Evaluation of mechanical properties of fixed bone cells with sub ...

Eur. Phys. J. Appl. Phys. (2013) 61: 11201 DOI: 10.1051/epjap/2012120279

THE EUROPEAN PHYSICAL JOURNAL APPLIED PHYSICS

Regular Article

Evaluation of mechanical properties of fixed bone cells with sub-micrometer thickness by picosecond ultrasonics Mathieu Ducousso1,2 , Omar El-Farouk Zouani3 , Christel Chanseau3 , Céline Chollet3 , Clément Rossignol1,2,a , Bertrand Audoin1,2 , and Marie-Christine Durrieu3 1 2 3

University Bordeaux, I2M, UMR 5295, 33400 Talence, France CNRS, I2M, UMR 5295, 33400 Talence, France University Bordeaux, INSERM U1026, 33076 Bordeaux, France Received: 17 July 2012 / Received in final form: 27 November 2012 / Accepted: 3 December 2012 c EDP Sciences 2013 Published online: 14 January 2013 – Abstract. The picosecond ultrasonics technique is used to investigate the viscoelastic properties of nucleus of fixed single osteoblast progenitor cells adhering on a titanium alloy substrate. A two-color probing picosecond ultrasonics and a fluorescence visualization setups were developed and combined to allow to distinguish subcomponents inside the cell under investigation. It opens the way for quantitative measurements of the viscoelastic properties of single cells and of their sub-micrometer thickness. It is shown that a blue probe, λ = 400 nm, is preferable to a red probe, λ = 800 nm, to perform these measurements with fixed sub-micrometer bone cells. 26 GHz acoustic frequencies are detected in cells as thin as 135 nm. A 1D analytical model of the acoustic generation and of the optical detection is used to describe the experimental results. The nucleus longitudinal elastic moduli (13–16 GPa) and dynamic viscosities (13–30 cP) are measured at high frequencies (GHz) from a time-frequency analysis of the experimental data of fixed single cells.

1 Introduction Cell is considered as the building block of life. However, some of its mechanical properties are still not known although their knowledge could deepen our understanding of cellular biology or pathologies. Following this idea, a focus has been turned toward biomechanics of cancer cells, as they have different mechanical properties compared to healthy ones. For example, it has been reported that cancer cells can be more than 70% softer than healthy cells despite showing a similar shape [1]. This difference could be related to the cytoskeleton which is highly organized in healthy cells but disorganized in cancer cells. In the same way, many diseases, such as Parkinson disease, are associated with changes in cellular structure, particularly with the cytoskeleton, that could be mechanically probed. Cell biomechanics can also be used to quantify cellular adhesion on biomaterials, with a direct application for tissue or bone substitutes engineering. In the context of a global increase of life expectancy, implantable biomaterials are often used to replace malfunctioning parts of the aging body. For joint repair for instance, one way to improve the bone prosthesis biocompatibility and lifetime is to enhance the cell adhesion at the prosthesis surface [2]. To perform a joint refit, the understanding of the phenomena involved in cell adhesion is of crucial importance. a

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The cell adhesion on the prosthesis surface is mainly governed by the cell cytoskeleton through the spatial distribution of its focal adhesion points [3]. Several experimental techniques suited for the investigation of mechanical properties of single cells have been developed (atomic force microscopy, micropipettes, optical traps . . . ), thanks to the onset of nanotechnologies that enable nanometer displacements and piconewton force measurements. However, almost all these techniques impose to perturb the medium to probe its mechanical properties, which can strongly disturb the experimental signal. Moreover, the perturbation is often localized, currently on the surface of the cell, and the cell bulk properties are difficult to evaluate (see [4,5] for a review). In this context, acoustic microscopy offers a great advantage. Indeed, similarly to conventional medical ultrasounds that can be used to probe viscoelastic properties of human tissue [6,7], this technique is non-invasive and allows bulk evaluation of the cell viscoelastic properties [8]. It has already been used successfully to probe mechanical properties of single HeLa cells [9] as well as elasticity as a function of the cytoskeleton organization in XTH-2 cells [10]. However, at room temperature, because of the high acoustic attenuation of the coupling liquid, the acoustic frequency cannot exceed a few GHz. Therefore, the technique appears to be better suited for studying cells of micrometers thicknesses.

