Keywords

1 Introduction

Ultrasonic phantoms are test-object materials that simulate acoustic properties of living tissues, such as acoustic velocity, impedance and attenuation coefficient; intended to study and develop new treatment and diagnose techniques without the need for living guinea pigs [1, 2]. Several substances have been studied in the interaction with ultrasound. Chemical gels are obtained by chemical reactions. Polyacrylamide gels are toxic in the initial stages of their complex preparation, and expensive also. In contrast, phantoms composed of physical gels have the advantages of easy preparation, safety and lower cost of their components [3, 4].

Carbopol is an anionic synthetic polymer derived from Acrylic Acid. Carbopol is a high-molecular-weight polymer that comes in the form of semitransparent granulate. Due to its solubility and non-reactivity with the other components in a formula, it is widely used in the pharmaceutical industry as emulsifying, viscosifying, suspending and gelling agents [5].

In the pre-dissolved state, carbopol molecule is extremely coiled and its thickening capacity is limited. When dispersed in water, moisturizes and forms an aqueous dispersion with a pH value in the range of 2.8–3.2 [6]. The backbone of carbopol possesses carboxyl (COOH) groups, which dissociate into fixed anions and mobile counter cations. Carboxyl groups ionize upon titration with inorganic bases such as sodium hydroxide or low molecular weight amines [7]. Ionic repulsion then leads to the expansion of polymeric chains, increasing carbopol solubility and swelling, yielding clear, crystalline, aqueous or hydroalcoholic gels that contain large amount of water, as well as human tissues [8, 9]. Maximum viscosity is achieved with pH between 6 and 11 [6].

To evaluate the performance of this gel, it is necessary first to characterize the materials that compose it so it will be possible to analyze the effect of chain crosslinking on the acoustic properties of the gel and to modulate the properties of the gels. Thus, the present work proposes to characterize the acoustic properties of a solution of poly (acrylic acid) and of the respective gel, aiming at the later confection of stable ultrasonic phantoms with acoustic properties similar to those of the living tissues (Table 1).

Table 1 Values of acoustic properties of biological tissues [10,11,12,13,14,15]
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2 Materials and Methods

The method adopted in this work consisted of the following stages:

2.1 Preparation of the Solution

To prepare the solutions with final concentration of 0.5% w/v, Carbopol (934P, NF High Performance Polymers, BFGoodrich) was added to deionized water and left under magnetic stirring until complete dissolution. The solution was allowed to rest for 24 h in a closed flask so air bubbles could migrate out of the solution. The pH was measured with a pH indicator paper tape (Merck).

2.2 Gel Preparation

An aqueous solution of sodium hydroxide (PA, PROQUIMIOS) was prepared with concentration of 18% w/v. Five drops were added to the Carbopol solution for gel formation and carefully mixed to minimize the incorporation of air. The pH of the gel was checked until it reaches 6.0. Figure 1 shows the final gel prepared only with water, Carbopol polymer and pH adjuster. It can be seen that the gel does not flow rapidly and remains attached to the glass rod.

Fig. 1
figure 1

Photograph of a aqueous solution of Carbopol 0.5% w/v and b the respective gel with pH 6.0

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2.3 Acquisition and Processing of Signals

For the acoustic characterization of solutions and gels based on poly(acrylic acid), a cylindrical polyacetal 27.53-mm-height sample was used. The inner chamber possesses a diameter of 19.70 and the two opened faces opened (Fig. 2).

Fig. 2
figure 2

Photograph of the sample port. a side wall; b face with window

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Initially, only one face is sealed with poly(vinyl chloride) (PVC) film, then the gel is placed in the inner chamber and kept under vacuum for ten minutes to remove air bubbles. Subsequently, the other side is closed with PVC film and the gel. The sample holder is submerged in the water tank for the measurement of its acoustic properties.

Longitudinal propagation velocity and attenuation coefficient. The velocity of longitudinal propagation of the ultrasonic wave and attenuation coefficient were estimated by the transmission-reception method, as shown in Fig. 3, in which two ultrasonic transducers are fixed and aligned with each other on a rail and immersed in an acoustic tank filled with distilled water. The sample is placed between the two transducers.

