregnancy with the aim to describe the physiological biomechanical changes throughout gestation in order to eventually detect pregnant women at risk for cervical insufficiency (CI). Results: Out of 15 aspiration measurements, 12 produced valid results. The stiffness values were in the range between 0.013 and 0.068 bar/mm. The results showed a good reproducibility of the aspiration test. In our previous test series on non-pregnant cervices our repetitive measurements showed a standard deviation of > 20% compared to <+/- 10% to our data on pregnant cervices. Stiffness values are decreasing with gestational age which indicates a progressive softening of cervical tissue towards the end of pregnancy. Three pregnant women had two subsequent measurements within a time interval of four weeks. Decreasing stiffness values in the range of 20% were recorded. Discussion: This preliminary study on the clinical practicability of aspiration tests showed promising results in terms of reproducibility (reliability) and clinical use (feasibility). Ongoing studies will provide further insights on its usefulness in clinical practice and in the detection of substantial changes of the cervix in pregnancy indicative for threatened preterm birth or cervical insufficiency.

  • 10. Bock, N.
    et al.
    Holzapfel, Gerhard A.
    A new two-point deformation tensor and its relation to the classical kinematical framework and the stress concept2004In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 41, no 26, p. 7459-7469Article in journal (Refereed)
    Abstract [en]

    Starting from the issue of what is the correct form for a Legendre transformation of the strain energy in terms of Eulerian and two-point tensor variables we introduce a new two-point deformation tensor, namely H = (F-F-T)/2, as a possible deformation measure involving points in two distinct configurations. The Lie derivative of H is work conjugate to the first Piola-Kirchhoff stress tensor P. The deformation measure H leads to straightforward manipulations within a two-point setting such as the derivation of the virtual work equation and its linearization required for finite element implementation. The manipulations are analogous to those used for the Lagrangian and Eulerian frameworks. It is also shown that the Legendre transformation in terms of two-point tensors and spatial tensors require Lie derivatives. As an illustrative example we propose a simple Saint Venant-Kirchhoff type of a strain-energy function in terms of H. The constitutive model leads to physically meaningful results also for the large compressive strain domain, which is not the case for the classical Saint Venant-Kirchhoff material.

  • 11. Bustamante, R.
    et al.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Methods to compute 3D residual stress distributions in hyperelastic tubes with application to arterial walls2010In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 48, no 11, p. 1066-1082Article in journal (Refereed)
    Abstract [en]

    In this paper the problem of modeling three-dimensional residual stress distributions in hyperelastic tubes is addressed. First, the problem of a radially opened straight and bent tube, where the opening angle depends on the axial position, is explored with the semi-inverse method. As a result a rather complicated system of nonlinear partial differential equations is achieved which is difficult to solve. Second, a different approximate method considers the tube as a composition of two, three, four or more rings in the axial direction. Also here the opening angle of the tube depends on the axial position. Some numerical solutions for the stress components in the radial, circumferential and axial directions are analyzed in more detail. Third, the tube wall is divided into a number of radial layers, with different mechanical properties, and an approximate method to treat that problems is presented. It is emphasized that the proposed approach can also be used to compute 3D residual stress distributions in arterial walls. A final conclusion points to possible future research directions.

  • 12. Böl, M.
    et al.
    Gunawan, F. E.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.). Graz University of Technology, Austria.
    3D Finite element analysis of smooth muscle contraction considering calcium diffusion2009In: Computational plasticity X: fundamentals and applications, 2009Conference paper (Refereed)
    Abstract [en]

    Recently a model of the mechanochemical response of smooth muscle cells has been developed by Murtada et al. [1]. The model is based on a strain-energy function incorporating only a few physical-based material parameters. The main focus of their approach is on the modeling of the response of the cross-bridge interactions and on the related force generation. Based on a one-dimensional analysis the performance of the modeling approach has been shown by comparing to experimental data of smooth muscle cells. The results of the combined coupled model are broadly consistent with isometric and quick-release experiments on smooth muscle tissue. In the present study the aforementioned model has been implemented into a finite element program in order to solve more complex boundary-value problems. In doing so we present here a first three-dimensional simulation of the Fick's law-driven diffusion of calcium into a cell as well as the related smooth muscle contraction.

  • 13. Cacho, F.
    et al.
    Elbischger, P. J.
    Rodriguez, J. F.
    Doblare, M.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    A constitutive model for fibrous tissues considering collagen fiber crimp2007In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 42, no 2, p. 391-402Article in journal (Refereed)
    Abstract [en]

    A micromechanically based constitutive model for fibrous tissues is presented. The model considers the randomly crimped morphology of individual collagen fibers, a morphology typically seen in photomicrographs of tissue samples. It describes the relationship between the fiber endpoints and its arc-length in terms of a measurable quantity, which can be estimated from image data. The collective mechanical behavior of collagen fibers is presented in terms of an explicit expression for the strain-energy function, where a fiber-specific random variable is approximated by a Beta distribution. The model-related stress and elasticity tensors are provided. Two representative numerical examples are analyzed with the aim of demonstrating the peculiar mechanism of the constitutive model and quantifying the effect of parameter changes on the mechanical response. In particular, a fibrous tissue, assumed to be (nearly) incompressible, is subject to a uniaxial extension along the fiber direction, and, separately, to pure shear. It is shown that the fiber crimp model can reproduce several of the expected characteristics of fibrous tissues.

  • 14. Cacho, Fernando
    et al.
    Doblare, Manuel
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    A procedure to simulate coronary artery bypass graft surgery2007In: Medical and Biological Engineering and Computing, ISSN 0140-0118, E-ISSN 1741-0444, Vol. 45, no 9, p. 819-827Article in journal (Refereed)
    Abstract [en]

    In coronary artery bypass graft (CABG) surgery the involved tissues are overstretched, which may lead to intimal hyperplasia and graft failure. We propose a computational methodology for the simulation of traditional CABG surgery, and analyze the effect of two clinically relevant parameters on the artery and graft responses, i.e., incision length and insertion angle for a given graft diameter. The computational structural analyses are based on actual three-dimensional vessel dimensions of a human coronary artery and a human saphenous vein. The analyses consider the structure of the end-to-side anastomosis, the residual stresses and the typical anisotropic and nonlinear vessel behaviors. The coronary artery is modeled as a three-layer thick-walled tube. The finite element method is employed to predict deformation and stress distribution at various stages of CABG surgery. Small variations of the arterial incision have relatively big effects on the size of the arterial opening, which depends solely on the residual stress state. The incision length has a critical influence on the graft shape and the stress in the graft wall. Stresses at the heel region are higher than those at the toe region. The changes in the mechanical environment are severe along all transitions between the venous tissue and the host artery. Particular stress concentrations occur at the incision ends. The proposed computational methodology may be useful in designing a coronary anastomotic device for reducing surgical trauma. It may improve the quantitative knowledge of vessel diseases and serve as a tool for virtual planning of vascular surgery.

