2.1.

Digital Holography

Holography techniques were developed by Gabor in 1948 with the aim of improving the detection of spatial resolution in the X-ray wavelength by exploiting its lensless imaging capabilities. This resulted in the possibility of generating an exact replica during the illumination of the recorded hologram (reconstruction process) with a specific magnification of the full object wavefront created by the observed specimen.¹⁴ The use of digital means in holography gradually occurred at the end of the 1960s, when Goodman used a vidicon detector to encode a hologram which could be reconstructed on a computer.¹⁵ However, the interest in digital holography rose with the availability of cheaper digital detectors and charge-coupled device cameras.^16,17 The two practical main approaches to recover the object wave from the recorded hologram are namely temporal decoding, i.e., phase shifting and spatial decoding i.e., off-axis methods. Phase-shifting reconstruction methods are based on the combination of several frames, and enable the suppression of the zero order and one of the cross terms through temporal sampling.^18,19 The most well-known phase-shifting algorithm, proposed by Yamaguchi,²⁰ is based on the recording of four frames separated by a phase shift of a quarter of a wavelength. Various combinations of frames derived from interferometry have been considered^19,21 and many different approaches have been developed to produce the phase shift including high precision piezo-electric transducers, which move a mirror in the reference wave or acousto-optics modulators using the light frequency shift, etc. One of the main issues in phase-shifting methods is the requirement of several frames for reconstruction in interferometric setups, which are commonly very sensitive to vibrations. Thus, it could be difficult to ensure stable phase shifts and an invariant sample state during acquisition. In addition, the requirements on the accuracy of the phase shifts are rather high in regard to displacements on the order of magnitude of hundreds of nanometers, implying the use of high-precision transducers. Consequently, several attempts were made to either reduce the required number of frames for reconstruction, which led to two-frame reconstruction,^22,23 or to simultaneously enable the recoding of the various phase-shift frames, by employing, for example, multiplexing methods.²⁴ On the other hand, more refined algorithms were developed to relax the accuracy requirements of phase-shift methods.^25–27 It should also be mentioned that the development of a fast temporal phase-shifting procedure within the framework of tomography²⁸ as well as approaches based on the spatial analysis of fringe pattern,^29,30 sometimes referred as spatial phase shifting, has permitted to successfully reconstruct the object wave in an off-axis configuration.^31,32

The second main approach for recovering the object wave is based on an off-axis configuration, so that the different diffraction terms encoded in the hologram (zero-order wave, real and virtual images) are propagating in different directions, enabling their separation for reconstruction.³³ This configuration was the one employed for the first demonstration of a fully numerical recording and reconstruction holography.^16,17

In practice, reconstruction methods based on an off-axis configuration usually rely on Fourier methods to filter one of the diffraction terms. This concept was first proposed by Takeda et al.³⁴ in the context of interferometric topography. The method was later extended for smooth topographic measurements for phase recovery³⁵ and generalized for use in DHM with amplitude and phase recovery.³⁶ As discussed in the following paragraphs, the main characteristic of this approach is its capability for recovering the complex object wave through only one acquisition, thus greatly reducing the influence of vibrations. However, as the diffraction terms are spatially encoded in the hologram, this one shot capability potentially comes at the cost of the usable bandwidth. In addition, the frequency modulation, induced by the angle between the reference and the object wave, has to guarantee the separability of the information contained in the different diffraction terms that are encoded in the hologram while carrying a frequency compatible with the sampling capacity of the digital detectors.

2.2.

Quantitative Phase Digital Holographic Microscopy

A digital holographic microscope³⁷ comprises both an optical setup devoted to hologram formation and software specially developed to numerically process the digitized hologram. The hologram results from the interference of the object beam with a reference wave that can be kept separate from the object beam. The goal is to precisely estimate the propagated wavefront corresponding to either the virtual or the real image of the specimen. Different optical setups have been proposed to perform microscopy with holography. Some lensless setups have been proposed to image small fields^38–40 by using strongly diverging wavefields, such as spherical waves emitted by punctual sources. Optical setups that make use of a microscope objective (MO) offer the largest numerical apertures.^36,41 A typical DHM arrangement we have developed and used to explore transparent specimens including living cells, is the quantitative monitoring of the phase retardation of the transmitted wavefront [Fig. 1(a)].⁴¹

Fig. 1

(a) Transmission optical setup for QP-DHM (b) role of the microscope objective (MO): magnifying the image of the specimen but also, in terms of wavevectors, decreasing the lateral wavevector component $k_x$ or $y$ by a factor proportional to the magnification (M) of the MO, so that the hologram can be sampled by an electronic camera according to the Shannon’s rules (c,d) three-dimensional (3-D) perspective images in false colors of a living human red blood cell (RBC) and a mouse cortical neuron in culture, respectively. Each pixel represents a quantitative measurement of the phase retardation or cellular optical path length (OPL) induced by the cell with a sensitivity corresponding to a few tens of nanometers. By taking into account the measured mean values of the RBC and neuronal cell body refractive indices (RIs) resulting from the decoupling procedure (cf. below), scales (at right), which relate OPL (deg) to morphology in the $z$-axis ($\mu \text{m}$), can be constructed. Abbreviations: BS, beam splitter; CCD, camera; M1 and M2, mirrors; MO, microscope objective; O, object beam; R, reference beam; RL, reference lens and OC, object condenser; object or specimen.

