Harrison, Donald C. A. INTRODUCTION 1. Objectives Imaging and image processing of data from the heart and cardiovascular system have become increasingly important for evaluating cardiovascular function in patients with heart disease. While in the past, angiographic image processing has been the most im- portant technique for evaluating ventricular volume, valve function, the presence or absence of shunts, and wall motion abnormalities, other techniques requiring imaging and processing of new types of imaging are also becoming increasingly important. These new methods include isotope scanning techniques and ultrasonic imaging. The ability to measure ventricular volumes and quantitate wall motion provides powerful tools for assessment of the effects of coronary artery disease upon cardiac function. Since cardiac bypass procedures and the effects of myocardial infarction are being assessed in patients with increasing frequency, the need for developing im- proved methods for image analysis for angiography is readily apparent. Coronary artery disease results in the death of more than 650,000 Americans each year, and more than 8,000,000 Americans now have symptomatic coronary artery disease. Many of these individuals will undergo studies of catheterization and angiography to determine the extent of their disease and to quantitate the severity of the abnormality in cardiac function which has been caused by the disease. The overall objective of this proposal is to develop methods for automatically de- fining the ventricular margin on contrast angiocardiographic studies. Utilizing the information gained by automatically defining ventricular margins on a long sequence of angiographic frames, it will be possible to assess quantitatively hydraulic function and ejection characteristics of the heart and to define quantitatively wall motion abnormalities. Thus the major objectives of this proposal are to: a. Develop an automated computer system for margin definition which is based on mini-computer technology and can be readily utilized in a clinical setting; b. Utilize the much more detailed information which will be gained from a frane- by-frame analysis of the cardiac cycle for the quantitation of functional charactecis— tics of the ventricle and segmental wall abnormalities. In this process a model for ventricular contraction will be developed. At the present time our ability to analyze quantitatively the large amount of in- formation contained in a left ventriculogram is limited by the fact that a time con- suming and expensive process of manual margin definition must be performed frame-by- frame on a long sequence of frames. There have been substantial advances in the field of image processing, many of which lend themselves to application to the particular problem presented by cardiac angiography. Several such advances have been made for image processing outside the field of medicine, and we hope to utilize these effec- tively in our technique development. 2. Background Introduction During the past seven years the Stanford Cardiology Division has focused a major area of its activities on developing computer systems for clinical applications. A computer system for the analysis of cardiac catheterization data, which was developed at Stanford and has become available commercially, has to date been adopted by Harrison, . Donald Cc. 5 x approximately 45 other catheterization laboratories (1). A dedicated CCU monitoring system for continuous ECG observation has been developed and will be made available on a widespread basis during 1975 (2). In addition, a small computer system for pro- cessing ECGs recorded on magnetic tape in ambulatory patients has been developed to provide accurate analysis in clinically useful formats (3). Moreover, during the past three years our efforts have been directed towards de- veloping a system for computer processing of not only hemodynamic data, but also angiocardiographic data, utilizing a video disc light-pen computer system (4). This system still depends entirely upon manual definition of ventricular margins; however, the light-pen and computer processing substantially reduce the time required for quantitative analysis. This system is now used for routine clinical processing of all left ventriculograms in the Stanford Cardiac Catheterization Laboratories. a. Description of Video Disc Light-Pen Computer System This system utilizes an Ampex DR-10 video disc for recording the left ventriculo- gram at frame rates up to a maximum of 30 fps. The present storage capacity is 600 frames. A variable speed control for playback is provided. At the time the ventricu- logram is recorded, both the electrocardiogram and the left ventricular pressure (if simultaneously available) are converted into horizontal histograms, which are recordec synchronously with the video frames. Thus, superimposed on each video frame in the upper portion of the screen are two "bars," the length of which is proportional to the analog ECG and/or pressure signals. Calibration capability has been provided for the two "histograms." A Tektronix 4551 light-pen unit is used to manually trace the margins of the left ventricle as it appears on the video monitor. A pressure-sensitive switch on the light-pen allows the operator to instruct a laboratory mini-computer to sample the \-Y