Abstract

Capillary waves are associated with fluid mechanical properties. Optical coherence tomography (OCT) has previously been used to determine the viscoelasticity of soft tissues or cornea. Here we report that OCT was able to evaluate phase velocities of capillary waves in fluids. The capillary waves of water, porcine whole blood and plasma on the interfacial surface, air-fluid in this case, are discussed in theory, and phase velocities of capillary waves were estimated by both our OCT experiments and theoretical calculations. Our experiments revealed highly comparable results with theoretical calculations. We concluded that OCT would be a promising tool to evaluate phase velocities of capillary waves in fluids. The methods described in this study could be applied to determine surface tensions and viscosities of fluids for differentiating hematological diseases in the future potential biological applications.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

R. Khnouf, D. Karasneh, E. Abdulhay, A. Abdelhay, W. Sheng, and Z. H. Fan, “Microfluidics-based device for the measurement of blood viscosity and its modeling based on shear rate, temperature, and heparin concentration,” Biomed. Microdevices 21(4), 80 (2019).
[Crossref]

K. S. Yemul, A. M. Zysk, A. L. Richardson, K. V. Tangella, and L. K. Jacobs, “Interpretation of Optical Coherence Tomography Images for Breast Tissue Assessment,” Surg. Innov. 26(1), 50–56 (2019).
[Crossref]

2017 (4)

K. V. Larin and D. D. Sampson, “Optical coherence elastography - OCT at work in tissue biomechanics [Invited],” Biomed. Opt. Express 8(2), 1172–1202 (2017).
[Crossref]

M. A. Kirby, I. Pelivanov, S. Song, L. Ambrozinski, S. J. Yoon, L. Gao, D. Li, T. T. Shen, R. K. Wang, and M. O’Donnell, “Optical coherence elastography in ophthalmology,” J. Biomed. Opt. 22(12), 1–28 (2017).
[Crossref]

Z. L. Han, J. S. Li, M. Singh, C. Wu, C. H. Liu, R. Raghunathan, S. R. Aglyamov, S. Vantipalli, M. D. Twa, and K. V. Larin, “Optical coherence elastography assessment of corneal viscoelasticity with a modified Rayleigh-Lamb wave model,” J. Mech. Behav. Biomed. 66, 87–94 (2017).
[Crossref]

D. T. Chiu, A. J. deMello, D. Di Carlo, P. S. Doyle, C. Hansen, R. M. Maceiczyk, and R. C. R. Wootton, “Small but Perfectly Formed? Successes, Challenges, and Opportunities for Microfluidics in the Chemical and Biological Sciences,” Chem 2(2), 201–223 (2017).
[Crossref]

2016 (4)

X. Xu, J. Zhu, and Z. Chen, “Dynamic and quantitative assessment of blood coagulation using optical coherence elastography,” Sci. Rep. 6(1), 24294 (2016).
[Crossref]

L. Ambrozinski, S. Z. Song, S. J. Yoon, I. Pelivanov, D. Li, L. Gao, T. T. Shen, R. K. K. Wang, and M. O’Donnell, “Acoustic micro-tapping for non-contact 4D imaging of tissue elasticity,” Sci Rep-Uk 6(1), 38967 (2016).
[Crossref]

Y. Qiu, Y. Wang, Y. Xu, N. Chandra, J. Haorah, B. Hubbi, B. J. Pfister, and X. Liu, “Quantitative optical coherence elastography based on fiber-optic probe for in situ measurement of tissue mechanical properties,” Biomed. Opt. Express 7(2), 688–700 (2016).
[Crossref]

S. Zaitsev, “Dynamic surface tension measurements as general approach to the analysis of animal blood plasma and serum,” Adv. Colloid Interface Sci. 235, 201–213 (2016).
[Crossref]

2015 (5)

D. J. Vitello, R. M. Ripper, M. R. Fettiplace, G. L. Weinberg, and J. M. Vitello, “Blood Density Is Nearly Equal to Water Density: A Validation Study of the Gravimetric Method of Measuring Intraoperative Blood Loss,” J. Vet. Med. 2015, 1–4 (2015).
[Crossref]

Z. L. Han, S. R. Aglyamov, J. S. Li, M. Singh, S. Wang, S. Vantipalli, C. Wu, C. H. Liu, M. D. Twa, and K. V. Larin, “Quantitative assessment of corneal viscoelasticity using optical coherence elastography and a modified Rayleigh-Lamb equation,” J. Biomed. Opt. 20(2), 020501 (2015).
[Crossref]

S. Wang and K. V. Larin, “Optical coherence elastography for tissue characterization: a review,” J. Biophotonics 8(4), 279–302 (2015).
[Crossref]

