Jiří Stehlík

Multivariate stochastic downscaling model for generating daily precipitation series based on atmospheric circulation

The goal of the paper is to present a model for generating daily precipitation time series and its applications to two climatologically different areas. The rainfall is modeled as stochastic process coupled to atmospheric circulation. Rainfall is linked to the circulation patterns using conditional model parameters. Any kind of circulation pattern classification can be used for this purpose. In this study a new fuzzy rule based method of circulation patterns classification was used. The advantage of this classification technique is the fact that in contrast to common circulation patterns classifications its objective is to explain the variability of local precipitation. It means that the circulation patterns explain the relation between large-scale atmospheric circulation and surface climate (precipitation). Therefore the circulation patterns obtained by this classification method are suitable as input for the subsequent precipitation downscaling. The model was successfully applied in two regions with different climate conditions: Central Europe (Germany) and Eastern Mediterranean (Greece). Several tests like comparison of mean seasonal cycles, comparison of mean values and deviations of yearly totals and other standard diagnostics showed that simulated values agree fairly well with historical data.

Numerical simulation of some biomechanical problems

The paper is concerned with the numerical solution of non-linear conservation laws, and the contribution biomechanical models of spine and of loaded wrist are formulated and analysed. The models are based on a contact problem in non-linear elastic rheology. The stress-strain relation is derived from a positive definite strain energy density function. For a weak solution of the problem, a variational inequality approach is used. Then the secant modules method and the finite element method are applied. First, the model of the weight bearing wrist, and secondly, the model of the Chances fracture of lumbar spine are discussed.

On the 2D and 3D finite element simulation in orthopaedy using MRI

Abnormality in human joint biomechanics is the main cause of the degenerative disease development, therefore the description and correction of the joint biomechanics is essential for adequate treatment. We present an approach how to obtain the data of a patient and how to use these data subsequently in 3D mathematical models. The magnetic resonance imaging (MRI) of the hip joint is used as a base for 3D simulations. The MRI output has to be transformed into a form readable by our finite element (FE) software. Two transformators were developed for this purpose. To analyse the model as a contact problem, some further transformations are necessary. A contact is assumed between the femur and the pelvis. We compare the results both from the elastic and from the contact analyses.

Application of numerical modelling of osteotomy to orthopaedic practice

During the development of an osteoarthritic hip joint, osteophytes, cysts as well as arthrosis originate on the contact boundary between the femoral head and the acetabulum in highly loaded human joints. The purpose of proximal femur osteotomy is to bring the femoral head into a new position inside the acetabulum. The corrective options of intertrochanteric osteotomy most frequently used in orthopaedic practice are valgization, varization, displacements, oblique displacements, lateralization, extension, rotation or shortening of the shaft. The present widespread tomographic measurement methods, such as computer tomography (CT), magnetic resonance imaging (MRI) and 2D or 3D reconstruction involve the simulation of surgical problems of osteotomy, as well as the simulation of the reconstruction of the function of the hip joint after the operation. The results of numerical modelling of osteotomy concerning contact problems, will be presented in the contribution.

Numerical methods for constrained optimization in 2D and 3D biomechanics

This paper formulates, analyses and discusses 2D and 3D static and dynamic model problems in the orthopaedic practice. Finite element approximations, algorithms and iterative methods for constrained optimization are discussed. Since the conjugate gradient method is one of the most effective methods for both unconstrained and constrained optimization, it can be applied without or with preconditioning for solving the basic step of the discretized problem. A comparison of several preconditioned conjugate gradient methods is discussed. The problems discussed are applied to analyses of real patients. Finally, the the numerical results are discussed. Copyright

Mathematical simulation of osteotomy. Numerical analysis and results

Abstract In this paper, a model problem of one vital surgical technique in orthopaedics, the so-called osteotomy, will be analyzed numerically. The model problem will be formulated mathematically. The problem leads to solving the variational equality and inequality. The finite element method will be used in numerical solution, and the algorithm will be given.

Mathematical and computational methods in biomechanics of human skeletal systems : an introduction

