2.1.

Cells

Human pancreatic ductal adenocarcinoma cells (PaTu 8988 T)³⁸ used in this study were obtained from the German Collection of Microorganisms and Cell Cultures (DSMZ, Braunschweig, Germany). The cells were cultured in dulbecco’s modified eagle’s medium (DMEM) supplemented with 5% fetal calf serum, 5% horse serum, and 2-mM L-glutamine under standard cell culture conditions (37°C and 10% ${\mathrm{CO}}_2$).

For quantitative DHM phase imaging of adherent cells the cells were seeded in Petri dishes ($\mu$-dish, ibidi GmbH, Munich, Germany). For quantitative phase analysis of suspended cells, the cells were trypsinized and investigated in Petri dishes with an uncoated “hydrophobic” bottom ($\mu$-dishes, ibidi GmbH, Munich, Germany) to prevent cell adherence during the experiments. In order to manipulate the cellular refractive index, the cells were observed in diluted cell culture medium with decreased osmolality. Therefore, deionized water was added to the initial Hepes buffered cell culture medium.

Human fibro sarcoma cells HT-1080³⁹ were cultured in DMEM supplemented with 10% fetal calf serum and 2-mM L-glutamine at 37°C with 10% ${\mathrm{CO}}_2$. These cells were observed after adherence in microfluidic channels ($\mu$-Slides, ibidi GmbH, Munich, Germany). To induce a decrease and increase of the cellular refractive index the initial Hepes buffered cell culture medium with an osmolality of $320\mathrm{mOsmol}/\mathrm{kg}$ was replaced by medium that was diluted with deionized water to $160\mathrm{mOsmol}/\mathrm{kg}$. An automated pump system (ibidi pump system, ibidi GmbH, Munich, Germany) was applied to achieve a reproducible exchange of the medium.

2.2.

Incubation of the Cells with Microparticles

The cells were incubated with uncoated silica (${\mathrm{SiO}}_2$) microspheres (Microparticle GmbH, Berlin, Germany, $\text{diameter}\approx 3.44\mathrm{\mu m}$). Uncoated silica microspheres were chosen due to the non-toxicity of the material. The refractive index of the spheres amounts to about 1.43 (see also Sec. 3.1) and is in combination with the diameter of $\approx 3.44\mathrm{\mu m}$ particularly suitable for usage with DHM as in aqueous solutions and living cells diffraction patterns at the particles borders are minimized [for illustration see Fig. 1(a) and 1(b)]. The diameter of the spheres was also chosen as a minimum particle size, and is required for imaging with the used DHM setups and the utilized microscope lenses (see Sec. 2.3) to achieve a sufficient number of image pixels and an adequate quantitative phase contrast to the surrounding medium suitable for the fitting procedure described in Sec. 2.4.

Fig. 1

Verification of the internalization of silica microspheres in adherent and suspended PaTu 8988 T cells by quantitative digital holographic microscopy (DHM) phase imaging. (a), (d), (g) white light images of a ${\mathrm{SiO}}_2$ microsphere, an adherent cell with an incorporated microsphere and a suspended cell with an incorporated microsphere. (b), (e), (h) quantitative phase images corresponding to (a), (d) and (g), respectively. (c), (d), (i) cross-sections through the phase contrast images in (b), (e) and (h), respectively, through and near the microspheres [see arrows in (b), (e) and (h)].

Prior to incubation with the cells, the particles were autoclaved ($T>121°\mathrm{C}$, $P=2\text{bar}$). Then, during the cultivation in cell culture flasks, PaTu 8988 T and HT-1080 cells were incubated for 48 h with a concentration of about five particles per cell in DMEM (see Sec. 2.1). Afterwards, the cells were detached and seeded into the Petri dishes or the microfluidic channels used for observation with DHM. After incubation for additional 24 h with a concentration of five microspheres per cell, about 20% of the cells internalized at least a single microsphere. Prior to the DHM measurements, non-engulfed microspheres were removed by washing the sample twice with cell culture medium. For investigations on suspended cells, the cells were detached again. A 5-Brom-2-desoxyuridin (BrdU) assay,⁴⁰ which was performed with a flow cytometer (Cyflow space, Partec GmbH, Muenster, Germany), showed no influence of the microparticles on cell proliferation. This correlates with the appearance of the cells in white light images and quantitative DHM phase images in which no morphologic alterations of the cells with internalized microspheres in comparison to control cells were observed [for illustration see Fig. 2(a) and 2(b)].

