PDF European Congress of Mathematics: Stockholm, June 27-july 2, 2004

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Pavlov, Gh. Atanasiu, V. Lilia Print, , pp.

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Generalized n-ary laws in the algebra H 4. Ibid, pp Automatic Control and Comp. Arithmetic method in the theory of discrete orthogonal transforms. SPIE , V. Algorithms, relalizable in Hamilton-Eisenstein codes, for two-dimensional discrete orthogonal transforms. Problem Inform. Transmission , No 3. Discrete orthogonal transforms with data representation in composition algebras. On the group algebras' hierarchy pertaining to the parametrization of fast algorithms of discrete orthogonal transforms.

In: V. Hlavac, R. Springer Verlag. Lecture Note Computer Science No ,-pp. Parametrization of some classes of fast algorithms of discrete orthogonal transforms. Pattern Recogn. On the parametrization of fast algorithms of discrete orthogonal transforms. Pattern Recognition and Image Analysis. A metric unified treatment of two-dimensional FFT. Track B. Vector-radix FFT with splitting the radix of fractional order. Chernov A. Sommer, J. Sommer, K. Daniilidis, J. In particular, new multiscale constitutive models that include innovative parameters and failure criteria will be developed, which will allow the simulation of the rupture of aortic tissue and propagation of the false lumen.

The development of thrombus in the false lumen will be modeled by using the theory of porous media, while the blood will be modeled as a non-Newtonian fluid. The 3D geometry of patient-specific morphologies will be reconstructed from medical images of carefully selected AD patients. Finally, computational fluid-structure interaction simulations will be performed in order to investigate the wall stresses, the hemodynamics, the false lumen propagation, and the thrombus formation and growth, etc. In addition, the 3D computational simulation results will be visualized by virtual reality techniques.

We expect that this project will improve awareness of this life-threatening disease, and lead to its more effective treatment and control within the general public of Austria and beyond. The Lead project will be carried out in the frame of the Graz Center of Computational Engineering GCCE , which has been founded in as an interdisciplinary cooperation platform for basic research in the realm of computational science and engineering.

The mission of GCCE is to improve computational techniques and its applicability by bringing together the expertise of leading scientists form different areas. TEM images: a various tissue components including collagen fibrils coming in and out of the imaging plane at various angles; b subdomain of a highlighting cross-sectioned collagen fibrils green circles and their nearest neighbors white lines that were automatically identified by a custom made ImageJ plugin.

Scale bars: a nm; b nm. The orange strings indicate the orientations of collagen fibrils, while the green structures correspond to proteoglycans PGs. Such 3D images are used to extract and quantify angular distributions between collagen and PGs, and to investigate their potential changes as a function of supra-physiological loading conditions.

For example, clinical interventions for treating atherosclerotic degeneration resulting in luminal narrowing often include balloon angioplasty. This invasive procedure involves the inflation of a catheter with the aim of increasing the lumen dimensions by pushing the obstructing plaque into the vessel wall.

Naturally, for this procedure a much higher pressure than the physiological blood pressure is required, and this causes microscopic-level tissue damage and results in stress-softening of the collagenous tissue. A database for the qualitative and quantitative description of arterial tissues will be obtained from uniaxial and biaxial extension tests performed on the tissue components of individual arterial layers loaded far beyond the physiological domain.

Towards this end cyclic tension-tests will be carried out on healthy as well as on collagenase and elastase treated arterial tissues to investigate component-specific stress softening behavior. Such tests enable the analysis of the macroscopic mechanical tissue response. In addition, structural analysis techniques such as Fourier transform infrared spectroscopy, scanning electron microscopy and nano-tomography will be used to study damage at the microscopic length scale, with a special focus on damage induced changes in the interfibrillar collagen distances and angular proteoglycan distributions.

The macroscopic response of the fiber-reinforced tissues will be described by a formulation based on micro-mechanical models characterizing the individual tissue components. These models take into account alterations of stochastic distributions of fiber properties as a consequence of the tissue overstretch.

In order to obtain a quantitative prediction of the material response, the model parameters will be adjusted to so as to fit data from the performed experiments based on least-squares minimization. Finally, the models will be validated by comparing finite element calculations with experiments performed on whole arterial wall segments.

Histological image characterizing the morphology of the thrombus-covered arterial wall. Mounted patch of a carotid artery a before the peeling test, shown from the side, and b during the testing procedure, shown from the top. An abdominal aortic aneurysm AAA is a vascular pathology associated with permanent and localized dilatation ballooning of the abdominal aorta. Continuous growth of AAAs may lead to wall rupture, which is a catastrophic event frequently associated with high mortality and serious life-threatening morbidity if not addressed.