coordinates of the light-pen position. The light-pen is interfaced with a Tektronix 4501 scan converter unit which permits retention of the traced margin. A video mixer incorporated in the Ampex video disc merges the scan converter output with the re- corded picture on the video disc. Similarly, the laboratory computer (Hewlett-Packar¢ 2100) generates alpha numeric and graphic data on the scan converter, which in turn is displayed on the video screen, mixed with the angiographic picture. Synchroniza- tion of the scan converter, light~pen and video disc is performed by a Telemation model TSG-200 broadcast synchronizing generator. Results of computational analysis are printed out on a Versatec hard copy unit which provides 8-1/2 x 11 sheets suitable for medical record use. b. Digitization of the Video Image We have developed a video digitization system as a prerequisite step towards auto- matic margin definition. The recorded left ventriculogram is digitized in the fotlew- ing manner. A single cardiac cycle recorded prior to contrast injection is digitized field by field. The recorded ventriculogram is digitized over two or three cardiac cycles. Frame advance and identification of frame number on the video disc is under direct computer control. The purpose of digitizing a single cardiac cycle without contrast is to provide data for subtraction on a field by field basis, based on Ctining with the QRS. The QRS is recorded as a horizontal bar at the top of the video screen, The length of the horizontal bar corresponds to the amplitude of the ECG signal at the time the video image is recorded. This visual ECG signal is in a format such that it can be readily detected by the computer for use as synchronizing information for the computer subtraction of frames which occur at the same times of different cardiac cycles. Harrison, Donald C. A Colorado Video 260 unit is used for digitizing the standard video image. The CV-260 generates a buffer of 256 six bit values which represent the intensity (brightness) of the image along a vertical line which is located at a position de- termined by an external computer imput. The system is designed to separately digitize the two fields within each frame such that temporal information at 60 times per second is obtained. The CV-260 is interfaced to a Hewlett-Packard 2100 computer which con- trols the field selection and horizontal location of the digitizer. During one field time (16.7 milliseconds) one point is converted from each of 256 horizontal raster lines in the selected fields. The vertical position is increased by the horizontal syne pulse. The horizontal location of the point on the line is de- termined by the voltage applied to the external horizontal scan input. The brightness of the point is converted to a six-bit number (64 Gray Scale Levels) and then inserted into a 256 word buffer. Under computer control, the buffer is transferred sample by sample to an array in computer memory. Four 256 sample vertical lines are buffered in computer memory and transferred as a single record to a Hewlett-Packard digital mag- netic tape drive. Using a 2400 foot tape length, with an 800 bits per inch density and an interrecord gap of 0.6 inches, it is possible to store four seconds of real time video on a single reel of tape. The time presently required for digitization is 35 seconds per video field, or approximately two hours 15 minutes for a full four seconds of real time video. Clearly this digitization time is too long for clinical application. We specifically propose to implement in year 02 a higher speed digitizer which will require approximately two seconds per field (10 minutes for 150 frame study at 60 fields/second). c. Collaboration with Stanford Artificial Intelligence Laboratory Over the past two years the Stanford Cardiology Division has worked with the Arti- ficial Intelligence Laboratory at Stanford in a collaborative effort to investigate the possibility of applying the state of the art image processing techniques to the problems of cardiac angiography. Vision research efforts at this laboratory date back to 1965 and were applied to projects such as the development of the robotics and auto- mated assembly project (5-11). These efforts were directed towards developing the techniques for computer understanding of real scenes and resulted not only in a large collection of useful, debugged code, but perhaps more importantly, in a wealth of experience and insight into scene analysis technique. The fundamental design of this research effort has been strongly influenced by the problem solving philosophies which have been developed by this group. The following summarizes some of the relevant work of the Artificial Intelligence Laboratory: Baumgart (12) developed a 3-D geometric modeling system for application to computer vision. In computer vision geometric models provide a goal for descriptive image analysis, an origin for verification image synthesis, and a context for spatial problem solving. Some of the design ideas presented have been implemented in two programs named GEOMED and CRE; the programs are demonstrated in situations involving camera motion relative to a static world. Baumgart's GEOMED system was developed for doing 3-D geometric modeling; used from a keyboard, it is an interactive drawing program; used as a package