Fig. 2

Refractive index determination of the cytoplasm in osmotically stimulated adherent PaTu 8988 T cells. (a) using microspheres that were incorporated by three different cells; left: white light image, middle: quantitative digital holographic microscopy (DHM) phase image for $320\mathrm{mOsmol}/\mathrm{kg}$; right: quantitative DHM phase image for $160\mathrm{mOsmol}/\mathrm{kg}$. (b) using two microspheres within a single cell; left: white light image; middle: quantitative DHM phase image for $320\mathrm{mOsmol}/\mathrm{kg}$; right: quantitative DHM phase image for $160\mathrm{mOsmol}/\mathrm{kg}$. (c) $n_{\text{cell}}$ versus osmolality detected with the microspheres denoted with (1), (2), (3) in (a). (d) left and middle panel: $n_{\text{cell}}$ vs. osmolality detected with the microspheres denoted with (4), (5) in (b); right panel: data from microspheres (4) and (5) plotted in a single graph. (e) mean values ${\overline{n}}_{\text{cell}}$ versus osmolality obtained from the plots in (c) and (d). The solid lines in (c), (d), (e) correspond to linear fits ($R$: Pearson correlation coefficient, $p$: p-value).

2.3.

Quantitative Phase Imaging with DHM

PaTu 8988 T cells were observed with an inverted microscope (Zeiss Axio Observer A1, Carl Zeiss Micro Imaging GmbH, Goettingen, Germany) with an attached DHM module that is based on a principle which has been described elsewhere.⁴¹ HT-1080 cells were investigated with a recently developed self-interference DHM setup⁴² which was adapted to the same inverted microscope. For both setups the coherent light source was a frequency-doubled Nd: YAG laser (Compass 315M-100, Coherent, Luebeck, Germany, $\lambda =532\mathrm{nm}$). Digital off-axis holograms and self-interference digital holograms of selected adherent and suspended cells were recorded with a charge-coupled device sensor (CCD, $1280\times 960\text{pixels}$, The imaging source DMK 41BF02, Bremen, Germany). For imaging, $20x$ and $40x$ microscope lenses (Zeiss LD Acroplan $20x/0.4\mathrm{Korr}$, Zeiss LD Plan-Neofluar, $40/0.6\mathrm{Korr}$) were used. All holograms were captured with exposure times below one millisecond to minimize influence of vibrations, movements of suspended cells, and flow of the cell culture medium. The numerical reconstruction of the quantitative DHM phase images from the digital holograms was performed subsequently by spatial phase shifting^4,17 in combination with numerical autofocusing.⁴³ All experiments in this study were performed at room temperature and normal atmosphere.

2.4.

Procedure for Determining the Cellular Refractive Index

It is possible to determine the refractive index of spherical objects like suspended cells or microspheres in suspension from quantitative DHM phase images.^30,31 For a sharply focused mainly transparent specimens with a known homogeneously distributed refractive index $n_{\mathrm{s}}$ in a surrounding medium with refractive index $n_{\text{medium}}$, the relation between the thickness of the sample $d_{\mathrm{s}}(x,y)$ and the induced optical path length change $\mathrm{\Delta }{\phi }_{\mathrm{s}}$ to the surrounding medium is:

For suspended spherical cells or microspheres with radius $R_s$ that are located at $x=x_0$, $y=y_0$, the thickness of the specimen $d_s(x,y)$ is:

Insertion of Eq. (1) in Eq. (2) yields:

To obtain the unknown parameters of interest $n_s$, (or $n_{\text{medium}}$) and $R_s$, Eq. (3) is fitted iteratively in two-dimensions to the experimentally obtained phase data.^30,31 Iterative two-dimensional fitting of Eq. (3) to phase data was performed in order to consider a maximum number of phase values for the refractive index and size determination of small specimens like the microspheres used in this study. In order to minimize the influence of diffraction, phase values close to the outer borders of the particles or cells in the image plane were excluded by application of an adequate threshold value.³⁰ For the retrieval of the refractive indices of suspended spherical particles ($n_{\text{part}}$) or cells ($n_{\text{cell}}$) with Eq. (3) for $n_{\text{medium}}$, the refractive index of the surrounding medium is used while $n_s≔n_{\text{part}}$ (or $n_s≔n_{\text{cell}}$) is determined by fitting. For the determination of the refractive index of adherent or suspended cells with incorporated particles, $n_s≔n_{\text{part}}$ is used while $n_{\text{medium}}≔n_{\text{cell}}$ is obtained by the fitting process.

