Bernhard Quatember

Geometric modeling and motion analysis of the epicardial surface of the heart

Pathological processes cause abnormal regional motions of the heart. Regional wall motion analyses are important to evaluate the success of therapy, especially of cell therapy, since the recovery of the heart in cell therapy proceeds slowly and results in only small changes of ventricular wall motility. The usual ultrasound imaging of heart motion is too inaccurate to be considered as an appropriate method. MRI studies are more accurate, but insufficient to reliably detect small changes in regional ventricular wall motility. We thus aim at a more accurate method of motion analysis. Our approach is based on two imaging modalities, viz. cardiac CT and biplane cineangiography. The epicardial surface represented in the CT data set at the end of the diastole is registered to the three-dimensionally reconstructed epicardial artery tree from the angiograms in end-diastolic position. The motion tracking procedures are carried out by applying thin-plate spline transformations between the epicardial artery trees belonging to consecutive frames of our cineangiographic imagery.

Radial Basis Functions and Splines for Landmark‐Based Registration of Medical Images

We propose the use of a class of spline functions, called Lobachevsky splines, for landmark‐based registration. We recall the analytic expressions of the Lobachevsky splines and some of their properties, reasoning in the context of probability theory. These functions have simple analytic expressions and compact support. Numerical tests appear to be promising.

Visualization Aspects of Motion Tracking and Analysis of the Outer Surface of the Left Ventricle

The quantitative assessment of the motion and deformation of the heart is instrumental to diagnosis. We developed an accurate method for tracking and analysing the regional motion and deformation of the heart. To be of clinical value, the results must be visualized, and we paid much attention to all relevant visualization aspects.

Development of an accurate method for motion analyses of the heart wall based on medical imagery

In the field of diagnosis and therapy of coronary artery disease, it is highly important to acquire a fair knowledge of the heart wall motion and its regional variations. Unfortunately, the accuracy of all currently applied methods for the acquisition and analysis of the regional heart wall motion is rather limited. We developed a sufficiently accurate technique for tracking and analysing the regional motion of the epicardium throughout the cardiac cycle which is based on cardiac CT and biplane angiography. In the end-diastolic position, the epicardial surface in the 3D CT data is segmented and registered to the skeleton representation of the coronary artery tree obtained from the end-diastolic frame of a biplane cineangiogram. In doing so, a landmark-based approach based on TPS transformations has been chosen. The motion tracking is accomplished by carrying out further landmark-based TPS transformations of the surface to the successive frames of the cineangiogram.

Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration

In image registration, a proper transformation should be topology preserving. Especially for landmark-based image registration, if the displacement of one landmark is larger enough than those of neighbourhood landmarks, topology violation will be occurred. This paper aims to analyse the topology preservation of some Radial Basis Functions (RBFs) which are used to model deformations in image registration. Matern functions are quite common in the statistic literature (see, e.g. [9, 13]). In this paper, we use them to solve the landmark-based image registration problem. We present the topology preservation properties of RBFs in one landmark and four landmarks model respectively. Numerical results of three kinds of Matern transformations are compared with results of Gaussian, Wendland’s, and Wu’s functions.

Mathematical Modelling and Simulation of Coronary Blood Flow

As in vivo observations and measurements of flow conditions in the coronary circulation are extremely difficult and clinically almost infeasible, the use of mathematical models and the performance of simulation studies are the only practical way for a good understanding of coronary haemodynamics. As the range of clinical applicability of known models in this field is rather limited, we developed a detailed lumped parameter model of the coronary haemodynamics. From the beginning we aimed at its use as an aid for interventional cardiologists and heart surgeons. At this stage of development, our lumped parameter model can already be of some help to physicians, when appraising the adverse effects of stenoses on myocardial blood supply and assessing the attainable improvement of the supply by therapy. The crude approximations inherent in lumped parameter modelling restrict the applicability of this unsophisticated approach to an imprecise global assessment of the blood supply to the myocardium and its detoriation in the case of coronary artery disease. However, to be able to assess other specific pathophysiological processes, such as thrombus development and stenoses growth, for instance, we need precise knowledge of the local three-dimensional flow pattern in a stenosed section of the coronary artery tree, especially around the apex of the stenosis. We present simulation studies of the three-dimensional flow in stenosed sections of the coronary arteries, based on a distributed parameter modelling approach. In these studies, the governing partial differential equations are solved with the finite element method. Particular attention is given to the acquisition of patient-specific data, especially of data describing the geometry of the patient’s epicardial arteries, derived from medical images. These data are required not only for the patient-specific adaptation of our lumped parameter model but also, in the case of our three-dimensional flow simulations, for the generation of a finite element mesh in the flow domain under investigation. However, we deal with the mesh generation issues only very briefly.

Simulation of Flow Patterns Within the Human Respiratory System

A nonlinear simulation model of the respiratory system is presented here. It describes the flow patterns as well as the specific gas mixing and distribution processes that occur in the tracheobronchial tree. The model is based on the commonly used morphometric scheme of E. Weibel. It consists of a “pressure‐flow submodel” and a “gas mixing submodel. The former is a lumped parameter model consisting of 24 lumped components. The second type, the “gas mixing submodel,” enables the simulation of the mixing processes in the trachea and in the larger bronchi (up to the 10th generation). Several simulation studies that are based on it have been carried out; they deal with both the physiological conditions and the specific pathological changes that occur in the small airways during the early stages of chronic obstructive bronchitis.

GRID software solution for the segmentation of the coronary artery tree in biplane angiograms

We are developing a computer system that will enable the precise diagnosis and the planning of therapy in the field of coronary artery disease. The implementation of this system is carried out within the framework of a computational GRID (Austrian GRID). Our aim is to obtain patient-specific simulations of coronary hemodynamics. The geometry of the flow domain is derived from biplane angiograms. In these images, the coronary artery tree must be segmented. Thereafter, a three-dimensional reconstruction method is applied. However, biplane angiograms are subject to noise, blur, and image deterioration caused by background structures. In order to eliminate these disturbances, several image pre-processing steps and a newly developed segmentation method must be carried out. In this paper we will concentrate on our new segmentation approach and show that the segmentation of the coronary artery tree can be solved advantageously within the framework of a computational GRID.