Stiffness measurement using terahertz and acoustic waves for biological samples

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1 Stiffness measurement using terahertz and acoustic waves for biological samples Jong-Hyun Yoon, 1 Young-Joong Yang, 1 Jinho Park, 1 Heyjin Son, 2 Hochong Park, 3 Gun- Sik Park, 2 and Chang-Beom Ahn 1,* 1 Department of Electrical Engineering, Seoul National University, Seoul, South Korea 2 Department of Physics and Astronomy, Seoul National University, Seoul, South Korea 3 Department of Electronics Engineering, Kwangwoon University, Seoul National University, Seoul, South Korea *cbahn@kw.ac.kr Abstract: A method is proposed to measure sample stiffness using terahertz wave and acoustic stimulation. The stiffness-dependent vibration is measured using terahertz wave (T-ray) during an acoustic stimulation. To quantify the vibration, time of the peak amplitude of the reflected T-ray is measured. In our experiment, the T-ray is asynchronously applied during the period of the acoustic stimulation, and multiple measurements are taken to use the standard deviation and the maximum difference in the peak times to estimate the amplitude of the vibration. Some preliminary results are shown using biological samples Optical Society of America OCIS codes: ( ) Terahertz imaging; ( ) Terahertz imaging; ( ) Tissue characterization. References and links 1. J. L. Katz, Anisotropy of Young s modulus of bone, Nature 283(5742), (1980). 2. J. Ophir, I. Céspedes, H. Ponnekanti, Y. Yazdi, and X. Li, Elastography: A quantitative method for imaging the elasticity of biological tissues, Ultrason. Imaging 13(2), (1991). 3. J. L. Gennisson, T. Deffieux, M. Fink, and M. Tanter, Ultrasound elastography: principles and techniques, Diagn. Interv. Imaging 94(5), (2013). 4. R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf, A. Manduca, and R. L. Ehman, Magnetic resonance elastography by direct visualization of propagating acoustic strain waves, Science 269(5232), (1995). 5. Y. K. Mariappan, K. J. Glaser, and R. L. Ehman, Magnetic resonance elastography: a review, Clin. Anat. 23(5), (2010). 6. A. Samani, J. Bishop, C. Luginbuhl, and D. B. Plewes, Measuring the elastic modulus of ex vivo small tissue samples, Phys. Med. Biol. 48(14), (2003). 7. H. J. Ko, W. Tan, R. Stack, and S. A. Boppart, Optical coherence elastography of engineered and developing tissue, Tissue Eng. 12(1), (2006). 8. B. F. Kennedy, X. Liang, S. G. Adie, D. K. Gerstmann, B. C. Quirk, S. A. Boppart, and D. D. Sampson, In vivo three-dimensional optical coherence elastography, Opt. Express 19(7), (2011). 9. A. Itoh, E. Ueno, E. Tohno, H. Kamma, H. Takahashi, T. Shiina, M. Yamakawa, and T. Matsumura, Breast disease: clinical application of US elastography for diagnosis, Radiology 239(2), (2006). 10. L. Sandrin, B. Fourquet, J.-M. Hasquenoph, S. Yon, C. Fournier, F. Mal, C. Christidis, M. Ziol, B. Poulet, F. Kazemi, M. Beaugrand, and R. Palau, Transient elastography: a new noninvasive method for assessment of hepatic fibrosis, Ultrasound Med. Biol. 29(12), (2003). 11. M. Yin, J. A. Talwalkar, K. J. Glaser, A. Manduca, R. C. Grimm, P. J. Rossman, J. L. Fidler, and R. L. Ehman, Assessment of hepatic fibrosis with magnetic resonance elastography, Clin. Gastroenterol. Hepatol. 5(10), 1207 (2007). 12. D. L. Cochlin, R. H. Ganatra, and D. F. R. Griffiths, Elastography in the detection of prostatic cancer, Clin. Radiol. 57(11), (2002). 13. J. J. Wortman and R. A. Evans, Young s modulus, shear modulus, and Poisson s ratio in silicon and germanium, J. Appl. Phys. 36(1), (1965). 14. K. M. Kennedy, L. Chin, R. A. McLaughlin, B. Latham, C. M. Saunders, D. D. Sampson, and B. F. Kennedy, Quantitative micro-elastography: imaging of tissue elasticity using compression optical coherence elastography, Sci. Rep. 5(4), (2015). 15. J. H. Yoon, Y. J. Yang, J. Park, J. Jang, H. Park, G. S. Park, and C. B. Ahn, Stiffness measurement using terahertz and acoustic waves, in Proc. 6th International THz-Bio Workshop, (2015), paper P-12. (C) 2015 OSA 14 Dec 2015 Vol. 23, No. 25 DOI: /OE OPTICS EXPRESS 32671

