## Sonomicrometry

Sonomicrometry is a basic laboratory tool that uses the transmission of ultrasound energy through tissue to measure distance. Ultrasound sonomicrometry is typically used to measure the distance between two fixed points in a soft tissue environment and to quantify the function and dynamics of cardiac, skeletal, or smooth muscles. The piezoelectric (sono-micrometry) crystals function omnidirectionally and act as both receiver and transmitter, with some systems allowing for as many as 32 peers. Complex, moving, 3D geometry can be modeled using techniques like sonomicrometry array localization.

Understanding the velocity of ultrasound through tissue is critical to acquiring accurate dimensions in a sonomicrome-try system. The velocity of ultrasound is affected by a variety of factors, including muscle fiber direction and composition, as well as the contractile state. In most biological tissues, the velocity of sound is approx 1540 m/s.

Traditionally, sonomicrometry has been used to determine cardiac function on large research animals (dogs, pigs, sheep, and so forth). Both in vivo and in vitro studies can be performed to elucidate global cardiac function under a variety of conditions. A typical study parameter includes the assessment of ventricular volume, which when coupled with ventricular pressure, gives the experimenter access to a variety of cardiac parameters, including heart rate, cardiac output, and stroke volume.

Regional studies, which focus on specific areas of the heart, are also popular. The advent of 3D sonomicrometry, or "sonomicrometry array localization," has made possible the detailed study of discrete anatomical points throughout the cardiac cycle (55,56). A volume of data exists describing the motion of valves, papillary muscles, ventricles, and atria. Another application involves tracking mobile components through the heart, such as cardiac catheters (57).

A sonomicrometry system can use as few as 2 crystals, but typically between 6 and 32 are employed. Transducers are the piezoelectric crystals that are attached to electronics consisting of a pulse generator and a receiver. Distance is measured by energizing the transmitter with a train of high-voltage spikes or square waves (both less than a microsecond in duration) to produce ultrasound. This excites the piezoelectric crystal to begin oscillating at its resonant frequency. This vibratory energy propagates through the medium and eventually comes in contact with the piezoelectric crystal acting as the receiver. This crystal begins vibrating and generates a signal on the order of 1 mV. The piezoelectric signal is amplified, and the distance between the pair of crystals is calculated. By monitoring the difference in time from transmission to reception of the signal and knowing the speed of sound through the particular medium, the intercrystal distance can be calculated. These computations take less than 1 ms.

In sonomicrometry array localization, the 3D position of each crystal is calculated from multiple intertransducer dis tances. This is done using a statistical technique called multidimensional scaling; such scaling gives the experimenter the ability to take the scalar sonomicrometer measurements and to generate 3D geometry. Multidimensional scaling generates 3D coordinates for each crystal from a group of chord lengths in the array.

By starting with an initial coordinate estimate and applying the Pythagorean theorem, a matrix of estimated distances is generated that corresponds to the actual measured distances. Using an iterative approach, multidimensional scaling then optimizes the value for the distance calculation by minimizing what is called the stress function. If the distances measured between crystals are exact (no measurement error), then one solution with zero stress exists that represents the intercrystal distances exactly. As measurement error increases, a zero solution to the stress function becomes impossible, and the iterations begin seeking a minimum value. The globally minimum stress point defines the optimum 3D configuration. A similar style is used to generate an estimate of the error associated with each distance. The result of this analysis is a 3D moving model with an average error of approx 2 mm.

The advent and feasibility assessment of this technique was described in detail by Ratcliffe et al. (55) and Gormann et al. (56). The first application of this technology described the 3D modeling of the ovine left ventricle and mitral valve. The study involved a 16-transducer array in which 3 transducers were sutured to the chest wall, and the remaining 13 were placed both epicardially and endocardially on the ventricular wall, the papillary muscles, and the mitral valve. The 3 crystals attached to the chest wall provided a fixed-coordinate system from which whole-body motion could be differentiated from cardiac motion. This study produced 3D depictions of the shape of the mitral annulus throughout the cardiac cycle, as well as quantitative images of ventricular torsion. This type of application opens up many possibilities relative to chronic studies focusing on ventricular remodeling following traumas like myocardial infarction.

Another interesting application of sonomicrometry, available because of the development of sonomicrometry array localization, is the cardiac catheter tracking described by Meyer et al. (57). The system involved placing seven sono-micrometric crystals epicardially around an ovine heart and tracking the position of a catheter with anywhere from one to five attached crystals. In this system, average distance errors on the order of 1.0 mm were demonstrated. The clinically relevant end point for this tool would be to replace the epicar-dial transceivers with transceivers mounted in catheters and deployed endocardially in a minimally invasive manner.

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