- Open Access
Acoustic and thermal characterization of agar based phantoms used for evaluating focused ultrasound exposures
© The Author(s). 2017
- Received: 4 January 2017
- Accepted: 1 March 2017
- Published: 1 June 2017
This study describes a series of experimental work completed towards characterizing candidate materials for fabricating brain and muscle tissue mimicking phantoms.
The acoustic speed, attenuation, impedance, thermal diffusivity, specific heat and thermal conductivity were measured.
The resulting brain (2% w/v agar-1.2% w/v Silica Dioxide-25%v/v evaporated milk) and muscle tissue recipe (2% w/v agar-2% w/v Silica Dioxide-40%v/v evaporated milk) introduced a total attenuation coefficient of 0.59 dB/cm-MHz and 0.99 dB/cm-MHz respectively. Acrylonitrile Butadiene Styrene (ABS) possessed an attenuation coefficient of 16 dB/cm at 1 MHz which was found within the very wide range of attenuation coefficient values of human bones in literature. The thermal conductivity of the brain tissue phantom was estimated at 0.52 W/m°C and at 0.57 W/m.°Cfor the muscle. These values demonstrated that the proposed recipes conducted heat similar to the majority of most soft tissues found from bibliography. The soft tissue phantoms were also evaluated for their thermal repeatability after treating them repeatedly at different locations with the same sonication protocol and configuration. The average coefficient of variation of the maximum temperature at focus between the different locations was 2.6% for the brain phantom and 2.8% for the muscle phantom.
The proposed phantom closely matched the acoustic and thermal properties of tissues. Experiments using MR thermometry demonstrated the usefulness of this phantom to evaluate ultrasonic exposures.
Phantoms of tissue mimicking materials (TMM) are valuable tools for translating knowledge towards developing ultrasound applications. The effort of researchers in this area is concentrated in the phantom materials used to the mimicked tissue’s acoustic properties. Acoustic properties control the propagation of ultrasound through a medium and therefore a close matching is a prerequisite before translating knowledge reliably to the clinical setting.
A large variety of different TMM is found in literature for replicating soft tissue. Several low cost gelatin gel based recipes have been introduced for mimicking accurately soft tissue for imaging purposes that differ between them in the selection of the additive materials used for controlling acoustic scattering and speed [1–3]. Amongst the reported disadvantages of gelatin gels is their low melting point (35 °C). Unless treated with preservatives gelatin gels are susceptible to microbial and bacterial invasion and difficult to achieve a uniform distribution of the chosen scattering material.
Agar based gels are cheap and easy to produce, durable in high temperatures, nontoxic and disposable but they lack long term stability and repeatability of acoustic properties measurement over time [4–6]. Under ideal storage conditions agar gels can remain stable up to two and a half years  and can serve as a perfect replacement for gelatin gels which suffer for temperature dependent structural instability .
Polyurethane gels have also been used as alternatives to tissue substitutes. The molecular design of these gels is rather complex and very difficult to standardize. In a reported study a polyurethane TMM phantom was produced with an attenuation coefficient and speed of sound in the lower range of soft tissue values .
Polyacrylamide gels have been developed by crosslinking copolymerization of acrylamide and N,N′-methylene bisacrylamide (bis) in an aqueous solution . Polyacrylamide phantoms were doped with bovine serum albumin (BSA) known to enhance acoustic absorption. Attenuation was found to vary linearly with BSA concentration. The gels were optically transparent with adjustable acoustic properties in the lower range of human soft tissues. Fabrication of polyacrylamide gels should be done with caution since it involves handling acrylamide which a known neurotoxin. Acrylamide has been classified as probable carcinogen following evidence from animal studies. A relatively cheaper alternative of BSA doped polyacrylamide gel was described by Takegami et al. , where BSA was replaced with egg white. Egg white possesses high protein content and enhances acoustic attenuation via the thermal denaturation process. High egg white concentrations gels induced increased levels of acoustic attenuation and speed compared to the BSA counterparts. Commercially available polyacrylamide gel phantoms manufactured by Onda Corporation are widely used for characterizing transducer geometry, frequency and power profiles. The synthetic gel is transparent and white three dimensional lesions are formed when temperature exceeds 70 °C, making it easy to assess lesion growth, position and shape over time. They are suitable tools for performing quality control tests on HIFU equipment and treatment protocol testing but have fixed acoustic properties and geometry.
