2.1.

Experimental Setup

The basic principles of the instrument were described previously.²⁶ However, we provide a summary of the experimental setup here for clarity. The apparatus is designed to analyze scattered light in the frequency domain. The object is illuminated by the main laser beam, whose field $E_L$ undergoes dynamic scattering. The scattered (or object) field $E_O$ carries the signature of the local dynamic state of the object within its spectrum. Early studies²⁷ of Doppler broadening of light by flows showed that the Doppler shift for one scattering event is

In the experimental setup, the object (a mouse cranium) was illuminated over the region to be imaged with an average incidence angle $\alpha \approx 60\mathrm{deg}$ . The scattered field $E_O$ was mixed with a frequency-shifted LO field $E_{\mathrm{LO}}$ , split off from the main laser beam. To achieve sensitive detection, a spatiotemporal heterodyning of the scattered field was performed. The optical configuration is based either on a classic off-axis lensless Fourier holography scheme²⁸ [sketched in Fig. 1b ] or a slightly modified one, into which a microscope objective (Olympus, $\times 4$ magnification) took place in the object arm [Fig. 1a]. The choice of the presence of a microscope objective in the apparatus is dictated by spatial resolution demand. A single-mode $80\text{-}\mathrm{mW}$ cw Mitsubishi ML120G21 diode provided the main laser beam at $658\mathrm{nm}$ (angular frequency ${\omega }_L$ ). Two Bragg cells (acousto-optic modulators, AOMs), were used to shift the LO frequency by the tunable difference $\Delta {\omega }_{\mathrm{AOM}}$ of their (coherent) driving frequencies: ${\omega }_{\mathrm{LO}}={\omega }_L+\Delta {\omega }_{\mathrm{AOM}}$ . The LO beam was focused by a $1\text{-}\mathrm{cm}$ -focal-length lens, to place the virtual LO focal point in the object plane (Fig. 1). A beamsplitter was used to combine $E_O$ and $E_{\mathrm{LO}}$ with a small off-axis angle $\theta \approx 1\mathrm{deg}$ . The distance between the detection plane and the object plane (or virtual object plane) was $50\mathrm{cm}$ . A $1.3\text{-}\text{megapixel}$ PCO PixelFly camera [frame rate ${\omega }_S∕\left(2\pi \right)=8\mathrm{Hz}$ , square pixels, pixel size $6.7\mu \mathrm{m}$ ] was used to record a sequence of $m$ images $\left\{I_k\right\}$ , where $k=1,\dots ,m$ . For each detuning frequency of interest, the camera sampled a modulated interference pattern. This modulation is a consequence of optical mixing of the object field with the detuned LO field.

Fig. 1

Optical configuration (the whole apparatus is described in Ref. 26). The field $E_L$ shines the mouse cranium whose skin was excised, with an average incidence angle $\alpha$ . The object (scattered) field $E_{\mathrm{O}}$ and reference field $E_{\mathrm{LO}}$ propagation axes make a $\theta$ angle. (a) An $\times 4$ microscope objective (obj.) is used to reduce the field of view and (b) configuration without objective in the object arm. A pupil prevents parasitic light to be recorded by the camera.

2.2.

Data Acquisition

A digital hologram was recorded according to the frequency-shifting method introduced in the heterodyne holography technique, used in several imaging and detection schemes^{29, 30, 31} and that turns out to be sensitive enough to discriminate Doppler-shifted photons among heavily scattered light^{29, 31} according to their frequency. The frequency-shifting method was chosen for its accuracy.³²

The LO frequency was set to ${\omega }_{\mathrm{LO}}={\omega }_L+\Delta \omega +{\omega }_S∕n$ , where $n=4$ , to sample a map of the $\Delta \omega$ angular frequency component [corresponding to the $\Delta f=\Delta \omega ∕\left(2\pi \right)$ frequency, in hertz] of the scattered field $E_O$ impinging on the camera.²⁵ The choice of $n=4$ meant that four images were used to measure both quadratures of the scattered field. A sequence of $m=32$ images was recorded at each detuning frequency for averaging purposes to improve the signal-to-noise ratio (SNR). Each spatial map at a given temporal frequency point was measured in $4\times 1∕8=0.5\mathrm{s}$ and averaged over $32\times 1∕8=4\mathrm{s}$ .

2.3.

Signal Demodulation

The power $S\left(\Delta \omega \right)$ of the ${\omega }_L+\Delta \omega$ frequency component of the measured object field $E_O$ was computed onto the pixels of the image, according to the $n$ -phase demodulation method.^{29, 30, 32} It is calculated as

2.4.

Image Reconstruction

Two similar optical configurations were used. One is a modified lensless Fourier holographic setup, into which a $4\times$ magnification microscope objective was placed in the object arm [as sketched in Fig. 1a]. The other is a regular lensless Fourier setup [Fig. 1b]. In both cases, the LO focal point was positioned in the relevant object plane to cause the $E_O$ and $E_{\mathrm{LO}}$ average curvatures to match in the detection plane. The presence of the microscope objective in the setup was guided by the desired spatial extent of the image. The field of view was $\sim 8\times 12\mathrm{mm}$ without and $\sim 2\times 3\mathrm{mm}$ with the $4\times$ objective.

