Steven A. Mackay

Methods for evaluating cardiac wall motion in three dimensions using bifurcation points of the coronary arterial tree.

An accurate three-dimensional (3D) representation of heart wall motion would be an important means of evaluating cardiac function. To accomplish this, we have developed an interactive computer graphics system designed to enter the time-dependent 3D positions of bifurcations of the coronary arterial tree. These bifurcations are precise markers of the epicardial surface, and their motions accurately represent the motion of the underlying heart wall. We demonstrate techniques for calculating local wall motion, including displacement and velocity, for determining a time-dependent center-of-contraction point towards which the epicardium tends to move and for tracking the mechanical contraction wave using cross-correlation methods. We have applied these techniques to study seven patients with normal left ventriculograms and coronary arteriograms. We have found these methods to be generally applicable and to provide information not obtainable without 3D analysis.

Graphics methods for tracking three-dimensional heart wall motion

Abstract An analysis of heart wall motion requires that specific points on the wall be identified and their movements tracked in three dimensions over several heart beats. A method to reconstruct time-dependent 3D coordinates from any two or more perspective views has been developed. We have used this method to determine accurately the 3D dynamics of bifurcation points of the coronary arteries or surgically implanted markers by tracking their projections in both views of a biplane coronary cineangiogram. The tracking operation is aided by a sophisticated interactive computer system which superimposes an animated graphics display onto the film image. This allows entries to be checked and corrected immediately. The most powerful tool provided by the graphics system is the ability to display the backprojections of positions from one view as auxiliary lines across the other view on which the projection of the point of interest must lie. We provide some examples of cardiac wall motion measures we have made using this system.

Graphics input tools for interactive motion analysis

Abstract The use of Galatea, an interactive animated graphics system for analyzing dynamic phenomena recorded on movie film, is discussed. An analyst views a film with a stop-motion projector and uses a digitizing pen to transcribe features of interest, for example, by following a wandering amoeba. Simultaneously, an animated graphics image corresponding to the data entries is generated and, using a projection kinescope, is superimposed on the film image, synchronized with it as it runs. The system acts like “dynamic tracing paper” for the film and provides a set of real-time hand-eye input tools and graphical data types useful for motion analysis. After a brief overview of Galatea and a discussion of the advantages of interactive motion analysis systems, the paper lists the input tools and data types that have been used. An accuracy experiment is described. The use of the system to solve a number of different motion analysis problems is discussed, illustrated by applications in cell biology, anatomy, and radiology.

3D Galatea: Entry of three-dimensional moving points from multiple perspective views

We describe an interactive graphics system for the entry of three-dimensional moving points from multiple perspective views. This work represents a major extension of Galatea, our system for graphics-assisted 2D motion analysis. 3D Galatea permits reconstruction of 3D time-dependent positions from 2D entries in two or more perspective views. The system supports a general approach for calibrating perspective views. This method, based on work of Sutherland, uses a known 3D reference object to calibrate completely arbitrary perspective projections. A somewhat restricted class of perspective views may be calibrated without an explicit calibration object using another approach developed from photogrammety. In 2D Galatea, we have used an animated graphics overlay onto the source image to give the analyst feedback regarding current and previous data entries. This capability is extended in 3D Galatea by overlaying auxiliary lines, which are the backprojections of previous 2D entries from one view into other views. This concept amounts to a fourth interpretation of the well-known Roberts homogeneous matrix equation describing perspective projections of 3D space into a 2D image. The auxiliary line is useful in locating a point which is obscured in one of the images, or in determining the correspondence of projected points as seen in different views, which may be ambiguous or easily confused.

Left ventricular wall motion: its dynamic transmural characteristics.

Cardiac wall motion has been studied extensively. It is usually determined by indirect two-dimensional measurements for the true three-dimensional (3D) motion with its specific speed and direction. Errors are also introduced by using internally fixed reference systems and by the inability to identify precise points on the heart wall during the cardiac cycle. Because of these limitations, the endocardial and epicardial wall motion and their relationship are still unclear. This study was designed to assess endocardial and epicardial wall motion by measuring the direction and speed of implanted markers in an externally fixed 3D coordinate system. Fifty-seven pairs of endocardial and epicardial metallic markers were placed at anterior, lateral, posterior, basal, and apical regions of the left ventricles of 14 normal mongrel dogs. Biplane cineradiographs were performed at 50 frames/sec, and the 3D motions of the markers were analyzed using a specially designed computer system. It was found that the speeds, directions, displacements, and phases of the movements of corresponding endocardial and epicardial points were highly correlated. The correlation coefficients were 0.77 to 0.95 for the mean directions, 0.61 to 0.96 for the mean speeds, and 0.59 to 0.96 for the mean displacements at various regions of the heart, and the periodic movements of the endocardium and epicardium were always in phase. The mean epicardial speeds and displacements are fixed proportions (approximately 70%) of the mean endocardial speeds and displacements despite the differences in absolute values between regions in the same dog and the same regions in different dogs. The correlation coefficients for endocardial and epicardial instantaneous speeds, directions, and velocities ranged from 0.68 to 0.83, 0.81 to 0.88, and 0.77 to 0.86, respectively, for different regions of the heart. The correlation coefficients were significant for both the mean values and the instantaneous values. Thus, when only fixed epicardial points are accessible for wall motion measurements in clinical situations, it is possible to infer the endocardial motion from the epicardial motion.