1
|
Kim MG, Yu K, Niu X, He B. Investigation of displacement of intracranial electrode induced by focused ultrasound stimulation. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2021; 70:9600509. [PMID: 34819696 PMCID: PMC8608250 DOI: 10.1109/tim.2021.3125978] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Transcranial focused ultrasound (tFUS) is an emerging neuromodulation technique to modulate brain activity non-invasively with high spatial specificity and focality. Given the influence of tFUS on brain activity, combining tFUS with multi-channel intracranial electrophysiological recordings enables monitoring of the activity of large populations of neurons with high temporal resolution. However, the physical interactions between tFUS and the electrode may affect a reliable assessment of neuronal activity, which remains poorly understood. In this paper, high-frequency ultrasound (HFUS) system was developed and integrated into tFUS neuromodulation system. The performance of the HFUS-based displacement tracking and analysis was evaluated by the theoretical analysis in the literature. The effects of various pressure levels on the displacements of the silicon-based microelectrode array in ex vivo brain tissue were investigated. The developed approach was capable of tracking and measuring the motion of a solid sphere in a tissue-mimicking phantom and measured displacements were comparable to theoretical predictions. The significant changes in the averaged peak displacements of the microelectrode array in ex vivo brain were observed with a pulse duration of 200 μs and a peak-to-peak pressure from 131 kPa at a center frequency of 500 kHz compared with the values from the negative control group. The present results demonstrate the relationship between several pressure levels and displacements of the microelectrode array in ex vivo brain through the developed approach. This approach can be used to determine a vibration-free threshold of ultrasound parameters in multi-channel intracranial recordings for a reliable assessment of electrophysiological activities of living neurons.
Collapse
Affiliation(s)
- Min Gon Kim
- Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Kai Yu
- Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Xiaodan Niu
- Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Bin He
- Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| |
Collapse
|
2
|
Kim S, Moon S, Rho S, Yoon S. Measurements of acoustic radiation force of ultrahigh frequency ultrasonic transducers using model-based approach. APPLIED PHYSICS LETTERS 2021; 118:184102. [PMID: 33981116 PMCID: PMC8096457 DOI: 10.1063/5.0044512] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2021] [Accepted: 04/19/2021] [Indexed: 05/13/2023]
Abstract
Even though ultrahigh frequency ultrasonic transducers over 60 MHz have been used for single-cell-level manipulation such as intracellular delivery, acoustic tweezers, and stimulation to investigate cell phenotype and cell mechanics, no techniques have been available to measure the actual acoustic radiation force (ARF) applied to target cells. Therefore, we have developed an approach to measure the ARF of ultrahigh frequency ultrasonic transducers using a theoretical model of the dynamics of a solid sphere in a gelatin phantom. To estimate ARF at the focus of a 130 MHz transducer, we matched measured maximum displacements of a solid sphere with theoretical calculations. We selected appropriate ranges of input voltages and pulse durations for single-cell applications, and the estimated ARF was in the range of tens of μN. To gauge the influence of pulse duration, an impulse of different pulse durations was estimated. Fluorescence resonance energy transfer live cell imaging was demonstrated to visualize calcium transport between cells after a target single cell was stimulated by the developed ultrasonic transducer.