2 16. H. P. Schlemmer, B. J. Pichler, M. Schmand, Z. Burbar, C. Michel, R. Ladebeck, K. Jattke, D. Townsend, C. Nahmias, P. K. Jacob, W. D. Heiss, and C. D. Claussen, Simultaneous MR/PET imaging of the human brain: feasibility study, Radiology 248(3), (2008). 17. J. K. Enholm, M. O. Köhler, B. Quesson, C. Mougenot, C. T. W. Moonen, and S. D. Sokka, Improved volumetric MR-HIFU ablation by robust binary feedback control, IEEE Trans. Biomed. Eng. 57(1), (2010). 18. P. N. Wells and H. D. Liang, Medical ultrasound: Imaging of soft tissue strain and elasticity, J. R. Soc. Interface 8(64), (2011). 19. S. H. Cho, S. H. Lee, C. Nam-Gung, S. J. Oh, J. H. Son, H. Park, and C. B. Ahn, Fast terahertz reflection tomography using block-based compressed sensing, Opt. Express 19(17), (2011). 20. K. Kim, D. G. Lee, W. G. Ham, J. Ku, S. H. Lee, C. B. Ahn, J. H. Son, and H. Park, Adaptive compressed sensing for the fast terahertz reflection tomography, IEEE J. Biomed. Health Inform. 17(4), (2013). 1. Introduction Stiffness (or elasticity) is an important physical property that is useful for diagnosis [1 8]. For example some cancerous tissues have higher stiffness than normal tissues [9 12]. The stiffness is often represented using Young s modulus defined as the ratio of the stress applied to the sample divided by the resulting strain [13]. A stiffer tissue shows less strain for a given stress, and thus has a larger Young s modulus. The elasticity may be represented as the inverse of Young s modulus. If a tissue is homogeneous and has a linear relationship between the stress and the strain, the stiffness is represented by the slope of the force and the displacement response in a one dimensional configuration. Various efforts have been made to measure the tissue stiffness for clinical and biological applications [2 8]. In general, an external force is applied to the tissue ( mechanical loading ), and the response or movement of the tissue is measured. The external force may be either static (or quasistatic) or dynamic [3]. The elasticity can be mapped by combining the stiffness measurement technique with an imaging method, e.g., elastography with a clinical ultrasound [2,3], magnetic resonance elastography [4,5], and more recently optical coherence elastography [7,8]. These methods have been successfully applied to diagnose breast cancer [9], liver cirrhosis [10,11], prostate cancer [12], etc. The spatial resolution and the depth of the measurement plane are closely related to the mechanical loading technique and the imaging method. Since the ultrasound elastography and magnetic resonance elastography usually use clinical systems, their spatial resolutions are limited to 0.1 to 3mm to map superficial organs of the human body. Optical coherence tomography has a higher spatial resolution of 10 to 100μm, however, it has a limited penetration depth of only a few mm [14]. To overcome the relatively short penetration depth, an endoscopic approach is suggested. In this paper, we propose a method to measure stiffness using terahertz waves [15]. An acoustic stimulation is applied to the sample to introduce a sample vibration. The amplitude of the vibration is dependent on the stiffness of the sample as a function of the spatial coordinates, as measured using the peak time of the reflected T-rays. The T-rays can penetrate some samples farther compared to the optical waves. Due to the high resolution of T-rays together with accuracy and ease of the measurement, the technique has advantages over existing techniques [2 8]. Furthermore, no additional, or minimal changes are needed in the hardware of existing terahertz systems to measure stiffness. Acoustic stimulator can be easily added without electric interface to the terahertz system. As in this application, fusion or integration of existing techniques to measure new parameters or to perform new functions with improved sensitivity and specificity becomes an important trend in modern diagnostic imaging and therapy systems [16,17]. 2. Stiffness measurement using T-rays and acoustic waves Figure 1(a) shows the schematics of the setup used to measure the stiffness with T-rays and an acoustic stimulation. A sample is located on the measurement plate. Terahertz time-domain spectroscopy system is used to generate and measure the terahertz pulse waveform. If a linear model is assumed, the stiffness is inversely proportional to the displacement for a given (C) 2015 OSA 14 Dec 2015 Vol. 23, No. 25 DOI: /OE OPTICS EXPRESS 32672