Fig. 3
figure 3

Photograph of the experimental setup of the transmission-reception method employed in this work

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An arbitrary function generator (Tektronix INC., AFG 3021B, Beaverton, OR, USA) was used to excite the emitter transducer with a 5-cycle burst of sine-wave of nominal frequency of 1 MHz, 1 V peak-to-peak amplitude and pulse repetition period 1 ms. The emitted signal crossed the sample and was collected by the receiver transducer. The properties were measured for nominal frequencies of 1, 2.25, 5 and 7.5 MHz, using planar transducers (Olympus, Tokyo, Japan). A 1 kbyte-memory oscilloscope (TDS2024B, Tektronix INC., OR, USA) was employed to exhibit the collected signals in the average mode of 64 signals. Finally, the signals were processed using Matlab software (Mathworks, Natick, MA, USA).

The experimental procedure consisted in initially recording the water temperature of the acoustic tank, collecting 10 ultrasonic signals with the sample port containing only distilled water (reference signal), refilling it with solution and later with gel. Ten ultrasonic signals were acquired from each sample.

The velocity of the acoustic wave in sample (C) is expressed in m s−1 in Eq. 1, in which x represents the thickness of the sample in meters and Δt represents the time difference between the pulse propagation time through water only or sample [16, 10]. The thickness of the sample was determined by the length of the acoustic path of the sample holder.

$$ {\text{C}} = \frac{{{\text{x}} \cdot {\text{C}}_{\text{ref}} }}{{{\text{x}} - \Delta {\text{t}} \cdot {\text{C}}_{\text{ref}} }}, $$
(1)

and the reference velocity (water), Cref, is given as a function of temperature (T), in Eq. 2 [17].

$$ \begin{aligned} {\text{C}}_{\text{ref}} & = 1402.38 + 5.03 {\text{T}} - 0.05 {\text{T}}^{2} + 3.34 \times 10^{ - 4} {\text{T}}^{3} \\ & \quad - 1.47 \times 10^{ - 6} {\text{T}}^{4} + 3.14 \times 10^{ - 9} {\text{T}}^{5} \\ \end{aligned} $$
(2)

The attenuation coefficient (α), in dB cm−1, is calculated by the measuring the amplitude difference between the sample and the Ref. [10]. In Eq. 3, Asample represents the peak-to-peak amplitude of the sample signal, Aref is the peak-to-peak amplitude of the reference signal and x is the sample thickness in cm.

$$ \upalpha = \frac{{ - 20\log_{10} \cdot \left( {\frac{{{\text{A}}_{\text{ref}} }}{{{\text{A}}_{\text{sample}} }}} \right)}}{\text{x}} $$
(3)

The acoustic impedance (Z) in kg m−2 s−1 is calculated by the Eq. 4 for planar waves [10, 18], in which, μ is the density of the medium in kg m−3. The absolute density (μ) in kg m−3 was determined by calculating the cylinder volume and weighting the mass difference between the empty and filled sample holder.

$$ {\text{Z}} =\upmu \cdot {\text{C}} $$
(4)

The volumetric compressibility (k), in m kg−1 s2, is calculated by the Eq. 5 [10, 19, 15].

$$ {\text{k}} = \frac{1}{{\upmu \cdot {\text{C}}^{2} }} $$
(5)

2.4 Statistics

Data were analyzed by position and dispersion measurements (mean and standard deviation). The independent Student t-test was used to verify the significance, considering 95% of significance.

3 Results

The acoustic properties of a 0.5% w/v Carbopol solution and the respective gel upon pH modification with NaOH were evaluated. The densities of the samples were obtained by dividing the mass difference between the empty and filled sample holder by the volume of its inner chamber. The solution and gel densities were 1067 ± 2 and 1081.5 ± 0.8 kg m−3, respectively. It is possible to observe relatively higher values for the gel sample but both the values found in gel and in the solution of Carbopol are close to the mean values attributed to biological tissues.

Table 2 shows the mean and standard deviation of the values of the propagation velocity, attenuation, impedance and compressibility measured on the 0.5% w/v carbopol solution.

