WO2008135956A2 - Space-filling, aperiodic arrays for ultrasonic transducers - Google Patents

Abstract

A device is disclosed that includes an array of transducer elements that exhibit space- filling, aperiodic placement. The disclosed placement of transducer elements reduces grating lobe artefacts, facilitates full three-dimensional steerability, and permits maximal power delivery. The disclosed device may be used in a variety of applications and implementations, e.g., as an ultrasound transducer that is adapted for therapeutic purposes, such as hyperthermia or drug delivery. In such applications, the disclosed transducer meets requirements for spatial localization and power delivery.

Description

SPACE-FILLING, APERIODIC ARRAYS FOR ULTRASONIC TRANSDUCERS

The present disclosure is directed to systems and methods for delivering ultrasound energy to a target location and, more particularly, to ultrasound transducer systems/apparatus that include space-filling, aperiodic transducer elements that provide enhanced performance and advantageous flexibility across a range of applications and implementations.

Ultrasound technology has wide ranging applications in the field of healthcare. One of the possible growth markets for ultrasound is in the area of therapeutic intervention. In particular, there is increasing interest in the use of ultrasound for treatments involving hyperthermia, drug delivery, haemostasis, cavitation, lithotripsy and sonothrombolysis. In each of these applications, it is often desirable to employ transducers that can insonify a specified finite volume with intensities requiring large power output. This requirement generally necessitates construction of large aperture transducers to be capable of focusing to a small volume of tissue with adequate power delivery.

Several approaches to transducer design have been undertaken to address the above- noted requirements. These approaches can be broken into two discrete sets. In both cases, it is desirable to use finite sized elements to allow for phase delay control to focus in three dimensions. In the first set of approaches/solutions, a large number of transducer elements are used with half- wavelength spacing (or less). This design allows for the reduction/elimination of artefacts, such as grating lobes (i.e., one or more secondary focal points around or adjacent to the target location), at the expense of increasing the element count and reducing power capabilities. The second set of approaches/solutions involves the use of a finite set of transducer elements at spacings that are greater than a half- wavelength. In this latter approach, sparse sampling of a regularly spaced array (see, e.g., Goss, Frizzell et al., "Sparse random ultrasound phased array for focal surgery," Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions, 43(6): 1111-1121, 1996) or aperiodic placement of elements (see, e.g., Hutchinson and Hynynen; "Evaluation of an aperiodic phased array for prostate thermal therapies," 1995) is used. Sparse arrays have also been proposed for three-dimensional imaging (see, e.g., Lockwood, Talman et al., "Real-time 3-D ultrasound imaging using sparse synthetic aperture beamforming, "Ultrasonics, Ferroelectrics and Frequency Control, IEE Transactions, 45(4): 980-988, 1998) as well as therapy.

Thus, current designs for steerable, ultrasonic therapy transducers rely on (i) fully sampled arrays with half-wavelength spacing, or (ii) sparsely aperiodic sampled arrays with incomplete coverage of the aperture. These approaches drive several expensive and inefficient design choices. Namely, in the case of a therapeutic transducer with a fully sampled array, the number of elements can reach large values (e.g., for a 1 MHz transducer, lamda/2 = 0.75mm, 8 cm per side rectangular aperture, leads to >11,000 elements). In the case of random, aperiodic placement of elements, the packing fraction or surface coverage is generally significantly less than 100% (e.g., 50 %), which limits the amount of power delivered by the device to an undesirable degree (e.g., a power decrease of 75%).

To focus energy to a more spatially localized volume with increased absorption, higher frequency ultrasound energy may be employed. However, higher frequency energy increases issues associated with grating lobes. Indeed, grating lobe issues are even more significant for reasonable channel/element counts. Microbeamformer technologies enable the use of a large number of elements. However, therapeutic applications require even larger number of elements and higher energy levels than have been contemplated for microbeamformer applications, and current microbeamformer technologies are not designed to address such requirements.