Collapse
Affiliation(s)
| | | | | | - Sangpil Yoon
- Author to whom correspondence should be addressed: . Tel.: +1-514-631‐6510
| |
Collapse
|
3
|
Jafarzadeh E, Amini MH, Sinclair AN. Determination of the Ultrasonic Non-linearity Parameter B/A versus Frequency for Water. ULTRASOUND IN MEDICINE & BIOLOGY 2021; 47:809-819. [PMID: 33353785 DOI: 10.1016/j.ultrasmedbio.2020.11.027] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2020] [Revised: 11/19/2020] [Accepted: 11/21/2020] [Indexed: 06/12/2023]
Abstract
For tissue characterization, it is desirable to determine B/A using high-frequency transducers. Moreover, an accurate estimate of B/A at elevated frequencies (or at least the assumption of frequency independence of B/A) is required to evaluate the safety of high-frequency systems. However, common finite-amplitude approaches become increasingly inaccurate at high frequencies. In this article, a practical variation of the finite-amplitude method is proposed which combines experiments with numerical simulations of the Khokhlov-Zabolotskaya-Kuznetsov equation and can be used at elevated frequencies. The results at low frequencies show that the proposed approach is accurate with lower uncertainties compared with the finite-amplitude method because it avoids assumptions and approximations. The measured values of B/A versus frequency for water at 2.25-20 MHz show that there is no statistically significant variation in B/A values with frequency, and therefore the assumption of frequency independence of B/A is realistic.
Collapse
Affiliation(s)
- Ehsan Jafarzadeh
- Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada.
| | | | - Anthony N Sinclair
- Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada
| |
Collapse
|
4
|
Rajagopal S, Cox BT. 100 MHz bandwidth planar laser-generated ultrasound source for hydrophone calibration. ULTRASONICS 2020; 108:106218. [PMID: 32721650 DOI: 10.1016/j.ultras.2020.106218] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Revised: 05/25/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
High-frequency calibration of hydrophones is becoming increasingly important, both for clinical and scientific applications of ultrasound, and user safety. At present, the calibrations available routinely to the user community extend to 60 MHz. However, hydrophones that can measure beyond this are available, and ultrasonic fields often contain energy at higher frequencies, e.g., generated through nonlinear propagation of high-amplitude ultrasound used for therapeutic applications, and the increasing use of higher frequencies in imaging. Therefore, there is a need for calibrations up to at least 100 MHz, to allow ultrasonic fields to be accurately characterized, and the risk of harmful bioeffects to be properly assessed. Currently, sets of focused piezoelectric transducers are used to meet the pressure amplitude and bandwidth requirements of Primary Standard calibration facilities. However, when the frequency is high enough such that the size of the ultrasound focus becomes less than the hydrophone element's diameter, the uncertainty due to spatial averaging becomes significant, and can be as high as 20% at 100 MHz. As an alternate to piezoelectric transducers, a laser-generated ultrasound calibration source was designed, fabricated, and characterized. The source consists of an optically absorbing carbon-polymer nanocomposite excited by a large-diameter 1064 nm laser pulse of 2.6 ns duration. Peak pressure amplitudes of several Mega-Pascal were readily achievable, and the signal contained measurable frequency components up to 100 MHz. The variation in the pressure amplitudes was less than 2% from its mean over a three-hour test period. The ultrasound beam was sufficiently broad that the uncertainties due to spatial averaging were negligible.
Collapse
Affiliation(s)
- Srinath Rajagopal
- Ultrasound and Underwater Acoustics Group, National Physical Laboratory, Hampton Road, Teddington TW11 0LW, UK.
| | - Ben T Cox
- Department of Medical Physics and Biomedical Engineering, University College London, Malet Place Engineering Building, Gower Street, London WC1E 6BT, UK
| |
Collapse
|
5
|
Jafarzadeh E, Sinclair AN. Non-linear Wave Propagation and Safety Standards for Diagnostic Ultrasound Devices. ULTRASOUND IN MEDICINE & BIOLOGY 2019; 45:11-20. [PMID: 30292462 DOI: 10.1016/j.ultrasmedbio.2018.08.021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2018] [Revised: 08/23/2018] [Accepted: 08/28/2018] [Indexed: 06/08/2023]
Abstract
Safety standards for clinical diagnostic ultrasonic devices were developed for use in relatively low-frequency systems (1-10 MHz), under the assumption that non-linear effects would be negligible. This article reviews ways in which neglecting non-linear wave propagation affects the measurements and calculations required to comply with safety standards and U.S. Food and Drug Administration guidance that recognizes these standards. An attempt is made to evaluate whether ignoring non-linear effects could result in significant error in the exposure quantities defined in these standards at either low or high frequencies, based on published literature. This article maintains that although non-linear effects have been considered in some parts of safety standards related to hydrophone requirements, the coverage is inadequate, especially for modern equipment with high working frequencies. A new approach is required to assess the magnitude of thermal heating for recently developed high-frequency systems to incorporate non-linear effects. In contrast, the current approach for evaluating the risk of cavitation can be used after appropriate modifications.