of SAIL or LISP accessible subroutines, it is a graphics language. With GEOMED, arbitrary polyhedra can be constructed, moved ahout and viewed in perspec- tive with hidden lines eliminated. In addition to polyhedra, camera and image models are provided so that simulators relevant to computer vision, problem solving, and animation may be constructed. These techniques will be useful for building 3-dimen- sional models for the heart. Nevatia (13) developed techniques for description and recognition of three- dimensional objects from range data obtained by a laser triangulation technique. Harrison, Donald C. A complex object is described by decomposition into sub-parts and relations of these sub-parts. The individual parts are described by generalized cones, which are defined by a space curve known as the axis, and arbitrary shaped normal cross-sections along this axis. These techniques will be particularly useful for 3-dimensional analysis of bi-plane and multiplane ventriculograms. Pingle (14) developed a fast, feature-driven program for extracting depth informa- tion from stereoscopic sets of digitized TV images. This is achieved by two means: in the simplest case, by statistically correlating variable-sized windows on the basis of visual texture, and in the more complex case by pre-processing the images to extract significant visual features such as corners, and then using these features to control the correlation process. The significance of this work is the feature-directed ap- proach to information extraction from images, which will be useful to automatic margin detection. Quam (15, 16) developed techniques for geometric registration and differencing of images to detect changes. Misregistration of the images was measured using a small area correlation technique. One of the images was then geometrically distorted to remove the misregistration. Finally, the images were point-by-point subtracted in such a manner that subtle differences between the images were made obvious. These tech- niques will be particularly important in the removal of background from ventriculo- grams. d. Previous Work by Others There are several prominent investigators who are actively working in the field of automated margin definition. At the present state of the art, it appears that no system has reached the point of routine utility in a clinical setting. Although scome- what different approaches are being taken by individual investigators, the general pattern is to process video images recorded on an analog video disc. Most present systems incorporate operator interactive pre-processing, either by masking areas around the ventricle, identifying areas for digitization, or manually selecting voltage levels to exclude background images. Most systems incorporate capability for operator input of manually defined margins, usually via a pen-tablet apparatus. A complex pre-processing system has been developed at the Mayo Clinic which incorporates many of the above features (17). The systems developed by Heintzen in Kiel, West Germany (18) and Reiber at NASA-Ames Research Center use pre-processing analog deviccs to identify the ventricular margin while scanning across the raster lines of the video image. Edge-finding computer algorithms, operating on digitized data alone, which avoid the limitation of horizontal raster lines, have been reported by Robb in Salt Lake City (19) and Kaneko in Yorktown Heights (20). Probably the most advanced margin detection system presently developed is that of Clayton et al. (21), which is the first system to constrain the edge detector using assumptions of smoothness and conti- nuity of the margin in both space and time. Most systems described above utilize large-scale computer systems, with the exception of Stewart in Philadelphia (22). The present trend in automated margin definition by most investigators is to uti- lize pre-processing hardware to perform the difficult task of eliminating extranecus densities which impinge upon the ventricular margin, relying heavily on operator io- teraction. Some systems are dependent upon the horizontal scanning lines of the video image, which causes considerable difficulty when approaching the inferior and apic.1 portions of the ventricle, where the margin runs parallel to the video scanning lines. These systems impose severe limits on development of sophisticated techniques to handle low signal to noise ratio images with poor contrast. There has gencrally been limited use of computer software to solve the problems of automated margins Harrison, Donald C. because of the complexities of programming such algorithms. Because of the substantial expertise in vision research in the Computer Sciences Department, our approach will emphasize sophisticated computer handling of the angio- graphic images. We feel that our approach will differ from previous ones and be unique in the following major respects: 1) Provision for image subtraction capability; 2) Multidirectional capability of edge finding; 3) Detection not only of the position of the edge but also the direction in which the edge is traveling; 4) Use of modeling techniques to provide a set of expectations with capability to fill in "gaps" (static modeling); 5) Use of data from previous frames and models to provide increasing ac- curacy for later frames (dynamic modeling). It is anticipated that by application of the above sophisticated computer techniques and other differences in approach, pre- processing hardware can be minimized, as well as requirements for operator inter~- action. 