Ultrasound Phased Array Research Articles

An ultrasound cylindrical phased array for deep heating in the breast: theoretical design using heterogeneous models

The objective of this theoretical study is to design an ultrasound (US) cylindrical phased array that can be used for hyperthermia (40–44 °C) treatment of tumours in the intact breast. Simultaneously, we characterize the influence of acoustic and thermal heterogeneities on the specific absorption rate (SAR) and temperature patterns to determine the necessity of using heterogeneous models for a US applicator design and treatment planning. Cylindrical configurations of monopole transducers are studied on their ability to generate interference patterns that can be steered electronically to the location of the target region. Hereto, design parameters such as frequency, number of transducers per ring, ring distance and number of rings are optimized to obtain a small primary focus, while suppressing secondary foci. The models account for local heterogeneities in both acoustic (wave velocity and absorption) and thermal (blood perfusion rate, heat capacity and conductivity) tissue properties. We used breast models with a central tumour (30 × 20 × 38 mm3) and an artificial thorax tumour (sphere with a radius of 25 mm) to test the design. Simulations predict that a US cylindrical phased array, consisting of six rings with 32 transducers per ring, a radius of 75 mm and 66 mm distance between the first and sixth transducer ring, operating at a frequency of 100 kHz, can be used to obtain 44 °C in the centre of tumours located anywhere in the intact breast. The dimensions of the volumes enclosed by the 41 °C iso-temperature are 19 × 19 × 21 mm3 and 21 × 21 × 32 mm3 for the central and the thorax tumours, respectively. It is demonstrated that acoustic and thermal heterogeneities do not disturb the SAR and temperature patterns.

Optimal simulations of ultrasonic fields produced by large thermal therapy arrays using the angular spectrum approach.

The angular spectrum approach is evaluated for the simulation of focused ultrasound fields produced by large thermal therapy arrays. For an input pressure or normal particle velocity distribution in a plane, the angular spectrum approach rapidly computes the output pressure field in a three dimensional volume. To determine the optimal combination of simulation parameters for angular spectrum calculations, the effect of the size, location, and the numerical accuracy of the input plane on the computed output pressure is evaluated. Simulation results demonstrate that angular spectrum calculations performed with an input pressure plane are more accurate than calculations with an input velocity plane. Results also indicate that when the input pressure plane is slightly larger than the array aperture and is located approximately one wavelength from the array, angular spectrum simulations have very small numerical errors for two dimensional planar arrays. Furthermore, the root mean squared error from angular spectrum simulations asymptotically approaches a nonzero lower limit as the error in the input plane decreases. Overall, the angular spectrum approach is an accurate and robust method for thermal therapy simulations of large ultrasound phased arrays when the input pressure plane is computed with the fast nearfield method and an optimal combination of input parameters.

Optimization of ultrasound array designs for high intensity focused treatment of prostate cancer and benign prostatic hyperplasia

This paper describes the optimization of designing a two-dimensional (2-D) ultrasound phased array to be used for the treatment of both prostate cancer and benign prostatic hyperplasia. The optimization study took into consideration the physical constraints of the conventional method of treatment, and arrived at an optimized array design with the overall dimensions of 10 cm x 2.2 cm. The optimization study also addressed the following additional parameters: The maximum possible depth of penetration (DOP), the maximum possible steering angle, the Grating lobe level, the operating frequency, and the element size. In optimizing the design, the DOP and the steering angle are maximized while the grating lobe value is minimized. A 56 x 12 element 2-D array was found to be the optimum choice allowing both focusing and steering within the entire prostate without inducing damage at locations other than that of the focal point.

Lateral mode coupling to reduce the electrical impedance of small elements required for high power ultrasound therapy phased arrays

A method that uses lateral coupling to reduce the electrical impedance of small transducer elements in generating ultrasound waves was tested. Cylindrical, radially polled transducer elements were driven at their length resonance frequency. Computer simulation and experimental studies showed that the electrical impedance of the transducer element could be controlled by the cylinder wall thickness, while the operation frequency was determined by the cylinder length. Acoustic intensity (averaged over the cylinder diameter) over 10 W / cm(2) (a therapeutically relevant intensity) was measured from these elements.

