Analytical and numerical calculations of optimum design frequency for focused ultrasound therapy and acoustic radiation force

Focused ultrasound therapy relies on acoustic power absorption by tissue. The stronger the absorption the higher the temperature increase is. However, strong acoustic absorption also means faster attenuation and limited penetration depth. Hence, there is a trade-off between heat generation efficacy and penetration depth. In this paper, we formulated the acoustic power absorption as a function of frequency and attenuation coefficient, and defined two figures of merit to measure the power absorption: spatial peak of the acoustic power absorption density, and the acoustic power absorbed within the focal area. Then, we derived “rule of thumb” expressions for the optimum frequencies that maximized these figures of merit given the target depth and homogeneous tissue type. We also formulated a method to calculate the optimum frequency for inhomogeneous tissue given the tissue composition for situations where the tissue structure can be assumed to be made of parallel layers of homogeneous tissue. We checked the validity of the rules using linear acoustic field simulations. For a one-dimensional array of 4 cm acoustic aperture, and for a two-dimensional array of 4 × 4 cm² acoustic aperture, we found that the power absorbed within the focal area is maximized at 0.86 MHz, and 0.79 MHz, respectively, when the target depth is 4 cm in muscle tissue. The rules on the other hand predicted the optimum frequencies for acoustic power absorption as 0.9 MHz and 0.86 MHz, respectively for the 1D and 2D array case, which are within 6% and 9% of the field simulation results. Because radiation force generated by an acoustic wave in a lossy propagation medium is approximately proportional to the acoustic power absorption, these rules can be used to maximize acoustic radiation force generated in tissue as well.     

High-overtone self-focusing acoustic transducers for high-frequency ultrasonic Doppler

This work reports the potential use of high-overtone self-focusing acoustic transducers for high-frequency ultrasonic Doppler. By using harmonic frequencies of a thick bulk Lead Zirconate Titanate (PZT) transducer with a novel air-reflector Fresnel lens, we obtained strong ultrasound signals at 60 MHz (3rd harmonic) and 100 MHz (5th harmonic). Both experimental and theoretical analysis has demonstrated that the transducers can be applied to Doppler systems with high frequencies up to 100 MHz.     

Optimization of un-tethered, low voltage, 20-100kHz flexural transducers for biomedical ultrasonics applications

This paper describes optimization of un-tethered, low voltage, 20-100 kHz flexural transducers for biomedical ultrasonics applications. The goal of this work was to design a fully wearable, low weight (<100 g), battery operated, piezoelectric ultrasound applicator providing maximum output pressure amplitude at the minimum excitation voltage.Such implementation of ultrasound applicators that can operate at the excitation voltages on the order of only 10-25 V is needed in view of the emerging evidence that spatial-peak temporal-peak ultrasound intensity (I_SPTP) on the order of 100 mW/cm² delivered at frequencies below 100 kHz can have beneficial therapeutic effects. The beneficial therapeutic applications include wound management of chronic ulcers and non-invasive transdermal delivery of insulin and liposome encapsulated drugs.The early prototypes of the 20 and 100 kHz applicators were optimized using the maximum electrical power transfer theorem, which required a punctilious analysis of the complex impedance of the piezoelectric disks mounted in appropriately shaped metal housings.In the implementation tested, the optimized ultrasound transducer applicators were driven by portable, customized electronics, which controlled the excitation voltage amplitude and facilitated operation in continuous wave (CW) or pulsed mode with adjustable (10-90%) duty cycle. The driver unit was powered by remotely located rechargeable lithium (Li) polymer batteries. This was done to further minimize the weight of the applicator unit making it wearable. With DC voltage of approximately 15 V the prototypes were capable of delivering pressure amplitudes of about 55 kPa or 100 mW/cm² (I_SPTP). This level of acoustic output was chosen as it is considered safe and side effects free, even at prolonged exposure.     

