Journal of Medical and Biological Engineering, 25(4): 171-177 171 Detecting the Process of Blood Coagulation and Clot Formation with High Frequency Ultrasound Chih-Chung Huang1 2 Shyh-Hau Wang1,* Po-Hsiang Tsui1,2 Chun-Yi Chiu1 1 Department of Biomedical Engineering, Chung Yuan Christian University, Chung Li, Taiwan, 320 ROC Department of Biomedical Engineering, Yuan Pei Institute of Science and Technology, Hsin Chu, Taiwan, 300 ROC Received 31 Aug 2005; Accepted 17 Oct 2005 Abstract High frequency ultrasounds, up to 50 MHz, were applied to assess changes of blood properties during coagulating and clotting. Experiments were performed using calcium chloride solution to induce the blood coagulation (BC) and clot formation (CF) in porcine whole blood of various hematocrits ranged from 25 to 55 %. The ultrasonic signals backscattered from the whole blood were digitized at a 500 MHz sampling frequency and collected for 30 minutes at one A-line per second temporal resolution. The corresponding M-mode images and integrated backscatters acquired from four transducers of different frequencies were processed to characterize blood properties. Two parameters, denoted as Sr and tc respectively in response to the rate of change and duration between the onset of blood coagulation and the end of clot formation, were derived from the integrated backscatter as a function of time to further evaluate the sensitivity and accuracy for measurements. Results showed that backscattered signals acquired from different frequencies and their relative analysis may be applied to effectively detect the process of BC and CF. In particular, measurements using high frequency ultrasound tended to exhibits a better sensitivity to detect the coagulation, with larger average Sr and shorter tc respectively corresponding to 0.23 dB/sec and 756 seconds measured from a hematocrit of 35 % using a 50 MHz transducer. The discrepancy between results of tc measured by different frequencies may be readily associated with the resultant size of the resolution cell of the transducer and the pulse duration. Both ultrasonic M-mode image and integrated backscatter in this study were validated to monitor the process of BC and CF and specifically with those quantitative parameters, Sr and tc. It enables a potential to further apply high frequency ultrasounds for early detecting BC and CF in clinical diagnoses. Keywords: Blood coagulation, Clot formation, High frequency ultrasound. Introduction The blood clot is a meshwork of fibrin fibers running in all directions that composed of a part of blood cells and entrapped plasma. Normally the formation of clot provides a protective mechanism to stop bleeding from a wounded tissue. However, an abnormal clot, called thrombus, could be developed and attached inside the vessel wall. As there is an adequate force of blood flow exerting the thrombus, it could be come off from the attachment site to form an embolus and to flow in a blood vessel [1]. The emboli developed in a large artery or the left heart is severely hazardous for that it could flow downstream into peripheral vessels to further occlude blood supply in arteries or arterioles such as the brain, kidneys, or other vital organs [1]. A vulnerable embolus originated in the venous system or in the right heart could subsequently flow into vessels in the lung leading to such a dreadful syndrome as the pulmonary arterial embolism [2]. In addition, those * Corresponding author: Shyh-Hau Wang Tel: +886-3-2654504; Fax: +886-3-2654599 E-mail: [email protected] immobile patients confined to bed frequently suffer from the formation of the intravascular clot corresponding to the obstructed flowing blood in any vessel for a few hours. Consequently, it is crucial to develop techniques capable of detecting the process of the blood coagulation and clot formation in blood vessels for early diagnosing the formation of any embolism. To date, the simplest method to qualitatively characterize the process of BC and CF is to withdraw a certain amount of blood that is subsequently placed in a testing tube for observing and recording the transient time of BC and CF [3]. Further typical modalities developed to quantitatively detect the BC are based on three of the following principles: mechanical impedance, electromagnetism, and photometry [4]. Most of these modalities however are not appropriate for continuous and dynamic monitoring of the changes of blood properties as well as remain invasive sampling of the blood. Other feasibility studies by ultrasound techniques were carried out due to low cost and real-time capability with the