Other configurations are possible depending on the targeted application,^12,42 but will not be reviewed in detail here. An important issue is the need for a reference beam that is controllable in both in intensity and polarization, thus enabling one to improve contrast and signal. The holographic principle also permits other valuable concepts which particularly building on the possibility of superimposing several holograms. Holograms with several reference waves corresponding to several polarization states can be generated in order to analyze the birefringence properties of specimens including strained dielectrics or biological molecules.^43,44 Reference waves corresponding to different wavelengths can also be generated, permitting the use of synthetic wavelengths from a single hologram.⁴⁵

As in other developments in digital holography, the hologram reconstruction method in DHM is based on the theory of diffraction. When an MO is used and the specimen can be maintained in the MO’s focal plane, the image is formed at infinity. The hologram at infinity is simply the Fourier transform of the specimen. Inverse Fourier transformation straightforwardly provides the reconstructed wavefront in the focal plane of the MO. However, specimens are generally not fully contained in the focal plane of the MO, and thus a real and/or virtual image is formed at a finite distance from the MO [Fig. 1(b)]. Intercepting the wavefront at a finite distance from the specimen image gives rise to holograms in the Fresnel zone. Thus, the Huygens-Fresnel expression of diffraction can be used to calculate the propagation of the reconstructed wave. It should be noted that the MO introduced in the interferometer allows one to adapt the wavefield to the sampling capacity of the camera. Indeed, the lateral components of the wavevector $k_x$ or $y$ can be divided by the magnification factor M of the MO. Taking advantage of a full digital approach, a computer can perform the reconstruction by simulating the reference wave and multiplying it by the hologram intensity distribution. Then, the distribution of the wavefront in space is obtained by simulating the propagation of the wavefront reconstructed in the plane of the hologram. As previously mentioned, the wavefront gives rise to several propagated beams corresponding to the zero,$+1$ and $-1$ diffracted orders. When an MO is used, the latter two orders give rise to real and virtual images, respectively, that appear as twin images which are the reflection of one another on a virtual mirror that takes the place of the hologram plane.

The off-axis geometry introduces a spatial carrier frequency, and demodulation restores the full spatial frequency content of the wavefront. The main advantage of this approach is that all the information for reconstructing the complex wavefield comes from a single hologram.³⁶ In microscopy, the full bandwidth of the beam delivered by the MO can be acquired without limitation. Scale adjustments can made to preserve the correct sampling of the MO’s full bandwidth so that no loss of resolution is conceded. Finally, selection of a signal corresponding to a diffraction order of $+1$ in the Fourier domain of the hologram allows for the full restoration of the object wavefront transmitted by the MO. Therefore, reconstructing the wavefront in 3-D is simply done by propagating the wavefront generated in the hologram plane $x\text{-}y$ to the image plane $\xi \text{-}\eta$, which is situated at a distance $d_{\text{rec}}$. This could be efficiently achieved by computing the Fresnel transform of the wavefield. Thus, DHM brings quantitative data simultaneously derived from the amplitude and the phase of the complex reconstructed wavefront that is diffracted by the object. Our method requires the adjustment of several reconstruction parameters, which can be done using a computer-aided method we developed. Some image processing is also needed to improve the accuracy of the reconstructed phase.⁴⁶ Moreover any type of aberrations can also be corrected during such a numerical reconstruction process.^47,48 Using a high numerical aperture, submicron transverse resolution has been achieved to a 300-nm lateral resolution. Accuracies of approximately 0.1° have been estimated for phase measurements. In reflection geometry, this corresponds to a vertical resolution of less than 1 nm at a wavelength of 632 nm.⁴⁹ In transmission geometry, the resolution is limited to a few nanometers as far as living cells are concerned. It is also worthwhile to note that when the experimental configuration of the hologram recording requires distances of reconstruction for which the Fresnel approximation does not properly work, the propagation of the wavefront generated by the hologram can be efficiently performed with the angular spectrum approach.^50,51 On the other hand, the characterization of the effect of noise on the formation of the hologram and on the reconstruction of the image results in an improved signal-to-noise ratio (SNR), using the coherent detection of scattered light.^52,53 This improvement is often described as “coherent amplification” of the signal.

2.3.

Quantitative Phase Tomographic Microscopy: Full Three-Dimensional Imaging Technique