Table 2 Values of the acoustic properties of the aqueous solution samples 0.5% w/v Carbopol in function of the transducer frequency at 27 ℃
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Table 3 presents the acoustic properties of the carbopol gel. It can be noted that the acoustic speed remains almost constant during frequency variation.

Table 3 Values of the acoustic properties of the gel at pH 6.0, produced with the solution of Carbopol 0.5% m/v in function of the transducer frequency at 27 ℃
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Figure 4 shows the mean values and respective standard deviations of the wave velocity as a function of the frequency.

Fig. 4
figure 4

Variation of the propagation velocity of the ultrasonic wave in aqueous solution of 0.5% w/v carbopol and gel at pH 6.0 produced with this solution with different transducer frequencies

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Figure 5 shows the values of the mean and it is respective standard deviation of the attenuation of the longitudinal wave as a function of the frequency. It can be observed that the variation of the frequency influences the attenuation, as expected.

Fig. 5
figure 5

Graph of the variation of the attenuation coefficient values in aqueous solution of Carbopol 0.5% w/v and gel at pH 6.0 produced with this solution with different transducer frequencies

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It is possible to observe a significant difference (p < 0.05) when comparing the values found for the velocity of 0.5% w/v Carbopol aqueous solution with the gel velocity at all frequencies of the transducer used. For the attenuation, there was a significant difference (p < 0.05) for the frequencies 1.0 and 7.5 MHz comparing the solution with the gel, however for the frequencies 2.25 and 5 MHz there was no significant difference (p > 0.05).

4 Discussion

It is important to produce phantoms that simulate acoustic properties of the biological tissues to develop new diagnosis and therapeutic techniques. This work consisted of a study of the acoustic properties of the solution and the gel of a poly(acrylic acid)-derived polymer, Carbopol, and evaluate their uses in the production of ultrasonic phantoms.

Regarding the propagation velocity of the ultrasonic pulse, it was possible to conclude that in an aqueous solution of 0.5% w/v Carbopol the value remained around 1508 m s−1 and for the Carbopol gel at pH 6.0 the value remained around 1511 m s−1. The pH-induced gelification provoked this slight variation in the acoustic velocity. These values are close to others published in the literature for water-based materials, such as 2% agar gels and 20% PVA cryogels, which exhibited acoustic speed around 1500 m s−1 [10, 20]. Those values are also observed in most biological tissues because the variation of tissue velocity occurs around the velocity of propagation in water, once living tissues and hydrogels possess high water content [18]. Once the acoustic impedance depends on the velocity, no significant variation was observed within the studied range.

By observing the attenuation values of the gel, as expected, the higher the frequency of the ultrasonic pulse, the higher the attenuation coefficient value. For the aqueous Carbopol solution, attenuation does not increase gradually, although the values show small variation. Previously reported 10% polyacrylamide gels present attenuation coefficients within the same range, around 0.05–0.75 dB cm−1 [10] and 20% polyacrylamide gels present around 0.08–0.14 dB cm−1 [21].

For the volumetric compressibility, a slight change in the values of the gel sample was observed as the frequency increased, but these values are compatible with those described in this literature for biological tissues.

Regarding stability, it was possible to observe visually that during three months the aqueous solution of 0.5% w/v Carbopol and the respective gel formed with pH 6.0 have higher resistance to the attack of microbial agents when compared to other biological fabric simulant materials that are already used in the production of phantoms. But it is still necessary to explore a certain period of time to study this behavior. Thus, carbopol gels are promising materials for the production of acoustic phantoms once they possess acoustic properties similar to the living tissues and are more resistant to biological degradation that other gels. Further studies will use this hydrogel as a point of reference to modulate the acoustic properties in order to mimic different living tissues.

5 Conclusion

After characterizing the poly(acrylic acid) solution and gel through the transmission-reception technique, this study demonstrated promising results of a new material that could be used in the manufacture of ultrasonic phantoms. There were no reported results to compare with those obtained in this study.

For future work, it is suggested to explore the addition of materials that may help to tailor the properties of the Carbopol gel sample to values even closer to the biological tissues, and thus allow the elaboration of phantoms that better mimic living tissues.