involved ultrasound technique. Jacobs et al. [5] utilized two frequency 172 J. Med. Biol. Eng., Vol. 25. No. 4 2005 Table 1. Characteristics of employed transducers in the experiment. The -6 dB bandwidth and pulse length were estimated from the pulse echo response of transducers. The corresponding F-number and diameter were obtained from the manufacturer’s specifications. Figure 1. Block diagram for the experimental arrangement. scanning ultrasonic spectrographs that allow measurements to be implemented continuously over a frequency range from 1 to 10 MHz. The instrument was applied to monitor changes of blood property in sound velocity as a function of frequency during BC in the purified human fibrinogen solution and human plasma. Grybauskas et al. [6] developed a digital ultrasonic interferometer of a fixed path that used only a small amount of testing blood sample for investigating the coagulation, retraction, and clot melting processes in the whole blood. Machado et al. [7] employed the acoustic streaming to assess BC, in which a 2.7 MHz transducer was applied to measure ultrasonic scattering associated with moving spherical glass particles, with an average size of 200 µm diameter immersed in a 0.1 ml of plasma, driven by the incident ultrasonic energy. The amplitude of varying backscattered signals associated with the motion of these particles was gradually reduced in response to the formation of clot. Alves et al. [8] employed ultrasonic shear wave of a 2 MHz frequency to measure the prothrombin time and activated partial thromboplastin time by two AT-cut quartz crystal transducers. Hartley [9] utilized a 20 MHz pulsed Doppler ultrasound to evaluate the characteristics of acoustic streaming during BC and found that the acoustic streaming decreased with the increase of blood viscosity during BC. Alternatively, the variation of ultrasonic quantitative parameters, including sound velocity, attenuation, and scattering, was known corresponding to the elastic properties of media where the acoustic wave was propagated. Shung et al. [10] indicated that ultrasound backscattering may be used to determine the onset of the formation of fibrin clot in plasma and whole blood. They later measured ultrasonic attenuation, acoustic velocity, and backscatter of the human blood as a function of time for up to 24 hours following the onset of BC with a 7.5 MHz ultrasound [11]. These parameters were found to increase significantly with the clot formation. Voleišis et al. [12] measured the sound velocity in the coagulating whole blood by a 5 MHz ultrasound and observed that a fine change of ultrasonic velocity was registered corresponding to the very Frequency 5 MHz 10 MHz Manufacturer Panametrics Panametrics Model Diameter F-number -6 dB bandwidth Lateral profile Pulse length Resolution cell V309 12.7 mm 1.5 A311R 12.7 mm 1.6 2-8 MHz 6-13 MHz 1.21 mm 0.55 mm 0.35 mm 0.26 mm 3 0.4022 mm 3 0.0617 mm 35 MHz 50MHz Penn state 5.0 mm 2.0 22-43 MHz Penn state 2.5 mm 2.0 32-62 MHz 0.21 mm 0.14 mm 0.15 mm 0.0052 mm3 0.11 mm 0.0017 mm3 beginning of the clotting to lysis. Ultrasonic attenuation coefficient of coagulating blood was measured by Wang et al. [13] using a 4.5 MHz ultrasound. The results were consistent with those of measurements for blood viscosity as a function of time using a viscometric method [14]. Among those ultrasonic parameters, backscattered signals has been shown dependent on the size, shape, concentration, density, and other elastic properties of the scatterers in a biological tissue as well as the employed ultrasonic frequency [15]-[20]. Accordingly, ultrasonic backscattered signals may be sensitive to detect the local variation of scattereres in the microstructure for early detecting the process of BC and CF. To further explore a better sensitive and accurate ultrasonic backscattering technique to detect BC and CF, measurements by high frequency ultrasounds up to 50 MHz were carried out from porcine blood of different hematocrits ranged from 25 to 55%. The process of BC and CF was detected and assessed by both the M-mode backscattering image and its corresponding integrated backscatter. Results were analyzed and discussed to better elucidate the effects of ultrasonic frequency on the sensitivity and accuracy of detecting the process of BC and CF from different hematocrits of blood. Materials and Methods The experiments were performed with the porcine blood. The acid citrate dextrose (ACD) solution was immediately added to the porcine blood at a volume concentration of 15% to prevent the coagulation. The blood was processed by filtering out impurity contents and