Determination of displacement, stress- and strain-distribution in the human heart: a FE-model on the basis of MR imaging.

The determination of characteristic cardiac parameters, such as displacement, stress and strain distribution are essential for an understanding of the mechanics of the heart. The calculation of these parameters has been limited until recently by the use of idealised mathematical representations of biventricular geometries and by applying simple material laws. On the basis of 20 short axis heart slices and in consideration of linear and nonlinear material behaviour we have developed a FE model with about 100,000 degrees of freedom. Marching Cubes and Phong's incremental shading technique were used to visualise the three dimensional geometry. In a quasistatic FE analysis continuous distribution of regional stress and strain corresponding to the endsystolic state were calculated. Substantial regional variation of the Von Mises stress and the total strain energy were observed at all levels of the heart model. The results of both the linear elastic model and the model with a nonlinear material description (Mooney-Rivlin) were compared. While the stress distribution and peak stress values were found to be comparable, the displacement vectors obtained with the nonlinear model were generally higher in comparison with the linear elastic case indicating the need to include nonlinear effects.

Changes in Running Mechanics and Spring-Mass Behaviour during a 5-km Time Trial

Research into the biomechanical manifestation of fatigue during exhaustive runs is increasingly popular but additional understanding of the adaptation of the spring-mass behaviour during the course of strenuous, self-paced exercises continues to be a challenge in order to develop optimized training and injury prevention programs. This study investigated continuous changes in running mechanics and spring-mass behaviour during a 5-km run. 12 competitive triathletes performed a 5-km running time trial (mean performance: 17 min 30 s) on a 200 m indoor track. Vertical and anterior-posterior ground reaction forces were measured every 200 m by a 5-m long force platform system, and used to determine spring-mass model characteristics. After a fast start, running velocity progressively decreased (- 11.6%; P<0.001) in the middle part of the race before an end spurt in the final 400-600 m. Stride length (- 7.4%; P<0.001) and frequency (- 4.1%; P=0.001) decreased over the 25 laps, while contact time (+ 8.9%; P<0.001) and total stride duration (+ 4.1%; P<0.001) progressively lengthened. Peak vertical forces (- 2.0%; P<0.01) and leg compression (- 4.3%; P<0.05), but not centre of mass vertical displacement (+ 3.2%; P>0.05), decreased with time. As a result, vertical stiffness decreased (- 6.0%; P<0.001) during the run, whereas leg stiffness changes were not significant (+ 1.3%; P>0.05). Spring-mass behaviour progressively changes during a 5-km time trial towards deteriorated vertical stiffness, which alters impact and force production characteristics.

An objective anisotropic elastic plastic model and Algorithm applicable to bone mechanics

The implicit projection algorithm of isotropic plasticity is extended to an objective anisotropic elastic perfectly plastic model. The recursion formula developed to project the trial stress on the yield surface, is applicable to any non linear elastic law and any plastic yield function.A curvilinear transverse isotropic model based on a quadratic elastic potential and on Hill's quadratic yield criterion is then developed and implemented in a computer program for bone mechanics perspectives. The paper concludes with a numerical study of a schematic bone-prosthesis system to illustrate the potential of the model.

Online estimation of respiratory mechanics in non-invasive pressure support ventilation: a bench model study.

An online algorithm for determining respiratory mechanics in patients using non-invasive ventilation (NIV) in pressure support mode was developed and embedded in a ventilator system. Based on multiple linear regression (MLR) of respiratory data, the algorithm was tested on a patient bench model under conditions with and without leak and simulating a variety of mechanics. Bland-Altman analysis indicates reliable measures of compliance across the clinical range of interest (± 11-18% limits of agreement). Resistance measures showed large quantitative errors (30-50%), however, it was still possible to qualitatively distinguish between normal and obstructive resistances. This outcome provides clinically significant information for ventilator titration and patient management.

Multisensor change detection with nonlinear canonical correlation

The analysis of multi-modal and multi-sensor images is nowadays of paramount importance for Earth Observation (EO) applications. There exist a variety of methods that aim at fusing the different sources of information to obtain a compact representation of such datasets. However, for change detection existing methods are often unable to deal with heterogeneous image sources and very few consider possible nonlinearities in the data. Additionally, the availability of labeled information is very limited in change detection applications. For these reasons, we present the use of a semi-supervised kernel-based feature extraction technique. It incorporates a manifold regularization accounting for the geometric distribution and jointly addressing the small sample problem. An exhaustive example using Landsat 5 data illustrates the potential of the method for multi-sensor change detection.

