Large Transducer Research Articles

In vivo Multi-perspective 3D + t Ultrasound Imaging and Motion Estimation of Abdominal Aortic Aneurysms.

Time-resolved three-dimensional ultrasound (3D + t US) is a promising imaging modality for monitoring abdominal aortic aneurysms (AAAs), providing their 3D geometry and motion. The lateral contrast of US is poor, a well-documented drawback which multi-perspective (MP) imaging could resolve. This study aims to show the feasibility of in vivo multi-perspective 3D + t ultrasound imaging of AAAs for improving the image contrast and displacement accuracy. To achieve this, single-perspective (SP) aortic ultrasound images from three different angles were spatiotemporally registered and fused, and the displacements were compounded. The fused MP had a significantly higher wall-lumen contrast than the SP images, for both patients and volunteers (P < .001). MP radial displacements patterns are smoother than SP patterns in 67% of volunteers and 92% of patients. The MP images from three angles have a decreased tracking error (P < .001 for all participants), and an improved SNRe compared to two out of three SP images (P < .05). This study has shown the added value of MP 3D + t US, improving both image contrast and displacement accuracy in AAA imaging. This is a step toward using multiple or large transducers in the clinic to capture the 3D geometry and strain more accurately, for patient-specific characterization of AAAs.

Ultrasonic imaging assisted by Phase Coherence and Synthetic Aperture Focusing Technology

Abstract B-Scan is widely applied in ultrasonic testing. However, the imaging quality is affected by noise and acoustic diffusion. This paper proposed a method combining synthetic aperture focusing technology (SAFT) and phase-coherent imaging (PCI) technology to improve image quality. In SAFT, a transducer at different positions is utilized to form an array, which represents a large aperture transducer to obtain high resolution. By constructing a weight matrix based on the phase of signals, PCI is used to modify the SAFT imaging, thus the signal-to-noise ratio is significantly improved. In this paper, finite element models were built and the corresponding simulations were carried out first. Then, the Hilbert transform was implemented to all the simulated echoes with artificial white noise. The amplitudes and phases were extracted, whilst the amplitudes were used to construct SAFT images. The phases were used to construct a coherent weight matrix. Finally, images of SAFT modified by phase-coherent matrix were reconstructed and compared with SAFT images and B-scan. It verifies that the SAFT-PCI method can improve the image effectively.

A Giant Magneto-Superelasticity of 5% Enabled by Introducing Ordered Dislocations in Ni34Co8Cu8Mn36Ga14 Single Crystal.

Elasticity, featured by a recoverable strain, refers to the ability that materials can return to their original shapes after deformation. Typically, the elastic strains of most metals are well-known 0.2%. In shape memory alloys and high entropy alloys, the elastic strains can be several percent, as called superelasticity, which are all triggered by external stresses. A superelasticity induced by magnetic field, termed as magneto-superelasticity, is extremely important for contactless work of materials and for developing brand-new large stroke actuators and high efficiency energy transducers. In magnetic shape memory alloys, the twin boundary motion driven by magnetic field can output a strain of several percent. However, this strain is unrecoverable when removing the magnetic field and hence it is not magneto-superelasticity. Here, a giant magneto-superelasticity of 5% in a Ni34Co8Cu8Mn36Ga14 single crystal is reported by introducing arrays of ordered dislocations to form preferentially oriented martensitic variants during the magnetically induced reverse martensitic transformation. This work provides an opportunity to achieve high performance in functional materials by defect engineering.

Volumetric beamforming in real-time using commodity hardware

Ultrasound imaging is widely used in medicine for its safety and affordability. However, it demands large transducer arrays because the image resolution is proportional to the number of elements, N, typically around 128 for 2D imaging. Three-dimensional imaging requires N2 audio channels (≈350 GB/s of data) if the equivalent 2D matrix array is used, which is practically impossible to process. To solve this issue, row-column arrays (RCAs) aggregate rows and columns of elements, reducing data rate and processing demands by a factor of N. A novel dual-stage beamforming algorithm further lowers the beamforming operations by N/2, with negligible impact on the image quality. For N = 128, the processing is 8192 times faster than with a matrix array, and it is hypothesized the 3D RCA beamforming can be done in real-time using a commodity graphics card. The beamforming rate of an NVIDIA RTX 4090 GPU was measured for in-vivo data from a rat kidney, achieving 1394 full volumes per second, which is over 150 times faster than previous implementations. Combining RCAs with the new beamforming algorithm and GPU processing thus enables volumetric beamforming to be done affordably at the bedside in real-time using a standard scanner and PC.

