Finding natural ways to help patients with dry eyes is a goal of mine. I hate taking pills and using prescription eye drops and ointments like everyone else. Thus it was a wonderful surprise when a patient came in saying that her little ultrasound wand helped her dry eyes when she used them near her lids. She has dry eyes and has been using a new Arbonne Ultrasound wand to help her skin. When she applied it near her lids and massaged them, her dry eyes got better.
I=p202ρc→p0=I×2ρc−−−−−−√,
This sounded interesting.
For years, we have asked patients do do lid massaging to help push out the meibomian gland oil, but usually a rubbing will not “melt” the oil in the glands enough to notice an immediate effect on most patients.
Could this little portable device work better than what we have?
So we brought in her Arbonne “Genius Ultra” Ultrasound Wand to compare it’s effect with IPL for treatment of the glands with expression.
We tried 2 patients: 1 eye Ultrasound Wand (right eye on both patients); Other eye, IPL standard protocol for skin type like we usually do.
The results were very exciting!
I will post the video on Youtube asap.
It looked like the wand did a better job melting the oil than the IPL for expression. This is only 2 cases but exciting if patients can use this daily.
I do not think there is any harm in using this machine on the eyelid skin. Studies below suggest it might be even safe to use it over the eye though more studies are needed.
I am not a consultant for this company but I am very excited on possibility this might help.
And the wand is much less expensive that other portable options like portable IPL wands.
How does it help? Maybe thru intra-meibomian gland and inertial cavitation
Coming soon: Videos of both patients so you can see the oil expression compared between eyes and the first patient using the Arbonne Ultrasound Wand.
Future studies we plan to do would include:
1. Warm compresses vs IPL
2. Warm compresses vs Arbonne Ultrasound Wand
3. Portable IPL vs warm compresses
4. Portable IPL vs Arbonne Ultrasound Wand.
Finally, potentially more options for patients other than warm cloth-compresses!
Sandra Lora Cremers, MD, FACS
If you want more information, email Lynn at LynnMakris@gmail.com & Allie at ablankenship@voeyedr.com & let them know Dr. Cremers mentioned this on her blog.
Key points:
1. Results of our previous in vitro study showed that the exposure of the cornea to 880 kHz ultrasound for 5 min at intensities of 0.19, 0.34, and 0.56 W/cm2resulted in 2.1, 2.5, and 4.2 times increase of the corneal permeability to sodium fluorescein (a small hydrophilic dye), respectively, as compared to sham treatment and
2. 2 times and 1.5 times increase in the delivery of ophthalmic steroid dexamethasone sodium phosphate in vitro as compared to sham treatment,
3.The e increase in dexamethasone sodium phosphate concentration in aqueous humor samples was 2.8 times (p < 0.05) with ultrasound application (0.8 W/cm2 for 5 min) at 400 kHz and 2.4 times (p < 0.01) at 600 kHz as compared to sham-treated samples in our previous in vivo study.8
4. Similar results were also obtained in a recent study by Lamy et al. where ultrasound application at similar parameters (1 W/cm2 at 880 kHz for 6 min) was shown to result in 3–3.6 times increase in riboflavin delivery into corneal stroma through intact corneal epithelium.11
5. Further, Nuritdinov showed that application of 880 kHz ultrasound at 0.2 W/cm2 for 5 min produced a 4.6 times increase in the corneal permeability for a hydrophilic compound, fluorescein, in an aerated solution.12 It was also shown that ultrasound at frequencies of 470–880 kHz and intensities of 0.2–0.3 W/cm2 applied for 5 min in a continuous mode produced up to 10-fold increase in the corneal permeability for a radioactive compound, 125I in a rabbit model, in vivo with the maximal increase observed at 660 KHz.13
3. Several recent studies indicated that ultrasound-mediated delivery was effective in delivering macromolecules into the posterior segment of the rabbit eye via trans-scleral route.14–16
4. No adverse effects were observed for up to 2 weeks after ultrasound application in the posterior segment of the eye. Another recent study by Razavi et al. showed that ultrasound can enhance the delivery of fluorescein sodium via the scleral route with no significant alteration observed in the eye tissues.17
5. In this study, inertial cavitation was shown to be the mechanism responsible for this delivery enhancement.
Med Phys. 2015 Oct; 42(10): 5604–5615.
Published online 2015 Sep 8. doi: 10.1118/1.4929553
PMCID: PMC4567579
PMID: 26429235
Thermal safety of ultrasound-enhanced ocular drug delivery: A modeling study
This article has been cited by other articles in PMC.
1. INTRODUCTION
Rise in temperature and overheating of sensitive eye structures is a concern in the clinical application of ultrasound for drug delivery into the eye.1–5 The absence of blood flow in the cornea and lens, which is avascular, exacerbates potential harmful effects of increased temperature due to decreased ability for heat dissipation.2,6
Ultrasound application was shown to increase the permeability of the cornea and provide enhancement in drug delivery, and has a potential to provide an effective and safe method for ocular drug delivery in the treatment of eye infections and inflammations.7,8 Results of our previous in vitro study showed that the exposure of the cornea to 880 kHz ultrasound for 5 min at intensities of 0.19, 0.34, and 0.56 W/cm2resulted in 2.1, 2.5, and 4.2 times increase of the corneal permeability for sodium fluorescein (a small hydrophilic dye), respectively, as compared to sham treatment.9 The permeability increase in vivo using the same ultrasound parameters was 2 times at 0.19 W/cm2, 4 times at 0.34 W/cm2, and 10.6 times at 0.56 W/cm2, as compared to sham treatment.10 The results of our previous study demonstrated 2 times and 1.5 times increase in the delivery of ophthalmic steroid dexamethasone sodium phosphate in vitro as compared to sham treatment, with statistical significance, at intensity of 1.0 W/cm2 and frequency of 400 and 600 kHz, respectively.7 Further, the increase in dexamethasone sodium phosphate concentration in aqueous humor samples was 2.8 times (p < 0.05) with ultrasound application (0.8 W/cm2 for 5 min) at 400 kHz and 2.4 times (p < 0.01) at 600 kHz as compared to sham-treated samples in our previous in vivo study.8Similar results were also obtained in a recent study by Lamy et al. where ultrasound application at similar parameters (1 W/cm2 at 880 kHz for 6 min) was shown to result in 3–3.6 times increase in riboflavin delivery into corneal stroma through intact corneal epithelium.11 Further, Nuritdinov showed that application of 880 kHz ultrasound at 0.2 W/cm2 for 5 min produced a 4.6 times increase in the corneal permeability for a hydrophilic compound, fluorescein, in an aerated solution.12 It was also shown that ultrasound at frequencies of 470–880 kHz and intensities of 0.2–0.3 W/cm2 applied for 5 min in a continuous mode produced up to 10-fold increase in the corneal permeability for a radioactive compound, 125I in a rabbit model, in vivo with the maximal increase observed at 660 KHz.13 Feasibility of ultrasound-enhanced trans-scleral drug delivery has also been tested. For example, several recent studies indicated that ultrasound-mediated delivery was effective in delivering macromolecules into the posterior segment of the rabbit eye via trans-scleral route.14–16 No adverse effects were observed for up to 2 weeks after ultrasound application in the posterior segment of the eye. Another recent study by Razavi et al. showed that ultrasound can enhance the delivery of fluorescein sodium via the scleral route with no significant alteration observed in the eye tissues.17 In this study, inertial cavitation was shown to be the mechanism responsible for this delivery enhancement.