The concept of space-filling is an established field of study in mathematics known as "tessellation." The problem of filling all of a two-dimensional surface with the smallest set of tiles in an aperiodic manner was the subject of study through out the 1960's and 1970's. Initially, it was thought that a large number of tiles of different shapes and sizes would be required to adequately fill a desired space. However, Penrose determined that there exists a set of two shapes that can be used to fill space (U.S. Patent No. 4,133,152).

The patent literature includes additional teachings relative to ultrasound transducer designs. For example, U.S. Patent No. 5,164,920 to Bast et al. discloses a composite ultrasound transducer that includes transducer elements having irregularly-shaped square structures. The irregular square shapes of the Bast '920 patent do not lead to space filling arrays because gaps remain in the array. In addition, the Bast '920 patent describes a method for making composite piezoelectric material, but not individually addressable elements.

U.S. Patent No. 6,135,971 to Hutchinson et al. discloses an apparatus for deposition of ultrasound energy in body tissue that includes random arrays of transducer elements for reduced grating lobes. However utilization of random arrays of rectangularly- shaped elements, in the manner disclosed by Hutchinson et al., generally yields gaps between individual elements, particularly when scaling to larger arrays, e.g., to maintain aperiodicity in all directions on a two-dimensional or three-dimensional surface. Moreover, the determination/selection of a random array is generally through "monte-carlo" simulations. Despite efforts to date, a need remains for transducer designs that are effective to reduce grating lobe artifacts, allow three-dimensional steerability and permit desired levels of power delivery. These and other needs are satisfied by the disclosed systems and methods, as will be apparent from the description which follows. The present disclosure provides advantageous ultrasound transducer designs wherein a space-filling array of transducer elements are positioned on a transducer surface. The transducer elements are arranged in a tiling pattern that is aperiodic. The aperiodicty and space-filling aspects of the disclosed element array offer enhanced ultrasound delivery/performance in a variety of applications and implementations, including specifically therapeutic treatments involving hyperthermia/tissue ablation, drug delivery, haemostasis, lithotripsy, diagnostic imaging and/or sonothrombolysis, as well as a full range of additional applications that employ heat, cavitation and/or shock waves to achieve desired therapeutic and/or diagnostic results.

The disclosed transducer element array overcomes limitations of prior art designs and prior art systems, which fail to provide designs/systems that include both aperiodicity and space-filling functionalities to address competing clinical needs and requirements. Thus, exemplary embodiments of the disclosed transducer element array advantageously break symmetries to reduce acoustic artifacts, while simultaneously achieving space-filling to maximize power output for use in a variety of therapeutic and/or imaging applications. In exemplary embodiments, the present disclosure provides a device that includes an ultrasound transducer. The ultrasound transducer is generally fabricated from a piezoelectric material. Exemplary embodiments utilize piezoelectric composite materials, although piezo -ceramic materials and/or a piezo-crystal materials may be used to fabricate the disclosed transducer elements.

The disclosed ultrasound transducer is fabricated from a plurality of transducer elements that define at least one or more discrete shapes. The one or more discrete shapes are deployed on the transducer surface in such a way that the entire surface area is covered. In addition, deployment/positioning of the transducer elements is effected such that the centers of the transducer elements are aperiodic. The aperiodicity of the array elements describes the fact that, under any translation of the transducer elements, the centers of the transducer elements will not overlap with those of other elements in the pattern/array.

For purposes of the present disclosure, "aperiodic elements" are to be understood as elements where the centers of the elements do not repeat in a regular pattern. In strict mathematical terms, aperiodicity can be differentiated from non-periodic patterns.

Aperiodicity means that the elements cannot be re-arranged in any manner that is periodic. Non-periodic means that there are arrangements of the elements can be re-arranged, if desired, into a pattern that is still space filling, but is periodic. For purpose of the present disclosure, the differentiation is not critical because any aperiodic (or non-periodic in an aperiodic arrangement), space-filling pattern is of interest for the applications disclosed herein. The critical outcome of also including non-periodic arrays is that there are patterns that are aperiodic and space filling that are the result of repeating a single shaped element in a non-overlapping manner. (See Andrew Glassner's Notebook, Aperiodic Tiling, IEEE Computer Graphics and Applications, May/June 1998, p 83-90). For the remainder of the present disclosure, the term "aperiodic" arrays shall include both aperiodic and non-periodic arrays in the mathematical nomenclature.

