Selection of laser pulse width for efficient generation of photoacoustic signals in liquid-filled thin capillary embedded in soft material

Photoacoustic contrast agents have been a hot topic for several years and are prospected to be developed^1–5 intensively because of their proved effectiveness in improving the imaging quality and depth as well as a possibility to expand the application area.^6–14 For the process of developing new contrast agents, a scientific method is required to properly measure the photoacoustic activity as a contrast agent. Until now, most of the researchers have employed photoacoustic imaging systems to demonstrate the sensitivity of their developed materials.^15–18 However, the imaging results were significantly affected by the design and setting of the imaging system, such as the laser pulse width, center frequency of the receiving transducer, and signal processing and imaging algorithm.^19–23 As a first step for fair evaluation, the physical understanding of the photoacoustic capability of samples is thought to be important.

The authors developed the first prototype evaluation system based on intensity modulated semiconductor laser and lock-in detection.²⁴ The wavelength could be chosen from a wide variety of commercially available low-cost laser diodes. The feasibility of the prototype was successfully proved through several experiments for indocyanine green²⁴ and chloroaluminum phthalocyanine nanoparticles.²⁵ However, the modulation frequency was 4–8 kHz, which was far lower than the main frequency range utilized in practical imaging machines. Although it was thought that basic photoacoustic capability could be evaluated even if at a lower frequency, its accuracy should be further studied by comparing with pulsed excitation in the MHz range with a more realistic setup.

In this paper, we developed a new evaluation platform based on a low power pulsed semiconductor laser and a MHz-range ultrasonic transducer to satisfy the demand of realistic evaluation. Sample liquid is confined in a thin glass capillary. First, the frequency dependence of the photoacoustic signal on the inner diameter of the capillaries was experimentally investigated. Second, the influence of the pulse width was discussed in association with the peak frequencies for many capillaries of different inner diameters. Then, we discussed the influence of the pulse width on the amplitude of the generated photoacoustic signal. To match the acoustic resonance of the target with the center frequency of the receiving transducer, several resonance modes were extracted and investigated. A series of experiments on the chosen resonance mode were conducted, and the relationship between the laser pulse width and the maximal amplitude of the resonance mode was studied. Third, as a help to understand the excitation of the resonance, we simulated the experimental results through the combination of two delayed damping vibrations of the modes. Finally, we experimentally investigated the influence of the sample concentration on the results.

We prepared a soft phantom of 21 mm in length, 21 mm in width, and 20 mm in height (H00-600J, Exseal), filled in an acrylic container as illustrated in Fig. 1. A glass capillary (WPI-TW100F-4, WPI) of 1.0 mm in outer diameter and 0.75 mm in inner diameter is embedded in the phantom horizontally with keeping the distance of 3.5 mm from the upper surface. The capillary is filled with black ink, which is thought as a primary photoacoustic absorber.

Pulsed light of 1 W in peak power was generated using a solid state light source (NPL64C, Thorlabs) and focused on the sample capillary with an objective lens (×10) from the vertical direction as shown in Fig. 1. The center wavelength of the illumination light was 640 nm. The generated photoacoustic signal was received using a non-focused piezoelectric transducer with the center frequency of 5 MHz (5K5I, Japan Probe) located on the side surface of the phantom through a window of the container. The central axis of the ultrasonic transducer was maintained to meet the focusing point of the excitation light.

A schematic diagram of the electrical instrumentation is shown in Fig. 2. The light source was triggered using a function generator (WF1946, NF) at the repetition rate of 1 kHz. The laser pulse width can be varied from 10 to 129 ns. The output signal of the ultrasonic transducer was amplified using a 40-dB low noise amplifier (SA-240F5, NF) and the receiving circuit of a pulser-receiver (5900PR, Panametrics). The settings for the high-pass and low-pass filtering frequencies, attenuation, and gain of the receiver were 1 kHz, 20 MHz, 20 dB, and 54 dB, respectively. The received signals were observed and saved using a digital oscilloscope with a sufficient bandwidth.