Palte et al. investigated thermal and mechanical effects of ultrasound exposure (by utilizing thermocouple temperature measurements and histological evaluations) to determine potential adverse changes in different regions of the eye.1 In this study, the eye temperature was increased above the recommended limits (eye tissue temperature increase of greater than 1.5 °C above physiological levels) as a result of 10 min of ultrasound application (using nonorbital rated diagnostic ultrasound); however, the authors failed to find any evidence of eye tissue damage.1 The conclusion of this study was that regulatory recommendations may be too strict in the case of ocular ultrasound. In the study by Lamy et al., the maximal temperature increase due to 6 min of ultrasound application (at 880 kHz and 1 W/cm2) was 6.1 °C from baseline temperature of 34 °C. This temperature increase did not appear to cause any changes in biomechanical properties of the cornea.11
In the study reported here, we focused on modeling of the interaction between ultrasound and eye tissues for determination of ultrasound thermal safety in drug delivery applications. Measuring the temperature increase in different eye tissues, by using thin wire thermocouples, was not possible during our previous drug delivery studies7,8 since it would compromise the drug delivery measurements. This modeling study developed a temperature map that gives the exact location and temperature increase in different eye tissues during ultrasound application. To the best of our knowledge, this is the first study to report these findings. The method is also applicable where tissue damage, by placing thermocouples, should be avoided, or placing thermocouples in the tissue of interests is not possible.
2. METHODS
2.A. Human eye model
A theoretical model of the human eye was designed based on the accurate geometrical measurements for different eye structures obtained from the published literature.18–20 A rabbit model was used in our previous in vitro and in vivo experimental studies, but an actual human eye was used for modeling studies since it offers results that are more relevant for eventual patient treatment. Rabbit eyes have been used as an acceptable ophthalmic research model because they are similar to the human eye.21 Further, acoustic and thermal properties of the rabbit eye tissues are expected to be similar to human eye tissue.22Dimensions of human and rabbit eye structures are shown in Table TableII.
TABLE I.
Dimensions for rabbit and human eyeball structures (Refs. 18–20). All dimensions are shown in mm.
| Rabbit | Human | |
|---|---|---|
| Anteroposterior length | 16–19 | 23–25 |
| Anterior chamber depth | 2.9 | 3.5 |
| Diameter of cornea | 13.5–14 | 10.6 |
| Thickness of cornea at its center | 0.3–0.4 | 0.5 |
| Thickness of cornea in periphery | 0.45 | 0.7 |
| Thickness of lens | 6.36 | 3.5–4.3 |
| Thickness of sclera | 0.33 | 0.5–1.0 |
| Thickness of choroid | 0.07 | 0.1–0.5 |
| Thickness of retina | 0.05 | 0.1–0.5 |
The eyeball model used in this study included cornea, aqueous humor, lens, vitreous humor, sclera, choroid, retina, and optic nerve. Figure Figure11 shows a schematic of human eye anatomy.
Acoustic and thermal specifications for different modeled eye tissues had to be known, to be able to establish all of the eye structures in the model accurately. These parameters for human eye are provided in Table TableII.II. Tissue density of 1070 kg/m3 was used in the whole PZFlex model which is an average estimation for different eye tissues (average value for density of different eye tissues is 1066 kg/m3 with the range of 1034–1088 kg/m3.23
TABLE II.
Acoustic and thermal characteristics of different eye structures (Refs. 22–26).
| Speed of sound (m/s) | Acoustic attenuation (dB cm−1MHz−1) | Specific heat (J/kgK) | Thermal conductivity (W/mK) | |
|---|---|---|---|---|
| Cornea | 1586 | 0.78 | 4178 | 0.58 |
| Sclera | 1647 | 0.97 | 4178 | 0.58 |
| Aqueous humor | 1497 | 0.01 | 3997 | 0.59 |
| Choroid | 1527 | 0.95 | 3840 | 0.60 |
| Lens | 1647 | 1.19 | 3000 | 0.40 |
| Vitreous humor | 1532 | 0.01 | 3999 | 0.60 |
| Retina | 1538 | 1.15 | 3680 | 0.57 |
| Optic nerve | 1644 | 0.7 | 3750 | 0.53 |
The perfusion was assumed to be negligible because there is no blood supply in cornea, lens, and vitreous body.26 This assumption is not correct in the case of retina and choroid, and our model overestimates the temperatures achieved in these tissues. The baseline temperature for the model was set to be 37 °C, which is the normal temperature of the human eye.27
2.B. Acoustic simulations
Modeling studies were conducted using a finite-element analysis software package (PZFlex, Weidlinger Associates, Mountain View, CA). This numerical program uses a finite-element and explicit time-domain approach for modeling ultrasound propagation, frequency dependent attenuation, thermal effects over time, etc. A desktop computer (Dell T5500, Round Rock, TX) with dual-core 64-bit 2.66 GHz Intel processors and 40 GB memory was used in our modeling studies. Both acoustic and thermal simulations were performed using this software to obtain quantitative information on interaction between ultrasound and eye tissues. In this model, the axis was set to be symmetric, and the boundary conditions at the sides and bottom of the model were set to be absorbing. In our modeling experiments, the maximum computation time was 30 min.
