# Scattering of coherent acoustic phonons by silica nanoparticles reveals the 3D-morphology of cells in solution down to nanometer thicknesses

Marie-Fraise Ponge, François Bruno, Louise Le Ridant, Liwang Liu, Murielle Rémy, Dongsheng Shi, Marie-Christine Durrieu, Bertrand Audoin

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## ► To cite this version:

Marie-Fraise Ponge, François Bruno, Louise Le Ridant, Liwang Liu, Murielle Rémy, et al.. Scattering of coherent acoustic phonons by silica nanoparticles reveals the 3D-morphology of cells in solution down to nanometer thicknesses. Journal of Applied Physics, 2023, 133, pp.143103. 10.1063/5.0141168. inserm-04970176

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# Scattering of coherent acoustic phonons by silica nanoparticles reveals the 3D-morphology of cells in solution down to nanometer thicknesses

Marie-Fraise Ponge,¹ François Bruno,² Louise Le Ridant,² Liwang Liu,² Murielle Rémy,³ Dongsheng Shi,³ Marie-Christine Durrieu,³ and Bertrand Audoin²

¹) University of Bordeaux, CNRS UMR 5295, Bordeaux-INP, I2M, Talence, FRANCE

²) University of Bordeaux, CNRS UMR 5295, I2M, Talence, FRANCE

³) University of Bordeaux, CNRS UMR 5248, Bordeaux-INP, CBMN, Pessac, FRANCE

(*Electronic mail: marie-fraise.ponge@bordeaux-inp.fr)

In this work, we show that the use of silica nanoparticles improves the imaging and 3D-morphological measurement down to nanometer thicknesses of fixed cells in solution with picosecond ultrasonics (PU). Synchronized ultrafast fs-laser pulses are used to generate coherent acoustic phonons (CAPs) that evoke the Brillouin light scattering and enable the recording of the time-resolved Brillouin oscillations along with the propagation of the acoustic nanopulses through a thin transparent cell in solution. Silica nanoparticles, whose size matches the phonon wavelength at the frequency of the Brillouin scattering in the solution, are used to strongly scatter the CAPs in the solution. Suppressing the Brillouin signature of the surrounding liquid, this protocol improves significantly the PU imaging and makes it possible to measure the mechanical properties of a transparent cell, including the thin peripheral region where the thickness is less than the Brillouin wavelength, equal to half the probe light wavelength in the cell, and where crucial interaction of the cell with its surroundings occurs. We present experimental evidence of the considerable improvement in the cartography of the entire cell using nanoparticles. The intricate frequency dependence of Brillouin scattering and of resonances for a very thin cell is analyzed using a semi-analytical model leading to the challenging measurement of the 3D-morphology of the immersed cell at thicknesses down to 1/9 of the optical wavelength.
# I. INTRODUCTION

The importance of measuring the mechanical properties of biological cells has recently become very recognized, particularly to understand the physical phenomena that underlie the dysfunction of cellular mechanisms associated with pathologies¹ such as cancer². Several characterization techniques³,⁴, such as Atomic Force Microscopy (AFM)⁵, traction force microscopy⁶ or microaspiration⁷, have been developed to enable the microscopic study of cell mechanics. However, these techniques require mechanical contact with the cells that can trigger a response of the cell and strongly influences the measured physical properties⁸. Picosecond ultrasonics (PU) consists in using an ultrafast optical pump-probe set-up to create broadband high-frequency coherent acoustic phonons (CAPs)⁹. CAPs are then used to acousto-mechanically probe and image biological cells in a non-invasive fashion with a sub-micrometer lateral resolution¹⁰. In this approach, ultrafast laser pulses generate coherent phonons that enhance the Brillouin light scattering and enable the recording of the time-resolved Brillouin oscillations with ps time-resolution. This technique is thereby termed Time Domain Brillouin Spectroscopy (TDBS)¹¹ and is extensively used to characterize transparent media¹² without involving mechanical contact. TDBS also allows for the acquisition of images based on mechanical contrast for fixed cells¹³,¹⁴ or living cells in vitro¹⁵, and for in-depth profiling with an axial resolution of half an optical wavelength¹⁶. Using TDBS and combining it with the tracking of acoustic phonons and of their resonance harmonics, it has also been possible to map the 3D-morphology of fixed dehydrated cells in air and to correlate the inhomogeneity of the thickness of the cell nucleus to degenerative processes¹⁷. Indeed, for 3D morphology study, PU has an obvious advantage over the commonly-used AFM based approach as it involves no active physical contact with cells¹⁸.

However, few results refer to living cells¹⁹. Indeed, immersion is a *sine qua non* condition for studying and characterizing live cells as they need to be in a nutritive thermostated solution. Yet, the optical and acoustic properties of cells in liquid are very similar to the properties of water, which imposes experimental challenges on elastic-waves-based techniques¹⁵,¹⁹ as the optically detected signal is then dominated by the strong Brillouin scattering in the liquid. Until now, images of living or hydrated cells have been obtained with TDBS for cells of thickness much greater than the Brillouin wavelength, $\lambda_{TDBS}^{20}$. $\lambda_{TDBS}$ is defined as the spatial length of one cycle of Brillouin oscillation and is equal to half the probe light wavelength in the sample.

PU 3D-morphology can be obtained in two ways. For a thick area (e.g. nucleus), where the cell
thickness is greater than $\lambda_{TDBS}$, it is possible to determine the speed of elastic waves by measuring the frequency of the Brillouin oscillations. For a thin area (e.g. the peripheral region), where the cell thickness is less than $\lambda_{TDBS}$, the thickness can be deduced from the resonance frequency of thin cell film and its harmonics. In the case of thin cells immersed in solution, measuring thickness is a challenge because the frequencies of the Brillouin oscillations (in the solution or in the cell) are very close to the resonance frequencies. Additionally, the amplitude of the resonance peaks and their quality factor are lower than in the case of dehydrated cells in the air due to the leaking of acoustic waves in the liquid.

We have previously shown²¹ that inserting silica nanoparticles of proper size into a liquid results in a strong attenuation of the acoustic phonons at gigahertz frequency without scattering the probe light photons. The phonon attenuation results of acoustic multiple scattering when the size of the particles matches $\lambda_{TDBS}$. We also demonstrated that the scattering can be used to enhance the Brillouin detection of coherent acoustic phonons in a thin film (e.g., PMMA) that was immersed in water. When a very thin transparent layer lies underneath the liquid, particles make it possible to measure the mechanical properties and also the thickness of this very thin transparent medium by removing the Brillouin signature of the acoustic phonons in the liquid.