  • 15. Eberlein, R.
    et al.
    Holzapfel, Gerhard A.
    Frohlich, M.
    Multi-segment FEA of the human lumbar spine including the heterogeneity of the annulus fibrosus2004In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 34, no 2, p. 147-163Article in journal (Refereed)
    Abstract [en]

    This study pursues the numerical validation of human lumbar spine segments. By means of the finite element (FE) method, computational analyses are carried out of various load cases. In particular Flexion-Extension, Lateral Bending and Axial Torque are considered. By means of a literature review the underlying constitutive data is verified. In this context, the heterogeneity of the annulus fibrosus, the transversely isotropic stress response of the spinal ligaments and aspects of the FE discretization are particularly emphasized. The numerical results show good agreement with experimental investigations for Extension and Axial Torque for a FE model that accounts for intact human lumbar spine response. In Flexion and Lateral Bending, however, the results of the intact FE-model do not properly account for the experimental data. A good correlation for these load cases can be found by taking disc degeneration into account in the FE-model. This fact shows that tissue degeneration plays a key role in the current validation process and must be accounted for if the lumbar spine specimen is employed for spinal implant evaluation. A degenerated FE-model that represents the stage of degeneration of the specimen and fits the experimental data for all load cases could not be found in this study and warrants further work in this area.

  • 16. Eriksson, T. S. E.
    et al.
    Prassl, A. J.
    Plank, G.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Influence of myocardial fiber/sheet orientations on left ventricular mechanical contraction2013In: Mathematics and mechanics of solids, ISSN 1081-2865, E-ISSN 1741-3028, Vol. 18, no 6, p. 592-606Article in journal (Refereed)
    Abstract [en]

    At any point in space the material properties of the myocardium are characterized as orthotropic, that is, there are three mutually orthogonal axes along which both electrical and mechanical parameters differ. To investigate the role of spatial structural heterogeneity in an orthotropic material, electro-mechanically coupled models of the left ventricle (LV) were used. The implemented models differed in their arrangement of fibers and sheets in the myocardium, but were identical otherwise: (i) a generic homogeneous model, where a rule-based method was applied to assign fiber and sheet orientations, and (ii) a heterogeneous model, where the assignment of the orthotropic tissue structure was based on experimentally obtained fiber/sheet orientations. While both models resulted in pressure-volume loops and metrics of global mechanical function that were qualitatively and quantitatively similar and matched well with experimental data, the predicted deformations were strikingly different between these models, particularly with regard to torsion. Thus, the simulation results strongly suggest that heterogeneous structure properties play an important nonnegligible role in LV mechanics and, consequently, should be accounted for in computational models.

  • 17. Eriksson, T. S. E.
    et al.
    Prassl, A. J.
    Plank, G.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Modeling the dispersion in electromechanically coupled myocardium2013In: International Journal for Numerical Methods in Biomedical Engineering, ISSN 2040-7939, Vol. 29, no 11, p. 1267-1284Article in journal (Refereed)
    Abstract [en]

    We present an approach to model the dispersion of fiber and sheet orientations in the myocardium. By utilizing structure parameters, an existing orthotropic and invariant-based constitutive model developed to describe the passive behavior of the myocardium is augmented. Two dispersion parameters are fitted to experimentally observed angular dispersion data of the myocardial tissue. Computations are performed on a unit myocardium tissue cube and on a slice of the left ventricle indicating that the dispersion parameter has an effect on the myocardial deformation and stress development. The use of fiber dispersions relating to a pathological myocardium had a rather big effect. The final example represents an ellipsoidal model of the left ventricle indicating the influence of fiber and sheet dispersions upon contraction over a cardiac cycle. Although only a minor shift in the pressure-volume (PV) loops between the cases with no dispersions and with fiber and sheet dispersions for a healthy myocardium was observed, a remarkably different behavior is obtained with a fiber dispersion relating to a diseased myocardium. In future simulations, this dispersion model for myocardial tissue may advantageously be used together with models of, for example, growth and remodeling of various cardiac diseases.

  • 18.
    Eriksson, Thomas
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Kroon, Martin
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Influence of Medial Collagen Organization and Axial In Situ Stretch on Saccular Cerebral Aneurysm Growth2009In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 131, no 10Article in journal (Refereed)
    Abstract [en]

    A model for saccular cerebral aneurysm growth, proposed by Kroon and Holzapfel (2007, "A Model for Saccular Cerebral Aneurysm Growth in a Human Middle Cerebral Artery," J. Theor. Biol., 247, pp. 775-787; 2008, "Modeling of Saccular Aneurysm Growth in a Human Middle Cerebral Artery," ASME J. Biomech. Eng., 130, p. 051012), is further investigated. A human middle cerebral artery is modeled as a two-layer cylinder where the layers correspond to the media and the adventitia. The immediate loss of media in the location of the aneurysm is taken to be responsible for the initiation of the aneurysm growth. The aneurysm is regarded as a development of the adventitia, which is composed of several distinct layers of collagen fibers perfectly aligned in specified directions. The collagen fibers are the only load-bearing constituent in the aneurysm wall; their production and degradation depend on the stretch of the wall and are responsible for the aneurysm growth. The anisotropy of the surrounding media was modeled using the strain-energy function proposed by Holzapfel et al. (2000, "A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models," J. Elast., 61, pp. 1-48), which is valid for an elastic material with two families of fibers. It was shown that the inclusion of fibers in the media reduced the maximum principal Cauchy stress and the maximum shear stress in the aneurysm wall. The thickness increase in the aneurysm wall due to material growth was also decreased. Varying the fiber angle in the media from a circumferential direction to a deviation of 10 deg from the circumferential direction did, however, only show a little effect. Altering the axial in situ stretch of the artery had a much larger effect in terms of the steady-state shape of the aneurysm and the resulting stresses in the aneurysm wall. The peak values of the maximum principal stress and the thickness increase both became significantly higher for larger axial stretches. [DOI: 10.1115/1.3200911]

  • 19. Famaey, Nele
    et al.
    Sommer, Gerhard
    Vander Sloten, Jos
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Arterial clamping: Finite element simulation and in vivo validation2012In: Journal of The Mechanical Behavior of Biomedical Materials, ISSN 1751-6161, E-ISSN 1878-0180, Vol. 12, p. 107-118Article in journal (Refereed)
    Abstract [en]

    Commonly used techniques in cardiovascular interventions such as arterial clamping always entail a certain degree of unavoidable iatrogenic tissue damage. Therefore, studies have been directed towards the decrease of undesired intraoperative trauma, for example, through the design of less traumatic surgical instruments. Obviously, the effectiveness of new clamp designs and techniques depends on how well damage mechanisms are understood and how accurate thresholds for safe tissue loading can be set. This information can in part be derived from reliable finite element simulations. This study is the first to describe a finite element simulation of the clamping of a rat abdominal aorta with occlusion and in vivo validation. Material nonlinearity, large deformations, contact interactions and residual strains are hereby taken into account. The mechanical parameters of the model are derived from inflation experiments. The effect of the residual strains, different clamp geometries as well as the effect of variations in material properties are studied. In all simulations, stress concentrations in different regions of the tissue are noticed, especially for a corrugated clamp design. This shows the importance of finite element modeling in understanding the relation between mechanical loading and damage mechanisms. The inclusion of residual strains has its effect not only in the physiological loading regime, but also during clamping. Just as in the physiologic regime, it lowers the stress gradients through the wall thickness. Varying the material properties with the measured standard deviation between specimens leads to an average change of +/- 17% in the maximum and minimum principal stresses. Finally, the model is validated with an in vivo clamping experiment on a Wistar rat in which the clamping force was measured, showing good correspondence with the modeled clamping force.