In general, a single wavefront determination obtained from a single hologram is not sufficient to obtain a full 3-D image of an object. An exception concerns sparse media, similar to those found in particle image velocimetry (PIV), where each particle can be considered as an isolated punctual object and its position determined in 3-D by the methods of “in-line” holography.^54,55 Thus, the combination of data reconstructed from several holograms, obtained at either several wavelengths (variable $k$-vector amplitude) or at several incidence angles (variable $k$-vector direction), is needed to achieve true 3-D imaging. Several articles report results obtained by changing the wavelength (variable $k$-vector amplitude) as shown by Marron.⁵⁶ However, in this study, the range of the wavelength scan remained very small and consequently the resolution was weak. Arons et al. using “Fourier synthesis holography”⁵⁷ have also discussed a similar approach. In digital holography, multiple wavelengths have been used to reconstruct 3-D structures.⁵⁸ In the field of microscopy, such multiwavelength tomographic imaging techniques, based on reconstruction from multiple holograms, have yielded very accurate images of cells, erythrocytes in particular.^59,60 An alternative, but somehow similar approach, is to use a wide bandwidth source and form a hologram in the plane where the mutual coherence between the object and reference wave is nonzero: this concept introduces coherence gating in the space domain. It has been proven to perform well.^61,62 On the other hand, the variable $k$-vector direction approach more exactly meets the concept found in the literature under the name of “diffraction tomography”⁶³ for reconstruction of the scattering potential associated with the structure of the diffracting object. A diffracted wave can be collected and reconstructed from the holograms at various incidences. Practically, the phase and amplitude of the diffracted wave are directly reconstructed from the hologram and can be used to compute the scattering potential at every point of the specimen. From these data, the 3-D distribution of the RI can be established providing a 3-D tomographic image of the cell constituents. Tomography of cells based on DHM is new and original. In 2006, a first approach consisting of the rotation of the specimen,^64,65 has been developed. It was demonstrated that the RI of the cell body could be measured in 3-D with a spatial resolution better than $3\mu \mathrm{m}$ in all directions. Other approaches consisting of rotating the beam rather than the object have been proposed.^28,66–69 Kou⁷⁰ and Sheppard⁷¹ have compared both approaches in their principles and shown consistent differences in the performance of each modality. Different reconstruction algorithms have been used to reconstruct objects from several holograms obtained at variable $k$-vector directions or amplitudes including projection^28,64 and diffraction algorithms.^72–74

3.1.

Cell Counting, Classification Analysis, and Cytotoxic Screening Assay

Practically, the QPS is particularly well suited to the development of algorithms, allowing automated cell counting,^75–79 recognition, and classification.^80–89 As far as red blood cells (RBCs) are concerned, QPM allows one to achieve a morphometry-based RBCs’ analysis. Indeed, the intracellular content of mature nucleus-and organelle-free RBCs, which can be assimilated from an optical point of view to a homogeneous solution mainly containing hemoglobin, induces a quantitative phase shift directly proportional to the RBC thickness.^{78,85,87,88,90–96}

Since the QPS is also sensitive to intracellular RI, it specifically provides some information about the intracellular content. Based on this information, interesting applications allowing discrimination between physiological and pathophysiological states have been achieved, particularly in the fields of assisted reproduction^86,97,98 and cancer research.^99–102 In addition, in vitro label-free cytotoxicity screening assays based on QP-DHM have been recently validated due to the flexibility offered by numerical reconstruction.^103–106

3.2.

Exploration of Cell Movements and Dynamics

QPM approaches as nonscanning techniques are usually well suited to monitor dynamic cell processes. Dynamic motions during the migrations of human dendritic cells¹⁰⁷ and subcellular contraction of embryonic cardiomyocytes^108,109 have been successfully measured. On the other hand, due to the numerical propagation of the reconstructed object wavefront, QP-DHM allowing, one to apply autofocusing^{32,110,111–114,115} and extended depth of focus^116–122 has opened the possibility of efficiently monitoring cell migration in 3-D.^{110,112,123–130} In addition, these numerical possibilities offer an alternative to the shallow depth of field of conventional microscopy, which hampers any fast 3-D tracking of cells in their environment specifically when microfluidic devices are considered.^131,132 Coherently, autofocusing and extended depth of focus abilities also facilitate the 3-D tracking of micro- or nano-particles,^{126,133–135} particularly in combination with approaches capable of second harmonic generation,^136,137 the use of which is highly promising in medical fields including drug carrier, tumor detection and treatment, gene therapy.

3.3.

Dry Mass, Cell Growth, and Cell Cycle

As described by Eq. (1), the measured quantitative phase shift induced by an observed cell on the transmitted light wavefront is proportional to the intracellular RI, which mainly depends on protein content. Therefore, this measure can be used to directly monitor protein production, owing to a relation established more than 50 years ago by Barer.⁸ Practically, the phase shift induced by a cell is related to its dry mass (DM) by the following equation (converted to the International System of Units):

Recently, several groups using various QPM techniques have begun to exploit this phase-DM relationship to study the dynamics of cell growth as well as to the characterization of the cell cycle.^138–143 As far as RBCs are concerned, this relationship has also been explicitly and implicitly used to calculate hemoglobin content, which corresponds to the RBC DM.^92,144–147

3.4.

Cell Membrane Fluctuations and Biomechanical Properties

RBCs, while being carried throughout the vascular tree to deliver oxygen from the lungs to the tissues, are squeezed as they pass capillaries which are often smaller than the cell diameter. This ability can be attributed to the remarkable elastic properties of the membrane structure. As a consequence of these elastic properties, RBCs show cell membrane fluctuations (CMFs) at the nanometric scale, often called flickering. Owing to their high sensitivity allowing one to quantitatively measure RBC membrane fluctuations over the whole cell surface, different QPM techniques have shed new light on these CMFs by providing quantitative information about the biomechanical properties of the RBC membrane.^{145,148–153} We should also mention the integration of QPM with optical tweezers, which represents a very promising tool, especially with respect to monitoring trapped objects along the axial direction including nanoparticles,^154,155 as well as manipulating and testing the biomechanical properties of cells).^81,156–160

3.5.