PREFACE. ACKNOWLEDGMENTS. PART I ANATOMY, BIOMECHANICS, AND ALLOARTHROPLASTY OF HUMAN JOINTS. 1 BIOMECHANICS OF THE HUMAN SKELETON ANDTHE PROBLEM OF ALLOARTHROPLASTY. 1.1 Introduction to History of Biomechanics and Alloarthroplasty. 1.2 Biomechanics of Human Joints and Tissues. 2 INTRODUCTION TOTHE ANATOMY OF THE SKELETAL SYSTEM. 2.1 Anatomy of the Skeletal System. 2.2 Human Joints and Their Functions. 2.3 Tribology of Human Joints. 2.4 Biomechanics of the Skeletal System. 3 TOTAL REPLACEMENT OF HUMAN JOINTS. 3.1 View of Arthroplasty Developments. 3.2 Static and Dynamic Loading of Human Joint Replacements. 3.3 Mechanical Destruction of Implants and Demands on Human Joint Arthroplasty. 3.4 Biomaterials in Ostheosynthesis and Alloarthroplasty. 3.5 Artificial Joint Replacements. PART II MATHEMATICAL MODELS OF BIOMECHANICS. 4 BACKGROUND OF BIOMECHANICS. 4.1 Introduction. 4.2 Fundamentals of Continuum Mechanics. 4.3 Background of the Static and Dynamic Continuum Mechanics in Different Rheologies. 4.4 Background of the Quasi-Static and Dynamic Continuum Mechanics in Thermo(visco)elastic Rheology. 5 MATHEMATICAL MODELS OF PARTICULAR PARTS OF THE HUMAN SKELETON AND JOINTS ANDTHEIR REPLACEMENTS BASED ON BOUNDARY VALUE PROBLEM ANALYSES. 5.1 Introduction. 5.2 Mathematical Models of Human Joints and of Their Total Replacements asWell as of Parts of the Human Body. 5.3 Mathematical Models of Human Body Parts and Human Joints and Their Total Replacements Based on the Boundary Value Problems in (Thermo)elasticity. 5.4 Biomechanical Model of a Long Bone. 5.5 Mathematical Model of a Loaded Long Bone Based on Composite Biomaterials. 5.6 Stochastic Approach. 5.7 Mathematical Model of Heat Generation and Heat Propagation in the Neighborhood of the Bone Cement. Problems of Bone Necrosis. 6 MATHEMATICAL ANALYSES AND NUMERICAL SOLUTIONS OF FUNDAMENTAL BIOMECHANICAL PROBLEMS. 6.1 Background of Functional Analysis, Function Spaces, and Variational Inequalities. 6.2 Variational Equations and Inequalities and Their Numerical Approximations. 6.3 Biomechanical Models of Human Joints and Their Total Replacements. 6.4 Stress Strain Analysis of Total Human Joint Replacements in Linear, Nonlinear, Elasticity, and Thermoelasticity: Static Cases, Finite Element Approximations, Homogenization and Domain Decomposition Methods, and Algorithms. 6.5 Stress Strain Analyses of Human Joints and Their Replacements Based on Quasi-Static and Dynamic Multibody Contact Problems in Viscoelastic Rheologies. 6.6 Algorithms. 6.7 Viscoplastic Model of Total Human Joint Replacements. 6.8 Optimal Shape Design in Biomechanics of Human Joint Replacements. 6.9 Worst-Scenario Method in Biomechanics of Human Joint Replacements. 6.10 Biomechanical Models of Human Joint Replacements Coupling Bi- and Unilateral Contacts, Friction, Adhesion, and Wear. PART III BIOMECHANICAL ANALYSES OF PARTICULAR PARTS OF THE HUMAN SKELETON, JOINTS, AND THEIR REPLACEMENTS. 7 BIOMECHANICAL MODELS BASED ON CONTACT PROBLEMS AND BIOMECHANICAL ANALYSES OF SOME HUMAN JOINTS,THEIR TOTAL REPLACEMENTS, AND SOME OTHER PARTS OF THE HUMAN SKELETON. 7.1 Introduction to the Biomechanics of Statically Loaded and of Moving Loaded Human Body. 7.2 Bone Remodeling and the Corresponding Mathematical Model. 7.3 Biomechanical Studies of Cysts, Osteophytes, and of Inter- and Subtrochanteric Osteotomy of the Femur and the Knee Joint. 7.4 Biomechanical Analysis of the Loosened Total Hip Arthroplasty (THA). 7.5 Biomechanical Analysis of the Hip Joint after THA Implanting and Subtrochanteric Osteotomy Healing. 7.6 Analysis of Loaded Tubular Long Bone Filled with Marrow Tissue. 7.7 Numerical Analysis of theWeight-Bearing Total Knee Replacement Analysis of Effect of Axial Angle Changes onWeight-bearing Total Knee Arthroplasty. 7.8 Total Knee Replacement with Rotational Polyethylene Insert. 7.9 Computer-Assisted Surgery in Orthopedics: A Perspective. 7.10 Biomechanical and Mathematical Models of the Thoracolumbal Spine. 7.11 Biomechanical and Mathematical Models of Joints of the Upper Limbs. 7.12 Mathematical and Biomechanical Analyses of the Temporomandibular Joint. APPENDIX. A.1 List of Notations. A.2 Cartesian Tensors. A.3 Some Fundamental Theorems. A.4 Elementary Inequalities. A.5 Finite Element Method. REFERENCES. INDEX.

On the Stress-Strain Analysis of the Knee Replacement

The paper deals with the stress/strain analysis of an artificial knee joint. Three cases, where femoral part of the knee joint part is cut across under 3, 5 and 7 degrees, are analysed. Finite element method and the nonoverlapping decomposition technique for the contact problem in elasticity are applied. Numerical experiments are presented and discussed.

Numerical analysis of the loosened total hip replacements (THR)

The paper deals with mathematical simulation of a loosened hip joint, simulation of mechanical processes taking place during static and dynamic burdening and their mathematical description. The main result of the paper consists of the existence theorem and the analysis of the loosened total hip replacement (THR).