Scaling of the viscoelastic shell properties of phospholipid encapsulated microbubbles with ultrasound frequency

Phospholipid encapsulated microbubbles are widely employed as clinical diagnostic ultrasound contrast agents in the 1–5 MHz range, and are increasingly employed at higher ultrasound transmit frequencies. The stiffness and viscosity of the encapsulating “shells” have been shown to play a central role in determining both the linear and nonlinear response of microbubbles to ultrasound. At lower frequencies, recent studies have suggested that shell properties can be frequency dependent. At present, there is only limited knowledge of how the viscoelastic properties of phospholipid shells scale at higher frequencies. In this study, four batches of in-house phospholipid encapsulated microbubbles were fabricated with decreasing volume-weighted mean diameters of 3.20, 2.07, 1.82 and 1.61 μm. Attenuation experiments were conducted in order to assess the frequency-dependent response of each batch, resulting in resonant peaks in response at 4.2, 8.9, 12.6 and 19.5 MHz, respectively. With knowledge of the size measurements, the attenuation spectra were then fitted with a standard linearized bubble model in order to estimate the microbubble shell stiffness S_p and shell viscosity S_f, resulting in a slight increase in S_p (1.53–1.76 N/m) and a substantial decrease in S_f (0.29 × 10⁻⁶–0.08 × 10⁻⁶ kg/s) with increasing frequency. These results performed on a single phospholipid agent show that frequency dependent shell properties persist at high frequencies (up to 19.5 MHz).     

Research on adaptive temperature control in sound field induced by self-focused concave spherical transducer

Temperature control of hyperthermia treatments is generally implemented with multipoint feedback system comprised of phased-array transducer, which is complicated and high cost. Our simulations to the acoustic field induced by a self-focused concave spherical transducer (0.5 MHz, 9 cm aperture width, 8.0 cm focal length) show that the distribution of temperature can keep the same “cigar shape” in the focal region during ultrasound insonation. Based on the characteristic of the temperature change, a two-dimensional model of a “cigar shape” tumor is designed and tested through numerical simulation. One single-point on the border of the “cigar shape” tumor is selected as the control target and is controlled at the temperature of 43 °C by using a self-tuning regulator (STR). Considering the nonlinear effects of biological medium, an accurate state-space model obtained via the finite Fourier integral transformation to the bioheat equation is presented and used for calculating temperature. Computer simulations were performed with the perfusion rates of 2.0 kg/(m³ s) and 4.5 kg/(m³ s) to the different targets, it was found that the temperatures on the border of the “cigar shape” tumor can achieve the desired temperature of 43 °C by control of one single-point. A larger perfusion rate requires a higher power output to obtain the same temperature elevation under the same insonation time and needs a higher cost for compensating the energy loss carried away by blood flow after steady state. The power output increases with the controlled region while achieving the same temperature at the same time. Especially, there is no overshoot during temperature elevation and no oscillation after steady state. The simulation results demonstrate that the proposed approach may offers a way for obtaining a single-point, low-cost hyperthermia system.     

Osteocytes exposed to far field of therapeutic ultrasound promotes osteogenic cellular activities in pre-osteoblasts through soluble factors

Low intensity pulsed ultrasound (LIPUS) was reported to accelerate the rate of fracture healing. When LIPUS is applied to fractures transcutaneously, bone tissues at different depths are exposed to different ultrasound fields. Measurement of LIPUS shows pressure variations in near field (nearby transducer); uniform profile was found beyond it (far field). Moreover, we have reported that the therapeutic effect of LIPUS is dependent on the axial distance of ultrasound beam in rat fracture model. However, the mechanisms of how different axial distances of LIPUS influence the mechanotransduction of bone cells are not understood. To understand the cellular mechanisms underlying far field LIPUS on enhanced fracture healing in rat model, the present study investigated the effect of ultrasound axial distances on (1) osteocyte, the mechanosensor, and (2) mechanotransduction between osteocyte and pre-osteoblast (bone-forming cell) through paracrine signaling. We hypothesized that far field LIPUS could enhance the osteogenic activities of osteoblasts via paracrine factors secreted from osteocytes. The objective of this study was to investigate the effect of axial distances of LIPUS on osteocytes and osteocyte–osteoblast mechanotransduction. In this study, LIPUS (plane; 2.2 cm in diameter, 1.5 MHz sine wave, I_SATA = 30 mW/cm²) was applied to osteocytes (mechanosensor) at three axial distances: 0 mm (near field), 60 mm (mid-near field) and 130 mm (far field). The conditioned medium of osteocytes (OCM) collected from these three groups were used to culture pre-osteoblasts (effector cell). In this study, (1) the direct effect of ultrasound fields on the mechanosensitivity of osteocytes; and (2) the osteogenic effect of different OCM treatments on pre-osteoblasts were assessed. The immunostaining results indicated the ultrasound beam at far field resulted in more β-catenin nuclear translocation in osteocytes than all other groups. This indicated that osteocytes could detect the acoustic differences of LIPUS at various axial distances. Furthermore, we found that the soluble factors secreted by far field LIPUS exposed osteocytes could further promote pre-osteoblasts cell migration, maturation (transition of cell proliferation into osteogenic differentiation), and matrix calcification. In summary, our results of this present study indicated that axial distance beyond near field could transmit ultrasound energy to osteocyte more efficiently. The LIPUS exposed osteocytes conveyed mechanical signals to pre-osteoblasts and regulated their osteogenic cellular activities via paracrine factors secretion. The soluble factors secreted by far field exposed osteocytes led to promotion in migration and maturation in pre-osteoblasts. This finding demonstrated the positive effects of far field LIPUS on stimulating osteocytes and promoting mechanotransduction between osteocytes and osteoblasts.     