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The European Physical Journal Applied Physics

The picosecond ultrasonics technique [11] has proved its suitability to probe physical properties of condensed matter. The technique requires sub-picosecond laser pulses, which play the dual role of both phonon generation and phonon detection by phonons-photons coupling. It is currently used to probe mechanical, thermal or optical properties of nano-objects [12], and it has been recently used to investigate magnetism properties of ferromagnetic nanosamples [13,14]. Experiments have been performed in various solid media for non-destructive evaluation [12], but only a few applications in liquid [15] or viscoelastic [16] media have been reported. The technique can be used in temperature [15], pressure [17] or magnetic controlled environment [13]. As it allows to generate and to detect sub-THz acoustic phonon in the vicinity of an interface of an optically opaque material, the technique appears to be well suited for probing very thin cells, in the sub-micrometer range, adhering on a substrate. Moreover, it presents similar advantages as acoustic microscopy for investigations of biological materials. The demonstration of the picosecond ultrasonic method for the improvement of the non-invasive in vitro single cell acoustic imaging has already been reported for vegetal cells of a few micrometers thickness [18]. The sensitivity of the technique has also been demonstrated probing the nucleus of the cells of different varieties of same specie of Allium cepa [19]. In this paper, the picosecond ultrasonics technique is used to probe fixed animal cells of sub-micrometer thickness adhering on a titanium alloy material. For this purpose, a setup is developed which can be used with red (λ = 800 nm) or blue (λ = 400 nm) laser detection and combined with a fluorescence imaging of the cell. Viscoelastic measurements are presented in fixed bone osteoblast progenitor cells (MC3T3-E1) [20,21]. In the following section, basic considerations of the technique based on a 1D simulation model of the phonons generation, propagation and their optical detection in a thin optically transparent film are presented. In the next section, the experimental setup built for the cell investigation is described. Finally, experimental results confronted with simulations are proposed and discussed in the fourth section.

2 1D picosecond ultrasonics generation, propagation and detection model in a thin transparent film In this section, optical generation and detection phenomena are described for a thin optically transparent film (noted 1) of thickness h adhering on a semi-infinite opaque substrate (noted 0). This presentation is based on a straightforward one-dimensional analytical model. The surface of the film is exposed to air. Figure 1a shows the considered geometry. In picosecond ultrasonic experiments, the acoustic generation results from the absorption of the energy of a subpicosecond laser pulse in an optically opaque substrate

Fig. 1. (a) Principle of the 1D photoelastic model. A thin transparent film is embedded between a substrate (z ≥ 0) and air (z ≤ −h). A bipolar acoustic pulse propagates in the substrate and a monopolar pulse propagates in the film. (b) Film thickness variation, i.e., difference of the displacement of the two interfaces, as a function of time t with (solid) or without (dash) the source term in equation (2) for medium 1. The film thickness changes when t is an integer multiple of the acoustic travel time TA = h/v1 in the film. v1 is the sound velocity in the film.

(i.e., typically with an optical penetration depth, β −1 , in the range of 10–30 nm). The absorbed energy produces a sudden thermal rise in the substrate, in a volume defined by the focused laser spot diameter at the substrate surface and β −1 . The substrate is considered semi-infinite (z ≥ 0; z = 0 corresponds to the substrate surface) in regard to optical, thermal and acoustical phenomena. The temperature rise, Ti , provided by a laser pulse of energy Q, focalized on an optical spot area A of optical reflectivity R, is [22]: ∂Ti (z, t) ∂ 2 Ti (z, t) Q − κi = (1 − R)βi f (t)e−βi z , 2 ∂t ∂z A (1) where f (t) is the normalized dimensionless laser pulse function in time and the specific heat capacities, densities and thermal conductivities in medium i are denoted by Cpi , ρi and κi , respectively. Since medium 1 is assumed transparent, its optical absorption is neglected and, the source term in equation (1) is located in the substrate. The temperature and heat flux are considered continuous at the interfaces. The thermal rise in medium 1 results from this continuity. Physical values used for the simulations are given in Table 1. About 100 ps after the pump pulse was absorbed, the heated depth in the film (∼10 nm) is one tenth of that in metal (∼160 nm) [19]. The thermal rise creates a thermoelastic expansion of the substrate. Subsequently an acoustic pulse is generated and propagates in the medium. Neglecting the effects of electron diffusion, the equation of the acoustic displacement in the 1D space-time domain can be written as follows: ρi Cpi

Ci

∂ 2 Ui (z, t) ∂ 2 Ui (z, t) ∂Ti (z) , − ρ = Ci αi i ∂t2 ∂z 2 ∂z

(2)

where Ci , αi and Ui define the stiffness coefficients, the thermal dilatation and the acoustic displacements in medium i, respectively.