C. H. Li, G. Y. Guan, Y. T. Ling, Y. T. Hsu, S. Z. Song, J. T. J. Huang, S. Lang, R. K. K. Wang, Z. H. Huang, and G. Nabi, “Detection and characterisation of biopsy tissue using quantitative optical coherence elastography (OCE) in men with suspected prostate cancer,” Cancer Lett. 357(1), 121–128 (2015).
[Crossref]

S. Song, N. M. Le, Z. Huang, T. Shen, and R. K. Wang, “Quantitative shear-wave optical coherence elastography with a programmable phased array ultrasound as the wave source,” Opt. Lett. 40(21), 5007–5010 (2015).
[Crossref]

2014 (4)

2013 (4)

S. Song, Z. Huang, and R. K. Wang, “Tracking mechanical wave propagation within tissue using phase-sensitive optical coherence tomography: motion artifact and its compensation,” J. Biomed. Opt. 18(12), 121505 (2013).
[Crossref]

Y. Jun Kang, E. Yeom, and S. J. Lee, “A microfluidic device for simultaneous measurement of viscosity and flow rate of blood in a complex fluidic network,” Biomicrofluidics 7(5), 054111 (2013).
[Crossref]

L. Campo-Deano, R. P. A. Dullens, D. G. A. L. Aarts, F. T. Pinho, and M. S. N. Oliveira, “Viscoelasticity of blood and viscoelastic blood analogues for use in polydymethylsiloxane in vitro models of the circulatory system,” Biomicrofluidics 7(3), 034102 (2013).
[Crossref]

A. Nahas, M. Tanter, T. M. Nguyen, J. M. Chassot, M. Fink, and A. Claude Boccara, “From supersonic shear wave imaging to full-field optical coherence shear wave elastography,” J. Biomed. Opt. 18(12), 121514 (2013).
[Crossref]

2012 (4)

A. L. Oldenburg, G. Wu, D. Spivak, F. Tsui, A. S. Wolberg, and T. H. Fischer, “Imaging and Elastometry of Blood Clots Using Magnetomotive Optical Coherence Tomography and Labeled Platelets,” IEEE J. Sel. Top. Quantum Electron. 18(3), 1100–1109 (2012).
[Crossref]

M. Razani, A. Mariampillai, C. R. Sun, T. W. H. Luk, V. X. D. Yang, and M. C. Kolios, “Feasibility of optical coherence elastography measurements of shear wave propagation in homogeneous tissue equivalent phantoms,” Biomed. Opt. Express 3(5), 972–980 (2012).
[Crossref]

C. H. Li, G. Y. Guan, R. Reif, Z. H. Huang, and R. K. K. Wang, “Determining elastic properties of skin by measuring surface waves from an impulse mechanical stimulus using phase-sensitive optical coherence tomography,” J. R. Soc. Interface 9(70), 831–841 (2012).
[Crossref]

C. H. Li, G. Y. Guan, S. A. Li, Z. H. Huang, and R. K. Wang, “Evaluating elastic properties of heterogeneous soft tissue by surface acoustic waves detected by phase-sensitive optical coherence tomography,” J. Biomed. Opt. 17(5), 057002 (2012).
[Crossref]

2011 (4)

C. Sun, B. Standish, and V. X. Yang, “Optical coherence elastography: current status and future applications,” J. Biomed. Opt. 16(4), 043001 (2011).
[Crossref]

R. K. Manapuram, S. A. Baranov, V. G. R. Manne, N. Sudheendran, M. Mashiatulla, S. Aglyamov, S. Emelianov, and K. V. Larin, “Assessment of wave propagation on surfaces of crystalline lens with phase sensitive optical coherence tomography,” Laser Phys. Lett. 8(2), 164–168 (2011).
[Crossref]

M. Bernal, I. Nenadic, M. W. Urban, and J. F. Greenleaf, “Material property estimation for tubes and arteries using ultrasound radiation force and analysis of propagating modes,” J. Acoust. Soc. Am. 129(3), 1344–1354 (2011).
[Crossref]

F. Behroozi, J. Smith, and W. Even, “Effect of viscosity on dispersion of capillary-gravity waves,” Wave Motion 48(2), 176–183 (2011).
[Crossref]

2010 (4)

M. W. Urban, M. Fatemi, and J. F. Greenleaf, “Modulation of ultrasound to produce multifrequency radiation force,” J. Acoust. Soc. Am. 127(3), 1228–1238 (2010).
[Crossref]

X. Liang, S. G. Adie, R. John, and S. A. Boppart, “Dynamic spectral-domain optical coherence elastography for tissue characterization,” Opt. Express 18(13), 14183–14190 (2010).
[Crossref]

F. Behroozi, J. Smith, and W. Even, “Stokes’ dream: Measurement of fluid viscosity from the attenuation of capillary waves,” Am. J. Phys. 78(11), 1165–1169 (2010).
[Crossref]