For purposes of the present disclosure, all aperiodic, space-filling array geometries are embraced and contemplated, but with particular emphasis on geometries that can be generated by different methods using grids, projections, substitutions or colorings. In general, the term substitution can have several meanings. In connection with tilings, substitution describes a simple but powerful method to produce tilings with many interesting properties. The main idea is to use a finite set of building blocks (Tl, T2 ... Tm) (the prototiles), an expanding linear map Q (the inflation factor) and a rule (how to dissect each scaled tile QTi into copies of the original prototiles Tl, T2...Tm). This information can be encoded in terms of parameterized tiles and affϊne maps, or, more appealing, in a diagram. Essentially, from such a diagram one can extract all needed information about the substitution. An important object in this context is the substitution matrix, which contains substantial information about the corresponding tilings.

An excitation mechanism is provided in communication with the transducer elements. The excitation mechanism supplies electrical excitation to the individual transducer elements. The excitation mechanism may be adapted to supply excitation energy of differing and/or adjustable phase with respect to individual transducer elements. In the case of transducer elements fabricated from piezo-composite material, excitation energy may be supplied to individual transducer elements through an electrical connection "mask" applied to the transducer. In the case of transducer elements fabricated from a piezo-ceramic and/or piezo- crystal material, the excitation energy isolation as between individual transducer elements may require dicing of the transducer.

In exemplary embodiments of the present disclosure, the aperiodic transducer array includes a limited number of transducer element geometries. Thus, transducer arrays that include between one and six (inclusive) transducer element geometries of the same (or substantially the same) size may be advantageously employed to produce advantageous transducer designs. By employing a limited number of distinct transducer element geometries (e.g., 1-6) that are of equal area/size, numerous advantages are realized, e.g., positioning and construction of the matching electrical network is simplified. It is to be noted, however, that the present disclosure is not limited to embodiments having six or less transducer element geometries. Rather, aperiodic, space-filling arrays having greater numbers of transducer element geometries may be employed without departing from the spirit or scope of the present disclosure.

Although the space-filling aspect of the disclosed devices/systems advantageously maximizes the power output by the transducer, the present disclosure also encompasses a class of transducers where the removal of specific elements is applied to a space- filling, aperiodic pattern of elements in order to improve grating lobe metrics.

Additional features, functions and benefits of the disclosed transducer systems and methods will be apparent from the description which follows, particularly when read in conjunction with the appended figures.

To assist those of skill in the art in making and using the disclosed transducer array systems and methods, reference is made to the accompanying figures, wherein:

FIGURE 1 is a schematic depiction of an exemplary two-dimensional array of transducer elements (Penrose tiling) according to the present disclosure; FIGURE 2 is a schematic depiction of an exemplary square aperture filled with an array of transducer elements (Penrose tiling) according to the present disclosure;

FIGURE 3 provides a series of beam plots in a plane 60mm from the aperture based on an exemplary transducer array of FIG. 2 according to the present disclosure (color printout); FIGURE 4 is a schematic depiction of a control periodic, space-filling transducer array;

FIGURE 5 provides a series of beam plots in a plane 60mm from the aperture for a control periodic transducer array according to FIG. 4 (color printout);

FIGURE 6 is a schematic depiction of a control semi-periodic space-filling two- dimensional array;

FIGURE 7 provides a series of beam plots in a plane 60mm from the aperture for the control semi-periodic transducer array of FIG. 6 (color printout);

FIGURE 8 is a schematic depiction of a square array of circular elements (control);

FIGURE 9 provides a series of beam plots in a plane 60mm from the aperture based on the square array of circular transducer elements (control) of FIG. 8 (color printout);

