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Focused ultrasound (FUS) is a powerful tool for noninvasive modulation of deep brain activity with promising therapeutic potential for refractory epilepsy; however, tools for examining FUS effects on specific cell types within the deep brain do not yet exist. Consequently, how cell types within heterogeneous networks can be modulated and whether parameters can be identified to bias these networks in the context of complex behaviors remains unknown. To address this, we developed a fiber Photometry Coupled focused Ultrasound System (PhoCUS) for simultaneously monitoring FUS effects on neural activity of subcortical genetically targeted cell types in freely behaving animals. We identified a parameter set that selectively increases activity of parvalbumin interneurons while suppressing excitatory neurons in the hippocampus. A net inhibitory effect localized to the hippocampus was further confirmed through whole brain metabolic imaging. Finally, these inhibitory selective parameters achieved significant spike suppression in the kainate model of chronic temporal lobe epilepsy, opening the door for future noninvasive therapies.

Transcranial focused ultrasound (FUS) is a noninvasive treatment for brain tumors and neuromodulation. Based on normal incidence, conventional FUS techniques use a focused or an array of ultrasonic transducers to overcome the attenuation and absorption of ultrasound in the skull; however, this remains the main limitation of using FUS. A dual-mode conversion technique based on Lamb waves is proposed to achieve high transmission efficiency. This concept was validated using the finite element analysis (FEA) and experiments based on changes in the incident angle. Aluminum, plexiglass, and a human skull were used as materials with different attenuations. The transmission loss was calculated for each material, and the results were compared with the reflectance function of the Lamb waves. Oblique incidence based on dual-mode conversion exhibited a better transmission efficiency than that of a normal incidence for all of the specimens. The total transmission losses for the materials were 13.7, 15.46, and 3.91 dB less than those associated with the normal incidence. A wedge transducer was designed and fabricated to implement the proposed method. The results demonstrated the potential applicability of the dual-mode conversion technique for the human skull.

The most common neurostimulation method is the stimulation of the focal point by using a focused ultrasound transducer. In the field of particle manipulation using ultrasound, research using acoustic vortices is ongoing and presents promising characteristics. In neurostimulation using ultrasound, the acoustic radiation force is a leading candidate for a physical mechanism. In this study, the acoustic radiation forces generated by a general-focused transducer and a vortex transducer were compared. For the experiment, a 70 mm diameter transducer with a center frequency of 1 MHz was fabricated using a piezoceramic plate. The ultrasound transducer frame was made of aluminum, and air backing was used to maximize the output pressure. A large-scale Fresnel focused lens and focused vortex lens were fabricated using polydimethylsiloxane (PDMS). A mold of an 8-step Fresnel lens with a diameter of 70 mm was developed using 3-D printing. We compared the pressure field and radiation force according to the two manufactured lenses to determine whether there was any difference in neurostimulation.

Compared with the conventional method of transcranial focused ultrasound stimulation using a single transducer or a focused beam, the compression and tensile forces are generated from the high-pressure gradient of a standing wave that can generate increased stimulation. We experimentally verified a neuromodulation system using patterned interference radiation force (PIRF) and propose a method for obtaining the magnitude of the radiation force, which is considered the main factor influencing ultrasound neuromodulation. The radiation forces generated using a single focused transducer and a standing wave created via two focused transducers were compared using simulations. Radiation force was calculated based on the relationship between the acoustic pressure, radiation force and time-averaged second-order pressure obtained using an acoustic streaming simulation. The presence of the radiation force was verified by measuring the time-averaged second-order pressure generated due to the radiation force, by using a glass tube.

Using a focused ultrasound transducer is one of the most preferred methods for neurostimulation. Due to its high spatial resolution, high penetration depth, ultrasonic property, and its ability to be combined with other methods, a focused ultrasound transducer is suitable for non-invasive brain neurostimulation and is widely used. Generally, only one transducer is used or all transducers face one direction for focusing. Unlike previous cases, neurostimulation using a pattern interface radiation force (PIRF) uses more than two focused transducers and makes standing wave patterns inside the brain for neurostimulation. This paper presents the fabrication and application of a large-scale focused transducer using a Fresnel lens for PIRF application. The focused transducer is made with polydimethylsiloxane (PDMS) and a hybrid-type piezoelectric (PZT) ceramic plate similar to PZT-4 with a size of 100 mm × 80 mm × 2.2 mm. The lens was designed for a 1-MHz frequency, which is the center frequency of the PZT plate. Using these two transducers, a standing wave pattern was created inside the skull, and the radiation force was calculated using the measured pressure field.