The lensless Fourier setup was used to avoid the necessity for a general Fresnel reconstruction algorithm³³ to assess the spatial distribution of the scattered field in the object plane. In this case, the reconstruction algorithm consisted of one spatial fast Fourier transform³⁴ (FFT).

2.5.

Postprocessing

A logarithmic-scale quantity $S_{\mathrm{dB}}$ was formed to display spectral maps

To assess bioflow,^{7, 35} the quadratic mean (or root mean square, rms) of the frequency shift is calculated as

To increase the SNR, a sequence of $m=32$ images was taken to build each $S\left(\Delta \omega \right)$ map at one given $\Delta \omega$ frequency point, setting $\Delta {\omega }_{\mathrm{AOM}}=\Delta \omega +{\omega }_S∕n$ , where $n=4$ . Note that $S\left(\Delta \omega \right)$ was averaged over the $m$ -image sequence. Each frequency point of the spatial distribution $S\left(\Delta \omega \right)$ was measured in $32\times 1∕8=4\mathrm{s}$ . The measurement of a whole cube of data (space, frequency) took $5\min$ and $20\mathrm{s}$ ( $=32\text{images}\times 80\text{frequency}\text{shifts}\times 1∕8\mathrm{s}$ exposure time).

3.1.

Detection of Reduced Blood Flow

The laser Doppler technique is a useful complement to other noninvasive methods, especially clinical assessment, in the determination of brain death in the newborn. Brain death is characterized by well-defined sequences in deterioration of the flow velocity waveform in blood vessels. This sequence was previously shown to consist of a loss of diastolic flow, appearance of retrograde flow during diastole, diminution in systolic flow in the anterior cerebral artery, and ultimately, lack of flow in the anterior cerebral artery.³⁶ These modifications are the results of a progressive increase in cerebrovascular resistance and a progressive decrease in cerebral perfusion, compatible with the diffuse cerebral necrosis and oedema documented postmortem. Our first set of experiments aimed to determine the threshold of sensitivity of our apparatus. We sought to determine whether our apparatus would detect the Doppler signature of the remaining perfusion in a dead animal. The animal was deeply anesthetized using an overdose of the xylazine-ketamine mixture. A cranial window (excision of a small part of the skull) was performed and images of CBF were collected more than 10 min after cessation of visible heart-beating. Figures 2a, 2b, 2c, 2d represent $S_{\mathrm{dB}}$ maps at the Doppler shift $\Delta f=10\mathrm{Hz}$ , taken at $1\text{-}\min$ intervals, and possibly suggest a residual capillary flow. Those images are consistent with the presence of a residual flow in the brain persisting soon after death, although the exact origin of this observed Doppler signal is not known.

Fig. 2

Dimensionless $S_{\mathrm{dB}}$ maps with $\Delta f=10\mathrm{Hz}$ of measurements in dead mice (test animals), with the optical configuration sketched in Fig. 1a obtained (a) $\sim 10\min$ after death and (b), (c), and (d) at $1\text{-}\min$ consecutive intervals. Images were made in a $5\text{-}\times 5\text{-}\mathrm{mm}$ cranial window carved out from the skull. The colorbar is scaled to the amplitude of the recorded signal.

3.2.

Minimally Invasive Assessment of Cerebral Blood Flow

Images of the brains of two mice were done through their intact skulls (measured thickness of $0.27\mathrm{mm}$ medial and $0.22\mathrm{mm}$ lateral), without altering it. A sequence of $S_{\mathrm{dB}}$ maps at different frequency shifts is reported in Figs. 3a, 3b, 3c, 3d, 3e, 3f . Each of the maps represented in Fig. 3 was obtained in the same mouse in a measurement time of $4\mathrm{s}$ [from 32 images recorded at ${\omega }_S∕\left(2\pi \right)=8\mathrm{Hz}$ ]. The most striking result is the contrast reversal between the vessels and the parenchyma regions in the map at $\Delta f=0\mathrm{Hz}$ [Fig. 3a] and the map at $\Delta f=384\mathrm{Hz}$ [Fig. 3c]. A more subtle difference can be observed between Figs. 3c and 3d, corresponding to the 384- and $512\text{-}\mathrm{Hz}$ Doppler shifts. The flow in the right arm of the central Y-shaped vessel (arrow) has a weak contribution at the $512\mathrm{Hz}$ , suggesting a lower CBF through it than through its left counterpart. An even more subtle effect can be seen in Fig. 3e: One can distinguish the presence of a transversal vessel (arrows), which cannot be perceived below $1\mathrm{kHz}$ , suggesting it has a high CBF. Those preliminary results attest to a sensitivity and dynamic range suitable for CBF studies. The typical response frequencies of the flow in the Y-shaped vessels in Figs. 3c and 3d are in the 400- to 500-Hz range, whereas in Fig. 2, we see this signal for a $10\text{-}\mathrm{Hz}$ frequency shift, which demonstrates the ability of the setup to map the Doppler signature of very small flows. As an indication, if we make the assumption that the collected light undergoes one scattering event and only in-plane velocities participate in the Doppler shift of light, then, according to Eq. 1, the order of magnitude of the velocity corresponding to a Doppler signal at $10\mathrm{Hz}$ , mapped in Fig. 2, would be $\sim 10\mu \mathrm{m}{\mathrm{s}}^{-1}$ .