In this work, we demonstrate the use of the scattering of CAPs by silica nanoparticles to measure the 3D-morphology of fixed mesenchymal stem cells in solution. By analyzing reflectivity signals calculated using an analytical model for both opto-acoustic generation and elasto-optic detection, we discuss the advantages of strongly attenuating the acoustic wavefront in the liquid and highlight the intricate frequency behavior of Brillouin scattering and resonances. In light of these analyses, we then present stepwise experimental evidences for the considerable improvement in Brillouin frequency mapping of the entire cell using nanoparticles, including the peripheral region where the thickness is less than the Brillouin wavelength. The ability of imaging this area is of considerable relevance because it is where crucial interaction of the cell with its surroundings occurs. In the last section, we demonstrate how the resulting frequency mapping and the understanding provided by the model make it possible to carry out the difficult task of measuring the 3D-morphology of a thin immersed cell.
## II. EXPERIMENTAL CONFIGURATION

### A. Picosecond-ultrasonics setup

The experimental setup is illustrated in Fig. 1. Human mesenchymal stem cells (hMSCs) (Fig. 1 (a)) were seeded on a 300 nm thick titanium (Ti) bio-compatible layer sputtered by physical vapor deposition on top of a sapphire substrate of thickness 1 mm. This metallic layer is an opto-acoustic transducer as it absorbs and partially converts the pulsed optical energy into acoustic phonons via the thermoelastic effect. The sapphire substrate acts as a heatsink to dissipate the possible laser heating and thus protect cells from any damage<sup>15,22-24</sup>. A detailed thermal and mechanical analysis of the transducer can be found in Refs 22 and 25.

A dual-oscillator (Amplitude System®) was used to deliver two trains of laser pulses of 400 fs duration, one serving as the pump (optical wavelength of $\lambda_{pump} = 1030$ nm) and the other as the probe ($\lambda_0 = 515$ nm). Both lasers were operated at a repetition rate of $f_0 \approx 48$ MHz, with a slight shift, to perform asynchronous optical sampling (ASOPS)<sup>26,27</sup>. Fig. 1 (b) shows the experimental setup for picosecond ultrasonics experimenting on cells. Both beams were co-axially aligned at opposite sides of the titanium transducer. The probe beam was focused through the cell at the top interface of the transducer while the pump beam was focused at the sapphire-titanium interface. Both microscope objectives are equivalent to a lens of magnification x50 (N.A. = 0.8).

Each pump pulse ($\approx 4$ nJ) absorbed at the sapphire-titanium interface launches CAPs that propagate through the titanium layer and are partially transmitted and reflected at the titanium-cell interface. Two contributions modify the optical reflectivity. The probe beam ($\approx 0.3$ nJ) detects both the changes in the optical reflection at the cell-titanium interface, which are proportional to the integral of the acoustic strain over the titanium skin depth<sup>28</sup>, and the Brillouin interaction with the coherent phonons propagating in the cell. A photodetector, at the end of the top arm, monitored the optical reflectivity relative changes in the probe light $\Delta R(t)/R$. The transducer was situated on a translation stage making possible a raster-scan measurement of the reflectivity of the sample pixel by pixel with a step of $1\mu$m. The switchable mirror that was located between the top objective nosepiece and the filter cube could be translated to enable reflected-field microscopy also.
<figure><img src="image_3.png" /></figure>

FIG. 1. (a) Typical top-view white-light image of an hMSC seeded on the titanium bio-transducer. (b) Experimental setup for picosecond ultrasonics measurements on cells. The repetition rates of pump and probe lasers are slightly shifted to perform an asynchronous optical sampling (ASOPS). Cells were seeded onto a titanium optoacoustic transducer sputtered on a sapphire substrate that dissipates laser heating. The pump pulses of optical wavelength $\lambda_{Pump} = 1030$ nm (red, bottom arm) were focused by a x50 objective lens at the sapphire-titanium interface, while the probe pulses of optical wavelength $\lambda_0 = 515$ nm (green, top arm) were focused through the cell at the top titanium interface. A translation stage makes it possible to perform a raster scanning of the sample surface. M, mirror; SM, switchable mirror; BS, beam splitter, PBS, polarized beam splitter; LED, light emitting diode; CCD, charged coupled device camera; QWP, quarter-wave plate; HWP, half-wave plate.

## B. Cell preparation

hMSCs (human mesenchymal stem cells) were purchased from Promocell (C-12974) and cultured in growth medium (Promocell, C-28009) at 37°C and 5% CO₂ according to the specifications of Promocell and until cells reached 80% confluency. At this point, hMSCs were detached by trysin/EDTA treatment (GibcoTM, 15050-065), numerated by the use of a LunaTM fl device (Logo Biosystem SARL) and either used for the experiments, either amplified to obtain more cells that can be feeded in 90% Fetal Bovine Serum (GibcoTM, 10270-106)/10% DMSO (Corning, 25-950-CQC) in liquid nitrogen for further experiments.
### C. Cell seeding on materials

Prior to seeding, titanium optoacoustic transducers were sterilized by immersion overnight in ethanol 70% (v/v) / sterile H₂O. After three washes in Phosphate Buffer Saline 0.1M (DPBS1X, Corning 21-031-CV), hMSCs (passage from 4 to 8) were seeded on the top of a titanium optoacoustic transducer at a density of 1500 hMSCs /cm² in α-Minimal Essential Medium (α-MEM, Gibco™, A1049001) during three hours at 37°C and 5% CO₂. After this incubation period, α-MEM was gently removed and replaced by Mesenchymal Stem Cell Osteogenic Differentiation Medium (Promocell, C-28013) and kept in culture during 15 days with changing of the medium twice a week. At the desired time point, the sample was fixed by immersion in a paraformaldehyde solution (ThermoFisher, 28908, 4% in PBS1X) for 20 minutes at room temperature before washing in PBS1X and storage in PBS buffer at 4°C until analyses. PBS was removed prior to optoacoustic experiments.

The biological sample was either dried and covered with solution (which is water here, as the cells are fixed), or dried and covered first with a drop of solution with silica beads, and then with water after evaporation of the solvents. We consider that the silica particles of 200 nm in diameter were sedimented at the sample top surface with the maximum concentration of $π/6$ in volume. The comparison of the results with and without particles required the cells to be fixed, because the results in both configurations had to be obtained for the same cell. Fig. 1 (a) shows a typical top-view white-light image of an hMSC seeded on titanium and fixed after fifteen days of seeding.

## III. CALCULATION OF THE RELATIVE CHANGES OF THE REFLECTED PROBE INTENSITY

The acoustic attenuation in a pure liquid is weak. Yet, we have shown that when silica nanoparticles of appropriate size are sedimented into it, the optically detected acoustic phonons at GHz frequency are strongly attenuated²¹. This decrease is a result of the strong acoustic scattering by the random particles of 200 nm in diameter close to the phonon wavelength in water $λ₀/(2n_w) = 194$ nm. In this section, we first present an analytical model of the opto-acoustic generation and the elasto-optic detection used to calculate the reflectivity changes probed through a cell of thickness $L^{28–30}$: we discuss the modeling of the acoustic scattering and explain why, in this configuration, the cell layer behaves as a quarter wavelength acoustic resonator. We then present and analyze the
obtained time-resolved waveforms. The second part of the section deals with the analysis of the
spectrum and the conjugate effects of Brillouin scattering and resonances lying in close frequency
ranges.