D. Mark, S. Haeberle, G. Roth, F. von Stetten, and R. Zengerle, “Microfluidic lab-on-a-chip platforms: requirements, characteristics and applications,” Chem. Soc. Rev. 39(3), 1153–1182 (2010).
[Crossref]

2009 (1)

A. Chen and J. Teruya, “Global hemostasis testing thromboelastography: old technology, new applications,” Clin. Lab. Med. 29(2), 391–407 (2009).
[Crossref]

2008 (2)

G. Kesmarky, P. Kenyeres, M. Rabai, and K. Toth, “Plasma viscosity: a forgotten variable,” Clin. Hemorheol. Microcirc. 39(1–4), 243–246 (2008).
[Crossref]

M. L. Palmeri, M. H. Wang, J. J. Dahl, K. D. Frinkley, and K. R. Nightingale, “Quantifying hepatic shear modulus in vivo using acoustic radiation force,” Ultrasound Med Biol. 34(4), 546–558 (2008).
[Crossref]

2004 (1)

F. Behroozi, “Fluid viscosity and the attenuation of surface waves: a derivation based on conservation of energy,” Eur. J. Phys. 25(1), 115–122 (2004).
[Crossref]

2000 (1)

Y. V. Sanochkin, “Viscosity effect on free surface waves in fluids,” Fluid Dyn. 35(4), 599–604 (2000).
[Crossref]

1997 (2)

K. A. Rosentrater and R. A. Flores, “Physical and rheological properties of slaughterhouse swine blood and blood components,” Trans. ASAE 40(3), 683–689 (1997).
[Crossref]

E. Hrncir and J. Rosina, “Surface tension of blood,” Physiol. Res. 46(4), 319–321 (1997).

1993 (1)

T. Somer and H. J. Meiselman, “Disorders of blood viscosity,” Ann. Med. 25(1), 31–39 (1993).
[Crossref]

1991 (1)

E. Ernst, K. L. Resch, A. Matrai, M. Buhl, P. Schlosser, and H. F. Paulsen, “Impaired blood rheology: a risk factor after stroke?” J. Intern. Med. 229(5), 457–462 (1991).
[Crossref]

1984 (1)

O. Linderkamp, H. T. Versmold, K. P. Riegel, and K. Betke, “Contributions of Red-Cells and Plasma to Blood-Viscosity in Preterm and Full-Term Infants and Adults,” Pediatrics 74(1), 45–51 (1984).

1975 (1)

G. W. Tietjen, S. Chien, E. C. Leroy, I. Gavras, H. Gavras, and F. E. Gump, “Blood viscosity, plasma proteins, and Raynaud syndrome,” Arch. Surg. 110(11), 1343–1346 (1975).
[Crossref]

1974 (1)

R. J. Trudnowski and R. C. Rico, “Specific gravity of blood and plasma at 4 and 37 degrees C,” Clin. Chem. 20(5), 615–616 (1974).

1971 (1)

J. Harkness, “The viscosity of human blood plasma; its measurement in health and disease,” Biorheology 8(3-4), 171–193 (1971).
[Crossref]

1970 (1)

R. Wells, “Syndromes of hyperviscosity,” N. Engl. J. Med. 283(4), 183–186 (1970).
[Crossref]

1969 (2)

L. Dintenfass, “Blood rheology as a factor in the pathogenesis of coronary heart disease,” Isr. J. Med. Sci. 5(4), 652–656 (1969).

L. Dintenfass, “Blood rheology in pathogenesis of the coronary heart diseases,” Am. Heart J. 77(1), 139–147 (1969).
[Crossref]

1968 (1)

R. C. Williams, “Hyperviscosity syndromes,” Circulation 38(3), 450–452 (1968).
[Crossref]

1966 (1)

E. Fukada, “Measurement of blood viscosity with respect to clinical diagnosis,” Ann. N Y Acad. Sci. 130(3), 920–924 (1966).
[Crossref]

1965 (1)

J. L. Fahey, W. F. Barth, and A. Solomon, “Serum Hyperviscosity Syndrome,” JAMA 192(6), 464–467 (1965).
[Crossref]

Aarts, D. G. A. L.

L. Campo-Deano, R. P. A. Dullens, D. G. A. L. Aarts, F. T. Pinho, and M. S. N. Oliveira, “Viscoelasticity of blood and viscoelastic blood analogues for use in polydymethylsiloxane in vitro models of the circulatory system,” Biomicrofluidics 7(3), 034102 (2013).
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Supplementary Material (1)

NameDescription
» Visualization 1       Capillary waves on water by using 3D-OCT image.