3 pressure (acoustic stimulation). The displacement is measured by the time of the peak amplitude of the reflected T-rays (peak time). Phase offset caused by laser jitter may be removed by taking magnitude of the terahertz waveform in the peak amplitude. As an example, two reflected terahertz waveforms are shown in Fig. 1(b) with different peak times resulting from the vibration of the sample. Since the terahertz spectroscopy system has a high temporal resolution, it can accurately measure the displacement. Fig. 1. Schematic diagram of system to measure the stiffness of the sample using T-rays and an acoustic stimulation. (a) Schematic system setup, (b) schematic diagram to show the variation in the peak time due to the vibration. Figure 2 shows the experimental setup used to measure the stiffness. The system consists of an acoustic stimulator with a speaker driven using a function generator (Protek 9301), the sound collector to focus the stimulation on the sample effectively, and a terahertz timedomain spectroscopy system (Terahertz Spectroscopic System, TAS7500SP, Advantest Inc.). The reflected T-ray is measured for a duration of 131ps (65536 samples), with a sampling interval (Δ t) of 2fs which is the unit step time of the time delay stage employed. It takes 8ms to measure the terahertz waveform, and thus the actual time elapsed (Δ te) between the sampling points is 0.122μs ( = 8ms/65536). The resolution of the T-ray along the transmission direction (Δ z) is 0.6μm in free space (Δ z = c Δ t, with the light velocity, c), thus a displacement of up to 0.6μm can be measured. For the acoustic stimulation, a 200Hz sine wave is continuously applied to the sample. The stimulation frequency was chosen by considering the frequency response of the audio system. The speaker generates a pressure of 0.364Pa (85.2dB) at the sample. The pressure is measured using a decibel meter (TES-52A) having a resolution of 0.1dB. # (C) 2015 OSA Received 21 Oct 2015; revised 4 Dec 2015; accepted 7 Dec 2015; published 10 Dec Dec 2015 Vol. 23, No. 25 DOI: /OE OPTICS EXPRESS 32673

4 as Fig. 2. Experimental setup for the stiffness measurements. The displacement of the sample in a steady state due to the vibration may be represented dt () = Asin(2 π ft+ φ) (1) 0 where A is the stiffness-dependent amplitude of the vibration in the transmission direction, f 0 is the stimulation frequency, and φ is the phase related to the boundary condition and time delay between the stimulation and response. The time delay due to various factors including sample decompression speed is assumed to be shorter than the period of the stimulation. Sample fatigue was not considered during the measurement. Since the stimulation frequency is relatively low, the sample is almost stationary during each terahertz pulsing period (Δ t e = 0.122μs). The displacement during a terahertz pulsing period is about 4 Asin(2 π f0δte) A (2 π f0δ te) = 1.53 x 10 A for our experimental setup. The amplitude A is in the range of 0 ~250μm (see Table 1), thus the displacement is maximally 0.038μm, which is much smaller than the depth resolution of 0.6μm and has little effect on the measurement of d(t). There may be some distortion, however, in the overall waveform of the T-ray due to the vibration. Since the terahertz waveform has a length of about 2500fs (1250 samples with the actual measurement time of 1250 Δ t e ), a maximum shift of up to 67 samples may be observed during the time. The measured waveform can be contracted or expanded by up to about 5.4% ( = 67/1250) of the one without vibration, and this can generate a distortion in the spectral response as well. If the waveform is used for further analysis, the stimulation frequency needs to be reduced or optimally adjusted. Since the time when d(t) reaches a maximum value ( = A) is not known, multiple measurements are needed. In principle, two measurements of d(t) at t 1 and t 2 would be good enough to estimate A by A = d ( t ) + d ( t ) (2) where, t 1 is an instance arbitrarily chosen, and t 2 = t 1 + (2k + 1)/(4f o ), for any integer k 0. In our experiment, since we could not control the time interval of (t 2 - t 1 ) precisely, we chose the instances randomly, and estimated the amplitude using the standard deviation and the maximum differences in the peak times. If N multiple measurements are made at random phases of the stimulation, then the standard deviation (SD) and the maximum difference (MD) is expressed for a large number N as (C) 2015 OSA 14 Dec 2015 Vol. 23, No. 25 DOI: /OE OPTICS EXPRESS 32674