**A. Configuration and time-resolved signal**

We consider the configuration presented in Fig. 2: the cell and the titanium transducer are represented as a bilayer surrounded by two semi-infinite media (liquid on the top and sapphire at the bottom). Elastic waves are generated at the sapphire-titanium interface using the pump laser due to the photo-thermal and thermo-elastic effects. The lateral dimension of the focused laser spot on the surface is around 1 µm, comparable to conventional diffraction-limited optical imaging techniques. As the acoustic propagation distance is small compared to the width of the laser spot, we neglect acoustic diffraction, and we assume here that only plane longitudinal waves are generated and that the photoelastic generation process can be modeled using a one-dimensional model.

<figure><img src="image_4.png" /><figcaption>FIG. 2. The cell and the titanium transducer are represented as a bilayer surrounded by two semi-infinite media (liquid on the top and sapphire on the bottom). i = 0, 1, 2, 3 stands for the semi-infinite sapphire medium, the titanium layer, the cell layer and the liquid semi-infinite medium, respectively.</figcaption></figure>

In our configuration, the thickness of the metal layer (300 nm) is larger than the optical absorp-
tion depth (or skin depth) in titanium for the pump laser (approximately 20 nm). Local conserva-
tion of the electromagnetic energy links the density of the electromagnetic energy Q(z,t) absorbed
in the titanium layer to the temporal average of the Poynting vector, and Q(z,t) can be expressed
as :
$$Q(z,t) = \beta_{1,p} I_0(1 - R_{01}) \delta(t) e^{-\beta_{1,p} z}, \quad (1)$$

$\beta_{1,p} = 1/\xi_{1,p}$ is the optical absorption coefficient with $\xi_{1,p}$ the penetration depth at the pump wavelength, $R_{01}$ is the optical intensity reflection coefficient at the sapphire-titanium interface, $I_0$ is the incident electromagnetic energy per unit area, and $\delta(t)$ is the impulse time dependence of the electromagnetic source$^{28}$.

At the time-scale of propagating acoustic waves, the temperature rise inside the metallic layer obeys the heat equation in the absence of thermal diffusion:

$$\frac{\partial T(z,t)}{\partial t} = \frac{1}{\rho c_p} Q(z,t), \quad (2)$$

with $\rho$ and $c_p$ the mass density and specific heat capacity of the metallic layer, respectively. We first solve eq. (2) by integrating the density of energy according to time$^{31}$. In each medium $i$ ($i = 0, 1, 2, 3$ for the semi-infinite sapphire medium, the titanium layer, the cell layer and the liquid semi-infinite medium, respectively), the displacement fields $u_i(z, \omega)$ resulting from the thermal stress generated by the increase in temperature $T_i(z, \omega)$ (compared to the temperature of the layer before the arrival of the optical wave) are the solution of the equation of motion that we solve in the Fourier domain:

$$\frac{\partial^2 \tilde{u}_i(z, \omega)}{\partial z^2} + k_i^2 \tilde{u}_i(z, \omega) = \alpha_i \frac{\partial \tilde{T}_i(z, \omega)}{\partial z}, \quad (3)$$

with $k_i = \omega/v_i$, the acoustic wavenumber, $v_i$, the speed of longitudinal acoustic waves, $\alpha_i$, the thermal dilatation coefficient. The amplitudes of the forward and backward elastic waves inside the structure can be obtained by applying the displacement and stress continuity conditions at the interfaces, and using a transfer matrix formalism$^{30}$.

The elastic waves propagate through the titanium transducer and are partially transmitted at the titanium-cell interface. The changes in optical reflectivity are probed by the second laser through the cell covered either by water or by a sediment layer of silica beads in water. The probe beam penetrates the titanium layer within the skin depth (about 20 nm$^{32}$). In this configuration, the detected signal is the superposition of the contribution of the changes in reflectivity in the absorbing titanium layer, the transparent cell layer, the sediment of nanoparticles (if any), and the transparent top liquid. The semi-analytical method to calculate the relative changes of the reflected probe intensity $\Delta R/R$ is detailed in Ref. 29.
According to the conservation of momentum, the interaction of the coherent acoustic phonons of wavelength $\lambda_{TDBS} = \lambda_0/(2n)$ ($n$ is the optical refraction index of the medium, $\lambda_0$ is the probe optical wavelength in vacuum) in the cell, the sediment or the liquid, with the probe light photons, gives rise to so-called time-resolved Brillouin oscillations$^{11}$. At normal incidence, the frequency of these oscillations depends on $n$, on the sound velocity $v$ and on $\lambda_0$, according to:

$$f_B = \frac{2nv}{\lambda_0}. \qquad (4)$$

The attenuation of the wavefront in water was determined by a fit of experimental signals with an exponentially decreasing function. Using a Kelvin-Voigt analogy, we modeled the dissipation due to attenuation in the liquid with a complex rigidity $C = C' + j\omega\theta$ with $\theta$ the dynamic attenuation. The dynamic attenuation of liquid was estimated at $\theta_w \approx (2.0 \pm 0.1) \times 10^{-3}$ GPa.ns, in good agreement with that reported in Ref. 33. Regarding the sediment layer of nanoparticles which are used as phonon scatterers, we have chosen silica beads because silica refractive index at the probe wavelength, $n_s = 1.46$, is close to that for water, $n_w = 1.33$, and because the multiple scattering is heightened by the strong mismatch of acoustic impedance between water and silica : $1.5 \times 10^6$ kg.m$^2$.s$^{-1}$ and $12.7 \times 10^6$ kg.m$^2$.s$^{-1}$, respectively. Moreover, assuming that the refractive index $n_{eff}$ of the effective liquid medium, constituted by the sediment of nanoparticles in water, lies between those for water and silica, we obtain $1.87 < n_{eff}v_{eff} < 2.05$ nm/ps, e.g., $n_{eff}v_{eff} \approx n_wv_w$, with $v_{eff}$ and $v_w$ the sound velocity in the effective medium and water, respectively. With a higher refractive index and lower sound velocity in the effective medium than in water, the Brillouin signature of the effective medium is then roughly at the same frequency as in water$^{21}$. Furthermore, when a plane wavefront propagates in the medium made from nanoparticles sedimented in liquid, its multiple scattering by the beads gives rise to both a diffuse field and a strongly attenuated coherent plane wavefront$^{34}$. Finally, We modeled the scattering of the acoustic wavefront in the sediment of nanoparticles by merely increasing the attenuation in the liquid. The attenuation in the sediment of nanoparticles in water was determined by a fit of experimental signals with their calculated counterparts. As with water only, we modeled the effective attenuation using a Kelvin-Voigt analogy and we identified an equivalent dynamic dissipation by realizing a fit of the experimental data. As a result, we obtained the associated attenuation of the sediment at $\theta_s \approx (3 \pm 0.2) \times 10^{-2}$ GPa.ns, ten times higher than in water. The chosen speed of acoustic waves inside the cell layer was $v_c = 2$ nm/ps, in line with the values found for hydrated cells$^{23}$.