subsequently was centrifuged to separate into the blood cells and plasma. Different hematocrits of whole blood ranged from 25 to 55% were made by reconstituting certain volume of separated erythrocytes and plasma. The experimental arrangement is shown in Figure 1 in which the blood sample was placed in a rectangular plexiglass container in a water bath where temperature was regulated at 32oC using a thermocirculator. Four focused transducers with frequencies centered at 5, 10, 35, and 50 MHz were used. The pulse-echo test of 50 MHz transducer is shown in Figure 2. The pulse length, bandwidth, and other characteristics of each transducer are listed in Table I. Detecting the Process of Blood Coagulation 173 (a) (b) Figure 2. Pulse echo (a) and associated spectrum (b) of 50 MHz transducer used for measurement. A pulser/receiver (5900PR, Panametrics, Waltham, Massachusetts, USA) was used to drive transducers for transmitting and receiving ultrasound. The received radio-frequency (RF) signals backscattered from blood were respectively amplified and filtered with a 54 dB variable gain amplifier and a bandpass filter built-in in the pulser/receiver. RF signals were subsequently digitized with a 8-bit analog-to-digital (A/D) converter (PDA500, Signatec, Corona, California, USA) by a maximum of 500 MHz sampling frequency. Measurements were performed by the procedure described as follows. (1) The sample volume was located near the focal zone of the transducer which was positioned perpendicularly to the side wall of a container. (2) A 5 ml blood of a specific hematocrit was placed in the container, which was stored for 3 minutes to achieve thermal equilibrium with the surrounding water in the tank. (3) The RF signals was acquired at a 1 A-line per second temporal resolution. (4) One minute after the acquisition of signals, a drop of 2.5 ml 0.2 M CaCl2 solution was delivered into blood to induce BC and CF. (5) The total data acquisition was lasted for 30 minutes. A total of five measurements for each hematocrit of blood samples were carried out with the employed ultrasound at frequencies ranged from 5 to 50 MHz. The M-mode image for monitoring the process of BC and CF was obtained from envelopes calculated by the Hilbert transform for each A-line of RF backscattered signals. Moreover, the integrated backscatter (IB) for better quantifying the variation of ultrasonic backscattering was calculated by the following equation [21]-[22], IB = 1 f 2 − f1 2 f2 Sr ( f ) f1 S ref ( f ) ∑ 2 (1) where f1 and f 2 respectively denote the lower and upper frequencies of the –6 dB bandwidth of the ultrasonic spectrum and those of S r ( f ) and S ref ( f ) represent the spectra acquired from backscattered signals of blood and echoes reflected from a stainless steel reflector in the distilled water, respectively. A five-point moving average filter was subsequently applied to smooth out the integrated backscatter as a function of time. Results Figures 3 and 4 respectively are typical M-mode image and integrated backscatter as a function of time measured from a 35% porcine blood with different ultrasonic frequencies from 5 to 50 MHz, which correspond measurements to the whole process of BC and CF. The echogenicity demonstrated that the M-mode image progressively increased toward the region in the axial direction away from the transducer within the first minute of the measurement, which is partially due to the combination effect of red cell aggregation and sedimentation [23]. The highest variation of both echogenicity and integrated backscatter corresponds to measurements carried out using a 50 MHz ultrasound, shown in Figures 3(d) and 4(d), and which agrees with the frequency dependency of ultrasonic scattering described in Rayleigh scattering theory [23]-[24]. At the first minute after the beginning of measurement, the addition of CaCl2 solution into the blood led both the echogenicity and integrated backscatter gradually decrease to a minimum owing to partially the disruption of red cell aggregation and decrease of hematocrit in the blood. As the effect of CaCl2 solution induced the BC, the echogenicity and integrated backscatter tended to increase dramatically. To better elucidate the whole process of BC and CF, typical results of Figures 3 and 4 were divided into five phases with dashed line indicated in figure 4(a). These phases may be empirically applied to differentiate variation of blood properties during BC and CF, in which show phase I of the original blood, phase II of the addition of CaCl2 solution, phase III of the increase of blood coagulation, phase IV of the variation