The transcranial ultrasound technique has been researched as a non-invasive method for the treatment of brain tumors, neuromodulation, and the delivery of cancer therapeutics. Focused ultrasound is one of the most common methods for noninvasive treatments, but the present technology generally uses an array of transducers of normal incidence. The general focused ultrasound technique has high transmission loss and heating of the skull because of the normal incidence. In this study, we present the design, analysis, and implementation of a wedge transducer array consisting of piezoelectric (PZT) ceramic elements for the dual-mode conversion technique, which means that the longitudinal wave in the wedge is converted to the Lamb wave in the skull and the Lamb wave is converted to the longitudinal wave in the brain. This technique enables efficient transmission, reduces heating of the skull, and extends the focal spot range. We fabricated the partial wedge transducer and conducted the experiments to calculate the total transmission loss of this system.

Ultrasound (US) can modulate the electrical activity of the excitable tissues, but the mechanisms underlying this effect are not understood at the molecular level or in terms of the physical modality through which US exerts its effects. Here, we report an experimental system that allows for stable patch-clamp recording in the presence of US at 43 MHz, a frequency known to stimulate neural activity. We describe the effects of US on two ion channels proposed to be involved in the response of excitable cells to US: the mechanosensitive Piezo1 channel and the voltage-gated sodium channel NaV1.2. Our patch-clamp recordings, together with finite-element simulations of acoustic field parameters indicate that Piezo1 channels are activated by continuous wave US at 43 MHz and 50 or 90 W/cm2 through cell membrane stress caused by acoustic streaming. NaV1.2 channels were not affected through this mechanism at these intensities, but their kinetics could be accelerated by US-induced heating.

This paper presents an application of the Waveform inversion approach to localization of objects in reverberant fields and with limited spatial measurements. Reverberant fields in enclosures can potentially carry useful information, however, in an incoherent way. Incoherency comes from the consecutive reflections of the wave energy several times in the domain. This, along with diffraction and dispersion effects, can ultimately lead to mixing of the wave energy in a seemingly random way. However, spreading of the wave energy can lead to multiple interrogations of each point in the enclosure. Hence, any substructural changes in the enclosure can be sensed with sufficient information carried by the wave energy flow. Furthermore, the temporal information buried in the data makes it feasible to conduct only a few spatial measurements. The authors present a localization scheme that benefits from the reverberant field and can reduce the required number of spatial measurements.

This paper presents a novel method to significantly broaden the bandwidth of airborne capacitive micromachined ultrasonic transducers (CMUTs) by introducing a gaseous squeeze film as a damping mechanism. The damping and stiffening effects of the squeeze film can be tuned to lower the pull-in voltage while improving the sensitivity by optimizing fluidic trenches of various heights within the gap. By only adjusting the trench height, we can control the bandwidth from 0.89% to 8.1% while keeping the pull-in voltage under 55 V and achieving the minimum detectable pressure (MDP) from 2.2 μPa/√Hz to 4.88 μPa/√Hz. We also present a vacuum CMUT with high sensitivity and extremely low MDP as low as to 1.2 μPa/√Hz with 0.93 kHz bandwidth, in which a thick plate is chosen to reduce the geometric nonlinearity. This demonstration of the high sensitivity and wide bandwidth CMUTs with low driving voltage make them applicable to medical imaging, thermoacoustics, and nondestructive testing.