The value of the acoustic impedance (and thus the acoustic velocity), in the cell, titanium and
<figure><img src="image_5.png" /><figcaption>FIG. 3. (a) Acoustic impedance of the effective medium constituted by the sediment of nanoparticles in water. (b) Transmission coefficient of the layer as a function of the normalized frequency when the velocity of acoustic waves in the layer varies from 1 nm/ps to 2.5 nm/ps. To highlight the odd (solid white lines) and even (dashed white lines) multiples of $f_0 = v_c/(4L)$, the frequency axis is normalized using the lowest value of the velocity range, i.e. $v_{c0} = 1$ nm/ps.</figcaption></figure>

liquid, respectively, influences the resonant behavior of the cell layer. The dynamic homogenization of the sediment allows for the prediction of the propagation of the coherent acoustic wave using calculations³⁵ based on the Waterman-Truell model³⁶. The effective acoustic impedance of the effective medium constituted by the sediment of nanoparticles in water is shown in Fig. 3 (a). The impedance is at a minimum of 1.4 GPa.ns/µm at 5.41 GHz. Above this frequency, the impedance remains lower than $Z_{NP} = 1.5$ GPa.ns/µm. Fig. 3 (b) shows the transmission coefficient³⁷ of the layer of thickness $L$, defined as the ratio of the amplitude of the acoustic wave transmitted at the cell/liquid interface to that of the incident wave at the Ti/cell interface (Fig. 2). The transmission coefficient was calculated for the highest impedance of sediment in the liquid, $Z_{NP}$, in the frequency range [5-15] GHz. This value is close to the value for the acoustic impedance of water and less than the value for the acoustic impedance of the cell. The speed of acoustic waves in the layer varies from 1 nm/ps to 2.5 nm/ps. To highlight the odd and even multiples of the fre-
quency $f_0 = v_c/(4L)$, in solid and dashed white lines, respectively, we have chosen to represent the transmission coefficient according to the normalized frequency $4fL/v_{c0}$ ($v_{c0}$ = 1 nm/ps is the lowest value of the velocity range). In Fig. 3 (b), we see that when the velocity of acoustic waves in the cell $v_c$ is lower than the speed of waves in the liquid $v_{liquid} = 1.5$ nm/ps, the maxima of the transmission coefficient, and thus, the resonances of the layer, occur at even multiples of $f_0$. When $v_c > v_{liquid}$, the resonances of the layer occur at odd multiples of $f_0$. Consequently, in the case of cells in water (either with our without nanoparticles), as the sound velocity in the nucleus is around 2 nm/ps, the resonance frequency and its harmonics are odd multiples of $f_0$.

<figure><img src="image_6.png" /><figcaption>FIG. 4. Time-resolved waveform calculated using the opto-acoustic model for a 500 nm-thick cell covered with water only (blue line) and when nanoparticles are sedimented in water (red line).</figcaption></figure>

Fig. 4 shows an example of the time-resolved waveforms calculated using the optoacoustic model for a cell of thickness 500 nm, in water only (blue line) and when nanoparticles are sedimented in water (red line). In order to facilitate their comparison, the magnitude of each signal is normalized with respect to the maximum of the signal calculated for the cell covered with water only. The material properties used for the simulations are listed in table I. The oscillations are due to the Brillouin interaction of the probe light with the transmitted phonons at the Ti-Cell interface, and propagating first inside the cell, at frequency $f_c = 2n_c v_c / \lambda_0$ and then in the surrounding liquid, at frequency $f_w = 2n_w v_w / \lambda_0$. $v_w$ is the speed of acoustic waves in water. We observe slightly more than two and a half wavelengths of these oscillations inside the cell layer because the ratio between its thickness $L$ and the wavelength of the coherent acoustic phonon that gives rise to the Brillouin acousto-optic interaction, $\lambda_{TDBS} = \lambda_0/(2n_c)$, is $L/\lambda_{TDBS} = 2.67$. As expected, the signal obtained for the first configuration presents damped oscillations followed by oscillations of
<table><caption>TABLE I. Properties of the materials used for the simulations. The parameters marked with * are obtained by fitting the model to the experimental data. $\vartheta$ is such that the longitudinal elastic modulus is $C = C' + j\omega\vartheta$, with $\vartheta$ the dynamic attenuation.</caption><thead><tr><th>Properties</th><th>Sapphire<sup>38-40</sup></th><th>Titanium<sup>32,41</sup></th><th>Cell<sup>23,24</sup></th><th>Solution<sup>24</sup></th><th>Sediment<sup>21</sup></th></tr></thead><tbody><tr><td>$n_{\lambda_{515}}$</td><td>1,77</td><td>1,78</td><td>1.35</td><td>1.33</td><td>1.33</td></tr><tr><td>$n_{\lambda_{1030}}$</td><td>1,91</td><td>2,95</td><td></td><td></td><td></td></tr><tr><td>$\xi_{\lambda_{515}}$ (nm)</td><td></td><td>17.1</td><td></td><td></td><td></td></tr><tr><td>$\xi_{\lambda_{1030}}$ (nm)</td><td></td><td>21.3</td><td></td><td></td><td></td></tr><tr><td>$\partial n/\partial \eta^*$</td><td></td><td>0.5+0.5j</td><td>1+1j</td><td>0.8+1j</td><td>0.8+1j</td></tr><tr><td>$c_p$ (J.kg<sup>-1</sup>K<sup>-1</sup>)</td><td></td><td>523</td><td></td><td></td><td></td></tr><tr><td>$\alpha$ (K<sup>-1</sup>)</td><td></td><td>9.10<sup>-6</sup></td><td></td><td></td><td></td></tr><tr><td>$\rho$ (g.cm<sup>-3</sup>)</td><td>3.98</td><td>4.5</td><td>1</td><td>1</td><td>1</td></tr><tr><td>$\vartheta^*$ (GPa.ns)</td><td></td><td></td><td></td><td>2.10<sup>-3</sup></td><td>3.10<sup>-2</sup></td></tr><tr><td>$\nu$ (nm/ps)</td><td>11</td><td>6.14*</td><td>2</td><td>1.5</td><td>&lt; 1.5</td></tr></tbody></table>

larger amplitude and lower frequency. The transmission coefficient of strain $t_\epsilon$ between cell and water is higher than 1. Indeed, assuming that the mass density of the cell in water is close to that of water, $t_\epsilon = 2v_c z_c / (v_w(z_w + z_c)) \approx 1.53$, $z_w$ and $z_c$ are the acoustic impedance of water and cell, respectively$^{21}$. Next, with a fit of experimental measurements, we fixed the elasto-optic coefficient of water and of the cell layer at $\partial n/\partial \eta|_w = 0.8 + j$ and $\partial n/\partial \eta|_c = 1 + j$, respectively$^{42}$. When the acoustic wavefront is strongly attenuated by the sediment of particles in the liquid, the calculated reflectivity represented in Fig. 4 by the red line shows Brillouin oscillations inside the cell up to approximately 280 ps, followed by strongly attenuated oscillations due to the large acoustic attenuation in the sediment of nanoparticles.