FIGURES 10(a) and 10(b) provide histogram plots of transducer element counts according to square aperture geometries based on 1000 trials for two element sizes (control);

FIGURE 11 is a schematic depiction of a two-dimensional array of randomly distributed circular elements according to a further control geometry; and FIGURE 12 provides a series of beam plots in a plane 60mm from the aperture based on the further control geometry of FIG. 11 (color printout);

The present disclosure is directed to advantageous ultrasound transducer systems and associated transducer-related methods that include/employ a space-filling, aperiodic array of transducer elements. The transducer elements are configured and dimensioned such that one or more discretely sized and shaped transducer elements are included in the transducer array. In exemplary embodiments of the present disclosure, between one and six (inclusive) distinctly sized/shaped transducer elements are combined to form an advantageous transducer array. The transducer aperture may be flat or curved (e.g., the aperture may define a substantially spherical surface).

The transducer elements are typically fabricated from a piezoelectric material. In exemplary embodiments, the piezoelectric material is a piezo-composite material, e.g., for ease of manufacturing, although alternative piezoelectric materials may be employed, e.g., piezo -ceramics and/or piezo -crystals may be employed in fabricating the disclosed transducer element arrays.

An excitation mechanism is provided in communication with the transducer elements to supply electrical excitation to the individual transducer elements. Excitation energies of differing and/or adjustable phase may be supplied to the individual transducer elements. Control systems may be provided to control the nature and/or phase of such electrical energy, as are known in the art. In the case of a piezo-composite material, element isolation is generally achieved through the etching of electrical contacts on the composite, e.g., using a mask in the pattern of the disclosed aperiodic array. In the case of transducer elements fabricated from a piezo -ceramic and/or piezo -crystal material, dicing of the transducer may be employed to isolate excitation energy as between transducer elements. The present disclosure embraces a range of transducer element arrays/placements, provided each such array is aperiodic and space-filling. Thus, exemplary transducer element arrays/placements include aperiodic, space-filling patterns where elements have been omitted/removed in such a way as to create "voids" in the shape of what would otherwise be an active element. The inclusion of one or more "void" spaces in the transducer element array/positioning may be desirable to facilitate control of the surface coverage, e.g., for power control and/or to minimize grating lobes.

Exemplary space-filling and aperiodic patterns may be devised and/or implemented in whole or in part using, inter alia, known tiling techniques. For example, transducer element positioning may be devised using techniques such as Penrose tiling (see below), Amman- Beenker tiling, Shield tiling, Dodecagonal Wheel Tiling, Dodecagonal Socolar Tiling, Robinson tiles, and other relevant tiling or tessellation patterns. In addition, devices and systems of the present disclosure include transducer element positioning/arrays that include one or more kerfs, i.e., non-zero separation between individual transducer elements. As noted herein, the disclosed ultrasound transducer systems, including specifically the aperiodic, space-filling transducer element arrays, have wide ranging applicability. Thus, for example, the disclosed ultrasound transducer systems utilizing an aperiodic, space-filling positioning approach have advantageous applicability in therapeutic and diagnostic fields, including imaging and non-imaging implementations. Imaging applications wherein relatively large field of view transducers are desired, the disclosed transducer systems/devices may have particular applicability.

Exemplary Embodiment - Penrose Tiling based space-filling array In a first exemplary embodiment of the present disclosure, the design of an ultrasound transducer array is undertaken using the well-known Penrose tiles. According to this exemplary embodiment, tessellation or space-filling tiling provides two or more discrete tiles repeated to infinity. So repeated, the transducer element positioning/array is characterized by no regular spacing or orientation, yet complete space-filling of the aperture region.