The acoustic properties of our modeling setup were similar to those present in our previously performed in vitro and in vivo drug delivery experiments.7,8 The modeling setup included a continuous ultrasound beam at frequencies of 400 kHz–1 MHz, intensities of 0.3–1 W/cm2, and exposure duration of 5 min. The ultrasound field was modeled as an unfocused beam with uniform cross-sectional intensity. In the acoustic model, the pressure was applied to the cylindrical surface of the flat transducer to generate an ultrasound beam. The regions of the eye that were along the beam path included cornea, lens, and optic nerve in the back of the eye. The active diameter of the transducer was 15 mm. The distance from the transducer to the surface of the cornea was at near field to far field transition distance, dff, which was calculated to be 1.5, 2.25, 3.0, and 3.75 cm for 400, 600, 800 kHz, and 1 MHz, respectively. dff is the location of the furthest maximum pressure for the flat ultrasound transducer.28 The material between eye and transducer was water. The drug solutions used in our previous experimental studies7,8 were hydrophilic with water base properties; therefore, water was a suitable choice. The complete design of our model is shown in Fig. Fig.22.
Geometric model of the eye that is axisymmetric. White rectangle shows the 2D representation of the ultrasound transducer. The dotted line represents the axisymmetric model.
The main areas of interest in our modeling studies were cornea, lens, and optic nerve in the back of the eye. Thermal conductivity and specific heat capacity for each structure in the eyeball had to be known to run the model—these values were obtained from the published literature and are provided in Table TableIIII.
There are two ways to design the acoustic model, using pulsed and ultrasound continuous wave propagation. We used the continuous model to match the actual ultrasound parameters used in our previous drug delivery experiments.7,8 In this model, continuous sinusoidal drive of a specific frequency (400 kHz–1 MHz) and amplitude were applied until the whole system reached steady state, and after that the energy loss data were gathered. The amplitude of this sinusoidal drive was calculated using the following equation:
(1)
where I is intensity averaged over one or more cycles of continuous wave propagation in W/m2, p0 is the pressure amplitude in kg/s2 m, ρ is density in kg/cm3, and c is speed of ultrasound in m/s.
2.C. Calculations of pressure intensity and heat source
The heat production rate per unit volume, as a result of ultrasound application, depends on characteristics of the medium, biological tissues in our study, and ultrasound field, and it is equal to dissipation rate for ultrasound,29
qv = 2αI,
(2)
where α is the absorption coefficient in Np/unit length and I is the time-averaged intensity. Heat production rate, qv, varies from one region to another as the ultrasound beam passes through the tissue.29,30 As shown in Eq. (3), absorption and frequency can have both a linear as well as a nonlinear relationship when the power m is not unity, and frequency can be expressed as
α(f) = α1fm,
(3)
where α1 is the absorption coefficient at 1 MHz, f is the frequency in MHz, and m is a number between 1 and 1.3.29
In many applications of ultrasound where the pressures are low enough that nonlinearity effects are negligible,29 the relation between medium density and pressure is assumed to be linear. The maximum pressure at the highest intensity (1.0 W/cm2) used in our studies was 0.146 MPa. The threshold for nonlinearity is highly dependent on both the ultrasound systems used and the bioeffects of interests. At our applied ultrasound parameters, the nonlinearity effects as related to tissue heating should be negligible as shown in the work by Soneson and Myers31 and Curra et al.32
Further assumption as related to linearity is that the plane wave traveling through the medium with pressure amplitude varies in a sinusoidal pattern over time and is characterized by single frequency. The relation between the intensity I(z) of a plane wave, at specific frequency and tissue depth, with I0 at initial location or depth is shown by29,30
I(z) = I0e−2az,
(4)
where I0 is the intensity at z = 0 and a is the attenuation coefficient (both scattering and absorption) at frequency f. The attenuation and absorption coefficients were shown to be similar in the liver, and it is assumed that the same is true for other soft tissues.22,33 If the attenuation is just based on absorption, then Eq. (3) can be changed to
I(z) = I0e−2αfz,
(5)
where α is the absorption coefficient (Np/cm) and is a function of frequency.
The exact equations used in the PZFlex modeling approach can be found in the references by Abboud et al.34 and Wojcik et al.35 The PZFlex finite-element implementation for acoustic wave propagation is based on a first order system of equations. In our modeling experiments, the initial conditions were set at zero. The boundary conditions were chosen to be perfect matching layer (PML). In thermal simulations (described below), the governing equation was the bioheat transfer equation.36,37 The initial condition was body temperature, and the boundary conditions were set to body temperature.
2.D. Thermal simulations
The acoustic wave propagation through the whole eye model was investigated. Then, the acoustic energy deposition due to absorption (or reflection), as a result of ultrasound wave propagation across the model, was the driving force for thermal model. Thermal and acoustic model cannot be coupled because even though energy deposition and temperature can be calculated simultaneously, the differences in time scale between thermal effects (in scale of seconds) and acoustical effects (wave propagation in scale of microseconds) would make this modeling effort inefficient. Therefore, the best approach was to run the ultrasound wave propagation model until it reaches steady state, then one cycle of wave propagation was calculated; the energy loss due to attention through the whole model was recorded and used to run the thermal model as described in our previous publications.38,43 Based on the software specifications, the acoustic field simulation was run with a continuous sinusoidal drive of a given frequency, with identical cycles, over the entire model. The steady state is case dependent and was observed by monitoring the time-domain trace in the field in front of the transducer until it was found to be steady. This time can be estimated as 1.5 × length of model/speed of sound in tissue (as based on PZFlex manual). The steady state is typically noted in the continuous mode after 10–20 waves have passed through the point of interest. Figure Figure33 shows the result of acoustic simulation, which includes the pressure map of the entire model, and loss map as a result of energy attenuation.
2.E. Finite-element mesh
A dense elemental mesh, which contains greater number of elements, was utilized to achieve a constructive interface between all waves in the acoustic model. The meshing could be less dense in the thermal model as compared to the acoustic model because the variation of temperature across the model could be captured using a smaller number of elements in the system. To set the meshing for simulation, the average velocity (in this case, the average of ultrasound velocity in different parts of the eye was 1560 m/s) and frequency variables (400 kHz–1 MHz) were defined; the wavelength was determined, and size of elements was set accordingly. The more elements the model has, the more accurate is the representation of the object. The PZFlex user manual suggests at least 12 elements per wavelength. The number of elements used for our acoustic and thermal models was 30, to ensure adequate accuracy of the model. To investigate the effect of number of elements per wavelength on the results, a distinct test was implemented. For one of the parameters (400 kHz and 0.8 W/cm2), the model was run for different number of meshing elements (20, 30, 40, 50, 60, and 70) to determine whether our choice of 30 elements provided adequate results. Figure Figure44shows the effects of different number of elements and their relation to peak pressure during the simulation. The results indicated that the peak pressure did not deviate when using number of elements that were equal to or greater than 30 in our simulations.