3. Rationale Introduction At the present time ventricular volume and wall motion abnormalities due to disease of the heart are estimated by most sophisticated cardiovascular laboratories studying patients with coronary artery disease. High quality angiograms are recorded on film, the images projected upon a screen, and hand methods used to trace the outline of the ventricular chamber and cardiac wall with each cardiac cycle. These are frequently processed at 60 frames per second and require that a technician or physician manually draw each frame of the heart for up to five seconds. Thus, the result is the time necessary for tracing 100 to 200 images for each patient processed. Planimetric methods are used to determine the area and appropriate corrections made for magnifi- cation and distortion due to radiographic systems. Specific cords on the circum- ference of the wall of the ventricular chamber may be designated for study; this re~ quires even more complex human interaction. Since such studies are carried out in more than 200,000 patients each year, the investment of time by the individual tech- nicians and physicians is enormous. In addition, subjective criteria are used for defining the margins and for identifying individual segments of the wall on a frame- by-frame basis. The data are also obtained in a form difficult to manipulate by a computer. The specific rationale for developing an automated method for evaluating angio- graphic images is to obviate the need for human interaction with the image analysis. Computer software to do better definition, to follow the borders through the various frames of the contraction cycle, and to specifically analyze the hydraulic function of the wall will be possible. Data recorded on a video disc, digitized, and placed into a computer in which advance technologic methodology for border definition can be incorporated will permit this automatic analysis. A number of graphic methods for presenting the data, for interacting with it mathematically, and for comparing it to models which have been developed of the normal contracting process will permit quanti- tative assessment of changes in wall motion and ejection characteristics. The overall rationale will be to develop such a system utilizing technology de- veloped in other basic disciplines of imaging and image processing, to test it in a non-clinical situation using models of the ventricle for validating many of the as-~ sumptions now inherent in angiographic volume measurement and ejection characteristic determination, to validate it in a clinical laboratory where it can be compared to presently available methods and techniques, to utilize it in clinical research to demonstrate its applicability for studying patients, to develop the computer imaging Harrison, Donald C. %, ; system in a small computer so that it will be exportable to a number of laboratories throughout the country, and to utilize the technology developed for angiographic image processing for processing other types of images from ultrasounds and isotopes. There are several important considerations which lead us to believe that this pro- ject can be successfully pursued at Stanford with the likelihood for achieving a clinically effective system. a. The Cardiology Division has had substantial experience in developing computer systems with direct clinical application to problems in cardiology. These include the Cardiac Catheterization Laboratory system, the Coronary Care Unit monitoring sys- tem, a computer system for processing ambulatory ECG tape recordings, and a light-pen computer system for manual margin definition. Previous activities of the Cardiology Division in these areas have led to a close collaboration between computer scientists and cardiologists, with a mutual understanding that clinical utility and enhancement of medical knowledge are primary goals. b. The presence of the Artificial Intelligence Laboratory at Stanford, with its high degree of expertise in image processing, provides significant ongoing system sup- port for the code which has been produced, keeping it both continually up-to-date and improved. Moreover, Dr. Quam represents a large resource of expertise and experience in the field of computer image analysis. c. Modelling techniques are an important prerequisite for defining both the normal and abnormal range for cardiac wall motion and ventricular geometry. Stanford is unique in having available wall »otion data derived from postoperative patients who have implanted radio-opaque intiamyocardial markers. d. The availability of a large computer facility (SUMEX) which can be utilized for developing software and for processing data initially will aid this project. e. The computer approaches we propose are relatively unique in the field of pro- cessing cardiac angiography. The use of both static and dynamic modelling of the ventricular margin to provide a set of expectations within which the contour is to be searched offers significant advantages. There is sufficient overlap of radiographical- ly dense structures, such as ribs and aorta, and difficulty in discerning the sys- tolic margin to necessitate a model-directed approach and image subtraction. Although these techniques will require computer extrapolation to complete missing perimeter segments, this approach closely resembles the approach normally used by experienced angiographic technicians. B. SPECIFIC AIMS The specific aim of the proposed program is to apply advanced image processing technology developed by other scientific disciplines to angiographic image processing. The ultimate goal is a reliable, validated system for automatic left ventricular margin definition which can be utilized for clinical application. In order to meet these ob- jectives, a number of subsidiary goals must be accomplished. 