5 SD { d, i = 1,2, N} = A / 2 i MD{ d, i = 1,2, N} = 2 A i (3) where { di} = { Asin(2 π f0 ti + φ)} = { Asin( θi)}, and the angle θ i is assumed to be uniformly distributed. Thus the amplitude of the vibration is estimated from the standard deviation ( A = 2SD ) or from the maximum difference (A = MD/2). A computer simulation is performed using a uniform random number generation for θ i, and SD and MD are evaluated as a function of the number of measurements (N) in Fig. 3(a). Relative errors of the estimation are shown in Fig. 3(b). No measurement error or noise is involved in the simulation. Figure 3 shows that reasonable estimation of the amplitude can be obtained when N> = 30, with relative errors of less than 5%. Note that the relative errors with MD are smaller than those with SD, and thus a more reliable estimation can be achieved with MD. The nature of the MD results in a monotonic decrease in the estimation error as N increases. The standard deviation method is, however, more robust to random measurement noise compared to the maximum difference. One of the advantages of using SD and MD is that the mean or dc offset value can be easily removed. Thus the surface of the sample is not required to remain flat, which makes it easy to prepare samples, especially when measuring biological samples. If the acoustic stimulation applies uniform stress over the sample, and the strain is proportional to the displacement, then Young s modulus is inversely proportional to the displacement. Since these assumptions are hardly met in real situations, the stiffness is represented by the displacement only without further conversion or calibration in our application, as is done in some elastography techniques. 3. Result Fig. 3. Estimation of the amplitude of the vibration as a function of the number of measurements (N) using the standard deviation (SD) and the maximum difference (MD) from the computer simulation. (a) Normalized SD and MD, and (b) relative errors in the estimation. The blue circle represents MD and the asterisk denotes SD. Three samples were prepared to test the validity of the proposed stiffness measurement method, including (a) aluminum foil, (b) bacon, and (c) plant leaf. For each sample, two spots of different stiffness were chosen, as shown in Fig. 4. For the aluminum foil, (1) a spot on regular foil and (2) a spot where correction fluid had applied to strengthen the stiffness were chosen; for bacon, spots on (3) the fat and (4) lean meat were chosen; and for the plant leaf spots on (5) the mesophyll and (6) the vein having tubular structure were chosen. (C) 2015 OSA 14 Dec 2015 Vol. 23, No. 25 DOI: /OE OPTICS EXPRESS 32675

6 Fig. 4. Samples for which stiffness is measured. For each sample, two spots of different stiffness were chosen for comparison. (a) Aluminum foil: (1) regular foil and (2) foil coated with correction fluid; (b) bacon: (3) fat and (4) lean meat; and (c) plant leaf: (5) mesophyll and (6) vein. Figure 5 shows the peak times in femtoseconds without and with the acoustic stimulation, and the horizontal axis denotes the measurement number. When the acoustic stimulation is applied, a pressure of 0.364Pa (85.2dB) is applied to the sample, and when no acoustic stimulation is applied (no input, with all the instruments on), a pressure of Pa (45.2dB) is observed on the sample due to the terahertz system noise and environmental noise of the laboratory, including ventilation noise. As seen in Fig. 5, variations in the peak times without a stimulation (left) are much smaller than those with the stimulation (right). Furthermore, the variation in the spot 1 is much larger than that in spot 2. Similarly, the variations at spots 3 and 5 are larger than those at 2 and 4, respectively. Note that the foil at spot 2 is stiffer than that at spot 1; the lean meat of the bacon at spot 4 is harder than the fat at spot 3; in the plant leaf, the vein with the tubular structure at spot 6 is less flexible than the mesophyll at spot 5. Table 1 provides a summary of the standard deviations and the maximum differences of the T-ray peak times in femtoseconds. The stiffness-dependent amplitudes of the vibration obtained from SD and MD are also shown below in boldface by the unit of micrometers. To compensate for the systematic error (for instance different tensions that may fix the samples to the measurement plates), the values are normalized by those without the stimulation as represented by the B/A. The stiffness ratios (SR) between the two spots are also shown. As seen in Table 1, all quantitative values (SD, MD, amplitudes, and stiffness ratio) are in agreement with the physical characteristics of the samples at the spots. The amplitudes of vibration estimated with SD and MD of peak times show consistent results (within average 15% variations). Measurements of stiffness for similar materials used in this paper were not found in the literature. There are wide variations in the published values of Young s modulus for various types of tissues [18]. It was reported that Young s modulus of glandular tissue is larger than that of fat by a factor of 1.56~2.4 in the breast tissues [18]. (C) 2015 OSA 14 Dec 2015 Vol. 23, No. 25 DOI: /OE OPTICS EXPRESS 32676