N-isopropylacrylamide (NIPAM) gels were designed to become opaque above a threshold temperature, which can be controlled by altering the concentration of acrylic acid (AAC) . By testing different concentrations of AAC, NIPAM based gels were able to match the acoustic and thermal properties of different swine tissues. The NIPAM gels are superior to polyacrylamide BSA or egg white based phantoms since they are reusable. Unlike these phantoms where lesion formation depends on the opaqueness created by protein denaturation which is an irreversible effect, the NIPAM thermal lesions gradually disappear and the phantom gel can be reused.
A polyvinyl alcohol cryogel (PVAC) tissue mimicking phantom gel was presented by Surry et al.  suitable for magnetic resonance (MR) and ultrasound (US) imaging. The gel was solidified through a freeze-thaw cycle process and was characterized for the speed of sound which was found in the range from 1520 to 1540 m/s. The gel’s attenuation coefficients were in the range of 0.075–0.28 dB/cm.MHz. T1 and T2 relaxation values were found to be 718–1034 ms and 108–175 ms, respectively. Reinertsen et al.  designed a multi-layer phantom made out of PVAC to characterize and correct for brain shift during image guided surgery. Each gel in this study was treated with different number of freeze-thaw cycles to control its mechanical and imaging characteristics.
Magnetic Resonance guided Focused Ultrasound Surgery (MRgFUS) is an emerging therapeutic modality that meets a very wide spectrum of applications in clinical medicine. The purpose of this study is dedicated in describing the methodology of characterizing acoustic and thermal properties of agar and Acrylonitrile Butadiene Styrene (ABS) materials which are used as mimicking phantoms suitable for testing MRgFUS thermal protocols [14, 15]. A novel approach of enhancing acoustic attenuation by doping agar based gels with materials that allow independent control of acoustic absorption and scattering was assessed. The suitability of using ABS as a bone replica was also characterized for its acoustic properties. ABS is a very convenient material to consider since it is used in rapid prototyping of 3D models. The introduction of a bone mimicking phantom in composite phantoms that include also the targeted soft tissue phantom is very important. The constructive and destructive thermal effects that result from the interaction of bone with ultrasound in various MRgFUS applications can be explored under controlled conditions and different configurations. Thermal properties characterization is also crucial before translating results to the clinic since the efficacy of MRgFUS depends on the conversion of acoustic energy to heat and its distribution to the targeted tissue.
Estimation of acoustic properties using immersion techniques
In order to assess the suitability of the materials used to construct tissue mimicking phantoms, a method for assessing their acoustic properties is needed. The most relevant acoustic properties for phantoms designed for MRgFUS is the attenuation coefficient and propagation speed. The first property controls the degree of acoustic energy converted to heat and therefore a close matching with the attenuation coefficient of the replicated tissue is desirable. Acoustic speed along with mass density set the reflection coefficient at every interface and consequently the actual fraction of incident acoustic energy propagating through the phantom is dependent on it. Pulse echo and transmission through methods are broadly used for characterizing the attenuation coefficient and acoustic speed of ultrasound in specimens. They involve submerging the specimen under examination in a tank filled with degassed liquid and all measurements are performed with immersion ultrasonic transducers. The most frequently used modern techniques found from literature are presented below. The techniques differ in experimental configuration, the assumptions taken, the type of signals measured and their advantages.
Transmission through method for measuring acoustic attenuation coefficient
The expression above contains no reflection or transmission coefficient. The coefficients cancel each other out when we calculate the ratio of intensities as a function of the measured voltages for the two different thicknesses.