Dynamics of Absolute Cell Volume and Transmembrane Water Movements

Membranes of animal cells are highly permeable to water; therefore, movement of water across membranes is dictated in large part by osmotic pressure gradients.^161,162 Any imbalance in intracellular and extracellular osmolarity is paralleled by water movements across cell membranes affecting the cell volume along with the concentration of intracellular compounds.¹⁶³ However, even at constant extracellular osmolarity, the volume constancy of any mammalian cell is permanently challenged by the normal activity of the cells.¹⁶⁴ Thus, the maintenance of a constant volume is critical for cell homeostasis and requires the continued operation of cell volume regulatory mechanisms.¹⁶¹ Water crosses cell membranes through several routes (simple diffusion through the lipid bilayer, transmembrane proteins such as specialized water channels, aquaporins, etc.).¹⁶² Consequently, the accurate measurement of both the absolute cell volume and water membrane permeability represents indices which can provide highly relevant information about the mechanisms involved in the cell volume regulatory processes. However, the noninvasive measurement of these two parameters at the single cell level is not a trivial issue.¹⁶⁵ Below, we present how these parameters can be calculated from the QPS although, as indicated by Eq. (1), information concerning the intracellular content related to ${\overline{n}}_c$ is intrinsically mixed with morphological information relating to a thickness $d$. Practically, different strategies have been developed to separately measure cell morphology and RI. Some authors^166,167 measured the intracellular RI by trapping cells between two cover slips separated by a known distance. However, this approach which prevents cell movement, precludes the possibility of exploring dynamic cellular processes, including cell volume regulation. Recently, spectroscopy phase microscopy approaches^145,147,168 have addressed this limitation, at least as far as cells with high intrinsic dispersion properties are considered, including red blood cells (owing to presence of hemoglobin pigment). However, such spectroscopy approaches are only applicable to a very limited variety of cell types, most of which have intrinsic dispersion almost identical to that of water. We have developed another approach called the decoupling procedure, to separately measure the parameters ${\overline{n}}_c$ and $d$ from the phase signal $\phi$, based on a modification of the extracellular RI, $n_m$. Basically, this method consists of performing a slight alteration of the extracellular RI $n_m$ and recording two holograms corresponding to the two different values of $n_m$, providing two quantitative phase images from which ${\overline{n}}_c$ and $d$ can be calculated. We have considered two different approaches to modify $n_m$: the first approach requires sequentially perfusing a standard cell perfusion solution and a second solution with a different RI, but with the same osmolarity to record the two corresponding holograms at a single wavelength.¹⁶⁹ Practically, this procedure has permitted us to quantitatively measure some highly relevant RBC parameters, including mean corpuscular volume and mean corpuscular hemoglobin concentration.⁹² However, owing to the solution exchange time, this approach precludes the possibility of monitoring dynamic changes of cell morphology and RI that occur during fast biological processes. To overcome these drawbacks, we have developed a second approach based on a dual-wavelength DHM (DW-DHM)⁴⁵ which exploits the dispersion of the extracellular medium, enhanced by the utilization of an extracellular dye, to achieve separate measurements of the intracellular RI and the absolute cell volume in real time.¹⁷⁰ These approaches have been successfully applied to study the osmotic water membrane permeability $P_f$—representing the water volume flux per unit of time per unit of membrane surface for a given applied osmotic gradient—by monitoring cell volume changes while retaining the cell functionality.¹⁶⁵ In addition, resulting from the linear relationship between the intracellular RI and the DM as well as from a DM balance equation, it has been possible to determine the RI of the transmembrane flux $n_f$.¹⁶⁵ The high precision with which $n_f$ can be determined reveals if the transmembrane water flux is accompanied by solute transport and provides some important information about the underlying mechanisms involved in the transmembrane water movements.

4.1.

Background

Within the brain, water is distributed between blood, cerebrospinal fluid, and interstitial and intracellular compartments. Practically, water moves across these compartments following the differences in osmotic and hydrostatic pressures. At constant hydrostatic pressure gradients, water movements largely depend on the osmotic gradients, which are created by the concentration of osmolytes, including ions, amino acids, and derivatives, in particular, some neurotransmitters, in the extracellular and intracellular compartments. At the microscopic level, water transport is involved in cell volume regulation and in controlling the dimensions of the extracellular space (ECS).^171,172 However, neuronal activity challenges the hemostasis of these intra and extra cellular compartments. Indeed, considering a low intracellular concentration of ${\mathrm{Na}}^{+}$, resulting from both a neuronal membrane with a low permeability to ${\mathrm{Na}}^{+}$ and sodium-potassium transporters continuously pumping out ${\mathrm{Na}}^{+}$, if the ${\mathrm{Na}}^{+}$ conductances suddenly increase it will cause ${\mathrm{Na}}^{+}$ to rush into the neuronal cell. This movement of ${\mathrm{Na}}^{+}$ ions along their concentration gradient is also enhanced by the transmembrane electrostatic gradient corresponding to a negative resting membrane potential ($-70\mathrm{mV}$) mainly due to a large quantity of negatively charged intracellular proteins. This inward flow of ${\mathrm{Na}}^{+}$ ions changes the electrochemical gradient, which in turn produces a further rise in the membrane potential called a depolarization. This mechanism is precisely what initiates the action potential. Otherwise, the ${\mathrm{Na}}^{+}$ currents flowing inward at a point on the axon during an action potential spread out along the axon and depolarize the adjacent sections of its membrane. When actions potentials are conducted down an axon—their size remains undiminished as they travel— they finally induces a depolarization in a presynaptic terminal button, which is the end of axonal branches which generally face the postsynaptic membrane of the neuron that receives the message. The two membranes face each other across the synaptic cleft which is a gap of around 20-nm wide. Practically, when the depolarization reaches the terminal button, small vesicles containing molecules of the neurotransmitter and located just inside the presynaptic membrane, fuse with the membrane and then break down, spilling their contents into the synaptic cleft. Then, the neurotransmitter diffuses across the synaptic clef and by attaching postsynaptic membrane opens neurotransmitter–receptor ion channels, which permit the passage of specific ions into or out the cell, thus changing the local membrane potential of the postsynaptic neuron, which could, in turn, induces or inhibits the generation of action potentials.¹⁷³