Figure 3(a) shows examples of signals captured using the prepared platform with and without black ink in the capillary, where the laser pulse width was set at 129 ns. We can confirm from the results that the black ink absorbed the light energy and generated an ultrasonic signal because no obvious signal was observed when the ink was removed. A number of ringing waves were observed due to resonance since the sample liquid was confined in a hard boundary of the glass capillary. In Fig. 3(b), the red curve shows the signal processed using a low pass filter with the cut-off frequency of 5 MHz. The sound speed in the phantom was estimated to be 1122 m/s by dividing the distance between the capillary and the transducer by the time interval between the origin (laser pulse) and the arrival time of the first peak. This is close to the value 1192 m/s, which was measured beforehand through the time-of-flight in the pulse-echo measurement made between the transducer and the wall of the container. We can confirm from this coincidence in the sound speeds that the observed signal was considered as the photoacoustically excited signal propagated in the phantom. The signal in the frequency domain, which was converted from Fig. 3(b) using fast Fourier transform, exhibits two major peaks as shown in Fig. 3(c). These peaks could be explained with the resonant acoustic modes of the ink filled in the tube. Although several useful studies for photoacoustic signals under similar structures have been already made,^26–28 let us explain the resonance phenomenon by introducing a simpler model based on a stiff-boundary infinite cylindrical waveguide. The corresponding wave equation for acoustic pressure in the cylindrical coordinate system is solved under the condition of a homogeneous boundary where displacement is zero at r = a. The resonance wave number k_z, which stands for the component along the tube, is considered as 0 because of the infinite extent assumption of the tube. Therefore, only the resonance mode in the section of the tube contributes to the observed resonance frequency. The resonance conditions inside the tube are determined as follows:

Here, J_m represents the mth order Bessel function, and k_m,n stands for the resonance wave number in the section, while a is the inner radius of the tube. m is the angular order, and n is the radial order for polar coordinates. The calculated resonance frequencies corresponding to each k_m,n are summarized in Table I. In the simulation, the sound speed 1492 m/s of the ink and the inner diameter 0.67 mm of the capillary were used. The sound speed of the ink was measured separately through the time-of-flight method before this experiment. The inner diameter of the capillary was found by measuring the volume of liquid filled up inside a 100-mm long capillary with the same cross section. Note that the actual inner diameter was smaller than the one stated in Sec. II A, but it was in the deviation range (±0.1 mm) indicated in the datasheet of the capillary.

From Table I, we can conclude that the observed peaks result from the resonance mode (0,1) (first angular order and zeroth radial order) and (0,2) (second angular order and zeroth radial order) because all the other simulated results are extremely deviated from the experimental results. The definition of these two modes’ description is explained in Fig. 4. The simulated results are also indicated with vertical lines in Fig. 3(c). The lower one (1.31 MHz) stands for the mode (1,0), while the higher one (2.17 MHz) represents the mode (2,0), whose percentage errors in frequency are 6.4 and 2.7% comparing the experimental results (1.40 and 2.23 MHz), respectively.

To further investigate the resonance phenomenon in different conditions, we conducted the experiments using nine different concentrations of ink. The concentrations were 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%, respectively. Here, the capillary inner diameter was fixed as 0.67 mm. The experimental and simulated frequencies are plotted in Fig. 5(a) combining with the previous result for the ink of 100% concentration. The results show that the concentration of the sample has little influence on the peak frequencies, which indicates that the optical absorption ability of the sample has very little impact on the resonance modes.

Next, 11 capillaries of different inner diameters were also tested. The inner diameters of the capillaries were 0.14, 0.20, 0.28, 0.34, 0.40, 0.45, 0.63, 0.92, 1.02, 1.12, and 1.30 mm, respectively. Here, the ink concentration was fixed as 100%. The experimental and simulation results are plotted in Fig. 5 combining with the previous result for the 0.67-mm capillary. In the figure, periodic time is used for the vertical axis instead of frequency because the time should be proportional to the diameter, and it may be convenient to compare the results. It is noticed that the simulation results match the experimental ones well. The deviation in larger diameters can be explained by the limitation of diameter precision in the experimental capillaries and the imperfect hard boundary of the inside wall of the capillary.

Optimal selection of the laser pulse width is considered to be essential in order to efficiently utilize the laser power. Here, the influence of the pulse width on the captured waveform was investigated by varying the inner diameter of the capillary. In the experiment, we employed 12 capillaries with different inner diameters, which are the same as the ones in Sec. III A, and the pulse widths of 15, 23, 31, 39, 46, 54, 63, 72, 80, 88, 96, 104, 112, 121, and 129 ns were adopted, which the pulse laser used here could output. The ink concentration of 100% was adopted. Peak frequencies are plotted as a function of the laser pulse width in Fig. 6. In the data processing, peaks to be considered as originated from the mode (2,0) were extracted in the frequency domain. Note that the peak frequency for mode (2,0) was not necessarily the dominant for all the capillary sizes and pulse widths because the location and direction of laser illumination on the capillary were deviated by samples in the practical experiments, and such deviation finally resulted in different excitation magnitudes for the different acoustic resonance modes. The results indicate that the pulse width exhibited extremely small correlation with the peak frequency. This is because the acoustic resonance of the sample liquid confined in the hard capillary is mainly determined with the geometrical dimensions of the capillary as expected.

