Modern 3DE matrix-array transducers are composed of about 3000 individually connected and simultaneously active (fully sampled) piezoelectric elements with operating frequencies ranging from 2 to 4 MHz and 5 to 7 MHz for transthoracic and transoesophageal transducers, respectively. To steer the ultrasound beam in 3D, a 3D array of piezoelectric elements needs to be used in the probe, therefore piezoelectric elements are arranged in rows and columns to form of a rectangular grid (matrix configuration) within the transducer (Fig. 1.1, right upper panel). The electronically controlled phasic firing of the elements in that matrix generates a scan line that propagates radially (y or axial direction) and can be steered both laterally (x or azimuthal direction) and in elevation (z direction) in order to acquire a volumetric pyramidal data set (Fig. 1.1, right lower panel). Matrix array probes can also provide real-time multiple simultaneous 2D views, at high frame rate, oriented in predefined or user-selected plane orientations by activacting multiple lines of piezoelectric elements within the matrix (Fig. 1.2).

The main technological breakthrough which allowed manufacturers to develop fully sampled matrix transducers has been the miniaturization of electronics that allowed the development of individual electrical interconnections for every piezoelectric element which could be independently controlled, both in transmission and in reception.

Beamforming (or spatial filtering) is a signal processing technique used to produce directionally or spatially selected signals sent or received from arrays of sensors. In 2DE, all the electronic components for the beamforming (high-voltage transmitters, low-noise receivers, analog-to-digital converter, digital controllers, digital delay lines) are inside the system and consume a lot of power (around 100 W and 1500 cm² of personal computer electronics board area). If the same beamforming approach would have been used for matrix array transducers used in 3DE, it would have required around 4 kW power consumption and a huge PC board area to accommodate all the needed electronics to control 3000 piezoeletric elements. To reduce both power consumption and the size of the connecting cable, several miniaturized circuit boards are incorporated into the transducer, allowing partial beamforming to be performed in the probe (Fig. 1.3). This unique circuit design results in an active probe which allows microbeamforming of the signal with low power consumption (<1 W) and avoids to connect every piezoelectric element to the ultrasound machine. The 3000 channel circuit boards within the transducer controls the fine steering by delaying and summing signals within subsections of the matrix, known as patches (microbeamforming, Fig. 1.3). A typical patch for a cardiac matrix probe contains approximately 25 piezoelextric elements configured in 5 × 5 matrix. Only patches are connected to the mainframe beamformer within the system. This microbeamforming works like a very small electronic beamformer by pointing its 25 elements (on both transmit and receiving) toward the desired scan line and allows to reduce the number of the digital channels to be put into the cable that connects the probe to the ultrasound system from 3000 (which would make the cabling too heavy for practical use) to the conventional 128–256 allowing the same size of the 2D cable to be used with 3D probes. Each micro-beamformer has its own output, which is wired back to the ultrasound systemtrough the transducer cable. Coarse steering is controlled by the ultrasound system where the patches are time-aligned to produce the parallel receive beams for each transmit beam (Fig. 1.3).

However, the electronics inside the probe produce heat whose amount is directly proportional to mechanical index used during imaging, therefore the engineering of active 3DE transducer should include thermal management.

Finally, new and advanced crystal manufacturing processes allows production of single crystal materials with homogeneous solid state technology and unique piezoelectric properties. These new transducers result in reduced heating production by increasing the efficiency of the transduction process to improve the conversion of transmit power into ultrasound energy and of received ultrasound energy into electrical power. Increased efficiency of the transduction process together with a wider bandwidth result in increased ultrasound penetration and resolution which improve image quality with the additional benefits of reducing artifacts, lowering power consumption and increase Doppler sensitivity.

Further developments in transducer technology have resulted in a reduced transducer footprint, improved side-lobe suppression, increased sensitivity and penetration, and the implementation of harmonic capabilities that can be used for both gray-scale and contrast imaging. The last generation of matrix transducers are significantly smaller than the previous ones and the quality of 2D and 3D imaging has improved significantly, allowing a single transducer to acquire both 2D and 3DE studies, as well as of acquiring the whole LV cavity in a single beat.