Focused ultrasound has been shown to be effective at stimulating neurons in many animal models, both in vivo and ex vivo. Ultrasonic neuromodulation is the only noninvasive method of stimulation that could reach deep in the brain with high spatial-temporal resolution, and thus has potential for use in clinical applications and basic studies of the nervous system. Understanding the physical mechanism by which energy in a high acoustic frequency wave is delivered to stimulate neurons will be important to optimize this technology. We imaged the isolated salamander retina of either sex during ultrasonic stimuli that drive ganglion cell activity and observed micron scale displacements, consistent with radiation force, the nonlinear delivery of momentum by a propagating wave. We recorded ganglion cell spiking activity and changed the acoustic carrier frequency across a broad range (0.5–43 MHz), finding that increased stimulation occurs at higher acoustic frequencies, ruling out cavitation as an alternative possible mechanism. A quantitative radiation force model can explain retinal responses and could potentially explain previous in vivo results in the mouse, suggesting a new hypothesis to be tested in vivo. Finally, we found that neural activity was strongly modulated by the distance between the transducer and the electrode array showing the influence of standing waves on the response. We conclude that radiation force is the dominant physical mechanism underlying ultrasonic neurostimulation in the ex vivo retina and propose that the control of standing waves is a new potential method to modulate these effects. SIGNIFICANCE STATEMENT Ultrasonic neurostimulation is a promising noninvasive technology that has potential for both basic research and clinical applications. The mechanisms of ultrasonic neurostimulation are unknown, making it difficult to optimize in any given application. We studied the physical mechanism by which ultrasound is converted into an effective energy form to cause neurostimulation in the retina and find that ultrasound acts via radiation force leading to a mechanical displacement of tissue. We further show that standing waves have a strong modulatory effect on activity. Our quantitative model by which ultrasound generates radiation force and leads to neural activity will be important in optimizing ultrasonic neurostimulation across a wide range of applications.

This paper presents a novel method to increase the bandwidth (BW) of airborne capacitive micromachined ultrasonic transducers (CMUTs). This method introduces a gaseous squeeze film as a damping mechanism, which induces a stiffening effect that lowers the pull-in voltage and improves the sensitivity. The optimal behavior of this stiffening effect versus the damping mechanism can be controlled by creating optimized fluidic trenches of various heights within the gap. The fractional BW can be controlled from 0.89% to 8.1% by adjusting the trench height while lowering the pull-in voltage to less than 54 V at the gap height of 1.0 $\mu \text{m}$ . To achieve the largest sensitivity and lowest pull-in voltage at a given BW, we have developed a multi-parameter optimization method to adjust all combinations of design parameters. A novel multiple hard-mask process flow has been developed to enable fabrication of CMUTs with different cavity and trench heights on the same wafer. These devices provided an equivalent noise pressure level of 4.77 $\mu $ Pa/ $\surd $ Hz with 6.24-kHz BW for 7.6- $\mu \text{m}$ deep fluidic trenches and 4.88 $\mu $ Pa/ $\surd $ Hz with 7.48-kHz BW for 14.3- $\mu \text{m}$ deep fluidic trenches. This demonstration of the wide-BW CMUTs with high sensitivity and low pull-in voltage makes them applicable to medical and thermoacoustic imaging, nondestructive testing, and ultrasonic flow metering.

Focused ultrasound has been shown to be effective at stimulating neurons in vivo, ex vivo and in vitro preparations. Ultrasonic neuromodulation is the only non-invasive method of stimulation that could reach deep in the brain with high spatial-temporal resolution, and thus has potential for use in clinical applications and basic studies of the nervous system. Understanding the physical mechanism by which energy in a high acoustic frequency wave is delivered to stimulate neurons will be important to optimize this technology. Two primary candidates for a physical mechanism are radiation force, the delivery of momentum by the acoustic wave, and cavitation, oscillating gas bubbles. We imaged the isolated salamander retina during ultrasonic stimuli that drive ganglion cell activity and observed micron scale displacements consistent with radiation force. We recorded ganglion cell spiking activity with a planar multielectrode array and changed the acoustic carrier frequency across a broad range (0.5 - 43 MHz), finding that increased stimulation occurs at higher acoustic frequencies, a result that is consistent with radiation force but not cavitation. A quantitative radiation force model can explain retinal responses, and could potentially explain previous in vivo results in the mouse, suggesting a new hypothesis to be tested in vivo. Finally, we found that neural activity was strongly modulated by the distance between the transducer and the electrode array showing the influence of standing waves on the response. We conclude that radiation force is the physical mechanism underlying ultrasonic neurostimulation in the ex vivo retina, and that the control of standing waves is a new potential method to modulate these effects.

