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  • 1. Dankowicz, H.
    et al.
    Adolfsson, J.
    Nordmark, Arne B.
    KTH, Superseded Departments, Mechanics.
    Repetitive gait of passive bipedal mechanisms in a three-dimensional environment2001In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 123, no 1, p. 40-46Article in journal (Refereed)
    Abstract [en]

    The inherent dynamics of bipedal, kneed mechanisms are studied with emphasis on the existence and stability of repetitive gait in a three-dimensional environment, in the absence of external, active control. The investigation is motivated by observations that sustained anthropomorphic locomotion is largely a consequence of geometric and inertial properties of the mechanism. While the modeling excludes active control, the energy dissipated in ground and knee collisions is continuously re-injected by considering gait down slight inclines. The paper describes the dependence of the resulting passive gait in vertically constrained and unconstrained mechanisms on model parameters, such as ground compliance and ground slope. We also show the possibility of achieving statically unstable gait with appropriate parameter choices.

  • 2.
    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]

  • 3. 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.

  • 4.
    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.

  • 5.
    Halvorsen, Kjartan
    et al.
    Swedish School of Sports and Health Sciences.
    Johnston, Christopher
    Swedish University of Agricultural Sciences.
    Back, Wim
    Utrecht University.
    Stokes, Virgil
    Uppsala University.
    Lanshammar, Håkan
    Uppsala University.
    Tracking the motion of hidden segments using kinematic constraints and Kalman filtering2008In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 130Article in journal (Refereed)
    Abstract [en]

    Motion capture for biomechanical applications involves in almost all cases sensors or markers that are applied to the skin of the body segments of interest. This paper deals with the problem of estimating the movement of connected skeletal segments from 3D position data of markers attached to the skin. The use of kinematic constraints has been shown previously to reduce the error in estimated segment movement that are due to skin and muscles moving with respect to the underlying segment. A kinematic constraint reduces the number of degrees of freedom between two articulating segments. Moreover kinematic constraints can help reveal the movement of some segments when the 3D marker data otherwise are insufficient. Important cases include the human ankle complex and the phalangeal segments of the horse, where the movement of small segments is almost completely hidden from external observation by joint capsules and ligaments. This paper discusses the use of an extended Kalman filter for tracking a system of connected segments. The system is modeled using rigid segments connected by simplified joint models. The position and orientation of the mechanism are specified by a set of generalized coordinates corresponding to the mechanism's degrees of motion. The generalized coordinates together with their first time derivatives can be used as the state vector of a state space model governing the kinematics of the mechanism. The data collected are marker trajectories from skin-mounted markers, and the state vector is related to the position of the markers through a nonlinear function. The Jacobian of this function is derived The practical use of the method is demonstrated on a model of the distal part of the limb of the horse. Monte Carlo simulations of marker data for a two-segment system connected by a joint with three degrees of freedom indicate that the proposed method gives significant improvement over a method, which does not make use of the joint constraint, but the method requires that the model is a good approximation of the true mechanism. Applying the method to data on the movement of the four distal-most segments of the horse's limb shows good between trial consistency and small differences between measured marker positions and marker positions predicted by the model.

  • 6.
    Halvorsen, Kjartan
    et al.
    Swedish School of Sports and Health Sciences.
    Söderström, Torsten
    Uppsala University.
    Stokes, Virgil
    Uppsala University.
    Lanshammar, Håkan
    Uppsala University.
    Using an extended Kalman filter for rigid body pose estimation2005In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 127, p. 475-483Article in journal (Refereed)
    Abstract [en]