New design for an endoesophageal sector- based array for the treatment of atrial fibrillation: a parametric simulation study

Atrial fibrillation (AF) is the most frequent and sustained cardiac arrhythmia affecting humans. The electrical isolation by ablation of the pulmonary veins (PV) in the left atrium (LA) of the heart has proved to be an effective cure for the AF. The ablation consists mainly of the formation of a localized circumferential thermal coagulation of the cardiac tissue surrounding the PVs. In this article, a parametric study was carried out to establish an optimal configuration of endesophageal ultrasound phased arrays intended to treat the AF. The devices are spherical-surface sections truncated at 15 mm, with a depth of 4 mm, and they are cut in concentric-rings, each composed of independently driven sectors. The number of independent elements (N(e)) was minimized for different values of ratio of pressure amplitude of the secondary lobe over the main lobe (eta) of 0.35, 0.4, 0.45, and 0.5 inside a volume of interest (VOI). After assuming a Cartesian system with the origin in the center of the device, the VOI was defined as the prism enclosed by the coordinates (-12, 10, -9) mm and (12, 37, 9) mm. The VOI has its center at (0, 23.5, 0) mm and is large enough to contain all the targets identified in the Visible Human Project Male specimen. Operating at 1 MHz, eta and N(e)were calculated in function of the element size and focal length (F). Four devices for each value of eta were found. After keeping values of F and normalized dimensions of the independent elements in terms of wavelength, higher frequencies were considered: 1.25 MHz, 1.5 MHz, and 2 MHz. In total, 16 device configurations were obtained. Realistic modeling of lesion formation in the heart chamber showed that the 16 configurations were able to produce the typical lesion used to treat the AF while preserving surrounding structures. At higher frequencies, lower power was required, and a greater number of array elements was required. For an exposure of 5 s and a maximum temperature of 70 degrees C, the average (+/-s.d.) acoustical intensity at transducer surface varied from 22.3(+/-5.8) W/cm(2) for a device with F = 98 mm at 1 MHz to 5.8(+/-1.2) W/cm(2) for a device with F = 186 mm at 2 MHz, while requiring 319 and 2093 elements, respectively, and achieving values of eta of 0.5 and 0.41, respectively. For the intended application, the selected devices implied a better focusing when compared with more traditional planar 2-D arrays, while requiring less power and fewer independent elements.

Optimal control point distributions for waveform diversity.

Waveform diversity is a method for tumor heating with ultrasound phased arrays that extend the concept of multiple focusing to achieve an optimal sequence of power depositions. Waveform diversity minimizes the power deposited at control points in normal tissue while maximizing the power at control points in the tumor through an approach that employs semi‐definite programming. As with other spot scanning and multiple focusing techniques, the performance of waveform diversity depends on the location of the control points. For example, single spot scanning is limited by intervening tissue heating, so the ideal spot scanning approach in large tumors focuses on the back half of the tumor and allows intervening tissue heating to fill in the remaining tumor region. In contrast, waveform diversity combined with mode scanning tends to preferentially deliver heat beyond control points placed in the tumor. In an effort to exploit this feature, the energy delivered to control points on the front face of the tumor is maximized, and the energy delivered to control points along the tumor axis and directly behind the tumor is minimized. Results show that this control point distribution applied to waveform diversity combined with mode scanning achieves conformal heating in a 3‐cm‐diameter spherical tumor model that is heated by a 1444 element spherical section array.

Image-based refocusing of ultrasound arrays in the presence of strongly scattering objects.

Ultrasound phased arrays are currently being investigated for a dual-mode (imaging/therapy) operation in targeting deep-seated abdominal tumors for selective destruction noninvasively. In some cases, e.g., liver tumors, the target is partially obstructed by the ribcage, which limits the array gain at the target. In addition, the intensity at the ribs may be high enough to cause treatment-limiting pain and/or collateral damage to the tissues surrounding the ribs in the path of the therapeutic beam. Using the imaging capabilities of these dual-mode arrays, we have formulated and experimentally verified a robust minimum variance beamforming algorithm for adaptive refocusing in the presence of the ribs. The algorithm utilizes image data of the treatment region formed using conventional beamforming in estimating the array steering vector at the target and the weighting matrix that maximizes the array gain at the target. In this paper, we will describe the mathematical formulation and present experimental data to demonstrate its robustness. We will also discuss the implications of the method, the use of ultrasound phased arrays for imaging, and therapy of trans-thoracic targets such as the liver and the heart.