Touchscreen sensors are widely used in many devices such as smart phones, tablets, laptops, etc. There are many different types of modalities that enable sensing the touch. The dominant technologies on the market are the capacitive, resistive, acoustic or ultrasound, and optical touch systems. None of these technologies are perfect and each has some advantages and disadvantages. Capacitive touch technologies are the most common in the industry. However, hardware complexity, high manufacturing cost, and high power consumption have impeded their feasibility for certain applications such as larger screens. Acoustic/ultrasound technologies due to their simplicity, ease of manufacturing, and low cost have been identified as suitable alternatives for a wide spectrum of applications. However, lack of robustness and multi-touch capability have made them fall short as competitive technologies. We present design, analysis, and implementation of an ultrasonic touchscreen system that utilizes interaction of transient Lamb waves with objects in contact with the screen. It attempts to improve on the existing ultrasound technologies, with the potential of addressing some of the weaknesses of the dominant technologies, such as the capacitive or resistive ones. Compared with the existing ultrasonic and acoustic modalities, among other advantages, it provides the capability of detecting several simultaneous touch points and also a more robust performance.

Transcranial focused ultrasound is approved for non-invasive treatment of essential tremor, and is being researched as a noninvasive means of ablating brain tumors, neuromodulation, and of increasing delivery of cancer therapeutics through the blood-brain barrier. Present technology relies on the use of an array of transducers placed in a helmet and aimed at the skull at normal incidence, leading to inefficient transmission, excess heating of the skull, and limited treatment envelope to the center of the brain. We propose an array of ultrasound wedge transducers capable of efficiently delivering focused ultrasound energy into the brain with minimal heating of the skull and expanding the treatment envelope to include the entire brain.

This paper reports vented CMUTs with wide bandwidth and high sensitivity, optimized by multi-parameter optimization method. The dominated parameters, including the radius and thickness of the flexible plate, gap height, and the size and distribution of vented holes have been individually optimized. The impedance measurements well-match the simulation results. Then the multi-parameter optimization method in place of the individual parameter optimization method is used to optimize the design parameters all together. Finally, keeping the approximate bandwidth, the multi-parameter optimization makes the sensitivity improved by 11% at the same percentage of pull-in voltage, and driving voltage is lowered by 49% compared with the individual parameter optimization.

Ultrasound (US) can modulate the electrical activity of the excitable tissues but the mechanisms underlying this effect are not understood at the molecular level or in terms of the physical modality through which US exerts its effects. Here we report an experimental system that allows for stable patch-clamp recording in the presence of US at 43 MHz, a frequency known to stimulate neural activity. We describe the effects of US on two ion channels proposed to be involved in the response of excitable cells to US: the mechanosensitive Piezo1 channel and the voltage-gated sodium channel NaV1.2. Our patch-clamp recordings, together with finite-element simulations of acoustic field parameters indicate that Piezo1 channels are activated by continuous wave US at 43 MHz and 50 or 90 W/cm2 through cell membrane stress caused by acoustic streaming. NaV1.2 channels were not affected through this mechanism at these intensities, but their kinetics could be accelerated by US-induced heating.

This article presents a learning (training)-based method for localizing objects in enclosures. Wave propagation in enclosures can lead to mixing of the wave energy, ultimately leading to incoherent spreading of information. This makes the localization problem challenging. However, spreading of the wave energy can lead to multiple interrogations of each point in the enclosure, which is in essence reminiscent of an ergodic or a closely ergodic behavior. Hence, any substructural changes in the enclosure can be sensed with sufficient information carried by the wave energy flow. Furthermore, temporal information buried in data makes it feasible to conduct only a few spatial measurements. A localization scheme is presented that benefits from the reverberant field and can reduce the required number of spatial measurements.