    Rigid body pose is commonly represented as;he rigid body transformation from one (often reference) pose to another. This is usually computed for each frame of data without any assumptions or restrictions on the temporal change of the pose. The most common algorithm was proposed by Soderkvist and Wedin (1993, "Determining the Movements Of the Skeleton Using Well-configured Markers," J. Biomech., 26, pp. 1473-1477), and implies the assumption that measurement errors are isotropic and homogenous. This paper describes an alternative method based on a state space formulation and the application of an extended Kalman filter (EKF). State space models are formulated, which describe the kinematics of the rigid body. The state vector consists of six generalized coordinates (corresponding to the 6 degrees of freedom), and their first time derivatives. The state space models have linear dynamics, while the measurement function is a nonlinear relation between the state vector and the observations (marker positions). An analytical expression for the linearized measurement function is derived Tracking the rigid body motion using an EKF enables the use of a priori information on the measurement noise and type of motion to tune the filter. The EKF is time variant, which allows for a natural way of handling temporarily missing marker data. State updates are based on all the information available at each time step, even when data from fewer than three markers are available. Comparison with the method of Soderkvist and Wedin on simulated data showed a considerable improvement in accuracy with the proposed EKF method when marker data was temporarily missing. The proposed method offers an improvement in accuracy of rigid body pose estimation by incorporating knowledge of the characteristics of the movement and the measurement errors. Analytical expressions for the linearized system equations are provided, which eliminate the need for approximate discrete differentiation and which facilitate a fast implementation.

  • 7. 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.

  • 8. 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.

  • 9. Holzapfel, Gerhard A.
    et al.
    Stadler, M.
    Gasser, T. Christian
    Changes in the mechanical environment of stenotic arteries during interaction with stents: Computational assessment of parametric stent designs2005In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 127, no 1, p. 166-180Article in journal (Refereed)
    Abstract [en]

    Clinical studies have identified factors such as the stent design and the deployment technique the success rate may also depend on the stenosis type. Hence, for a particular stenotic artery, the optimal intervention can only be identified by studying the influence of factors such as stent type, strut thickness, geometry of the stent cell, and stent-artery radial mismatch with the wall. We propose a methodology that allows a set of stent parameters to be varied, with the aim of evaluating the difference in the mechanical environment within the wall before and after angioplasty with stenting. Novel scalar quantities attempt to characterize the wall changes inform of the contact pressure caused by the stent struts, and the stresses within the individual components of the wall caused by the stent. These quantities are derived numerically and serve as indicators, which allow the determination of the correct size and type of the stent for each individual stenosis. In addition, the luminal change due to angioplasty may be computed as well. The methodology is demonstrated by using a full three-dimensional geometrical model of a postmortem specimen of a human iliac artery with a stenosis using imaging data. To describe the material behavior of the artery, we considered mechanical data of eight different vascular tissues, which formed the stenosis. The constitutive models for the tissue components capture the typical anisotropic, nonlinear and dissipative characteristics under supra-physiological loading conditions. Three-dimensional stent models were parametrized in such a way as to enable new designs to be generated simply with regard to variations in their geometric structure. For the three-dimensional stent-artery interaction we use a contact algorithm based on smooth contact surfaces of at least Cl-continuity, which prevents numerical problems known from standard facet-based contact algorithm. The proposed methodology has the potential to provide a scientific basis for optimizing treatment procedures and stent geometries and materials, to help stent designers examine new stent designs virtually, and to assist clinicians in choosing the most suitable stent for a particular stenosis.

  • 10. Kiousis, D. E.
    et al.
    Rubinigg, S. F.
    Auer, M.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    A Methodology to Analyze Changes in Lipid Core and Calcification Onto Fibrous Cap Vulnerability: The Human Atherosclerotic Carotid Bifurcation as an Illustratory Example2009In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 131, no 12Article in journal (Refereed)
    Abstract [en]