FIG. 1 schematically depicts one possible embodiment of a 2D array with 255 elements that are shaped/arrayed in the form of an annulus. The entire transducer element array has only two types/geometries of transducer elements. The annular array design defines a central opening/region that facilitates/accommodates the placement of an imaging transducer, such as the Philips X3-1 or X7-2, therethrough. Thus, the exemplary embodiment of FIG. 1 provides a transducer element that includes an aperiodic, space- filling deployment of individual transducer elements (255) exhibiting two distinct geometries, such deployment defining an annular ring with a substantially circular hole at the center for receipt, e.g., of an imaging transducer. Of note, in a modified version of the exemplary embodiment of FIG. 1, the aperture could be spherically curved (rather than planar), and such spherically curved geometry could be provided as an annular ring defining a central hole, or in an alternative geometry that does not define a central hole.

FIG. 2 schematically depicts another exemplary embodiment of transducer arrays developed with Penrose tiles according to the present disclosure. In the exemplary embodiment of FIG. 2, the aperture is 40 mm square and includes 255 transducer elements. Of note, the embodiment of FIG. 2 offers isotropic coverage with a relatively small-scale structure, facilitating isotropic performance for focusing of ultrasound energy, while minimizing potential negative effects (e.g., grating lobes) associated with regularity that is encountered at larger scales.

The beam patterns from the array of FIG. 2 is compared with several 2D arrays to illustrate the advantages of the aperiodic, space-filling positioning of transducer elements according to the present disclosure. With reference to FIG. 3, a series of beam plots are provided which demonstrate the superior focus-related performance of the disclosed transducer constructed with aperiodic, space-filling positioning according to the present disclosure. Simulations were performed in Field II. All simulations assume a center frequency = 1.2 MHz, with bandwidth 80%. The beam plots were calculated in a plane 60 mm from the aperture at several locations in the x-y plane. The beam plot images of FIG. 2 show that with Penrose tiling according to the present disclosure, the ability to steer the focus in three dimensions is equivalent in all directions, with no marked degradation in main lobe to grating lobe ratio.

Several comparisons were made relative to existing transducer system/design approaches to measure the benefit of the aperiodic, space-filling tiling transducer patterns of the present disclosure. The first comparison is to a periodic, space-filling array of rectangular elements (16x16 = 256 elements). FIG. 4 schematically depicts a control periodic array and FIG. 5 shows the performance for focusing at various locations in a plane 60 mm from the aperture for such control periodic array. Significant grating lobes are seen. The second comparison is made relative to a design approach that features semi- periodic, space-filling transducer patterns. This class of transducers uses two types of elements, where the two elements are characterized by different areas. The transducer elements are chosen to have a fixed height and a width that is selected from one of two possible sizes. The widths are randomly chosen to be within the range of 1 to 4 mm in such a manner than the total number of elements is fixed at 256 and the full-aperture is covered (or substantially covered).

With reference to FIG. 6, the control transducer array is designed such that each row in the array is independent in the selection of the number and ordering of the two types of elements. The only constraint is that each row has the same total width and the same number of elements (16 in this case). This control array is used for comparison because it is also space-filling, like the Penrose tiling array, and can be designed in a straightforward manner by filling each row of elements.

To evaluate the performance of the control semi-periodic array, 100 realizations of such control array were randomly generated, and the best array in terms of minimal mean grating lobe level for focusing among several directions was selected. FIG. 7 shows that the focus-related performance with respect to grating lobe artifacts is good in the direction with greater randomness, but poor in the elevation direction, i.e., the direction with regular spaced heights. The third comparison is made relative to an approach wherein regularly sized circles are placed aperiodically within a bounded geometry. Such an approach works well for the breaking symmetries to reduce the size of grating lobes. However, the price that is paid is the loss of power due to incomplete spatial packing of the elements. FIG. 8 schematically depicts an ideal case of packing, wherein randomly spaced circles are positioned in a square aperture with a maximal packing fraction of about 85% (the theoretical maximal packing fraction is -91% with hexagonal packing in the case of infinitely large 2D space). This geometry was obtained from wvwv packomania.com and is considered to be the best packing configuration known to date. The diameter of the circles is 2.606 mm. With the maximal packing arrangement, the regularity of the spacing is high. This leads to unwanted increase in the grating lobe construction as seen in FIG. 9. The fourth comparison is similar to the previous one in that it also uses circular elements on a square, but the element locations are chosen in a completely random order until the total number of elements is achieved. Extensive simulations for random placement of the elements of a fixed diameter were done in order to select an array that had the maximal packing fraction. The simulations were done, one by one for each diameter, for circular elements with increasing diameter from 1.7 mm onwards in steps of 0.05 mm. For a given diameter, the circles were attempted to fill the square aperture in a random fashion ensuring no overlap until the total number of elements (255) were filled. If the placement became unfeasible after an extended period (100,000 attempts to place an element without overlapping), another fresh trial for random placement was attempted.