Real-Time Intraoperative Ultrasound Using a Minimally Invasive Transducer During Anterior Cervical Spine Surgery.

Intraoperative ultrasound (IOUS) during anterior cervical surgery is hindered by large transducer size and small operative corridor. We hypothesized that a linear (minimally invasive) transducer designed for transsphenoidal surgery can visualize the spinal cord, nerve roots, and surrounding structures during anterior cervical approaches, facilitating intraoperative assessment of central and foraminal decompression. IOUS was used to evaluate 26 levels in 17 patients (15 anterior cervical discectomy and fusion, 1 corpectomy, 1 arthroplasty) with a linear probe (7 × 6-mm end-fire transducer, 150-mm length, 12-15 MHz). After pin-based distraction, discectomy, and posterior longitudinal ligament resection, IOUS assessed adequacy of cord decompression and, following proximal foraminotomy or uncinectomy, nerve root decompression. If indicated, additional decompression was completed. Criteria for adequate central and foraminal decompression were visualization of subarachnoid space around the cord and cerebrospinal fluid pulsatility along the root sleeve/absence of nerve root compression distal to the root sleeve, respectively. IOUS successfully visualized the cord, nerve roots, and surrounding structures in all 26 levels and influenced management in 11 levels (42.3%). IOUS indicated persistent cord and nerve root compression in 2 and 7 levels, respectively. Planned uncinectomy was aborted in 2 levels after IOUS demonstrated adequate nerve root decompression with intervertebral distraction/proximal foraminotomy alone. IOUS identified persistent nerve root compression after initial proximal foraminotomy in 4 levels and uncinectomy in 2 levels. An unplanned uncinectomy was performed in 1 level after IOUS showed persistent nerve root compression after multiple iterations of proximal foraminotomy. At follow-up (mean 3.1 months), the mean improvement in Numeric Rating Scale neck and arm pain, Neck Disability Index, and modified Japanese Orthopedic Association was 4.0%, 3.2%, 3.7%, and 0.7%, respectively. The neural elements and their relationships to surrounding bone/soft tissue can be visualized using a minimally invasive IOUS transducer during anterior cervical surgery without having to remove pin-based distraction. This allows surgeons to intraoperatively verify the extent of central and foraminal decompression.

Ultrasound-Guided Mechanical High-Intensity Focused Ultrasound (Histotripsy) Through an Acoustically Permeable Polyolefin-Based Cranioplasty Device.

Recently, a biocompatible, polyolefin-based cranioplasty device was developed to allow ultrasound (US) transmission into the intracranial space with minimal distortion. In this study, we investigated the in vitro feasibility of applying US-guided histotripsy procedures across the prosthesis. Pressure waveforms and beam profiles were collected for single- and multi-element histotripsy transducers. Then, high-speed optical images of the bubble cloud with and without the prosthesis were collected in water and tissue-mimicking agarose gel phantoms. Finally, red blood cell (RBC) tissue phantom and excised brain tissue experiments were completed to test the ablative efficacy across the prosthesis. Single element tests revealed increased pressure loss with increasing transducer frequency and increasing transducer-to-prosthesis angle. Array transducer measurements at 1 MHz showed average pressure losses of >50% across the prosthesis. Aberration correction recovered up to 18% of the pressure lost, and high-speed optical imaging in water, agarose gels, and RBC phantoms demonstrated that histotripsy bubble clouds could be generated across the prosthesis at pulse repetition frequencies of 50-500 Hz. Histologic analysis revealed a complete breakdown of brain tissue treated across the prosthesis. Conclusion & Significance: Overall, the results of this study demonstrate that the cranial prosthesis may be used as an acoustic window through which intracranial histotripsy can be applied under US guidance without the need for large transcranial array transducers.