AAA development is multifactorial and is primarily related to elastolysis. From a pathohistological point of view, aneurysmal degeneration is mainly attributed to loss of elastin and turnover of collagen within the aortic wall. Therefore, investigation of the biomechanical properties of AAA tissues provides an essential insight into growth and remodeling, and advances our understanding of disease progression and intrinsic rupture mechanism.

In our lab we focus on a few fields in AAA research:. By performing biaxial extension and peeling tests of the intraluminal thrombus ILT and the thrombus-covered wall see figure , the mechanical responses are systematically explored and more appropriate 3D material models developed. The microstructural characterization of ILT samples serves as the basis for the determination of relative thrombus ages.

We propose the four age phases: very fresh, young, intermediate and old. Mass fraction analyses determine dry weight percentages of elastin and collagen within the layer-specific aneurysmal aortic structure, which, in turn, affect the mechanical properties at the tissue level. In addition, our effort is also aimed at a refined understanding of the effect of ILT age on AAA wall mechanics and gender differences. Multiscale assessment of human aortic tissues: biaxial extension testing simultaneously applied to two-photon fluorescence microscopy and second harmonic generation imaging to obtain material properties of collagen, elastin and SMC at the micro and macroscales.

Arteries have a remarkable ability to adapt in response to altered hemodynamics, disease progression, and injury. Altered arterial tissue properties in diseased conditions such as atherosclerosis arise from tissue remodeling which is associated with changes in wall constituents at different length scales. This project is based on the fact that multiscale biomechanical analyses of healthy and diseased arteries and its modeling can be used to better understand several pathophysiological processes at different length scales. This also allows the identification of relationships between structural alterations and diseases.

In this study aortic tissue imaging and mechanical characterization techniques will be combined at the macro-, micro- and nanoscale to develop and validate next generation multiscale constitutive models. Moreover, load-dependent ultrastructural characteristics of interfibrillar proteoglycans, and of constituents of collagen e.

The combination of the obtained data is used for the development of novel constitutive models based on multiscale homogenization techniques that explicitly incorporate nanoscale, microscale and macroscale mechanisms as well as their coupling effects. The novelties of this project are the application and development of experimental methods on different hierarchical scales, and the intelligent combination, integration and validation of experimental techniques to give an explanation for the role of important constituents in arterial mechanics, physiology, and pathology.

The pursued approach is a step forward to investigate and understand the development, growth and remodeling principles of biological tissues and their response to pathological conditions. This project approaches well-defined clinical problems from engineering and biological perspectives.

Three main stages of the intracellular vesicle transport; graphics adapted from Olkkonen and Ikonen Within the multiscale FEM the simulation of a material with a heterogeneous microstructure is split into two boundary-value problems. One important characteristics of eukaryotic cells are the enormous complexity of their membrane anatomy and the high level of organization of the transport processes.

The surprisingly precise manner of the routing of vesicles to various intracellular and extracellular destinations can be illustrated by numerous examples such as the release of neurotransmitters into the presynaptic region of a nerve cell and the export of insulin to the cell surface. The key idea of this particular project is to couple results of biomedical investigations and mechano-mathematical models with the highly efficient engineering software packages in order to simulate this type of processes, in particular the vesicle transport.

The results bridge the theoretical investigations and medical practice and shift the paradigm in understanding and remedying different diseases, which certainly is the primary and long-term goal of the project. The project objectives coincide with the modeling of single aspects of the vesicle transport, namely with the simulation of mechanisms by which the vesicles form, find their correct destination, fuse with organelles and deliver their cargo.

The application of several different approaches is envisaged for this purpose, but three main strategies build the underlying skeleton: the theory of lipid bilayer membranes, the homogenization method and the diffusion theory. The mentioned approaches will furthermore be combined with the modern numerical techniques such as the finite element method and the multiscale finite element method. In the final stage, the realization of single objectives will allow the simulation of vesicle transport as a continuous process and the study of the impact of various factors on the whole process.


  1. The symbol theory.
  2. Midsummer.
  3. Natural Computing and Beyond: Winter School Hakodate 2011, Hakodate, Japan, March 2011 and 6th International Workshop on Natural Computing, Tokyo, Japan, March 2012, Proceedings.