It was found that for diameters 2.10 mm and less, it was possible to find at least one array with 255 elements within about 100 trials. When the diameter was increased to 2.15 and 2.2 mm, it became impossible to fit in 255 elements after 100 trials. FIGS. 10(a) and 10(b) show histograms for the number of elements filled for these two cases (i.e., two diameters) based on 1000 trials. The maximum number of elements that could be fit was only 240 and 230 for the case of 2.15 and 2.2 mm diameter circles, respectively. While it is certainly true that 255 elements of larger size could be fit, finding such a design is not trivial when the elements are being distributed randomly. Moreover, with increasing coverage area, the regularity in the array increases, as can be seen from the earlier control design with maximal packing.

FIG. 11 shows the 2D array being filled with 255 elements of diameter 2.10 mm and FIG. 12 shows beam plots for this array at a distance of 60 mm from the aperture. It can be seen that this array has good performance in terms of grating lobe levels. However, the drawback is that the area covered was only 55.2% of the total area of the aperture, thereby significantly reducing the power capabilities of the design.

The possibility of filling the square aperture with two types of elements (two diameter circles) was also studied. However, in this case also, the maximum coverage area achieved was only 53.7% of the total area and occurred for the case when the two diameters were 2.034 mm and 2.096 mm. FIG. 13 shows a comparison of the performance of all the arrays described herein. Among the four space-filling arrays studied, the aperiodic one based on Penrose tiling performs the best. The performance of the Penrose array is also seen to be iostropic with little variations from one direction of steering to another. The random 2D array with circular elements, shown for comparison, performs better than the Penrose array; however, the array suffers from a significant loss in energy due to reduced area coverage.

As noted herein, Penrose tiling is an exemplary approach to transducer element deployment. However, the disclosed devices and systems are not limited to the use of Penrose tiling in designing/developing advantageous aperiodic, space-filling transducer element arrays. Indeed, alternative techniques may be employed and techniques that employ more than two element geometries (as is the case with Penrose tiling) in generating an aperiodic, space-filling array would yield superior performance. Indeed, if an increased number of element geometries are employed, e.g., 3 or 4, then the system performance would be further enhanced relative to the exemplary Penrose tiling array disclosed herein. As is apparent from the description and comparisons provided herein, aperiodic space-filling transducer element arrays of the present disclosure offer significantly enhanced performance, e.g., reduced grating lobes and high energy delivery. The systems and methods of the present disclosure are particularly useful for large aperture transducers, where the element count needed to obtain half-wavelength spacing is unreasonably high. Therefore, natural applications for the disclosed systems and methods are in the area of tightly focused, therapeutic treatments, such as HIFU ablation, site -targeted drug delivery, haemostasis and sonothrombolysis. However, the disclosed systems and methods are susceptible to many variations and alternative applications, without departing from the spirit or scope of the present disclosure.

Claims

1. A transducer system, comprising: an aperiodic, space-filling array of transducer elements, the transducer elements being of at least one geometric size and/or shape.

2. A transducer system according to claim 1, wherein the transducer elements are fabricated from a piezoelectric material.

3. A transducer system according to claim 2, wherein the piezoelectric material is selected from the group consisting of a piezoelectric composite, a piezoelectric ceramic and a piezoelectric crystal.

