Showing papers in "Handbook of Numerical Analysis in 2004"

Mathematical Modelling and Numerical Simulation of the Cardiovascular System

Abstract: Publisher Summary The development of mathematical models, algorithms and numerical simulation tools for the investigation of the human cardiovascular system has received a great impulse in the past years This chapter addresses the problem of developing models for the numerical simulation of the human circulatory system It particularly focuses on the problem of hemodynamics in large human arteries There are several important aspects, which require the use of sophisticated mathematical and numerical tools, such as the reconstruction of geometries from medical data; the transport of biochemicals in blood and vessel wall tissue; the heart dynamics; and blood rheology Besides, the need of validating the models calls for development of accurate in-vivo measurement techniques The number and complexity of the mathematical, numerical and technological problems involved makes the development of tools for accurate, reliable and efficient simulations of the human cardiovascular system one of the challenges of the next decades

Soft Tissue Modeling for Surgery Simulation

Abstract: This chapter presents different algorithms for modeling soft tissue deformation in the context of surgery simulation These algorithms make radical simplifications about tissue material property, tissue visco-elasticity and tissue anatomy The chapter describes the principles and the components of a surgical simulator It also presents the process of building a patient-specific hepatic surgery simulator from a set of medical images The different stages of computation leading to the creation of a volumetric tetrahedral mesh from a medical image are especially emphasized Later, it describes the five main hypotheses that are made in the proposed soft tissue models Moreover, the main equations of isotropic and transversally anisotropic linear elasticity in continuum mechanics are also presented The discretization of these equations is presented that are based on finite element modeling The simple linear tetrahedron element is presented that provide closed form expressions of local and global stiffness matrices After describing the types of boundary conditions existing in surgery simulation, the static and dynamic equilibrium equations in their matrix form are derived The chapter introduces a first model of soft tissue; it is based on the off-line inversion of the stiffness matrix and can be computed very efficiently as long as no topology change is required A second soft tissue model allows to perform cutting and tearing but with less efficiency as the previous model A combination of the two previous models, called “hybrid model” is also presented in the chapter It also introduces an extension of the second soft tissue model that implements large displacement elasticity

Human models for crash and impact simulation

Abstract: Publisher Summary This chapter discusses the application of computational impact biomechanics to the consequences of real world passenger car accidents on human occupants, using computer models in numerical simulations with industrial crash codes. The corresponding developments are illustrated on the subject of safety simulations of human passenger car occupants. With some adaptations, the developed models apply equally well to the simulation of pedestrian accidents and to the design for occupant safety of motorbikes, trucks, railway vehicles, airborne vehicles, seagoing vessels and more. The human models elaborated in the chapter belong to the class of finite element models. They can be adapted, specialized and packaged for other industrial applications in human ergonomics and comfort analysis and design, in situations where humans operate at their work place, as military combatants, or in sports and leisure activities and more. In the medical field, biomechanical human models can serve as a basis for the simulation and design of orthopedic prostheses, for bone fracture planning, physical rehabilitation analysis, the simulation of blood flow, artificial blood vessels, artificial heart valves, bypass operations, and heart muscle activity, and virtual organ surgery.

Computational Methods for Cardiac Electrophysiology

Abstract: Computational methods for tissue biomechanics, electrophysiology, and cellular physiology separately provide frameworks for modeling functions of cardiac tissue We review strategies currently available for meeting the goal of structurally and functionally integrated models of cardiac electromechanical function that combine data-intensive cellular systems models with compute-intensive anatomically detailed multiscale simulations

Mathematical Analysis, Controllability and Numerical Simulation of a Simple Model of Avascular Tumor Growth

Abstract: Publisher Summary This chapter presents the study of the mathematical analysis, the controllability and a numerical simulation for a simple, avascular model of growth of a tumor. It describes the biological phenomenology of several processes, which influence the growth and development of tumors. The mathematical modelling is presented by describing different models of partial differential equations (PDE). The chapter presents the proofs of the solvability of the model equations and discusses the uniqueness of solutions under additional conditions. It discusses the controllability of the growth of the tumor by a localized internal action of the inhibitor on a nonnecrotic tumor. It is obvious that this type of results has merely a mathematical interest and it does not suggest any special therapeutical strategy to inhibit tumor growth. Nevertheless the results show that there is not any obstruction to the controllability (as it appears, for instance, in some similar PDE's models). The chapter addresses the numerical simulation of the problem.

Recovering Displacements and Deformations from 3D Medical Images Using Biomechanical Models

Abstract: Publisher Summary This chapter describes the use of biomechanical models for the estimation of non-rigid displacement fields from sequences of three-dimensional medical images Later, the chapter describes two case studies—namely, (1) the estimation of brain shift for neurosurgery and (2) the estimation of left ventricular deformation, the proper modeling of the underlying tissue is important in order to ensure reliable and robust estimation of the underlying displacement and consequently the deformation Modeling is needed as the image-derived displacement estimates generated from a number of methods have the following characteristics: (1) they are sparse, (2) they are noise-corrupted, and (3) they may contain only partial information The both case studies illustrate the use of this underlying mathematical framework The chapter also describes methodology to compensate for brain shift in image guided neurosurgery and algorithms to estimate the deformation of the left ventricle of the heart The specifics of the mechanical model are presented, followed by validation results on real and simulated data

Methods for Modeling and Predicting Mechanical Deformations of the Breast under External Perturbations

Abstract: Currently, high field (1.5 T) superconducting MR imaging does not allow live guidance during needle breast procedures. The current procedure allows the physician only to calculate approximately the location and extent of a cancerous tumor in the compressed patient breast before inserting the needle. It can then become relatively uncertain that the tissue specimen removed during the biopsy actually belongs to the lesion of interest. A new method for guiding clinical breast biopsy is presented, based on a deformable finite element model of the breast. The geometry of the model is constructed from MR data, and its mechanical properties are modeled using a non-linear material model. This method allows imaging the breast without or with mild compression before the procedure, then compressing the breast and using the finite element model to predict the tumor’s position during the procedure. A silicon phantom containing a stiff inclusion was imaged uncompressed then compressed. A model of the phantom was constructed and compressed using custom-written software, and also using a commercial FEM simulation package. The displacement of the inclusion’s corners was recorded both in the real phantom and in the two compressed models. A patient’s breast was imaged uncompressed then compressed. A deformable model of the uncompressed breast was constructed, then compressed. The displacement of a cyst and of two vitamin E pills taped to the surface of the breast were recorded both in the real and in the modeled breast. The entire procedure lasted less than a half-hour, making it clinically useful. The results show that it is possible to create a deformable model of the breast based on finite elements with non-linear material properties, capable of modeling and predicting breast deformations in a clinically useful amount of time.