Blood flow measurement in the in vivo mouse model by the combination of Doppler OCT and the signal power decrease in

Spectral Domain OCT

Julia Walther*,a, Gregor Muellerb, Henning Morawietzb, Edmund Kocha

aClinical Sensoring and Monitoring, Clinic of Anaesthesiology and Intensive Care Medicine bDevision of Vascular Endothelium and Microcirculation, Medical Clinic and Policlinic III,

Faculty of Medicine Carl Gustav Carus, University of Technology Dresden, Fetscherstrasse 74, 01307 Dresden, Germany

ABSTRACT

Blood flow measurement with spectrometer-based Fourier domain optical coherence tomography (FD OCT) is limited by the motion-induced signal fading and the resulting reduction of flow sensitivity. In this study, a combination of the established Doppler OCT and the numerically simulated signal damping due to obliquely moved scatterers is used to estimate the systolic blood flow velocities in the in vivo mouse model at which the standard Doppler OCT does not work any longer.

Keywords: Fourier domain optical coherence tomography, Doppler, signal damping, oblique sample motion, blood flow, in vivo mouse model

1. INTRODUCTION It is generally known that by using spectrometer-based FD OCT any sample motion during the integration time leads to a signal power decrease. Analytical and numerical expressions were developed for describing the modality and dimension of the signal damping. At first, S. H. Yun et al. [1] has described motion artifacts caused by transverse and axial sample movement separately which was extended by A. H. Bachmann et al. [2] taking the intrinsic chromaticity of FD OCT into account. A numerical solution of the signal power decrease caused by obliquely moving samples and their experimental verification were given afterwards by our group [3]. There, we have shown that high sample velocities and large Doppler angles of the investigated structures lead to a strong signal decrease or even the loss of it. This strong signal damping is fatal for the visualization and quantification of spatially localized motion such as blood flow.

In OCT functional imaging, the most common method for blood flow measurement called Doppler OCT (DOCT) determines the axial velocity component of the moving scatterers by measuring the Doppler frequency shift in time-domain OCT (TD-OCT) [4-6] or by calculating the phase difference between adjacent A-scans in FD OCT [7-12]. The favored spectrometer-based FD OCT using the Doppler method can be complicated due to a low signal-to-noise-ratio (SNR) and motion artifacts [1,4]. A few research groups have proposed new techniques to overcome the signal power decrease due to sample movement. J. W. You et al. have presented pulsed illumination FD OCT to reduce the signal drop caused by transverse motion e.g. sample beam scanning [13]. A recent intensity-based approach called resonant Doppler OCT (resonant DOCT) [2] requires an electro-optic phase modulator to recover the interference signal by phase-matching the reference signal to the sample movement. The velocities were calculated by comparing the intensity signals with and without moving reference arm. In contrast to the described methods, we propose not to avoid the motion-induced signal fading, but taking advantage of this effect to measure high flow velocities which are not available via standard phase-resolved Doppler FD OCT. Therefore, we have combined the established Doppler OCT and the numerically simulated signal damping due to obliquely moved scatterers to measure the high systolic blood flow velocities of the saphenous artery in the in vivo mouse model.

*julia.walther@mailbox.tu-dresden.de; phone +49 351 458 6134; fax +49 351 458 6325; www.tu-dresden.de/medksm/

Optical Coherence Tomography and Coherence Techniques IV, edited by Peter E. Andersen,Brett E. Bouma, Proc. of SPIE-OSA Biomedical Optics, SPIE Vol. 7372, 73721Y

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2. MATERIAL AND METHODS 2.1 Spectral domain optical coherence tomography – System setup

The utilized spectrometer-based FD OCT system as shown in Fig. 1 has been described in detail by our group elsewhere [3,14]. Shortly summarized, the system consists of a broadband short coherent light source (SLD 371MP, λ0 = 845 nm, FWHM = 50 nm, Superlum, Russia), a fiber-coupled 3D-scanner and a self-developed spectrometer. In contrast to previous publications, a circulator (Thorlabs, USA) is used instead of a 50:50 fiber coupler. For determination of the angle β between the sample beam and the obliquely moving sample, the 3D-scanner was used with an experimentally measured beam diameter (FWHM) of w0 = 6.7 µm.