    A lipid core that occupies a high proportion of the plaque volume in addition to a thin fibrous cap is a predominant indicator of plaque vulnerability. Nowadays, noninvasive. imaging modalities can identify such structural components, however morphological criteria alone cannot reliably identify high-risk plaques. Information, such as stresses in the lesions components, seems to be essential. This work presents a methodology able to analyze the effect of changes in the lipid core and calcification on the wall stresses, in particular on the fibrous cap vulnerability. Using high-resolution magnetic resonance imaging and histology of an ex vivo human atherosclerotic carotid bifurcation, a patient is gen-specific three-dimensional geometric model, consisting of four tissue components, erated. The adopted constitutive model accounts for the nonlinear and anisotropic tissue behavior incorporating the collagen fiber orientation by means of a novel and robust algorithm. The material parameters are identified from experimental data. A novel stress-based computational cap vulnerability index is proposed to assess quantitatively the rupture-risk of fibrous caps. Nonlinear finite element analyses identify that the highest stress regions are located at the vicinity of the shoulders of the fibrous cap and in the stiff calcified tissue. A parametric analysis reveals a positive correlation between the increase in lipid core portion and the mechanical stress in the fibrous cap and, hence, the risk for cap rupture. The highest values of the vulnerability index, which cot-relate to more vulnerable caps, are obtained for morphologies for which the lipid cores were severe; heavily loaded fibrous caps were thus detected. The proposed multidisciplinary methodology is able to investigate quantitatively the mechanical behavior of atherosclerotic plaques in patient-specific stenoses. The introduced vulnerability index may serve as a more quantitative tool for diagnosis, treatment and prevention. [DOI: 10.1115/1.4000078]

  • 11.
    Kroon, Martin
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Modeling of Fibroblast-Controlled Strengthening and Remodeling of Uniaxially Constrained Collagen Gels2010In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 132, no 11, p. 111008-Article in journal (Refereed)
    Abstract [en]

    A theoretical model for the remodeling of collagen gels is proposed. The collagen fabric is modeled as a network of collagen fibers, which in turn are composed of collagen fibrils. In the model, the strengthening of collagen fabric is accomplished by fibroblasts, which continuously recruit and attach more collagen fibrils to existing collagen fibers. The fibroblasts also accomplish a reorientation of collagen fibers. Fibroblasts are assumed to reorient collagen fibers toward the direction of maximum material stiffness. The proposed model is applied to experiments in which fibroblasts were inserted into a collagen gel. The model is able to predict the force-strain curves for the experimental collagen gels, and the final distribution of collagen fibers also agrees qualitatively with the experiments.

  • 12.
    Kroon, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Modeling of saccular aneurysm growth in a human middle cerebral artery2008In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 130, no 5Article in journal (Refereed)
    Abstract [en]

    Saccular aneurysm growth in a human middle cerebral artery is modeled. The aneurysm growth model was presented in a companion paper by Kroon and Holzapfel ("A Model for Saccular Cerebral Aneurysm Growth by Collagen Fibre Remodelling," J. Theor. Biol., in press) and was assessed there for axisymmetric growth. The aneurysm growth model is now evaluated for a more realistic setting. The middle cerebral artery is modeled as a two-layered cylinder, where the layers correspond to the media and the adventitia. An instant loss of the media in a region of the artery wall initiates the growth of the saccular aneurysm. The aneurysm wall is assumed to be a development of the adventitia of the original healthy artery, and collagen is assumed to be the only load-bearing constituent in the adventitia and in the aneurysm wall. The collagen is organized in a number of distinct layers where fibers in a specific layer are perfectly aligned in a certain fiber direction. The production of new collagen is taken to depend on the stretching of the aneurysm wall, and the continuous remodeling of the collagen fibers is responsible for the aneurysm growth. The general behavior of the growth model is investigated and also the influence of the structural organization of the collagen fabric. The analysis underlines the fact that the material behavior of aneurysmal tissue cannot be expected to be isotropic. The model predictions agree well with clinical and experimental results, for example, in terms of aneurysm size and shape, wall stress levels, and wall thickness.

