# Pulsatile microvascular blood flow imaging by short-time Fourier transform analysis of ultrafast laser holographic interferometry

L. Puyo, I. Ferezou, A. Rancillac, M. Simonutti, M. Paques, José-Alain Sahel, M. Fink, Michael Atlan

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L. Puyo, I. Ferezou, A. Rancillac, M. Simonutti, M. Paques, et al., Pulsatile microvascular blood flow imaging by short-time Fourier transform analysis of ultrafast laser holographic interferometry. 8th Biomedical Engineering International Conference(BMEiCON), IEEE Nov 2015, Pattaya, Thailand. pp.1 - 5, 10.1109/BMEiCON.2015.7399525. [hal-01386362](https://hal.science/hal-01386362)

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Pulsatile microvascular blood flow imaging by short-time Fourier transform analysis of
ultrafast laser holographic interferometry

L. Puyo,¹ I. Ferezou,² A. Rancillac,³ M. Simonutti,⁴ M. Paques,⁴ J. A. Sahel,⁴ M. Fink,¹ and M. Atlan¹

¹ Centre National de la Recherche Scientifique (CNRS) UMR 7587,
Institut Langevin. Fondation Pierre-Gilles de Gennes. Institut National
de la Santé et de la Recherche Médicale (INSERM) U 979, UPMC,
Université Paris 7. Ecole Supérieure de Physique et de Chimie
Industrielles ESPCI ParisTech - 1 rue Jussieu. 75005 Paris. France

²Unit of Neuroscience, Information and Complexity (UNIC), UPR CNRS 3293, France

³Brain Plasticity Unit, CNRS UMR 8249, ESPCI ParisTech, 10 Rue Vauquelin, 75005 Paris, France

⁴Institut de la Vision, INSERM UMR-S 968. CNRS UMR 7210. UPMC. 17 rue Moreau, 75012 Paris. France

We report on wide-field imaging of pulsatile microvascular blood flow in the exposed cerebral cor-
tex of a mouse by holographic interferometry. We recorded interferograms of laser light backscattered
by the tissue, beating against an off-axis reference beam with a 50 kHz framerate camera. Videos of
local Doppler contrasts were rendered numerically by Fresnel transformation and short-time Fourier
transform analysis. This approach enabled instantaneous imaging of pulsatile blood flow contrasts
in superficial blood vessels over 256 × 256 pixels with a spatial resolution of 10 microns and a
temporal resolution of 20 ms.

Microvascular blood flow plays a central role in funda-
mental physiology and in the pathophysiology of many
diseases, yet imaging of hemodynamic signals down to
capillaries without contrast agent remains a challenging
task. Functional magnetic resonance imaging [1] and
functional ultrasound [2, 3] are capable of imaging hemo-
dynamic parameters non-invasively through several mil-
limeters of living tissue, with a spatial resolution down
to capillary levels. Optical techniques can also measure
blood flow or oxygenation contrasts within microvessels
in tissue at even higher spatial and temporal resolutions,
but they are limited to superficial vascularisation imag-
ing. Functional optical coherence tomography [4, 5] can
reach intermediate depths (tens to hundreds of microns),
and photoacoustic techniques [6, 7] can go deeper in tis-
sue (> 700 µm). In parallel, wide-field coherent light
imaging approaches of superficial microcirculation by di-
rect recording of self-interference images, and processing
of their temporal [8–12] and spatial [13, 14] fluctuations
enables microvascular blood flow monitoring, deprived
of depth-sectioning abilities. With a similar outcome,
time-averaged heterodyne holographic interferometry in
off-axis and frequency-shifting recording conditions per-
mits frequency down-conversion of Doppler signals in
the bandwidth of video cameras with high sensitivity,
which enables monitoring of superficial blood flow in the
cerebral cortex [15–17] and the retina [17, 18]. Nowa-
days, high throughput cameras provide detection band-
widths compatible with time-resolved measurements of
optical phase fluctuations resulting from light-tissue in-
teraction. In this context, and in contrast with self-
interference imaging methods, off-axis holographic inter-
ferometry may circumvent the issue of imaging at ex-
tremely low irradiance levels, required to comply with
exposure safety limits.