2.F. Thermal safety
In our studies, we set safety limits for temperature increase during ocular ultrasound application as up to 1.5 °C above physiological temperature levels based on European Federation of Societies for Ultrasound in Medicine and Biology recommendations39 and previous experimental safety studies.1 Current US Food and Drug Administration guidance for ophthalmic ultrasound manufacturers recommends ISPTA of lower than 50 mW/cm2 and thermal index (TI) of less than 1.36,40 TI is the ratio of device’s total acoustic power to the power needed to increase tissue’s temperature by 1 °C. However, it is important to keep in mind that these are guidance documents and different ultrasound parameters can be approved by US FDA and used clinically if safety and effectiveness of the approach is justified.41 The loss of acoustic energy was used as a heat source input to observe temperature distribution in the eye. After modeling studies were performed using the following combination of ultrasound parameters, frequencies of 400, 600, 800 kHz, and 1 MHz at intensities of 0.3, 0.5, 0.8, and 1 W/cm2 for 5 min, the peak temperature was obtained in different eye tissues. To better observe areas that were affected by heat generated from ultrasound application, a matlabalgorithm38 was used which could access the lost data from thermal simulation, draw a contour of eye structures of interest, and map the areas with different temperatures. Since the simulations were axisymmetric, just one side of the model is shown in the relevant figures in Sec. 3.
3. RESULTS
The results for each ultrasound parameter combination are shown in Figs. 5–8. The baseline temperature was set to 37 °C, and temperature changes indicated below are based on changes from this value. Our results showed (Fig. (Fig.5)5) that using ultrasound at a frequency of 400 kHz in drug delivery experiments had minimal effects on the eye tissues. It is worth noting that this frequency was shown in our previous experiments to lead to the highest increase in transcorneal drug delivery (at an intensity of 0.8 W/cm2, and exposure duration of 5 min).7,8
Temperature distribution after 5 min of ultrasound application at a frequency of 400 kHz and intensities of 0.3, 0.5, 0.8, and 1 W/cm2. Each subplot represents the flat ultrasound transducer located at dff from the surface of the eye and eye structures of interest including cornea, lens, and optic nerve in the posterior eye. The left side of each subplot shows temperature contours at several locations, and the right side shows the temperature pattern.
Temperature distribution after 5 min of ultrasound application at a frequency of 600 kHz and intensities of 0.3, 0.5, 0.8, and 1 W/cm2.
Temperature distribution after 5 min of ultrasound application at a frequency of 800 kHz and intensities of 0.3, 0.5, 0.8, and 1 W/cm2.
Simulated temperature distribution after 5 min of ultrasound application at frequency of 1 MHz and intensities of 0.3, 0.5, 0.8, and 1 W/cm2.
The temperature increase at an intensity of 0.3 W/cm2 was 0.3 °C in the cornea, and was 0.5 °C in the lens. The change in temperature in the lens was higher (1 °C), at 0.5 W/cm2 as compared to 0.3 W/cm2. At an intensity of 0.8 W/cm2, temperature elevation was 1.5 °C in the lens and 1 °C in the cornea. The maximal temperature increase of 2.5 °C was observed inside the lens at the highest intensity of 1 W/cm2. Also, ultrasound application caused an increase of 1 °C in the cornea at intensity of 1 W/cm2. No temperature increase was observed in the back of the eye.
In case of ultrasound application at 600 kHz (Fig. (Fig.6),6), the increase in temperature was more pronounced. The temperature increase at 0.3 W/cm2 was 0.5 °C in the cornea and was 1 °C in the lens. Increase in temperature in the cornea and lens was 1 and 1.5 °C, respectively, at 0.5 W/cm2. At higher intensity (0.8 W/cm2), temperature elevation was 2.5 °C in the lens, and 1.5 °C in the cornea. The maximum increase of 3 °C was in the center of the lens while applying ultrasound at an intensity of 1 W/cm2 for 5 min. Using the same parameters, the temperature of the cornea was increased by 2 °C. No temperature increase in the back of the eye was observed at these ultrasound parameters.
Application of ultrasound at 800 kHz (Fig. (Fig.7)7) caused the temperature in the back of the eye (at the optic nerve location) to increase 1.5 °C at an intensity of 1 W/cm2. The temperature increase observed in the center of the lens was 4 °C at 0.8 W/cm2 and 5 °C at 1 W/cm2. The temperature of the cornea increased by about 2.5 °C at this frequency and at the highest intensity of 1 W/cm2.
Among all the frequencies tested during thermal simulations, a frequency of 1 MHz ultrasound produced the highest temperature increase on all structures of interest, i.e., cornea, lens, and optic nerve (Fig. (Fig.8).8). The temperature increase observed, even at lowest tested intensity of 0.5 W/cm2, was 3 °C in the center of the lens, 1.5 °C in the cornea, and 1 °C in the back of the eye. The most significant temperature elevation (6 °C in the lens, 3 °C in the cornea, and 2 °C in the back of the eye) was observed at 1 W/cm2. The summary of maximal temperatures observed in eye tissues at different ultrasound frequencies is provided in Table III.
TABLE III.