  • 20. Franceschini, G.
    et al.
    Bigoni, D.
    Regitnig, P.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Brain tissue deforms similarly to filled elastomers and follows consolidation theory2006In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 54, no 12, p. 2592-2620Article in journal (Refereed)
    Abstract [en]

    Slow, large deformations of human brain tissue-accompanying cranial vault deformation induced by positional plagiocephaly, occurring during hydrocephalus, and in the convolutional development-has surprisingly received scarce mechanical investigation. Since the effects of these deformations may be important, we performed a systematic series of in vitro experiments on human brain tissue, revealing the following features. (i) Under uniaxial (quasi-static), cyclic loading, brain tissue exhibits a peculiar nonlinear mechanical behaviour, exhibiting hysteresis, Mullins effect and residual strain, qualitatively similar to that observed in filled elastomers. As a consequence, the loading and unloading uniaxial curves have been found to follow the Ogden nonlinear elastic theory of rubber (and its variants to include Mullins effect and permanent strain). (ii) Loaded up to failure, the shape of the stress/strain curve qualitatively changes, evidencing softening related to local failure. (iii) Uniaxial (quasi-static) strain experiments under controlled drainage conditions provide the first direct evidence that the tissue obeys consolidation theory involving fluid migration, with properties similar to fine soils, but having much smaller volumetric compressibility. (iv) Our experimental findings also support the existence of a viscous component of the solid phase deformation. Brain tissue should, therefore, be modelled as a porous, fluid-saturated, nonlinear solid with very small volumetric (drained) compressibility.

  • 21.
    Gasser, T. Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    3D Crack propagation in unreinforced concrete. A two-step algorithm for tracking 3D crack paths2006In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 37-40, p. 5198-5219Article in journal (Refereed)
    Abstract [en]

    Tensile failure of unreinforced concrete involves progressive micro-cracking, and the related strain-softening can coalesce into geometrical discontinuities, which separate the material. Advanced mechanical theories and numerical schemes are required to efficiently and adequately represent crack propagation in 3D. In this paper we use the concept of strong discontinuities to model concrete failure. We introduce a cohesive fracture process zone, which is characterized by a transversely isotropic traction-separation law. We combine the cohesive crack concept with the partition of unity finite element method, where the finite element space is enhanced by the Heaviside function. The concept is implemented for tetrahedral elements and the failure initialization is based on the simple (non-local) Rankine criterion. For each element we assume the embedded discontinuity to be flat in the reference configuration, which leads to a non-smooth crack surfaces approximation in 3D, in general; different concepts for tracking non-planar cracks in 3D are reviewed. In addition, we propose a two-step algorithm for tracking the crack path, where a predictor step defines discontinuities according to the (non-local) failure criterion and a corrector step draws in non-local information of the existing discontinuities in order to predict a 'closed' 3D crack surface; implementation details are provided. The proposed framework is used to analyze the predictability of concrete failure by two benchmark examples, i.e. the Nooru-Moharned test, and the Brokenshire test. We compare our numerical results, which are mesh independent, with experimental data and numerical results adopted from the literature.

  • 22.
    Gasser, T. Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    A numerical framework to model 3-D fracture in bone tissue with application to failure of the proximal femur2007In: IUTAM SYMPOSIUM ON DISCRETIZATION METHODS FOR EVOLVING DISCONTINUITIES / [ed] Combescure, A; DeBorst, R; Belytschko, T, DORDRECHT: SPRINGER , 2007, Vol. 5, p. 199-211Conference paper (Refereed)
    Abstract [en]

    Bone can be regarded as a quasi-brittle material. Under excessive loading nonlinear fracture zones may occur ahead the crack tips, where, typically, cohesive mechanisms are activated. The finite element method provides a powerful tool to analyze fracture formations on a numerical basis, and to better understand failure mechanisms within complex structures. The present work aims to introduce a particular numerical framework to investigate bone failure. We combine the partition of unity finite element method with the cohesive crack concept, and a two-step predictor-corrector algorithm for tracking 3-D non-interacting crack paths. This approach renders a numerically efficient tool that is able to capture the strong discontinuity kinematics in an accurate way. The prediction of failure propagation in the proximal part of the femur under compressive load demonstrates the suitability of the proposed concept. A 3-D finite element model, which accounts for inhomogeneous fracture properties, was used for the prediction of the 3-D crack surface. The achieved computational results were compared with experimental data available in the literature.

  • 23. Gasser, T. Christian
    et al.
    Holzapfel, Gerhard A.
    A rate-independent elastoplastic constitutive model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation2002In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 29, no 05-apr, p. 340-360Article in journal (Refereed)
    Abstract [en]

    This paper presents a rate-independent elastoplastic constitutive model for (nearly) incompressible biological fiber-reinforced composite materials. The constitutive framework, based on multisurface plasticity, is suitable for describing the mechanical behavior of biological fiber-reinforced composites in finite elastic and plastic strain domains. A key point of the constitutive model is the use of slip systems, which determine the strongly anisotropic elastic and plastic behavior of biological fiber-reinforced composites. The multiplicative decomposition of the deformation gradient into elastic and plastic parts allows the introduction of an anisotropic Helmholtz free-energy function for determining the anisotropic response. We use the unconditionally stable backward-Euler method to integrate the flow rule and employ the commonly used elastic predictor/plastic corrector concept to update the plastic variables. This choice is expressed as an Eulerian vector update the Newton's type, which leads to a numerically stable and efficient material model. By means of a representative numerical simulations the performance of the proposed constitutive framework is investigated in detail.

  • 24.
    Gasser, T. Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Finite element modeling of balloon angioplasty by considering overstretch of remnant non-diseased tissues in lesions2007In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 40, no 1, p. 47-60Article in journal (Refereed)
    Abstract [en]

    The paper deals with the modeling of balloon angioplasty by considering the balloon-induced overstretch of remnant non-diseased tissues in atherosclerotic arteries. A stenotic artery is modeled as a heterogenous structure composed of adventitia, media and a model plaque, and residual stresses are considered. The constitutive models are able to capture the anisotropic elastic tissue response in addition to the inelastic phenomena associated with tissue stretches beyond the physiological domain. The inelastic model describes the experimentally-observed changes of the wall during balloon inflation, i.e. non-recoverable deformation, and tissue weakening. The contact of the artery with a balloon catheter is simulated by a point-to-surface strategy. The states of deformations and stresses within the artery before, during and after balloon inflation are computed, compared and discussed. The 3D stress states at physiological loading conditions before and after balloon inflation differ significantly, and even compressive normal stresses may occur in the media after dilation.