Collapse
Affiliation(s)
- Ehsan Jafarzadeh
- Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada.
| | - Anthony N Sinclair
- Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada
| |
Collapse
|
6
|
Roberts PR, Jani AB, Packianathan S, Albert A, Bhandari R, Vijayakumar S. Upcoming imaging concepts and their impact on treatment planning and treatment response in radiation oncology. Radiat Oncol 2018; 13:146. [PMID: 30103786 PMCID: PMC6088418 DOI: 10.1186/s13014-018-1091-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2018] [Accepted: 07/31/2018] [Indexed: 12/14/2022] Open
Abstract
For 2018, the American Cancer Society estimated that there would be approximately 1.7 million new diagnoses of cancer and about 609,640 cancer-related deaths in the United States. By 2030 these numbers are anticipated to exceed a staggering 21 million annual diagnoses and 13 million cancer-related deaths. The three primary therapeutic modalities for cancer treatments are surgery, chemotherapy, and radiation therapy. Individually or in combination, these treatment modalities have provided and continue to provide curative and palliative care to the myriad victims of cancer. Today, CT-based treatment planning is the primary means through which conventional photon radiation therapy is planned. Although CT remains the primary treatment planning modality, the field of radiation oncology is moving beyond the sole use of CT scans to define treatment targets and organs at risk. Complementary tissue scans, such as magnetic resonance imaging (MRI) and positron electron emission (PET) scans, have all improved a physician’s ability to more specifically identify target tissues, and in some cases, international guidelines have even been issued. Moreover, efforts to combine PET and MR to define solid tumors for radiotherapy planning and treatment evaluation are also gaining traction. Keeping these advances in mind, we present brief overviews of other up-and-coming key imaging concepts that appear promising for initial treatment target definition or treatment response from radiation therapy.
Collapse
Affiliation(s)
- Paul Russell Roberts
- Department of Radiation Oncology, University of Mississippi Medical Center, 350 Woodrow Wilson Drive Suite 1600, Jackson, MS, 39213, USA
| | - Ashesh B Jani
- Department of Radiation Oncology, Winship Cancer Institute of Emory University, 1365 Clifton Rd, Atlanta, GA, 30322, USA
| | - Satyaseelan Packianathan
- Department of Radiation Oncology, University of Mississippi Medical Center, 350 Woodrow Wilson Drive Suite 1600, Jackson, MS, 39213, USA
| | - Ashley Albert
- Department of Radiation Oncology, University of Mississippi Medical Center, 350 Woodrow Wilson Drive Suite 1600, Jackson, MS, 39213, USA
| | - Rahul Bhandari
- Department of Radiation Oncology, University of Mississippi Medical Center, 350 Woodrow Wilson Drive Suite 1600, Jackson, MS, 39213, USA
| | - Srinivasan Vijayakumar
- Department of Radiation Oncology, University of Mississippi Medical Center, 350 Woodrow Wilson Drive Suite 1600, Jackson, MS, 39213, USA.