2.5.

Characterization of the Osmolality and Refractive Index of Dilutions Used

The osmolality of all dilutions in this study was determined by an osmometer (Osmomat 030, Gonotec GmbH, Berlin, Germany). The refractive indices of all media were measured by an Abbe refractometer (WYA-2W, Hinotek Ltd, Ningbo, China).

3.1.

Characterization of the Microspheres

From the manufacturer no precise information about the refractive index of the microspheres at the observation wave length of $\lambda =532\mathrm{nm}$ was available. Furthermore, adsorption of intracellular solutes may induce changes in the size and the integral refractive index of the particles. Thus, in a first experiment the radius and the refractive index of the microspheres were determined by quantitative DHM phase imaging in deionized water ($n_{\text{medium}}≔1.334$), in a solution with fetal calve serum (FCS, $n_{\text{medium}}≔1.335$) that includes various different proteins and in a phosphate buffered saline (PBS) solution with 10% bovine serum albumin (BSA, $n_{\text{medium}}≔1.339$) using the procedure described in Sec. 2.4. Table 1 shows the experimentally obtained mean values for the radius $R_s≔R_{\text{part}}$ and the refractive indices $n_s≔n_{\text{part}}$ of the microspheres.

Table 1

Radius Rpart and refractive index npart of SiO2 microspheres in different solutions (N: number of investigated microspheres, FCS: fetal calve serum, BSA: bovine serum albumin). The measurement uncertainty is quantified by the standard deviation from the mean value.

The values for $R_{\text{part}}$ slightly increase in the two protein solutions while within the measurement uncertainty no significant changes of the refractive indices are detected. The increase of the particle radius in the FCS and BSA solutions indicates that for measurements within cells adsorption of intracellular solutes can be expected. However, this does not influence the particle refractive index within the statistical error range. Thus, for the refractive index determination experiments with microspheres in cells as reference in quantitative phase images that are described in Secs. 3.4 to 3.6, the mean value of all $N=183$ measurements $[n_{\text{part}}({\mathrm{H}}_2\mathrm{O})+n_{\text{part}}(\mathrm{FCS})+n_{\text{part}}(\mathrm{BSA})]/3=1.435\pm 0.005$ was used.

3.2.

Verification of Internalization of Microspheres by DHM Phase Contrast

The incorporation of microspheres due to phagocytic behavior in adherent and suspended cells was checked by analysis of DHM phase images. Figure 1 depicts representative results. Figure 1(a) and 1(b) shows a white light image and a corresponding DHM phase contrast image of a microsphere in cell culture medium ($n_{\text{medium}}=1.339$). A cross-section through the phase map along the white arrows in Fig. 1(b) is plotted in Fig. 1(c). Note that at the particle borders a slight phase decrease due to diffraction is observed. This justifies the application of a threshold value to the phase data prior the fitting procedure for refractive index determination that is described in Sec. 2.4. The maximum particle induced phase contrast amounts to $\approx 4\mathrm{rad}$. Figure 1(d) shows a white light image of a living adherent PaTu 8988 T cell that contains a microsphere. In Fig. 1(f), three different cross-sections through the corresponding quantitative phase image of the cell [Fig. 1(e)] near and through the particle are plotted. The phase difference that is caused by the particle in addition to the cell induced phase change amounts to $\approx 2\mathrm{rad}$ [Fig. 1(f)]. This is significantly lower than the phase contrast of the pure particle in cell culture medium [see Fig. 1(c)]. Taking into account the result in Fig. 1(c), for microparticle adherence outside the cell a phase contrast difference of $\approx 4\mathrm{rad}$ in addition to the cell induced phase change would be expected. Figure 1(g) to 1(i) illustrates the verification of particle internalization in a suspended PaTu 8988 T cell. In correspondence to the results in Fig. 1(f), the phase contrast of the microsphere in the analyzed cell [white arrows in Fig. 1(h)] amounts to $\approx 2.5\mathrm{rad}$ [black line in Fig. 1(i)] which is lower than in cell culture medium.

The observed phase contrast decrease of the particles in cells is plausible and in agreement with Eq. (1) as the refractive index of the cytoplasm is higher than that of the cell culture medium. Note that in Fig. 1(e) to 1(i), within the measurement uncertainty, no influence of diffraction at the lateral borders of the microspheres is observed in the DHM quantitative phase images. This is also plausible as the refractive index difference between the internalized particles and the cytoplasm is lower than for the particle in cell culture medium. In conclusion, the results in Fig. 1 demonstrate the label-free verification of the internalization of microspheres in living adherent and suspended cells by DHM phase contrast.

