Metrological Approach for Characterizing Ultrasonic Properties of Soft Tissue-Mimicking Material

Abstract

This paper reports the investigation of the metrological impact of temperature variation on ultrasonic velocity and attenuation coefficient of a standardized tissue-mimicking material (TMM), in temperatures ranging from 20 °C to 45 °C, in steps of 5.0 °C, using a new experimental method. One calibrated thermo-hygrometer was used to measure the temperatures of the water-bath in which the TMM was inserted. The pulse-echo technique was used to measure the TMM’s properties. The Guide to the Expression of Uncertainty in Measurement was used to estimate the measurements uncertainties. The experiments were performed under repeatability conditions (n = 4). Based on the results, it was observed that the values of the ultrasonic velocity tend to increase as the temperature increases, whilst the values of the attenuation coefficient tend to decrease. The group velocity varied from 1,533.7 m s⁻¹ to 1,575.6 m s⁻¹ with expanded uncertainties lower than 6.9 m s⁻¹ (α = 0.05), for temperature varying from 19.9 °C to 45.8 °C. The attenuation coefficient varied from 2.55 dB cm⁻¹ to 1.80 dB cm⁻¹ with expanded uncertainties lower than 0.19 dB cm⁻¹ (α = 0.05) for the same temperature range. The uncertainties found in this study are relevant to provide metrological reliability of the results since it takes into account the influence of the most relevant quantities involved in the measurement process for TMM characterization.

1 Introduction

Knowing the internal temperature of biological tissues by means of non-invasive methods can be very useful and necessary both to assist in therapies that make use of ultrasound to heat the tissue and for the safety evaluation of ultrasound physiotherapy equipment. There is an absence of relevant thermal data to guide thermal therapies [1]. Besides that, there is a concern about the biological effects caused by ultrasound [2]. Among the relevant non-invasive thermometry methods by ultrasound, the following stand out: change in backscattered energy (CBE) [1, 3], the average gray level (AVGL) variation of ultrasound images [4,5,6], the time shift (TS) [7], and the variation in the attenuation coefficient [1].

Many authors have studied these thermometry methods by using biological tissues and phantoms [3,4,5,6, 8]. Phantoms or tissue-mimicking materials (TMM) are test object models intended to mimic the thermal and acoustical properties of a specific tissue [9].

According to [1], there are ultrasonic methods, which can be used for estimating temperature if the temperature-dependent ultrasonic properties are properly defined. Ultrasonic velocity and attenuation are highly dependent on temperature and their dependence may vary among different sort of phantoms [10].

Straube and Arthur [11] had predicted CBE behavior under temperature rise for certain medium and scatterer combinations. They used attenuation coefficient and ultrasonic velocity data reported in literature. Later, Arthur et al. [8] validated experimentally the theoretical model proposed in [11].

Similarly, to validate the results obtained by means of AVGL, Alvarenga et al. [6] proposed a method for estimating AVGL values theoretically. For this, the authors carried out the characterization of a TMM, by measuring its ultrasonic group velocity and attenuation coefficient at different temperatures. They estimated the measurement uncertainty of the ultrasonic properties whilst presented the sources of uncertainty about the experimental setup used.

As observed in the literature, few studies involving the characterization of biological tissues or TMM give importance to metrological rigor. To estimate measurements uncertainties is relevant to provide metrological reliability of the results since it takes into account the influence of all the quantities involved in the measurement process.

Based on the foregoing, and aiming to improve and contribute to the state of the art, this paper presents a metrological approach to a new experimental method for characterizing ultrasound propagation velocity and attenuation coefficient of a soft tissue-mimicking material.

2 Materials and Methods

2.1 Manufacturing of the Soft Tissue-Mimicking Material

The preparation of TMM can influence directly on the accurate reporting of its ultrasonic properties [11]. According to the international standard IEC 60601-2-5 [9], a soft tissue model shall have the acoustic and thermal properties similar to human soft tissue. The reference values of the ultrasonic velocity and the attenuation coefficient of the soft TMM are respectively 1,540 m s⁻¹ and 0.5 dB cm⁻¹ MHz⁻¹ [9].

In the research reported in the present paper, it was manufactured a soft TMM based on the standard operating procedure described in [12], which presents a detailed step-by-step procedure to develop an agar phantom, according to the recipe described on [9].

The agar phantom was made from the materials described in [9], as can be seen in Table 1. The second column shows the percentage mass of each pure component. The mass of the component was calculated according to the necessary amount of water to produce the desired batch. Considering 1,123 g of water, the mass of components are show in the last column of Table 1.

Table 1. Mass of components.