This paper presents the theory of the $k$ -space method generalized to model elastic wave propagation in heterogeneous anisotropic media. The $k$ -space methods are promising time integration techniques giving, in conjunction with collocation spectral methods, accurate and efficient numerical schemes for problems in heterogeneous media. In this paper, the $k$ -space operator is derived in a spatially continuous form using the Fourier analysis of the displacement formalism of elastodynamics. An efficient numerical algorithm is then constructed by applying a Fourier collocation spectral method, leading to define the discrete $k$ -space scheme. The proposed method is temporally exact for homogeneous media, unconditionally stable for heterogeneous media, and also allows larger time steps without loss of accuracy. Implementation of the method is discussed in detail. The method is validated through a set of numerical tests. The numerical results show the efficacy of the method compared with the conventional schemes.

We developed a fully-populated 2-D capacitive micromachined ultrasonic transducer (CMUT) array for high intensity focused ultrasound (HIFU) treatment. The 2-D CMUT array, which consists of 20 × 20 square CMUT elements with an element-to-element pitch of 1 mm, was designed and fabricated using the thick-buried-oxide (BOX) fabrication process. It was then assembled on a custom interface board that can provide various array configurations depending on the desired applications. In this study, the interface board groups the CMUT array elements into eight channels, based on the phase delay from the element to the targeted focal point at a 20-mm distance from the array surface, which corresponds to an F-number of 1. An 8-channel phase generating system supplies continuous waves with eight different phases to the eight channels of the CMUT array through bias-tees and amplifiers. This array aperture, grouped into eight channels, gives a focusing gain of 6.09 according to field simulation using Field II. Assuming a...

Touchscreen sensors are widely used in many devices such as smart phones, tablets, and laptops with diverse applications. We present the design, analysis, and implementation of an ultrasonic touchscreen system that utilizes the interaction of transient Lamb waves with objects in contact with the screen. It attempts to improve on the existing ultrasound technologies, with the potential of addressing some of the weaknesses of the dominant technologies, such as the capacitive or resistive ones. Compared with the existing ultrasonic and acoustic modalities, among other advantages, it provides the capability of detecting several simultaneous touch points and also a more robust performance. The localization algorithm, given the hardware design, can detect several touch points with a very limited number of measurements (one or two). This in turn can significantly reduce the manufacturing cost.

Photoacoustic imaging offers significant potential as a biomedical imaging modality. For some applications, however, there is a need for contrast enhancement. In this paper, a theoretical comparison is presented of the efficacy of three different designs for photoacoustic contrast agents (PACAs), specifically, a droplet of dye, a bubble filled with gas coated by a dye loaded shell, and a droplet of volatile dye. For each case, the governing equations describing the dynamics of a single PACA in a homogenous incompressible fluid are derived. The coupled sets of equations describing the bubble oscillation and resulting radiated pressure, the photo-acoustic energy equation, and the equation of state are then solved numerically. The numerical results predict a stronger radiated acoustic signal for the same optical source energy density in the case of the volatile dye droplet by a factor of up to two orders of magnitude compared with the other two types of agent.

Touchscreen sensors are widely used in many devices such as smart phones, tablets, laptops, etc. We present the design, analysis, and implementation of an ultrasonic touchscreen system that utilizes interaction of transient Lamb waves with objects in contact with the screen. The governing principle revolves around the propagation and reverberation of guided elastic waves in a bounded space, in which the localization of touch points can be challenging. Reverberant fields in enclosures can potentially carry useful information, however, in an incoherent way. Incoherency comes from consecutive reflections of the wave energy several times in the domain, ultimately leading to mixing of the wave energy in a seemingly random way. However, spreading of the wave energy can lead to multiple interrogations of each point in the enclosure. Hence, temporal information buries information about substructural changes making it feasible to conduct only a few spatial measurements. We present a learning localization algorithm capable of localizing multiple simultaneous touch points (up to 12 touches on a tablet) and with a very limited number of measurements (one or two). This in turn can significantly reduce the manufacturing cost. We also present an algorithm to improve on robustness to environmental and thermal noise.

Transient Lamb waves induced by finite piezoelectric transducers have been widely used in ultrasonic touch systems, where a tactile object is localized through its interaction with the Lamb waves. However, this problem has not been looked in-depth theoretically, which is essential for development of robust systems. The two-dimensional theory often fails to provide a true picture as the diffraction effects are of great significance in these technologies. Reduced order models such as the plate theories, on the other hand, can support diffraction. However, they fail to support mid to higher spectrum of the Lamb modes. Moreover, many introduce errors in the range of the supported modes. Hence, for many problems, the design confidence level is only achieved upon a three-dimensional theory. We present the mathematical modeling of piezoelectrically induced elastic waves propagating through homogeneous plates subjected to a tactile object. We use a finite element method to solve the model problem. The model is validated against the experimental data.