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M. Ducousso et al.: Mechanical properties of sub-micrometer cell by picosecond ultrasonics Table 1. Physical constants considered in the simulation for Figure 1b. The physical constants of medium 0 correspond to a Ti6AL4V substrate. The physical constants of medium 1 marked with “∗” are representative of first measurements performed in Allium cepa cells by picosecond ultrasonics [19]. Cp (J kg−1 K) κ (W m−1 K−1 ) ρ (kg m−3 ) β (m−1 ) C (GPa) C (cP) α (K−1 )

Medium 0 500 21.9 4500 5.2 × 107 155 0 9 × 10−6

Medium 1 9460* 0.7* 1100 0 2.9* 0.2* 3.5 × 10−4

Cells’ viscoelastic properties are still not known in the sub-THz regime [23], but are of great interest since both longitudinal modulus and loss modulus could be used as a specific marker to diagnose the vitality of the cell or its aging [1,24]. Thus, it was decided to model the attenuation of sound in cells with a similar damping law as for water, i.e., with an attenuation factor proportional to the square of the frequency [15,25,26], to measure both parameters. It is achieved assuming a frequency-dependent complex stiffness [27]: Ci = Ci + jωCi , where ω is the acoustic pulsation. C stands for the longitudinal elastic modulus and C for the dynamic viscosity. In medium 0, the substrate, duration of the acoustic −1 pulse is given by (β0 v0 ) where v0 is the speed of sound usually equal to a few nm/ps. The resulting spatial extension of the acoustic strain pulse is about 20 nm, with a bipolar shape due to the acoustic reflection at the substrate interface, Figure 1a [28]. Let us now consider the transparent medium 1, adhering at the surface of the substrate. The displacement and strain are considered continuous at the 0/1 interface. The dilatation of medium 0 creates a compressive strain in medium 1. A monopolar acoustic pulse is transmitted in medium 1 and propagates within (Fig. 1a), as it is generally the case for thermoelastic generation close to a transparent-opaque media interface [29]. The spatial extension of this compressive acoustic pulse in medium 1 is, in first approximation, dA = (v1 /v0 )β −1 [30]. Note that if v1 is smaller than v0 , the spatial extension of the pulse is smaller in the film than in the substrate. Amplitude of the pulse depends on the acoustic transmission coefficient of the interface 0/1 and on the thermoelastic expansion in medium 1 due to the acoustic source term in equation (2) [31]. If h is larger than dA and smaller than the acoustic absorption distance, reflections occur at medium 1 interfaces. Amplitude and polarization of the pulse after each reflection are determined by the reflection coefficient, defined by rij = (Zi − Zj )/(Zi + Zj ), where Zn is the impedance coefficient and n = i, j stand for medium i and j, respectively [32]. Considering that Zair Z1 Z0 , the boundary conditions are closed to displacement free at

the film/air interface and stress free at the 1/0 interface. Thus, the amplitude of the acoustic displacement is larger at the film/air interface compared to the film/substrate interface. A periodic step-like change of the film thickness results from the acoustic propagation which time decay is function of rij and of the acoustic loss in medium 1, driven by jωC1 . Figure 1b shows the resulting thickness variation of the film as a function of the acoustic time of flight across the film, TA = h/v1 . Large steps correspond to thickness variations created by reflections at the film/air interface while small jumps (downward arrows) are related to acoustic reflections at the 0/1 interface. The dashed curve is a calculation where the source term of equation (2) in medium 1 is omitted, i.e., the amplitude of the signal is related only to the acoustic transmission and reflection coefficients at the interfaces, while the continuous line shows the acoustic signal where the source term of equation (2) in medium 1 is taken into account. The difference in the amplitude of the curves is related to the thermal dilatation in medium 1 that is by two decades larger than the thermal dilatation in medium 0. Moreover, the smoothing of the shape of the crenel is the signature of the thermal diffusion in medium 1 when the source term of equation (2) is taken into account in medium 1. The physical parameters of the titanium alloy substrate and of a typical vegetal cell used for this simulation are presented in Table 1. The experimental pump fluence is considered at 16 mJ/m2 ; it corresponds to the fluence used for experiments. Thickness variations of few picometers are obtained [33]. The frequency of the resulting acoustic signal is v1 fA = . (3) 4h The optical detection of the acoustic pulse in medium 1 is now described. The laser probe passes through the transparent film and is focused at the same point as the pump laser. Discussions of the optical detection have already been reported elsewhere [30,31,34,35]. Only general concepts of the involved phenomena are reminded in this text. As the acoustic pulse propagates in a material, it creates a variation εsi of the film dielectric properties εi through the acousto-optic effect. In picosecond ultrasonics, since the perturbation is small, the dependence of εsi on acoustic strain can be supposed to be linear. The spatial variation of the dielectric permittivity can be formalized as the sum of a homogeneous part and of a perturbed part (noted with h and s, respectively) [31,36]: equation εi (z, ω) = εhi + εsi (z) = εhi +

∂ni ηi (z, ω) , ∂η

(4)

where ∂ni /∂η and ηi stand for the piezo-optic coefficient and the acoustic strain propagating in medium i, respectively. Since the detection is investigated in an optically transparent material, the optical index ni is supposed real in a first approximation. In the Fourier domain, the nonlinear Maxwell equation in the perturbed medium is then:

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∂ 2 Ei (z, ω) + q 2 εi (z, ω) Ei (z, ω) = 0, ∂z 2

(5)


h

Ei (z, ω) =

Mih e−jqni z h +Nih ejqni z

jq − h 2ni

h s h s 2jqn + Ni εi (z ) e Mi h εi (zs ) dz −2jqn z h

h iz

− Mi

where Ei (z, ω) is the electric field in medium i and q is the optical wave vector in vacuum. Considering a small transient perturbation, the electric field can be written as the sum of a homogeneous part and of a perturbed part: Ei (z, ω) = Eih (z, ω) + Eis (z, ω). Equation (5) can then be linearized as: ∂ 2 Ei (z, ω) + q 2 εhi Ei (z, ω) = −q 2 εsi (z, ω) Eih (z, ω) . (6) ∂z 2 Equation (6) is solved in the first-order Born approximation [31]. Its solution is: see equation (7) above, Mih

Nih

where and are coefficients appearing in the homogeneous equation and are derived from the optical boundary conditions at medium 1 interfaces. The electric and magnetic fields are considered continuous at each interface. The interface displacement has to be considered to model the optical detection of the film thickness variation due to the transient acoustic wave within, Figure 1b. A time-dependent reflection coefficient is obtained of same frequency as the acoustic signal in the film. Integrals are also calculated from substrate/film to film/air interfaces taking into account the film thickness variation to model the optical detection in the transparent film of varying thickness. Finally, the relative reflectivity variation is deduced from the ratio between the perturbed optical reflectance rs and the initial reflectance rh of the system [37]: s r ΔR = 2Re . (8) R rh Relation (7) describes all the physics involved in the optical detection of the transient perturbation: the interface motion detection is modeled considering the boundary conditions and the acousto-optic interaction which appears in the bulk of the transparent material is described considering the four integral terms. They can be understood by Fourier optics. The optical phase reference is defined when there is no perturbation, i.e., when the interface motion is not taken into account. The terms containing the phase shift ±2qnhi z with respect to the reference result from the optical backscattering induced by the acoustic perturbation. These terms may be understood as Stokes and anti-Stokes scattering modes [38]. In picosecond ultrasonics, these scattering modes give rise to so-called Brillouin oscillations, which frequency is for a normal probe incidence [28]: fB =

2n1 v1 , λ

(9)

where v1 and λ stand for the acoustic velocity and for the probe wavelength, respectively. The amplitude of the

εi (z ) e

h i

dz + Ni

h

dz e−jqni z

h

εsi (z ) dz ejqni

z

(7)

Brillouin oscillations is proportional to the piezo-optic coefficient [35]. If the complex optical index of the inspected medium is known, the frequency and attenuation of the Brillouin signal yield to the evaluation of the elastic properties of the probed media, such as its velocity and its attenuation of sound. From these, if the density is known, the bulk viscoelasticity can be derived. Indeed, the speed of sound and the damping of the oscillations are related to the longitudinal elastic modulus and the dynamic viscosity, respectively. Finally, the acousto-optic interaction and the optical detection of the film-interface displacements allow measuring the visco-acoustic properties and the film thickness variation, respectively. At last, the terms which are not phase shifted in relation (7) correspond to forward scattering beams on the perturbation. They do not create interferences and hence are not detected. The optical detection of the acoustic propagation is sensitive to Brillouin scattering phenomena and interfaces displacements. While the film thickness does not appear explicitly in the Brillouin frequency relation, equation (9), its value can be of fundamental importance for the detection of Brillouin oscillation, i.e., the detection of the acousto-optic interaction in the bulk of the film [31]. Figure 2 illustrates the optical detection of the acoustic propagation in a thin transparent film. Abscissas correspond to the dimensionless time, with respect to the acoustic time of flight across the film, TA = h/v1 (bottom) and to the period of the Brillouin oscillations TB = 1/fB (top). On the one hand, the curve with stars represents the optical detection of the interfaces motion. One can note the similitude of this detection with the simulation of the film thickness variation plotted in Figure 1b. On the other hand, the detection of the acousto-optic detection is plotted with square labels in Figure 2. The spatial extent of a period of the Brillouin oscillations is Λ = λ/(2n), half of the optical wavelength in the film. This length corresponds to the acoustic wavelength that is optically probed in the transparent film by the acousto-optic interaction. If h is larger than Λ, Brillouin oscillations can be detected by the optical detection, see Figure 2a. On the contrary, if h is smaller than Λ the acousto-optic interaction in the bulk of the film cannot appear on a full period. While this signal cannot be called Brillouin oscillations, the beginning of an oscillation resulting from acousto-optic interaction can still be detected, Figure 2b, square labeled line. Finally, Λ is proportional to the probe wavelength but is not dependent on the acoustic celerity in the film. The simulations of the corresponding detected signals are plotted with unlabeled lines in Figure 2. If h is large enough compared to Λ, the two contributions of the optical detection, steps and oscillations, can be identified in Figure 2a. The acoustic velocity in the film can be