Design and Experimental Evaluations of a Low-Frequency Hemispherical Ultrasound Phased-Array System for Transcranial Blood–Brain Barrier Disruption

The purpose of this paper is to demonstrate a prototype design of a low-frequency multiple-channel hemispherical focused-ultrasound phased-array system for transcranial disruption of the blood-brain barrier (BBB). A 32-channel ultrasound driving system tunable in the frequency range from 200 to 400 kHz was designed for producing a suitable ultrasound output for BBB disruption. The driving system includes a microcontroller/field-programmable gate-array-based control kernel with multiple-channel driving circuits implemented by a high-voltage switching/LC-resonance/impedance-matching circuit module. Three hemispherical phased arrays comprising 22, 31, and 80 elements were fabricated and tested. The pressure distributions at the geometric center and at off-center positions were tested experimentally. The focal performance of the different hemispherical arrays was also evaluated theoretically. The results showed that the developed phased-array system can successfully drive the hemispherical array with multiple-channel ultrasound signals with independent phase control at 8-bit resolution. Good focusing abilities were evident both at the geometric center and at specific off-center target positions. Preliminary animal experiments show that the BBB in rat can be locally disrupted successfully. The system will serve as a reference platform for developing a focused-ultrasound system for clinical use in brain drug delivery applications.

The Design and Characterization of an Ultrasound Phased Array Suitable for Deep Tissue Hyperthermia

In this paper we describe the design and evaluation of a planar phased-array ultrasound transducer suitable for producing localized hyperthermia in solid tumors deep within the body. Simulation using a customized version of Ultrasim has been used to determine the relationship between the size and position of the focus and parameters of the array. These parameters include the overall size of the array and the size, shape and distribution of the individual elements. A 15-element prototype array has been constructed using the results of the simulation. Beam profile measurements on this transducer made in an acoustic tank were compared with the beam profile predicted by simulation. The results showed good agreement in the shape of the focal region, but with the focus closer to the surface of the physical transducer when compared with the simulation and with small high-intensity areas between the surface of the transducer and the focus in the measured profile. A sensitivity analysis using a simulated factorial experiment indicated that the presence of a secondary vibrational mode within the elements of the array was the principal cause for both the shift in the position of the focus and for the unwanted maxima close to the surface of the array. The results also showed that the array was tolerant of a large variation in output intensity of the individual elements in the array in producing a focal region. Extrapolation of the results obtained in this study indicate that an array of 60 elements, based on the design described, driven by 550 V peak-to-peak pulses would be capable of producing a peak focal intensity of 50 Wcm −2 at a depth of 60 mm in tissue, which would be appropriate for hyperthermia used as an adjunct to radiotherapy or chemotherapy. (E-mail: a.h.aitkenhead@warwick.ac.uk)

Feasibility of transrib focused ultrasound thermal ablation for liver tumors using a spherically curved 2D array: A numerical study

The use of focused ultrasound thermal ablation to treat hepatocarcinoma and other liver tumors produces promising clinical results. However, one of the major drawbacks is the high absorption of ultrasonic energy by the rib, making partial rib removal necessary in many cases. This study numerically investigated the feasibility of using a spherical ultrasound phased array for transrib liver-tumor thermal ablation. An independently array-element activitation scheme, which switches off the transducer elements obstructed by the ribs based on feedback anatomical medical imaging, was proposed to reduce the rib-overheating problem. The numerical results showed that the proposed treatment planning strategy can effectively reduce the specific energy absorbed by the rib while maintaining the energy at the target position, which both reduces the rib-overheating problem and increases the possibility of treating a target lesion under an intact rib. The analysis also demonstrated that the target position and the ultrasound frequency play key roles in the treatment. Patients with diverse characteristics were also tested to show the generality of the proposed strategy. The proposed treatment planning strategy also provides useful information for evaluating the treatment effectiveness prior to clinically performing transrib ultrasound liver-tumor thermal ablation.