4. A transducer system according to claim 1, wherein the aperiodic, space- filling array of transducer elements is defined by a tessellation technique.

5. A transducer system according to claim 4, wherein the tessellation technique is selected from the group consisting of Penrose tiling, Ammann-Beenker tiling, Ammann A3, Ammann A4, Shield tiling, Dodecagonal Wheel Tiling, and Dodecagonal Socolar Tiling, Robinson Tiling, Danzer Tilings, Chair Aperiodic Tiling, Pinwheel Tiling, Trilobite-Cross Aperiodic Tiling, or any other aperiodic tiling that can be obtained by using grids, projections, substitutions or coloring methods.

6. A transducer system according to claim 1, wherein the aperiodic, space-filling array of transducer elements is projected or directly mapped onto a non-planar surface.

7. A transducer system according to claim 1, wherein the predominant surface of the transducer is covered by an aperiodic, space-filling array of transducer elements except for "voids" made by removal of specific elements from the same general pattern.

8. A transducer system according to claim 1, wherein the aperiodic, space- filling array of transducer elements is positioned on a transducer head.

9. A transducer system according to claim 8, wherein the transducer head defines a geometry selected from the group consisting of a planar geometry and a spherical geometry.

10. A transducer system according to claim 1, wherein the aperiodic, space-filling array of transducer elements are characterized by between one and six (inclusive) different geometric sizes and/or shapes.

11. A transducer system according to claim 1 , wherein the aperiodic, space- filling array of transducer elements are positioned in a substantially ring-like deployment.

12. A transducer system according to claim 11 , wherein the substantially ring-like deployment defines a central hole that is adapted to receive an imaging transducer.

13. A transducer system according to claim 1, further comprising electrical connections with respect to the transducer elements.

14. A transducer system according to claim 13, wherein the electrical communications are provided by a mask structure.

15. A method for delivering ultrasound energy to a target location, comprising: providing a transducer element that includes an aperiodic, space-filling array of transducer elements, the transducer elements being of at least one geometric size and/or shape; energizing the transducer elements to deliver ultrasound energy to the target location.

16. A method according to claim 15, wherein the transducer elements are fabricated from a piezoelectric material.

17. A method according to claim 16, wherein the piezoelectric material is selected from the group consisting of a piezoelectric composite, a piezoelectric ceramic and a piezoelectric crystal.

18. A method according to claim 15, wherein the aperiodic, space-filling array of transducer elements is defined by a tessellation technique.

19. A method according to claim 16, wherein the tessellation technique is selected from the group consisting of Penrose tiling, Amman-Beenker tiling, Shield tiling, Dodecagonal Wheel Tiling, and Dodecagonal Socolar Tiling, Robinson Tiling, Danzer Tilings, Chair Aperiodic Tiling, Pinwheel Tiling, Trilobite-Cross Aperiodic Tiling, or any other aperiodic tiling that can be obtained by using grids, projections, substitutions or coloring methods.

20. A method according to claim 15, wherein the aperiodic, space-filling array of transducer elements is positioned on a transducer head.

21. A method according to claim 20, wherein the transducer head defines a geometry selected from the group consisting of a planar geometry and a spherical geometry.

22. A method according to claim 15, wherein the aperiodic, space-filling array of transducer elements are characterized by between one and six (inclusive) different geometric sizes and/or shapes.

23. A method according to claim 15, wherein the aperiodic, space-filling array of transducer elements are positioned in a substantially ring-like deployment.

24. A method according to claim 23, wherein the substantially ring-like deployment defines a central hole and further comprising positioning an imaging transducer in the central hole.

25. A method according to claim 15, wherein the ultrasound energy is delivered to human tissue in connection with a procedure selected from the group consisting of hyperthermia/tissue ablation, drug delivery, haemostasis, lithotripsy, diagnostic imaging, sonothrombolysis, a heat -based procedure, a cavitation-based procedure, shock wave -based procedure, and combinations thereof.