Bulk—general design requirements

The bulk part of the phantom was made of SEBS-type copolymers mixed in mineral oil with added ultrasound scatterers. This specific copolymer was chosen for its tunable viscoelasticity and acoustic properties, which closely resemble those of human tissue. Notably, it offers temporal stability in its Young’s modulus as well as speed of sound and attenuation measurements similar to that of human fat [ ]. Additionally, SEBS phantoms are homogeneous, easy to produce, non-toxic, and relatively inexpensive. Composition of the phantom was initially based on the formulation proposed by Oudry et al. [ ], but the parameters were modified to more accurately match the conditions modeled in this study.

The aim was to have a Young’s modulus resembling human fat, measured by Samani et al. [ ] to be 3 ± 1 kPa. In polymerized SEBS, the Young’s modulus increases with concentration following the relation (Eqn [1]) given by Oudry et al.:

Attenuation is commonly adjusted in phantoms by adding graphite, but in SEBS it was found to cause excessive attenuation at the targeted frequency of 10 MHz. The attenuation coefficient for human breast fat was found by d’Astous and Foster [ ] to obey the relation 0.158 ± 0.03 dB/(cm MHz ^1.7 ), valid between 3 and 7 MHz. However, a wide range of values with large uncertainty has been reported for human fat, even up to several dB cm ⁻¹ MHz ⁻¹ [ , ]. Based on observations from our ongoing clinical study, we chose to evaluate the relation by d’Astous and Foster at 10 MHz. This calculation resulted in a value of 7.9 dB/cm, a value more closely achieved by adding glass beads only at a concentration of 3 wt%.

The speed of sound in mesenteric fat was found by Errabolu et al. [ ] to be 1427 m s ⁻¹ , while for fat tissues in general it can reach up to 1470 m s ⁻¹ [ , ].

Bulk material preparation

The bulk material was prepared in an autoclave bottle. In total, 94 g of mineral oil with a dynamic viscosity of 14.2–17 mm ² s ⁻¹ at 40°C (catalog no. 330779, Sigma-Aldrich, Darmstadt, Germany) and 3 g of SEBS (Kraton G 1650E, Kraton Polymers, Houston TX, USA) were mixed before being heated in a temperature-controlled oven (VWR DRY-Line, VWR, Radnor PA, USA) at 120°C for 2 h. A stirrer magnet was placed inside the bottle prior to heating to prevent the formation of gas bubbles when placed on the hot plate. At this step, only 90% of the final mineral oil mass was used. The remaining 10% was reserved to pre-mix the glass bead powder (type A2429 glass, Potters Industries, Malvern, PA, USA) before adding it to the main solution. This approach helped to prevent glass bead aggregates, maintaining a concentration 3 wt% of the total solution. Once this secondary solution was homogeneously mixed, it was added to the heated SEBS solution and stirred at 500 rpm for 5 min. This speed was chosen as a balance between preventing bead sedimentation and ensuring an even distribution of heat throughout the solution.

After mixing, the mixture was slowly and carefully poured into the mold ( Fig. 1 ) and allowed to cool at room temperature, during which the gel formed. The temperature of the solution during pouring was critical; if too low, it may trap bubbles that form while pouring the viscous liquid. Conversely, if poured when too hot, the glass beads may have time to sediment before the solution solidifies. A total of 20 mL of the bulk solution was reserved and kept at room temperature to be used as a sealant at a later stage. Note that from this point, the gel could be re-used by re-heating it.

Top view of the phantom showing the different distances ( white arrows ) between the insert ( black ) and the semi-circular cutouts on the sides where the probe can be placed. The distances exclude the phantom wall, which is 2.5 mm. The insert has a diameter of 5 mm.

Solutions with glass bead concentrations of 0, 1, and 2 wt% were prepared similarly.

Insert—general design requirements

The nanoparticles used were water-soluble, necessitating a water-based phantom material. For this reason, a PVA polymer was chosen as the material for the insert. As the insert was designed to be encapsulated in the bulk material, we hypothesized that water evaporation from the PVA should not be an issue for the phantom’s durability. The production method of the insert was inspired by Surry et al. [ ]. However, the parameters were adjusted to achieve an acceptable balance between viscoelastic and acoustic properties to better resemble a human lymph node.