  • 13.
    Manda, Krishnagoud
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Modeling of articular cartilage growth around localized defect-filling metal implantIn: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951Article in journal (Other academic)
  • 14. Martufi, Giampaolo
    et al.
    Di Martino, Elena S.
    Amon, Cristina H.
    Muluk, Satish C.
    Finol, Ender A.
    Three-Dimensional Geometrical Characterization of Abdominal Aortic Aneurysms: Image-Based Wall Thickness Distribution2009In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 131, no 6, p. 061015-Article in journal (Refereed)
    Abstract [en]

    The clinical assessment of abdominal aortic aneurysm (AAA) rupture risk is based on the quantification of AAA size by measuring its maximum diameter from computed tomography (CT) images and estimating the expansion rate of the aneurysm sac over time. Recent findings have shown that geometrical shape and size, as well as local wall thickness may be related to this risk; thus, reliable noninvasive image-based methods to evaluate AAA geometry have a potential to become valuable clinical tools. Utilizing existing CT data, the three-dimensional geometry of nine unruptured human AAAs was reconstructed and characterized quantitatively. We propose and evaluate a series of 1D size, 2D shape, 3D size, 3D shape, and second-order curvature-based indices to quantify AAA geometry, as well as the geometry of a size-matched idealized fusiform aneurysm and a patient-specific normal abdominal aorta used as controls. The wall thickness estimation algorithm, validated in our previous work, is tested against discrete point measurements taken from a cadaver tissue model, yielding an average relative difference in AAA wall thickness of 7.8%. It is unlikely that any one of the proposed geometrical indices alone would be a reliable index of rupture risk or a threshold for elective repair. Rather, the complete geometry and a positive correlation of a set of indices should be considered to assess the potential for rupture. With this quantitative parameter assessment, future research can be directed toward statistical analyses correlating the numerical values of these parameters with the risk of aneurysm rupture or intervention (surgical or endovascular). While this work does not provide direct insight into the possible clinical use of the geometric parameters, we believe it provides the foundation necessary for future efforts in that direction.

  • 15.
    Martufi, Giampaolo
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Gasser, Thomas Christian
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Review: The role of biomechanical modeling in the rupture risk assessment for abdominal aortic aneurysms2013In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 135, no 2, p. 021010-Article, review/survey (Refereed)
    Abstract [en]

    AAA disease is a serious condition and a multidisciplinary approach including biomechanics is needed to better understand and more effectively treat this disease. A rupture risk assessment is central to the management of AAA patients, and biomechanical simulation is a powerful tool to assist clinical decisions. Central to such a simulation approach is a need for robust and physiologically relevant models. Vascular tissue senses and responds actively to changes in its mechanical environment, a crucial tissue property that might also improve the biomechanical AAA rupture risk assessment. Specifically, constitutive modeling should not only focus on the (passive) interaction of structural components within the vascular wall, but also how cells dynamically maintain such a structure. In this article, after specifying the objectives of an AAA rupture risk assessment, the histology and mechanical properties of AAA tissue, with emphasis on the wall, are reviewed. Then a histomechanical constitutive description of the AAA wall is introduced that specifically accounts for collagen turnover. A test case simulation clearly emphasizes the need for constitutive descriptions that remodels with respect to the mechanical loading state. Finally, remarks regarding modeling of realistic clinical problems and possible future trends conclude the article.

  • 16. Pandolfi, A.
    et al.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Three-Dimensional Modeling and Computational Analysis of the Human Cornea Considering Distributed Collagen Fibril Orientations2008In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 130, no 6Article in journal (Refereed)
    Abstract [en]

    Experimental tests on human corneas reveal distinguished reinforcing collagen lamellar structures that may be well described by a structural constitutive model considering distributed collagen fibril orientations along the superior-inferior and the nasal-temporal meridians. A proper interplay between the material structure and the geometry guarantees the refractive function and defines the refractive properties of the cornea. We propose a three-dimensional computational model for the human cornea that is able to provide the refractive power by analyzing the structural mechanical response with the nonlinear regime and the effect the intraocular pressure has. For an assigned unloaded geometry we show how the distribution of the von Mises stress at the top surface of the cornea and through the corneal thickness and the refractive power depend on the material properties and the fibril dispersion. We conclude that a model for the human cornea must not disregard the peculiar collagen fibrillar structure, which equips the cornea with the unique biophysical, mechanical, and optical properties.