## B. Spectrum of time-resolved reflectivity

To investigate the effect of the silica beads on the measurement of the properties of thin (with respect to the Brillouin wavelength) cells, we calculated the spectrum of time-resolved reflectivity. The spectra we obtained are shown normalized in Fig. 5 for a film of thickness $L$ ranging from 0 to 750 nm. Fig. 5 presents the normalized spectrum of the reflectivity signal of the overall structure
as a function of the cell thickness without (a) and with (b) silica particles in the water on top of the cell.

<figure><img src="image_7.png" /><figcaption>FIG. 5. Normalized spectrum of the modeled reflectivity changes at the cell-titanium interface as a function of cell thickness *L* without (a) and with (b) silica particles in the liquid on top of the cell. The amplitude is presented using a logarithmic scale. The right axis is the dimensionless thickness regarding the optical wavelength in the cell *L/λ* with *λ* = *λ*₀/*n*<sub>c</sub>. (c) Normalized spectrum of the difference in displacements at the Ti-cell and the cell-water interfaces |FFT(*u*<sub>Ti/c</sub> − *u*<sub>c/w</sub>)|. The dotted white lines represent the odd multiples of the acoustic resonance frequency of the layer *f*₀ = *v*<sub>c</sub>/(4*L*).</figcaption></figure>

When the cell is covered with water only, Fig. 5 (a), the main frequency component, visible
at 7.8 GHz for the whole range of thicknesses, corresponds to the frequency of the Brillouin
oscillations in water, f<sub>w</sub>. In addition, the spectrum presents other local maxima whose frequencies
decrease when the thickness increases. Owing to the values of the acoustic impedance on both
sides of the cell, the cell film is comparable to a quarter wavelength acoustic resonator and the
eigenmode frequencies are odd multiples of its acoustic resonance frequency : f<sub>0</sub> = v<sub>c</sub>/(4L).
These can clearly be identified in Fig. 5 (c), where we have chosen to remove optical effects by
presenting the spectrum of the difference in the displacements at the titanium-cell and the cell-
water interfaces, u<sub>Ti/c</sub> - u<sub>c/w</sub>. These eigenmodes are drawn in Figs. 5 (a) and (b) with dotted
white lines superimposed on the spectrum. This allows for the identification of the peak frequency
as the resonance frequency f<sub>0</sub> of the layer, for the lower peak frequency, and its harmonics. As
already observed in Ref. 43, Figs. 5 (a) and (b) show that the dips are equally spaced by a
quarter of the optical probe wavelength in the cell. This counterintuitive result is due to the fact
that during opto-acoustic measurements, the photodetector detects the optical intensity reflectivity
$\Delta R(t) = |r_c^L + \Delta r(t)|^2 - |r_c^L|^2$. The optical reflectivity $r_c^L$, related to the optical resonance in the cell layer, and the dynamical reflectivity $\Delta r(t)$ both present $\lambda/2$ spaced dips, but their superposition results in $\lambda/4$ spaced dips.

The frequency spectrum of the reflectivity changes, calculated when we consider strong acoustic scattering by nanoparticles in the liquid, is presented in Fig. 5 (b). Around $f_c$ and for small thicknesses, the frequency positions of the maxima are shifted slightly downward compared to the curves shown with dotted white lines. This can be caused by the combined influences of the higher acoustic attenuation, the superposition of the resonance modes of the layer and the Brillouin oscillations, and the optical cavity effect.

In Fig. 5 (b), we observe that the Fourier transform amplitude at the frequency of the Brillouin oscillations in the liquid, $f_w$, is almost entirely canceled. This is simply due to the addition of nanoparticles and not to an increase in acoustic impedance. The acoustic impedance of the sediment is very close to that of water (see Fig. 3). At low frequency, this results in an increase in the relative amplitude of the frequency components associated with the quarter wavelength acoustic resonances, at $f_0$, and its harmonics. Around the peak frequency of the Brillouin oscillations in the cell, whose value is equal to $f_c = 10.5$ GHz, in the frequency range [10–11] GHz, it can also be seen that the amplitude of the frequency component at $f_c$ increases when the layer thickness $L$ is greater than $\lambda_{TDBS}$, corresponding to $L/\lambda$ greater than 0.5 on the right axis.

Lastly, Fig. 5 (b) shows that removing the frequency component associated with the Brillouin oscillations in water $f_w$ also eliminates the overlapping of the Brillouin oscillations in water and the resonance harmonics. As an example, for a 360 nm thick layer, the peak coincides with the white dotted line representing the third resonance harmonic at 7.02 GHz, whereas the peak is at 7.6 GHz, when there is no particle, Fig. 5 (a). Likewise, the second harmonic at 6 GHz, for a thickness of 250 nm, is visible in (b) but not in (a). As the whole set of odd harmonics is visible in Fig. 5 (c), we attribute the unexpected disappearance of the second odd harmonic in the reflectivity spectra to a complex interaction between optics and acoustics which is beyond the scope of this work. The consequence is a more accurate determination of the frequencies associated with the layer resonances around $f_w$. This remains true for layers of thickness $L < \lambda_0/(2n_c)$, where a full cycle of Brillouin oscillations cannot take place.

We have seen that overlapping occurs between the Brillouin scattering spectrum, either in water or in the cell, and the acoustic resonances of the cell. Therefore, the variations in the frequency of the resonance and its harmonics with varying cell thickness do not match the theoretical predic-
tions for a quarter wave layer. These numerical investigations have shown that the addition of a
layer of sedimented nanoparticles strongly attenuates Brillouin scattering in the liquid. In addition,
reducing the amplitude of the spectrum at the frequency of Brillouin oscillations in water increases
the relative amplitude of the frequency of Brillouin oscillations in the cell and of the resonance
modes which will make them easier to detect experimentally.