Demonstration of medical imaging using flexible polymer ultrasound technology

We present a novel ultrasound transducer technology based on piezo polymers. Its fabrication process (PillarWaveTM), based on creating hexagonal micro-structured PVDF-TrFE pillars. This makes it fully flexible and allows scaling to large apertures (&amp;gt;15 × 15 cm2). Large area flexible transducers enable to select relevant field of view in automated post-processing. This can alleviate the need for a skilled sonographer and enable applications of echography outside clinics. To demonstrate its performance, a 128 element 8 MHz linear array is designed and manufactured. Its total thickness is 0.1 mm. Its acoustic characteristics are determined demonstrating 5.2 kPa/V transmit efficiency and 150 mV/Pa sensitivity. The receive bandwidth at -6dB is larger than 100%. A peak pressure in excess of 1 MPa at 4 cm from the array is measured in water. The transducer array is connected to a Verasonics Vantage research medical ultrasound system. The imaging performance of the array is demonstrated experimentally. Real-time imaging of an in vitro- medical phantom using plane wave compounding and delay-and-sum beamforming is demonstrated at 15 frames per second, with point spread functions at -20 dB of 1.3 and 0.92 mm in the lateral and depth directions, respectively. Finally, imaging of a human carotid in vivo is demonstrated.

Fast volumetric ultrasound facilitates high-resolution 3D mapping of tissue compartments.

Volumetric ultrasound imaging has the potential for operator-independent acquisition and enhanced field of view. Panoramic acquisition has many applications across ultrasound; spanning musculoskeletal, liver, breast, and pediatric imaging; and image-guided therapy. Challenges in high-resolution human imaging, such as subtle motion and the presence of bone or gas, have limited such acquisition. These issues can be addressed with a large transducer aperture and fast acquisition and processing. Programmable, ultrafast ultrasound scanners with a high channel count provide an unprecedented opportunity to optimize volumetric acquisition. In this work, we implement nonlinear processing and develop distributed beamformation to achieve fast acquisition over a 47-centimeter aperture. As a result, we achieve a 50-micrometer -6-decibel point spread function at 5 megahertz and resolve in-plane targets. A large volume scan of a human limb is completed in a few seconds, and in a 2-millimeter dorsal vein, the image intensity difference between the vessel center and surrounding tissue was ~50 decibels, facilitating three-dimensional reconstruction of the vasculature.

Ultrasonic needle hydrophone calibration in air by a parabolic off-axis mirror focused beam using three-transducer reciprocity

An acoustic field distribution investigation in air requires a small receiving sensor. Needle hydrophones seem to be an attractive solution, and it has previously been demonstrated that needle hydrophones designed for use in water can be used in air. The metrology problem is that an absolute sensitivity calibration is needed, because needle hydrophones are not characterized in air, especially for frequencies below 1 MHz, which is of interest for air-coupled ultrasound. Conventional, three-transducer/microphone reciprocity calibration requires measurements to be done in the far field. However, when transducer diameter is large and the frequency is high, the required measurement distance becomes very large: 3 m for a 20 mm source, transmitting at 1 MHz. Large propagation distance leads to high attenuation and nonlinear effects in air propagation, and distortion and losses accumulate. Small needle hydrophones have low sensitivity, so that high excitation amplitudes would be required, which can lead to transducer heating and increase nonlinearity effects. A derivative of the three-transducer reciprocity calibration method is proposed, where a large aperture transducer is focused onto a hydrophone, using hybrid of plane wave and spherical wave reciprocity. Use of a focused source minimizes the frequency-dependent diffraction effects, and the spherical wave approximation is valid at the focal distance, and low level excitation signals can be used. Focusing is accomplished using a parabolic off-axis mirror. Calibration is in transmission, which reduces the complexity of the electrical measurements. The corresponding equations have been derived for this setup. Calibration of the transducer and needle hydrophone absolute sensitivity is obtained.

Transcranial 3D ultrasound localization microscopy using a large element matrix array with a multi-lens diffracting layer: an in vitro study

Objective. Early diagnosis and acute knowledge of cerebral disease require to map the microflows of the whole brain. Recently, ultrasound localization microscopy (ULM) was applied to map and quantify blood microflows in 2D in the brain of adult patients down to the micron scale. Whole brain 3D clinical ULM remains challenging due to the transcranial energy loss which reduces significantly the imaging sensitivity. Approach. Large aperture probes with a large surface can increase both the field of view and sensitivity. However, a large active surface implies thousands of acoustic elements, which limits clinical translation. In a previous simulation study, we developed a new probe concept combining a limited number of elements and a large aperture. It is based on large elements, to increase sensitivity, and a multi-lens diffracting layer to improve the focusing quality. In this study, a 16 elements prototype, driven at 1 MHz frequency, was made and in vitro experiments were performed to validate the imaging capabilities of this new probe concept. Main results. First, pressure fields emitted from a large single transducer element without and with diverging lens were compared. Low directivity was measured for the large element with the diverging lens while maintaining high transmit pressure. The focusing quality of 4 × 3cm matrix arrays of 16 elements without/with lenses were compared. In vitro experiments in a water tank and through a human skull were achieved to localize and track microbubbles in tubes. Significance. ULM was achieved demonstrating the strong potential of multi-lens diffracting layer to enable microcirculation assessment over a large field of view through the bones.