Pulse echo method for measuring acoustic attenuation coefficient
The authors described equations of the acoustic wave’s intensity arriving at the transducer face for two different scenarios. First the transducer (T) is immersed in tank of fixed dimensions and on the opposite side of the tank a perfect reflector is placed. The reflector can be any flat and smooth material with a high acoustic impedance like aluminum or plastic. The transducer measures the signal intensity (I w ) arriving in the absence of a specimen in the path of the beam. The intensity of the signal is dependent only on the attenuation coefficient of the immersion liquid and the distance travelled.
In the second scenario, a specimen of thickness L is positioned in the pathway of the beam. The transducer records echoes rising from reflections produced by every interface met along the wave’s pathway. The echo returning from the front face of the specimen and travelling a distance 2x 1 is denoted as intensity I 3 , while the signal with intensity I 12 travels the full pathway of distance 2(x 1 + L + x 2 ). A system of equations describing the reflected echoes intensities at every interface (I 1 to I 12 ) is solved and by using multiple substitutions we end up in a simple system of two equations containing two unknown variables.
Once again I 12 and I w are deduced from the transducer’s voltage signals whereas r 2 is calculated from Eq. 2. The attenuation coefficient α 2 is calculated using Eq. 3. The single transducer method is valid if the reflection and transmission coefficients at both faces of the specimen are equal.
Estimation of attenuation coefficient variation for agar gels doped with different concentrations of SiO2 using transmission through technique
Agar gels (granulated form, microbiology grade– Merck Millipore, Darmstadt, Germany) of a 2% w/v doped with silica dioxide powder of different concentrations (0%, 1%, 2%, 3% w/v) were prepared. The silica particles size ranged between 0.5 and 10 μm (Silica Dioxide, Sigma-Aldrich, St. Louis, Missouri, United States). The variable thickness technique was used because of its simplicity and because it did not require determination of reflection coefficient. For each silica dioxide concentration a set of two samples of different thicknesses (16 mm and 26 mm) were prepared. The samples were poured in plastic 3D printed plastic containers and were left to solidify overnight. Custom made plastic holders were designed and manufactured to accommodate the specimen containers of different thicknesses (16 and 26 mm) in between the immersion transmitter and receiver. The holder had two cylindrical cavities that could fit tightly the two 10 mm circular 3.5 MHz transducers (Etalon, ESN-410-SCBI) facing each other while the specimen was positioned in between and with side openings perpendicular to the acoustic beam’s pathway emitted by the transmitting transducer. The −3 dB bandwidth of the transducers is 1.8 MHz. The transmitter (T/R) and receiver (R) were connected via coaxial cables to a Panametrics pulser/receiver (Panametrics 500PR, Olympus Corp, Tokyo, Japan).
The signal of the receiving transducer was fed to a 20 MHz oscilloscope (Hameg HM203-7, HAMEG Instruments GmbH, Mainhausen, Germany) to observe voltage over time. The attenuation coefficient in dB/cm was calculated using Eq. 1 for every set of gels. The coefficient for different silica concentrations was normalized to more useful units of dB/cm.MHz by dividing with the frequency (3.5 MHz). This approach resulted to almost linear dependence of attenuation of with frequency (n = 1.08) of the prescribed heterogeneous phantom. A similar approach was used in a study by Nam et al. , where attenuation data induced by glass bead scatterers of similar size (10–100 μm) in tissue mimicking phantoms fitted almost linearly in the frequency range between 2.5 and 10 MHz.
Estimation of attenuation coefficient variation for agar gels doped with different concentrations of evaporated milk using transmission through technique
A recipe described by Madsen et al. was used , where evaporated milk was added to agar gels to produce a solid gel of very low scatter tissue mimicking material. Evaporated milk is a dehydrated version of fresh milk, where approximately 50% of water is removed. In the absence of silica dioxide from the gel any drop in the intensity of the acoustic field could be attributed primarily to acoustic absorption by the evaporated milk. Four sets of agar-milk gel samples of different milk concentrations (10%, 20%, 40% and 50% v/v) in a 2% w/v agar based gel were prepared. The evaporated milk used was a product by Friesland Campina, Marousi, Greece (NOUNOU condensed milk). According to the manufacturer’s nutritional datasheet, 100 ml of milk included 4.2 g of fats and 3.5 g of proteins. The agar-milk gel was poured and left to solidify overnight in the custom made plastic sample containers (16 mm and 26 mm). The sample containers were used to determine the attenuation coefficient from each agar-milk concentration sample.