  • 17. Pierce, D. M.
    et al.
    Trobin, W.
    Trattnig, S.
    Bischof, H.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    A Phenomenological Approach Toward Patient-Specific Computational Modeling of Articular Cartilage Including Collagen Fiber Tracking2009In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 131, no 9Article in journal (Refereed)
    Abstract [en]

    To model the cartilage morphology and the material response, a phenomenological and patient-specific simulation approach incorporating the collagen fiber fabric is proposed. Cartilage tissue response is nearly isochoric and time-dependent under physiological pressure levels. Hence, a viscoelastic constitutive model capable of reproducing finite strains is employed, while the time-dependent deformation change is purely isochoric. The model incorporates seven material parameters, which all have a physical interpretation. To calibrate the model and facilitate further analysis, five human cartilage specmiens underwent a number of tests. A series of magnetic resonance imaging (MRI) sequences is taken, next the cartilage surface is imaged, then mechanical indentation tests arc completed at 2-7 different locations per sample, resulting in force/displacement data over time, and finally, the underlying bone surface is imaged. Imaging and mechanical testing are performed with a custom-built robotics-based testing device. Stereo reconstruction of the cartilage and subchondral bone surface is employed, which, together with the proposed constitutive model, led to specimen-specific finite element simulations of the mechanical indentation tests. The force-time response of 23 such indentation experiment simulations is optimized to estimate the mean material parameters and corresponding standard deviations. The model is capable of reproducing the deformation behavior of human articular cartilage in the physiological loading domain, as demonstrated by the good agreement between the experiment and numerical results (R-2 = 0.95 +/- 0.03, mean +/- standard deviation of force-time response for 23 indentation tests). To address validation, a sevenfold cross-validation experiment is performed on the 21 experiments representing health), cartilage. To quantify the predictive error, the mean of the absolute force differences and Pearson's correlation coefficient are both calculated. Deviations in the mean absolute difference, normalized by the peak force, range from 4% to 90%, with 40 +/- 25% (M +/- SD). The correlation coefficients across all predictions have a minimum of 0.939, and a maximum of 0.993 with 0.975 +/- 0.013 (M +/- SD), which demonstrates an excellent match of the decay characteristics. A novel feature of the proposed method is 3D sample-specific numerical tracking of the fiber fabric deformation under general loading. This feature is demonstrated by comparing the estimated fiber fabric deformation with recently published experimental data determined by diffusion tensor MRI. The proposed approach is efficient enough to enable large-scale 3D contact simulations of knee joint loading in simulations with accurate joint geometries. [DOI: 10.1115/1.3148471]

  • 18. Rodriguez, J. F.
    et al.
    Ruiz, C.
    Doblare, M.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Mechanical stresses in abdominal aortic aneurysms: Influence of diameter, asymmetry, and material anisotropy2008In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 130, no 2Article in journal (Refereed)
    Abstract [en]

    Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. In this regard, a reliable and accurate stress analysis of an in vivo AAA requires a suitable 3D constitutive model. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated in which the maximum diameter and length of the aneurysm were individually controlled. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The, results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress. Results confirm that the relative aneurysm length and the degree of aneurysmal asymmetry should be considered in a rupture risk decision criterion for AAAs.