Fig. 1. The principle of the FD OCT with spectrometer and the 3D-scanner head, as well as the data processing is shown.

Abbreviations: I(λ) – intensity, λ - wavelength, FFT – Fast Fourier Transformation, A(z) – Amplitude in dB, z – depth

2.2 Phase-resolved Doppler FD OCT

By processing the detected interference spectrum, the complex depth-encoded signal (A-scan) Γ(z) containing both the amplitude A(z) and phase φ(z) of the light backscattered from the sample is obtained [15,16].

( ) ( ) ( )ziezAz ϕ⋅=Γ (1)

The parameter z in Eq. (1) corresponds to the optical length difference between reference and a particular backscattering sample layer. The OCT morphological images are generated by using the amplitudes A(z) of the reflected light. Although the phases φ(z) are generally random for biological samples, phase-sensitive images can be obtained by simply determining phase changes. Therefore, flow imaging can be achieved by analysing the phase differences Δφ(z) between points at the same depth in adjacent A-scans. The phase difference Δφ(z) at each depth is proportional to the axial flow velocity component vz of the obliquely moved sample. In this study, the phase difference Δφ(z) is calculated by the multiplication of the complex A-scan Γj+1(z) with the adjacent, conjugate one Γj*(z) [9] as shown in Eq. (2),

( ) ( ) ( ) ( ) ( )[ ]zzij1j

j1jezAzz ϕ−ϕ∗+

+⋅=Γ⋅Γ (2)

where φj(z) is the phase of Γj(z) and j is the A-scan number. The phase difference Δφ(z) corresponds to φj+1(z) – φj(z). With known Doppler angle β between the incident sample beam and the direction of movement, the absolute sample velocity v(z) can be described by Eq. (3) where n is the refractive index of the sample.

( ) ( )( )

( )( )β⋅⋅⋅π

λ⋅ϕΔ=

β=

− cosTn4z

coszvzv

scanA

0z (3)

As shown in Eq. (3), the maximum of the linearly measured axial velocity component vz(z) is limited by fA-scan and amounts to 2.5 mm/s at an A-scan rate of fA-scan = 11.88 kHz and a center wavelength being λ0 = 845 nm. The minimum of vz(z) is given by the phase noise present in the system and can be reduced by averaging the complex values in Eq. (2).

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2.3 Signal damping method

The feasibility of flow measurement by using the signal damping of obliquely moving scatterers in spectrometer-based FD OCT was recently presented [3,17]. In Fig. 2a, a contour plot is shown which presents the signal power decrease as function of the dimensionless transverse (δx) and axial (δz) components of the oblique sample movement. This coordinates are defined as

0wxx Δ

=δ and

n2

zz0λΔ

=δ (4)

where Δx and Δz are the transverse and axial displacement during the integration time TA-scan. In Fig. 2a, contour lines of the calculated signal power decrease are drawn in steps of 1 dB and color-separated in intervals of 5 dB for the range of δx and δz from 0 to 4. The vertical axis shows the known signal drop caused by purely axial motion and the horizontal one describes the signal damping due to purely transverse motion [1,10]. The signal power decrease of an obliquely moving sample with the Doppler angle β is defined by a linear slope through the origin of the coordinate system, exemplarily shown for the angle β of 85.7° occuring in the experiment. Please note, that the angle β’ in Fig. 2a may not equate with the real world angle β of the experimental setup. Therefore, β can be transformed to β’ by using Eq. (5).