| |
Collapse
|
7
|
Kothapalli SVVN, Partanen A, Zhu L, Altman MB, Gach HM, Hallahan DE, Chen H. A convenient, reliable, and fast acoustic pressure field measurement method for magnetic resonance-guided high-intensity focused ultrasound systems with phased array transducers. J Ther Ultrasound 2018; 6:5. [PMID: 29988649 PMCID: PMC6027582 DOI: 10.1186/s40349-018-0113-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2018] [Accepted: 06/13/2018] [Indexed: 01/11/2023] Open
Abstract
BACKGROUND With the expanding applications of magnetic resonance-guided high-intensity focused ultrasound (MR-HIFU), there is an urgent need for a convenient, reliable, and fast acoustic pressure field measurement method to aid treatment protocol design, ensure consistent and safe operation of the transducer, and facilitate regulatory approval of new techniques. Herein, we report a method for acoustic pressure field characterization of MR-HIFU systems with multi-element phased array transducers. This method integrates fiber-optic hydrophone measurements and electronic steering of the ultrasound beam with MRI-assisted HIFU focus alignment to the fiber tip. METHODS A clinical MR-HIFU system (Sonalleve V2, Profound Medical Inc., Mississauga, Canada) was used to assess the proposed method. A fiber-optic hydrophone was submerged in a degassed water bath, and the fiber tip location was traced using MRI. Subsequently, the nominal transducer focal point indicated on the MR-HIFU therapy planning software was positioned at the fiber tip, and the HIFU focus was electronically steered around the fiber tip within a 3D volume for 3D pressure field mapping, eliminating the need for an additional, expensive, and MRI-compatible 3D positioning stage. The peak positive and negative pressures were measured at the focus and validated using a standard hydrophone measurement setup outside the MRI magnet room. RESULTS We found that the initial MRI-assisted HIFU focus alignment had an average offset of 2.23 ± 1.33 mm from the fiber tip as identified by the 3D pressure field mapping. MRI guidance and electronic beam steering allowed 3D focus localization within ~ 1 h, i.e., faster than the typical time required using the standard laboratory setup (~ 3-4 h). Acoustic pressures measured using the proposed method were not significantly different from those obtained with the standard laboratory hydrophone measurements. CONCLUSIONS In conclusion, our method offers a convenient, reliable, and fast acoustic pressure field characterization tool for MR-HIFU systems with phased array transducers.
Collapse
Affiliation(s)
| | | | - Lifei Zhu
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO USA
| | - Michael B. Altman
- Department of Radiation Oncology, Washington University School of Medicine, St. Louis, MO USA
| | - H. Michael Gach
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO USA
- Department of Radiation Oncology, Washington University School of Medicine, St. Louis, MO USA
- Mallinckrodt Institute of Radiology, Washington University School of Medicine, St. Louis, MO USA
| | - Dennis E. Hallahan
- Department of Radiation Oncology, Washington University School of Medicine, St. Louis, MO USA
| | - Hong Chen
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO USA
- Department of Radiation Oncology, Washington University School of Medicine, St. Louis, MO USA
| |
Collapse
|
8
|
Kim MG, Yoon S, Chiu CT, Shung KK. Investigation of Optimized Treatment Conditions for Acoustic-Transfection Technique for Intracellular Delivery of Macromolecules. ULTRASOUND IN MEDICINE & BIOLOGY 2018; 44:622-634. [PMID: 29284555 PMCID: PMC5800999 DOI: 10.1016/j.ultrasmedbio.2017.11.005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2016] [Revised: 11/09/2017] [Accepted: 11/13/2017] [Indexed: 05/03/2023]
Abstract
Manipulation of cellular functions and structures by introduction of genetic materials inside cells has been one of the most prominent research areas in biomedicine. High-frequency ultrasound acoustic-transfection has recently been developed and confirmed by intracellular delivery of small molecules into HeLa cells at the single-cell level with high cell viability. After we proved the concept underlying the acoustic-transfection technique, treatment conditions for different human cancer cell lines have been intensively investigated to further develop acoustic-transfection as a versatile and adaptable transfection method by satisfying the requirements of high-delivery efficiency and cell membrane permeability with minimal membrane disruption. To determine optimal treatment conditions for different cell lines, we developed a quantitative intracellular delivery score based on delivery efficiency, cell membrane permeability and cell viability after 4 and 20 h of treatment. The intracellular delivery of macromolecules and the simultaneous intracellular delivery of two molecules under optimal treatment conditions were successfully achieved. We found that DNA plasmid was delivered by acoustic-transfection technique into epiblast stem cells, which expressed transient mCherry fluorescence.