1. Subsidiary Goals a. Reliable Margin Detection First, reliable techniques must be developed to locate the margin in the low signal to noise ratio video images that are typical in angiography. (Cine film based Harrison, Donald C. digitization is rejected for actual clinical use because of the additional processing steps, and the problems in exposure control.) In typical angiogram sequences, por- tions of the margin are not visually apparent when looking at individual frames, but must be inferred from surrounding frames in the sequence, and from familiarity of the normal shape and dynamic motion of the margin. The best available techniques for detecting weak, noisy edges are based on appro- priate statistical averages of the data and least squares minimization. These tech- niques can be made more reliable and more efficient if there is a computer model to predict the approximate location and orientation of the margin. This necessitates a knowledge of dynamic ventricular wall motion, which is an additional goal of this proposal. b. Two-Dimensional Dynamic Modelling A two-dimensional dynamic model for wall motion will predict the normal outline of the ventricular margin in the right anterior oblique projection as a function of time in the cardiac cycle. We propose to develop this model using the above-mentioned margin detection techniques and using models of cardiac motion developed both from manually defined margins and from the motions of intramyocardial markers. c. Quantitative Measurements of Left Ventricular Function Having an accurate and reliable technique for locating the margin in a sequence of angiograms gives us the ability to evaluate the performance of the heart as a pump. Standard measures of end diastolic, end systolic, and stroke volumes can be calculated for each of the frames in the sequence. We can also calculate segmental shortening and wall motion to determine the contribution of each segment of the wall to the over- all performance of the heart. Abnormal behavior can be detected by comparing these measurements with ones for a normal heart. d. Biplane Angiographic Analysis It is a goal of this project to adopt the single plane techniques, specifically reliable margin definition, modelling and ventricular performance evaluation, for biplane angiography. In order to do this, it will be necessary to develop reliable margin definition, not only for the right anterior oblique projections, but also for other projections such as biplane antero-posterior and lateral projections, or biplane RAO and LAO views. Dynamic modelling in the multiplane dimension will be needed, and for this purpose the intramyocardial markers will provide substantial assistance, since in the future these markers will be positioned in multiple dimensions. Similarly, techniques to evaluate ventricular performance and deviations from normal will be de- veloped using biplane data. e. Dedicated Computer Application A critically important goal in this project is to implement the above single plane and biplane techniques on a small dedicated computer system, which in both software and hardware design automatically processes the ventriculographic images. The goal is to develop an automated system sufficiently compact and efficient in design that it might be readily exportable for general clinical application. f. Routine Clinical Use We propose to develop validation techniques for this automatic image processing Harrison, Donald C. | system which can be compared to the standard methods for determining ventricular volume and wall motion abnormalities now used in cardiovascular laboratories throughout the United States. We specifically plan to objectively evaluate the effectiveness of this system in processing routine clinical angiographic studies. g. Research on Ventricular Performance The development of a reliable system for automated margin definition, once com- pleted, will become a valuable tool for further research studies in ventricular per- formance. Specific areas for proposed research applicability are an analysis of seg- mental wall motion abnormalities and analysis of cardiac motion during systole and diastole. h. Application to Ultrasound and Isotope Image Analysis Finally, our aims and objectives are to apply the techniques developed for angio- graphy to processing of images obtained from ultrasound and isotope scanning tech- niques. Clearly this is a long range objective and will require from three to five years before it can be incorporated into any clinical studies. However, the tech- niques developed for processing of angiographic images should be applicable to pro- cessing of these more complex images when advances in hardware and transducer units have occurred. 