In this way, the project will yield a significant shift from "static" bio-computations related to the single cell compartments and substeps of its activities, to the "dynamic" simulation of the real living processes. Cross-section of an intraluminal thrombus with its three individual layers: luminal L , medial M , abluminal A. The individual natural configurations of the constituents are stress free and separated for each constituent.

Effective biomechanical modeling of the development of an intraluminal thrombus ILT has the potential to help us answer the question "Why do certain abdominal aortic aneurysms AAAs grow and eventually rupture? The goal of this project, therefore, is to quantify the development of ILT from the initial blood clot to a mature formation, with special attention to axial changes in the clot structure.

We combine and exploit three recent advances: development of a general theoretical framework for ILT growth and remodeling, FE simulations capable of addressing mass changes, and a well-equipped laboratory with precisely defined experimental procedures for ILT specimens. Thus, the aims for this project are:. To develop a mathematical theory of growth and remodeling of ILT considering its three main layers. To employ a rule-of-mixtures relation for the stress response and a full mixture theory for the turnover of constituents in a stressed configuration on axially symmetric geometry axial and radial changes are addressed.

To perform a set of experiments with samples harvested from open surgical aneurysm repair. To use specimens for mechanical tests and histological analyses radial and axial changes of biomolecules, including proteases. To use the results to tune unknown parameters in the numerical model with mechanical and histological data.

This leads to more accurate ILT models capable of predicting the layered thrombus structure, concentrations of elastases and collagenases, and eventually the rate of AAA enlargement. To implement the developed model in a FE code capable of simulating evolving changes in AAA structures and properties. To verify the results with available experimental data. Successful realization advances the field of vascular mechanics by allowing, for the first time, quantification of the kinetics of an ILT within AAAs, and factors that influence aneurysmal growth and rupture risk.

Finite elment analysis of two different geometrical AAA models. Maximum principal stress fields in an asymmetric a and a symmetric b aneurysm. Abdominal aortic aneurysms AAAs are most common in men aged 65 and older, and the incidence of this disease is therefore on the rise in our aging population.

Vicentiu Radulescu | Universitatea din Craiova - odacolug.tk

It is universally agreed that mechanical factors play key roles in the natural history of AAAs and their response to treatment, yet there is no widely accepted tool for quantifying or predict the mechanobiology and biomechanics of AAAs. We bring together expertise from different institutions: JD Humphrey Yale University has expertise in developing complex constitutive theories for soft tissues, D Vorp University of Pittsburgh has expertise in quantifying biomechanical properties of abdominal aortic aneurysms and associated intraluminal thrombi, GA Holzapfel TU Graz has expertise in computational biosolid mechanics, C Taylor Stanford University with expertise in computational biofluid mechanics, and C Zarins Stanford University with expertise in vascular surgery and animal models of disease progression.

Together, we will develop the first computational tool to better understand the natural history of aneurysms and responses to intervention of AAA. The tool extends the cardiovascular research capabilities at the Stanford University National Center for Biomedical Computing. Prepared myocardial specimen, clamped into a biaxial testing device. The orientation of the fiber directions are in red; b contour plots of the fiber stress component of the strain-energy function for mmHg. In the research area of cardiac mechanics and electrophysiology it is of utmost importance to identify accurate material properties of the myocardium.

This is important for the description of various phenomena such as mechanoelectric feedback or heart wall thickening. To better understand the highly nonlinear mechanics of complex structures such as the passive myocardium under different loading conditions, a rationally-based material model is required. Unfortunately, there are insufficient experimental data of the human myocardium available for material parameter estimation and for the development of adequate material models.

This project aims at determining the biaxial tensile and triaxial shear properties of the passive human myocardium. Moreover, the underlying microstructure of tissues will be determined, and structurally-based material models will be fitted to experimental data.

Mircea Mustață

Using new state-of-the-art equipment, planar biaxial extension tests will be performed to determine the biaxial tensile properties of the human myocardium. Shear properties will be examined using triaxial shear tests on cubic specimens excised from an adjacent region of the biaxial tensile specimens. Multiphoton microscopy will be used to study the 3D microstructure of the tissue to emphasize the 3D orientation and dispersion of the muscle fibers and the adjacent collagen fabrics.

The novel combination of biaxial tensile test data with different loading protocols and shear test data at different specimen orientations will facilitate capture of the direction-dependent material response. With these mechanical data sets, combined with structural data, a better material model can be constructed.

Such a model will then be used in numerical simulations to better understand ventricular mechanics, a step that is needed for the improvement of the medical treatment of heart diseases. Photograph of a prepared adipose tissue specimen inserted in a biaxial tensile device ready for biaxial tensile tests. Photograph of a cube-shaped adipose tissue specimen inserted in a triaxial testing device and subjected to simple shear loading.