Development of a 16-Channel Broadband Piezoelectric Micro Ultrasonic Transducer Array Probe for Pipeline Butt-Welded Defect Detection.

Butt welding is extensively applied in long-distance oil and gas pipelines, and it is of great significance to conduct non-destructive ultrasonic testing of girth welds in order to avoid leakage and safety accidents during pipeline production and operation. In view of the limitations of large transducer size, single fixed beam angle, low detection resolution and high cost of conventional ultrasonic inspection technologies, a 16-channel piezoelectric micro ultrasonic transducer (PMUT) array probe was developed through theoretical analysis and structural optimization design. After the probe impedance characterization, the experimental results show that the theoretical model can effectively guide the design of the ultrasonic transducer array, offering the maximum operating frequency deviation of less than 5%. The ultrasonic echo performance tests indicate that the average −6 dB bandwidth of the PMUT array probe can be up to 77.9%. In addition, the fabricated PMUT array probe has been used to successfully detect five common internal defects in pipeline girth welds. Due to the multiple micro array elements, flexible handling of each element, large bandwidth and high resolution of defect detection, the designed PMUT array probe can provide a good application potential in structural health monitoring and medical ultrasound imaging fields.

Shock Wave Characterization Using Different Diameters of an Optoacoustic Carbon Nanotube Composite Transducer

Carbon nanotube–polymethyl siloxane (CNT-PDMS) composite transducers generate shock waves using optoacoustic technology. A thin layer of thermally conductive CNT and elastomeric polymer, PDMS, is applied on the concave surface of transparent polymethylmethacrylate (PMMA) to convert laser energy to acoustic energy using the thermoelastic effect of the composite transducer. The efficient conversion of laser energy requires an optimum utilization of the different properties of composite transducers. Among these properties, the diameter of composite transducers is a significant parameter. To practically verify and understand the effect of the diameter of composite transducers on the properties of shock waves, CNT-PDMS composite transducers with different diameters and focal lengths were constructed. Increases in the diameter of the composite transducer and input laser energy resulted in increased peak pressures of the shock waves. The maximum positive and negative pressures of the shock waves generated were 53 MPa and −25 MPa, respectively. This practically demonstrates that high peak amplitudes of shock waves can be achieved using larger transducers, which are suitable for practical applications in transcranial studies.

Effects of phase aberration on transabdominal focusing for a large aperture, low f-number histotripsy transducer

Objective. Soft tissue phase aberration may be particularly severe for histotripsy due to large aperture and low f-number transducer geometries. This study investigated how phase aberration from human abdominal tissue affects focusing of a large, strongly curved histotripsy transducer. Approach. A computational model (k-Wave) was experimentally validated with ex vivo porcine abdominal tissue and used to simulate focusing a histotripsy transducer (radius: 14.2 cm, f-number: 0.62, central frequency f c: 750 kHz) through the human abdomen. Abdominal computed tomography images from 10 human subjects were segmented to create three-dimensional acoustic property maps. Simulations were performed focusing at 3 target locations in the liver of each subject with ideal phase correction, without phase correction, and after separately matching the sound speed of water and fat to non-fat soft tissue. Main results. Experimental validation in porcine abdominal tissue showed that simulated and measured arrival time differences agreed well (average error, ∼0.10 acoustic cycles at f c). In simulations with human tissue, aberration created arrival time differences of 0.65 μs (∼0.5 cycles) at the target and shifted the focus from the target by 6.8 mm (6.4 mm pre-focally along depth direction), on average. Ideal phase correction increased maximum pressure amplitude by 95%, on average. Matching the sound speed of water and fat to non-fat soft tissue decreased the average pre-focal shift by 3.6 and 0.5 mm and increased pressure amplitude by 2% and 69%, respectively. Significance. Soft tissue phase aberration of large aperture, low f-number histotripsy transducers is substantial despite low therapeutic frequencies. Phase correction could potentially recover substantial pressure amplitude for transabdominal histotripsy. Additionally, different heterogeneity sources distinctly affect focusing quality. The water path strongly affects the focal shift, while irregular tissue boundaries (e.g. fat) dominate pressure loss.