At the end of the preparation, the mixture was poured into a rectangular mold (300 mm × 150 mm × 28 mm). After the cooling process, the phantom was demolded, cut and stored. Six samples of this phantom were used in the present study, all with the same size (Ø 70 mm × 28 mm) and named as: A; B; C; D; E; and F (Fig. 1).

Fig. 1.

Six phantoms (A, B, C, D, E, and F) stored in pairs in three beakers.

2.2 Characterization of the Soft Tissue-Mimicking Material

The ultrasonic velocity and the attenuation coefficient of the six phantoms were measured at different temperatures, as disclosed in Table 2. Four replicates were carried out in four days for each temperature. T₀ is the room temperature, whereas a step of approximately 5.0 °C was used for the others temperatures, until reaching T₅, as follows: T₁ = T₀ + 5.0 °C; T₂ = T₁ + 5.0 °C; T₃ = T₂ + 5.0 °C; T₄ = T₃ + 5.0 °C; and T₅ = T₄ + 5.0 °C.

Table 2. Phantoms arrangement for measurements.

Measurement System.

The measurement system (Fig. 2) consists of a 5 MHz central frequency transducer (model A309S) (Olympus-NDT, USA) that acts as transmitter and receiver and is excited by a waveform generator model 33250A (Agilent, USA) with a sine burst of 20 cycles, 20 V peak-to-peak amplitude at 5 MHz. An oscilloscope model DSO-X 3012A (Agilent, USA) digitalizes the acquired signals. The experimental setup includes a temperature controlled Ø 300 mm × 110 mm high water-bath model 557 (Fisatom, Brazil) filled with distilled water, and a stainless steel cylindrical reflector (Ø 63 mm × 10 mm). A positioning system with three linear and two goniometric stages was used to align the transducer [14]. A calibrated thermohygrometer was used to measure the temperatures of water and TMM. In order to preserve their properties during all the process of measurement, inside the water-bath the phantoms were stored in pairs in three beakers containing a water-glycerol-benzalkonium chloride mixture to prevent them from drying out and to avoid air contact [9], as can be seen in Fig. 2. The mixture contains 88.1% (mass) demineralized water, 11.9% (mass) glycerol and 0.5% (mass) solution of benzalkonium chloride.

Fig. 2.

Experimental setup illustration.

Measurement Procedure.

The TMM’s properties were estimated by the pulse-echo technique. For the ultrasonic velocity and attenuation coefficient calculation, it was necessary to measure different times of flight and amplitude of the signals using the oscilloscope.

Before starting the measurements at each temperature, all the experimental setup, including the water, the reflector and the phantoms had to reach the thermal equilibrium. Hence, the temperatures of the phantoms and of the water-bath were monitored with the thermohygrometer. To acquire the reference signal, the transducer output beam was normally aligned to the stainless steel reflector surface, maximizing the echo. Then, the time of flight in the water ($t_{W}$), without the TMM, was measured (Fig. 3a). After that, the time of flight on the surface of the TMM ($t_{1}$) (Fig. 3b) and the time of flight in reflector with the TMM inserted ($t_{2}$) were measured (Fig. 3a). In turn, for the attenuation coefficient determination, it was also necessary to measure the time of flight in the water, the time of flight on the surface of the TMM, the amplitude of these signals, $\left( {V_{in1} } \right)$ and $\left( {V_{in2} } \right)$, and the amplitude of signal on the reflector surface with the TMM inserted $\left( {V_{in3} } \right)$ (Fig. 3).

Fig. 3.

(a) Pulse-echo technique scheme; (b) Experimental setup: 1: Transducer; 2: phantom; 3: stainless steel target; 4: oscilloscope and the TMM’s surface signal; 5: beaker with phantoms inside covered by aluminum to avoid evaporation; 6: temperature controlled water-bath; 7: positioning system for transducer alignment.

The measurements were carried out four times at each temperature, and all this process was repeated four times in four days.

2.3 Measurements Uncertainty

The measurement uncertainties of the ultrasonic group velocity and the attenuation coefficient were calculated based on the Guide to the Expression of Uncertainty in Measurement [13]. The measurements were carried out under repeatability conditions, and the number of repetition was n = 4.

An uncertainty model for velocity and attenuation coefficient in soft TMM has already been proposed by [14], but the experimental setup was different. Thus, this paper presents new uncertainty models of the velocity and attenuation for characterizing TMM and is disclosed below.

Ultrasonic Group Velocity.

The mathematical model for group velocity is presented in [14]. The contribution of each source of uncertainty is presented in Ishikawa’s diagram in Fig. 4.

Fig. 4.