Properties and characteristics of P(VDF/TrFE) transducers manufactured by a solution casting method for use in the MHz-range ultrasound in air

Highly effective piezoelectric polymer transducers operating in air at high frequencies have been successfully made by casting a solution of ferroelectric poly(vinylidene fluoride-co-trifluoroethylene) P(VDF/TrFE) directly on a backing metal plate, and their performance has been evaluated. By utilizing this method, it has been possible to develop the three kinds of transducers that operate respectively at 4, 6 and 10 MHz in air. For precise evaluation of the performance of the P(VDF/TrFE) transducers, the absorption loss in air was measured up to 10 MHz. It was confirmed that the empirical formula obtained from the measured absorption values in air at high frequencies was in alignment with its theoretical value. In addition, a high lateral resolution acoustic image of a ROM-Chip (amplitude-image) at 6 MHz in air was successfully displayed using an air coupled concave type P(VDF/TrFE) transducer by bonding an epoxy adhesive.     

Fixation of bioactive calcium alkali phosphate on Ti6Al4V implant material with femtosecond laser pulses

Bone implants made of metal, often titanium or the titanium alloy Ti6Al4V, need to be surface treated to become bioactive. This enables the formation of a firm and durable connection of the prosthesis with the living bone. We present a new method to uniformly cover Ti6Al4V with a thin layer of ceramics that imitates bone material. These calcium alkali phosphates, called GB14 and Ca10, are applied to the metal by dip coating of metal plates into an aqueous slurry containing the fine ceramic powder. The dried samples are illuminated with the 790 nm radiation of a pulsed femtosecond laser. If the laser fluence is set to a value just below the ablation threshold of the ceramic (ca. 0.4 J/cm²) the 30 fs laser pulses penetrate the partly transparent ceramic layer of 20-40 μm thickness. The remaining laser fluence at the ceramic-metal interface is still high enough to generate a thin metal melt layer leading to the ceramic fixation on the metal. The laser processing step is only possible because Ti6Al4V has a lower ablation threshold (between 0.1 and 0.15 J/cm²) than the ceramic material. After laser treatment in a fluence range between 0.1 and 0.4 J/cm², only the particles in contact with the metal withstand a post-laser treatment (ultrasonic cleaning). The non-irradiated rest of the layer is washed off. In this work, we present results of a successful ceramic fixation extending over larger areas. This is fundamental for future applications of arbitrarily shaped implants.     

Investigation of the effect of power ultrasound on the nucleation of water during freezing of agar gel samples in tubing vials

Nucleation, as an important stage of freezing process, can be induced by the irradiation of power ultrasound. In this study, the effect of irradiation temperature (−2 °C, −3 °C, −4 °C and −5 °C), irradiation duration (0 s, 1 s, 3 s, 5 s, 10 s or 15 s) and ultrasound intensity (0.07 W cm⁻², 0.14 W cm⁻², 0.25 W cm⁻², 0.35 W cm⁻² and 0.42 W cm⁻²) on the dynamic nucleation of ice in agar gel samples was studied. The samples were frozen in an ethylene glycol-water mixture (−20 °C) in an ultrasonic bath system after putting them into tubing vials. Results indicated that ultrasound irradiation is able to initiate nucleation at different supercooled temperatures (from −5 °C to −2 °C) in agar gel if optimum intensity and duration of ultrasound were chosen. Evaluation of the effect of 0.25 W cm⁻² ultrasound intensity and different durations of ultrasound application on agar gels showed that 1 s was not long enough to induce nucleation, 3 s induced the nucleation repeatedly but longer irradiation durations resulted in the generation of heat and therefore nucleation was postponed. Investigation of the effect of ultrasound intensity revealed that higher intensities of ultrasound were effective when a shorter period of irradiation was used, while lower intensities only resulted in nucleation when a longer irradiation time was applied. In addition to this, higher intensities were not effective at longer irradiation times due to the heat generated in the samples by the heating effect of ultrasound. In conclusion, the use of ultrasound as a means to control the crystallization process offers promising application in freezing of solid foods, however, optimum conditions should be selected.     