Next, the influence of the pulse width on the amplitude of the generated photoacoustic signal was investigated. The positive maximum amplitude of the signal in the time domain is plotted in Fig. 7(a) as a function of the laser pulse width. The amplitudes are normalized in order to compare the results among capillaries with different diameters. From the figure, the trend that the amplitude increases and then decreases along with the increasing laser pulse width can be concluded. However, the trend of the results exhibits rather complicated variations, especially for the diameters of 0.14 and 0.34 mm. This complexity is thought to be originated from the existence of multiple resonance modes. Thus, we need to extract the contribution of one mode by considering the results in the frequency domain as in Fig. 3(c). We first choose the (1,0) mode, and the corresponding signal amplitudes are summarized in Fig. 7(b) as a function of the laser pulse width. Although the result for the diameter of 0.14 mm still exhibits a clear peak, the amplitudes for the diameters 0.28 and 0.34 mm do not. This is because the optimal pulse width to excite the (1,0) mode for these thicker capillaries is longer than the possible range in this experiment.

The signal amplitude behavior for the (2,0) mode is then investigated and summarized in Fig. 8(a) as a function of the laser pulse width. The optimal pulse width giving the highest signal level is plotted in Fig. 8(b) as the capillary inner diameter. Since the longest pulse width available with the laser used in the experiment was 129 nm, the data for the inner diameter smaller than 0.45 mm are plotted in the figure. The optimal laser pulse width is proportional to the inner diameter of the capillary. The data for 0.45 mm exhibited abnormal behavior since the predicted optimal pulse width reached the longest pulse width available in our experiment.

To explain these results in the time domain, we conducted the calculation based on our previously proposed model,²⁹ which is written as

Here, A, α, t, and τ stand for the amplitudes, damping factor, time, and delay (laser pulse width), respectively. f₀ is used to represent the resonance frequency. Fourier transform of Eq. (3) gives

Here, ω₀ represents the angular resonance frequency and is equal to 2πf₀, while the angular frequency is ω(=2πf).

Equation (4) exhibits the maximum when $ω=ω02−α2≈ω0$⁠. Therefore, the optimal delay τ_op (laser pulse width), which maximizes the response, can be calculated as (0.5 + k)/f₀. Here, k is an integer number,

In the condition of the (2,0) mode, the optimal delay should be

Here, l is the inner diameter of the capillary, and c stands for the sound speed of the ink, which equals to 1492 m/s. When k = 0, the optimal delay τ_op = 345l. The unit of τ_op is ns while that of l is mm. Other choices for the integer k are unsuitable because the corresponding optimal delay is out of the range available with our laser (129 ns) even if for the smallest capillary of 0.14 mm in inner diameter.

The calculated results can precisely fit the experimental data. The fact that the error in the pulse width is positive for smaller inner diameters and negative for larger inner diameters is consistent with the simulation results in Sec. III A. Therefore, the error can be attributed to the limited precision of the inner diameter of the capillaries and the imperfect hard boundary of the inside wall of the capillary.

Finally, the optimal pulse width for different concentrations of black ink is investigated and summarized in Fig. 9(a) as a function of the laser pulse width and Fig. 9(b) as a function of the concentration. Ten different concentration inks, the same as mentioned in Sec. III A, were selected as samples. The points in Fig. 9(b), such as percentage concentrations from 10 to 40, are not plotted because the faint photoacoustic signal was hard to be identified. In Fig. 9(a), it is noticed that the normalized amplitude becomes smaller when the concentration of the black ink is lower. On the other hand, Fig. 9(b) shows that the optimal pulse width did not change with the concentration as expected. These facts can be explained by our simulation model that only sound speed c and capillary inner diameter l have impact on the optimal pulse width, and the optical absorption ability only contributes to the overall amplitude A according to Eqs. (6) and (3), respectively.

In this paper, we have developed a platform to evaluate the sensitivity of contrast agents for photoacoustic imaging by introducing a liquid-filled thin glass capillary embedded in a phantom. Comparing with the former kHz-ranged prototype,²⁴ the present prototype made the evaluation possible in the MHz range, which is a more realistic frequency utilized in practical imaging. Moreover, this platform requires a very small amount of sample and provides a good signal-to-noise ratio with limited laser power.

The output signal of the proposed platform exhibited ringing responses having certain specific frequencies. The mechanism of the ringing was illustrated with the acoustic resonance model of the inside space of the cylindrical structure, and the (0,2) mode had major contribution in the case of a sub-millimeter capillary. The optimal selection of pulse width for the excitation laser was discussed by varying the inner diameter of the capillary. We also demonstrated that the concentration of samples has very little influence on the optimal pulse width selection as explained by the proposed model.

The results obtained in this paper shall be further utilized to prove the effectiveness of our previously proposed kHz platform.²⁴ In the future study, selection of the capillary diameter is needed to be discussed for wider applications.

This work was supported by the JSPS KAKENHI, Grant No. 18H01449.

The data that support the findings of this study are available from the corresponding author upon reasonable request.