Thermal therapy for breast tumors by using a cylindrical ultrasound phased array with multifocus pattern scanning: a preliminary numerical study

The purpose of this study is to investigate the feasibility of using a 1 MHz cylindrical ultrasound phased array with multifocus pattern scanning to produce uniform heating for breast tumor thermal therapy. The breast was submerged in water and surrounded by the cylindrical ultrasound phased array. A multifocus pattern was generated and electrically scanned by the phased array to enlarge the treatment lesion in single heating. To prevent overheating normal tissues, a large planning target volume (PTV) would be divided into several planes with several subunits on each plane and sequentially treated with a cooling phase between two successive heatings of the subunit. Heating results for different target temperatures (Ttgt), blood perfusion rates and sizes of the PTV have been studied. Furthermore, a superficial breast tumor with different water temperatures was also studied. Results indicated that a higher target temperature would produce a slightly larger thermal lesion, and a higher blood perfusion rate would not affect the heating lesion size but increase the heating time significantly. The acoustic power deposition and temperature elevations in ribs can be minimized by orienting the acoustic beam from the ultrasound phased array approximately parallel to the ribs. In addition, a large acoustic window on the convex-shaped breast surface for the proposed ultrasound phased array and the cooling effect of water would prevent the skin overheating for the production of a lesion at any desired location. This study demonstrated that the proposed cylindrical ultrasound phased array can provide effective heating for breast tumor thermal therapy without overheating the skin and ribs within a reasonable treatment time.

Investigation of a spherical-section ultrasound phased array for hepatic ablation

A 3D ultrasound thermal model with a 3D finite element representation for modeling the thermal diffusion effects for hepatic ablation induced by spherical-section ultrasound phased array was developed. The model was first validated against available published measured data in rat liver. Using the validated model, effects of blood perfusion and heating schemes on lesion formation were studied for both single focus and split-focus intensity patterns. It was shown that for single focus sonication pattern the short-duration (∼2 s) and high-intensity (∼1250 W/cm2) heating scheme can completely reduce the cooling effect of the blood perfusion. The lesion shape and size were significantly altered by perfusion for split-focus pattern even with a rapid heating scheme when the focus spacing was larger than 2.4 mm. Underdosed areas might be present between two foci. Prolonging exposure time or shortening focus spacing can reduce the cool region between two foci. In addition, the influences of thermal and acoustic parameters were also studied. When the therapy depth is short (<5 cm), the lesion size monotonically increases with increasing attenuation coefficient that ranges from 5.4 to 11 Np/(m·MHz).

A novel strategy to increase heating efficiency in a split‐focus ultrasound phased array

Focus splitting using sector-based phased arrays increases the necrosed volume in a single sonication and reduces the total treatment time in the treatment of large tumors. However, split-focus sonication results in a lower energy density and worse focal-beam distortion, which limits its usefulness in practical treatments. Here, we propose a new heating strategy involving consecutive strongly focused and split-focus sonications to improve the heating efficiency. Theoretical predictions including linear and thermal-dose-dependent attenuation change were employed to investigate potential factors of this strategy, and ex vivo tissue experiments were conducted to confirm its effectiveness. Results showed that the thermal lesions produced by the proposed strategy could be increased when comparing with the previous reported strategies. The proposed heating strategy also induces a thermal lesion more rapidly, and exhibits higher robustness to various blood perfusion conditions, higher robustness to various power/heating time combinations, and superiority to generate deep-seated lesions through tissues with complex interfaces. Possible mechanisms include the optimization of the thermal conduction created by the strongly focused sonication and the temperature buildup gained from thermally induced tissue attenuation change based on the theoretical analysis. This may represent a useful technique for increasing the applicability of split-focus and multiple-focus sonication techniques, and solve the obstacles encountered when attempting to use these methods to shorten the total clinical treatment time.

