Abstract

The retinal volumetric flow rate contains useful information not only for ophthalmo-logy but also for the diagnosis of common civilization diseases such as diabetes, Alzheimer's disease, or cerebrovascular diseases. Non-invasive optical methods for quantitative flow assessment, such as Doppler optical coherence tomography (OCT), have certain limitations. One is the phase wrapping that makes simultaneous calculations of the flow in all human retinal vessels impossible due to a very large span of flow velocities. We demonstrate that three-dimensional Doppler OCT combined with three-dimensional four Fourier transform fast phase unwrapping (3D 4FT FPU) allows for the calculation of the volumetric blood flow rate in real-time by the implementation of the algorithms in a graphics processing unit (GPU). The additive character of the flow at the furcations is proven using a microfluidic device with controlled flow rates as well as in the retinal veins bifurcations imaged in the optic disc area of five healthy volunteers. We show values of blood flow rates calculated for retinal capillaries and vessels with diameters in the range of 12–150 µm. The potential of quantitative measurement of retinal blood flow volume includes noninvasive detection of carotid artery stenosis or occlusion, measuring vascular reactivity and evaluation of vessel wall stiffness.

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

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References

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2020 (1)

G. Kissas, Y. Yang, E. Hwuang, W. R. Witschey, J. A. Detre, and P. Perdikaris, “Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks,” Comput. Methods Appl. Mech. Eng. 358, 112623 (2020).
[Crossref]

2019 (2)

S. Pi, A. Camino, X. Wei, T. T. Hormel, W. Cepurna, J. C. Morrison, and Y. Jia, “Automated phase unwrapping in Doppler optical coherence tomography,” J. Biomed. Opt. 24(01), 1 (2019).
[Crossref]

E. Pijewska, I. Gorczynska, and M. Szkulmowski, “Computationally effective 2D and 3D fast phase unwrapping algorithms and their applications to Doppler optical coherence tomography,” Biomed. Opt. Express 10(3), 1365 (2019).
[Crossref]

2018 (2)

T. Yoshioka, A. Yoshida, T. Omae, K. Takahashi, T. Tani, A. Ishibazawa, Y. Song, and M. Akiba, “Retinal blood flow reduction after panretinal photocoagulation in Type 2 diabetes mellitus: Doppler optical coherence tomography flowmeter pilot study,” PLoS One 13(11), e0207288 (2018).
[Crossref]

R. F. Spaide, J. G. Fujimoto, N. K. Waheed, S. R. Sadda, and G. Staurenghi, “Optical coherence tomography angiography,” Prog. Retinal Eye Res. 64, 1–55 (2018).
[Crossref]

2017 (5)

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22(3), 036014 (2017).
[Crossref]

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Fast and accurate phase-unwrapping algorithm based on the transport of intensity equation,” Appl. Opt. 56(25), 7079–7088 (2017).
[Crossref]

T. Tani, Y. S. Song, T. Yoshioka, T. Omae, A. Ishibazawa, M. Akiba, and A. Yoshida, “Repeatability and reproducibility of retinal blood flow measurement using a Doppler optical coherence tomography flowmeter in healthy subjects,” Invest. Ophthalmol. Visual Sci. 58(7), 2891–2898 (2017).
[Crossref]

M. Sylwestrzak, D. Szlag, P. J. Marchand, A. S. Kumar, and T. Lasser, “Massively parallel data processing for quantitative total flow imaging with optical coherence microscopy and tomography,” Comput. Phys. Commun. 217, 128–137 (2017).
[Crossref]

T. Luo, T. J. Gast, T. J. Vermeer, and S. A. Burns, “Retinal vascular branching in healthy and diabetic subjects,” Invest. Ophthalmol. Visual Sci. 58(5), 2685–2694 (2017).
[Crossref]

2016 (6)

2014 (2)