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Figures (5)

Fig. 1.
Fig. 1. Illustration of the system structure of acoustic radiation forced OCT. (a) left side displays our SD-OCT scanner and right side is the ultrasound system to generate acoustic radiation force. Three function generators were used to manage all signals for the whole system including ultrasound excitation signals (blue lines) and trigger signals for synchronizing all instruments (purple lines). The BPF stands for band pass filter and RF is radio frequency. (b) Illustration of a double sideband suppressed carrier amplitude modulation (DSB-SC AM) signal in 2 kHz modulation during 2 ms.
Fig. 2.
Fig. 2. (a) The theoretical calculations of capillary waves and gravity waves in deep water and shallow water. The critical wavelength ${\lambda _c}$ is found to be 17.25 mm and the associated minimum phase velocity ${C_{p({min} )}}$ is 0.231 m/s. The blue line and black line are waves in deep water and in shallow water, respectively. (b) The critical wavelengths ${\lambda _c}$ in three fluids, water, plasma and whole blood, were calculated.
Fig. 3.
Fig. 3. An example of a 3D-OCT wave motion image to display capillary waves on water. The colorbars indicate surface displacement amplitude. The (a-c) at different time points clearly shown that the shorter wave goes faster and the longer wave is behind the shorter waves. The white arrow and orange arrow in (a-c) indicated the wavefront of the longer waves and wavelengths, respectively. (d) The theoretical results of phase velocities of the capillary waves based on the wavelengths measured from (a-c).
Fig. 4.
Fig. 4. An example illustrates the phase velocity of capillary waves in water. (a) A 2D-OCT displacement image. The shorter waves (black dashed quadrilateral) and longer waves (white dashed quadrilateral) were clearly observed and it is shown that shorter waves were faster than longer waves. The k-space of longer waves and shorter waves were displayed in (b) and (c), respectively. The wavenumber range was selected with a 70% bandwidth centered at the peak of the magnitude distribution (yellow arrow). (d) The mean dispersion curves with the standard deviation of shorter waves (red line) and longer waves (blue line) were presented as the experimental results. (e) The theoretical results of shorter waves and longer waves were illustrated, based on the ranges of wavenumbers indicated in (b) and (c). The colorbar in (a) indicate surface displacement.
Fig. 5.
Fig. 5. The phase velocities of capillary waves in whole blood and plasma were exhibited. (a) and (c) are the 2D-OCT lateral time to peak displacement image in whole blood and in plasma, respectively. The longer waves (white dashed quadrilateral) in whole blood and plasma were clearly observed. (b) and (d) The k-space of longer waves in whole blood and in plasma were displayed and the wavenumber range was 70% centered at the peak of the magnitude distribution (yellow arrow). (e) The mean dispersion curves with standard deviations in plasma (red line) and whole blood (blue line) were presented as the experimental results. (f) The phase velocities from the theory in plasma and whole blood were represented. The wavelengths were selected by the range of wavenumbers in (b) and (d). The colorbars in (a) and (c) indicate surface displacement.

Equations (17)

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x ( t ) = A s i n ( 2 π f c t )
y ( t ) = k A s i n ( 2 π ( f c + f m ) t + θ )
m ( t ) = A s i n ( 2 π f c t ) + k A s i n ( 2 π ( f c + f m ) t + θ )
m ( t ) = A s i n ( 2 π f c t ) A s i n ( 2 π ( f c + f m ) t )
C p = ω k = 1 ( ρ ρ ) 1 + ( ρ ρ ) ( g k + σ k Δ ρ ) tanh ( k h )
ω 2 = 1 ( ρ ρ ) 1 + ( ρ ρ ) ( g k + σ k 3 Δ ρ ) tanh ( k h )
E o = Δ ρ g σ k 2 = Δ ρ g λ 2 σ ( 2 π ) 2 = ( λ 2 π λ c a p i l l a r y ) 2
C p G r a = g k tanh ( k h )
C p G r a _ d e e p = g k h > 0.5 λ o r k h > π
C p G r a _ s h a l l o w = g h h < 0.05 λ o r k h < 0.1 π
C g G r p _ d e e p = d ω d k = d g k d k = 0.5 C p G r a _ d e e p
C p C a p = 1 ( ρ ρ ) 1 + ( ρ ρ ) ( σ k Δ ρ ) tanh ( k h )
C p C a p _ d e e p = 1 ( ρ ρ ) 1 + ( ρ ρ ) ( σ k Δ ρ ) h > 0.5 λ o r k h > π
C p C a p _ s h a l l o w = 1 ( ρ ρ ) 1 + ( ρ ρ ) ( σ h k 2 Δ ρ ) h < 0.05 λ o r k h < 0.1 π
C g C a p _ d e e p = d ω d k = d d k 1 ( ρ ρ ) 1 + ( ρ ρ ) ( σ k 3 Δ ρ ) = 3 2 C p C a p _ d e e p
μ = α ρ 2 k 2 C g
α = ln ( a 1 a 2 ) x 2 x 1

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