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M. Ducousso et al.: Mechanical properties of sub-micrometer cell by picosecond ultrasonics

determined from Brillouin oscillations if the optical index is known. Then the detection of the interface motion is used to measure the film thickness. The sub-picosecond resolution of the time detection can lead to an accuracy of this measurement in the nanometer range [34]. If Λ and h are of similar dimensions, the reflected intensity strongly depends on the film thickness [39] and, consequently, the amplitude of the optical detection of the interface motion is related to h and to the amplitude of the film thickness variation. The steps of the optical detection of the interface motion are superimposed to the acousto-optic detection [34]. In this last case or if h is smaller than Λ, it is not straightforward to identify separately the acousto-optic and the interface motion detections. The

(a)

(b)

Fig. 2. (Color online) Relative reflectivity change calculated for h > Λ (a) and for h < Λ (b). Λ is half the optical wavelength in the film and corresponds to the probed acoustic wavelength. For each plot, signals labeled with round and star markers represent the acousto-optic and the interface displacement contributions, respectively. The unlabeled plot is the sum of the acousto-optic and interface displacement contributions.

simulation model should be used to fit the experimental results and to evaluate the acoustic parameters and the thickness of the film. This global procedure will be used to perform the acoustic and thickness measurements in the inspected cells.

3 Experimental setup: two-color probing of ultrafast acoustic propagation combined with fluorescence visualization in thin fixed cell Time-resolved reflectometric experiments are performed with a pump-probe setup [28]. In this setup, the red radiation (800 nm) of a mode-locked Ti:sapphire laser at a repetition rate of 82 MHz with a pulse duration of 100 fs is split using a polarizing beam splitter to provide pump and probe beams. The pump beam is chopped by an acoustooptic modulator (AOM) to supply the reference signal for lock-in detection. The probe beam passes through a delay line to tune the pump-probe time delay and is detected using a photodiode. A BBO crystal is inserted in a beampath to generate the second harmonic of the laser beam. This setup allows to measure relative reflectivity variations as small as 10−7 , with a sub-picosecond time resolution. The two-color probing picosecond ultrasonics experimental setup is presented in Figure 3a. Two AOM are used, one per beampath. Both AOM are powered, however only the one on the pump beampath received a reference frequency signal. The pump and probe beams energies are controlled using a polarizing beam splitter and λ/2 wave plates. The blue and red beams are then spatially superposed using a dichroic mirror. They are focused on the sample at the same point. Both reflected beams from the sample are then spatially separated using the same dichroic mirror. Polarizing beam splitters and λ/4 wave plates allow guiding the selected reflected beams toward the photodiodes. This setup allows to pick the color of the detection. The laser beams are focused at a normal incidence with a X20 microscope objective. The full width at halfmaximum of the space cross-correlation of the pump and probe beams is approximately 6 μm. This focus is smaller than the lateral dimensions of the cell nucleus, measured around 10 μm from profilometry measurements, Figure 4 (details of the measurement are given in the following). The pump mean power is less than 500 μW and the probe is twice weaker. Such a small beam power allows a noninvasive evaluation of the cell because of both limited thermal rise (∼1 K) and elastic strain amplitude generated into the cells [19]. Due to this small power, the acoustic signal is low and the optical detection is close to the limit of the experimental setup. To improve the signal-to-noise ratio of the detection, a differential scheme between the reflected probe from the sample and a small part of the incident beam with the same energy for both color detections is implemented. This technique allows to suppress some external fluctuations and the laser intensity noise and reduce beam walking noise effect [40,41].

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Fig. 3. (Color online) (a) Principle of the two-color probing of the experimental setup. The fundamental mode of the laser radiation is converted using a BBO. The intensities of the incident beams are controlled using λ/2 wave plates and the reflected beams from the samples are directed toward a photodiode using λ/4 wave plates. Spatial superposition and separation of the incident and reflected beams, respectively, are performed using a dichroic mirror. A differential detection scheme is used to improve the sensitivity of the pump-probe setup. (b) Scheme of the microscope inserted in the experimental setup which allows fluorescence visualization of the cells and a picosecond ultrasonics measurement. A photograph of a fixed cell in air environment with the laser beam focused on it is presented in the inset.