Consequently, these transmembrane ions movements and neurotransmitter releases including glutamate, glycine, and GABA (gamma-aminobutyric acid) related to the neuronal activity are accompanied by transmembrane water movements for osmotic reasons. This results in the regulation of both the ECS and the cell volume being affected by the level of neural activity.

On the other hand, a distinct feature of nervous tissue is the intricate network of synaptic connections among neurons with diverse morphologies. Although initial connections are formed largely through molecular mechanisms, it has been clearly established that electrical activities influence not only the structure and efficacy of existing synapses, but can also contribute to the production of new synapses, in particular through changes in the size and shape of dendritic spines and the formation on new ones. Indeed, synapses can mainly occur in three places of the postsynpatic neuron: on the soma, on other axons, and on the smooth surface of dendrites—branched projections which compose most of the receptive surface of a neuron- or on dendritic spines—small membranous protrusions, with typical sizes of a few hundred nanometers, that stud the dendrites. The axodendritic synapses represent the largest proportion of the excitatory synapses in the mammalian brain and the glutamate is the most common excitatory neurotransmitter, inducing a depolarization of the postsynaptic neurons particularly by opening the (NMDA), the 2-amino-3-(3-hydroxy-5-methylisoxazole-4-yl) propionate (AMPA), and the kainate ionotropic receptors, representing the three main classes of glutamate-receptor ion channels. All these abilities of synapses to strengthen, weaken or to be created over time in response to increases or decreases to the neuronal network activity, called synaptic plasticity, that have been intensively studied in recent years, have been significantly stimulated by the development of new optical methods, which have permitted the resolution of the morphology and the dynamics of dendritic spines.¹⁷⁴ Furthermore, plasticity mechanisms affect information transfer on multiple time scales and levels of specificity and play a pivotal role in integrative function and learning. However, with a few exceptions, including activity-induced LTP and LTD (long-term potentiation and long-term depression) and some specific activity-dependent mechanisms that can modulate the density of dendritic spines onto which the majority of fast excitatory synaptic transmission operates, our understanding of how electrical activity affects the structure and function of neuronal networks is very limited. Within this framework, the development of techniques that provide a noninvasive resolution of both local neuronal network activity and dendritic spine dynamics is highly relevant. In light of this, we present how QP-DHM can start to originally address both of these issues due to the possibilities of high resolution and of monitoring cell volume and transmembrane water.

4.2.

Imaging Neuronal Activity by Measuring Transmembrane Water Movements with Quantitative Phase Digital Holographic Microscopy

With respect to the study of neuronal activity, electrophysiological approaches, in particular patch-clamp techniques, have permitted major breakthroughs leading, in particular, to the discovery of LTP and LTD, by setting a voltage across the neuronal membrane and directly measuring the current flowing through a single ion channel. Basically, a patch clamp is the best standard for assessing ion channel function because it allows the discrimination of ionic currents in the femto-ampere (10–15 fA) range with microsecond time resolution. Practically, the most commonly used patch-clamp mode is the whole-cell mode. In short, in this configuration, an open tip thin glass micropipette, which contains both an ionic solution mimicking the intracellular solution and chlorided silver electrode connected to a highly sensitive electronic amplifier, is pressed against a cell membrane. A brief strong suction is applied to both assist in the formation of a high-resistance seal between the glass and the cell membrane and to disrupt the membrane patch. The interior of the pipette becomes continuous with the cytoplasm and a bath electrode is used to set the zero level. In whole-cell measurements, the two main configurations are the (1) voltage-clamp mode and the (2) current-clamp mode. In the voltage-clamp mode, the cell membrane potential is kept constant via a negative feedback loop injecting a compensating current into the cell that resembles the current that is flowing through the whole-cell membrane. Practically, the recording of this compensating current provides information about the whole-cell membrane conductance. In addition, the current-voltage relationships can be investigated since the membrane potential can be manipulated independently of ionic currents. In contrast, in the current-clamp mode, the injected current is kept constant and changes in the membrane potential can be measured. However, a patch clamp is still a highly invasive laborious process requiring precise micromanipulations and a high degree of operations, which generally impose the recording of voltages on a limited number of cells that form a neuronal network. Optical techniques, however, seem to be an ideal solution for measuring membrane potentials since they are relatively noninvasive and could work both at low and high magnifications. For instance, calcium indicators used in combination with high resolution two-photon microscopy allow the performing measurements of the spiking activity from hundreds to several thousand neurons in mammalian circuits while still keeping track of the activity of each neuron individually.^175,176 However, calcium imaging has its shortcomings and cannot substitute for voltage imaging.¹⁷⁶ Practically, voltage imaging methods have lagged behind calcium imaging due to important challenges related to physical constraints of the measurements themselves, including an electrical field highly located in the thin membrane region, an essentially two-dimension plasma membrane which cannot contain an arbitrary number of voltage chromophores without disrupting its properties, as well as the fact that the plasma membrane represents only a small proportion of the total membrane surface in the neuron on which the chromophores are attached. Finally, the relatively high speed of the electrical responses of mammalian neurons also represents a serious challenge for voltage measurements. Consequently, despite some promising perspectives, the different voltage imaging methods suffer from poor SNR and secondary side effects, and they have up to now fallen short of providing single-cell resolution when imaging the activity of neuronal populations.¹⁷⁶