  • 25. Gasser, T. Christian
    et al.
    Holzapfel, Gerhard A.
    Geometrically non-linear and consistently linearized embedded strong discontinuity models for 3D problems with an application to the dissection analysis of soft biological tissues2003In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 192, no 47-48, p. 5059-5098Article in journal (Refereed)
    Abstract [en]

    Three different finite element formulations with embedded strong discontinuities are derived on the basis of the enhanced assumed strain method. According to the work by Jirasek and Zimmermann [Int. J. Numer. Methods Engrg. 50 (2001) 1269] they are referred to as statically optimal symmetric (SOS), kinematically optimal symmetric (KOS) and statically and kinematically optimal non-symmetric (SKON) formulations. The effect of the discontinuities are characterized by additional degrees of freedom on the element level. Modifications to the standard KOS and SKON formulations are proposed in order to achieve consistency with the employed type of a three-field Hu-Washizu principle under mode-I condition. Under this condition the formulation satisfies the internal compatibility at the discontinuity, i.e. the relation between the stress in the bulk material and the traction across the discontinuity surface, which is not the case for the classical KOS formulation. We propose a suitable explicit expression for a transversely isotropic traction law in form of a displacement-energy function and assume that softening phenomena in the cohesive zone are modeled by a damage law, which depends on the maximum gap displacement of the deformation path. A linearization of all quantities, which are related to the non-linear problem, leads to new closed form expressions. In particular, we focus attention on the linearization of the cohesive traction vector. The associated element residua and stiffness matrices are provided. Standard static condensation of the internal degree of freedom leads to a generalized displacement model. A comparative study of the modified formulations, carried out by means of two numerical examples, show the performance of the individual approach. We employ constant-strain tetrahedral elements with a single discontinuity embedded. Among the known stress locking phenomena associated with the SOS formulation, we recognized that the (non-symmetric) SKON formulation was not able to provide meaningful results for the dissection process of an arterial layer in three-dimensions on distorted meshes. For both numerical examples the (symmetric) KOS formulation seems to be most suitable for representing the embedded discontinuities.

  • 26. Gasser, T. Christian
    et al.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Modeling 3D crack propagation in unreinforced concrete using PUFEM2005In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 194, no 25-26, p. 2859-2896Article in journal (Refereed)
    Abstract [en]

    Concrete is a quasi-brittle material, where tensile failure involves progressive micro-cracking, debounding and other complex irreversible processes of internal damage. Strain-softening is a dominate feature and advanced numerical schemes have to be applied in order to circumvent the ill-posdness of the Boundary-Value Problem to deal with. Throughout the paper we pursue the cohesive zone approach, where initialization and coalescence of micro-cracks is lumped into the cohesive fracture process zone in terms of accumulation of damage. We develop and employ a (discrete) constitutive description of the cohesive zone, which is based on a transversely isotropic traction separation law. The model reflects an exponential decreasing traction with respect to evolving opening displacement and is based on the theory of invariants. Non-negativeness of the damage dissipation is proven and the associated numerical embedded representation is based on the Partition of Unity Finite Element Method. A consistent linearization of the method is presented, where particular attention is paid to the (cohesive) traction terms. Based on the proposed concept three numerical examples are studied in detail, i.e. a double-notched specimen under tensile loading, a four point shear test and a pull-out test of unreinforced concrete. The computational results show mesh-independency and good correlation with experimental results. © 2004 Elsevier B.V. All rights reserved.

  • 27.
    Gasser, T. Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Modeling plaque fissuring and dissection during balloon angioplasty intervention2007In: Annals of Biomedical Engineering, ISSN 0090-6964, E-ISSN 1573-9686, Vol. 35, no 5, p. 711-723Article in journal (Refereed)
    Abstract [en]

    Balloon angioplasty intervention is traumatic to arterial tissue. Fracture mechanisms such as plaque fissuring and/or dissection occur and constitute major contributions to the lumen enlargement. However, these types of mechanically-based traumatization of arterial tissue are also contributing factors to both acute procedural complications and chronic restenosis of the treatment site. We propose physical and finite element models, which are generally useable to trace fissuring and/or dissection in atherosclerotic plaques during balloon angioplasty interventions. The arterial wall is described as an anisotropic, heterogeneous, highly deformable, nearly incompressible body, whereas tissue failure is captured by a strong discontinuity kinematics and a novel cohesive zone model. The numerical implementation is based on the partition of unity finite element method and the interface element method. The later is used to link together meshes of the different tissue components. The balloon angioplasty-based failure mechanisms are numerically studied in 3D by means of an atherosclerotic-prone human external iliac artery, with a type V lesion. Image-based 3D geometry is generated and tissue-specific material properties are considered. Numerical results show that in a primary phase the plaque fissures at both shoulders of the fibrous cap and stops at the lamina elastica interna. In a secondary phase, local dissections between the intima and the media develop at the fibrous cap location with the smallest thickness. The predicted results indicate that plaque fissuring and dissection cause localized mechanical trauma, but prevent the main portion of the stenosis from high stress, and hence from continuous tissue damage.

  • 28.
    Gasser, T. Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Modeling the propagation of arterial dissection2006In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 25, no 4, p. 617-633Article in journal (Refereed)
    Abstract [en]

    Arterial dissections are frequently observed in clinical practice and during road traffic accidents. In particular, the lamellarly arrangement of elastin, collagen, in addition to smooth muscle cells in the middle arterial layer, the media, favors dissection failure. Experimental studies and related biomechanical models are rare in the literature. Finite strain kinematics is employed, and the discontinuity in the displacement field accounts for tissue separation. Dissection is regarded as a gradual process in which separation between incipient material surfaces is resisted by cohesive traction. Two variational statements together with their consistent linearizations form the basis for a finite element implementation. We combine the cohesive crack concept with the partition of unity finite element method, where nodal degrees of freedom adjacent to the discontinuity are enhanced. The developed continuum mechanical and numerical frameworks allow the analysis of the propagation of dissections within general nonlinear boundary-value problems, where the constitutive description for the continuous and the cohesive material is considered independent from each other. The continuous material is modeled as a fiber-reinforced composite with the fibers corresponding to the collagenous component which are assumed to be embedded in a non-collagenous isotropic groundmatrix. Dispersion of the collagen fiber orientation is considered in a continuum sense by one structure parameter. A novel cohesive potential per unit undeformed area is used to derive a traction separation law appropriate for the description of the mechanical properties of medial dissection. The cohesive stiffness contribution to the element stiffness matrix is explicitly derived. In particular, the dissection propagation of a rectangular strip of a human aortic media is investigated. Cohesive material properties are quantified by comparing the experimentally measured load with the computed dissection load.

  • 29.
    Gasser, T. Christian
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Physical and numerical modeling of dissection propagation in arteries caused by balloon angioplasty2005In: Proceedings of the Third IASTED International Conference on BIOMECHANICS / [ed] Hamza, MH, 2005, p. 229-233Conference paper (Refereed)
    Abstract [en]

    Arterial dissections Caused by balloon angioplasty has been implicated as a contributing factor to both acute procedural complications and chronic restenosis of the treatment site. However, no related biomechanical studies are known in the literature. The mechanical properties of the arterial wall are controlled by the rubber-like protein elastin, fibrous protein collagen and smooth muscle cells. In the media of elastic arteries these constituents are found in thin layers that are arranged in repeating lamellar units and favor dissection type of failure. The presented approach models the dissection of the media by means of strong discontinuities and the application of the theory of cohesive zones. Thereby, the dissection is regarded as a gradual process in which separation between incipient material surfaces is resisted by cohesive traction. The applied numerical frame is based on the Partition of Unity Finite Element Method (PUFEM) and has been utilized for tetrahedral elements. A tracking algorithm for 3D non-planar cracks captures the evolution of multiple non-interacting dissections. The proposed concept is applied to investigate the dissection of the media due to balloon angioplasty, where the associated material parameters are determined from failure experiments on human tissue.