O. Tan, R. Konduru, X. Zhang, S. R. Sadda, and D. Huang, “Dual-Angle Protocol for Doppler Optical Coherence Tomography to Improve Retinal Blood Flow Measurement,” Transl. Vis. Sci. Technol. 3(4), 6 (2014).
[Crossref]

J. Walther and E. Koch, “Relation of joint spectral and time domain optical coherence tomography (jSTdOCT) and phase-resolved Doppler OCT,” Opt. Express 22(19), 23129 (2014).
[Crossref]

2013 (4)

W. M. Association, “World Medical Association Declaration of Helsinki: ethical principles for medical research involving human subjects,” JAMA 310(20), 2191–2194 (2013).
[Crossref]

A. Bouwens, D. Szlag, M. Szkulmowski, T. Bolmont, M. Wojtkowski, and T. Lasser, “Quantitative lateral and axial flow imaging with optical coherence microscopy and tomography,” Opt. Express 21(15), 17711 (2013).
[Crossref]

A. P. Cherecheanu, G. Garhofer, D. Schmidl, R. Werkmeister, and L. Schmetterer, “Ocular perfusion pressure and ocular blood flow in glaucoma,” Curr. Opin. Pharmacol. 13(1), 36–42 (2013).
[Crossref]

S. Frost, Y. Kanagasingam, H. Sohrabi, J. Vignarajan, P. Bourgeat, O. Salvado, V. Villemagne, C. C. Rowe, S. Lance MacAulay, C. Szoeke, K. A. Ellis, D. Ames, C. L. Masters, S. Rainey-Smith, and R. N. Martins, “Retinal vascular biomarkers for early detection and monitoring of Alzheimer’s disease,” Transl. Psychiatry 3(2), e233 (2013).
[Crossref]

2011 (1)

J. T. Durham and I. M. Herman, “Microvascular modifications in diabetic retinopathy,” Curr. Diabetes Rep. 11(4), 253–264 (2011).
[Crossref]

2010 (3)

2009 (5)

2008 (5)

H. R. Williams, R. S. Trask, P. M. Weaver, and I. P. Bond, “Minimum mass vascular networks in multifunctional materials,” J. R. Soc., Interface 5(18), 55–65 (2008).
[Crossref]

A. Szkulmowska, M. Szkulmowski, A. Kowalczyk, and M. Wojtkowski, “Phase-resolved Doppler optical coherence tomography—limitations and improvements,” Opt. Lett. 33(13), 1425 (2008).
[Crossref]

B. A. Bower, O. Tan, Y. Wang, J. A. Izatt, and D. Huang, “Retinal blood flow measurement by circumpapillary Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 13(6), 064003 (2008).
[Crossref]

M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 16(9), 6008 (2008).
[Crossref]

B. Pemp and L. Schmetterer, “Ocular blood flow in diabetes and age-related macular degeneration,” Can. J. Ophthalmol. 43(3), 295–301 (2008).
[Crossref]

2007 (2)

2006 (1)

2005 (1)

Y. W. Tien and R. McIntosh, “Hypertensive retinopathy signs as risk indicators of cardiovascular morbidity and mortality,” Br. Med. Bull. 73-74(1), 57–70 (2005).
[Crossref]

2003 (2)

2002 (1)

J. Strand and T. Taxt, “Two-dimensional phase unwrapping using robust derivative estimation and adaptive integration,” IEEE Trans. Image Process. 11(10), 1192–1200 (2002).
[Crossref]

2000 (1)

1999 (1)

J. Strand, T. Taxt, and A. K. Jain, “Two-dimensional phase unwrapping using a block least-squares method,” IEEE Trans. Image Process. 8(3), 375–386 (1999).
[Crossref]

1992 (1)

A. R. Pries, D. Neuhaus, and P. Gaehtgens, “Blood viscosity in tube flow: Dependence on diameter and hematocrit,” Am. J. Physiol. - Hear. Circ. Physiol. 263(6), H1770–H1778 (1992).
[Crossref]

1985 (1)

C. E. Riva, J. E. Grunwald, S. H. Sinclair, and B. L. Petrig, “Blood velocity and volumetric flow rate in human retinal vessels,” Invest. Ophthalmol. Vis. Sci. 26(8), 1124–1132 (1985).

