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Advances in the field of laser ultrasonics have opened up new possibilities in medical applications. This paper evaluates this technique as a method that would allow for rapid characterization of the elastic properties of soft biological tissue. In doing so, we propose a novel approach that utilizes a low coherence interferometer to detect the laser-induced surface acoustic waves (SAW) from the tissue-mimicking phantoms. A Nd:YAG focused laser line-source is applied to one- and two-layer tissue-mimicking agar-agar phantoms, and the generated SAW signals are detected by a time domain low coherence interferometry system. SAW phase velocity dispersion curves are calculated, from which the elasticity of the specimens is evaluated. We show that the experimental results agree well with those of the theoretical expectations. This study is the first report that a laser-generated SAW phase velocity dispersion technique is applied to soft materials. This technique may open a way for laser ultrasonics to detect the mechanical properties of soft tissues, such as skin.
©2011 Optical Society of America
1. Introduction
Laser ultrasonics (LUS) is a remote, non-contact technique that uses a short pulsed laser to excite surface acoustic waves (SAW) (dominated by Rayleigh waves) to characterize the mechanical properties of material by means of measuring the phase velocity dispersion curves of SAW. The SAW technology has been used in industry applications such as analyzing the surface structure, compositions, geometry, roughness, plainness and elastic properties of metallic specimens [1–5]. To detect the laser-induced SAW, the most common method is to employ contact ultrasound transducers. The ultrasound transducer requires physical contact with the sample. This requirement leads to a number of drawbacks: the sensing area is limited by the size of transducer contact area, wave energy leakage occurs at the boundary of contact area, and the influence of transducer weight onto the sample, etc. [6]. To mitigate these problems, a preferred method is to use a non-contact and non-destructive approach to detect the laser-induced SAW. One of such methods is optical interrogation. Optical interrogation method has been widely used because it is non-contact and remote, therefore there is no surface loading. Also the sensitivity of optical measuring system is inherently high which allows detection of significantly small displacement with a very high detection bandwidth. As a remote sensing approach, at the same time it provides access to the samples in a hostile environment and generally not sensitive to surface orientation.
In recent years, LUS started to attract attention for applications in medical area. Wang et al. was the first to describe an application of LUS for clinical dental diagnosis [7,8]. L’etang and Huang introduced a finite element simulation procedure that showed the possibility that LUS could be used to diagnosis skin diseases by evaluating the mechanical properties of skin [9,10]. This was the first time that the concept of LUS was considered to evaluate the elastic properties of soft rather than solid materials. However, there has been no report so far on applying the LUS for evaluating of the elastic properties of soft tissues.
This paper demonstrates for the first time that a laser-generated SAW phase velocity dispersion technique can be used to evaluate the mechanical properties of soft materials. In this study, a ~532 nm Nd:YAG focused laser line-source was applied to generate the SAW signals from tissue-mimicking phantoms. The phantoms were made of agar solution with different concentrations to simulate the varying degrees of the elastic properties of biological tissues. The feasibility of using LUS to measure the mechanical properties of the sample was evaluated. The generated SAW signals from the phantoms were detected by a low coherence interferometry system. Then, dispersion phase velocity curves were calculated to obtain the elastic properties of tissue-mimicking phantoms with well-defined layers that exhibit different mechanical properties.
2. Brief theoretical background
When a material is illuminated with a short laser pulse, the absorption of laser energy would result in a rapid increase of temperature in the irradiated volume that in turn causes a rapid thermal expansion. The consequence is the generation of ultrasonic waves that propagate within the material. Among these waves, ultrasonic SAW, which is dominated by Rayleigh waves, has been widely used to characterize the elastic properties of surface of hard solid materials and thin films [11–15]. The propagation of surface waves in a heterogeneous medium (i.e. layered materials) shows a dispersive behavior [6], where dispersion means that in surface waves the different frequency components have different phase velocities (Fig. 1 ).
Fig. 1 In homogeneous material (left), the phase velocity is constant while in layered material (right), the wave dispersion occurs because the phase velocity depends on the frequency [3].