Linear combination of the tested attenuating agents for creating acoustically realistic soft tissue phantom recipes
Recipes for a brain and a muscle mimicking gel phantom were deduced from results based on agar gel attenuation measurements doped with the two additives in previous sections. The targeted values of αt, αsc and αabs for human brain [19, 20] and muscle tissue [21, 22] were extracted from literature.
Estimation of attenuation coefficient of Acrylonitrile Butadiene Styrene (ABS) samples using transmission through technique
ABS was tested as the candidate material for replicating bone tissue. Two square plates of ABS specimens of different thicknesses, 2.5 mm and 5 mm respectively, were produced (4 × 4 cm) using a rapid prototyping machine (Stratasys, Fortus FDM 400mc, Eden Prairie, Minnesota, USA). A solid interior printing style was used to fill up the model completely with raw material without any air gaps. Attenuation from the plastic was expected to be large and therefore in order to measure adequately a signal, specimens’ thicknesses were kept small. The ABS plates were secured tightly in the rails of a custom made holder approximately midway between the transmitter and receiver. This way it was ensured that the beam leaving the transmitter was incident at 90° to the specimen, and only longitudinal propagation was considered. The setup used was identical to the one used while testing the attenuation of agar gels doped with various additives.
Estimation of acoustic speed in brain and muscle phantom using pulse echo technique
The pulse echo immersion technique was used for estimating the acoustic speed of the brain and muscle agar gel recipes. The method involved one transducer (Etalon, ESN-410-SCBI) operating at a central frequency of 3.5 MHz. Specimens of each recipe with 2.6 cm thickness were prepared and molded in custom made containers similar to the ones used for the attenuation measurements. The transducer-specimen setup was immersed in a tank filled with degassed water.
Specimens of both gel recipes were prepared and molded inside the 2.6 cm containers used for the attenuation measurements. A thicker sample was selected to increase time difference for the echo to travelling echo and produce a more accurate estimation for the acoustic speed in each sample.
Estimation of acoustic speed in ABS samples using transmission through technique
Estimation of the acoustic speed in ABS specimens using the pulse echo technique was not possible. The main problem with ABS was that only echoes from the front wall of the specimen were detected (E 1 ) by the transceiver and none from the back wall (E 2 ). The main reason for not detecting the reflection echo was due the disturbance of the propagating wave from the inner layers of the specimen and heavy attenuation. Instead transmission through method was used to determine ABS acoustic velocity by observing the change in the time of flight of the transmission signal (S) detected by the receiver. The acoustic speed of the agar-based phantom was also measured using the transmission technique, just to compare the estimate with the pulse-echo method. The difference in acoustic speed using the two methods was within the measurement error.
A specimen of intermediate thickness was used (d 2 = 1 cm) to balance between heavy attenuation of attenuation of the transmitted signal by ABS (approximately −56 dB at 3.5 MHz) and sufficient change in the time of flight.
Mass density measurements using water volume displacement method
The aforementioned phantom recipes were tested to quantify for their mass density. Samples of 100 ml volume for the gel recipe were prepared. The gels were sliced in approximately equal volumes, with dimensions small enough to fit inside a volumetric tube. Each piece was first weighed with a high precision electronic scale (±0.01 g) and then its volume was deduced by measuring water displacement in a volumetric tube (±1 ml). The greatest source of error recognized in these measurements was the precision of the volumetric tube therefore we used specimens as large as possible to minimize the fractional error in volume measurements. Six specimens from the same batch were taken and the average mass density in g/cm was calculated.