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

TECTONICS OF THE HELVETIC NAPPE SYSTEM (W SWITZERLAND): CONTROL OF STRAIN LOCALIZATION AND BASEMENT-COVER DEFORMATION. Insights from models based on continuum mechanics

The Helvetic nappe system in Western Switzerland is a stack of fold nappes and thrust sheets em-placed at low grade metamorphism. Fold nappes and thrust sheets are also some of the most common features in orogens. Fold nappes are kilometer scaled recumbent folds which feature a weakly deformed normal limb and an intensely deformed overturned limb. Thrust sheets on the other hand are characterized by the absence of overturned limb and can be defined as almost rigid blocks of crust that are displaced sub-horizontally over up to several tens of kilometers. The Morcles and Doldenhom nappe are classic examples of fold nappes and constitute the so-called infra-Helvetic complex in Western and Central Switzerland, respectively. This complex is overridden by thrust sheets such as the Diablerets and Wildhörn nappes in Western Switzerland. One of the most famous example of thrust sheets worldwide is the Glariis thrust sheet in Central Switzerland which features over 35 kilometers of thrusting which are accommodated by a ~1 m thick shear zone. Since the works of the early Alpine geologist such as Heim and Lugeon, the knowledge of these nappes has been steadily refined and today the geometry and kinematics of the Helvetic nappe system is generally agreed upon. However, despite the extensive knowledge we have today of the kinematics of fold nappes and thrust sheets, the mechanical process leading to the emplacement of these nappe is still poorly understood. For a long time geologist were facing the so-called 'mechanical paradox' which arises from the fact that a block of rock several kilometers high and tens of kilometers long (i.e. nappe) would break internally rather than start moving on a low angle plane. Several solutions were proposed to solve this apparent paradox. Certainly the most successful is the theory of critical wedges (e.g. Chappie 1978; Dahlen, 1984). In this theory the orogen is considered as a whole and this change of scale allows thrust sheet like structures to form while being consistent with mechanics. However this theoiy is intricately linked to brittle rheology and fold nappes, which are inherently ductile structures, cannot be created in these models. When considering the problem of nappe emplacement from the perspective of ductile rheology the problem of strain localization arises. The aim of this thesis was to develop and apply models based on continuum mechanics and integrating heat transfer to understand the emplacement of nappes. Models were solved either analytically or numerically. In the first two papers of this thesis we derived a simple model which describes channel flow in a homogeneous material with temperature dependent viscosity. We applied this model to the Morcles fold nappe and to several kilometer-scale shear zones worldwide. In the last paper we zoomed out and studied the tectonics of (i) ductile and (ii) visco-elasto-plastic and temperature dependent wedges. In this last paper we focused on the relationship between basement and cover deformation. We demonstrated that during the compression of a ductile passive margin both fold nappes and thrust sheets can develop and that these apparently different structures constitute two end-members of a single structure (i.e. nappe). The transition from fold nappe to thrust sheet is to first order controlled by the deformation of the basement. -- Le système des nappes helvétiques en Suisse occidentale est un empilement de nappes de plis et de nappes de charriage qui se sont mis en place à faible grade métamorphique. Les nappes de plis et les nappes de charriage sont parmi les objets géologiques les plus communs dans les orogènes. Les nappes de plis sont des plis couchés d'échelle kilométrique caractérisés par un flanc normal faiblement défor-mé, au contraire de leur flanc inverse, intensément déformé. Les nappes de charriage, à l'inverse se caractérisent par l'absence d'un flanc inverse bien défini. Elles peuvent être définies comme des blocs de croûte terrestre qui se déplacent de manière presque rigide qui sont déplacés sub-horizontalement jusqu'à plusieurs dizaines de kilomètres. La nappe de Mordes et la nappe du Doldenhorn sont des exemples classiques de nappes de plis et constitue le complexe infra-helvétique en Suisse occidentale et centrale, respectivement. Ce complexe repose sous des nappes de charriages telles les nappes des Diablerets et du Widlhörn en Suisse occidentale. La nappe du Glariis en Suisse centrale se distingue par un déplacement de plus de 35 kilomètres qui s'est effectué à la faveur d'une zone de cisaillement basale épaisse de seulement 1 mètre. Aujourd'hui la géométrie et la cinématique des nappes alpines fait l'objet d'un consensus général. Malgré cela, les processus mécaniques par lesquels ces nappes