An improvement of 10% in the signal-to-noise ratio of the detection using this balanced detection technique is quantified. The experiments are led on osteoblast cells, adhering on a Ti6Al4V titanium alloy substrate. Ti6Al4V is commonly used as material for prosthesis [42]. The thicknesses of fixed osteoblast cells have been measured by optical profilometry. The accuracy of the measurement is 10 nm [43]. A typical measurement of the cells’ profilometry is presented in Figures 4a and 4b. The inspected cell is shown in Figure 4a and the profilometry measurement, performed along the line crossing the cell, is presented in Figure 4b. The cell presents a typical fried egg shape. Its maximum thickness is on top of the nucleus, with a typical value of several hundred nanometers (100–400 nm) and elsewhere the thickness of the cell falls quickly down to few tens of nanometers. Otherwise, the nucleus diameter is around 10 μm, i.e., larger than the focus beam diameter. Thus, we assumed that the acoustic pulse should not be strongly affected by the curvature of the cell, at least on the 2 or 3 first acoustic flights in the cell which are mainly used to perform the measurement. Such values imply that Brillouin oscillations cannot be systematically detected in these cells considering the red color (λR = 800 nm) of the laser and a classical cell optical index of n1 = 1.4 [44]. Indeed, the minimal cell thickness should be larger than ΛR = 285 nm to detect Brillouin oscillations with a red probe. To overpass this limit, the cell is probed with the second harmonic of the laser radiation, i.e., a blue probe (λB = 400 nm). With this last color, the cell thickness limit is then reduced to ΛB = 142 nm. Thus, even if the thickness of the cell in the nucleus zone is as small

Fig. 4. (Color online) Thickness measurement of a MC3T3-E1 fixed cell adhering on a titanium alloy substrate. (a) The measured cell is presented. Its lateral dimensions are of few tens of microns. The profilometry measurement is performed across the cell (along the line), passing above its nucleus. (b) Plot of the profilometry of the cell. Its thickness presents a fried egg shape. The maximum thickness of few hundreds of nanometers is on top of the nucleus and the thickness falls quickly down to few tens of nanometers on other points.

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as ∼140 nm, it is still possible to measure its acoustic parameters with the help of the model presented in the previous section. To perform the acoustic measurements, the cells are placed on a sub-micrometer translation stage xy sample holder, at the focal point of the microscope objective to select the nucleus of the probed cell. Moreover, the cell nuclei must be well situated with respect to the laser beams, thus an optical microscope is inserted in the pump-probe setup. The experimental setup is also built to allow in vitro evaluation of cells adhering on a biological substrate. The cells are in a thermal and pH controlled biological serum to maintain them in vitro during the experiments. Thus, a biological sample holder has been built to preserve such conditions. It imposes to place the cell below 1 mm of biological serum and a 0.175 mm microscope glass slide. Hence the used high focusing microscope objectives must have long working distances. Moreover, the biological serum currently used has an optical index equal to 1.3, close to the cell optical index (considered as 1.4) [44] which reduces the optical contrast and makes it more difficult the achievement of optical images. In order to well situate the cell sub-components with respect to the pump-probe laser beams even for in vitro investigations, the microscope is doted of a fluorescence detection. The operation scheme of the microscope is presented in Figure 3b. It is composed of two superposed optical schemes, one for the fluorescence visualization and the other for the ultrafast acoustics probing of the cell. The microscope for cell fluorescence visualization is made of a highly stable white light source, injected in the microscope using an optical fiber. Filters for emission and detection of the cell fluorescence are placed vertically above the microscope objective. The optical visualization is performed using a cooled charge-coupled device (CCD) camera, placed above both fluorescence filters and microscope objective. The pump and probe beams of the picosecond ultrasonics setup are injected in the second optical scheme of the microscope, placed below the fluorescence scheme. Such scheme allows to preserve the laser pulse duration and its spatial coherence. A broadband (400–800 nm) nonpolarizing 50/50 beam splitter for ultrafast lasers is inserted, between the fluorescence filters and the microscope objective to separate the two detection channels. This optical scheme allows to visualize on a camera the laser beams of the pump-probe setup focused on the cell and/or cell fluorescence. The photography in the inset of Figure 3b shows a MC3T3-E1 cell in air environment with the pump-probe laser beam focused next to its nucleus. As the wideband 50/50 beam splitter reduces detection of the fluorescence, it is fixed on a high stability translation stage to allow classical use of the optical microscope when it is removed from the optical path of the sample visualization. A fluorescence image of osteoblast cells where both cytoskeletons and nuclei are marked with fluorescence is presented in Figure 5a for the case where the beam splitter has been removed from the fluorescence path. Camera binning can be used to improve the signal-to-noise ratio

Fig. 5. (Color online) (a) Fluorescence image of bone cells when the beam splitter of the picosecond ultrasonics arm of the microscope is removed from the visualization optical path. (b) Fluorescence image of MC3T3-E1 cells when the beam splitter of the picosecond ultrasonics arm of the microscope is in the optical path of the fluorescence visualization. Fluorescence markers have been fixed on cells nuclei. Cells are under 1 mm of biological serum and a 175 μm thick glass microscope slide. The laser beam of the picosecond ultrasonics setup is focalized between two nuclei at the substrate surface.

of the fluorescence detection when the beam splitter is in the optical path. In Figure 5b, a fluorescence image of MC3T3-E1 cells adhering on a titanium substrate placed in biological serum is presented. Only the cell nucleus has been treated with fluorescence markers. The beam splitter is inserted on the optical path of the fluorescence detection; however, the intensity of the fluorescence is high enough to have a good visualization even without binning. The laser pump beam, focused with a X20 microscope objective, is visible on the image between two nuclei of two different cells.