1926 (1)

C. D. Murray, “The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume,” Proc. Natl. Acad. Sci. 12(3), 207–214 (1926).
[Crossref]

a Izatt, J.

a Schofield, M.

Akiba, M.

T. Yoshioka, A. Yoshida, T. Omae, K. Takahashi, T. Tani, A. Ishibazawa, Y. Song, and M. Akiba, “Retinal blood flow reduction after panretinal photocoagulation in Type 2 diabetes mellitus: Doppler optical coherence tomography flowmeter pilot study,” PLoS One 13(11), e0207288 (2018).
[Crossref]

T. Tani, Y. S. Song, T. Yoshioka, T. Omae, A. Ishibazawa, M. Akiba, and A. Yoshida, “Repeatability and reproducibility of retinal blood flow measurement using a Doppler optical coherence tomography flowmeter in healthy subjects,” Invest. Ophthalmol. Visual Sci. 58(7), 2891–2898 (2017).
[Crossref]

Ames, D.

S. Frost, Y. Kanagasingam, H. Sohrabi, J. Vignarajan, P. Bourgeat, O. Salvado, V. Villemagne, C. C. Rowe, S. Lance MacAulay, C. Szoeke, K. A. Ellis, D. Ames, C. L. Masters, S. Rainey-Smith, and R. N. Martins, “Retinal vascular biomarkers for early detection and monitoring of Alzheimer’s disease,” Transl. Psychiatry 3(2), e233 (2013).
[Crossref]

Ang, Y. I. W.

Y. I. W. Ang, D. A. H. Uang, and X. S. T. Y. Ao, “Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography,” Opt. Express 24(23), 1271–1273 (2016).

Ao, X. S. T. Y.

Y. I. W. Ang, D. A. H. Uang, and X. S. T. Y. Ao, “Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography,” Opt. Express 24(23), 1271–1273 (2016).

Association, W. M.

W. M. Association, “World Medical Association Declaration of Helsinki: ethical principles for medical research involving human subjects,” JAMA 310(20), 2191–2194 (2013).
[Crossref]

Bajraszewski, T.

Barton, J. K.

J. A. Izatt, M. D. Kulkarni, J. K. Barton, and A. J. Welch, “In vivo Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Conf. Proc. - Lasers Electro-Optics Soc. Annu. Meet.11(18), 212–213 (1997).

Baumann, B.

Boas, D. A.

Bolmont, T.

Bond, I. P.

H. R. Williams, R. S. Trask, P. M. Weaver, and I. P. Bond, “Minimum mass vascular networks in multifunctional materials,” J. R. Soc., Interface 5(18), 55–65 (2008).
[Crossref]

Bouma, B. E.

Bourgeat, P.

S. Frost, Y. Kanagasingam, H. Sohrabi, J. Vignarajan, P. Bourgeat, O. Salvado, V. Villemagne, C. C. Rowe, S. Lance MacAulay, C. Szoeke, K. A. Ellis, D. Ames, C. L. Masters, S. Rainey-Smith, and R. N. Martins, “Retinal vascular biomarkers for early detection and monitoring of Alzheimer’s disease,” Transl. Psychiatry 3(2), e233 (2013).
[Crossref]

Bouwens, A.

Bower, B. A.

B. A. Bower, O. Tan, Y. Wang, J. A. Izatt, and D. Huang, “Retinal blood flow measurement by circumpapillary Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 13(6), 064003 (2008).
[Crossref]

Burns, S. A.

T. Luo, T. J. Gast, T. J. Vermeer, and S. A. Burns, “Retinal vascular branching in healthy and diabetic subjects,” Invest. Ophthalmol. Visual Sci. 58(5), 2685–2694 (2017).
[Crossref]

Camino, A.