se sont mises en place restent mal compris. Pendant toute la première moitié du vingtième siècle les géologues les géologues ont été confrontés au «paradoxe mécanique». Celui-ci survient du fait qu'un bloc de roche haut de plusieurs kilomètres et long de plusieurs dizaines de kilomètres (i.e., une nappe) se fracturera de l'intérieur plutôt que de se déplacer sur une surface frictionnelle. Plusieurs solutions ont été proposées pour contourner cet apparent paradoxe. La solution la plus populaire est la théorie des prismes d'accrétion critiques (par exemple Chappie, 1978 ; Dahlen, 1984). Dans le cadre de cette théorie l'orogène est considéré dans son ensemble et ce simple changement d'échelle solutionne le paradoxe mécanique (la fracturation interne de l'orogène correspond aux nappes). Cette théorie est étroitement lié à la rhéologie cassante et par conséquent des nappes de plis ne peuvent pas créer au sein d'un prisme critique. Le but de cette thèse était de développer et d'appliquer des modèles basés sur la théorie de la méca-nique des milieux continus et sur les transferts de chaleur pour comprendre l'emplacement des nappes. Ces modèles ont été solutionnés de manière analytique ou numérique. Dans les deux premiers articles présentés dans ce mémoire nous avons dérivé un modèle d'écoulement dans un chenal d'un matériel homogène dont la viscosité dépend de la température. Nous avons appliqué ce modèle à la nappe de Mordes et à plusieurs zone de cisaillement d'échelle kilométrique provenant de différents orogènes a travers le monde. Dans le dernier article nous avons considéré le problème à l'échelle de l'orogène et avons étudié la tectonique de prismes (i) ductiles, et (ii) visco-élasto-plastiques en considérant les transferts de chaleur. Nous avons démontré que durant la compression d'une marge passive ductile, a la fois des nappes de plis et des nappes de charriages peuvent se développer. Nous avons aussi démontré que nappes de plis et de charriages sont deux cas extrêmes d'une même structure (i.e. nappe) La transition entre le développement d'une nappe de pli ou d'une nappe de charriage est contrôlé au premier ordre par la déformation du socle. -- Le système des nappes helvétiques en Suisse occidentale est un emblement de nappes de plis et de nappes de chaînage qui se sont mis en place à faible grade métamoiphique. Les nappes de plis et les nappes de charriage sont parmi les objets géologiques les plus communs dans les orogènes. Les nappes de plis sont des plis couchés d'échelle kilométrique caractérisés par un flanc normal faiblement déformé, au contraire de leur flanc inverse, intensément déformé. Les nappes de charriage, à l'inverse se caractérisent par l'absence d'un flanc inverse bien défini. Elles peuvent être définies comme des blocs de croûte terrestre qui se déplacent de manière presque rigide qui sont déplacés sub-horizontalement jusqu'à plusieurs dizaines de kilomètres. La nappe de Morcles and la nappe du Doldenhorn sont des exemples classiques de nappes de plis et constitue le complexe infra-helvétique en Suisse occidentale et centrale, respectivement. Ce complexe repose sous des nappes de charriages telles les nappes des Diablerets et du Widlhörn en Suisse occidentale. La nappe du Glarüs en Suisse centrale est certainement l'exemple de nappe de charriage le plus célèbre au monde. Elle se distingue par un déplacement de plus de 35 kilomètres qui s'est effectué à la faveur d'une zone de cisaillement basale épaisse de seulement 1 mètre. La géométrie et la cinématique des nappes alpines fait l'objet d'un consensus général parmi les géologues. Au contraire les processus physiques par lesquels ces nappes sont mises en place reste mal compris. Les sédiments qui forment les nappes alpines se sont déposés à l'ère secondaire et à l'ère tertiaire sur le socle de la marge européenne qui a été étiré durant l'ouverture de l'océan Téthys. Lors de la fermeture de la Téthys, qui donnera naissance aux Alpes, le socle et les sédiments de la marge européenne ont été déformés pour former les nappes alpines. Le but de cette thèse était de développer et d'appliquer des modèles basés sur la théorie de la mécanique des milieux continus et sur les transferts de chaleur pour comprendre l'emplacement des nappes. Ces modèles ont été solutionnés de manière analytique ou numérique. Dans les deux premiers articles présentés dans ce mémoire nous nous sommes intéressés à la localisation de la déformation à l'échelle d'une nappe. Nous avons appliqué le modèle développé à la nappe de Morcles et à plusieurs zones de cisaillement provenant de différents orogènes à travers le monde. Dans le dernier article nous avons étudié la relation entre la déformation du socle et la défonnation des sédiments. Nous avons démontré que nappe de plis et nappes de charriages constituent les cas extrêmes d'un continuum. La transition entre nappe de pli et nappe de charriage est intrinsèquement lié à la déformation du socle sur lequel les sédiments reposent.