3.3.

Cytoplasm Refractive Index Determination in Adherent Cells Using Microspheres

In the next experimental step, the refractive index of adherent PaTu 8988 T cells was determined by using the internalized microspheres as reference in quantitative DHM phase images. In order to ensure that the whole microspheres were surrounded by the cytoplasm only engulfed particles with location near the nucleus were analyzed. Specimens near the outer cell borders were excluded as the cell thickness in this area is expected to be lower than the particle diameter.¹⁷ First, the incorporation of three selected microspheres [indicated with 1, 2, and 3 in Fig. 2(a)] was verified as described in Sec. 3.3. Then, the osmolality of the cell culture medium was successively decreased in 10 steps from $320\mathrm{mOsmol}/\mathrm{kg}$ to $160\mathrm{mOsmol}/\mathrm{kg}$. After each dilution step quantitative DHM phase images were generated and analyzed as described in Sec. 2.4.

Figure 2(a) shows a white light image and two representative quantitative DHM phase images of the cells for the initial and final osmolality. On the right panel of Fig. 2(a), cell swelling due to the dilution of the cell culture medium becomes visible. In Fig. 2(c), the intracellular refractive index determined with each particle is plotted versus the osmolality of the cell culture medium. The initial refractive index in isotonic cell culture medium for all three cells amounts to $n_{\text{cell}}(320\mathrm{mOsmol}/\mathrm{kg})\approx 1.38$, while for the final refractive index values around $n_{\text{cell}}(160\mathrm{mOsmol}/\mathrm{kg})\approx 1.36$ are detected. The comparison to a linear fit [see solid lines in Fig. 2(c)] illustrates a mainly proportional dependency (Pearson correlation coefficient $R\ge 0.960$, p-value $<0.0001$) between $n_{\text{cell}}$ and the osmolality for all three microspheres.

In a further experiment, $n_{\text{cell}}$ was determined with two microparticles that were incorporated in a single cell. Figure 2(b) shows a representative white light image (left) and quantitative DHM phase images for 320 and $160\mathrm{mOsmol}/\mathrm{kg}$ (middle and right, respectively). The microparticles labeled 4 and 5 were used to detect the intracellular refractive index; resulting refractive index values are plotted in Fig. 2(d). In analogy to the results in Fig. 2(c), the dependency from the osmolality is almost linear ($R\ge 0.988$, $p<0.0001$). The comparison of the data from microspheres 4 and 5 in the right panel of Fig. 2(d) shows only small differences ($\mathrm{\Delta }{n}_{\text{cell}}=0.001$), and thus demonstrates the reliability of the refractive index determination procedure.

Fig. 3

Refractive index ${\overline{n}}_{\text{cell}}$ versus osmolality of osmotically stimulated suspended PaTu 8988 T cells. (a) Determined with incorporated microspheres as a reference. (b) Obtained by analyzing whole spherical cells in cell culture medium. (c) Results from (a) and (b) plotted in a single graph ($R$: Pearson correlation coefficient, $p$: p-value).

Figure 2(e) depicts the mean values ${\overline{n}}_{\text{cell}}$ obtained from the plots of all five micropheres in Fig. 2(c) and 2(d). The measurement uncertainty is obtained by calculation of the standard deviation. A highly linear dependency between ${\overline{n}}_{\text{cell}}$ and the osmolality is found ($R=0.988$, $p<0.0001$).

3.4.

Verification of the Cytoplasm Refractive Index Determination

In order to verify the results in Sec. 3.3 for the cellular refractive index of adherent PaTu 8988 T cells with irregular shape, the method for refractive index determination was also applied to suspended PaTu 8988 T cells with incorporated microspheres. The morphology of detached cells in suspension typically changes to a spherical shape. Thus, the two-dimensional fitting procedure for refractive index determination of spherical objects described in Sec. 2.4 can be also used for comparative investigations on whole cells.³⁰ First, the refractive index of selected cells was analyzed with internalized microspheres in dependence of the osmolality of the cell culture medium in analogy to the experiments with adherent cells that are described in Sec. 3.3. Then, in comparison, the integral cellular refractive index was determined by fitting Eq. (3) to whole cells without incorporated microspheres. For each osmolality, $N=25$ suspended cells with and without internalized microspheres were investigated [for illustration see quantitative phase image in Fig. 1(h)].