#### IV. EXPERIMENTAL RESULTS

Configurations with and without nanoparticles have been experimentally tested for the fixed hMSC presented in Fig. 1 (a). The transient reflectivity signals were recorded with the pump laser focused at the sapphire-titanium interface, and with the probe beam focused at the opposite side of the titanium plate (Fig. 1 (b)). Relative optical reflectivity was first measured at a position located in the cell covered with water only. The biological sample was then dried and a drop of solution with silica beads was deposited; after evaporation of the solvents, the beads were covered again with water.

In this section, we first describe and interpret single time-resolved signals obtained by mea-
surements made at a position in the cell nucleus and in the cytoplasm. Secondly, we complete
this approach by investigating variations in the spectrum along the cell. We then make use of the
resulting knowledge to analyze the Brillouin frequency mapping of the cell in solution, either free
or covered with nanoparticles.

**A. Time-resolved signal and frequency analysis**

**1. TDBS measurements in the thick nucleus region**

Fig. 6 (a) shows the time-resolved waveforms measured for the cell covered with water (blue line) and when nanoparticles were sedimented in water (red line). The magnitude of each signal was normalized to unity by its maximum. For the same reasons as explained above for the simulated signals, the signal measured through the cell and water presents damped Brillouin oscillations in the cell followed by oscillations of larger amplitude, in the liquid. Fig. 6 (b) completes this result by showing the modulus of the spectrum of both normalized signals. The blue lines in Fig. 6 (a) and Fig. 6 (b) show that the first part of the time signal before 300 ps is the signature of the Brillouin oscillations at $f_N = 9.77$ GHz in the cell nucleus. They also show that the second
<figure><img src="image_8.png" /></figure>

FIG. 6. (a) Time domain optical relative reflectivity changes probed through the nucleus of the hMSC covered with water (blue line) and with silica particles at the cell-water interface (red line). Signal magnitudes are normalized with respect to their maximum. (b) Modulus of the spectrum of the normalized signal recorded without (blue line) and with (red line) silica particles in water.

part of the signal oscillates at $f_w = 7.64$ GHz because of the Brillouin scattering of the probe light by the acoustic wavefront in the solution.

The red line in Fig. 6 (a) shows the time-domain relative reflectivity changes when the cell is covered with nanoparticles sedimented in water. The contribution of the Brillouin scattering in water is strongly attenuated. This is confirmed by the spectrum presented in Fig. 6 (b) where the frequency component at $f_w$ is removed. With the refractive index of the cell nucleus at $n_N = 1.35^{24}$, and given that the probe wavelength is $\lambda_0 = 515$ nm, we can determine the velocity of acoustic waves inside the nucleus: $v_N = f_N\lambda_0/(2n_N) \approx 1.863$ nm.ps$^{-1}$. By removing the Brillouin scattering in water, more interestingly, another component frequency $f_r = 6.05$ GHz is visible in Fig. 6 (b). From the simulation analysis given in the previous section, we attribute this feature frequency to one of the harmonics of the acoustic resonance of the cell layer. The whole cell is surrounded by a few nanometers thick bilayer lipid membrane. In order to determine how sensitive the resonance is to this membrane, we compared the theoretical and experimental values
of the resonance Q-factor. In Fig. 6 (b), the Q-factor at $f_r$ was measured at $Q_{exp} = 3.1 \pm 0.2$. This value is very close to the value we estimated from the calculated transmission coefficient of Fig. 3 (b) when considering a perfect cell-liquid interface : $Q_{th} = 3.2$. This suggests that the thin bilayer lipid membrane surrounding the whole cell does not influence the cell resonances.

## 2. TDBS measurements in the thin cytoplasm region

<figure><img src="image_9.png" /><figcaption>FIG. 7. (a) Time domain reflectivity changes probed through the cytoplasm of the hMSC covered with water (blue line) and with silica particles at the cell-water interface (red line). Signal magnitudes are normalized with respect to their own maximum. Time-frequency wavelet transform of the signal recorded without (b) and with (c) silica particles at the cell-water interface.</figcaption></figure>

We now analyze the signal obtained when probing through the cytoplasm of the cell, Fig. 7 (a). Since this part of the cell is very thin, the time window for propagation inside the cell is very short. The frequency resolution of the Fourier transform over the short time window is thus very weak. For this reason, we carried out a time-frequency analysis to discriminate the frequency components within a short propagation time. We used a Morlet wavelet expressed as the product of a complex exponential and a Gaussian envelope :

$$W_m(t) = \exp(j2\pi ft) \exp\left(-\frac{1}{2}\left(\frac{t}{s}\right)^2\right). \qquad (5)$$

In Eq (5), $s$ is defined as $s = N/(2\pi f)$, with $N$ the number of wavelet cycles within the wavelet envelope. It controls the width of the mother wavelet spectrum and was set at 5 to yield an optimal trade-off between the temporal and frequency precision.

Fig. 7 shows the time-resolved signals and the time-frequency wavelet transform without and with the sediment of particles on top of the cell. Without nanoparticles, the time-resolved signal
plotted in blue in Fig. 7 (a), and its spectrogram shown in Fig. 7 (b), are dominated by the signature
of the Brillouin oscillations in water: large oscillations are visible at the frequency component of
7.8 GHz. However, with the addition of nanoparticles (time-resolved red signal in Fig. 7 (a)),
a short oscillation remains, followed by strongly damped oscillations. At time shorter than 100
ps, corresponding to a thickness slightly less than $\lambda_{TDBS}$ (assuming the same sound speed as the
one measured inside the nucleus $v_N$), the insert at the bottom right in Fig. 7 (c) shows that the
wavelet transform exhibits two frequency components at 7.35 GHz and 15.45 GHz. The ratio of 2
between these frequencies suggests that this is a resonance and its first even harmonic. However,
as demonstrated previously, due to the impedance ratio, the eigenmode frequencies should be
odd multiples of the acoustic resonance frequency $f_0$. Moreover, in the cytoplasm, the value
of the acoustic resonance frequency is close to the frequency of the Brillouin oscillations in the
sediment. We have already seen that due to the overlapping of acoustic resonances and Brillouin
oscillations, the variations in the resonance frequency as a function of thickness are not perfectly
inversely proportional. The lower frequency component at 7.35 GHz can thus be attributed to
the superposition of the resonance at $f_0 = v_N/(4L)$ of the thin layer with the remaining Brillouin
oscillations in the sediment. Thanks to the modal analysis highlighted in the previous section, we
attribute the 15.45 GHz peak frequency, to the first odd harmonic, $f_1 = 3f_0$ of the layer resonance
undisturbed by the propagation in the sediment. This will be confirmed by the results presented in
the last section of the paper.