The predictive value of trabecular bone score (TBS) on whole lumbar vertebrae mechanics: an ex vivo study.

We investigated the association of trabecular bone score (TBS) with microarchitecture and mechanical behavior of human lumbar vertebrae. We found that TBS reflects vertebral trabecular microarchitecture and is an independent predictor of vertebral mechanics. However, the addition of TBS to areal BMD (aBMD) did not significantly improve prediction of vertebral strength. INTRODUCTION: The trabecular bone score (TBS) is a gray-level measure of texture using a modified experimental variogram which can be extracted from dual-energy X-ray absorptiometry (DXA) images. The current study aimed to confirm whether TBS is associated with trabecular microarchitecture and mechanics of human lumbar vertebrae, and if its combination with BMD improves prediction of fracture risk. METHODS: Lumbar vertebrae (L3) were harvested fresh from 16 donors. The anteroposterior and lateral bone mineral content (BMC) and areal BMD (aBMD) of the vertebral body were measured using DXA; then, the TBS was extracted using TBS iNsight software (Medimaps SA, France). The trabecular bone volume (Tb.BV/tissue volume, TV), trabecular thickness (Tb.Th), degree of anisotropy, and structure model index (SMI) were measured using microcomputed tomography. Quasi-static uniaxial compressive testing was performed on L3 vertebral bodies to assess failure load and stiffness. RESULTS: The TBS was significantly correlated to Tb.BV/TV and SMI (râeuro0/00=âeuro0/000.58 and -0.62; pâeuro0/00=âeuro0/000.02, 0.01), but not related to BMC and BMD. TBS was significantly correlated with stiffness (râeuro0/00=âeuro0/000.64; pâeuro0/00=âeuro0/000.007), independently of bone mass. Using stepwise multiple regression models, we failed to demonstrate that the combination of BMD and TBS was better at explaining mechanical behavior than either variable alone. However, the combination TBS, Tb.Th, and BMC did perform better than each parameter alone, explaining 79 % of the variability in stiffness. CONCLUSIONS: In our study, TBS was associated with microarchitecture parameters and with vertebral mechanical behavior, but TBS did not improve prediction of vertebral biomechanical properties in addition to aBMD.

A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

On some numerical aspects of an active strain model in cardiac mechanics

We are interested in the development, implementation and testing of an orthotropic model for cardiac contraction based on an active strain decomposition. Our model addresses the coupling of a transversely isotropic mechanical description at the cell level, with an orthotropic constitutive law for incompressible tissue at the macroscopic level. The main differences with the active stress model are addressed in detail, and a finite element discretization using Taylor-Hood and MINI elements is proposed and illustrated with numerical examples.

Changes in running mechanics and spring-mass behaviour induced by a 5-hour hilly running bout.

Abstract The aim of this study was to investigate changes in running mechanics and spring-mass behaviour with fatigue induced by 5-hour hilly running (5HHR). Running mechanics were measured pre- and post-5HHR at 10, 12 and 14 km · h(-1) on an instrumented treadmill in eight ultramarathon runners, and sampled at 1000 Hz for 10 consecutive steps. Contact (t(c) ) and aerial (t(a) ) times were determined from ground reaction force (GRF) signals and used to compute step frequency (f). Maximal GRF, loading rate, downward displacement of the centre of mass (Δz), and leg length change (ΔL) during the support phase were determined and used to compute both vertical (K(vert) ) and leg (K(leg) ) stiffness. A significant decrease in t(c) was observed at 12 and 14 km · h(-1) resulting in an increase of f at all speeds. Duty factor and F(max) significantly decreased at 10 km · h(-1). A significant increase in K(vert) and K(leg) was observed at all running speeds with significant decreases in Δz and ΔL. Despite the shorter duration, the changes in running mechanics appeared to be in the same direction (increased f and K(vert) , decrease in Δz and F(max) ) but of lower amplitude compared with those obtained after an ultra-trail or an ultramarathon.