Otherwise, it is well known that neuronal activity induces modifications of the intrinsic optical properties at the subcellular,^177–180 cellular^181,182 and tissue level.^183–185 Consequently, we have attempted to establish an accurate relationship between QPS and the transmembrane current. Practically, we set out experiments combining electrophysiology in a whole-cell configuration and QP-DHM, performed in a well-established biological model involving ${\mathrm{Cl}}^{-}$ conductance, a human embryonic kidney (HEK) cell line, and transfected to express the neuronal ligand-gated chloride ion channel called ${\mathrm{GABA}}_{\mathrm{A}}$, the acronym of its endogenous ligand, the gamma-aminobutyric acid which is an inhibitory neurotransmitter. These experiments have stressed the fact that a net ionic influx corresponds to a phase decrease due to the osmotic water entry while a net ionic efflux induces a phase increase reflecting the osmotic exit of water. Under the following two assumptions—(1) the $n_c$ value linearly depends on the concentration of the different intracellular components according to the seminal work of Davies and Wilkins¹⁸⁶ and (2) the volume variations induced by the transmembrane water movements accompanying the ionic movements are proportional to the number of ions having passed through the membrane or channels—it has been possible to establish the following relation between the QP signal $\phi (t)$ and transmembrane current $I(t)$

Experiments with HEK cells have validated Eq. (3) regarding Cl^- currents mediated by GABA applications [Fig 2(a1)] with ${\epsilon }_{\mathrm{GABA}}$ lies within the range of $90–110\mu {\mathrm{m}}^3/\mathrm{nC}$, and have permitted us to construct a phase response as a function of the clamped membrane potential ($\phi /\mathrm{V}$ curve) allowing the determination of the equilibrium potential for ${\mathrm{Cl}}^{-}$ with the same precision as an electrophysiological approach measuring the classical I/V curves [Fig. 2(a2)].¹⁸⁷ Practically, ${\epsilon }_{\mathrm{GABA}}$ has been estimated for a membrane potential clamped at $-40\mathrm{mV}$ by performing a least-squares fit to adjust the phase current (Pred. Curr.) derived from Eq. (3) with the measured current (electrophysiological recordings in a voltage-clamp mode). Using this ${\epsilon }_{\mathrm{GABA}}$ determination, Pred. Curr. has been calculated for other values of the membrane potential by using Eq. (3) [Fig. 2(a1)].

Fig. 2

(A) HEK cells and GABA applications, (B) neurons in response to glutamate. (a1): (left) Example of three simultaneous traces of current (gray line) and phase shift (black line) recorded with 44 mM of ${[{\mathrm{Cl}}^{-}]}_{\mathrm{intrapip}}$ on the same ${\mathrm{HEK}}_{\mathrm{GABA}}$ after application of GABA ($3\mu \mathrm{M}$; 30 s; dot). At $-100\mathrm{mV}$, application of GABA triggered an inward current concomitantly to an increase in the phase signal. Conversely, at $+40\mathrm{mV}$, the same applications of GABA triggered an outward current accompanied by a decrease of the phase signal. Note that for $-40\mathrm{mV}$ (close to the resting potential for Cl), the current and the phase shift were very small. (a1) (right) Expansion of traces visualized in a1 (parts defined by rectangles). For each level of membrane potential, the peak of phase shift (indicated by the arrow head) was reached when the $I_{\mathrm{GABA}}$ was terminated. According to Eq. (3) the phase signal can predict the current (Pred. Curr.: dashed line) superimposed on the recorded current: (a2) The $\phi /\mathrm{V}$ curve (full square and thick line) and the I/V curve (empty circle and thin line) obtained with GABA ($n=7$) indicated an ${\mathrm{E}}_{\mathrm{Cl}}$ of $-26$ and $-26\mathrm{mV}$, respectively. (a2) inset representative quantitative phase image of patched a Hek cell. (b1): Local application of glutamate (500 μM, 200 ms; arrow head) on a patched neuron induces a strong transient decrease of the phase signal associated to an inward current. Phase is expressed in degrees (b2) application of glutamate triggers three main types of phase shifts, Left, representative quantitative phase image of three cultured cortical neurons visualized in DHM. Ovals in the middle of the cells corresponded to the region of interest for the phase signal (scale bar, 10 μm). Right, application of glutamate (30 μM, 30 s; arrowhead) triggered different types of shapes of optical signals from these three recorded neurons. (b3), averaged traces of the three characteristic optical signals induced by glutamate application (30_M, 30 s, arrowhead) and those recorded from 21–35 DIV neurons. These phase signals are classified into three categories: a biphasic response (Biph.; $n=137$), a reversible decrease of the phase signal (RD, $n=80$), and an irreversible decrease of the phase signal (ID, $n=35$). All these experiments were performed at room temperature.