4 Probing of thin fixed single cells using picosecond ultrasonics Measurements are performed on bone osteoblast progenitor MC3T3-E1 cells adhering on a Ti6Al4V substrate. To simplify interpretation of these pioneering picosecond

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ultrasonic biological investigations in animal cells, experiments are performed in air environment. Thus, the cells are chemically fixed. Experiments are led at the thicker area of the cells, where the nucleus, the cytoplasm, the cytoskeleton and the membranes are all superimposed under the focused pump and probe laser beams. The characteristic dimensions of the cytoskeletal elements and of the membrane are in the nanometer range [5], two decades smaller than the acoustic wavelength probed with the Brillouin detection. Consequently they are not detected here. It is also assumed that the thickness of the cytoplasm between the cell nucleus and the membrane is too thin to be experimentally probed. The simulation model presented in Section 2 is used to fit the experiments. The probed zone in the cell is considered as a homogeneous medium, corresponding to the cell nucleus. In Figure 6, red or blue lines represent experimental data of the picosecond ultrasonics measurements in a single cell. On the top graph, the experiment was performed using a blue probe λ = 400 nm while a red probe λ = 800 nm was used in the same cell at the same point in the bottom graph. Lines labeled with symbols stand for calculations made with the model presented in Section 2. Simulations of the interface motion detection are labeled with stars and simulations of the acousto-optic detection are labeled with squares. The simulation of the detection is plotted with triangles. The simulations are adjusted on the experimental data by varying the viscoelastic properties and the thickness of the cell. Using the blue probe, λ = 400 nm, both Brillouin oscillations and interface motion detections are identifiable. The experiment is accurately fitted by the simulation. Frequency variations are not observed from the comparison between experimental and simulated signals. This validates our simulation approximation, which considers the cell as a homogeneous medium. Assuming a cell optical index equal to 1.4 for both red and blue laser detections [44], and a density of 1100 kg/m3 [9,45], the longitudinal elastic modulus is evaluated at 15 GPa and the dynamic viscosity at 30 cP from the Brillouin detection using the blue probe. The uncertainty of the measurement is estimated around 0.5 GPa and 2 cP. The corresponding acoustic velocity is 3.7 nm/ps and Brillouin frequency is 26 GHz. The cell thickness is measured from the interface motion detection at 135 nm, close to ΛB . Such cell thickness appears to be the bottom limit to detect Brillouin oscillations using a blue probe. The simulation of the acousto-optic detection shows that using red probe detection the viscoelastic properties of the cell cannot be identified as frequency of the Brillouin signal is too low compared to the cell thickness, as presented in Figure 2b. Such prediction is confirmed by the experiment: it appears that it is not possible, with this technique, to distinguish the acoustic celerity from the cell thickness value in the red configuration. Indeed, experiments using the red probe are fitted with the same mechanical parameters identified for this cell using the blue probe, but varying the piezo-optic coefficient value, bottom graph in Figure 6. The amplitude of the signal detected with the red probe is by three times larger than

Fig. 6. (Color online) Reflectivity change for a MC3T3-E1 fixed cell adhering on titanium alloy (unlabeled line) probed by the picosecond ultrasonics technique using blue (up) and red (bottom) probes. The corresponding calculated signals (triangles), the sum of the acousto-optic contribution (squares) and the cell surface displacement (stars) are shown for each color detection. Fixed cell longitudinal elastic modulus, dynamic viscosity and thickness are measured at 15 GPa, 30 cP and 135 nm, respectively, from the blue probing.