In conclusion, these experimental results confirm the conclusion in the previous section. For a
cell layer of thickness less than the Brillouin wavelength, without nanoparticles, the large ampli-
tude of the Brillouin signal in water, both in time and frequency, prevents the determination of any
resonance frequency of the layer. However, the addition of nanoparticles allows for the precise
determination of the first odd harmonic at $f_1 = 3f_0$.

B. Spectrum as a function of position

In order to record the optoacoustic waveforms for the whole cell, an automated and computer-
controlled stage was used to scan the sample every micron to measure $\Delta R(t)/R$, pixel by pixel.
A 25 µm x 75 µm mapping of the cell was carried out. The scanned domain corresponds to the
cell image presented in Fig. 8 (a) : X and Y denote pixel indexes. In this section, we study the
time-resolved signals acquired along the vertical line X = 13 presented with the white rectangle
in the optical image. The spectra of these signals without and with nanoparticles are presented in Fig. 8 (b) and (c), respectively. Fig. 8 (d) presents the Fourier spectrum for $Y = 32$ (black curve), and for the whole $Y$ range at 15 GHz (red curve).

<figure><img src="image_10.png" /></figure>

FIG. 8. The relative reflectivity signal is probed through an hMSC in water along the Y axis and for $X=13$ (white rectangle in the optical image (a)), $X$ and $Y$ denote pixel indexes. The absolute value of the normalized fast Fourier transform of the relative reflectivity for each Y position without (b) and with (c) nanoparticles. The thick white lines in (c) are plotted to follow the frequency position of the two maximum peaks of the spectrogram. Panel (d) presents two slices of the image of the panel (c): in black, associated to the left ordinates, the spectrum for $Y=32$; in red, associated to the right ordinates, the amplitude of the spectrum at 15 GHz as a function of $Y$.

When the cell was covered with water only, the frequency component with the highest amplitude is that of the Brillouin oscillations in water. It is particularly visible in positions where the cell is very thin: $0 < Y < 20$ and $55 < Y < 75$. The addition of nanoparticles causes a decrease of the spectrum amplitude at this frequency and clearly reveals the frequency of the Brillouin oscillations inside the nucleus for $22 < Y < 45$. The average frequency is 9.5 GHz and leads to the sound velocity: $v_N = 1.8$ nm.ps$^{-1}$. For these positions, a secondary maximum, visible in the black curve of Fig. 8 (d), is present at 6 GHz and is attributed, as mentioned in the previous section, to a resonance mode of the nucleus. The thick white lines in Fig. 8 (c) are plotted to follow the frequency position of the two maximum peaks of the spectrogram. For the measurements made through the cytoplasm, $15 < Y < 25$ and $45 < Y < 55$, four frequency branches, highlighted by the white lines can be distinguished. The fact that they are quasi-symmetrical two by two with respect to the middle of the cell suggests that they are related to the thickness of the cell. The higher two frequency branches vary from 11.5 GHz to 20 GHz. The frequency increases as the
thickness decreases, which is consistent with the v/L variation in the resonance mode or its har-
monics and with the spectrum presented in Fig. 5 (b). The other two linear branches vary from
11.5 GHz to 7 GHz. However, unexpectedly, their frequency decreases as the thickness decreases.
Section III showed that for the thin parts of the cell the overlapping between the remaining of
Brillouin signature in the sediment at 8 GHz and the thickness resonances makes the variation in
the frequency resonance as a function of the thickness more complex. In addition, the thinner the
cell, the greater the transmission of the acoustic wavefronts in the sediment and the greater the
influence of the overlapping of Brillouin interaction and resonances.

C. Cell imaging using nanoparticles

We now present the values of the main frequency component at each pixel for the 25x75µm²
domain. At each pixel, the frequency is obtained by determining the maximum of the time-
frequency wavelet transform of the measured signal. The resulting image is a frequency map.

Panels (a) and (b) in Fig. 9 depict the frequency map for the cell in water without and with
nanoparticles, respectively. As seen in section III, the slight decrease in the Brillouin frequency
inside the nucleus, compared to the case with water only, is due to the combined influences of
acoustic attenuation, the superposition between the resonance modes of the layer and the Brillouin
oscillations, and the optical cavity effect, around $f_c$. Fig. 9 (c) shows the optical image of the cell
obtained in air with a x50 magnification. The comparison of both maps shows a clear improve-
ment in imaging when using nanoparticles. Only the nucleus and a thin border corresponding to
the white surrounding of the nucleus in the optical image are visible in panel (a). The average
frequencies for the nucleus and its contour are 10.5 GHz and 9.5 GHz, respectively. The remain-
der of the map, in blue, is dominated by the frequency of the Brillouin oscillations in water. The
whole cell, very thin parts included (light turquoise pixels), can be clearly distinguished in panel
(b). As an example, the local protuberances in the white dotted rectangle in the bottom right-hand
corner of the panel (b) are distinctly outlined and fit very well with the cell periphery in the optical
image, whereas they are not discernible when the cell is covered by water, Fig. 9 (a). The upper
edge of the cytoplasm is also well retrieved. The approach enables the Brillouin imaging of the
periphery of single cells, which is important as the periphery is the region where strong cell-cell
and cell-extracellular matrix (ECM) interactions take place.
<figure><img src="image_11.png" /><figcaption>FIG. 9. Map of the main frequency component of the reflectivity signal acquired from above the titanium transducer for: cell in water (a) and cell covered with sediment of silica nanoparticles in water (b). Optical image of the hMSC fixed on the titanium transducer in air obtained with a x50 magnification (c). The white dotted rectangles highlight the similarities of the contours of the cell between the acoustical (b) and optical images (c).</figcaption></figure>

V. QUANTITATIVE MEASUREMENT OF CELL 3D-MORPHOLOGY

We have combined two methods to measure the cell thickness. As in Ref. 24, the technique involves either determining the time when the acoustic phonons reach the top surface of the cell or identifying the resonance harmonics. In Ref. 24, cells were in air and the difference in acoustic impedance between cell and air is considerable, whereas in this study, the acoustic impedance of the liquid at the top interface of the cell is close to that of the cell. Moreover, the small thickness of the cell and the presence of liquid make the identification of the resonance harmonics more challenging.

The nucleus is usually the thicker part of the cell. As shown in Fig. 6 (a), for hMSC, it is thick enough for the Brillouin frequency to be measured. To deduce the thickness of the nucleus, we consider a refractive index of $n_N = 1.35$ and we determine the sound velocity at each pixel from the measured Brillouin frequency presented in Fig. 9 (b). We then identify time $τ$ when
the acoustic wavefront reaches the cell-water interface. As the use of nanoparticles deletes the Brillouin signature of the acoustic propagation in water, it facilitates the determination of $τ$. The thickness can then be obtained simply by $L = v_c τ$.