2. Scenario for Clinical Use The following is a description of how the automated model-directed system for pro- cessing cardiac angiography will look to the user. Specifically, this scenario out- lines our goals with respect to user (physician or technician) interaction with the computer system. a. Left ventriculograms are recorded on a video disc during contrast injection. Immediately prior to contrast injection, a brief recording is made in order to provide pictures of the cardiac silhouette for subsequent subtraction. b. The operator specifies (using a terminal) the beginning and end frame numbers for the sequence, as well as the frame number of dye injection. ce. The program automatically scans the sequence for ECG and left ventricular pressure. The electrocardiogram and left ventricular pressure are coded near the top of the video picture as a bright horizontal bar, allowing the computer to automatically identify end diastolic frames. d. The ECG data and the operator specified reference points of the aortic valve and ventricular apex are used to predict a "normal" left ventricular margin shape to guide the margin detection in the first "good" frame. Once there is satisfactory margin definition on the initial "good" frame, the automatic margin tracking program, using appropriate static and dynamic models of ventricular motion, will proceed through the remainder of the frame. e. Automatic digitizing and margin tracking programs do the rest. f. The final outputs are (1) standard quantitative measures of ventricular per- formance; (2) graphic overlays on top of the replayed video disc images of the auto- matically detected margins for validation of the automatic system. Thus, the operator can either single-step through the sequence or randomly sample frames in the sequence Harrison, Donald C. to view the computer generated margins and verify their accuracy; (3) graphic display of volume, pressure, wall motion and other measures as a function of time; (4) hard- copy graphic output of any of the traced margins or graphs on standard 8-1/2" x 11" paper for inclusion in the medical record; (5) permanent magnetic tape record of all digitized and reduced data which will expedite comparisons of system performance and individual patient performance over long periods of time. C. METHODS OF PROCEDURE Introduction The primary components in developing an automated system for processing left ven- triculography are illustrated in Figure 1. Specifically, they are: 1) technique re- search and development on the SUMEX PDP-10 machine; 2) implementation of margin de- tection system on a mini-computer system (PDP~11); and 3) clinical validation and applications. The proposed time scale for development over a three-year period is shown in Figure l. 1. SUMEX PDP-10 Based Technique Development We propose to start research in cardiac dynamic modelling and model guided margin detection using the SUMEX PDP-10 system and much of the image processing software which has been developed on the PDP-10 system at the Stanford Artificial Intelligence Labora- tory. In particular, we will use the imige enhancement, noise removal, image registra- tion, image differencing, edge detection, and edge verification alzorithms which are already developed for the PDP-10. The use of the SUMEX facility will concentrate on experiments with techniques in wall motion modelling and model guided margin detection which do not require extensive interactive facilities. Line drawing graphics and grey level display facilities, which are essential for image processing research and the development of an interactive clinical system, are presently missing from the SUMEX system. We will assemble an interim display facility on SUMEX, using a slow scan scope and Polaroid camera. For a more complete automatic margin detection and dynamic modelling system, we will need the display facilities and dedicated computer system for which funds are requested in this proposal. The specific techniques for automated margin detection, the processing steps to be followed, and the theory employed are outlined below. Shown in Figure 2 is an illus- tration of currently existing hardware which will be utilized at this initial phasc of development. The HP-2100 Cathlab system will be used to digitize sequences of angiograms stored on the video disc onto 9-track magnetic tape which is compatible with that used by the PDP-10 system, as shown in Figure 2. Initial processing will transfer the image data from magnetic tape to the disc file system. The initial PDP-1l system will receive image data communicated over a 9600 baud line between the PDP-11 and the HP-2100, as shown in Figure 3. The image data will be separated from the ECG and LV pressure data, which will be stored in two separate arrays. The ECG signal will then be processed to accurately locate the R wave peaks and determine the length of the cardiac cycle. Harrison, Donald C. The operator specifies the frame number of contrast injection. Using the pre- viously determined length of the cardiac cycle, frames from corresponding times in the cardiac cycle, both before and after contrast injection, are differenced to re- move background due to the diaphragm, ribs, and other parts of the anatomy