The experimental imaging scheme designed for this
study is sketched in Fig. 1; it consists of a fibered
Mach-Zehnder optical interferometer in off-axis config-

uration. The cerebral cortex of an anesthetized mouse
was exposed through a ~ 5 mm × 5 mm craniotomy
made above the primary somatosensory cortex of the
left hemisphere. The animal was anesthetized by an
intraperitoneal injection of urethane (1.7 g/kg). Paw
withdrawal, whisker movement, and eyeblink reflexes
were suppressed. A heating blanket maintained the
rectally measured body temperature at 37 °C. The
skin overlying the skull was removed and the bone
gently cleaned. A metal post was implanted on the
occipital bone to maintain the head of the animal
during the imaging session. Extreme care was taken
not to damage the cerebral cortex, especially during
the removal of the dura. The exposed surface of the
cortex was protected by an agarose gel (1%) and a
coverslip. Experiments were performed in conformity
with the European Community Council Directive of
22nd September 2010 (010/63/UE) and approved by the
local ethics committee (C2EA -59, 'Paris Centre et Sud',
authorization number: 2012-0068). The optical source
used for the experiments was a 150 mW, single-mode,
fibered diode-pumped solid-state green laser (Cobolt
Samba-TFB-150) at wavelength λ = 532 nm, and optical
frequency ω<sub>L</sub>/(2π) = 5.6 × 10<sup>14</sup> Hz. The preparation was
illuminated with ~ 3.0 mW of continuous optical power,
over ~ 4 mm × 4 mm. The reference wave is referred to
as optical local oscillator (LO); its power impinging over
the full sensor was ~ 400 µW. The backscattered optical
field E was mixed with the LO field E<sub>LO</sub> with a non-
polarizing beam splitter cube, tilted by ~ 1° to ensure
off-axis recording conditions. Light-tissue interaction
resulted in a local phase variation φ(t) of the backscat-
tered laser optical field E(t) = ε exp [iω<sub>L</sub>t + iφ(t)],
which was mixed with the LO field from the reference
channel E<sub>LO</sub>(t) = ε<sub>LO</sub> exp [iω<sub>L</sub>t]. The quantities ε
and ε<sub>LO</sub> are complex constants and i is the imaginary
unit. Optical interferograms of 768 × 328 pixels of
coordinates (x, y) were digitally acquired by the sensor
<figure><img src="image_2.png" /><figcaption>FIG. 1: Sketch of the fibered Mach-Zehnder holographic interferometer used for the experiment. The main laser beam is split into two channels. The optical field $E$ in the object channel, backscattered by the exposed part of the cerebral cortex of a mouse, beats against the optical field $E_{LO}$ in the reference channel. Interferograms are recorded by the sensor array of a high speed camera.</figcaption></figure>

array of a high throughput camera (Photron FAST-CAM SA-X2, 1024 × 1024 pixels), at a frame rate of $\tau_S^{-1} = \omega_S/(2\pi) = 50.0$ kHz, with a frame exposure time of $\tau_E = 18.98$ µs. The distance between the preparation and the sensor was ~ 50 cm. The off-axis cross-beating interferometric contribution $H = \mathcal{E}\mathcal{E}_{LO}^* \exp[i\phi]$ of the interferogram $I = |\mathcal{E}|^2 + |\mathcal{E}_{LO}|^2 + H + H^*$ (where * denotes the complex conjugate) was filtered spatially [19] from the other interferometric contributions.

Image rendering of off-axis holograms $H(x, y, t)$ was performed by discrete Fresnel transformation [20] of recorded interferograms $I(x, y, t)$

$$H(x, y, t) = \frac{i}{\lambda z} \exp(-ikz) \iint I(x', y', t) \times \exp\left[\frac{-i\pi}{\lambda z}((x-x')^2 + (y-y')^2)\right] dx'dy' \quad (1)$$

where $k = 2\pi/\lambda$ is the optical wavenumber, and $z = 0.16$ m is the hologram reconstruction distance. The calculation grid $(x', y')$ was zero-padded to a 1024 × 1024 pixels array. The squared magnitude of the short-time Fourier transform of $H$ is referred to as the optical signal

$$S(x, y, t, \omega) = \left| \int H(x, y, \tau)G(t-\tau)e^{-i\omega\tau} d\tau \right|^2 \quad (2)$$

where $G$ is a finite Gaussian window, centered around zero, spread over ± 2 standard deviations. The width of the frequency lineshape (assumed to be zero-mean) of the optical signal $S$ was calculated by the local quadratic

<figure><img src="image_3.png" /><figcaption>FIG. 2: Images of the quadratic mean of the frequency (Eq. 3) calculated in the bands [2.3 kHz, 5 kHz] (a) and [5 kHz, 25 kHz] (b). Composite color Doppler image (c). White-light microscope image of the same area (d). Scale bar: 1 mm. A video of the composite Doppler image is reported in Movie 1.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>FIG. 3: Time-averaged optical signal $S$ (top) and pulsatile modulation depth $\sigma$ (bottom) versus frequency. Both quantities are averaged spatially in the region 1 (blue) and region 2 (green) depicted in Fig. 2.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>FIG. 4: Optical signals averaged spatially in region 1 (left pane, blue lines) and region 2 (right pane, green lines), depicted in Fig. 2. Time-frequency spectrogram $S$ (Eq. 2, top left), quadratic mean of the frequency $\Omega$ versus time (Eq. 3, bottom left), time-averaged Fourier-transform spectrum (top right), regions of interest (bottom right).</figcaption></figure>

mean of the frequency $\Omega = \sqrt{\langle\omega^2\rangle}$, where

$$ \langle\omega^2\rangle(x, y, t) = \int S(x, y, t, \omega)\omega^2 d\omega \quad (3) $$