For modeling magnetomotion, the principal parameter for the insert was Young’s modulus, which should reflect the elastic properties of a lymph node. For axillary lymph nodes, this was measured at 6.9 ± 0.5 kPa [ ]. In a PVA phantom, elasticity depends on PVA concentration as well as the number of freeze-thaw cycles applied during fabrication. Several studies have suggested different PVA concentrations and freeze-thaw cycles to simulate biological tissue [ ]. Three PVA concentrations of 10, 12.5, and 15 wt% at a single freeze-thaw cycle were evaluated under these conditions based on Young’s modulus reported by Gordon [ ] to find the best match for the aforementioned lymph nodes.

Sound attenuation in human lymph nodes has been measured as 0.58 dB cm ⁻¹ MHz ⁻¹ [ ]; however, unclear over over what frequency range. As lymph nodes appear darker than their surrounding in an ultrasound image, graphite was preferred to achieve this appearance because it produces less scattering than glass beads. Additionally, graphite is able to increase attenuation to levels similar to those of lymph nodes. Note, however, that it was not possible to reach the desired attenuation by adding more graphite, as this would have increased echogenicity too much. Concentrations of 5, 15, and 30 mg mL ⁻¹ were investigated for sound speed, attenuation, and Young’s modulus, as well as apparent backscatter relative to the bulk tissue.

Sound speed in human lymph nodes was found by the same investigators to be 1514 m s ^{− 1} [ ].

Insert preparation

The material for the three inserts was made from PVA powder (Molecular weight 89,000–98,000, 99+% hydrolyzed, product no. 341584, Sigma-Aldrich, Darmstadt, Germany) at mass fractions of 10, 12.5, and 15 wt%. These were mixed with water to a total weight of 100 g for each sample and then heated in the oven at 100°C for 1 h. Water evaporation was compensated by adding water to maintain the correct PVA concentration. After heating, graphite powder was added at 5, 15, and 30 mg mL ⁻¹ for the 15 wt% PVA solution and mixed with a magnetic stirrer for 5 min at 500 rpm. The nanoparticles (Ferumoxtran-10, Ferrotran SPL Medical B.V., Nijmegen, The Netherlands) were prepared at different concentrations of 0.5, 1, 2, and 4 mg mL ⁻¹ and then directly added to the PVA and graphite solution. The preparation was left at room temperature to allow air bubbles to rise to the surface, which occurred spontaneously due to the solution’s low viscosity.

Solidification and polymerization of the PVA was induced by one freeze-thaw cycle of the entire bulk-insert combination (see the Measurements section below for phantom properties/Young’s modulus).

Bulk and insert combination—general design requirements

Due to the different properties of the base materials, it was found that the best way to avoid trapping air between them was to pour the insert in its molten form directly into a suitable cavity within the bulk material. Even so, the difference in acoustic impedance between the two substances should be similar to that observed in vivo . Fat, lymph nodes, and water have an acoustic impedance of 1.33 × 10 ⁶ , 1.6 × 10 ⁶ , and 1.48 × 10 ⁶ kg m ⁻² s ⁻¹ , respectively [ ], while mineral oil has an acoustic impedance of 1.21 × 10 ⁶ kg m ⁻² s ⁻¹ [ ]. Calculating the reflection coefficient for the two cases (with the PVA solution assigned the acoustic impedance of water) showed that the estimated reflection in the phantom was 10% compared with 9% in the tissue case. This calculation also neglects the influence of scattering from the presence of graphite and glass beads, or cellular structures in tissue.

The geometry of the final phantom was designed to allow imaging of the nanoparticle-laden insert from four directions by placing the transducer in semi-circular cutouts on each side of the insert ( Fig. 1 ). The insert was positioned to reflect the range of depths at which lymph nodes are typically found in humans [ ]. The height of the phantom was set at 10 mm, significantly greater than the elevation of the ultrasound image slice, providing some margin for placement of the transducer, including tilt.

Bulk and insert preparation

The mold for the bulk material was designed with a solid rod-shaped negative mass measuring 5 mm in diameter and 10 mm in height. After the gel had solidified and the rod was removed, the PVA solution could be poured into the hole left by the rod.

Before undergoing the freeze-thaw cycle, the insert solution was poured into the hole left in the bulk with the help of a syringe, which was tilted to minimize air bubbles. The bulk and insert ensemble were then placed in the freezer, with a single freeze-thaw cycle consisting of 18 h in the freezer at -20 ± 2°C followed by 2 h at room temperature.