The relation between volume rate, number of parallel receive beams, sector width, depth, and line density can be described by the following equation:
therefore the volume rate can be adjusted to the specific needs by either changing the volume width or depth. The 3D system allows the user to control the lateral resolution by changing the density of the scan lines in the pyramidal sector too. However, a decrease in spatial resolution also affects the contrast of the image. Volume rate can also be increased by increasing the number of parallel receive beams, but in this way the signal-to-noise ratio and the image quality will be affected.

To put all this in perspective let us assume that we would like to image up to 16 cm depth in the body and acquire a 60° × 60° pyramidal volume. Since the speed of sound is approximately 1540 m/s and each pulse has to propagate 16 cm × 2 (to go forth and come back to the transducer), 1540/0.32 = 4812 pulses can be fired per second without getting interference between the pulses. Assuming that 1° beam spacing in both X and Z dimension is a sufficient spatial resolution we would need 3600 beams (60 × 60) to spatially resolve the 60° × 60° pyramidal volume. As a result, we will get a temporal resolution (volume rate) of 4812/3600 = 1.3 Hz, which is practically useless in clinical echocardiography.

The example above shows that the fixed speed of sound in body tissues has been a major challenge to the development of 3DE imaging. Manufacturers have developed several techniques such as parallel receive beamforming, multibeat imaging and real-time zoom acquisition to cope with this challenge but, in practice, this is usually achieved by selecting the appropriate acquisition modality for different imaging purposes (see Image acquisition and display paragraph).

Parallel receive beamforming or multiline acquisition is a technique where the system transmits one wide beam and receives multiple narrow beams formed within the bounds of the trasmit beam. In this way the volume rate (temporal resolution) is increased by a factor equal to the number of the received beams. Each beamformer focuses along a slightly different direction that was insonated by the broad transmit pulse. As an example, to obtain a 90° × 90°, 16-cm depth pyramidal volume at 25 vps, the system needs to receive 200,000 lines/s. Since the emission rate is around 5000 pulsed/s, the system should receive 42 beams in parallel for each emitted pulse. However, increasing the number of parallel beams to increase temporal resolution leads to an increase in size, costs and power consumption of the beamforming electronics, and deterioration in the signal-to-noise ratio and contrast resolution. With this technique of processing the received data, multiple scan lines can be sampled in the amount of time a conventional scanner would take for a single line, at the expense of reduced signal strength and resolution, as the receive beam are steered farther and farther away from the center of the transmit beam (Fig. 1.4).

Another technique to increase the size of the pyramidal volume and maintain the volume rate (or the reverse, e.g. maintain volume rate and increase the pyramidal volume) is the multibeat acquisition. With this technique, a number of small, ECG-gated subvolumes acquired from consecutive cardiac cycles are stitched together to build up the final, large pyramidal volume (Fig. 1.5). Multibeat acquisition will be effective only if the subvolumes to stitch together will be constant in position and size, therefore any transducer movement, cardiac translation motion due to respiration, change in cardiac cycle length will create subvolume malalignment and stitching artifacts (Fig. 1.6).

Finally, the quality of the images of the cardiac structures which can be obtained by a 3DE system will be affected by the point spread function of the system. The point spread function describes the imaging system response to a point input. A point input, represented as a single pixel in the “ideal” image, will be reproduced as something other than a single pixel in the “real” image (Fig. 1.7). The degree of spreading (blurring) of any point object varies according to the dimension employed. In current 3DE systems it will be around 0.5 mm in the axial (y) dimension, around 2.5 mm in the lateral (x) dimension, and around 3 mm in the elevation (z) dimension. As a result we will obtain the best images (less degree of blurring, i.e. distortion) when using the axial dimension and the worst (greatest degree of spreading) when we use the elevation dimension.

These concepts have an immediate practical application in the choice of the best approach to image a cardiac structure. According to the point spread function of 3DE the best results is expected to be obtained by using the parasternal approach because structures are mostly imaged by the axial and lateral dimensions. Conversely, the worst result is expected to be obtained by the apical approach which mostly uses the lateral and elevation dimensions.