Figure 3(a) depicts the mean refractive index ${\overline{n}}_{\text{cell}}$ obtained with the internalized microspheres as a reference, while the corresponding values from the analysis of the whole cells in dependence of the osmolality are shown in Fig. 3(b). In Fig. 3(c), the data in Fig. 3(a) and 3(b) are compared. The intracellular refractive index obtained from the internalized particles increases linearly from ${\overline{n}}_{\text{cell}}(160\mathrm{mOsmol}/\mathrm{kg})=1.36\pm 0.01$ to ${\overline{n}}_{\text{cell}}(320\mathrm{mOsmol}/\mathrm{kg})=1.38\pm 0.02$ ($R=0.986$, $p<0.0001$). The same tendency is found in Fig. 3(b), where the corresponding refractive index data of the whole cells are plotted. In this case, the refractive index increases from an initial value ${\overline{n}}_{\text{cell}}(160\mathrm{mOsmol}/\mathrm{kg})=1.356\pm 0.003$ to ${\overline{n}}_{\text{cell}}(320\mathrm{mOsmol}/\mathrm{kg})=1.373\pm 0.004$ ($R=0.990$, $p<0.0001$).

The measurement uncertainty for the whole cells [Fig. 3(b)] is lower than the microspheres [Fig. 3(a)]. This is plausible as the area in the DHM image includes more phase values for the determination of $n_{\text{cell}}$ in the whole cell. However, the comparison in Fig. 3(c) shows that for all osmolalities, the refractive indices of the whole cells are slightly lower than the microspheres. This may be explained by the circumstance that the particles are located within the cytoplasm, while the refractive index of the whole cells also includes the refractive index of the nucleus, which has been reported in some cases to have a slightly lower refractive index than the cytoplasm.²³ Nevertheless, within the measurement uncertainty, the obtained refractive index values from the suspended cells in Fig. 3 are found in good agreement with the data in Fig. 2, and thus validate the procedure for refractive index determination of adherent cells with internalized microspheres.

3.5.

Analysis of Dynamic Refractive Index Changes in Adherent Cells

Investigations on the reproducibility of refractive index sensing with internalized microspheres in adherent cells are performed with self-interference DHM using the microfluidics chamber and the pump system. In a first experiment, a HT-1080 cell with an incorporated microsphere is observed for 35 min in an isotonic cell culture medium ($320\mathrm{mOsmol}/\mathrm{kg}$) under static conditions; $N=200$ digital self-interference holograms were recorded every 10 s and evaluated as described in Secs. 2.3 and 2.4. Figure 4 shows the resulting temporal dependency of the cellular refractive index, as well as representative white light and quantitative DHM phase images of the investigated cell. For the whole measurement period, only few fluctuations of $n_{\text{cell}}$ are observed. The mean refractive index and its standard deviation are determined as ${\overline{n}}_{\mathrm{cell}}=1.368\pm 0.002$.

Fig. 4

Temporal dependency of the cellular refractive index $n_{\text{cell}}$ under static conditions (evaluation of $N=200$ digital holograms, $\mathrm{\Delta }t=10\mathrm{s}$, $320\mathrm{mOsmol}/\mathrm{kg}$); the inserts show a white light image (left panel) and a DHM phase image (right panel) of the investigated cell with an incorporated microsphere.

In a second experiment, another cell is exposed after $t=8\min$ under static conditions, and for 10 min after exposure to a continuous flow (flow rate $1.99\mathrm{ml}/\min$). At $t=18\min$, the osmolality is changed with the pump system to $160\mathrm{mOsmol}/\mathrm{kg}$. After 12 min more, the osmolality is changed again to $320\mathrm{mOsmol}/\mathrm{kg}$. At $t=49\min$, the procedure is repeated. During the experiment, $N=485$ digital holograms are recorded ($\mathrm{\Delta }t=10\mathrm{s}$) and are evaluated in analogy to Fig. 4.

Figure 5(a) depicts the results. In the phase maps in the upper panel of Fig. 5(a), cell swelling and shrinking due to the osmolality changes is observed. In the lower panel of Fig. 5(a), for each osmolality change, the cellular refractive index $n_{\text{cell}}$ decreases and increases in a similar range as for the values that are obtained for the PaTu 8988 T cells (see Secs. 3.3 and 3.4). For each period of the experiment, the sensitivity for detection of refractive index changes is quantified by the calculation of the standard deviation of the temporal fluctuations of $n_{\text{cell}}$. Without flow, in the period from $t=0$ to 8 min, the standard deviation of $n_{\text{cell}}$ amounts to 0.001. After the start of the continuous flow from $t=8$ to 18 min, the standard deviation of $n_{\text{cell}}$ increases significantly to 0.007. This may be explained by rearrangement activities of the cell as a response to the flow. For all other periods from $t=18$ to 80 min, the refractive index fluctuations are found in the range from 0.002 to 0.006. These fluctuations may be induced by cell movements and motions of the microsphere inside the cell during the measurements as well as by an enhanced phase noise due to flow and diffraction patterns of moving dust particles inside the cell culture medium.