Estimation of soft tissue phantoms thermal properties using a noninvasive MR thermometry technique
The traditional methods for measuring thermal conductivity (W/m.°C) of a material can be categorized in steady state and transient methods. In steady state methods measurements are performed while the temperature of the material under examination does not change over time, whereas in transient techniques measurements are done while heating the material. Both methods require specialized equipment like heat sources and sensors of various geometries or well-engineered experimental setups. The aforementioned methods are partially invasive since they require embedding temperature sensors inside the material under examination affecting its structural integrity.
D is the thermal diffusivity coefficient in cm2/s. Thermal diffusivity determines the speed at which heat will flow from the source to colder surrounding. It is expressed as the ratio of thermal conductivity divided by the product of specific heat capacity and density.
The method described above was used to quantify the thermal properties of the two soft tissue phantom recipes (brain and muscle). A spherically focused ultrasound transducer (Sonic Concepts, Inc., Bothell, Washington, USA) driven by a 750 W amplifier (JJ&A Instruments, Duvall, WA, USA) was used to sonicate the gel phantoms and raise the temperature at focus. The transducer consisted of a single element piezoelectric crystal of 4 cm diameter and with a focal length of 95 cm.
The mean Gaussian radius for each point in time was calculated by averaging the radii of two orthogonal temperature profiles which were 15 pixels long (approximately 15 mm) and centered over the maximum temperature pixel.
Each of the phantom gels was molded inside a rectangular container with an open top to allow propagation of ultrasound. The transducer and gels were positioned inside a plastic tank filled up with degassed water. Samples were heated using the same sonication protocol (Acoustic Power: 25 W, 60 s of sonication duration). Acoustic power conversion efficiency was calculated using previously acquired radiation force calibration data for this particular transducer. The efficiency was calculated at 50% conversion of electric to acoustic power. The phantoms were targeted in their center in order to maintain uniform temperature gradients in all directions. The targeted depth was not exactly the same but this was not important since according to Cheng et al. , conductivity only affected the rate of the radial expansion and not the amplitude of the Gaussian profile.
MR temperature imaging was used to monitor temperature elevation and drop during the exposure. A flexible surface imaging coil (GPFLEX coil by General Electric, Milwaukee, USA) was positioned under the water tank. The setup was positioned at the isocentre of a 1.5 Tesla MRI scanner (General Electric Signa Excite, Milwaukee, USA). Temperature changes were calculated using the proton resonance frequency shift method. The acquisition protocol used for thermometry is presented in 2D SPGR sequence: repetition time (TR): 38.5 ms, echo time (TE): 20 ms, receiver bandwidth (rBW): 15 kHz, Matrix: 128 × 128 pixels, Slice Thickness: 5 mm, Number of excitation (NEX): 1, displayed field of view (DFOV): 25 × 25 cm2. The thermometry slice was prescribed in a plane perpendicular to sound propagation and at the level of the focus. Following analysis a single thermal map was produced every 12 s.
The heat capacity of each phantom was estimated by using a weighted sum of the heat capacity of the two main ingredients, which were water and evaporated milk. This was a reasonable assumption since both together consisted for more than 95% of the gel’s mass. From literature it was found that the nominal heat capacities for water is 4.19 J/g.°C and for evaporated milk 3.94 J/g.°C .
Thermal repeatability of the brain and muscle mimicking phantoms treated with focused ultrasound
The thermal repeatability performance of each TMM phantom was assessed with MR thermometry. Each phantom was positioned for a top to bottom sonication inside a water tank filled with degassed water. The phantoms were sonicated using a single element MR compatible HIFU transducer (Sonic Concepts, Bothell, Washington, USA) operating at 1.14 MHz. Five Sonications of 25 W-60 s were done in different locations in each phantom.