Theoretical and phantom based investigation of the impact of sound speed and backscatter variations on attenuation slope estimation

Quantitative ultrasound features such as the attenuation slope, sound speed and scatterer size, have been utilized to evaluate pathological variations in soft tissues such as the liver and breast. However, the impact of variations in the sound speed and backscatter due to underlying fat content or fibrotic changes, on the attenuation slope has not been addressed. Both numerical and acoustically uniform tissue-mimicking experimental phantoms are used to demonstrate the impact of sound speed variations on attenuation slope using clinical real-time ultrasound scanners equipped with linear array transducers. Radiofrequency data at center frequencies of 4 and 5 MHz are acquired for the experimental and numerical phantoms respectively. Numerical phantom sound speeds between 1480 and 1600 m/s in increments of 20 m/s for attenuation coefficients of 0.3, 0.4, 0.5, 0.6, and 0.7 dB/cm/MHz are simulated. Variations in the attenuation slope when the backscatter intensity of the sample is equal, 3 dB higher, and 3 dB lower than the reference is also evaluated. The sound speed for the experimental tissue-mimicking phantoms were 1500, 1540, 1560 and 1580 m/s respectively, with an attenuation coefficient of 0.5 dB/cm/MHz. Radiofrequency data is processed using three different attenuation estimation algorithms, i.e. the reference phantom, centroid downshift, and a hybrid method. In both numerical and experimental phantoms our results indicate a bias in attenuation slope estimates when the reference phantom sound speed is higher (overestimation) or lower (underestimation) than that of the sample. This bias is introduced via a small spectral shift in the normalized power spectra of the reference and sample with different sound speeds. The hybrid method provides the best estimation performance, especially for sample attenuation coefficient values lower than that of the reference phantom. The performance of all the methods deteriorates when the attenuation coefficient of the reference phantom is lower than that of the sample. In addition, the hybrid method is the least sensitive to sample backscatter intensity variations.     

Long range inductive power transfer with superconducting oscillators

Resonant inductive power transfer has demonstrated the transfer of 60 W at distances in excess of 2 m with as much as 40% efficiency. The loss mechanisms include internal dissipation and radiated power. By constructing superconducting oscillators and operating at lower frequencies, both of these loss mechanisms are reduced, and this same power can be transferred at distances in excess of 100 m. A performance analysis of such a system is presented, along with proposed low-loss coil and capacitor designs to achieve this performance.     

Self-Q-switched and mode-locked Nd,Cr:YAG laser with 6.52-W average output power

Simultaneous self-Q-switched and mode-locked have been demonstrated in a diode-pumped Nd,Cr:YAG laser. For the first time as we know, almost 100% modulation depth has been achieved at an intracavity intensity of 5.6 × 10⁵ W/cm². The maximum average output power of 6.52 W corresponding to a slope efficiency of 30% is obtained at 1064 nm. The laser produces high-quality pulses in a TEM₀₀-mode at the pump power of 16.5 W. The pulse duration of the mode-locked pulses is about 600 ps with 136 MHz repetition rate.     