After the freeze-thaw cycle, the remaining SEBS solution was reheated in the oven at 100 ± 5°C for 30 min and then poured over the hole containing the PVA insert, ensuring it was entirely enclosed by SEBS and thereby preventing exposure to air.

Young’s modulus

The Young’s modulus of both material components of the phantom, the bulk material and the insert, was measured individually using separately molded 75 × 35 × 35 mm blocks prepared as described for each material (the PVA also underwent one 18 h freeze-thaw cycle). The material samples were positioned on a weight scale and compressed using a translation stage. This setup allowed measurement of both the applied force and the change in length, which were then used to calculate stress and strain.

For the bulk material, stress and strain were plotted and the Young’s modulus was obtained from linear regression between the two variables. The PVA samples exhibited a more non-linear behavior between stress and strain, so the mean static Young’s modulus value was determined as the slope of this relationship in a strain range between 3% and 8%, as done by Duboeuf et al. [ ].

Speed of sound

The sound speed in the SEBS bulk material samples was measured using a 2 MHz transducer driven by a pulser receiver (Panametrics 5052PR, Olympus NDT Inc, Waltham, MA, USA) set in pulse-echo mode. The phantom was placed in a water tank, and echoes from the front and back walls were recorded on an oscilloscope. Sound speed was determined by measuring both the length of the phantom sample (multiplied by two) and the time elapsed between the echoes.

The high attenuation made pulse-echo measurement challenging for the PVA insert samples, so the through-transmission technique described by Chen et al. [ ] was used instead. During the measurements the temperature was 19°C, which was used to calculate the sound speed in water according to Lubbers and Graaff [ ].

Measuring the length of the PVA samples proved difficult due to the softness of the material and the uneven surface left open to transmit sound. As a result, the length measurement had relatively low accuracy (75 ± 0.5 mm), leading to higher uncertainty in sound speed measurements.

Attenuation coefficient

The attenuation coefficient of each part of the phantom was measured by transmitting ultrasound pulses through the rectangular samples (75 × 35 mm) along their long and short axes, respectively. A 10 MHz transducer (Olympus A327S-SU, Olympus NDT Inc.) was placed coaxially in front of a 0.5 mm hydrophone (Precision Acoustics, Higher Bockhampton, Dorchester, UK) in a water tank, with the sample positioned between them. The transducer was driven by a pulser/receiver (Panametrics 5052PR, Olympus NDT Inc.). After fast Fourier transform calculations of the received signals, the power spectra (expressed in dB) from the two cases were subtracted, yielding the power lost over the length corresponding to the difference between the length and the width (40 mm) for each sample, for each frequency component within the usable bandwidth for the received signals. The attenuation emanating from the added water path when measuring the short axis was much less than the expected measurement errors and was not accounted for. This method minimized errors caused by reflections occurring at the sample interfaces.

Magnetomotive displacement measurements

A MMUS imaging system from NanoEcho AB (Lund, Sweden) was used to measure material displacement induced by the magnetic field generated by the system. This system is described by Jansson et al. [ ], but in a version that is now updated with a center frequency of the transducer elements of 10 MHz. Displacement in the samples for each nanoparticle concentration (0.5, 1, 2, and 4 mg mL ⁻¹ at a PVA concentration of 14%) was calculated as the average displacement recorded within a circular region of interest, drawn slightly smaller than the insert in the ultrasound image (diameter of 4.5 mm). The final displacement value was determined as the average of three individual measurements taken at different image planes. The limited thickness of the phantom allowed for only three independent planes—at the center, near the top, and near the bottom—facilitating repeatable measurements.

Assessment of durability

Three additional phantoms were produced according to the procedure outlined above and stored at room temperature. Over a period of 3 weeks, the weight and magnetomotive displacement of each phantom were recorded nearly every other day. The regions of interest were selected as previously described, and the distance in the ultrasound image from the transducer face to the center of the insert was noted for each measurement.

Young’s modulus

The Young’s modulus for the bulk was found to be 2.1 ± 0.5 kPa for a copolymer concentration of 3 wt%, as shown by the graph equation in Figure 2 (R ² = 0.99). The theoretical values computed according to eqn (1) predict a Young’s modulus of 2.38 kPa.

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