with coagulating blood, and phase V of the clot formation. The process of BC mainly correlates to phases at III and IV, in which both M-mode image and integrated backscatter tend to be fluctuating with results measured from ultrasounds of all different frequencies. As the clot was formed, those backscattered signals become less fluctuated, indicated in phase V. Two additional parameters defined to characterize and assess the sensitivity and accuracy of detecting BC and CF were respectively denoted as Sr, derived from the rate of integrated backscatter as a function of time within the phase III of Figure 4, and tc of the clotting time for assessing the duration between the addition of CaCl2 solution and the J. Med. Biol. Eng., Vol. 25. No. 4 2005 174 (a) (b) (c) (d) Figure 3. Ultrasonic M-mode images acquired from a 35% hematocrit of porcine blood during the blood coagulation and clot formation measured by ultrasonic frequencies as: (a) 5 MHz, (b) 10 MHz, (c) 35 MHz, (d) 50 MHz. (a) (b) (c) (d) Figure 4. The integrated backscatter as a function of time during the process of blood coagulation and clot formation obtained from a 35% hematocrit of porcine blood measured by ultrasonic frequencies as: (a) 5 MHz, (b) 10 MHz, (c) 35 MHz, (d) 50 MHz. Detecting the Process of Blood Coagulation Figure 5. Sr as a function of ultrasound frequency associated with different hematocrits of blood. 175 and IV, shown in Figure. 4. The overall results of tc as a function of ultrasonic frequency are summarized in Figure. 6 in which data demonstrated a decrease of tc with the increase of ultrasonic frequency including blood samples of different hematocrits. Specifically, measurements from a 35% hematocrit of blood exhibited the decrease of average tc from 1040 to 756 seconds corresponding to the increase of the applied ultrasonic frequencies from 5 to 50 MHz. The tc was also found to be dependent on hematocrit with the increase of average tc from 758 to 1030 seconds relative to the increase of hematocrits from 25 to 55 %. The tc dependency on the ultrasound frequency becomes steady for the applied ultrasound higher than 35 MHz, which is similar to results in Figure. 5. These results consistently demonstrated that high frequency ultrasound is capable of accurately and sensitively detecting BC and CF. Discussion and Conclusion Figure 6. tc as a function of ultrasound frequency associated with different hematocrits of blood. instant clot was formed indicated by that the variation of integrated backscatter as a function of time finally approached to steady state. Higher value of Sr corresponds to faster reaction for blood coagulation which could be detected. Figure 5 summarizes Sr measured with ultrasonic frequencies ranged from 5 to 50 MHz and with blood of various hematocrits ranged from 25 to 55 %. The tendency of Sr was found to increase with the increase of ultrasonic frequency, which is consistent with measurements in blood of all hematocrits. An example adopted from results measured from blood of 35% hematocrit demonstrated that the average Sr increased from 0.12 to 0.23 dB/S in accordance with the increase of ultrasonic frequencies from 5 to 50 MHz. This also indicates that the higher the applied ultrasonic frequency was used, the higher sensitivity for the detection of blood coagulation can be achieved. Furthermore, Sr is not linearly dependent on the ultrasonic frequency, where Sr tends to approach steady state with the employed ultrasonic frequency higher than 35 MHz validated for all measurements from each hematocrit of blood. Specifically, the average Sr obtained by a 35 MHz ultrasound tended to decrease from 0.26 to 0.2 dB/S with the hematocrits increased from 25 to 55%, in which the tendency is consistent with measurements by other ultrasonic frequencies shown in Figure. 5. The tc is calculated from the duration between phase II The development of blood coagulation in a vessel could lead to the fatal formation of blood clot. It therefore is crucial to develop techniques capable of early detecting the BC and CF in clinical applications. Among those ultrasonic techniques, ultrasonic backscattered signals from blood have shown to be a great potential able to early detect variations of scattering properties in a local tissue [13],[25]. This enables a feasibility of applying ultrasonic backscattering to characterize the process of BC and CF. Present studies have demonstrated that both M-mode image and integrated backscatter measured from ultrasonic frequencies ranged from 5 to 50 MHz are able to effectively quantify the process of BC and CF in porcine blood of different