βλ

=β tannw2

'tan0

0 (5)

Apparently, in Fig. 2a no points of total fringe washout occur for a transverse component of the sample movement δx > 0. Depending on the set constant angle β the signal power decrease shows oscillations with rising velocity v. For axial displacements of the oblique sample motion δz < 1 the signal power decreases continuously. Oscillations appear at δz ≈ j, j being an integer but not zero. Therefore, the critical angle where oscillations occur is βcrit < arccos(λ0/2nw0). In addition, for transverse displacements δx > 2 the oscillations disappear. In that case, Δx is larger than twice the beam diameter w0. Consequently, for large angles (v ≈ vx) there will be no oscillations.

In Fig. 1b, the signal damping (in dB) for this experiment with β = 85.7° is separately shown as a function of the absolute sample velocity v. An oscillating part in the signal drop occurs which causes an ambiguity for the determination of the flow velocity. In the subsequently presented experiment, the maximum analyzed flow velocity is v = 40 mm/s corresponding to an axial displacement of δz = 0.8 which is smaller than the uniqueness limit of δz < 1. The measurement range of the in vivo experiment with β = 85.7° is marked by the dashed framed part in the diagram in Fig. 1b.

Fig. 2. (a) The contour plot shows the signal power decrease (in dB) of obliquely moving scatterers as a function of the

dimensionless transverse δx and axial component δz of the sample motion. The signal damping for β = 85.7° is marked by the linear slope (solid line) through the origin of the coordinate system. (b) The signal damping for β = 0° (dashed line at the top) and β = 85.7° (solid line) against the sample velocity.

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2.4 In vivo mouse model

For the analysis of the blood flow by using the combination of the phase-resolved Doppler OCT and the signal power decrease due to the obliquely moving blood cells, the saphenous artery of the right leg of a male C57BL/6 mouse is chosen. Before the examination, the mouse was narcotized by intraperitoneal application of 95 % ketamine (10 mg/ml) combined with 5 % xylazine (20 mg/ml) using a dose of 10 µl/1 g body weight. Because of the highly scattering properties of the fur covering the saphenous artery, the skin of the right hind leg was incised and removed in an area of 5 × 5 mm2 to gain access to the vessels. During investigation the mouse was fixed to a temperature-controlled operation table for small rodents. To quantify the blood flow velocities, temporally resolved B-scans with a transverse displacement of the sample beam of 0.5 µm were aquired. The angle β was measured from a 3D data set. The procedure was approved by the Institutional Ethic Commission for Animal Experiments of the medical faculty of the University of Technology Dresden and the government of Saxony.

3. COMBINATION OF DOPPLER OCT AND SIGNAL DAMPING METHOD Fig. 3 presents the consecutive cross-sectional images of the saphenous artery at the diastolic (a) and systolic (b) point of time. The shown B-scans originally consist of 800 A-scans and are decimated because of the high oversampling effect. By subtracting the logarithmic signal power of the systole from the one of the diastole, the difference image (c) can be achieved showing the signal decay of the blood flow in the systole in comparison to the diastole.

Fig. 3. Cross-sectional images of the saphenous artery at the diastole (a) and systole (b) as well as the difference image (c)

showing the signal power decrease of the blood flow in the systole compared to the diastole. The scale bar is 100 µm.

For the analysis of the blood flow velocities by using the signal damping method, a simple moving average of the amplitudes of 40 adjacent A-scans was applied to reduce the speckle noise. The resulting signal power (in dB) of the A-scan at the vessel center is shown in Fig. 4a for the diastole (black points) and the systole (gray points). The vessel lumen corresponds to 64 pixels representing an inner diameter of 230 µm. A strong signal power decrease probably caused by the refractive index-mismatch of blood [18] can be noted with increasing depth. Furthermore, the signal power in the systole is damped stronger than in the diastole. In Fig. 4b, the computed Doppler flow velocities v(z) calculated by Δφ(z) at the center of the artery are presented. A distorted parabolic flow profile can be seen which is probably caused by multiple scattering effects [19] within the vessel. As result, Δφ(z) and consequently v(z) are only reliably measurable in the upper vessel part [16]. Because of the high blood flow velocities and the resulting strong signal decrease in the systole, the analyzable lumen for Doppler OCT is reduced stronger compared to the diastole. For the fitting of a velocity profile to the reliable Doppler data, a parabolic flow was assumed though for pulsatile flow the occurring velocity profiles may deviate [20]. The fitted vmax results in 38 mm/s for the arterial blood flow in the diastole and is 85 mm/s for the systole (Fig. 4b).