Subsequently, Eq. (3) has been used to optically monitor neuronal network activity mediated by glutamate application, the main excitatory neurotransmitter in the brain released at 80% of the synapses. Practically, a multimodality microscope, QP-DHM, and electrophysiology setup has been developed to study the early stage of neuronal responses induced by glutamate on primary culture of mouse cortical neurons. This study involving pharmacological experiments revealed that glutamate produces three distinct optical responses, predominantly mediated by NMDA receptors: biphasic (Biph.), reversible decrease (RD), and irreversible decrease (ID) responses [Fig. 2(b3)]. The shape and amplitude of the optical signal were not associated with a particular cellular phenotype, but reflected the physio-pathological status of neurons linked to the degree of NMDA activity. Thus, the “Biph.”, “RD,” and “ID” responses respectively indicated low-, a high-, and “excito-toxic” levels of NMDA activation. For these three distinct responses, a strong inward current associated with the early phase decrease, whose amplitude is proportional to the concentration of glutamate and to the duration of the application, has been measured. This inward current is consistent with glutamate-mediated activation of specific ionotropic receptors including the NMDA, AMPA, and the kainate ionotropic receptors, whose opening induces influxes of ${\mathrm{Ca}}^{2+}$ and ${\mathrm{Na}}^{+}$ down their electrochemical gradient. Consistently, the phase decrease results from water entrance accompanying the influxes of ${\mathrm{Ca}}^{2+}$ and ${\mathrm{Na}}^{+}$ for osmotic reasons. Moreover, furosemide and bumetanide, two inhibitors of sodium and/or potassium-coupled chloride movement, strongly modify the phase shift suggesting an involvement of two neuronal co-transporters, Na-K-Cl (NKCC1) and K-Cl (KCC2) in the genesis of the optical signal. In addition, the phase responses can be decomposed into two components, a rapid one accompanying the glutamate-mediated current ($I_{\text{GLUT}}$)—the phase decrease on Fig. 2(b1), and a slow one generally corresponding to a phase recovery while $I_{\text{GLUT}}=0$. The phase recovery, which is much slower than the fast one, is likely to correspond to a nonelectrogenic neuronal volume regulation involving several mechanisms. Interestingly, the time course presented in Fig. 2(b1) shows that the water movements are not significantly delayed—at the tenth of second scale at least—relative to the recorded current. The measurements of $I_{\text{GLUT}}$ as well as the corresponding intracellular RI and neuronal volume changes allowed us to estimate the parameter “${\epsilon }_{\mathrm{GLUT}}$” $[\mathrm{mL}/\mathrm{C}]$. Practically, the values of ${\epsilon }_{\mathrm{GLUT}}$ lie within the range of $60–120\mu {\mathrm{m}}^3/\mathrm{nC}$ equivalent to 340–620 water molecules transported per ion having crossed the membrane. Interestingly, the typical intracellular RI change induced by a glutamate pulse (500 uM 0.2 s) is around 0.002–0.003. The associated neuronal swelling is around 100 femtoliter (fL) for a typical neuronal cell body of 1500 fL corresponding to a 6–7% cell volume variation. However, these orders of magnitude correspond to an exogenous glutamate application during a few tenths of seconds. Physiological release of endogenous glutamate is likely to induce smaller water movements and intracellular RI changes. Finally, it is important to note that, although we do not yet have a comprehensive understanding of the underlying mechanisms inducing these phase responses, these consequent transmembrane movements of water accompanying the neuronal activity are in good agreement with the typical amount of water co-transported by various cotransports including NKCC1.¹⁸⁸

Furthermore, information concerning transmembrane current obtained from electrophysiological recordings combined with QP-DHM signal allows us to pave the way for developing a simultaneous multiple sites optical recording of transmembrane currents capable of resolving local neuronal network activity. In addition, appropriate mathematical treatment of the optical signal affords the possibility to quantitatively determine the dynamics of the current triggered by the ionotropic receptor activity, making this technique amenable to use for pharmacological screenings of modulators developed for the management of human pathologies involving dysfunctions of specific ionotropic channel including chloride channels associated with cystic fibrosis.¹⁸⁹

4.3.

Three-Dimensional Visualization of Dendritic Spine Dynamics with Quantitative Phase Tomographic Microscopy

As previously mentioned, dendritic spines are the postsynaptic components of most excitatory synapses in the mammalian brain and are the loci of structural and functional plasticity. In past decades, studies have revealed that the number and size of dendritic spines are regulated by a variety of gene products and environmental factors, underscoring the dynamic nature of spines and their importance to brain plasticity. Because dendritic spines are the key elements for information acquisition and retention, understanding how spines are formed and maintained in relation to neuronal network activity will likely provide fundamental insights into how the brain possesses the extraordinary capacity to learn and to remember.¹⁹⁰ However, dendritic spines are tiny transparent processes whose visualization and resolution remain a challenge for optical approaches. However, the advent of two-photon (2P) excitation laser scanning microscopy, despite limitations inherent to the use of fluorescence, has greatly contributed to the understanding of dendritic spine function and plasticity.^191,192 On the other hand, the diffraction tomography, which is particularly efficient when the wavelength of the irradiating beam is comparable to the dimensions of the diffracting parts of the object, represents a promising approach to dynamically and noninvasively resolve subcellular structures including dendritic spines. Indeed, appealing applications to cell biology have already been obtained and published. Practically, the investigation of the RI 3-D map has been published for pollen grains (Charrière, Marian et al. 2006), amoeba,⁶⁵ human RBCs parasitized by plasmodium falciparum,¹⁹³ human influenza virus infected cells, epithelial cheek cells, and granulocytes.¹⁹⁴ Images of Hela cells at 0 deg and up to 50 deg illumination incidences have been published¹⁹⁵ and DIC has been derived from synthetic aperture phase contrast microscopy. Interestingly, an approach based on the rotation of the sample using a hollow optical fiber as a live-cell imaging chamber has permitted one to measure the RI 3-D maps of cell clusters.¹⁹⁶ Recently, Cotte et al. firmly established the benefit of synthetic aperture elevated to quasi $2\pi$ by pushing the occupation of the Fourier space up to a diameter equal to the diameter of the Ewald sphere.¹⁹⁷ Super-resolution could be obtained and details as small as 100 nm could be observed. Moreover, dynamic images showing the detailed evolution of dendrite spines (Fig. 3) could be obtained.