S. Pi, A. Camino, X. Wei, T. T. Hormel, W. Cepurna, J. C. Morrison, and Y. Jia, “Automated phase unwrapping in Doppler optical coherence tomography,” J. Biomed. Opt. 24(01), 1 (2019).
[Crossref]

Capps, A. G.

Cense, B.

Cepurna, W.

S. Pi, A. Camino, X. Wei, T. T. Hormel, W. Cepurna, J. C. Morrison, and Y. Jia, “Automated phase unwrapping in Doppler optical coherence tomography,” J. Biomed. Opt. 24(01), 1 (2019).
[Crossref]

Chen, T. C.

Chen, Z.

Cherecheanu, A. P.

A. P. Cherecheanu, G. Garhofer, D. Schmidl, R. Werkmeister, and L. Schmetterer, “Ocular perfusion pressure and ocular blood flow in glaucoma,” Curr. Opin. Pharmacol. 13(1), 36–42 (2013).
[Crossref]

Cuevas, M.

E. Koch, J. Walther, and M. Cuevas, “Limits of Fourier domain Doppler-OCT at high velocities,” Sens. Actuators, A 156(1), 8–13 (2009).
[Crossref]

Dai, C.

de Boer, J. F.

Detre, J. A.

G. Kissas, Y. Yang, E. Hwuang, W. R. Witschey, J. A. Detre, and P. Perdikaris, “Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks,” Comput. Methods Appl. Mech. Eng. 358, 112623 (2020).
[Crossref]

Durham, J. T.

J. T. Durham and I. M. Herman, “Microvascular modifications in diabetic retinopathy,” Curr. Diabetes Rep. 11(4), 253–264 (2011).
[Crossref]

Ellis, K. A.

S. Frost, Y. Kanagasingam, H. Sohrabi, J. Vignarajan, P. Bourgeat, O. Salvado, V. Villemagne, C. C. Rowe, S. Lance MacAulay, C. Szoeke, K. A. Ellis, D. Ames, C. L. Masters, S. Rainey-Smith, and R. N. Martins, “Retinal vascular biomarkers for early detection and monitoring of Alzheimer’s disease,” Transl. Psychiatry 3(2), e233 (2013).
[Crossref]

Falaggis, K.

Fingler, J.

Flammer, J.

S. A. Fraenkl, M. Mozaffarieh, and J. Flammer, “Retinal vein occlusions: The potential impact of a dysregulation of the retinal veins,” EPMA J. 1(2), 253–261 (2010).
[Crossref]

Fraenkl, S. A.

S. A. Fraenkl, M. Mozaffarieh, and J. Flammer, “Retinal vein occlusions: The potential impact of a dysregulation of the retinal veins,” EPMA J. 1(2), 253–261 (2010).
[Crossref]

Fraser, S. E.

Frost, S.

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T. Tani, Y. S. Song, T. Yoshioka, T. Omae, A. Ishibazawa, M. Akiba, and A. Yoshida, “Repeatability and reproducibility of retinal blood flow measurement using a Doppler optical coherence tomography flowmeter in healthy subjects,” Invest. Ophthalmol. Visual Sci. 58(7), 2891–2898 (2017).
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M. Sylwestrzak, D. Szlag, P. J. Marchand, A. S. Kumar, and T. Lasser, “Massively parallel data processing for quantitative total flow imaging with optical coherence microscopy and tomography,” Comput. Phys. Commun. 217, 128–137 (2017).
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T. Tani, Y. S. Song, T. Yoshioka, T. Omae, A. Ishibazawa, M. Akiba, and A. Yoshida, “Repeatability and reproducibility of retinal blood flow measurement using a Doppler optical coherence tomography flowmeter in healthy subjects,” Invest. Ophthalmol. Visual Sci. 58(7), 2891–2898 (2017).
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J. Walther and E. Koch, “Relation of joint spectral and time domain optical coherence tomography (jSTdOCT) and phase-resolved Doppler OCT,” Opt. Express 22(19), 23129 (2014).
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Supplementary Material (2)

NameDescription
» Visualization 1       An en-face fly-through movie of 3D Doppler OCT of human retina in the optic disc area with arterioles and veins. Human subject ID 2.
» Visualization 2       An en-face fly-through movie of 3D Doppler OCT of human retina in the optic disc area with a vessel bifurcation. Human subject ID 4.