The signal power and the determined Doppler velocities in the diastole (black points in Fig. 4a and b) provide the information for the calculation of the signal power of the stationary murine blood. For it, the signal power damping was calculated for each Doppler velocity value by using the simulated signal power decrease as a function of the absolute sample velocity (Fig. 2b). Because the velocities in the diastole were measured reliably only in the range from pixel 235 to 243, the signal damping is only calculated in this part of the vessel lumen. By considering the calculated signal power of the stationary blood, it is possible to ascertain the signal attenuation for the systolic point of time. With this, the corresponding flow velocity can be determined by the numerically simulated signal damping for β = 85.7°. The results of this computation are presented in Fig. 5. The diagram in Fig. 5a shows the cropped part of the signal power as a function of depth pixel for the diastole and the systole as well as the resulting fits for the range of pixel 235 to 243. The calculated

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signal power of the stationary blood is shown by the solid line. In Fig. 5b, the reliable Doppler flow velocities and their fitted parabolic profiles are presented for the diastole (black squares + solid line) and the systole (gray squares + solid line). Additionally, the blood flow velocities of the systole calculated by the signal damping method are shown by the white points and correspond well to the parabola fit of the Doppler velocities.

Fig. 4. Signal power (a) and flow velocity (b) as function of the depth pixel for the diastole (black points) and systole (gray

points). The vessel lumen ranges from pixel 235 to 299. The dashed framed parts mark the cropped parts shown in Fig. 5a and b.

Fig. 5. (a) Signal power of the flowing blood in the diastole (black point) and the systole (gray points) as well as the

corresponding fitted polynomial of the 2nd degree (dashed curves) in the range of pixel 235 to 243. The additional solid line represents the calculated signal power of the stationary murine blood and provides the reference for the determination of the signal damping in the systole. (b) Reliable Doppler flow velocities (black squares – diastole, gray squares – systole) and the corresponding fitted parabolic profile. The flow velocities of the systole computed by the signal damping method are shown by the white points and correspond well to the fitted flow profile based on the Doppler data.

4. SUMMARY AND CONCLUSION The most common method for blood flow measurement with spectrometer-based FD OCT is the phase-resolved Doppler analysis which can be complicated due to the occurring signal power decrease caused by oblique sample motion during the integration time. Therefore, the Doppler angle β has to be chosen in a way that the signal damping is small, but a sufficient phase shift can be measured. Therefore, the signal power decrease has been numerically analyzed in a previous study [3]. It was proposed to quantify high flow velocities which are not measurable by using the standard Doppler FD OCT [17]. In the present manuscript, the signal decay was used to estimate the systolic blood flow velocity of the saphenous artery in the in vivo mouse model. As shown in former studies, the signal damping method needs a reference

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signal power at a known velocity e.g. zero velocity. As this is not possible for the case of an in vivo measurement, a combination of Doppler OCT and the OCT signal damping is essential. We have shown that for the diastolic point of time, the Doppler phase shifts between adjacent A-scans provide reliable velocity values at the upper vessel part. By using the Doppler information as well as the signal power of the flowing blood in the diastole, the signal power decrease relative to the systolic blood flow can be calculated which in turn gives the systolic flow velocity. The advantage of this joined method is the improved velocity detection range in comparison to phase-sensitive Doppler analysis for the measurement of the murine systolic blood flow. In the future, this procedure should be evaluated by using a spectrometer-based FD OCT with a center wavelength of about 1300 nm because of the reduced scattering and absorption of the blood cells in this wavelength range.

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