We generalize the theory of the k-space method to the case of elastic wave propagation in heterogeneous anisotropic media. The k-space operator is derived in the spatially continuous form using the displacement formalism of elastodynamics. The k-space scheme is then discretized in space using a Fourier collocation spectral method. This leads to an efficient and accurate numerical algorithm, where the time advancement can be performed in order of N operations, where N is the number of unknowns. As opposed to the classical k-space theory for the elastic waves in isotropic media [1], [2], the new algorithm does not need any field splitting. Hence, it is more efficient once used to model isotropy. The proposed method is temporally exact for homogeneous media, unconditionally stable for heterogeneous media, and also allows larger time-steps without loss of accuracy. We validate the method against canonical model problems of elastodynamics.

A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Green's function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.

Capacitive micromachined ultrasonic transducers (CMUTs) have great potential to compete with traditional piezoelectric transducers in therapeutic ultrasound applications. In this paper we have designed, fabricated and developed an acoustic lens formed on the CMUT to mechanically focus ultrasound. The acoustic lens was designed based on the paraxial theory and made of silicone rubber for acoustic impedance matching and encapsulation. The CMUT was fabricated based on the local oxidation of silicon (LOCOS) and fusion-bonding. The fabricated CMUT was verified to behave like an electromechanical resonator in air and exhibited wideband response with a center frequency of 2.2 MHz in immersion. The fabrication for the acoustic lens contained two consecutive mold castings and directly formed on the surface of the CMUT. Applied with ac burst input voltages at the center frequency, the CMUT with the acoustic lens generated an output pressure of 1.89 MPa (peak-to-peak) at the focal point with an effective focal gain of 3.43 in immersion. Compared to the same CMUT without a lens, the CMUT with the acoustic lens demonstrated the ability to successfully focus ultrasound and provided a viable solution to the miniaturization of the multi-modality forward-looking endoscopes without electrical focusing.

Numerical studies on the detection of tumors using photoacoustic imaging have shown that relying on optical energy absorption by blood hemoglobin as the contrast mechanism leads to poor image quality. This provides a strong incentive for seeking suitable manufactured photoacoustic contrast agents (PACAs). We present a theoretical comparison of three different photoacoustic contrast agents, all incorporating dye particles with suitable optical absorption characteristics. The three different designs are as follows: (1) stabilized droplet: a droplet of dye; (2) stabilized bubble: a bubble filled with gas and coated by dye as the shell; and (3) phase shift droplet: a droplet of volatile dye, all pulsating in a homogenous incompressible fluid. For each case, the governing equations describing the dynamics of a single PACA and the radiated pressure are derived. Each case is expressed in terms of four coupled sets of equations as the pressure radiated from the bubble, equation of motion, photoacoustic energy equation and equation of state, by virtue of simplifying assumptions. The derived equations are numerically solved by the Runge–Kutta method, using appropriate photoacoustic properties. The numerical results predict a much stronger radiated acoustic signal for the same optical source energy in the case of the stabilized bubble (case 2).

Photoacoustic imaging has shown great promise for medical imaging, where optical energy absorption by blood haemoglobin is used as the contrast mechanism. A numerical method has been developed for the in silico assessment of the photoacoustic image reconstruction of the brain. Image segmentation techniques were used to prepare a digital phantom from MR images. Then, light transport through brain tissue was modeled using the finite element approach. The resulting acoustic pressure was then estimated by pulsed photoacoustics considerations. The forward acoustic wave propagation was modeled by linearized coupled first order wave equations and solved by the acoustic k‐space method. Since skull bone is an elastic solid and strongly attenuates ultrasound (due to scattering and absorption), a k‐space method was developed for elastic media. To model scattering effects, a new approach was introduced based on propagation in random media. In addition, absorption effects were incorporated using a power law. Finally, ...