Summary of maximal temperatures in different eye tissues (°C) during ultrasound application.
| 400 kHz | 600 kHz | 800 kHz | 1 MHz | |
|---|---|---|---|---|
| Cornea | 38 | 39 | 39.5 | 40 |
| Lens | 39.5 | 40 | 42 | 43 |
| Back of the eye (optic nerve) | 37 | 37.5 | 38.5 | 39 |
4. DISCUSSION
Modeling methods (utilizing PZFlex software) have been used in several previously published studies to investigate the safety of ultrasound application in biological tissues. For example, a study done by Nell and Myers indicated that mathematical modeling is a good method to investigate the amount of temperature rise due to ultrasound absorption in tissues in the proximity of the bone. These authors have successfully confirmed their modeling results with experimental measurements.42 Further, our previous studies showed a good correlation between PZFlex modeling results and thermocouple measurements in tissue-mimicking phantoms.43 Similar results were obtained when PZFlex model was compared to thermocouple measurements done in ex vivo rabbit eyes.38
Attenuation of ultrasound energy or loss of ultrasound wave amplitudes as the wave passes through a medium such as tissue can be caused by different mechanisms such as reflection, refraction, scattering, and most importantly absorption.28 From this list, scattering and absorption cause the most of energy attenuation. If the medium is not uniform and consists of different layers, the acoustic impedance differences between layers can cause reflection and refraction. Acoustic scattering happens when the medium is inhomogeneous, and the ultrasound wave encounters structures that have the same size or are smaller than its wavelength. In the case of absorption, the acoustical energy of ultrasound, as it is absorbed by medium, converts into heat.4,44 As the ultrasound frequency increases, the thermal effects become more pronounced,45 with their relation to ultrasound intensity and duty cycle directly proportional. As frequency increased in our experiments, more acoustic energy was converted to heat, which resulted in higher energy attenuation. Because of high acoustic attenuation in the lens,22 the greater temperature increase was observed in that area of the eye.
In addition to ultrasound frequency, the intensity of the ultrasound wave plays an important role in heat generation. The greater the intensity is, the higher the heat production will be.29 The graphic representation of energy loss after thermal simulation showed that the temperature of the lens increased the most as a result of ultrasound application. The temperature increase produced in the lens is higher as compared to cornea and optic nerve because of its high acoustic attenuation (see Table TableIIII).
The absence of blood flow in the cornea and lens which are avascular, results in slower cooling and more heat absorption in these tissues during ultrasound exposure.2,6 Overheating of the lens is a major concern since it may result in cataract formation.46 Guy et al. specified that the potential risk would be generated if the temperature increases above 41 °C.47 Cataracts have also been observed when a rabbit eye was exposed to localized, very high radiofrequency (RF) field at 2450 MHz for more than 30 min at power densities causing very high dose rates of 150 W/kg, and temperatures of 41 °C.48 Hyperthermia levels (of 41–43 °C) were also shown to cause functional changes in the corneal epithelial cells.49 Our modeling study showed that temperature increases obtained using ultrasound at higher frequencies may have resulted in temperatures that could cause adverse effects in the lens and cornea.
Previously reported experimental studies on the values of acoustic properties of eye lens resulted in a relatively large range of values. For example, a study by Huang et al.50 measured attenuation of healthy porcine lens as 0.48 ± 0.2 (dB/cm)/MHz, while a study by Raitelaitiene et al.51 reported attenuation values for human lens of 5.88 (dB/cm)/MHz. We have based our modeling studies on the experimental values for acoustic properties of different human eye structures including the lens reported by de Korte et al.25Further, a leading book reference for physical properties of different tissues by Duck22 reported human lens attenuation as 8 dB/cm at 10 MHz which would correspond to 0.8 (dB/cm)/MHz at 1 MHz since acoustic attenuation of the lens was reported to be linear with frequency.52 It should be noted that higher values of the lens attenuation that the ones used in our studies would lead to more concerning outcomes regarding temperature increase. This issue could be resolved by utilizing pulsed ultrasound exposures that were shown recently to be successful in achieving enhancement in ocular drug delivery,17 to minimize temperature increase inside the eye.
Ciliary body and ciliary zonules were not included in our eye model due to their small size and the lack of reported acoustic and thermal parameters for these tissues.22 However, the temperature values for these tissues are expected to be the same or lower than our modeled values in the sclera exposed to ultrasound in front of the eye and should not be of additional safety concern (please see temperature contours in Figs. 5–8). Ciliary body has been reported in previous studies to have the same acoustic attenuation as sclera (of 1.17 × f1.57 Np/m where f is frequency),52 and ciliary zonules are fibrous tissue similar to sclera’s fibrous tunic and are also expected to have similar acoustic and thermal properties as the sclera. Further, previous experimental work indicated that the mean temperatures during ultrasound exposure in ex vivo human and rabbit eyes were lower in the ciliary body as compared to the lens;6 therefore, safety limits imposed by the lens heating in our modeling studies should be sufficient to address heating of ciliary bodies as well.
Measuring the temperature of different eye tissues was not feasible in our previous in vitro and in vivostudies since thermocouple placement in different eye tissues would have compromised drug delivery measurements;7,8 therefore, this modeling study was needed to observe the impact of ultrasound application at our proposed parameters on potential heat generation in the lens and other eye tissues. Modeling can help with choosing the parameters that would not cause thermal damage to the eye while applying ultrasound to enhance ocular drug delivery. The ultrasound parameters used in the modeling studies were obtained from our previous in vitro and in vivo experiments.7,8 Combinations of ultrasound parameters were determined which did not result in a substantial temperature increase in the cornea, lens, and the back of the eye and could be considered safe. Fortunately, these same parameters were shown to be the most effective for drug delivery in our previous experimental studies. Our previous experimental thermal measurements provided the values for the cornea temperature,7 which were used to assess the validity of simulation results. The temperature was measured inside the donor compartment of the diffusion cell in proximity of the cornea, and maximal temperature increase was ∼3 °C.7 This value is equivalent to the maximal temperature change which was observed in the cornea at the most severe case, at 1 MHz and 1 W/cm2, in this modeling study.