7 4. Discussion Fig. 5. The peak times of the T-ray without (left) and with (right) the acoustic stimulation for three samples (a, b, and c). The unit of the vertical axis is femtoseconds. Two spots were chosen in each sample. Measurements were made for 100 times as denoted in the horizontal axis. The peak times are shown for (1) plain aluminum foil and (2) foil coated with the correction fluid; (3) fat and (4) lean meat in bacon; and (5) mesophyll and (6) vein in the plant leaf. For a better comparison, the mean value of the peak times was subtracted in each graph. Table 1. The SD and MD for the Peak Times without (Off) and with (On) the Acoustic Stimulation. The Vibration Amplitudes in boldface, the On and Off Ratios (B/A), and the Stiffness Ratios (SR) are also shown. SD [fs] and amplitude [μm] MD [fs] and amplitude [μm] Sample Off (A) On (B) B/A Off (A) On (B) B/A Aluminum foil Plain (1) Coated (2) SR((2)/(1)) Bacon Fat (3) Lean meat (4) SR((4)/(3)) Leaf Mesophyll (5) Vein (6) SR((6)/(5)) The stiffness measurements at the two spots may be extended into a 2-D grid to produce the terahertz elastograph, which is an interesting application of terahertz waves. Since this will increase the number of measurements dramatically, it is of prime importance to reduce the measurement time. There may be several ways to reduce the measurement time: First, the number of sampling points in the temporal direction that are needed to record the terahertz waveform may be reduced substantially without loss of accuracy. For instance the current number of acquisition points (65536) can be reduced down to 3000 which is enough to record (C) 2015 OSA 14 Dec 2015 Vol. 23, No. 25 DOI: /OE OPTICS EXPRESS 32677

8 the waveform (1500 points) and the time variation (1500 points) related to the vibration. An efficient data acquisition and recording program is needed to reduce the time it takes to record the waveform into a computer file, e.g., by employing double buffers to simultaneously measure and store the waveform. Thus, a reduction by a factor of 20 is expected for the measurement time. Second, the number of random measurements that are made to estimate the amplitude of the vibration can also be reduced. For the current experiment, 100 measurements were made, even though the computer simulation suggests that a reasonable estimation may be obtained using 30 measurements (Fig. 3). An adaptive sampling method is currently under development to control the sampling instances to efficiently estimate the amplitude (a reduction by a factor of 5 is expected). Finally, an adaptive compressed sensing technique [19,20] can be incorporated to reduce the spatial sampling points (for a reduction by a factor of 8). If these techniques are combined, a total reduction by a factor of 800 is achievable, and thus an elastograph with a matrix size of 50x50 can be obtained without an excessive increase in the measurement time. 5. Conclusion This paper proposes a method to measure the stiffness of biological samples using terahertz waves and acoustic stimulation. Stiffness is an important parameter that is useful for various applications, including diagnosis. Terahertz waves can provide a high resolution and can interact with biological tissue, so stiffness measurement using T-ray offer unique advantages. The experimental setup consists of an acoustic stimulator (speaker), acoustic coupler, and terahertz time-domain spectroscopy system. The stiffness-dependent amplitude of the vibration is measured by the time of the terahertz peak signal, and the amplitude is estimated by taking multiple measurements to obtain the standard deviation and the maximum difference of the times. The proposed method is tested using three different materials. By expanding the proposed scheme to two-dimensional scanning used in terahertz imaging and tomography, terahertz elastography can be implementable. Various techniques to reduce the measurement time for terahertz elastography are currently under investigation. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No and NRF-2015R1A2A2A ). The present research has also been conducted by the Research Grant of Kwangwoon University in (C) 2015 OSA 14 Dec 2015 Vol. 23, No. 25 DOI: /OE OPTICS EXPRESS 32678