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.     

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.     

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.     

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.