  • 30. Gasser, T. Christian
    et al.
    Schulze-Bauer, C. A. J.
    Holzapfel, Gerhard A.
    A three-dimensional finite element model for arterial clamping2002In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 124, no 4, p. 355-363Article in journal (Refereed)
    Abstract [en]

    Clamp induced injuries of the arterial wall may determine the outcome of surgical procedures. Thus, it is important to investigate the underlying mechanical effects. We present a three-dimensional finite element model, which allows the study of the mechanical response of an artery-treated as a two-layer tube-during arterial clamping. The important residual stresses, which are associated with the load free configuration of the artery, are also considered. In particular, the finite element analysis of the deformation process of a clamped artery and the associated stress distribution is presented. Within the clamping area a zone of axial tensile peak-stresses was identified, which (may) cause intimal and medial injury. This is an additional injury mechanism, which clearly differs from the commonly assumed wall damage occurring due to compression between the jaws of the clamp. The proposed numerical model provides essential insights into the mechanics of the clamping procedure and the associated injury mechanisms. It allows detailed parameter studies on a virtual clamped artery, which can not be performed with other methodologies. This approach has the potential to identify the most appropriate clamps for certain types of arteries and to guide optimal clamp design.

  • 31.
    Grytsan, Andrii
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Watton, Paul N.
    Holzapfel, Gerhard A.
    Graz Univ Technol, Austria.
    A Thick-Walled Fluid-Solid-Growth Model of Abdominal Aortic Aneurysm Evolution: Application to a Patient-Specific Geometry2015In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 137, no 3, article id 031008Article in journal (Refereed)
    Abstract [en]

    We propose a novel thick-walled fluid-solid-growth (FSG) computational framework for modeling vascular disease evolution. The arterial wall is modeled as a thick-walled nonlinearly elastic cylindrical tube consisting of two layers corresponding to the mediaintima and adventitia, where each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component. Blood is modeled as a Newtonian fluid with constant density and viscosity; no slip and no-flux conditions are applied at the arterial wall. Disease progression is simulated by growth and remodeling (G&R) of the load bearing constituents of the wall. Adaptions of the natural reference configurations and mass densities of constituents are driven by deviations of mechanical stimuli from homeostatic levels. We apply the novel framework to model abdominal aortic aneurysm (AAA) evolution. Elastin degradation is initially prescribed to create a perturbation to the geometry which results in a local decrease in wall shear stress (WSS). Subsequent degradation of elastin is driven by low WSS and an aneurysm evolves as the elastin degrades and the collagen adapts. The influence of transmural G&R of constituents on the aneurysm development is analyzed. We observe that elastin and collagen strains evolve to be transmurally heterogeneous and this may facilitate the development of tortuosity. This multiphysics framework provides the basis for exploring the influence of transmural metabolic activity on the progression of vascular disease.

  • 32.
    Grytsan, Andrii
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Watton, Paul N.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    A thick-walled fluid–solid–growth model of abdominal aortic aneurysm evolution: Application to a patient-specific geometry2014Report (Other academic)
    Abstract [en]

    We propose a model for abdominal aortic aneurysms that considers the wall (solid), the blood (fluid) and the wall growth within a three-dimensional finite element framework. The arterial wall is considered as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media-intima and adventitia, where each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component. The blood is modeled as a Newtonian fluid with constant density and viscosity; no slip and no-flux conditions are applied at the arterial wall. The metabolic activity in the arterial wall is reflected by elastin degradation which is coupled with the level of wall shear stress, while the collagen fiber network is continuously remodeled in the artery such that the collagen fiber strain tends towards a homeostatic strain. The computational framework consists of a structural FE-solver (CMISS), a fluid solver using a finite volume formulation and additional routines which pass the aneurysm geometry to the fluid solver and feeds CMISS with the information on the blood flow conditions. One illustrative patient-specific geometry of an abdominal aortic wall is discretized with hexahedral finite elements and the fluid domain is generated by an unstructured tetrahedral mesh with prism layers lining the boundary. The evolution of wall shear stress and elastin degradation is investigated over a time period of 10 years; the influence of transmurally non-uniform elastin degradation is analyzed. The results show that both the elastin and the collagen strains can become transmurally non-uniform during the aneurysm development. This effect cannot be captured by membrane formulations. The proposed methodology provides a realistic basis to further explore the development of patient-specific aneurysmal disease.

  • 33. Hariton, I.
    et al.
    deBotton, G.
    Gasser, T. Christian
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Stress-driven collagen fiber remodeling in arterial walls2007In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 6, no 3, p. 163-175Article in journal (Refereed)
    Abstract [en]

    A stress-driven model for the relation between the collagen morphology and the loading conditions in arterial walls is proposed. We assume that the two families of collagen fibers in arterial walls are aligned along preferred directions, located between the directions of the two maximal principal stresses. For the determination of these directions an iterative finite element based procedure is developed. As an example the remodeling of a section of a human common carotid artery is simulated. We find that the predicted fiber morphology correlates well with experimental observations. Interesting outcomes of the model including local shear minimization and the possibility of axial compressions due to high blood pressure are revealed and discussed.

  • 34.
    Holzapfel, Gerhard A.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Collagen in arterial walls: Biomechanical aspects2008In: Collagen: Structure and Mechanics, Springer-Verlag New York, 2008, p. 285-324Chapter in book (Other academic)
    Abstract [en]

    This chapter is written with an emphasis on the biomechanical role of collagen in normal and diseased arterial walls, its structural quantification and its consideration in material models including phenomena such as growth and remodeling. Collagen is the ubiquitous load-bearing and reinforcing element in arterial walls and thus forms an important structural basis. The structural arrangement of collagen leads to the characteristic anisotropic behavior of the arterial wall and its respective layers. The organization of collagen fibers, and the tension within, maintains the function, integrity and strength of arteries. This chapter starts by reviewing the structure of the arterial wall and the biomechanical properties of the individual wall layers. Subsequently, structural quantifications of the collagen fabric are discussed with focus on polarized light microscopy, small-angle X-ray scattering and computer vision analysis. A basic building block for soft collagenous tissues in which the material is reinforced by one family of collagen fibers is next presented. On this basis, a structural model for arteries with an ideal alignment of collagen fibers is reviewed, and subsequently extended to consider collagen crimping and the dispersion of collagen fiber orientations. In order to capture structural modifications such as collagen reorientation, phenomenologically based microstructural and continuum models are presented which consider stress-modulated collagen remodeling. Finally, a constitutive model in which continuous remodeling of collagen is responsible for the growth of saccular cerebral aneurysms is outlined. All of the provided models have been implemented in finite element codes, and have proven to be efficient in the computational analysis of clinically relevant problems. This chapter is by no means complete, but it might help to grasp the most important biomechanical aspects of collagen in arterial tissues, and may serve as the basis for a more intense study of this fascinating topic

  • 35.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.). Graz University of Technology, Austria .
    Computational mechanics of multi-layered collagenous soft tissues: State of the art and challenges ahead2009In: Computational Plasticity X - Fundamentals and Applications, 2009Conference paper (Refereed)
    Abstract [en]

    Accurate modeling and analysis of collagenous soft tissues is key in the field of biomechanics. This contribution describes the structural continuum framework and provides two applications.