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Figures (7)

Fig. 1.
Fig. 1. Comparison of B-scans extracted from 3D data processed with the two Doppler OCT methods: phase-resolved (PR) Doppler OCT and joint spectral and time domain OCT (STdOCT). The phase unwrapping was performed with 2D and 3D 4FT FPU. The processing times are listed in Table 2. The insets present zoomed-in vessels. Differences in the noise level (signal-to-noise ratio) and phase-unwrapping outcomes are clearly visible, including the artifacts in the areas with no signal (for the 2D 4FT FPU) and errors in phase unwrapping (phase remained wrapped in one of the vessels in PR-Doppler OCT with 2D 4FT FPU). The black rectangle indicates the result with the best SNR and phase unwrapping outcomes. The colors in the images represent the axial flow velocity values. Blue: flow direction against incoming beam of light; red: along with the light propagation. The increasing color intensity indicates increasing axial flow velocity values as indicated by the color bar.
Fig. 2.
Fig. 2. a) Schematic illustration of the flow phantom: a microfluidic device with a protein solution flowing through the trifurcated channels. The light beam propagates from the top. The green rectangles mark sets of N = 6 C-scans before and after trifurcation, which were used to obtain data presented in Table 3. The Roman numerals indicate the channels in the trifurcation. b) STdOCT Doppler C-scans selected from 3D data sets: one pre- and the second post-trifurcation. The two examples show data acquired for different volumetric flow rates, as labelled in the images. First column: wrapped phase. Second column: phase unwrapped with 3D 4FT FPU. The arrows indicate channels (I, II, III, IV), for which the flow rates are listed in Table 3. The noise in the images was intentionally not removed. The orange rectangles indicate the ROIs for volumetric flow rate calculation. The colors in the images represent the axial flow velocity values. Blue: flow direction against incoming beam of light; red: along with the light propagation. The increasing color intensity indicates increasing axial flow velocity values as indicated by the color bar.
Fig. 3.
Fig. 3. a) Schematic illustration of vessel bifurcation in the human retina. The orange ellipse illustrates an XY-cross section of the vessel. The minor axis of the ellipse is used as the lumen diameter of the vessel. The light beam propagates from the top. The green rectangles mark sets of N = 6 C-scans before and after bifurcations. The Roman numerals indicate the vessels in the bifurcation. b) Example STdOCT Doppler C-scans of the human retina near the optic nerve head at two depths. The images in the background show the data with the wrapped phase while the zoomed-in regions in the foreground show the result of the phase unwrapping. Arrows I, II, III: vessels whose flow rate values are listed in Table 4. The colors in the images represent the axial flow velocity values. Blue: flow direction against incoming beam of light; red: along with the light propagation. The increasing color intensity indicates increasing axial flow velocity values as indicated by the color bar. The orange ellipse illustrates an XY-cross section of the vessel. The minor axis of the ellipse is used as the lumen diameter of the vessel. The Doppler C-scans for the data set for subject ID 4 are presented in Visualization 1.
Fig. 4.
Fig. 4. Volumetric blood flow measurement in the vascular bifurcations sets of 3D data obtained in subjects ID 2 and ID 3 (Table 4.). Top: selected cross-sectional images of the wrapped phase. Bottom: outcomes of the 3D 4FT FPU algorithm. The arrows with Roman numerals indicate the selected vessels. The subscript “W” refers to the wrapped phase, while the subscript “U” refers to the same vessels after unwrapping. The figure insets show magnified regions of the indicated vessels. IU, IIIU: errors of the phase unwrapping (phase has remained wrapped). Arrows IIU, IVU: phase-wrap-free vessel (diameter: 18 µm, 31 