Limitations of our study included the absence of bone interfaces that are present in the orbit and not accounting for tissue perfusion. Because the normal cornea, lens, and vitreous body are avascular tissues, the perfusion effect in previously published ocular studies has been assumed to be negligible.26,53,54Further, for vascularized structures inside the eye, such as ciliary body, the impact of perfusion on tissue heating during ultrasound exposure is expected to be minor6 due to the lack of large blood vessels inside the eye.55
The impact of orbital bone is of safety concern.42,56 Depth of the orbit in human is 40–50 mm, with the eye located in front (with the depth of 25 mm).57 The remaining orbital area (between the eye and the bony eye socket) is 15–25 mm long and filled mostly with muscle and fat tissue. However, optic nerve passes through the optic canal in the bone and potential adverse heating in this area is of concern56,58,59 and should be explored further by modeling heating patterns in the whole orbit. These heating patterns would depend on a number of factors including the attenuation of ultrasound waves due to intervening tissues between the bone and ultrasound transducer located in the front of the eye (approximately 50 mm away), perfusion of surrounding tissues, and the impact of soft tissue–bone interface. If these future studies show concerning temperature values at the bone interface, utilization of pulsed ultrasound mode in ocular drug delivery may be a way to remedy this safety concern.17 Previous experimental studies that utilized ultrasound at physiotherapy levels of continuous exposure (similar to our levels) indicated that the impact of the bone can be substantial (up to 4-fold higher temperatures as compared to the same location in the tissue with no bone present) within close proximity (5–7 mm) of the bone.56 Moros et al.56 used 3 different temperature measurements techniques (fiber-optic temperature probes, infrared camera, and MRI) to determine temperature increases at the soft tissue phantom–bone interfaces exposed to planar 1 MHz transducer at acoustic powers of 5.4–30 W and exposure durations of 0.5–15 min. The findings of their studies indicated that significant heating of over 4-fold was induced at the tissue–bone interfaces in proximity (within 5 mm) from the bone (as compared to the tissues at equivalent distance with no bone present). For long exposure experiments (15 min of ultrasound exposure in continuous mode), the additional temperature increase due to the bone interface was present at 10 mm from the bone inside the soft tissue. This study indicated that the bone heating would be limited to the orbital tissues in the proximity of the bone and should not impact our results for the temperature increases inside the eye. Further, theoretical calculations that we performed indicated that potential additional heating at the bone interface would impact the soft tissues to up to 6.7 mm from the bone based on calculated diffusion length for our model after applying 5 min of ultrasound exposure in continuous mode.29,60 The diffusion length is calculated as (kt)1/2 where k is thermal diffusivity coefficient of soft tissue of 0.15 × 10−6 m2/s and t is exposure time in seconds. Therefore, both previous experimental studies and theoretical analysis indicated that the tissues impacted by the bone interface would be within 7 mm from the bone in our studies, and the presence of the bone should not impact the results that we have obtained for the tissues located within the eye.
5. CONCLUSIONS
In our study, modeling was used to investigate the amount of heat generated in a human eye model as a result of using continuous mode ultrasound application at different frequencies and intensities at the same parameters that were shown effective for enhancing ocular drug delivery. This modeling study provided further knowledge about heat distribution in the eye tissues and led to a better understanding of what ultrasound parameters should be used in future experiments and eventually in the clinical setting.
ACKNOWLEDGMENT
This work was supported by National Eye Institute Grant No. NIH5R21EY01873702.
REFERENCES
1. Palte H. D., Gayer S., Arrieta E., Scot Shaw E., Nose I., Lee E., Arheart K. L., Dubovy S., Birnbach D. J., and Parel J. M., “Are ultrasound-guided ophthalmic blocks injurious to the eye? A comparative rabbit model study of two ultrasound devices evaluating intraorbital thermal and structural changes,” Anesth. Analg. 115, 194–201 (2012).10.1213/ANE.0b013e318253622e [PMC free article] [PubMed] [Cross Ref]
2. Kowalczuk L., Boudinet M., El Sanharawi M., Touchard E., Naud M. C., Saied A., Jeanny J. C., Behar-Cohen F., and Laugier P., “In vivo gene transfer into the ocular ciliary muscle mediated by ultrasound and microbubbles,” Ultrasound Med. Biol. 37, 1814–1827 (2011).10.1016/j.ultrasmedbio.2011.07.010[PubMed] [Cross Ref]
3. Barnett S. B., TerHaar G. R., Ziskin M. C., Rott H. D., Duck F. A., and Maeda K., “International recommendations and guidelines for the safe use of diagnostic ultrasound in medicine,” Ultrasound Med. Biol. 26, 355–366 (2000).10.1016/S0301-5629(00)00204-0 [PubMed] [Cross Ref]
4. Polat B. E., Hart D., Langer R., and Blankschtein D., “Ultrasound-mediated transdermal drug delivery: Mechanisms, scope, and emerging trends,” J. Controlled Release 152, 330–348 (2011).10.1016/j.jconrel.2011.01.006 [PMC free article] [PubMed] [Cross Ref]
5. Boucaud A., Montharu J., Machet L., Arbeille B., Machet M., Patat F., and Vaillant L., “Clinical, histologic, and electron microscopy study of skin exposed to low frequency ultrasound,” Anat. Rec., Part A264, 114–119 (2001).10.1002/ar.1122 [PubMed] [Cross Ref]
6. Cucevic V., Brown A. S., and Foster F. S., “Thermal assessment of 40 MHz pulsed doppler ultrasound in human eye,” Ultrasound Med. Biol. 31, 565–573 (2005).10.1016/j.ultrasmedbio.2005.01.004 [PubMed][Cross Ref]
7. Nabili M., Patel H., Mahesh S. P., Liu J., Geist C., and Zderic V., “Ultrasound-enhanced delivery of antibiotics and anti-inflammatory drugs into the eye,” Ultrasound Med. Biol. 39(4), 638–646 (2013).10.1016/j.ultrasmedbio.2012.11.010 [PMC free article] [PubMed] [Cross Ref]
8. Nabili M., Shenoy A., Chawla S., Mahesh S. P., Liu J., Geist C., and Zderic V., “Ultrasound-enhanced ocular delivery of dexamethasone sodium phosphate: An in vivo study,” J. Ther. Ultrasound 2, 6 (13pp.) (2014). 10.1186/2050-5736-2-6 [PMC free article] [PubMed] [Cross Ref]
9. Zderic V., Clark J. I., Martin R. W., and Vaezy S., “Ultrasound-enhanced transcorneal drug delivery,” Cornea 23, 804–811 (2004).10.1097/01.ico.0000134189.33549.cc [PubMed] [Cross Ref]
10. Zderic V., Clark J. I., and Vaezy S., “Drug delivery into the eye with the use of ultrasound,” J. Ultrasound Med. 23, 1349–1359 (2004). [PubMed]
11. Lamy R., Chan E., Zhang H., Salgaonkar V. A., Good S. D., Porco T. C., Diederich C. J., and Stewart J. M., “Ultrasound-enhanced penetration of topical riboflavin into the corneal stroma,” Invest. Ophthalmol. Visual Sci. 54, 5908–5912 (2013).10.1167/iovs.13-12133 [PMC free article] [PubMed] [Cross Ref]
12. Nuritdinov V. A., “Phonophoresis and cavitation,” Vestn. Oftalmol. 1, 56–58 (1981). [PubMed]
13. Tsok R. M., Gereliuk I. P., Tsok O. B., and Kaminskii I. M., “The effect of ultrasonic oscillations of different frequencies on radionuclide accumulation in the eye tissues,” Oftalmol. Zh. 1, 46–49 (1990).[PubMed]
14. Cheung A. C. Y., Yu Y., Tay D., Wong H. S., Ellis-Behnke R., and Chau Y., “Ultrasound-enhanced intrascleral delivery of protein,” Int. J. Pharm. 401, 16–24 (2010).10.1016/j.ijpharm.2010.09.001 [PubMed][Cross Ref]
15. Suen W. L., Wong H. S., Yu Y., Lau L. C., Lo A. C., and Chau Y., “Ultrasound-mediated transscleral delivery of macromolecules to the posterior segment of rabbit eye in vivo,” Invest. Ophthalmol. Visual Sci.26, 4358–4365 (2013).10.1167/iovs.13-11978 [PubMed] [Cross Ref]
16. Huang D., Wang L., Dong Y., Pan X., Li G., and Wu C., “A novel technology using transscleral ultrasound to delivery protein loaded nanoparticles,” Eur. J. Pharm. Biopharm. 88, 104–115 (2014).10.1016/j.ejpb.2014.04.011 [PubMed] [Cross Ref]
17. Razavi A., Clement D., Fowler R. A., Birer A., Chavrier F., Mestas J. L., Romano F., Chapelon J. Y., Begle A., and Lafon C., “Contribution of inertial cavitation in the enhancement of in vitro transscleral drug delivery,” Ultrasound Med. Biol. 40, 1216–1227 (2014).10.1016/j.ultrasmedbio.2013.12.032 [PubMed][Cross Ref]
18. Gwon A., “The rabbit in cataract/IOL surgery,” in Animal Models in Eye Research Panagiotis, 1st ed., edited by Tsonic A., editor. (Elsevier, San Diego, CA, 2008), pp. 184–199.