  • 19. Schulze-Bauer, C. A. J.
    et al.
    Morth, C.
    Holzapfel, Gerhard A.
    Passive biaxial mechanical response of aged human iliac arteries2003In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 125, no 3, p. 395-406Article in journal (Refereed)
    Abstract [en]

    Inflation and extension tests of arteries are essential for the understanding of arterial wall mechanics. Data for such tests of human arteries are rare. At autopsy we harvested 10 non-diseased external iliac arteries of aged subjects (52-87 yrs). Structural homogeneity was ensured by means of ultrasound imaging, and anamneses of patients were recorded. We measured the axial in situ stretches, load-free geometries and opening angles. Passive biaxial mechanical responses of preconditioned cylindrical specimens were studied in 37degreesC calcium-free Tyrode solution under quasistatic loading conditions. Specimens were subjected to pressure cycles varying from 0 to 33.3 kPa (250mmHg) at nine fixed axial loads, varying from 0 to 9.90N. For the description of the load-deformation behavior we employed five two-dimensional orthotropic strain-energy functions frequently used in arterial wall mechanics. The associated constitutive models were compared in regard to their ability of representing the experimental data. Histology showed that the arteries were of the muscular type. In contrast to animal arteries they exhibited intimal layers of considerable thickness. The average ratio of wall thickness to outer diameter was 7.7, which is much less than observed for common animal arteries. We found a clear correlation between age and the axial in situ stretch lambda(is) (r = -0.72, P = 0.03), and between age and distensibility of sped. mens, i.e. aged specimens are less distensible. Axial in situ stretches were clearly smaller (1.07+/-0.09, mean+/-SD) than in animal arteries. For one specimen lambda(is) was even smaller than 1.0, i.e. the vessel elongated axially upon excision. The nonlinear and anisotropic load-deformation behavior showed small hystereses. For the majority of specimens we observed axial stretches smaller than 1.3 and circumferential stretches smaller than 1.1 for the investigated loading range. Data from in situ inflation tests showed a significant increase of the axial stretch with intraluminal pressure. Thus, for this type of artery the axial in situ stretch of a non-pressurized vessel is not representative of the axial in vivo stretch. None of the constitutive models were able to represent the deformation behavior of the entire loading range. For the physiological loading range, however some of the models achieved good agreement with the experimental data.

  • 20.
    Siegmund, Gunter
    et al.
    MEA Forensic Engineers and Scientists, Richmond, Canada.
    Blouin, Jean-Sebastien
    School of Human Kinetics, University of British Columbia, Vancouver.
    Brault, John
    MEA Forensic Engineers and Scientists, Lake Forest, United States.
    Hedenstierna, Sofia
    KTH, School of Technology and Health (STH), Neuronic Engineering.
    Inglis, Timothy
    International Collaboration on Repair Discovery, University of British Columbia, Vancouver.
    Electromyography of Superficial and Deep Neck Muscles During Isometric, Voluntary, and Reflex Contractions2007In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 129, no 1, p. 66-77Article in journal (Refereed)
    Abstract [en]

    Increasingly complex models of the neck neuromusculature need detailed muscle and kinematic data for proper validation. The goal of this study was to measure the electromyographic activity of superficial and deep neck muscles during tasks involving isometric, voluntary, and reflexively evoked contractions of the neck muscles. Three male subjects (28-41 years) had electromyographic (EMG) fine wires inserted into the left sternocleidomastoid, levator scapulae, trapezius, splenius capitis, semispinalis capitis, semispinalis cervicis, and multifidus muscles. Surface electrodes were placed over the left sternohyoid muscle. Subjects then performed: (i) maximal voluntary contractions (MVCs) in the eight directions (45 deg intervals) front the neutral posture; (ii) 50 N isometric contractions with a slow sweep of the force direction through 720 deg; (in) voluntary oscillatory head movements in flexion and extension; and (iv) initially relaxed reflex muscle activations to a forward acceleration while seated on a sled. Isometric contractions were performed against an overhead load cell and movement dynamics were measured using six-axis accelerometry, on the head and torso. In all three subjects, the two anterior neck muscles had similar preferred activation directions and acted synergistically in both dynamic tasks. With the exception of splenius capitis, the posterior and posterolateral neck muscles also showed consistent activation directions and acted synergistically during the voluntary motions, but not during the sled perturbations. These findings suggest that the common numerical-modeling assumption that all anterior muscles act synergistically as flexors is reasonable, but that the related assumption that all posterior muscles act synergistically as extensors is not. Despite the small number of subjects, the data presented here can be used to inform and validate a neck model at three levels of increasing neuromuscular-kinematic complexity: muscles generating forces with no movement, muscles generating forces and causing movement, and muscles generating,forces in response to induced movement. These increasingly complex data sets will allow researchers to incrementally tune their neck models' muscle geometry, physiology, and feedforward/feedback neuromechanics.