Surface modifications of AISI 1045 steel created by high intensity 1064 and 532 nm picosecond Nd:YAG laser pulses

Interaction of Nd:YAG laser, operating at 1064 or 532 nm wavelength and a pulse duration of 40 ps, with AISI 1045 steel was studied. Surface damage thresholds were estimated to be 0.30 and 0.16 J/cm² at the wavelengths of 1064 and 532 nm, respectively. The steel surface modification was studied at the laser energy density of 10.3 J/cm² (at 1064 nm) and 5.4 J/cm² (at 532 nm). The energy absorbed from Nd:YAG laser beam is partially converted to thermal energy, which generates a series of effects, such as melting, vaporization of the molten material, shock waves, etc. The following AISI 1045 steel surface morphological changes and processes were observed: (i) both laser wavelengths cause damage of the steel in the central zone of irradiated area; (ii) appearance of a hydrodynamic feature in the form of resolidified droplets of the material in the surrounding outer zone with 1064 nm laser wavelength; (iii) appearance of periodic surface structures, at micro- and nano-level, with the 532 nm wavelength and, (iv) development of plasma in front of the target. Generally, interaction of laser beam with the AISI 1045 steel (at 1064 and 532 nm) results in a near-instantaneous creation of damage, meaning that large steel surfaces can be processed in short time.     

A practical multinuclear transceiver volume coil for in vivo MRI/MRS at 7 T

A practical multinuclear transceiver RF volume coil with improved efficiency for in vivo small animal ¹H/¹³C/²³Na MR applications at the ultrahigh magnetic field of 7 T is reported. In the proposed design, the coil's resonance frequencies for ¹H and ¹³C are realized by using a traditional double-tuned approach, while the resonant frequency for ²³Na, which is only some 4 MHz away from the ¹³C frequency, is tuned based upon ¹³C channel by easy-operating capacitive “frequency switches”. In contrast to the traditional triple-tuned volume coil, the volume coil with the proposed design possesses less number of resonances, which helps improve the coil efficiency and alleviate the design and operation difficulties. This coil design strategy is advantageous and well suitable for multinuclear MR imaging and spectroscopy studies, particularly in the case where Larmor frequencies of nuclei in question are not separate enough. The prototype multinuclear coil was demonstrated in the desired unshielded design for easy construction and experiment implementation at 7 T. The design method may provide a practical and robust solution to designing multinuclear RF volume coils for in vivo MR imaging and spectroscopy at ultrahigh fields. Finite difference time domain method simulations for evaluating the design and 7-T MR experiment results acquired using the prototype coil are presented.     

Accumulation morphology on the surface of stainless steel irradiated by a nanosecond Nd:YAG pulsed laser

In this study, results in the irradiation of stainless steel AISI 304 in air with nanosecond laser pulses at laser irradiation power density 4×10⁷ W/cm² are reported. Laser processing parameters, such as wavelengths 532 and 1064 nm, pulse duration 20 ns and repetition rate 10 Hz were used. It is shown that the surface morphology of the stainless steel is related to the number of pulses applied to the same spot. The following surface morphological changes were observed: (i) occurrence of the micro-grains microstructures at wavelengths 532 and 1064 nm after 10 000 pulses irradiation and (ii) occurrence of vermiform-like microstructures at wavelength 1064 nm after 1000 pulses irradiation. Generally, it is concluded that irradiation due to several consecutive pulses caused significant damage and enhanced the stainless steel surface roughness.     

Self-Q-switched and mode-locked 946 nm Cr,Nd:YAG laser

A simultaneous self-Q-switched and mode-locked diode-pumped 946 nm laser by using a Cr,Nd:YAG crystal as gain medium as well as saturable absorber is demonstrated for the first time as we know. The maximum average output power of 751 mW with a slope efficiency of 18.38% is obtained at an intra-cavity average peak power intensity of 4.83 × 10⁶ W/cm². Under this circumstance, the repetition rate of Q-switched envelopes is 9.63 kHz and the pulse width is about 460 ns. Almost 100% mode-locked modulation depth is obtained at all time in the experiment process whether the incident pump power is low or high. The repetition rate of mode-locked pulses within a Q-switched envelope is 135.13 MHz and the mode-locked pulse width is within 600 ps. The laser produces high-quality pulses in TEM₀₀-mode in the simultaneous self-Q-switched and mode-locked experiment.     

Sub-gigahertz laser resonant ultrasound spectroscopy for the evaluation of elastic properties of micrometric fibers

The cross-section eigenmodes of micrometric cylinders were measured in the range of several tens of MHz to about 0.5 GHz. The vibrations were excited using subnanosecond laser pulses. The cross-section eigenmodes were simulated using finite element modeling in a 2D geometry. Using the method of resonant ultrasound spectroscopy, the vibration spectrum of an aluminum wire of diameter 33μm served to determine Young’s modulus and Poisson’s ratio with a precision of 0.7% and 0.3%, respectively. The calculated and measured frequencies of cross-section eigenmodes were fitted with a precision better than 0.5% in the 50–500 MHz range.     