19. Werner L., Chew J., and Mamalis N., “Experimental evaluation of ophthalmic devices and solutions using rabbit models,” Vet. Ophthalmol. 9, 281–291 (2006).10.1111/j.1463-5224.2006.00495.x [PubMed][Cross Ref]
20. Missel P. J., Horner M., and Muralikrishnan R., “Simulating dissolution of intravitreal triamcinolone acetonide suspensions in an anatomically accurate rabbit eye model,” Pharm. Res. 27, 1530–1546 (2010).10.1007/s11095-010-0163-1 [PMC free article] [PubMed] [Cross Ref]
21. Berry M. and Easty D. L., “Isolated human and rabbit eye: Models of corneal toxicity,” Toxicol. In Vitro 7, 461–464 (1993).10.1016/0887-2333(93)90047-9 [PubMed] [Cross Ref]
22. Duck F. A., in Physical Properties of Tissue: A Comprehensive Reference Book (Academic, London, 1990), Chap. 4, pp. 73–124.
23. Su X., Vesco C., Fleming J., and Choh V., “Density of ocular components of the bovine eye,” Optom. Vision Sci. 86(10), 1187–1195 (2009).10.1097/opx.0b013e3181baaf4e [PubMed] [Cross Ref]
24. Opie N. L., Burkitt A. N., Meffin H., and Grayden D. B., “Thermal heating of a retinal prosthesis: Thermal model and in-vitro study,” in Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2010), pp. 1597–1600.10.1109/IEMBS.2010.5626670 [PubMed][Cross Ref]
25. de Korte C. L., van der Steen A. F., and Thijssen J. M., “Acoustic velocity and attenuation of eye tissues at 20 MHz,” Ultrasound Med. Biol. 20, 471–480 (1994).10.1016/0301-5629(94)90102-3 [PubMed][Cross Ref]
26. Herman B. A. and Harris G. R., “Theoretical study of steady-state temperature rise within the eye due to ultrasound insonation,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 46, 1566–1574 (1999).10.1109/58.808882 [PubMed] [Cross Ref]
27. Holmberg A., “The temperature of the eye during the application of hot packs, and after milk injections,” Acta Ophthalmol. 30(4), 347–364 (1952).10.1111/j.1755-3768.1952.tb00011.x [PubMed][Cross Ref]
28. Christensen D. A., Ultrasonic Bioinstrumentation (John Wiley & Sons, New York, NY, 1988), pp. 91–94.
29. National Council on Radiation Protection and Measurements (NCRP), “Exposure criteria for medical diagnostic ultrasound: I. Criteria based on thermal mechanisms,” Recommendations of the National Council on Radiation Protection and Measurements, NCRP Report No.113 (NCRP, Bethesda, MD, 1992), pp. 84–86.
30. Nyborg W. L., “Solutions of the bio-heat transfer equation,” Phys. Med. Biol. 33(7), 785–792 (1988).10.1088/0031-9155/33/7/002 [PubMed] [Cross Ref]
31. Soneson J. E. and Myers M. R., “Thresholds for nonlinear effects in high-intensity focused ultrasound propagation and tissue heating,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 57, 2450–2459 (2010).10.1109/TUFFC.2010.1711 [PubMed] [Cross Ref]
32. Curra F. P., Mourad P. D., Khokhlova V. A., Cleveland R. O., and Crum L. A., “Numerical simulations of heating patterns and tissue temperature response due to high-intensity focused ultrasound,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control 47, 1077–1089 (2000).10.1109/58.852092 [PubMed] [Cross Ref]
33. Damianou C. A., Sanghvi N. T., Fry F. J., and Maass-Moreno R., “Dependence of ultrasonic attenuation and absorption in dog soft tissues on temperature and thermal dose,” J. Acoust. Soc. Am.102(1), 628–634 (1997).10.1121/1.419737 [PubMed] [Cross Ref]
34. Abboud N. N., Wojcik G. L., Vaughan D. K., Mould J., Powell D. J., and Nikodym L., “Finite element modeling for ultrasonic transducers,” Proc. SPIE 3341, 19 (24pp.) (1998). 10.1117/12.308015 [Cross Ref]
35. Wojcik G. L., Mould J. C., and Carcione L. M., “Transducer and nonlinear tissue propagation simulations,” The Proceedings of 1999 International Mechanical Engineering Congress and Exposition(1999).