Ishikawa’s diagram: sources of uncertainty for ultrasound group velocity.

As can be observed in the diagram, the following uncertainty sources for group velocity measurements of the TMM were considered:

Type A Standard Uncertainty.

The dispersion of speed of sound measurements. The evaluation of standard uncertainty was made from the statistical analysis of group velocity measurements repetition (n = 4) and it is computed as the standard deviation of the mean.

Type B Standard Uncertainty.

The ultrasound propagation velocity in water was considered in type B evaluation, which comprises the uncertainty of the equation [15] as a function of the temperature (u = 0.18 m s⁻¹) and the thermohygrometer certificate uncertainty (u = 0.15 °C for temperatures of 20 °C and 25 °C; and u = 0.1 °C for temperatures of 35 °C, 40 °C and 45 °C). Besides that, the uncertainty of the oscilloscope time base (u =  $2.4 \times 10^{ - 8}$  s) was used to the measurement uncertainties of the time of flight in the water (${\text{t}}_{\text{W}}$), the time of flight on the surface of the TMM (${\text{t}}_{1}$) the time of flight in reflector with the TMM over it (${\text{t}}_{2}$). The uncertainty of the measurement of phantom’s thickness was also considered and varied from 0.04 mm to 0.11 mm.

Uncertainty Arising from Mean Squared Error.

This source was obtained from the regression line fit for all measurements. MSE Uncertainty was calculated by the MSE’s root. The linear regression establishes a mathematical relation between the temperature and the ultrasonic parameter.

Attenuation Coefficient.

The mathematical model of the attenuation coefficient is described in [14]. The sources of uncertainty are shown in Ishikawa’s diagram (Fig. 5).

Fig. 5.

Ishikawa’s diagram: sources of uncertainty of the attenuation coefficient.

As can be seen in the diagram, the following uncertainty sources of the attenuation coefficient measurements of the soft TMM were considered:

Type A Standard Uncertainty.

The evaluation of standard uncertainty was made from the statistical analysis of attenuation measurements repetition (n = 4).

Type B Standard Uncertainty.

The uncertainty of the attenuation coefficient in the water [16] is $3.5 \times 10^{ - 3}$ dB cm⁻¹ and was used to estimate the Type B standard uncertainty. The uncertainty of the oscilloscope signal amplitude ($5.2 \times 10^{ - 3}$ V), and the uncertainty of the reflection coefficient in the stainless steel cylindrical reflector. ($8.68 \times 10^{ - 4}$) were also considered in the calculation. In addition, the same ones described for velocity uncertainty were used: the uncertainty of the determination of the ultrasound propagation velocity in water; the uncertainty of the oscilloscope time base and the uncertainty of the measurement of phantom’s thickness.

Uncertainty Arising from Mean Squared Error.

This source was obtained from the regression line fit for all attenuation coefficient measurements. The MSE Uncertainty was calculated by the MSE’s root.

3 Results

The thickness of the phantoms was measured using the pulse-echo technique under repeatability conditions (n = 4) and are disclosed on the Table 3 below.

Table 3. The thickness of phantoms measured under repeatability conditions and its respective expanded uncertainties (p = 0.95), together with Type A and Type B standard uncertainties and coverage factor (k).

Tables 4, 5, 6 and 7 show the results arising from the four replicates of the group velocity measurements at each temperature in four different days, the expanded uncertainties (U) together with Type A and Type B standard uncertainties and coverage factor (k).

Table 4. The results of the first day of the group velocity measurements, its respective expanded uncertainties (p = 0.95), together with MSE uncertainty, Type A and Type B standard uncertainties and coverage factor (k).

Table 5. The results of the second day of the group velocity measurements, its respective expanded uncertainties (p = 0.95), together with MSE uncertainty, Type A and Type B standard uncertainties and coverage factor (k).

Table 6. The results of the third day of the group velocity measurements, its respective expanded uncertainties (p = 0.95), together with MSE uncertainty, Type A and Type B standard uncertainties and coverage factor (k).

Table 7. The results of the fourth day of the group velocity measurements, its respective expanded uncertainties (p = 0.95), together with MSE uncertainty, Type A and Type B standard uncertainties and coverage factor (k).

Figure 6 shows the graphic of the group velocity measurements at each temperature in four different days, its respective expanded uncertainties and the regression line.

Fig. 6.

The results of the four replicates of group velocity measurements at each temperature, the uncertainty ranges and the regression line.

Tables 8, 9, 10 and 11 show the results arising from the four replicates of the attenuation coefficient measurements at each temperature in four different days, the expanded uncertainties (U) together with Type A and Type B standard uncertainties and coverage factor (k).