The phase velocity at different frequency is dependent on the elastic and geometric properties of the material [6]. In isotropic homogeneous material, the surface wave phase velocity can be approximated as [1,16]:
where E is the Young’s Modulus, v is the Poisson’s Ratio, and ρ is the density of material.For a multilayer medium, in which each layer has different elastic properties, the phase velocity of surface wave is influenced by the mechanical properties of all the layers it penetrates into. The elastic properties that affect the phase velocity dispersion curve include not only the Young’s modulus, Poisson’s ratio and density of each layer, but also the thickness of each layer. In this case, the surface waves with shorter wavelengths (higher frequency) penetrate in shallow depth with the phase velocity depending on the superficial layers. On the other hand, the surface waves with longer wavelengths (lower frequency) penetrate deeper in the material with the phase velocity asymptotically influenced by the elastic properties of the deeper layers.
3. System configuration and sample preparation
The system set up for generation and detection of laser-induced SAW in soft tissues is shown in Fig. 2 . In this study, we used a tissue-mimicking agar-agar phantom to simulate a soft tissue.
3. 1 Generation of laser-induced SAW
A solid state Nd:YAG laser (~532 nm central wavelength) (Continuum Surelite Laser) was used as the high energy laser pulse source. The short laser pulse was set to duration of 6 ns with an average energy of ~2.6-3 mJ and repetition rate of 0.5 Hz (2s). During the experiment, the laser irradiation on the tissue-mimicking phantoms was continuously monitored to make sure that there was no surface damage or melt under the energy level used. Before laser pulses were given to the sample, a cylindrical lens was employed to generate a line source with the line extent of ~2-2.5 mm. Compared with the focused laser pulse, the line source significantly reduced irradiated power density on the sample. Thus, the more affordable energy can be injected into the specimen, permitting an improved signal/noise ratio for measurement of surface wave-forms compared with that for a circularly symmetric source [17–20].
In order to record the dispersion of laser-induced surface waves, several detecting locations with a known separation distances are required by this technology. Here, we propose a novel use of low coherence interferometry to record the laser-induced SAW from the location near the excitation field to the location away from the excitation field (see below). We mounted the reflection mirror and cylindrical lens (shown in Fig. 2) on a translation stage, so that the excitation laser beam was translated to the required distances for the measurement of generated SAW signals. In this way without moving the interferometry detection arm, the stability of measured signals from the sample was kept well.
3. 2 Detection of laser-induced SAW by a low coherence interferometry
Detection of the laser-induced SAW was performed by a low coherence interferometry system. There are several reasons to adopt the low coherence interferometry as the detection method in this project. Firstly, compared with conventional interferometry, the low coherence interferometry is able to localize the targeted positions on the sample surface within a depth-extend defined by axial resolution of the system (which is determined by the coherence length of the light source). This is advantageous because when the probe beam is aimed at the surface of the sample, only the surface wave signal is detected, which reduces noise from environment. In addition, it can be developed into or combined with optical coherence tomography (OCT) imaging system to provide the geometrical structure of samples, i.e., the thickness of layers and the plainness of surface of samples. Thus, this novel combination gives a possibility to offer imaging the geometry and inner layer conditions and elastic properties of tissue at the same time.
The low coherence interferometry system consists of a ~1310 ± 28 nm broadband superluminescent diode (Dense Light sled broad band source) as the light source, a 3-port optical fiber circulator, a 4-port 50/50 optical fiber coupler, a balanced amplified photo detector (PDB120C-75MHz), a reference arm and a sample arm. Briefly, light from low-coherence broadband light source is split into two paths in a 50/50 fiber based Michelson interferometry. One beam is coupled onto a stationary reference mirror and the second is focused onto the phantom samples via an object lens. As mentioned before, the sample arm and agar-agar phantom were fixed in order to maintain the stability of measured signals.