Arbitrary shaped, liquid filled reverberators with non-resonant transducers for broadband focusing of ultrasound using Time Reversed Acoustics

The ability to generate short focused ultrasonic pulses with duration on the order of one period of carrier frequency depends on the bandwidth of the transmitter as the pulse duration is inversely proportional to the bandwidth. Conventional focusing arrays used for focusing ultrasound have limited bandwidth due to the resonant nature of the piezoelements generating ultrasound. Theoretically it is possible to build a broadband phased array composed of “non-resonant” elements: wedge-shaped or flat-concave piezotransducers, though there are numerous technical difficulties in designing arrays with hundreds of elements of complex shape. This task is much easier to realize in an alternative technique of ultrasound focusing based on the principles of Time Reversed Acoustics (TRA) because in TRA systems, effective focusing can be achieved with just a few, or even one, transducers. The goal of this study is to demonstrate the possibility of broadband focusing of ultrasonic waves using a TRA system with non-resonant transducers and to explore the factors affecting the performance of such a system. A new type of TRA reverberators, such as water-filled thin-wall plastic vessels, which can be used with the submersible piezotransducers fixed internally in the reverberator, are proposed and tested. The experiments are conducted in a water tank with the walls and bottom covered by a sound absorbing lining. A needle hydrophone mounted on a 3D positioning system is used as a beacon for the TRA focusing and then for measuring the spatial distribution of the focused ultrasound field. The bandwidth and spatial distribution of the signal focused by the TRA system using a single channel with the resonant versus non-resonant transducers have been analyzed. Two types of non-resonant transducers were tested: a flat-concave transducer with a diameter of 30 mm, and a thickness varying from 2 mm in the center to 11 mm at the edge, and a specially designed submersible transducer having an uneven shape with a diameter of about 25 mm and a thickness varying from 2 to 6 mm. It was shown that TRA focusing system using non-resonant transducer had a bandwidth at 10 dB of 500 kHz while the resonant transducer provided about 100 kHz bandwidth. Correspondingly, the extended bandwidth of the TRA focusing system, especially toward higher frequencies, provides a 50% sharper spatial distribution. Furthermore, the relative level of the background ultrasound was reduced by a factor up to 3 as more frequencies were added coherently in focus and incoherently out of focus. Advantages of water-filled reverberators made of thin-wall plastic vessels include easy manufacturing, low costs, extreme simplicity, and good acoustical matching with soft tissues, important for biomedical applications.     

A study of interface characteristics in HfAlO/p-Si by deep level transient spectroscopy

Deep level transient spectroscopy (DLTS) and high-frequency capacitance-voltage (HF-CV) measurement are used for the investigation of HfAlO/p-Si interface. The so-called “slow” interface states detected by HF-CV are obtained to be 2.68 × 10¹¹ cm⁻². Combined conventional DLTS with insufficient-filling DLTS (IF-DLTS), the true energy level position of interfacial traps is found to be 0.33 eV above the valance band maximum of silicon, and the density of such “fast” interfacial traps is 1.91 × 10¹² cm⁻² eV⁻¹. The variation of energy level position of such traps with different annealing temperatures indicates the origin of these traps may be the oxide-related traps very close to the HfAlO/Si interface. The interfacial traps’ passivation and depassivation effect of postannealing in forming gas are shown by comparing samples annealed at different temperatures.     

An experimentally validated electromagnetic energy harvester

A relatively simple method for determining the electromechanical parameters of electromagnetic energy harvesters are presented in this paper. The optimal power generated through a load resistor at both off-resonance and resonance is derived analytically. The experimentally measured performance of a rudimentary electromechanical energy harvester using a rare-earth magnet shows good agreement with the results from the model. The parasitic generator coil resistance can have a profound effect on the overall performance of an electromagnetic generator by essentially acting to degrade the effective coupling coefficient. Data from the setup electromagnetic generator shows normalized power densities of 1.7 μW/[(m/s²)² cm³] operating at a resonance frequency of 112.25 Hz. This power density is comparable with other electromagnetic devices of the same volume operating at these frequencies. The power output of the presented electromagnetic generator is comparable to equivalent piezoelectric generators.