Table 8. The results of the first day of the attenuation coefficient measurements, its respective expanded uncertainties (p = 0.95), together with MSE uncertainty, Type A and Type B standard uncertainties and coverage factor (k).

Table 9. The results of the second day of the attenuation coefficient measurements, its respective expanded uncertainties (p = 0.95), together with MSE uncertainty, Type A and Type B standard uncertainties and coverage factor (k).

Table 10. The results of the third day of the attenuation coefficient measurements, its respective expanded uncertainties (p = 0.95), together with MSE uncertainty, Type A and Type B standard uncertainties and coverage factor (k).

Table 11. The results of the fourth day of the attenuation coefficient measurements, its respective expanded uncertainties (p = 0.95), together with MSE uncertainty, Type A and Type B standard uncertainties and coverage factor (k).

Figure 7 shows the graphic of the attenuation coefficient measurements at each temperature in four different days, its respective expanded uncertainties and the regression line.

Fig. 7.

The results of the four replicates of attenuation coefficient measurements at each temperature, the uncertainty ranges and the regression line.

4 Discussions and Conclusion

This paper presents a new experimental setup for characterizing the ultrasonic properties of a soft TMM at temperature range from 20 °C to 45 °C. It was also made a metrological study, by estimating the uncertainties of measurements of group velocity and attenuation coefficient, taking into account all quantities involved in the measurement process.

Few works care about the metrological rigors of ultrasonic properties measurements at different temperatures [6]. Besides that, some issues require more attention in the experimental setup and may affect directly the results of the ultrasound propagation velocity, for example.

In general, ultrasonic phantom’s properties are measured in water. Moreover, to measure the ultrasonic properties, the phantom shall stay underwater for a while repeatedly. On this period, glycerol loss may occur. As the glycerol is responsible for providing the velocity required to the standardized phantom [17], the ultrasonic propagation velocity may be reduced. Therefore, the need to reduce the glycerol loss during the experimental measurements arises.

Herein, an experimental design was proposed to reduce the phantoms exposure to water and temperature variations. Six phantoms were produced from the same batch and stored on beakers contained the preservation solution proposed in the international standard [9] in order to preserve its properties during all measurement process. Each phantom was exposed to water four times during all measurements carried out. If just one phantom was used, the phantom would be submerged in water 24 times.

Based on the results of the present paper, it was noted that the values of the ultrasound propagation velocity tend to increase as the temperature increases, whilst the values of the attenuation coefficient tend to decrease as the temperature increases. The group velocity (Tables 4, 5, 6 and 7) varied from 1,533.7 m · s⁻¹ to 1,575.6 m·s⁻¹ with expanded uncertainties lower than 6.9 m · s⁻¹ (α = 0.05), for temperature varying from 19.9 °C to 45.8 °C. The attenuation coefficient (Tables 8, 9, 10 and 11) varied from 2.55 dB · cm⁻¹ to 1.80 dB · cm⁻¹ with expanded uncertainties lower than 0.19 dB · cm⁻¹ (α = 0.05) for the same temperature range.

Recently, Alvarenga et al. presented a model to predict temperature variations based on AVGL variation and TMM properties. They characterized a TMM at different temperatures, using an experimental setup different from the one presented here (details in [6]). According to the authors [6], there may have been a loss of phantom’s glycerol, because the phantom was placed underwater during measurements without protection. However, they used a larger phantom, aimed to reduce that loss, because [18] testified experimentally that the lower the thickness of the phantom, the greater the loss of glycerol. The authors [6] obtained group velocity results from 1,530.9 m s⁻¹ to 1,555.4 m s⁻¹ with combined uncertainty of 6 m · s⁻¹ (α = 0.05), for temperature varying from 26.2 °C to 40.7 °C, whilst the attenuation coefficient varied from 2.3 dB cm⁻¹ to 1.1 dB cm⁻¹, for the same range of temperature and the combined uncertainty was estimated as 0.08 dB cm⁻¹. In comparison, it is perceived that the new experimental setup has reached smaller uncertainties, and it was possible to minimize the glycerol loss.

Considering the means squared error on the uncertainty calculation, it was possible to include the influence of the regression line fit for all properties measurements. Moreover, with the uncertainties obtained on the present paper, as can be seen in Figs. 6 and 7, it is possible to say that all measurements were consistent with each other.

To conclude, this paper aimed to contribute to the state of the art about studies involving non-invasive thermometry methods. With the experimental setup proposed, it was possible to reduce the glycerol loss during the TMM characterizing process, whereas smaller uncertainties were obtained.