  • 36.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Similarities between soft biological tissues and rubberlike materials2005In: Constitutive Models for Rubber IV: Proceedings of the 4th European Conference for Constitutive Models for Rubber, ECCMR 2005, 2005, p. 607-617Conference paper (Refereed)
    Abstract [en]

    Several scientists have drawn attention to similarities between soft biological tissues and rubberlike materials. This dates back to Roy (1880) in the context of arterial wall mechanics and Karrer (1933) in respect of muscle mechanics. Both soft tissues and rubberlike materials consist of three-dimensional networks of macromolecules held together by covalent and van der Waals bonds. An underlying concept makes use of the idea of expressing the number of conformations that a chain molecule can assume as an 'entropic effect' (leading to entropic elasticity). As a result, the associated thermomechanical behavior of the macromolecules is significantly different from that of, e.g., metals for which an ordered collection of atoms is held together in a lattice structure by interatomic bonds (leading to energetic elasticity). This proceedings paper aims to highlight similarities in the structure, mechanical characteristics and constitutive modeling of soft biological tissues and rubberlike materials for which many advances in the past have gone hand in hand.

  • 37. Holzapfel, Gerhard A.
    et al.
    Gasser, T. Christian
    A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications2001In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 190, no 34, p. 4379-4403Article in journal (Refereed)
    Abstract [en]

    This paper presents a viscoelastic model for the fully three-dimensional stress and deformation response of fiber-reinforced composites that experience finite strains. The composites are thought to be (soft) matrix materials which are reinforced by two families of fibers so that the mechanical properties of the composites depend on two fiber directions. The relaxation and/or creep response of each compound of the composite is modeled separately and the global response is obtained by an assembly of all contributions. We develop novel closed-form expressions for the fourth-order elasticity tenser (tangent moduli) in full generality. Constitutive models for orthotropic, transversely isotropic and isotropic hyperelastic materials at finite strains with or without dissipation are included as special cases. In order to clearly show the good performance of the constitutive model, we present 3D and 2D numerical simulations of a pressurized laminated circular tube which shows an interesting 'stretch inversion phenomenon' in the low pressure domain. Numerical results are in good qualitative agreement with experimental data and approximate the observed strongly anisotropic physical response with satisfying accuracy. A third numerical example is designed to illustrate the anisotropic stretching process of a fiber-reinforced rubber bar and the subsequent relaxation behavior at finite strains. The material parameters are chosen so that thermodynamic equilibrium is associated with the known homogeneous deformation state.

  • 38. Holzapfel, Gerhard A.
    et al.
    Gasser, T. Christian
    Ogden, R. W.
    A new constitutive framework for arterial wall mechanics and a comparative study of material models2000In: Journal of elasticity, ISSN 0374-3535, E-ISSN 1573-2681, Vol. 61, no 03-jan, p. 1-48Article in journal (Refereed)
    Abstract [en]

    In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanically relevant layers in healthy tissue). Each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axis. The resulting constitutive law is orthotropic in each layer. Fiber orientations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires only three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The characteristic and very important residual stress in an artery in vitro is accounted for by assuming that the natural (unstressed and unstrained) configuration of the material corresponds to an open sector of a tube, which is then closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution through the deformed arterial wall in the physiological state is examined. The model is fitted to available data on arteries and its predictions are assessed for the considered combined loadings. It is explained how the new model is designed to avoid certain mechanical, mathematical and computational deficiencies evident in currently available phenomenological models. A critical review of these models is provided by way of background to the development of the new model.

  • 39. Holzapfel, Gerhard A.
    et al.
    Gasser, T. Christian
    Ogden, R. W.
    Comparison of a multi-layer structural model for arterial walls with a fung-type model, and issues of material stability2004In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 126, no 2, p. 264-275Article in journal (Refereed)
    Abstract [en]

    The goals of this paper are (i) to re-examine the constitutive law for the description of the (passive) highly nonlinear and anisotropic response of healthy elastic arteries introduced recently by the authors, (ii) to show how the mechanical response of a carotid artery under inflation and extension predicted by the structural model compares with that for a three-dimensional form of Fung-type strain-energy function, (iii) to provide a new set of material parameters that can be used in a finite element program, and (iv) to show that the model has certain mathematical features that are important from the point of view of material and numerical stability.

  • 40. Holzapfel, Gerhard A.
    et al.
    Gasser, T. Christian
    Stadler, M.
    A structural model for the viscoelastic behavior of arterial walls: Continuum formulation and finite element analysis2002In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 21, no 3, p. 441-463Article in journal (Refereed)
    Abstract [en]

    In this paper we present a two-layer structural model suitable for predicting reliably the passive (unstimulated) time-dependent three-dimensional stress and deformation states of healthy young arterial walls under various loading conditions. It extends to the viscoelastic regime a recently developed constitutive framework for the elastic strain response of arterial walls (see Holzapfel et al. (2001)). The structural model is formulated within the framework of nonlinear continuum mechanics and is well-suited for a finite element implementation. It has the special merit that it is based partly on histological information, thus allowing the material parameters to be associated with the constituents of each mechanically-relevant arterial layer. As one essential ingredient from the histological information the constitutive model requires details of the directional organization of collagen fibers as commonly observed under a microscope. We postulate a fully automatic technique for identifying the orientations of cellular nuclei, these coinciding with the preferred orientations in the tissue. The biological material is assumed to behave incompressibly so that the constitutive function is decomposed locally into volumetric and isochoric parts. This separation turns out to be advantageous in avoiding numerical complications within the finite element analysis of incompressible materials. For the description of the viscoelastic behavior of arterial walls we employ the concept of internal variables. The proposed viscoelastic model admits hysteresis loops that are known to be relatively insensitive to strain rate, an essential mechanical feature of arteries of the muscular type. To enforce incompressibility without numerical difficulties, the finite element treatment adopted is based on a three-field Hu-Washizu variational approach in conjunction with an augmented Lagrangian optimization technique. Two numerical examples are used to demonstrate the reliability and efficiency of the proposed structural model for arterial wall mechanics as a basis for large scale numerical simulations.