MAGNETIC RESONANCE IMAGING-GUIDED FOCUSED ULTRASOUND FOR THERMAL ABLATION IN THE BRAIN

Magnetic resonance imaging (MRI)-guided focused ultrasound is a novel technique that was developed to enable precise, image-guided targeting and destruction of tumors by thermocoagulation. The system, ExAblate2000, is a focused ultrasound delivery system embedded within the MRI bed of a conventional diagnostic MRI scanner. The device delivers small volumetric sonications from an ultrasound phased array transmitter that converge energy to selectively destroy the target. Temperature maps generated by the MRI scanner verify the location and thermal rise as feedback, as well as thermal destruction. To assess the safety, feasibility, and precision of this technology in the brain, we have used the ExAblate system to create predefined thermal lesions in the brains of pigs. Ten pigs underwent bilateral craniectomy to provide a bone window for the ultrasound beams. Seven to 10 days later, the animals were anesthetized and positioned in the ExAblate system. A predefined, 1-cm frontal para ventricular region was delineated as the target and treated with multiple sonications. MRI was performed immediately and 1 week after treatment. The animals were then sacrificed and the brains removed for pathological study. The size of individual sonication points and the location of the lesion were compared between the planned dose maps, posttreatment MRI scans, and pathological specimen. High-energy sonications led to precise coagulation necrosis of the specified targets as shown by subsequent MRI, macroscopic, and histological analysis. The thermal lesions were sharply demarcated from the surrounding brain with no anatomic or histological abnormalities outside the target. MRI-guided focused ultrasound proved a precise and an effective means to destroy anatomically predefined brain targets by thermocoagulation with minimal associated edema or damage to adjacent structures. Contrast-enhanced T1-, T2-, and diffusion-weighted MRI scans may be used for real-time assessment of tissue destruction.

A fast and conformal heating scheme for producing large thermal lesions using a 2D ultrasound phased array

The treatment conformability and the total treatment time of large tumors are both important issues in ultrasound thermal therapy. Previous heating strategies all show their restrictions in achieving these two issues to satisfactory levels simultaneously. This work theoretically presents a new heating strategy which is capable of both increasing the treatment conformability and shortening the treatment time, when using a 2D ultrasound phased array transducer. To perform this, a set of the multiple-foci patterns (considered the basic heating units) were temporally switched to steer the beam at different focal planes with the lesion length being well-controlled. Then, to conformally cover an irregular target volume, the 2D phased array was laterally shifted by a positioning system to deposit a suitable heating unit to cover a subvolume part. Results demonstrated that the totally treatment time can be largely reduced. The heating rate can be increased up to 0.96 cm3/min compared to the previously reported 0.26 cm3/min. Also, the proposed scheme showed that the tumor regions can be completely treated with the normal tissue damage at satisfactory level. The feasibility of the proposed strategy for irregular tumor treatment was also demonstrated. This study offers useful information in large tumor treatment in ultrasound thermal therapy.

MAGNETIC RESONANCE IMAGING-GUIDED, HIGH-INTENSITY FOCUSED ULTRASOUND FOR BRAIN TUMOR THERAPY

Magnetic resonance imaging-guided high-intensity focused ultrasound (MRIgFUS) is a novel technique that may have the potential for precise image-guided thermocoagulation of intracranial lesions. The system delivers small volumetric sonications from an ultrasound phased array transmitter that focuses energy selectively to destroy the target with verification by magnetic resonance imaging-generated thermal maps. A Phase I clinical study was initiated to treat patients with recurrent glioma with MRIgFUS. To date, three patients with histologically verified recurrent glioblastoma multiforme have been treated with MRIgFUS. All patients underwent craniectomy 7 to 10 days before therapy to create a bony window for the ultrasound treatment. Sonications were applied to induce thermocoagulation of the enhancing tumor mass. Long-term radiological follow-up and post-treatment tissue specimens were available for all patients. MRIgFUS treatment resulted in immediate changes in contrast-enhanced T1-, T2-, and diffusion-weighted magnetic resonance imaging scans in the treated regions with subsequent histological evidence of thermocoagulation. In one patient, heating of brain tissue in the sonication path resulted in a secondary focus outside the target causing neurological deficit. New software modifications were developed to address this problem. In this first clinical report, MRIgFUS was demonstrated to be a potentially effective means of destroying tumor tissue by thermocoagulation, although with an associated morbidity and the inherent invasive nature of the procedure requiring creation of a bone window. A modified technology to allow MRIgFUS treatment through a closed cranium is being developed.

MR thermometry characterization of a hyperthermia ultrasound array designed using the k-space computational method