Fig. 5

(a) Temporal response of the cellular refractive index $n_{\text{cell}}$ to repeated osmotic stimulation (evaluation of $N=485$ digital holograms, $\mathrm{\Delta }t=10\mathrm{s}$); upper panel: representative quantitative DHM phase images of a HT-1080 cell with an incorporated microsphere at indicated time; lower panel: temporal dependency of $n_{\text{cell}}$; the pump system is started at $t=8\min$ (i) with a continuous flow rate of $1.99\mathrm{ml}/\min$; at $t=18\min$ (ii) the osmolality of the cell culture medium is decreased from 320 to $160\mathrm{mOsmol}/\mathrm{kg}$; at $t=30\min$ (iii) the osmolality is increased to the initial value; at $t=49\min$ (iv) the osmolality is decreased again to $160\mathrm{mOsmol}/\mathrm{kg}$, at $t=57\min$ (v) the osmolality is increased to $320\mathrm{mOsmol}/\mathrm{kg}$; the pump system is stopped at $t=80\min$ (iv). (b) Temporal response of the cellular refractive index $n_{\text{cell}}$ to a single osmotic stimulation (evaluation of $N=180$ digital holograms, $\mathrm{\Delta }t=40\mathrm{s}$); upper panel: representative quantitative DHM phase images of a HT-1080 cell with an incorporated microsphere at indicated time; lower panel: temporal dependency of $n_{\text{cell}}$; the pump system is started at $t=0$ with a continuous flow rate of $1.99\mathrm{ml}/\min$; at $t=8\min$ (i) the osmolality of the cell culture medium is decreased from 320 to $160\mathrm{mOsmol}/\mathrm{kg}$; at $t=38\min$ (ii) the flow is stopped.

In a final series of experiments, we explored if the sensitivity of the method was sufficient to detect refractive index changes related to cellular volume regulation processes. Therefore, the response of the cellular refractive index is measured under the same flow conditions as in the previous experiment; however, in contrast to Fig. 5(a), only a single change of the osmolality of the cell culture medium was performed. Digital holograms were recorded every 40 s. At $t=0$ the flow was started, and at $t=8\min$, the osmolality was changed to $160\mathrm{mOsmol}/\mathrm{kg}$. At $t=38\min$ the flow was stopped and the cell was further observed until $t=120\min$.

Figure 5(b) shows representative DHM phase contrast images and the resulting temporal dependency of $n_{\text{cell}}$. Similarly to Fig. 5(a), swelling and slight detachment of the cell is observed until $t\approx 38\min$ [upper panel of Fig. 5(b)]; however, for $t>40\min$ the cell starts to shrink again. The shrinking process is accompanied with an increase of $n_{\text{cell}}$ that is detected with the microsphere. At $t=120\min$, the cell has nearly recovered its initial refractive index completely, and other than a slight detachment due to the swelling process, no significant morphology changes are observed in the DHM phase images. In order to study the effect that is shown in Fig. 5(b) more precisely, three additional cells were investigated in three independently performed measurements. Figure 6 shows the obtained temporal refractive index dependencies. Although no uniform response of the cells to the osmotic stimulation was observed, all cells reach within the uncertainty range of the measurement their initial refractive index values. The increase of the refractive index after the decrease of the osmolality may be explained by regularly volume decrease processes.⁴⁴

Fig. 6

Temporal response of the refractive indices $n_{\text{cell}}$ of three different HT-1080 cells to a single osmotic stimulation. (a) cell 1 (b) cell 2 (c) cell 3. For each measurement $N=180$ digital holograms were recorded ($\mathrm{\Delta }t=40\mathrm{s}$). The measurements started at $t=0$ with a continuous flow rate of $1.99\mathrm{ml}/\min$; at $t=8\min$ (i) the osmolality of the cell culture medium was decreased from 320 to $160\mathrm{mOsmol}/\mathrm{kg}$; at $t=38\min$ (ii) the flow is stopped.