  • 41.
    Holzapfel, Gerhard A.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Gasser, Thomas Christian
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Computational stress-deformation analysis of arterial walls including high-pressure response2007In: International Journal of Cardiology, ISSN 0167-5273, E-ISSN 1874-1754, Vol. 116, no 1, p. 78-85Article in journal (Refereed)
    Abstract [en]

    Background: Changes in the mechanical behavior of arteries after balloon angioplasty cause cell reactions that may be responsible for restenosis. Hence, the study of the stress-deforination changes in arterial walls following supraphysiological tissue loading is an essential task. Methods: A normal LAD coronary artery was modeled and computationally analyzed as a two-layer, thick-walled, anisotropic and inelastic circular tube including residual strains. Each layer was treated as a fibre-matrix composite. The tube was subjected to an axial stretch of 1. 1 and a transmural pressure of 750 min Hg. Since overstretch of rerrmant non-diseased tissue in lesions is a primary mechanism of lumen enlargement this model approach represents a reasonable first step. Results: At physiological loading, the residual stresses led to a significant reduction of the high circumferential stress values at the inner wall, and the stress gradients. At low pressure level the media was the mechanically relevant layer, while at supraphysiological loading, the adventitia was the predominant load-carrying constituent providing a stiff support for 'redistribution' of soft plaque components by means of radial compression. After unloading to physiological loading conditions the stress state in the arterial wall differed significantly from that before inflation; the stress gradient in the media even changed its sign. Complete unloading indicated lumen enlargement, material softening and energy dissipation, which is in agreement with experimental studies. Conclusions: This method may be useful to improve interventional protocols for reducing the dilatational trauma, and thereby the adverse biological reaction in arterial walls following balloon angioplasty.

  • 42.
    Holzapfel, Gerhard A.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Ogden, R. W.
    Constitutive modelling of passive myocardium: a structurally based framework for material characterization2009In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 367, no 1902, p. 3445-3475Article in journal (Refereed)
    Abstract [en]

    In this paper, we first of all review the morphology and structure of the myocardium and discuss the main features of the mechanical response of passive myocardium tissue, which is an orthotropic material. Locally within the architecture of the myocardium three mutually orthogonal directions can be identified, forming planes with distinct material responses. We treat the left ventricular myocardium as a non-homogeneous, thick-walled, nonlinearly elastic and incompressible material and develop a general theoretical framework based on invariants associated with the three directions. Within this framework we review existing constitutive models and then develop a structurally based model that accounts for the muscle fibre direction and the myocyte sheet structure. The model is applied to simple shear and biaxial deformations and a specific form fitted to the existing (and somewhat limited) experimental data, emphasizing the orthotropy and the limitations of biaxial tests. The need for additional data is highlighted. A brief discussion of issues of convexity of the model and related matters concludes the paper.

  • 43.
    Holzapfel, Gerhard A.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Ogden, R. W.
    Modelling the layer-specific three-dimensional residual stresses in arteries, with an application to the human aorta2010In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 7, no 46, p. 787-799Article in journal (Refereed)
    Abstract [en]

    This paper provides the first analysis of the three-dimensional state of residual stress and stretch in an artery wall consisting of three layers (intima, media and adventitia), modelled as a circular cylindrical tube. The analysis is based on experimental results on human aortas with non-atherosclerotic intimal thickening documented in a recent paper by Holzapfel et al. (Holzapfel et al. 2007 Ann. Biomed. Eng. 35, 530-545 (doi:10.1007/s10439-006-9252-z)). The intima is included in the analysis because it has significant thickness and load-bearing capacity, unlike in a young, healthy human aorta. The mathematical model takes account of bending and stretching in both the circumferential and axial directions in each layer of the wall. Previous analysis of residual stress was essentially based on a simple application of the opening-angle method, which cannot accommodate the three-dimensional residual stretch and stress states observed in experiments. The geometry and nonlinear kinematics of the intima, media and adventitia are derived and the associated stress components determined explicitly using the nonlinear theory of elasticity. The theoretical results are then combined with the mean numerical values of the geometrical parameters and material constants from the experiments to illustrate the three-dimensional distributions of the stretches and stresses throughout the wall. The results highlight the compressive nature of the circumferential stress in the intima, which may be associated with buckling of the intima and its delamination from the media, and show that the qualitative features of the stretch and stress distributions in the media and adventitia are unaffected by the presence or absence of the intima. The circumferential residual stress in the intima increases significantly as the associated residual deformation in the intima increases while the corresponding stress in the media (which is compressive at its inner boundary and tensile at its outer boundary) is only slightly affected. The theoretical framework developed herein enables the state of residual stress to be calculated directly, serves to improve insight into the mechanical response of an unloaded artery wall and can be extended to accommodate more general geometries, kinematics and states of residual stress as well as more general constitutive models.

  • 44.
    Holzapfel, Gerhard A.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Ogden, R. W.
    On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework2009In: Mathematics and mechanics of solids, ISSN 1081-2865, E-ISSN 1741-3028, Vol. 14, no 5, p. 474-489Article in journal (Refereed)
    Abstract [en]

    The mechanical testing of anisotropic nonlinearly elastic solids is a topic of considerable and increasing interest. The results of such testing are important, in particular, for the characterization of the material properties and the development of constitutive laws that can be used for predictive purposes. However, the literature on this topic in the context of soft tissue biomechanics, in particular, includes some papers that are misleading since they contain errors and false statements. Claims that planar biaxial testing can fully characterize the three-dimensional anisotropic elastic properties of soft tissues are incorrect. There is therefore a need to clarify the extent to which biaxial testing can be used for determining the elastic properties of these materials. In this paper this is explained on the basis of the equations of finite deformation transversely isotropic elasticity, and general planar anisotropic elasticity. It is shown that it is theoretically impossible to fully characterize the properties of anisotropic elastic materials using such tests unless some assumption is made that enables a suitable subclass of models to be preselected. Moreover, it is shown that certain assumptions underlying the analysis of planar biaxial tests are inconsistent with the classical linear theory of orthotropic elasticity. Possible sets of independent tests required for full material characterization are then enumerated.

  • 45.
    Holzapfel, Gerhard A.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Ogden, Ray W.
    Constitutive modelling of arteries2010In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 466, no 2118, p. 1551-1596Article, review/survey (Refereed)
    Abstract [en]

    This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thickwalled circular cylindrical tube in order to illustrate its extension-inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

  • 46.
    Holzapfel, Gerhard A.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.). Institute of Biomechanics, Center of Biomedical Engineering, Graz University of Technology, Austria .
    Ogden, Ray W.
    Elasticity of biopolymer filaments2013In: Acta Biomaterialia, ISSN 1742-7061, E-ISSN 1878-7568, Vol. 9, no 7, p. 7320-7325Article in journal (Refereed)
    Abstract [en]

    Within the general one-dimensional theory of nonlinear elasticity we analyze the elasticity of biopolymer filaments. The approach adopted is purely mechanical but is reconciled with statistical physics approaches and allows for a proper formulation of boundary-value problems. By specializing the general framework we obtain force-extension relations for inextensible filaments and show how previous work on the biophysics of filaments fits within the framework. On the other hand, within the same framework, the theory of extensible filaments, which is appropriate for semi-flexible filaments such as F-actin, enables us to fit representative F-actin data. The specific formulas derived are relatively simple and the parameters involved have direct mechanical interpretations and are immediately related to the filament properties, including the initial end-to-end length, contour length and persistence length.