The measured signal can be expressed as [21]:
where k = 2π/λ, ∆z is the change of optical path caused by laser induced SAW signals, φ is the initial phase different due to the optical path length difference between the sample and reference arms, which was carefully adjusted to be π/2, and φnoise is a random low frequency phase noise due to the optical system noise and environment vibration. The value of I(k) changed constantly and steadily due to the random noise φnoise. During the detecting procedure, I(k) was monitored by a digital oscilloscope (Tektronix TDS5104B Digital phosphor oscilloscope). We only recorded the SAW signals at the times when the system became most sensitive at φ + φnoise = ± kπ + π/2. This allowed the detection of SAW signals under the same conditions.In the typical measurement, the low coherence interferometry system is able to detect the displacement that is less than a quarter of the source wavelength. In our previous computer simulation studies [9,10], the Nd:YAG laser pulse (~532 nm central wavelength) with a duration of 6 ns and an average energy of ~3 mJ induced SAWs with the displacement from ~2.5 nm to ~10 nm in soft tissue materials. Thus in this study, the estimated range of SAW displacement in phantoms is around ~10 nm, which is much smaller than the source wavelength of low coherence interferometry system.
The SAW signal generated by the laser irradiation was recorded by the digital oscilloscope. The sampling frequency was set at ~5 MHz. It is known that the frequency range of laser induced SAW would drop when the Young’s modulus of material reduces [4,6,9,10]. In our previous studies, the frequency range for steel was between ~0-5 MHz, and it dropped to ~0-2.5 MHz for iron, and ~0-2 MHz for hard plastic plate. Since the Young’s modulus for soft materials is much lower than that of the hard materials, the maximum frequency content of a SAW in soft solid could be lower than hard solid such as hard plastic plates. In order to work out the full frequency content of SAW in soft solid, we used the sampling frequency of ~5 MHz in the current study to warrant sufficient sampling of the generated SAW signals.
3. 3 Preparation of tissue-mimicking agar-agar phantoms
In order to simulate soft tissue samples, we used tissue mimicking agar-agar phantoms. It is known that when making agar-gel mixture, the higher the agar concentration, the stiffer the gel-mixture would be. In order to show the potential of the proposed technique to measure the mechanical properties of soft tissue, we made two types of the agar phantoms, i.e., the homogenous and the multilayer phantoms. For the homogenous one-layer phantom, two concentrations of ~2% and ~3.5% agar phantoms were produced in order to test whether the proposed technique is feasible to differentiate the elastic properties of one from another. For multilayered phantoms, we used 2% agar in ~3.5% agar phantom and ~5% agar on ~3.5% agar phantom as double-layer samples. In double-layer phantoms, the thickness of upper layer was approximately between ~1 mm and ~2 mm. In previous simulation and experimental work, we observed that the thickness of layers only can influence the frequency content of SAW signals but not the value of phase velocity. Thus, the exact thickness of upper layer is not considered and discussed in this paper and we were only interested in whether the phase velocity can represent the Young’s modulus of the different layers. In addition, since the generation of laser-induced SAW is due to the thermal expansion of material surface, the absorption of materials becomes critical. In order to improve the absorption coefficient of tissue-mimicking agar-agar phantoms, during the manufacturing procedures, a drop of black ink was mixed in agar solution. Thus, all tissue-mimicking agar-agar phantoms used in this study were in black color.