Assessing the perfusion from the first moments of the power spectrum of the detector signal is commonplace for laser Doppler sensors [8, 21]; and the Doppler signal is often normalized with the DC signal in the spectrum, in order to cancel 1- laser amplitude noise, and 2- spatial inhomogeneities of illumination of the tissue. In our case, normalization had no noticeable effect. The pulsatile modulation depth $\sigma$ of a given Doppler component $\omega$ of the signal $S$ is defined as its standard deviation in time (the square root of its variance $Var_t$).

$$ \sigma(x, y, \omega) = [\mathrm{Var}_t S(x, y, t, \omega)]^{1/2} \quad (4) $$

The laser Doppler signal $S$ in the image plane $(x, y)$, at time $t$, and at frequency $\omega$ (Eq. 2) was processed from a series of 24576 consecutive raw interferograms $I$. The temporal resolution of ~ 20 ms is limited by the length of the apodization window $G$ at $\pm 1$ standard deviation. The Shannon bandwidth of the measurement is $[-\omega_S/2, \omega_S/2[$. Images of $\Omega$ (Eq. 3) are reported in Fig. 2; they were calculated in the bands [2.3 kHz, 5 kHz] (a) and [5 kHz, 25 kHz] (b). Those images are merged into the cyan and red channels of a composite color Doppler image (c), which exhibits common features with the white-light image of the same area, observed with a microscope. The temporal evolution of this image is reported in Movie 1. In this video, $\Omega$ was calculated

with a time step of ~ 2 ms, but the actual temporal resolution is limited by the width of the apodization window ~ 20 ms, which also implies that temporal variations are lowpass filtered with a ~ 50 Hz cutoff. In Fig. 3 (top), we reported the spectrum of the optical signal, averaged in the two regions of interest depicted in Fig. 2, and calculated from a time window of ~ 164 ms. In both cases, the signal is found to obey a power-law scaling $S \sim \omega^{-\beta}$, $1 \lesssim \beta \lesssim 2$. As reported previously [17], the Doppler spectrum is broader in regions with larger apparent vessels. A frequency sweep of local Doppler spectra of the preparation is reported in Movie 2. Fig. 3 (bottom) displays the pulsatile modulation depth $\sigma$ of the optical signal against the Doppler frequency $\omega$ (Eq. 4). This quantity was averaged in the two regions of interest depicted in Fig. 2(c). A frequency sweep of the local pulsatile modulation depth is reported in Movie 3. In this video, the signal $\sigma$ was convolved with an averaging window of ~ 500 Hz, for contrast enhancement. Cardiac cycles of ~ 0.1 s appear clearly in the time-frequency spectrograms reported in Fig. 4. The root mean square Doppler width versus time (Eq. 3, calculated in the band [2.3 kHz, 25 kHz], bottom left), the time-averaged Fourier-transform spectrum (Eq. 2, calculated in a time window of ~ 164 ms, top right), and the region of interest used for spatial averaging (bottom right) were also plotted as guides to the eye.

We demonstrated experimentally the measurement of superficial microvascular blood flow contrasts in the cerebral cortex of a mouse, exposed through a
craniotomy. For that purpose, we designed an off-axis Mach-Zehnder holographic interferometer with a high throughput camera. This approach enabled the observation of pulsatile blood flow in small superficial blood vessels over 256 × 256 pixels with a spatial resolution of 10 microns and a temporal resolution of 20 ms. The total power of the optical radiation impinging on the preparation was 3 mW. Many experiments involving cerebral blood flow monitoring might be hindered by the need for trepanation, but this demonstration could be an important step towards the realization of a retinal blood flow imager.

This work was supported by Agence Nationale de la Recherche (ANR-09-JCJC-0113, ANR-11-EMMA-046), Fondation Pierre-Gilles de Gennes (FPGG014), région Ile-de-France (C'Nano, AIMA), the Investments for the Future program (LabEx WIFI: ANR-10-LABX-24, ANR-10-IDEX-0001-02 PSL*), and European Research Council (ERC Synergy HELMHOLTZ).

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