Qualitative evaluation of focused ultrasound heating dependence with target depth
Sonication protocols used for evaluating depth phantom
Acoustic Power (W)
Temperature measurement using a thermocouple
A data acquisition board (6251 DAQ, National Instruments, Texas, USA) was used to measure the temperature. An analogue input of the board was used to capture the temperature. An Omega (M2813-1205, OMEGA Engineering, INC. Stamford, Connecticut, USA) voltage to temperature converter was used to measure temperature using a software written in MatLab (The Mathworks Inc., Natick, MA). A thermocouple (Omega engineering) was placed in the material under test in order to measure temperature elevation at the focal point. The size of the thermocouple was chosen to be 50 μm, so that the interaction with the beam of ultrasound was minimized. The DAQ station sampled temperature measurements every 1 s.
Using immersion techniques the dependence of the attenuation coefficient for a range of concentrations of silica dioxide and evaporated milk doped in 2% w/v agar gels was examined. The selection of these two materials was done to allow independent scatter and absorption induced attenuation control.
Data from attenuation measurements were linearly fitted and the slope was used to calculate the appropriate concentration for each additive depending on the acoustic characteristics of designed tissue mimicking phantom. It was found that the contribution of silica to attenuation (mostly scattering) was 0.28 ± 0.03 dB/cm-MHz per % of silica. The contribution of evaporated milk to attenuation (mostly absorption) was 0.01 dB/cm-MHz per % of evaporated milk. The factors produced from the slopes of the data were used to calculate appropriate recipes for the brain and muscle phantom. It was concluded that based on typical human tissues acoustic properties found from literature the appropriate recipes for the brain and muscle phantoms were Agar 2% w/v-Silica Dioxide 1.2% w/v-Evaporated Milk 25% v/v and Agar 2% w/v-Silica Dioxide 2.1% w/v-Evaporated Milk 40% v/v respectively. The calculated attenuation coefficients of the brain phantom recipe was 0.59 ± 0.05 dB/cm-MHz and 0.99 ± 0.08 dB/cm-MHz for the muscle phantom.
The attenuation coefficient of a common thermoplastic material ABS-M30 (Stratasys Ltd) was investigated to determine its suitability as a bone replicating material for focused ultrasound applications. The same technique was used as for the characterization of agar gels and it was found that the attenuation coefficient was 16.01 ± 6.18 dB/cm-MHz which was well within the very wide range of equivalent values of bone from literature. This large variation in the ABS attenuation measurement was attributed mostly to some variability in the texture of the printed samples that it was impossible to control.
Summary of the acoustic properties of soft and bone tissue mimicking materials
Brain Tissue Mimicking Agar Gel
Agar 2% (w/v)
+ Silica Dioxide 1.2% (w/v)
+ Evaporated Milk 25% (v/v)
Muscle Tissue Mimicking Agar Gel
Agar 2% (w/v)
+ Silica Dioxide 2.1% (w/v)
+ Evaporated Milk 40% (v/v)
Bone Mimicking Material
ABS-M30 (Stratasys Ltd)
Scatter enhancing agent
0.34 ± 0.04
0.59 ± 0.07
Absorption enhancing agent (dB/cm-MHz)
0.25 ± 0.03
0.40 ± 0.04
0.59 ± 0.05
0.99 ± 0.08
16.01 ± 6.18
Acoustic speed (m/s)
1485 ± 12
1529 ± 13
2048 ± 79
Mass Density (g/cm3)
1.05 ± 0.01
1.07 ± 0.01
1.56 ± 0.02
1.64 ± 0.02
2.13 ± 0.08
The linear dependence for both sets of data between R 2 (t) and time demonstrated that the radial expansion of the temperature profile “decelerates” with time. The two tested recipes resulted in slightly different slopes as a result of their difference in thermal conductivity. Thermal conductivity was estimated by equating the slopes of the fitted data and the right hand side of Eq. 11. Mass density (ρ t ) for each recipe was calculated previously using the water displacement technique. The weighted heat capacity for the brain phantom (75% v/v water-25% v/v evaporated milk) was calculated at 4.13 J/g.°C and for the muscle phantom (60% v/v water - 40% v/v evaporated milk) 4.09 J/g.°C.