Fig. 3

Three-dimensional (3-D) representation of a tomographic image of a neuronal process obtained by synthetic aperture quantitative phase image. The details of protruding dendritic spines can be visualized. Scale is in $\mu \mathrm{m}$ and the color code represents the difference of refractive index (RI) [from 0.04 (red) to 0.16 (cyan)] compared with the extracellular medium (Yann Cotte). These experiments were performed at room temperature.

5.1.

Background

Psychiatric disorders represent major public health problems and, while significant improvements of the conditions of the patients have been achieved due to the discovery of neuroleptics and antidepressants, the available treatments remain largely insufficient and unsatisfactory. A major paradigm shift is needed to move the field forward. Advances in the field are impaired in large part due to the lack of proper tools to conduct adequate biological measurements that can guide diagnosis and treatment. This is particularly critical in light of growing evidence showing that early treatment of psychiatric disorders, already in their prodromal phase and before the onset of debilitating symptoms, leads to significantly improved clinical outcomes.¹⁹⁸ It is therefore important to identify in children of parents affected by the disease, biomarkers or endophenotypes indicating a high risk of developing the disease later in life However, to date there are insufficient data to support any of these biomarkers as vulnerability or diagnostic or prognostic factors, notably regarding bipolar disorders.¹⁹⁹ In this field of research, the most relevant investigations are longitudinal studies conducted on cohorts consisting of patients with a specific psychiatric disorder and their children (high-risk children). Indeed, epidemiological studies, particularly in regard to mood disorders,^200,201 have clearly shown that children of patients with a psychiatric disorder usually have a significantly higher risk of developing the disease. In addition, psychiatric disorders are frequently comorbid with other mental illnesses as well as endocrine, metabolic (e.g., diabetes mellitus and obesity) and cardiovascular diseases. Thus, they must be considered as a multisystem condition, and as a consequence, their underlying neurobiological bases are complex. Coherently, only studies combining several biomarkers have been successful in separating acute mood states (mania and depression) from controls²⁰² and providing a high accuracy for the diagnosis of major depression.²⁰³ Consequently, the determination of high risk developmental trajectories for psychiatric disorders requires to identify and to longitudinally study, in high risk children, various sets of biomarkers very diverse in nature including, e.g., neuropsychological and neuroimaging (structural and functional MRI), as well as peripheral biomarkers or cellular biomarkers.

Practically, the study of cell biomarkers can be achieved from somatic cells (fibroblasts) obtained from patients as well as from high-risk children (skin biopsy). However, recent years have seen a renewed interest for the cell biomarkers due to the possibility, through induced pluripotent stem cells, to convert somatic cells (fibroblast) obtained from patients into neurons (grown in culture) with the genetic makeup necessary for the development of certain phenotypes of the disease. Although this approach currently has several limitations,²⁰⁴ it allows one to consider the particularly attractive hypothesis that some phenotypes are already found in vitro at the cell level or in a network of cells collected from patients or their offspring.²⁰⁵

Within this framework, a multimodality imaging approach developed around QP-DHM has the capacity to explore new, original optical cellular biomarkers down at the nanoscale that can then be put in contrast to other more conventional markers as mentioned above. Indeed, QP-DHM provides the unique monitoring of fine cell structure and dynamics due to its ability to yield quantitatively information on a wide variety of cellular parameters including volume, morphology, intracellular protein content, dry weight, nanoscale membrane fluctuations, membrane water permeability, transmembrane water movements, and volume regulation. The value of such an approach can be illustrated by a study we are conducting in a cohort of diabetic patients aimed at correlating energy distribution among vibrational eigenmodes of RBC membranes with the levels of glycosylated hemoglobin (Fig. 4).

Fig. 4

(a) Quantitative phase image of a red blood cell (RBC) in a perspective color coded representation and projections of three principal component analysis (PCA) modes of the RBC cell membrane fluctuations. (b) Degeneracy free representation of 20 PCA modes, measured experimentally. (c) Each $t$-value (i,j) in the matrix indicates how similar the energy distributions of the PCA modes between subject $i$ and subject $j$ are. At lower $t$-values, the energy distribution becomes more similar. Healthy (1–8) and diabetic (9–16) samples can be discriminated.

Building on these results, we are conducting a study monitoring the RBC membrane eigenmode energy distribution in a sample of the prodromal phase of first-episode psychosis patients before initial treatment, aimed at identifying specific biomarkers for early detection and intervention.