36. O’Brien W. D. Jr., “Ultrasound-biophysics mechanisms,” Prog. Biophys. Mol. Biol. 93(1-3), 212–255 (2007).10.1016/j.pbiomolbio.2006.07.010 [PMC free article] [PubMed] [Cross Ref]
37. Pennes H. H., “Analysis of tissue and arterial blood temperatures in the resting human forearm,” J. Appl. Phys. 1, 93–122 (1948). [PubMed]
38. Wang S., Mahesh S. P., Liu J., Geist C., and Zderic V., “Focused ultrasound facilitated thermo-chemotherapy for targeted retinoblastoma treatment: A modeling study,” Exp. Eye Res. 100, 17–25 (2012).10.1016/j.exer.2012.04.009 [PubMed] [Cross Ref]
39. European Federation of Societies for Ultrasound in Medicine and Biology, European Committee for Medical Ultrasound Safety Bylaw, Newsletter 12, 1998.
40. US FDA, Guidance for Industry and FDA Staff Information for Manufacturers Seeking Marketing Clearance of Diagnostic Ultrasound Systems and Transducers, Document issued on September 9, 2008.
41. AIUM (American Institute of Ultrasound in Medicine), “Consensus report on potenital bioeffects of diagnostic ultrasound. Executive summary,” J. Ultrasound Med. 27, 503–515 (2008). [PubMed]
42. Nell D. M. and Myers M. R., “Thermal effects generated by high-intensity focused ultrasound beams at normal incidence to bone surface,” J. Acoust. Soc. Am. 127, 549–559 (2010).10.1121/1.3257547[PubMed] [Cross Ref]
43. Wang S., Frenkel V., and Zderic V., “Optimization of pulsed focused ultrasound exposures for hyperthermia applications,” J. Acoust. Soc. Am. 130(1), 599–609 (2011).10.1121/1.3598464 [PubMed][Cross Ref]
44. Ensminger D. and Stulen S. B., Ultrasonic: Data, Equations, and Their Practical Uses (CRC, Taylor & Francis Group, Boca Raton, FL, 2008).
45. Ahmadi F., McLoughlin I. V., Chauhan S., and terHaar G., “Bio-effects and safety of low-intensity, low-frequency ultrasonic exposure,” Prog. Biophys. Mol. Biol. 108, 119–138 (2012).10.1016/j.pbiomolbio.2012.01.004 [PubMed] [Cross Ref]
46. Edwards M. J., “Congenital defects in guinea pigs following induced hyperthermia during gestation,” Arch. Pathol. 84(1), 42–48 (1967). [PubMed]
47. Guy A. W., Lin J. C., Kramar P. O., and Emery A. F., “Effect of 2450-MHz radiation on the rabbit eye,” IEEE Trans. Microwave Theory Tech. 23(6), 492–498 (1975).10.1109/TMTT.1975.1128606 [Cross Ref]
48. Elder J. A., “Ocular effects of radiofrequency energy,” Bioelectromagnetics 24(6), S148–S161 (2003).10.1002/bem.10117 [PubMed] [Cross Ref]
49. Yamaguchi K., Barbe M. F., Brown I. R., and Tytell M., “Induction of stress (heat shock) protein 70 and its mRNA in rat corneal epithelium by hyperthermia,” Curr. Eye Res. 9, 913–918 (1990).10.3109/02713689008999563 [PubMed] [Cross Ref]
50. Huang C. C., Chen R., Tsui P. H., Zhou Q., Humayun M. S., and Shung K. K., “Measurements of attenuation coefficient for evaluating the hardness of a cataract lens by a high-frequency ultrasonic needle transducer,” Phys. Med. Biol. 54(19), 5981–5994 (2009).10.1088/0031-9155/54/19/021 [PMC free article][PubMed] [Cross Ref]
51. Raitelaitiene R., Paunksnis A., Ivanov L., and Kurapkiene S., “Ultrasounic and biochemical evaluation of human diabetic lens,” Medicina 41(8), 641–648 (2005). [PubMed]
52. Charrel T., Aptel F., Birer A., Chavrier F., Romano F., Chapelon J. Y., Denis P., and Lafon C., “Development of a miniaturized HIFU device for glaucoma treatment with conformal coagulation of the ciliary bodies,” Ultrasound Med. Biol. 37(5), 742–754 (2011).10.1016/j.ultrasmedbio.2011.01.017[PubMed] [Cross Ref]
53. Barnett S. B., Rott H., ter Haar G. R., Ziskin M. C., and Maeda K., “The sensitivity of biological tissue to ultrasound,” Ultrasound Med. Biol. 23, 805–812 (1997).10.1016/S0301-5629(97)00027-6 [PubMed][Cross Ref]
54. Silverman R. H., Lizzi F. L., Ursea B. G., Cozzarelli L., Ketterling J. A., Deng C. X., Folberg R., and Coleman D. J., “Safety levels for exposure of cornea and lens to very high-frequency ultrasound,” J. Ultrasound Med. 20(9), 979–986 (2001). [PubMed]
55. Hariharan P., Myers M. R., and Banerjee R. K., “HIFU procedures at moderate intensities—Effect of large blood vessels,” Phys. Med. Biol. 52(12), 3493–3513 (2007).10.1088/0031-9155/52/12/011 [PubMed][Cross Ref]
56. Moros E. G., Novak P., Straube W. L., Kolluri P., Yablonskiy D. A., and Myerson R. J., “Thermal contribution of compact bone to intervening tissue-like media exposed to planar ultrasound,” Phys. Med. Biol. 49(6), 869–886 (2004).10.1088/0031-9155/49/6/001 [PubMed] [Cross Ref]
57. Hughes M. O., “A pictorial anatomy of the human eye/anophthalmic socket: A review for ocularists,” J. Ophthalmic Prosthetics, 51–63(2007), available at http://artificialeyeclinic.com/6Hughes.pdf.
58. Wu J. R. and Du G. H., “Temperature elevation generated by a focused Gaussian ultrasonic beam at a tissue-bone interface,” J. Acoust. Soc. Am. 87(6), 2887–2891 (1990).10.1121/1.399065 [PubMed][Cross Ref]
59. Ohwatashi A., Ikeda S., Harada Y., Kamikawa Y., Yoshida A., Inoue K., Yanagida N., Fukudome K., Kiyama R., Ohshige T., and Maeda T., “Temperature changes caused by the difference in the distance between the ultrasound transducer and bone during 1 MHz and 3 MHz continuous ultrasound: A phantom study,” J. Phys. Ther. Sci. 27, 205–208 (2015).10.1589/jpts.27.205 [PMC free article] [PubMed][Cross Ref]