By substituting the above to Eq. 11, the thermal conductivities of the brain and muscle phantom were estimated at 0.52 ± 0.06 W/m. °C and 0.57 ± 0.10 W/m. °C respectively. Thermal diffusivity (D) which is a thermal property derived by dividing conductivity with density and specific heat capacity, describes how quickly a material reacts to a change in temperature. The calculated diffusivity (D) for the brain phantom was 0.0012 ± 0.0001 cm2/s and for the muscle phantom 0.0013 ± 0.0001 cm2/s. Errors in conductivity and diffusivity coefficients were estimated by considering the error in slope of the fitted data.
This paper described the work done for characterizing important acoustic and thermal properties of materials destined to be used for constructing tissue mimicking phantoms for testing focused ultrasound thermal protocols. The soft tissue replicas were agar gel matrices with additives to control independently from each other, the two main acoustic energy loss mechanisms (scattering and absorption) of sound energy propagating through biological tissue. Agar gels were convenient to work with since they possess a high melting temperature, they are non-toxic and easy to prepare and can be prepared with relatively low cost.
Two calibration curves were calculated by fitting a linear model that characterized attenuation variation with the concentration of either silica dioxide or evaporated milk embedded in agar gels of 2% weight to volume concentration. It was assumed that silica dioxide primarily induced only Rayleigh scattering due to the small size of particles compared to ultrasound’s wavelength. Evaporated milk which was introduced as a very low scattering material, was the primary source of acoustic absorption. For the range of the concentrations tested, the agar-silica dioxide gels demonstrated a linear scattering induced attenuation coefficients of up to 0.85 dB/cm.MHz. Compared with the study of Partanen et al. , silica produced a higher degree of attenuation for the same concentration. Similarly agar-evaporated milk gels transmission through assessment resulted in absorption induced attenuation coefficients of up to 0.38 dB/cm.MHz. The slopes of the two calibration curves were used to interpolate and calculate the required concentration for each of the two additive materials to deliver a prescribed total attenuation coefficient while independently controlling the contributions of scattering and absorption.
Based on these calibration curves two soft tissue recipes were prepared. The brain recipe (2% w/w agar, 1.2% w/w SiO2, 25% v/v evaporated milk) combined the two additives previously tested to produce a final product with a total attenuation coefficient (0.59 dB/cm.MHz) within the range of bibliographic data [19, 25, 26]. The relative contributions of scattering and absorption of 0.34 dB/cm.MHz and 0.25 dB/cm.MHz respectively were achieved according to attenuation and absorption measurements in mammalian tissues presented by Goss et al.  and Sehgal et al. . The muscle phantom recipe (2% w/w agar, 2% w/w SiO2, 40% v/v evaporated milk) was designed with an attenuation coefficient equal to 0.99 dB/cm.MHz which agreed with values (0.5–4.1 dB/cm.MHz) found from bibliography [21, 22]. The relatively wide range of attenuation coefficients is due to the fact that muscles are highly anisotropic tissues since they have a strong directional distribution of fibers. Experiments exploring the anisotropy in acoustic speed, attenuation and backscattering in rodents skeletal muscles with fibers orientated at 90° and 45 ° relative to the incident beam were conclusive . It was suggested that the mechanisms which are responsible for anisotropy in these parameters were related to orientation of the elastic tissue structure and to muscle fibers acting as scatterers. It was assumed that there was no directional dependence of attenuation in our muscle phantom recipe since silica particles were orientated randomly inside the gel without any directional prevalence.