  • 47.
    Holzapfel, Gerhard A.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Ogden, Ray W.
    On the Bending and Stretching Elasticity of Biopolymer Filaments2011In: Journal of elasticity, ISSN 0374-3535, E-ISSN 1573-2681, Vol. 104, no 1-2, p. 319-342Article in journal (Refereed)
    Abstract [en]

    Elastic filaments play an important role in the behaviour of cells and biological tissues. In this paper a two-dimensional nonlinear elastic framework, incorporating both bending and stretching, for the behaviour of biopolymer filaments treated as one-dimensional continua is developed. Explicit formulas for the extension-force relationship are obtained which include dependence on the initial end-to-end distance of the filament, unlike some existing models in the literature of, for example, the worm-like chain. The approach adopted allows treatment of both flexible and semi-flexible filaments and has the flexibility to accommodate different degrees of approximation. A key ingredient in the application of the model is inclusion of a body force term in the equilibrium equation. This is essential for finding non-trivial solutions of the governing equations and boundary conditions for filaments under tension. This highlights certain inconsistencies in the mechanics evident in the biophysics literature. Since the behaviour of individual filaments has a strong influence on the behaviour of networks of filaments the theory developed here can serve as a basis for analyzing the elasticity of networks such as actin and other filamentous biopolymer networks.

  • 48. Holzapfel, Gerhard A.
    et al.
    Schulze-Bauer, C. A. J.
    Feigl, G.
    Regitnig, P.
    Single lamellar mechanics of the human lumbar anulus fibrosus2005In: Biomechanics and Modeling in Mechanobiology, ISSN 1617-7959, E-ISSN 1617-7940, Vol. 3, no 3, p. 125-140Article in journal (Refereed)
    Abstract [en]

    The mechanical behavior of the entire anulus fibrosus is determined essentially by the tensile properties of its lamellae, their fiber orientations, and the regional variation of these quantities. Corresponding data are rare in the literature. The paper deals with an in vitro study of single lamellar anulus lamellae and aims to determine (i) their tensile response and regional variation, and (ii) the orientation of lamellar collagen fibers and their regional variation. Fresh human body-discbody units (L1-L2, n=11) from cadavers were cut midsagittally producing two hemidisc units. One hemidisc was used for the preparation of single lamellar anulus specimens for tensile testing, while the other one was used for the investigation of the lamellar fiber orientation. Single lamellar anulus specimens with adjacent bone fragments were isolated from four anatomical regions: superficial and deep lamellae (3.9 +/- 0.21 mm, mean SD, apart from the outer boundary surface of the anulus fibrosus) at ventro-lateral and dorsal positions. The specimens underwent cyclic uniaxial tensile tests at three different strain rates in 0.15 mol/l NaCl solution at 37 degrees C, whereby the lamellar fiber direction was aligned with the load axis. For the characterization of the tensile behavior three moduli were calculated: E-low (0-0.1 MPa), E-medium (0.1-0.5 MPa) and E-high (0.5-1 MPa). Additionally, specimens were tested withthe load axis transverse to the fiber direction. From the second hemidise fiber angles with respect to the horizontal plane were determined photogrammetrically from images taken at six circumferential positions from ventral to dorsal and at three depth levels. Tensile moduli along the fiber direction were in the range of 28-78 MPa (regional mean values). Superficial lamellae have larger E-medium (p=0.017) and E-high (p=0.012) than internal lamellae, and the mean value of superficial lamellae is about three times higher than that of deep lamellae. Tensile moduli of ventro-lateral lamellae do not differ significantly from the tensile moduli of dorsal lamellae, and E-low, is generally indifferent with respect to the anatomical region. Tensile moduli transverse to the fiber direction were about two orders of magnitude smaller (0.22 +/- 0.2 MPa, mean SD, n = 5). Tensile properties are not correlated significantly with donor age. Only small viscoelastic effects were observed. The regional variation of lamellar fiber angle alpha is described appropriately by a regression line vertical bar rho vertical bar = 23.2 + 0.130x alpha (r(2) =0.55, p < 0.001), where a is the polar angle associated with the circumferential position. The single anulus lamella may be seen as the elementary structural unit of the anulus fibrosus, and exhibits marked anisotropy and distinct regional variation of tensile properties and fiber angles. These features must be considered for appropriate physical and numerical modeling of the anulus fibrosus.

  • 49. Holzapfel, Gerhard A.
    et al.
    Sommer, G.
    Regitnig, P.
    Anisotropic mechanical properties of tissue components in human atherosclerotic plaques2004In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 126, no 5, p. 657-665Article in journal (Refereed)
    Abstract [en]

    Knowledge of the biomechanical properties of human atherosclerotic plaques is of essential importance for developing more insights in the pathophysiology of the cardiovascular system and for better predicting the outcome of interventional treatments such as balloon angioplasty. Available data are mainly based on uniaxial tests, and most of the studies investigate the mechanical response of fibrous plaque caps on However stress distributions during, for example, balloon angioplasty are strongly influenced by all components of atherosclerotic lesions. A total number of 107 samples from nine human high-grade stenotic iliac arteries were tested; associated anamnesis of donors reported. Magnetic resonance imaging was employed to test the usability of the harvested arteries. Histological analyses has served to characterize the different tissue types. Prepared strips of 7 different tissue types underwent cyclic quasistatic uniaxial tension tests in axial and circumferential directions; ultimate tensile stresses and stretches were documented. Experimental data of individual samples indicated anisotropic and highly nonlinear tissue properties as well as considerable interspecimen differences. The calcification showed, however, a linear property, with about the same stiffness as observed for the adventitia in high stress regions. The stress and stretch values at calcification fracture are smaller (179+/-56 kf'a and 1.02+/-0.005) than for each of the other tissue components. Of all intimal tissues investigated, the lowest fracture stress occurred in the circumferential direction of the fibrous cap (254.8+/-79.8 kPa at stretch 1.182+/-0.1). The adventitia demonstrated the highest and the nondiseased media the lowest mechanical strength oil average.

  • 50.
    Holzapfel, Gerhard A.
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Sommer, Gerhard
    Auer, Martin
    Regitnig, Peter
    Ogden, Ray W.
    Layer-specific 3D residual deformations of human aortas with non-atherosclerotic intimal thickening2007In: Annals of Biomedical Engineering, ISSN 0090-6964, E-ISSN 1573-9686, Vol. 35, no 4, p. 530-545Article in journal (Refereed)
    Abstract [en]

    Data relating to residual deformations in human arteries are scarce. In this paper we investigate three-dimensional residual deformations for intact strips and for their separate layers from human aortas in their passive state. From 11 abdominal aortas with identified anamnesis, 16 pairs of rings and axial strips were harvested, and the rings cut open. After 16 h images of the resulting geometries were recorded, and the strips were separated into their three layers; after another 6 h images were again recorded. Image processing and analysis was then used to quantify residual stretches and curvatures. For each specimen histological analysis established that the intima, media and adventitia were clearly separated, and the separation was atraumatic. Axial in situ stretches were determined to be 1.196 +/- 0.084. On separation, the strips from the adventitia and media shortened (between 4.03 and 8.76% on average), while the intimal strips elongated on average by 3.84% (circumferential) and 4.28% (axial) relative to the associated intact strips. After separation, the adventitia from the ring sprang open by about 180 degrees on average, becoming flat, the intima opened only slightly, but the media sprang open by more than 180 degrees (as did the intact strip). The adventitia and intima from the axial strips remained flat, while the media (and the intact strip) bent away from the vessel axis. This study has shown that residual deformations are three dimensional and cannot be described by a single parameter such as 'the' opening angle. Their quantification and modeling therefore require consideration of both stretching and bending, which are highly layer-specific and axially dependent.

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