µm). Arrow VU: error-free phase unwrapping of the flow for a vessel with diameter of 79 µm. The insets for vessel IIU present five zoomed regions of adjacent C-scans. The indicated vessels are plotted in Fig. 7. The orange ellipse represents the ROI used for flow calculation. The orange line in the ellipse is the minor axis of the ellipse and indicates the lumen of the vessels. The colors in the images represent the axial flow velocity values. Blue: flow direction against incoming beam of light; red: along with the light propagation. The increasing color intensity indicates increasing axial flow velocity values as indicated by the color bar. A movie showing the Doppler C-scans for subject ID 2 is presented in Visualization 2.
Fig. 5.
Fig. 5. Identification of arterioles and veins in the STdOCT data set. a) Identification of the main vein and arteriole in the OCT angiography image (the grayscale inset) of the optic nerve head by comparison with a fundus photograph (background image). b) Overlay of the STdOCT intensity fundus images with STdOCT Doppler images generated from the same 3D OCT data set. Only areas with blood flow velocity above a threshold are shown from the Doppler images. The two columns show two example data sets from the same subject (ID 1). Top row: STdOCT images with no phase-unwrapping. Bottom row: STdOCT images with phase-unwrapped using 3D 4FT FPU method. The insets show one of the identified vessels before and after phase unwrapping. The colors in the images represent the axial flow velocity values. Blue: flow direction against incoming beam of light; red: along with the light propagation. The increasing color intensity indicates increasing axial flow velocity values as indicated by the color bar.
Fig. 6.
Fig. 6. Blood flow rates measured in arterioles, veins and capillaries of the optic nerve head of volunteer ID 1 (Table 4) plotted as a function of vessel lumen diameters (a) prior to phase unwrapping and (b) after phase unwrapping. The blue crosses indicate the flow rates in vessels with no phase-wrapping. The red dots indicate the flow values in vessels with wrapped phase (a) prior to phase unwrapping and (b) after phase unwrapping. Solid line in b: weighted least-square power curve fits. See text for details.
Fig. 7.
Fig. 7. Log-log plots of the blood flow rate versus the vessel lumen diameters. First row: venous blood flow. Second row: arterial blood flow. The green marks indicate capillaries with a diameter smaller than 20 µm. Each column shows combined results from 6 data sets obtained in one of the three subjects (ID 1 to ID 3, Table 4). Solid lines: linear fit (the equations obtained by the least-squares fit are given on the top of each plot). Dashed lines: 95% confidence interval of the fit. Example vessels IU, IIU, IVU, VU, and VIU presented in Fig. 4 are indicated with magenta outlines.

Tables (4)

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Table 1. Experimental protocols.

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Table 2. Mean computation times and their standard deviations for the implemented Doppler OCT and phase unwrapping algorithms.

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Table 3. Mean flow rate values in the flow phantom, in the data unwrapped with 3D 4FT FPU method. The errors were estimated from t-Student distribution at 0.05 significance level.

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Table 4. Mean volumetric blood flow rates in bifurcating vessels of the optic nerve head of five volunteers, calculated from six adjacent C-scans in the STdOCT data unwrapped with 3D 4FT FPU method. The errors were estimated from t-Student distribution at 0.05 significance level.

Equations (5)

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φ D ( r , Δ t ) = Im { ln ( A ( r , t ) A ( r , t + Δ t ) ) } = 2 k n v z ( r ) Δ t .
Q = 1 2 k n Δ t ROI ψ ( r ) s ,
v z max = π 2 k n Δ t .
ψ e s t ( r ) = 2 Im { exp ( i φ ) 2 exp ( i φ ) } ,
ψ ( r ) = φ ( r ) + 2 π round [ ( ψ e s t ( r ) φ ( r ) ) ( 2 π ) 2 ] .