the amplitude of the signal detected using the blue probe however it is not possible to identify an acousto-optic detection. These experiments allow us to confirm that some cells are too thin to extract their viscoelastic properties from the acousto-optic detection using a red probe. It can be concluded that experiments with a blue probe should be preferred because of the small thicknesses of the submicrometer cells. Attenuation of the Brillouin and of the interface motion signals is related to different phenomena. From the assumed density and the measured acoustic velocities, the impedance Z1 of the cell can be calculated at 4.0 Kg m−2 s−1 . The coefficient of the acoustic reflection at the cell/air interface is close to 1 and to 0.7 at the cell/substrate interface. Neglecting other sources of acoustic decay, the acoustic signal is reduced by more than 70% after the fifth reflection at the cell/substrate interface. At first order, the low frequency signal of the cell thickness variation, i.e., fA = 6.8 GHz, is attenuated owing to this acoustic loss. The interface motion signal can still be detected during ∼365 ps, i.e., after 10 back and forth propagations through the cell. The high frequency acousto-optic detection is attenuated faster, as the attenuation of the Brillouin detection depends on first order of the viscoelastic properties of the cell. Finally, the acoustooptic signal is detected during ∼110 ps. In Figure 7 is presented a set of five typical blue probe picosecond ultrasonics measurements in air environment fixed bone osteoblast progenitor MC3T3-E1 cells adhering on a Ti6Al4V substrate. In full blue lines are represented the experiments and in full black lines the calculations

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the mechanical sub-components of the cell. Finally, the validity of the considered Kelvin-Voigt rheological model, Ci = Ci + jωCi , could be tested using a continuum light for the optical detection [47].

5 Conclusion

Fig. 7. (Color online) Typical reflectivity changes for bone osteoblast progenitor fixed cells adhering on titanium alloy: calculated (black line) and probed by picosecond ultrasonics using blue probe (blue line).

with the 1D photoacoustic model respectively. The two acoustic signatures can be clearly seen: the Brillouin oscillations in the first 200 ps and the acoustic steps from the ultrasonic wave traveling back and forth in the cell. The measured frequencies are in the range (24–27 GHz). Using the previous cell parameters, cell longitudinal elastic moduli (13–16 GPa), dynamic viscosities (13–30 cP), acoustic velocities (3.5–3.8 nm/ps) and thicknesses (135–500 nm) are determined with the comparison between the measurements and the acoustic model. The measured acoustic velocities are twice larger than in previous measurements in living cells [8]. At this time, it could be related to: (i) the cell viscoelastic behavior in the GHz range, (ii) the cell nucleus longitudinal elastic modulus which can be by 10 times larger than that of cytoplasm [46], as it is essentially composed of proteins which are in the GPa order of rigidities [46] and/or (iii) the fixing process. Experiments are in progress to study these three assumptions. Future in vitro conditions experiments should allow a discussion of the influence of the fixing process over cell mechanical properties. In these future experiments, boundary conditions at the cell surface will be strongly changed, as a liquid serum will replace air. However, the acoustic reflection coefficient of the cell-serum interface should still be significant, as the measured nucleus cell rigidity is about one decade larger than the serum. Thus, several back and forth propagations through the cell should still be detected in this case. Moreover, the acoustic mismatch of the cell-substrate interface should be measured by comparison of the experimental signals obtained from the cell immersed in the serum and from the serum only. We also finally note that thicker cells could be used. In that way, both nucleus and vacuole of a single cell should be acoustically probed, giving access to an acoustic image of a single cell, and a quantitative evaluation of

A picosecond ultrasonics setup with a two-color probing, and doted with a detection of fluorescent markers, has been built to allow the mechanical evaluation of the nuclei of single sub-micrometer fixed cells. The experiments were realized on air environment fixed bone osteoblast progenitor MC3T3-E1 cells adhering on a Ti6Al4V substrate. On the basis of a two-color probing of the nucleus of a single fixed cell, it was shown that the acoustic evaluation must be performed using blue color detection, instead of red color detection, to evaluate cells as thin as 135 nm. It allowed remote quantitative measurements of the mechanical parameters of cells adhering on a titanium alloy substrate at acoustic frequency as high as 26 GHz. Assuming the cell optical index (n = 1.4) and density (ρ = 1100 kg/m3 ) values, fixed cell nucleus longitudinal elastic modulus (15 GPa), dynamic viscosity (30 cP) and thickness (135 nm) have been measured. The technique has also been applied to probe a set of similar cells: from 24 to 27 GHz acoustic frequencies are measured. Determined values are then in the 13–16 GPa, 13–30 cP, 135–500 nm ranges for fixed cells longitudinal elastic moduli, dynamic viscosities and thicknesses, respectively. In the next future, biological application fields could concern cell adhesion and differentiation on different microenvironment through the evaluation of mechanical properties which could be related to the cell cytoskeleton organization. Cell mechanics as a function of viability could also be studied, for instance, on cancer or aging cell properties’ evaluation. The in vitro inspection of the activity of various specific cell types, such as neuronal cells for instance, could also be performed with an application for researches in neurodegenerative disorders, like Parkinson’s disease. This work had been supported by Agence Nationale pour la Recherche through Grant PicoBio (ANR-07-BLAN-303) and the Conseil Régional d’Aquitaine for the PhD funding related of this research program. We acknowledge J.M. Rampnoux, T. Dehoux for fruitful discussions. We also acknowledge W. Boutu for careful reading of the manuscript.

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