  • 21. Sommer, G.
    et al.
    Gasser, T. Christian
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Regitnig, P.
    Auer, M.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Biomechanics.
    Dissection properties of the human aortic media: An experimental study2008In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 130, no 2Article in journal (Refereed)
    Abstract [en]

    Aortic dissection occurs frequently and is clinically challenging; the underlying mechanics remain unclear. The present study investigates the dissection properties of the media of 15 human abdominal aortas (AAs) by means of direct tension tests (n=8) and peeling tests (n=12). The direct tension test demonstrates the strength of the media in the radial direction, while the peeling test allows a steady-state investigation of the dissection propagation. To explore the development of irreversible microscopic changes during medial dissection, histological images (n=8) from four AAs at different peeling stages are prepared and analyzed. Direct tension tests of coin-shaped medial specimens result in a radial failure stress of 140.1 +/- 15.9 kPa (mean +/- SD, n=8). Peeling tests of rectangular-shaped medial strips along the circumferential and axial directions provide peeling force/width ratios of 22.9 +/- 2.9 mN/mm (n=5) and 34.8 +/- 15.5 mN/mm (n=7); the related dissection energies per reference area are 5.1 +/- 0.6 mJ/cm(2) and 7.6 +/- 2.7 mJ/cm(2), respectively. Although student's t-tests indicate that force/width values of both experimental tests are not significantly different (alpha=0.05, p=0.125), the strikingly higher resisting force/width obtained,for the axial peeling tests is perhaps indicative of anisotropic dissection properties of the human aortic media. Peeling in the axial direction of the aorta generates a remarkably "rougher" dissection surface with respect to the surface generated by peeling in the circumferential direction. Histological analysis of the stressed specimens reveals that tissue damage spreads over approximately six to seven elastic laminae, which is about 15-18% of the thickness of the abdominal aortic media, which forms a pronounced cohesive zone at the dissection front.

  • 22. Watton, P. N.
    et al.
    Raberger, N. B.
    Holzapfel, Gerhard A.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Ventikos, Y.
    Coupling the Hemodynamic Environment to the Evolution of Cerebral Aneurysms: Computational Framework and Numerical Examples2009In: Journal of Biomechanical Engineering, ISSN 0148-0731, E-ISSN 1528-8951, Vol. 131, no 10Article in journal (Refereed)
    Abstract [en]

    The physiological mechanisms that give rise to the inception and development of a cerebral aneurysm are accepted to involve the interplay between the local mechanical forces acting on the arterial wall and the biological processes occurring at the cellular level. In fact, the wall shear stresses (WSSs) that act on the endothelial cells are thought to play a pivotal role. A computational framework is proposed to explore the link between the evolution of a cerebral aneurysm and the influence of hemodynamic stimuli that act on the endothelial cells. An aneurysm evolution model, which utilizes a realistic microstructural model of the arterial wall, is combined with detailed 3D hemodynamic solutions. The evolution of the blood flow within the developing aneurysm determines the distributions of the WSS and the spatial WSS gradient (WSSG) that act on the endothelial cell layer of the tissue. Two illustrative examples are considered: Degradation of the elastinous constituents is driven by deviations of WSS or the WSSG from normotensive values. This model provides the basis to further explore the etiology of aneurysmal disease. [DOI: 10.1115/1.3192141]

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