Collapse
Affiliation(s)
- Min Gon Kim
- Department of Biomedical Engineering, University of Southern California, Los Angeles, California, USA
| | - Sangpil Yoon
- Department of Biomedical Engineering, University of Southern California, Los Angeles, California, USA.
| | - Chi Tat Chiu
- Department of Biomedical Engineering, University of Southern California, Los Angeles, California, USA
| | - K Kirk Shung
- Department of Biomedical Engineering, University of Southern California, Los Angeles, California, USA
| |
Collapse
|
9
|
Kothapalli SVVN, Altman MB, Partanen A, Wan L, Gach HM, Straube W, Hallahan DE, Chen H. Acoustic field characterization of a clinical magnetic resonance-guided high-intensity focused ultrasound system inside the magnet bore. Med Phys 2017. [PMID: 28626862 DOI: 10.1002/mp.12412] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
PURPOSE With the expanding clinical application of magnetic resonance-guided high-intensity focused ultrasound (MR-HIFU), acoustic field characterization of MR-HIFU systems is needed for facilitating regulatory approval and ensuring consistent and safe power output of HIFU transducers. However, the established acoustic field measurement techniques typically use equipment that cannot be used in a magnetic resonance imaging (MRI) suite, thus posing a challenge to the development and execution of HIFU acoustic field characterization techniques. In this study, we developed and characterized a technique for HIFU acoustic field calibration within the MRI magnet bore, and validated the technique with standard hydrophone measurements outside of the MRI suite. METHODS A clinical Philips MR-HIFU system (Sonalleve V2, Philips, Vantaa, Finland) was used to assess the proposed technique. A fiber-optic hydrophone with a long fiber was inserted through a 24-gauge angiocatheter and fixed inside a water tank that was placed on the HIFU patient table above the acoustic window. The long fiber allowed the hydrophone control unit to be placed outside of the magnet room. The location of the fiber tip was traced on MR images, and the HIFU focal point was positioned at the fiber tip using the MR-HIFU therapy planning software. To perform acoustic field mapping inside the magnet, the HIFU focus was positioned relative to the fiber tip using an MRI-compatible 5-axis robotic transducer positioning system embedded in the HIFU patient table. To perform validation measurements of the acoustic fields, the HIFU table was moved out of the MRI suite, and a standard laboratory hydrophone measurement setup was used to perform acoustic field measurements outside the magnetic field. RESULTS The pressure field scans along and across the acoustic beam path obtained inside the MRI bore were in good agreement with those obtained outside of the MRI suite. At the HIFU focus with varying nominal acoustic powers of 10-500 W, the peak positive pressure and peak negative pressure measured inside the magnet bore were 3.87-68.67 MPa and 3.56-12.06 MPa, respectively, while outside the MRI suite the corresponding pressures were 3.27-67.32 MPa and 3.06-12.39 MPa, respectively. There was no statistically significant difference (P > 0.05) between measurements inside the magnet bore and outside the MRI suite for the p+ and p- at any acoustic power level. The spatial-peak pulse-average intensities (ISPPA ) for these powers were 312-17816 W/cm2 and 220-15698 W/cm2 for measurements inside and outside the magnet room, respectively. In addition, when the scanning step size of the HIFU focus was increased from 100 μm to 500 μm, the execution time for scanning a 4 × 4 mm2 area decreased from 210 min to 10 min, the peak positive pressure decreased by 14%, the peak negative pressure decreased by 5%, and the lateral full width at half maximum dimension of pressure profiles increased from 1.15 mm to 1.55 mm. CONCLUSIONS The proposed hydrophone measurement technique offers a convenient and reliable method for characterizing the acoustic fields of clinical MR-HIFU systems inside the magnet bore. The technique was validated for use by measurements outside the MRI suite using a standard hydrophone calibration technique. This technique can be a useful tool in MR-HIFU quality assurance and acoustic field assessment.