Influence of different ultrasonic transducers on the precision of fastening force measurement

In the assembly process of aero-engines, the accurate measurement of bolt fastening force is particularly important, which is related to the normal operation of the entire system. Ultrasonic non-destructive testing has been applied to bolt fastening force measurement and has a broad application background. The core device of the ultrasonic transducer is a piezoelectric ceramic wafer, and the normal operation of the wafer is affected by the power frequency and external stress. For the same type of bolt with the same nominal diameter, the ultrasonic transducer wafers of different diameters will cause the transducer wafers to be subjected to different external stresses. According to the acoustoelastic effect, the relationship between the variation of time of flight (TOF) and bolt fastening force of different types of ultrasonic transducers is established. Then the measurement errors of various models are calculated and analyzed. The experimental results show that when the nominal diameter of the bolt is close to the diameter of the wafer of the ultrasonic transducer, the fastening force measurement accuracy of the bolt is the highest. When small or large size transducer is used, the measurement accuracy will be reduced due to energy and external stress. When a transducer with a higher center frequency is used to measure the fastening force of the bolt rod, the accuracy of the model established due to the faster attenuation of the sound wave is reduced, and the accuracy of the measurement result is reduced. Therefore, in order to ensure the accuracy of the fastening force measurement in the aerospace field, when selecting an ultrasonic transducer, the impact of the transducer size and center frequency should be fully considered.

Improving image quality in transcranial magnetic resonance guided focused ultrasound using a conductive screen

Transcranial Magnetic Resonance guided Focused Ultrasound (TcMRgFUS) has been proven to be an effective treatment for some neurological disorders such as essential and Parkinson's tremor. However, magnetic resonance guidance at 3 Tesla (3T) frequencies and using the large hemispherical transducers required for TcMRgFUS results in artifactual low-signal bands that pass through key regions of the brain. The purpose of this work was to investigate the use of a circular conductive Radio Frequency (RF) screen, that is bent to have a 12 cm radius in one direction and positioned near the top or back of the head, to reduce or remove these artifactual low-signal bands in TcMRgFUS.The impact of using an RF screen to remove these low signal bands was studied in both imaging experiments and electromagnetic simulations. Hydrophone measurements of the acoustic transparency of the bronze 2 mm diameter square mesh screen used in the imaging studies were compared with temperature measurements with and without the screen in heating studies in the TcMRgFUS system.The imaging and simulation studies both show that for the different screen configurations studied in this work, RF screen removes the low-signal bands and increases both homogeneity and signal-to-noise ratio (SNR) throughout the region of the brain. Hydrophone and heating studies indicate that even a 2 mm wire mesh provides minimal attenuation to the ultrasound beam. Simulation results also suggest that a 1 cm mesh will provide adequate artifact suppression with even less ultrasound attenuation.An RF screen that disrupts the natural waveguide nature of the transducer in the 3T MR environment can change the electromagnetic field profile to reduce unwanted artifacts and provide an imaging region which has more homogeneity and higher SNR throughout the brain.

The near field, Westervelt far field, and inverse-law far field of the audio sound generated by parametric array loudspeakers.

The near and far fields of traditional loudspeakers are differentiated by whether the sound pressure amplitude is inversely proportional to the propagating distance. However, the audio sound field generated by a parametric array loudspeaker (PAL) is more complicated, and in this article it is proposed to be divided into three regions: near field, Westervelt far field, and inverse-law far field. In the near field, the audio sound experiences strong local effects and an efficient quasilinear solution is presented. In the Westervelt far field, local effects are negligible so that the Westervelt equation is used, and in the inverse-law far field, a simpler solution is adopted. It is found that the boundary between the near and Westervelt far fields for audio sound lies at approximately a2/λ - λ/4, where a is transducer radius and λ is ultrasonic wavelength. At large transducer radii and high ultrasonic frequencies, the boundary moves close to the PAL and can be estimated by a closed-form formula. The inverse-law holds for audio sound in the inverse-law far field and is more than 10 meters away from the PAL in most cases. With the proposed classification, it is convenient to apply appropriate prediction models to different regions.

