IEEE Annual Northeast Bioengineering Conference, pages 64–67, 1998. 1 Three-Dimensional Digital Sonomicrometry: Comparison with Biplane Radiography Pengcheng Shi ‡ , Reza Mazhari † , Donald Dione * , Jeffrey Omens † , Andrew McCulloch † , and Albert Sinusas * Departments of ‡ Electrical Engineering and * Medicine, Yale University, New Haven, CT 06520, USA † Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093 email: Albert.Sinusas@yale.edu Abstract — This paper describes a three-dimensional (3D) digital sonomicrometry approach for locating and tracking 3D objects. A commercial digital sonomicrometry system was employed to measure scalar distances between omni- directional sonomicrometers. 3D coordinates were then derived using the statistical technique of multidimensional scaling (MDS). 3D digital sonomicrometry was directly com- pared with biplane radiography of the ultrasound crystals for estimation of 3D distances in static phantoms and in vivo using an experimental canine preparation. An excel- lent correlation (r=0.992) was seen when comparing inter- crystal distances derived from biplane radiography and so- nomicrometry 3D coordinate data in the gel phantom. A Bland-Altman analysis shows that the average difference in coordinate determined distance between these two differ- ent methodologies was only 0.63±0.46 mm, over a range of inter-crystal distances of 3.14 to 17.28 mm. In the in vivo canine preparation, the correlation between the so- nomicrometry derived and biplane derived distances was also excellent (r=0.992) with a slope of 1.05 and an intercept of 0.06. The Bland-Altman analysis shows that the average difference in coordinate determined distance between these two different methodologies was only 0.78±0.74 mm, over a range of inter-crystal distances of 2.90 to 27.66 mm. We have demonstrated the feasibility of accurately measuring scalar distances using 3D digital sonomicrometry. Digital sonomicrometry combines high spatial and temporal resolu- tion with availability and portability to accurately measure distances in a closely packed array of implanted piezoelectric crystals. I. Introduction Digital sonomicrometry, with high temporal and spatial resolution, can be a useful tool in locating and tracking three-dimensional (3D) objects when used with the sta- tistical technique of multidimensional scaling (MDS). The ability to locate an object’s position in 3D space, and to observe the change in that position over time has numerous applications in the biological sciences. Cardiovascular ap- plications include tracking a catheter as it moves through a blood vessel [12], investigating regional left ventricular (LV) deformation [3], and tracking the 3D geometry of the mitral valve [4]. Techniques involving 3D Magnetic Reso- nance Imaging (MRI), such as MR tagging and shape based boundary tracking may also be used for these purposes [10], [7]. However, these techniques employ beat averaging and long imaging times, which might cause them to miss cru- cial temporal changes in position. In addition, they have low spatial resolution in relation to sonomicrometry. Biplane radiography using radiopaque markers is another method used to determine 3D wall motions and regional strains [9], [6], [2]. This technique, which uses perspec- tive transformations to calculate the positions of implanted markers, offers relatively high spatial resolution (<0.2 mm) and temporal resolution (120 Hz). Digital sonomicrometry significantly improves spatial resolution (0.024 mm) and temporal resolution (>125 Hz). This may be particularly valuable for analyzing regional wall strains, since small er- rors in myocardial displacements can be amplified signifi- cantly in the computations [1]. Sonomicrometry also has the advantage of availability and portability that MRI and biplane radiography are lack- ing. However, it has yet to be validated in the in-vivo setting for the purposes of computing myocardial strain distributions. In these experiments, 3D digital sonomicrometry is di- rectly compared with biplane radiography of ultrasound crystals for estimation of 3D distances in static phantoms and in vivo using an experimental canine preparation. II. Methods A. Digital Sonomicrometry A commercial digital sonomicrometry system (Sonomet- rics Corp., London, Canada) was employed to measure scalar distances between omni-directional sonomicrome- ters. Sonomicrometry utilizes the time-of-flight principle of ultrasound to calculate distances between a transmitter and a receiver. A high speed digital counter starts when a pulse of ultrasound is emitted by the transmitter, and is stopped when the first peak of the ultrasound wave is detected by the receiver. Using the known speed of ultra- sound in tissue(∼1540m/s), the transit time is converted to a scalar distance. The distances between all possible pairs of crystals are recorded simultaneously for a given period of time, at a sampling frequency of greater than 100 Hz. Signal Processing. Due to several technical issues, the signals of recorded distances must be filtered to remove noise. This is accomplished through a two step process which involves first running the data through an automated filtering program, followed by a manual check. Occasion- ally, the system triggers on the second or subsequent ul- trasound waves, rather than the leading edge. This leads to a ”level shift” of the data trace, which is a brief in- crease in distance, corresponding roughly to a multiple of the ultrasound wavelength. Another type of error, a signal dropout, occurs when the system is triggered by external noise before the first peak reaches the receiver. The true distance data is a continuous and smooth trace of points. The continuity of the actual trace is examined by first and second order derivatives. The level-shift transition points are located, and the shifted segment is dropped down to its correct level. The dropout points are detected since they