BackgroundUltrasound induced hyperthermia is a useful adjuvant to radiation therapy in the treatment of prostate cancer. A uniform thermal dose (43°C for 30 minutes) is required within the targeted cancerous volume for effective therapy. This requires specific ultrasound phased array design and appropriate thermometry method. Inhomogeneous, acoustical, three-dimensional (3D) prostate models and economical computational methods provide necessary tools to predict the appropriate shape of hyperthermia phased arrays for better focusing. This research utilizes the k-space computational method and a 3D human prostate model to design an intracavitary ultrasound probe for hyperthermia treatment of prostate cancer. Evaluation of the probe includes ex vivo and in vivo controlled hyperthermia experiments using the noninvasive magnetic resonance imaging (MRI) thermometry.MethodsA 3D acoustical prostate model was created using photographic data from the Visible Human Project®. The k-space computational method was used on this coarse grid and inhomogeneous tissue model to simulate the steady state pressure wavefield of the designed phased array using the linear acoustic wave equation. To ensure the uniformity and spread of the pressure in the length of the array, and the focusing capability in the width of the array, the equally-sized elements of the 4 × 20 elements phased array were 1 × 14 mm. A probe was constructed according to the design in simulation using lead zerconate titanate (PZT-8) ceramic and a Delrin® plastic housing. Noninvasive MRI thermometry and a switching feedback controller were used to accomplish ex vivo and in vivo hyperthermia evaluations of the probe.ResultsBoth exposimetry and k-space simulation results demonstrated acceptable agreement within 9%. With a desired temperature plateau of 43.0°C, ex vivo and in vivo controlled hyperthermia experiments showed that the MRI temperature at the steady state was 42.9 ± 0.38°C and 43.1 ± 0.80°C, respectively, for 20 minutes of heating.ConclusionUnlike conventional computational methods, the k-space method provides a powerful tool to predict pressure wavefield in large scale, 3D, inhomogeneous and coarse grid tissue models. Noninvasive MRI thermometry supports the efficacy of this probe and the feedback controller in an in vivo hyperthermia treatment of canine prostate.

Design and experiment of 256-element ultrasound phased array for noninvasive focused ultrasound surgery

A 256-element phased array high intensity focused ultrasound system has been designed and constructed in our laboratory. The 256-element spherical-section ultrasound phased array made from piezocomposite material operates at 1.1 MHz with 11-cm radius of curvature, 14-cm outer diameter, and 3.4-cm diameter central hole for mounting diagnostic ultrasound imaging probe. First, the explicit sound field calculation approach for the spherical-section phased array and the genetic optimal algorithm are briefly introduced as the optimal focus pattern control methods. Then, the design guidelines of 256-element spherical-section focused ultrasound phased array and 256-channel driver system are given. The results of single on and off axial focus, multiple on and off axial foci, half sub-array focus pattern provide further evidence for the 3D focus steering and sub-array mode for avoiding obstacles in focused ultrasound surgery. The multi-foci pattern can enlarge the treatment volume to 22 times larger than that of a single focus in one sonication. Finally, in vitro and transparent tissue-mimicking phantom experiment results confirm the ability of 256-element spherical-section phased array system to induce thermal lesions for noninvasive ultrasound surgery.

Noninvasive transesophageal cardiac thermal ablation using a 2-D focused, ultrasound phased array: a simulation study

This simulation study proposes a noninvasive, transesophageal cardiac-thermal ablation using a planar ultrasound phased array (1 MHz, 60 x 10 mm2, 0.525 mm interelement spacing, 114 x 20 elements). Thirty-nine foci in cardiac muscle were defined at 20, 40, and 60-mm distances and at various angles from the transducer surface to simulate the accessible posterior left atrial wall through the esophageal wall window. The ultrasound pressure distribution and the resulting thermal effect in a volume of 60 x 80 x 80 mm3, including esophagus and cardiac muscle, were simulated for each focus. For 1, 10, and 20-s sonications with 60 degrees C and 70 degrees C peak temperatures in cardiac muscle and without thermal damage in esophageal wall, the transducer acoustic powers were 105-727, 28-117, 21-79 W and 151-1044, 40-167, 30-114 W, respectively. The simulated lesions (thermal dose in equivalent minutes at 43 degrees C > or = 240 minutes) at these foci had lengths of 1-6, 3-11, 3-13 mm and 3-15, 5-19, 6-23 mm, respectively, and widths of 1-4, 2-7, 3-9 mm and 3-9, 4-13, 4-17 mm, respectively. As a first step toward feasibility, controllable tissue coagulation in cardiac tissue without damage to the esophagus was demonstrated numerically.

Design And Evaluation Of A 3 × 21 Element 1.75 Dimensional Tapered Ultrasound Phased Array For The Treatment Of Prostate Disease

This paper describes the design, construction, and evaluation of a 1.75 dimensional (1.75-D) tapered ultrasound phased array to be used in the treatment of benign prostatic hyperplasia and prostate...