The cytoplasm is thin compared to $\lambda_{TDBS}$. However, we have seen previously that for this range of thickness, the resonance frequency at $f_0$ can be coupled with the remaining Brillouin oscillations in the sediment resulting in inaccuracies when using the simple equation $L = v_c/(4f_0)$. We have determined the thickness of the cytoplasm from the frequency of the first odd resonance harmonic $f_1 = 3f_0$. Nevertheless, we have seen in Fig. 5 (b) that the value of $f_1$ is biased by the acoustic attenuation and the presence of the Brillouin frequency. In the [13-20] GHz frequency range, the mean error introduced by the downward shift of the first odd harmonic was estimated at approximately 15 % resulting in an overestimation of same percentage for the thickness when using the formula $f_1 = (3v_c)/(4L)$.

For each X position, the estimation of the thickness was achieved by determining the Y positions and associated frequency $f_1$ of the two higher branches in Fig. 8 (c). As an example, for $X = 13$, this means finding the Y positions of both maxima of the red curve in Fig. 8 (d). Therefore, for each pixel, the thickness of the cytoplasm can be deduced from $L = 3v_c/(4f_1)$.

As the Brillouin frequency is not measurable in the cell region where the thickness is less than $\lambda_{TDBS}$, the value of $v_c$ is not known and has to be assumed. A first hypothesis could be to assume a continuity of thickness at the cytoplasm-nucleus interface and thus a sound velocity in the cytoplasm of 2.50 nm/ps, much larger than the mean value previously obtained in the nuclear part of the cell, $v_N = 1.86$ nm/ps. This value is not in agreement with what is commonly expected as the nucleus is made of an organized stiff chromatin fibers network whereas the cytoplasm is constituted of softer substructures. Therefore, the sound velocity in the cytoplasm should be less than in the nucleus. This value is neither consistent with what is established in the literature. Either for fixed cells in air$^{14,20,24}$ or immersed live cells$^{19,44,45}$, the Brillouin frequencies are around a few percent lower in the cytoplasm than in the nucleus and, under the assumption that the refractive index is the same in the whole cell, the celerity of acoustic waves is lower in the cytoplasm. Consequently, we rejected this hypothesis and assume a sound velocity fixed at $v_N^{24}$. This would results in a thickness discontinuity in thickness of 20% between nucleus and cytoplasm which is consistent with what was found in Ref. 18 where the thickness jump was corroborated using AFM measurements.

The cell morphologies obtained when the cell is in water and then using nanoparticles are
<figure><img src="image_12.png" /><figcaption>FIG. 10. Quantitative 3D cell thickness mapping of an hMSC covered by water only (a); covered by the sediment of nanoparticles and water (b); the results are obtained assuming the same value of the sound velocity $v_c = v_N = 1.86$ nm/ps in the whole cell; optical image of the hMSC fixed on the titanium transducer in air obtained with a x50 magnification (c).</figcaption></figure>

presented in Figs. 10 (a) and (b), respectively. For comparison, panel (c) depicts the optical image of the cell. The thicker part in the center and the thinner part in the surrounding area are clearly visible in both panels. They correspond to the cell nucleus and the cell cytoplasm, respectively. However, the top and bottom contours of the cell are better retrieved when using nanoparticles than without. Indeed, we have already seen in Figs. 8 and 9 that when the cell is in water, the spectrum is dominated by the frequency component of Brillouin oscillations in water, which prevents proper identification of the resonance harmonics. From a quantitative point of view, when the cell is in water, the thickness is measured for 75% of the total area of the cell. When using nanoparticles, this proportion reaches 85%.

The mean values of the thicknesses of the nucleus and the cytoplasm were calculated by selecting the corresponding zones of the image. Relevant results for the cytoplasm could only be obtained using nanoparticles. Assuming that the speed of sound is the same in the whole cell, $v_c = v_N = 1.86$ nm/ps, the mean thickness measured in water for the nucleus is $175 \pm 20$ nm. The values obtained with nanoparticles in the nucleus and cytoplasm are $192 \pm 21$ nm and $98$ nm $\pm 8$ nm, respectively. The standard deviation of thickness values obtained in the nucleus characterizes
the roughness of the cell¹⁸. The uncertainty range given for the cytoplasm corresponds to the over-
estimation of the thickness due to the downward shift in frequency compared to $f_1 = 3v_c/(4L)$.
The mean values measured without and with nanoparticles are similar, attesting that the sediment
of nanoparticles does not flatten the cell. Moreover, the order of magnitude of the nucleus thick-
ness is consistent with the frequency component of around 6 GHz for $22 < Y < 45$ visible in Fig.
8 (c). In both previous sections, we have attributed it to a resonance mode of the nucleus. Now
that the thickness is known, we can identify it as the first odd resonance harmonic $f_1$. In Figs. 10
(a) and (b), a thickness discontinuity of approximately 20 nm can be seen at the nucleus/cytoplasm
boundary surrounded by a sub-100 nm area, with thickness down to 60 nm. We thus demonstrate
the accuracy of the reported method for remote cell thickness measurements in water down to $\lambda_0/9$
and the ability to quantify cell roughness of the order of $\lambda_0/30$.

## VI. CONCLUSION

In this work, we have shown that the addition of nanoparticles to water improves the opto-
acoustic imaging of cells in solution by removing the strong signal due to Brillouin interactions
in the liquid. This technique not only improves the precision of the measured frequency of the
Brillouin oscillations in the cell but also reveals the layer resonance and its harmonics. This allows
for the precise imaging of the cytoplasm of thickness less than the Brillouin wavelength around the
nucleus, which was not possible with water only. Using two routes based on Brillouin oscillations
and harmonic resonances, the multiple scattering provided by nanoparticles made it possible to
measure the thickness for the very thin parts of the cytoplasm. We were able to remotely measure
thicknesses, down to $\lambda_0/9$, under the hypothesis of the same sound velocity in the whole cell.
This work is a significant progress for Brillouin imaging: the approach enables the imaging of the
cell periphery where crucial interaction of the cell with its surroundings occurs. It is also another
step towards the remote quantitative morphology measurement of thin live cells in nutritive liquid
down to nanometer thicknesses.

## VII. ACKNOWLEDGEMENTS

We acknowledge financial support from the Agence Nationale de la Recherche (grant ANR-
17-CE11-0020-01). We are also grateful to Lionel Teulé-Gay from ICMCB (Institut de Chimie
de la Matière Condensée de Bordeaux, CNRS UMR 5026) for manufacturing the opto-acoustic sapphire-titanium transducer, and to Serge Ravaine from CRPP (Centre de Recherche Paul Pascal, CNRS UMR 5031), for providing the silica nanoparticules. We also thank Emilie Prouvé from CBMN for her assistance in the cell experiments.

## DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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<footnote n="42">⁴²Both values were used as fitting parameters. They depend on the experimental fluence. An actual determination would require a dedicated work.</footnote>

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