A considerable number of plastic surgery procedures relate to reconstructive surgery associated with complex soft tissue contour defects, mainly subcutaneous adipose tissue, in different anatomical regions arising from trauma, burn injuries, cancer resections or congenital deformities.

The most appropriate surgical intervention necessary for reconstructing the contour defect is by use of equivalent soft tissues, resulting in optimal restoration of form and function. Promising results in the field of plastic and reconstructive surgery are apparent in breast and facial soft tissue simulation using the finite element method.

Currently, the development of a constitutive model for adipose tissues, which could be implemented in multilayer numerical models for human soft tissue deformation simulation, is difficult because knowledge of the mechanical parameters of fat tissue is limited.

Therefore, this study aims to determine the multiaxial mechanical properties and the underlying microstructure of human abdominal adipose tissues. Human abdominal adipose tissue samples remaining from breast reconstruction surgeries or from abdominal plastic surgeries are mechanically investigated.

Two types of mechanical tests are conducted: biaxial tensile and triaxial shear tests. Moreover, dynamic biaxial tensile and shear tests are performed in order to account for the viscous features of the adipose tissue. Additionally, the microstructure of the specimens is examined by histology. Second-harmonic generation image showing collagen fibers in a transversal section of the cartilage with calculated local 3D fiber directions projected onto the image red lines. Top: stress distribution based on a model with patient-specific collagen fibers and inhomogeneous material properties; Bottom: stress distribution based on a model without collagen fibers and homogeneous material properties.

Cartilage tissue is a multi-phase material composed of fluid, electrolytes, chondrocytes, collagen fibers, proteoglycans and other glycoproteins, and it contains a fiber network of predominantly Type II collagen which provides tensile strength and stiffness to the solid phase, a proteoglycan gel. Working with international collaborators, we proposed several 3D, large deformation constitutive models for articular cartilage to facilitate finite element FE simulation of cartilage morphology and material response. An initial phenomenological and patient-specific simulation approach focuses on incorporating the collagen fiber fabric in a 3D viscoelastic fiber-reinforced finite-strain setting, where each material parameter has a clear physical interpretation.

A novel feature of the proposed method is 3D sample-specific numerical tracking of the fiber fabric deformation under general loading. Next, we proposed an extended constitutive model for human articular cartilage that considers fiber dispersion, and demonstrated a numerical approach for incorporating DT-MRI We developed a FE approach to determine the geometry, the meshing, and the fiber structural input estimated principal fiber direction and dispersion. To further improve FE modeling fidelity, we quantified the 3D morphology of articular cartilage using second-harmonic imaging microscopy, and connected the imaging data to specific parameters of a new 3D large-strain constitutive model.

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Using representative numerical examples on the mechanical response of cartilage, we reproduced several features which have been demonstrated experimentally in the cartilage mechanics literature, e. Surface mesh of an abdominal aortic aneurysm extruded radially to determine the arterial wall layers. Modern medicine is irreversibly shifting towards less invasive surgical procedures.

fudurijypeci.tk Conventional open surgery approaches are systematically being replaced by interventions that reduce access trauma and thereby minimize pain and hospitalization periods for patients. The downside of this approach is that it is highly demanding for the interventionalist, entailing unacceptable risks for the patient. In the perspective of patient safety, the project SCATh, i. These procedures have the common denominator of dealing with cardiovascular disease, the main cause of death in the EU.

SCATh provides the interventionalist with visual and haptic tools for robust and accurate catheter guidance, which is developed through novel approaches, by fusing preoperative patient-specific anatomical and mechanical models and intra-operative data streams from in situ sensors.

By complementing and augmenting the skills of the interventionalist, patient safety drastically increases and at the same time, potentially life-threatening complications, which result from poor or damaging X-ray, use of contrast agents visualization or poor surgical technique, can be avoided. The new concept for tracking, sensing, modeling and manipulation of the surgical environment is integrated with existing technological state-of-the-art in close cooperation with clinical experts and industrial partners, both in the design and in the evaluation phases.

The common efforts delivered during this project result in a demonstrator applied to a carefully selected set of catheter procedures. Moreover, many of the technological advances created during SCATh touch upon minimally invasive surgical procedures in general.

Overview of Events in the Related Fields of Biomechanics (selected)

Budday receives the Acta Student Award of the Journal Acta Biomaterialia for the paper "Mechanical characterization of human brain tissue". Pierce, T.

Ricken and G.