which are not of interest. It is believed that automatic margin detection will be much easier and more reliable using these difference images. Our approach to margin detection is the use of dynamic models of wall motion to predict the approximate location and shape of the margin as a function of time in the cardiac cycle and the location of the margin in preceding frames. Knowing the approxi- mate location and orientation of the edge allows one to design edge detection algo- rithms which compare the brightness statistics on each side of the hypothesized edge. This technique gives an improvement in contrast to noise ratio roughly proportional to the square root of the number of image points used in the statistics. In order for other edge detection methods to find subtle, low contrast edges, they must use very low thresholds on the differences in brightness between adjacent points, making them much more susceptible to noise in the images. These individual processing steps used for margin detection are outlined in Figure 4. Our initial dynamic model for wall motion will be derived both from manually de- fined ventricular margins and data derived from motion of intramyocardial markers. The intramyocardial markers are small tantalum coils (0.5 mm in diameter and length), which at the time of surgery are positioned within the myocardial wall and on the aorta near the level of the aortic valve such as to outline the ventricle as seen in the right anterior oblique projection. This project is funded by a separate National Institutes of Health grant and provides in postoperative patients highly reproducible and precise measurements of dynamic wall motion. Many patients having coronary bypass graft surgery have these markers placed, and in the absence of any evidence for pre- operative or intraoperative myocardial damage, represent models of normal ventricular motion. The myocardial marker data derived from ventricles of patients with both normal and abnormal myocardial motion will be used to generate a dynamic model of wall motion, which provides predictions for computer detection of the contrast boundary. These projects do not in any way overlap with our proposals for an imaging and image processing system outlined herein. They complement them and permit the use of data from marker patients for modelling the ventricular contraction process. Initially, we will require a human operator to specify two points in the first frame: the aortic valve and the apex. These points will be used to position and scale a simple model for the shape of the left ventricle at this particular time in the cardiac cycle. The model will approximate the margin by a collection of linear seg- ments. The precise location of each segment will be determined by computing means and variances of intensities along lines parallel to and adjacent to the predicted segment. The location of the segment is then based on finding the edge in this one-dimensional array of means. The variances are used to. measure the uniformity of the intensities on either side of the resulting edge as a measure of signal to noise ratio and likeli- hood that we have chosen the proper orientation for edge. Figure 5 illustrates the technique. Some analysis of how the images are formed will allow us to predict the nature of the edge in this array of means. We assume that the only difference between the images before and after contrast injection is due to the contrast agent and Gaussian noise in the video signal. (The cathcter will be dark in both images, resulting in zero in the difference images.) Although there may be other systematic differences due to frame to frame variations in the X-ray source, we can discover and correct them by comparing the background areas in the two images. Consequently, the difference image” outside the heart should be constant (zero) in brightness plus noise. Harrison, Donald C. aa Inside the heart wall the brightness will decrease according to the Lambert—Beer law. I= 10: exp(-k+c-d) (eqn 1) where 10 is intensity of the radiation source is the intensity of radiation after passing through contrast material is the absorption coefficient of the contrast material is the path length of the radiation through the contrast material is the concentration of the contrast material QB RH or log I - log I0 = - k+e-d (eqn 2) In our previous discussion, we described the use of image differencing to remove the effects of background. The above equation suggests that we really want to sub- tract logarithms of the intensities, so that our difference data then corresponds to the left hand side of equation 2. If we assume that the heart has approximately a circular cross section, then we get the path length d as follows: d* (x) 7 he (x? - (x-xe)2) (eqn 3) where r is the radius of the circle x-xc is the distance of the radiation path from the center of the circle (log I - log(t0))? = (kee)? (2 - (x-xe)) density“ (x) +42 or density (x) pyex? + Pox + p3 (eqn 4) for parameters pj, p9, p3- Figure 6 shows the expected shape of the edge due to the contrast agent. Our method for accurately locating the wall will be based on finding the values of the background difference: Pg, edge location: x,g,~, and the three parameters in equation 4 which best approximate the actual data by the method of least squares: z (density* (x) - p9)° *