4. Signal processing of SAW phase velocity dispersion curve
Detecting system records the SAW in various locations on the surface of each sample. For each location on the sample surface, six measurements were made and their averages were digitally high-pass filtered to reduce the DC noise and de-noised by Hilbert-Huang method to reduce the high frequency random noise [22]. Then, the phase velocity dispersion of two measured signals, y1(t) and y2(t), at the selected locations x1 and x2 were analyzed. The phase difference Δφ between y1(t) and y2(t) was calculated by the phase of the cross-power spectrum Y12(f):
where Y1(f) and Y2(f) are Fourier transforms of the measured signals y1(t) and y2(t), A1 and A2 are the amplitude of cross-power spectrum and φ1-φ2 is the phase difference Δφ. The measured phase difference is 2π when the propagating wave has a wavelength that equals the distance ∆x. In general, the ratio between the phase difference and 2π equals to the ratio between the distance and the wavelength:Based on the relationship of frequency, velocity and wavelength, the relationship between phase velocity and frequency can be expressed as:
Here, both autocorrelation spectrum and phase velocity dispersion curves are the key functions in our analyses, as the former provides the available frequency range of the signals, while the latter provides the important elastic and structural information of the samples. Previously Wang et al. indicated that when signals dropped below 20 dB below maximum of autocorrelation spectrum, uncertainty of the dispersion curve increases [7]. Thus, cut-off frequency of signals should be defined before the analysis of phase velocity dispersion curves. All the signals are used to calculate the phase velocity dispersion curve. Every two possible SAW signals in different locations were selected to generate one phase velocity dispersion curve, so a group of phase velocities is calculated. The final phase velocity dispersion curve is the average of them.5. Experimental results
5.1 SAW on one layer tissue-mimicking agar-agar phantoms
Figure 4 shows the typical SAW signal recorded from one layer ~3.5% agar-agar phantom. The first detecting point (red) was located at a position ~0.5mm away from the excitation laser beam, and then moved with ~0.5 mm/step to ~3 mm away (magenta). It is clear from Fig. 4 that the SAW is moving away from the laser-excitation position. Because the sample was a one-layer homogeneous sample, no velocity-dispersion was found in the detected waveforms. Compared with the laser-induced SAW in the hard materials such as metal and tooth that reported previously [2,7,8], the SAW in the soft material had much higher wavelength and travelled at a much slower velocity with estimated amplitude at ~10 nm. In addition, attenuations between the waveforms were clearly observed. The spikes in every signal at the time of 0.08 ms are high frequency thermal expansion when laser pulse was given.
Fig. 4 SAW signal of one layer 3.5% agar-agar phantom with the distance of 0.5 mm (top) to 3 mm (bottom) to laser pulse, with 0.5 mm/step. Each SAW signal is purposely shifted vertically by equal distance in order to better illustrate the results captured from different positions. The same also applies to Fig. 7.
Figure 5 shows the autocorrelation spectra of all six SAW signals shown in Fig. 4. It serves as the indication of the signal strength of each frequency, from which an optimal cut-off frequency can be selected for further analyses. In this case, we chose the cut-off frequency at ~10 kHz because at this frequency, the autocorrelation spectrum dropped 20 dB below the maximum.
Figure 6 plots the phase velocity dispersion curves of both one-layer agar-agar phantoms with concentration of ~3.5% and ~2%, respectively. Both of the curves exhibit almost straight lines with a constant value, which agree with the condition of homogeneous one layer sample. The increase of the agar concentration increased the Young’s modulus of phantom. From the curves, the phase velocity of ~3.5% agar phantom is evaluated at ~13.08 ± 1.22 m/s, while the phase velocity of ~2% agar phantom is ~7.93 ± 1.56 m/s. As we expected, with the increasing of agar concentration, the phase velocity also increases due to the increase of the Young’s modulus.
Fig. 6 Comparison of phase velocity dispersion between 3.5% agar-agar phantom and 2% agar-agar phantom.
5.2 SAW on two-layer tissue-mimicking agar-agar phantoms
Figure 7 shows the typical SAW signals of two-layer agar-agar phantoms, with ~2% agar as the superficial layer and ~3.5% agar as the substrate layer. The detecting points were first 1mm (red) away from the laser excitation position, and then moved with 1mm/step to 6mm (magenta). The high frequency signal that the green arrow points at was a high frequency thermal expansion that caused by the heating of laser source. Red arrow points to the occurrence of wave dispersion, which becomes more apparent at the position of 6 mm.
Fig. 7 SAW signal of double layer 2% agar on 3.5% agar phantom with the distance of 1 mm to 6 mm to laser pulse, with 1 mm/step.