ABS was tested as a bone mimicking candidate material and its attenuation coefficient was assessed using the transmission through technique. We have found that ABS was very efficient in attenuating acoustic waves (16 dB/cm/.MHz). The measured attenuation coefficient was within the range of values found in literature. Human bone attenuation data reported in bibliography are very broad as a result of the wide range of porosity, mineralization, bone architecture, choice of anatomical structure and the experimental method followed. The broadband ultrasound attenuation (BUA) coefficient of cortical bone, which forms the compact outer shell surrounding cancellous bone, was measured at different frequencies and ranged between 3.5 and 8.5 dB/cm.MHz [28–33]. In a comprehensive report by Duck et al.  skull bone attenuation (all layers) was measured at 22 dB/cm at 1 MHz. Aubry et al.  presented a numerical model that correlated skull diploe layer porosity with absorption coefficient which ranged from 2 to 80 dB/cm at 1.5 MHz for the same skull sample.
Measurements of the longitudinal acoustic speed of the two soft tissue recipes were also within the range of biological soft tissues (1478–1595 m/s) . The speed inside the muscle phantom (1529 ± 13 m/s) was significantly higher from the brain’s (1485 ± 12 m/s) because of its higher evaporated milk content. These observations agreed with a recent study by Farrer et al.  where acoustic speed in gelatin gels increased with the concentration of evaporated milk concentration. Acoustic speed inside ABS (2048 ± 79 m/s) was in the lower end of a typical range of values found in literature. Culjat et al.  reported a speed of 1886 m/s in trabecular bone and of 3476 m/s in cortical bone.
The measured mass density of the muscle phantom (1.07 ± 0.01 g/cm3) was found higher from brain (1.05 ± 0.01 g/cm3). The densities of both soft tissue recipes were in good agreement of the values reported individually for brain (1.04 g/cm3) and muscle (1.09 g/cm3) tissue . Density of ABS (1.04 g/cm3) was obtained by the manufacturer’s datasheet and was considerably lower from typical cortical bone density (1.97 g/cm3).
Acoustic impedance was calculated by multiplying mass density with acoustic speed for each soft tissue recipe and the ABS bone replica. The acoustic impedance of ABS (2.13 ± 0.08 MRayl) was significantly lower from typical cortical bone (7.38 MRayl) . This difference should be taken in to account when using the proposed phantoms for validating numerical models since the degree of reflected energy at the interface will be significantly lower compared to bone.
The thermal properties of the brain and muscle recipes were assessed by correlating the change of the temperature profile’s Gaussian radius over time at a plane perpendicular to the thermal focus formed by a HIFU impulse sonication. The method was described in a publication by Cheng et al. . Thermal conductivity (0.52 ± 0.06 W/m.°C for brain - 0.57 ± 0.10 W/m.°C for muscle) and diffusivity (0.0012 ± 0.0001 cm2.s−1 for brain - 0.0013 ± 0.0001 cm2/s for muscle) for both phantom recipes were found to mimic published values for non-perfused soft tissues. Creeze et al.  reported a thermal conductivity range of 0.5–0.6 W/m.°C for non-perfused muscle while in another study by Diederich et al. a range of 0.3–0.7 W/m.°C for unspecified tissue samples was given. Thermal of properties of ABS, which was tested as a bone candidate material, were not assessed since in the majority of focused ultrasound applications energy is delivered to soft tissue. For bone applications apparent temperature is monitored in nearby adjacent soft tissue since bone possesses a very short T2 relaxation time and consequently the MR signal produced is short lived.
Evaluation of the brain and muscle phantoms showed that they possess adequate thermal repeatability properties which is essential while investigating hyperthermia applications. The attenuating capabilities of the brain phantom were demonstrated by observing the maximum temperature induced by focused ultrasound at different depths along the acoustic pathway.
This paper presented full characterization of an agar-based phantom intended for the evaluation of FUS protocols. The evaluation included the measurement of the acoustical, thermal and magnetic properties of the phantom. MR thermometry maps acquired from this phantom showed that the proposed phantom mimics successfully soft tissue. The agar-based material can be used in combination with ABS to mimic different applications such as brain, breast with ribs, bone, and liver with ribs.
Availability of data and materials
The data will not be shared, because all the data is MRI data, which is of huge size and most of it is provided in the manuscript as image.
GM developed the phantom and did all the measurements. CD performed the evaluation of the phantom and designed the ABS structures. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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