Collapse
Affiliation(s)
- Satya V V N Kothapalli
- Department of Biomedical Engineering, Washington University in St. Louis, Saint Louis, MO, 63130, USA
| | - Michael B Altman
- Department of Radiation Oncology, Washington University in St. Louis, Saint Louis, MO, 63108, USA
| | - Ari Partanen
- Clinical Science MR Therapy, Philips, Andover, MA, 01810, USA
| | - Leighton Wan
- Department of Biomedical Engineering, Washington University in St. Louis, Saint Louis, MO, 63130, USA
| | - H Michael Gach
- Departments of Radiation Oncology and Radiology, Washington University in St. Louis, Saint Louis, MO, 63108, USA
| | - William Straube
- Department of Radiation Oncology, Washington University in St. Louis, Saint Louis, MO, 63108, USA
| | - Dennis E Hallahan
- Department of Radiation Oncology, Washington University in St. Louis, Saint Louis, MO, 63108, USA
| | - Hong Chen
- Departments of Biomedical Engineering and Radiation Oncology, Washington University in St. Louis, Saint Louis, MO, 63130, USA
| |
Collapse
|
10
|
Xing G, Yang P, He L, Feng X. Spatial averaging effects of hydrophone on field characterization of planar transducer using Fresnel approximation. ULTRASONICS 2016; 71:51-58. [PMID: 27268164 DOI: 10.1016/j.ultras.2016.05.022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2016] [Revised: 05/25/2016] [Accepted: 05/26/2016] [Indexed: 06/06/2023]
Abstract
The purpose of this work was to improve the existing models that allow spatial averaging effects of piezoelectric hydrophones to be accounted for. The model derived in the present study is valid for a planar source and was verified using transducers operating at 5 and 20MHz. It is based on Fresnel approximation and enables corrections for both on-axis and off-axis measurements. A single-integral approximate formula for the axial acoustic pressure was derived, and the validity of the Fresnel approximation in the near field of the planar transducer was examined. The numerical results obtained using 5 and 20MHz planar transmitters with an effective diameter of 12.7mm showed that the derived model could account for spatial averaging effects to within 0.2% with Beissner's exact integral (Beissner, 1981), for k(a+b)2≫π (where k is the circular wavenumber, and a and b are the effective radii of the transmitter and hydrophone, respectively). The field distributions along the acoustic axis and the beam directivity patterns are also included in the model. The spatial averaging effects of the hydrophone were generally observed to cause underestimation of the absolute pressure amplitudes of the acoustic beam, and overestimation of the cross-sectional size of the beam directivity pattern. However, the cross-sectional size of the directivity pattern was also found to be underestimated in the "far zone" (beyond Y0=a(2)/λ) of the transmitter. The results of this study indicate that the spatial averaging effect on the beam directivity pattern is negligible for π(γ(2)+4γ)s≪1 (where γ=b/a, and s is the normalized distance to the planar transducer).
Collapse
Affiliation(s)
- Guangzhen Xing
- Institute of Ultra-precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China; Division of Mechanics and Acoustics, National Institute of Metrology, Beijing 100029, China.
| | - Ping Yang
- Division of Mechanics and Acoustics, National Institute of Metrology, Beijing 100029, China
| | - Longbiao He
- Division of Mechanics and Acoustics, National Institute of Metrology, Beijing 100029, China
| | - Xiujuan Feng
- Division of Mechanics and Acoustics, National Institute of Metrology, Beijing 100029, China
| |
Collapse
|