Figure 8 shows the autocorrelation spectra of all six SAW signals shown in Fig. 7. Because the high influence of the laser pulse, near field signals have high frequency noise. Here, we choose the available frequency range up to about ~10.05 kHz. There is also significant noise in very low frequency range (from 0 to 3.5 kHz) as well.
Figure 9 compares the phase velocity dispersion curves of two kinds of double-layer phantom: ~2% agar on ~3.5% agar phantom (green) and ~5% agar on ~3.5% agar phantom (blue). The result from one layer ~3.5% agar-agar phantom (red) is also plotted for comparison. The phase velocity dispersion curves of double layer phantom are no longer a straight line. ~5% agar on ~3.5% agar phantom has an initial phase velocity of ~13.08 ± 1.22 m/s, which matches very well with one layer 3.5% agar-agar phantom. However, with the increase of the frequency, the phase velocity increases to ~20.30 m/s, which indicates the phase velocity of ~5% agar. While in the case of ~2% agar on ~3.5% agar phantom, initial phase velocity agrees with that of ~3.5% agar-agar phantom and then drops to ~7.91m/s with the increase of the frequency, which indicates the phase velocity of ~2% agar. These results are in good agreement with the theoretical expectations, i.e., the phase velocity in the lower frequency region indicates the mechanical properties of the substrate layer, while the phase velocity in higher frequency indicates the mechanical properties of upper layer. The slope is not discussed in the paper because it is mainly influenced by the thickness of each layer.
Fig. 9 Comparison of phase velocity dispersion between one layer 3.5% agar-agar phantom and two layer phantoms 2% on 3.5% agar-agar phantom and 5% on 3.5% agar-agar phantoms.
From the experiments above, the measured phase velocities versus the concentrations of agar-agar phantom are summarized in Table 1 , and plotted in Fig. 10(a) , where the phase velocity of each agar sample increases linearly and monotonically with the increase of the agar concentration. This is expected. Based the previous studies, we can assume that the agar-agar phantoms we used here have a Passion’s ratio of ~0.47 and a density of ~1040 kg·m3 [23]. Therefore, with these measured phase-velocity values, we can calculate the Young’s modulus according to Eq. (1). The results are given in the left column of Table 1 and also plotted in Fig. 10(b). The resulted Young’s modulus increases quadratically with the increase of agar concentration. In Fig. 10(b) along with the values that we obtained from our experiments, we also plotted additional values of Young’s modulus that were extracted from the prior publications [23–25], where however the values were obtained from the different agar concentrations. As seen, the experimental results from ours are agreed well with those from others [23–25], indicating the validity of proposed approach using LUS and low coherence interferometer to evaluate the mechanical properties of the soft tissues.
Table 1. The relationship between concentration of agar-agar phantom and the phase velocity
Fig. 10 The relationship between agar concentration and phase velocity (a) and the relationship between agar concentration and Young’s modulus where the values pointed by the black arrows indicate the values extracted from the prior publications (b).
6. Conclusion
We have presented a technique that combines laser ultrasonics with a low coherence interferometry to characterize the mechanical properties of the soft tissue. We used a line laser-source to generate SAW in the tissue-mimicking phantoms. This study extends the applications of laser ultrasonics from the only field detection of the properties of hard solids, like metals, to the soft biological tissue. We have shown that the experimental results are in good agreement with that of the theoretical expectations.
At the current stage, there are a few straightforward studies and developments which would be logical. The novel combination of laser ultrasonics and low coherence interferometry system provides a possibility to combine laser ultrasonics with OCT imaging system. It can image the sample while give the elastic properties of it. Because OCT can image the depth-resolved structures of the sample with a micrometer-scale spatial resolution, it would be interesting to study the relationship between thickness of upper layer and phase velocity dispersion curves. Such approach may offer the possibility of laser ultrasonics for biomedical applications, for example to characterize the mechanical properties of skin tissue to aid the early diagnosis and treatment of skin diseases, e.g., cancer.
Acknowledgements
This work was made possible with the generous support received from Department of Bioengineering, College of Engineering at University of Washington.
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