hematocrits ranged from 25 to 55 %. The variation of blood properties corresponds to the initial stage of the development of BC associated with the addition of CaCl2 solution due to that the induced plasma protein prothrombin was firstly converted to enzyme thrombin. The thrombin would catalyze a subsequent reaction leading several polypeptides to be separated from molecules of the large rod-shaped plasma protein fibrinogen to be bound to each other to form fibrin fibers [26]. Accordingly, the varying size, shape, and density of scatterers in whole blood corresponding to the progress of BC may be discerned by the gradual change of both M-mode image and the integrated backscatter. As described in previous section, the sensitivity for detecting BC may be fairly evaluated with Sr. During the progressive development of BC, a great quantity of fibrinogens was subsequently converted to fibrin fibers tending to bind numerous red blood cells. This response corresponds to fluctuating M-mode image and integrated backscatter shown in phase IV. As the clot was formed, considerable erythrocytes were trapped in the fibrin meshwork firmly [26] leading to a fair stable M-mode image and integrated backscatter in the phase V of Figure. 4. The clotting time, tc, calculated from the duration between BC and CF provides as a quantity to characterize variations blood properties measured from various hematocrits of blood sample by different ultrasonic frequencies. J. Med. Biol. Eng., Vol. 25. No. 4 2005 176 The summations of Sr and tc with respect to different measurements by ultrasonic frequencies from 5 to 50 MHz in blood of different hematocrits are respectively given in Figures 5 and 6. These results showed that the BC can be more sensitively detected with high frequency ultrasound, discerned with higher Sr. The Sr dependency on ultrasonic frequency behaves as a nonlinear relationship in which Sr approaches to steady state as that the applied frequency is higher than 35 MHz. Moreover, the clotting time tc is also frequency-dependent, which is shorter as the applied frequency is higher. These results could be largely due to such factors as the pulse duration, beam width, and frequency-dependent scattering that allow high frequency ultrasounds to be more sensitive to detect BC than those of low frequency ultrasounds. Moreover, due to that the composition of plasma in blood is hematocrit dependent, the process of BC and CF tends to be affected indicated by slightly different values of Sr and tc from different hematocrits of blood [10]. The higher Sr corresponds to measurements with higher ultrasonic frequencies due to primarily that the high frequency ultrasound is with smaller size of wavelength and resolution cell defined by the pulse length and lateral beam profile of a transducer [27]. Assuming an ideal cylinder is with the resolution cell of a transducer [28], the sample volume of an applied 50 MHz transducer is approximately equal to 0.0017 mm3. The high frequency ultrasound with such small resolution cell and wavelength enables a better sensitivity for detecting the instantaneous change of blood properties during BC, verified by results in Figure. 5. Similar reason may be directly applied to account for shorter tc obtained using high frequency ultrasound in Figures 4 and 6. In summary, this study applied both ultrasonic M-mode image and integrated backscatter to monitor the process of blood coagulation and clot formation and were quantified by defined parameters Sr and tc. With both smaller wavelength and resolution cell, high frequency ultrasound tends to be more sensitive to detect BC and CF than those of by ultrasonic frequencies lower than 10 MHz. Fresh porcine whole blood collected from a local slaughterhouse was used in this study. A lot of studies indicate that many blood properties of pig are similar to human. Those blood properties include the shape of red blood cell (RBC), RBC mean diameter, packed cell volume, hematocrit, mean corpuscular hemoglobin, and thrombocyte [23]. Consequently, many studies used porcine blood to simulate human blood to explore the relationship between ultrasound and blood properties [17],[19-20]. In addition, the component of porcine plasma is different from human blood, however, blood plasma is an important factor that can influence the process of blood coagulation and clot formation. Consequently, we consider that the results from porcine blood may different from human blood but the difference is limitation. Current study showed that ultrasonic backscatter parameter might be applied for detecting the blood coagulation and clot formation. However, we think it is still difficult to implement the in vivo measurement. Acknowledgements This work was supported by the National Science Council of Taiwan, ROC, of the grants: NSC 93-2213-E-033-035 and NSC 94-2213-E-033-039. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] D. J. Kuter and R. D. Rosenberg, Hemorrhagic disorders III. Disorders of Hemostasis. Hematology 5th ed. MIT Press, 1991. G. Murano and R. L. Bick, Basic concepts of hemostasis and thrombosis. CRC Press, 1980. J. M. Thomson, Blood coagulation and haemostasis. Churchill Livingstone, 1991. L. A. Geddes and L. E. Baker. Principles of applied biomedical instrumentation. John Wiley & Sons, c1989. J. E. Jacobs, A. V. Malinka, P. Haque, and M. D. Jhabvala, “Ultrasound spectroscopy applied to blood coagulation studies,” Ultrasonics, 3: 84-90, 1976. P. Grybauskas, K Kundrotas, V Sukackas, and E. Yaronis, “Ultrasonic digital interferometer for investigation of blood clotting,” Ultrasonics, 16: 33-36, 1978. J. C. Machado, A. Lenzi, and W. G. Silva, “An ultrasonic method to measure human plasma coagulation time,” J. Acoust. Soc. Amer., 90(4): 1749-1753, 1991. C. H. F. Alves and J. C. Machado, “Measurement of plasma clotting time using ultrasonic shear waves,” Physio.l Meas., 15: 309-316, 1994. C. J. Hartley, “Characteristics of acoustic streaming created and measured by pulsed Doppler ultrasound,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr., 44: 1278-1285, 1997. K. P. Shung and R. A. Sigelmann, “Ultrasonic measurement of blood coagulation time,” IEEE. Trans. Biomed. Eng., 22: 334-337, 1975. K. K. Shung, D. Y. Fei, Y. W. Yuan, and W. C. Reeves, “Ultrasonic characterization of blood during coagulation,” J. Clin. Ultrasound, 12: 147-153, 1984. A. Voleišis, R. Kažys, L. Mažeika, R. Šliteris, B. Voleišienè, and P. Grybauskas, “Ultrasonic method for the whole blood coagulation analysis,” Ultrasonics, 40: 101-107, 2002. S. H. Wang and P. H. Tsui, “Ultrasonic techniques to assess the properties of hard and soft biological tissues,” Key Engineering Material, 247-273: 2055-2060, 2004. Y. H. Wang, T. W. Chung, J. Y. Lai, J. J. Hsu, and Y. S. Lin, “A viscometric method to study the effects of hematocrit of blood and different surfaces of biomaterials on blood clot formation,” J. Chin. Inst. Chem. Engrs., 31: 27-32, 2000. J. C. Bamber and C. R. Hill, “Acoustic properties of normal and cancerous human liver-I dependence on pathological condition,” Ultrasound Med. Biol., 7: 121-133, 1981. J. C. Bamber, C. R. Hill, and J. A. King, “Acoustic properties of normal and cancerous human liver-II dependence on tissue structure,” Ultrasound Med. Biol., 7: 135-144, 1981. K. K. Shung, “On the ultrasound scattering from blood as a function of hematocrit,” IEEE Trans. Sonics. Ultrason., 29: 327-311, 1982. Y. W. Yuan and K. K. Shung, “The effect of focusing on ultrasonic backscatter measurements,” Ultrason. Imaging, 8: 121-130, 1986. S. H. Wang and K. K. Shung, “An approach for measuring ultrasonic backscattering form biological tissues with focused transducers,” IEEE Trans. Biomed. Eng., 44: 549-554, 1997. S. H. Wang and K. K. Shung, “In vivo measurements of ultrasonic backscatter in blood,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 48: 425-431, 2001. M. O’Donnell, D. Bauwens, J. W. Mimbs, and J. G. Miller, “Broadband integrated backscatter: An approach to spatially localized tissue characterization in vivo,” IEEE Ultrason. Symp. Proc., 175-178, 1979. S. H. Wang, P. H. Chang, K. K. Shung, and H. B. Levene, “Some considerations on the measurements of mean frequency Detecting the Process of Blood Coagulation [23] [24] [25] shift and integrated backscatter following administration of Albunex®” Ultrasound Med. Biol., 22: 441-451, 1996. K. K. Shung and G. A. Thieme, Ultrasonic scattering in biological tissues. CRC Press, 1993. J.F. Greenleaf, Tissue characterization with ultrasound- volume II. CRC Press, Boca Raton, 1986. P. H. Tsui and S. H. Wang, “The effect of transducer characteristics on the estimation of Nakagami parameter as a function of scatterer concentration,” Ultrasound Med. Biol., 30: 1345-1353, 2004. [26] [27] [28] 177 A. Vander, J. Sherman, and D. Luciano. Human Physiology: The mechanisms of body function- 8th ed. McGraw-Hill. New York. 2001 J. A. Zagzebski, J. F. Chen, F. Dong, and T. Wilson, “Intervening attenuation affect first-order statistical properties of ultrasound echo signals,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 46: 35-40, 1999. D.A. Christensen. Ultrasonic bioinstrumentation. New York, Wiley, 1988.
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