Time Domain Analysis of Current Transducer Responses Using Impulsive Signals

For the measurement of impulsive currents, which might occur in cases of electromagnetic interference, for example currents generated by the non-linear behavior of electronic appliances, a wide-band large dynamic range current transducer is needed. The electrical response of such a transducer is determined using conventional techniques, that use frequency sweeps of sinusoidal continuous wave signals. For non-linear and/or time invariant systems the superposition of continuous wave signals of multiple frequencies might not be equal to an impulsive current, which is representative for the actual measured signals, and is therefore of interest. In this letter the electrical response of current transducers is determined using impulsive signals, and compared to continuous wave tests. Time domain parameters such as rise time and peak amplitude are extracted, and the frequency response is analyzed using a Fourier transform. The experiments show that the impulsive test is in agreement with the continuous wave method and provides a good alternative method. A combination of impulses could cover a large bandwidth, and is a fast and cost effective approach.

Label-Free Optical Biosensing Using Low-Cost Electrospun Polymeric Nanofibers

Polymeric nanofiber matrices are promising structures to develop biosensing devices due to their easy and affordable large-scale fabrication and their high surface-to-volume ratio. In this work, the suitability of a polyamide 6 nanofiber matrix for the development of a label-free and real-time Fabry–Pérot cavity-based optical biosensor was studied. For such aim, in-flow biofunctionalization of nanofibers with antibodies, bound through a protein A/G layer, and specific biodetection of 10 µg/mL bovine serum albumin (BSA) were carried out. Both processes were successfully monitored via reflectivity measurements in real-time without labels and their reproducibility was demonstrated when different polymeric nanofiber matrices from the same electrospinning batch were employed as transducers. These results demonstrate not only the suitability of correctly biofunctionalized polyamide 6 nanofiber matrices to be employed for real-time and label-free specific biodetection purposes, but also the potential of electrospinning technique to create affordable and easy-to-fabricate at large scale optical transducers with a reproducible performance.

Upgrading disk transducer to measure elastic waves on coarse-grained granular materials: Development and performance revelation

This paper describes a recently developed technique of evaluating elastic properties of geomaterials in the large size triaxial apparatus enabling to propagate elastic waves even in coarse-grained geomaterials. A flat surface transducer of 80 mm in diameter has been developed embedding four pairs of compressional and shear wave measuring piezoceramic elements. The assemblage of piezoceramics, interpretation of results, verification of performance and applicability are corroborated. It has been shown that an accumulated strength of numerous piezoceramics in form of a single transducer significantly improved the integrity of the transducer enabling to evaluate elastic wave velocity in a large size the triaxial specimen of 230 mm × 230 mm × 500 mm. An investigation on three sorts of granular materials; fine, (d50 = 0.2 mm), medium, (d50 = 1.7 mm) and coarse, (d50 = 12 mm) is carried out. Small strain stiffness of tested geomaterials is evaluated by newly developed large-size disk transducer method and small-strain cyclic loadings. Stiffness measured by both static and elastic wave measurement is confirmed to be followed similar trends. The large size disk transducer evinces the competent performance showing the stiffness evaluated by this method scattered within 20% of the stiffness achieved by a static method and compared with available previous researches as well.

Analysis and scaling study of vibration energy harvesting with reactive electromagnetic and piezoelectric transducers

The goal of this paper is to present a comparative study on the principal features and scaling properties of time-harmonic vibration energy harvesting with electromagnetic and piezoelectric reactive transducers. The study is organised around two prototype reactive harvesters having one end connected to ground. The two harvesters are composed respectively by a coil-magnet and a composite piezoelectric beam characterised by similar dimensions, weights and fundamental natural frequencies. The work is based on equivalent lumped parameter models and energy formulations for the two harvesters. The study shows that, to maximise the power harvesting, the electromagnetic and piezoelectric transducers should be connected respectively to a resistive load and to a resistive-reactive load. In this case, the spectra of the harvested power per unit base acceleration falls proportionally to the inverse of frequency squared and the spectra of the energy harvesting efficiency remains constant with frequency. The scaling study shows that the normalised harvested power density for the electromagnetic harvester grows proportionally to the square of dimension whereas that for the piezoelectric harvester does not vary with dimension. In parallel, the efficiency to absorb vibration energy of the electromagnetic harvester scales following a distinctive S-type law, which reaches the maximum of 0.5 for large transducers. Instead, the efficiency of the piezoelectric transducer is constant and limited to a maximum of 0.5, apart for large transducers where it drops for large scales.