Fig. 3

Dimensionless $S_{\mathrm{dB}}$ of maps of in vivo measurement with an intact skull and the skin removed for several $\Delta f$ frequency components. The optical configuration is sketched in Fig. 1a. The colorbar is scaled to the amplitude of the recorded signal, for each frequency point.

3.3.

Real-Time Assessment of Drug Effects

We tested whether our setup would enable detection of small and reversible variations of CBF under minimally invasive conditions. Therefore, we used a pharmacological paradigm well known to induce modification of blood flow. Effects of variation in monoamine levels (NE, 5-HT) on blood flow are well studied. We thought to monitor the modifications in CBF occurring after a single IP injection with pargyline ( $100\mathrm{mg}∕\mathrm{kg}∕\mathrm{IP}$ , single injection). Pargyline is an inhibitor of monoamine oxidase (I-MAO) type A and type B (MAOA; MAOB), which are two membrane-bound mitochondrial flavoproteines that oxidatively deaminate a broad range of biogenic amines, including monoaminergic neurotransmitters serotonin and catecholamines³⁷ (dopamine, norepinephrine, and adrenaline). In rodents, as in many other species, cerebral blood vessels display aminergic innervations and MAO activities.^{38, 39} I-MAOs are largely used and known to produce a fast increase in brain serotonin and norepinephrine levels within $5\text{to}60\min$ after a single intraperitoneal injection^{40, 41, 42} and are known to increase blood vessel pressure within minutes in vivo.⁴²

In this set of experiments we chose to increase the field of view of the control procedure. To make the image area match the whole cranium of the mouse $(\sim 1\times 1\mathrm{cm})$ , the microscope objective is removed from the setup to benefit from the natural heterodyne image field.⁴³ In our experiment, data were collected in the same animal from the instant of drug injection and every $10\min$ after the injection over a period of $1\mathrm{h}$ $20\min$ . An average rms Doppler shift map is shown in Fig. 4a , into which 16 regions of interest (ROIs) are defined. ROIs 1.x and 3.x correspond to vessels, ROIs 2.x to midline, and ROIs 4.x are in the parenchyma. We observed a decrease in CBF occurring between 10 and $20\min$ after the injection that mostly affects small-caliber blood vessels [10 to 20% decrease in rms Doppler shift see Figs. 4c, 4d, 4e, 4f]. At $1\mathrm{h}$ $20\min$ after pargyline injection, CBF had reached preinjection values. The most important relative CBF variation appears to occur in the parenchyma and the vessel ROIs. As an indication under the previously cited assumption, the order of magnitude of the rms velocity corresponding to a $1000\text{-}\mathrm{Hz}$ rms Doppler shift is $\sim 1\mathrm{mm}{\mathrm{s}}^{-1}$ .

Fig. 4

Mouse cranium from which the skin and subcutaneous tissue were excised observed in the retrodiffusion configuration [Fig. 1b]: (a) map of the rms Doppler frequency shift of light (in hertz), (b) replication of (a) intendeol to display the chosen ROIs for the calculus of the rms Doppler shift. In vivo measurement of the intact skull. The dorsal view of the mouse cranium shows the superficial dorsal venous system (transverse and sigmoid sinus and the retroglenoid veins) and some of the superficial cerebral arteries. The rostral part of the brain is to the left.⁴⁴ (c) to (f): plots of the rms Doppler frequency shift of light averaged in ROIs outlined in (b).

Our study is consistent with previous ones showing that blood vessel contractions are in part induced by activation of catecholaminergic and serotoninergic receptors. In vivo and in vitro, catecholamines have been shown to produce responses that are consistent with vasoconstriction (contraction, isometric tension, increase in perfusion pressure, and decrease in flow).^{45, 46} Serotonin has more complex effects on the cardiovascular system but is generally contractile in its effects,^{47, 48} except for meningal blood vessels.⁴⁹ Serotonin may act on S2-serotonergic receptors located on vascular smooth muscles and has also been described to act indirectly by amplifying the response to norepinephrine^{50, 51} and other agonists, of releasing constrictor substance(s) from the endothelium. In addition, the increase in heart rate elicited by monoamine elevation may partially account for an increase in blood pressure. The design of our study does not enable discrimination of whether the observed changes are the result of elevations of 5-HT and/or catecholamines, or whether changes in CBF are due to an increase in heart rate, but this was beyond the scope of our study.