2.1.

Multicellular Tumor Spheroids

Multicellular spheroids of normal cells or neoplastic cells (tumor spheroids) are balls of cells that may be easily cultured up to 1 mm in size in vitro.^{56, 57} The spheroids can be used to simulate the optical properties of a variety of tissues,⁵⁸ such as the epidermis and various epithelial tissues, and may be used to simulate the histological and metabolic features of small nodular tumors in the early avascular stages of growth.⁵⁷

Beyond a diameter of about 200 microns most spheroids develop a necrotic core surrounded by a shell of viable, proliferating cells, with a thickness varying from 100 to 300 μm. The limiting factor for necrosis development is oxygen—the oxygen consumption and oxygen transport reflecting the status of the spheroid.⁵⁹ Early work on spheroids⁶⁰ studied therapeutic strategies for cancer, especially the spheroid response to different drugs. The response to drug therapy was quantified from an analysis of spheroid volume growth delay, increase in the necrotic area, and change in survival capacity. This work focused on hypoxia and its induction by chemical agents.⁶¹ None of these studies considered cellular and sub-cellular motility as a diagnostic of cellular vitality, despite the obvious utility of this diagnostic, because there was no means of nondestructively detecting motility throughout a volume. Motility contrast imaging provides this capability up to a millimeter deep in tumor spheroids.

Tumor spheroids of permanent cell lines are a reliable model for systematic studies of tumor response to therapy.^{62, 63} Although the in vitro environment is artificial, the biochemistry, metabolism, and cell signaling response of cells grown as 3D constructs closely simulates in vivo tissue^{64, 65, 66} and more accurately captures their pathophysiology and response to therapy.⁶⁷ For example, spheroids from epithelial ovarian cancer,⁶⁸ hepatocellular carcinoma⁶⁹ and colon cancer⁷⁰ had expression profiles more like those from tumor tissues. The three-dimensional environment of the spheroids also presents different pharmacokinetics than 2D monolayer culture and produce differences in cancer drug sensitivities between monolayers and the spheroids.⁷¹ Therefore, in vitro experiments are a surrogate for in vivo response and have been used to test cancer therapeutics such as metabolic and chemical gradients, hypoxia, cell-cell and cell-matrix contacts, and chemor-esistance.^{61, 72}

We performed an experiment to identify apoptotic versus necrotic cells and tissues in a small (300 micron) tumor spheroid. Laser scanning confocal microscopy, using the dyes YO-PRO-1 and propidium iodide, permitted us to visualize live, apoptotic, and dead cells in small <300 μm spheroids using a Nikon A1R confocal microscope. We scanned into 100 microns of tissue at 1 micron intervals. The YO-PRO-1 dye is a nuclear green fluorophore that stains the nuclei of apoptotic cells. Propidium iodide is a vital red flourophore that stains necrotic or dead cells that have compromised membranes. The experimental results are shown Fig. 1a in two-channel color and numerically thresholded in Fig. 1b to show the central region of apoptotic cells and tissues (blue) and necrotic or dead cells (red). The confocal depth is shown in Fig. 1c, penetrating to the region containing many apoptotic cells and tissue between the proliferating shell and the necrotic core. The proliferating shell is composed of healthy cells that form a coherent tissue, while the core has many voids filled with extracellular debris and bounded by rafts of apoptotic or necrotic cells, shown in a SEM in Fig. 1d. In the spectrogram analysis described in Sec. 2.5, dynamic scattering is separately averaged over the proliferating shell and the necrotic core. The apoptotic transition region is relatively thin (about 50 microns thick) and is not explicitly contained in either the shell or core averages.

Fig. 1

Physiology of multicellular tumor spheroids. (a) The confocal image is a two-channel (green and red) image of apoptosis and necrosis. (b) The values are thresholded to show the apoptotic central region and necrotic cells. (c) The general structure of the spheroid with a proliferating shell surrounding a necrotic core and a transition region of apoptotic cells. (d) The spheroid has a shell of proliferating cells surrounding a core that contains voids of extracellular debris.

2.2.

Holographic Optical Coherence Imaging

The basic optical system for holographic optical coherence imaging is shown in Fig. 2a. We use a mode-locked Ti:sapphire laser (100 fs pulse duration, 100 MHz repetition rate) with a center wavelength of 840 nm and a bandwidth of 17 nm. The lenses L1 and L2 perform the Fourier transform of the object beam. The CCD camera is placed at the Fourier plane of the object, where the object beam interferes with the zero-path-matched reference beam that passes through the computer-controlled delay line. The typical object intensity for living tissue at the object plane is 5 mW/mm², and an 8-bit CCD camera with one mega-pixel resolution was used with an exposure time of 10 msec. Digital holograms were reconstructed by fast Fourier transform. An example of a pseudo-B-scan of a tumor spheroid is shown.

Fig. 2

(a) Experimental set-up. PBSs, polarizing beam splitters; BS, beam splitter; L1–L2, lenses; λ/2, half-wave plate; λ/4, quarter-wave plate. A pseudo B-scan showing reflectance in a vertical x–z section color coded on a log reflectance scale. (b) Motility contrast imaging from a horizontal x–y section, color-coded on a linear scale to intracellular motility. (c) Reconstructed volumetric motility image of a 800 micron-diameter tumor spheroid.

Holographic optical coherence imaging is based on off-axis digital holography using a CCD camera with a 7.4 micron pixel pitch. The nominal speckle size on the CCD chip is approximately nine pixels with approximately three optical fringes per speckle using a reference beam crossing angle of 3 deg at a wavelength of 840 nm. The intensity I _H(x′, y′) is electronically captured by the CCD camera. A Fourier transform is used to reconstruct the digital hologram because the digital hologram is recorded at the Fourier plane. The Fourier transform of the intensity I _H(x′, y′) is

The holographic image F ₃ is located at (λfv _xo, λfv _yo) and the conjugate image F ₄ is located at (−λfv _xo, −λfv _yo), which are spatially separated from the zero-order image. The numerical Fourier transformation of the digital hologram acquired at the Fourier plane provides both amplitude and phase information of the multiply-scattered light from the coherence-gated object depth. The zero-order image is removed by averaging the interference fringes over the fringe spacing interval. The fringe spacing for our crossing angle is approximately three pixels, and the digital hologram without interference is approximated by three-pixel averaging in the horizontal direction.

The resulting data format for holographic optical coherence imaging is a set of time-dependent two-dimensional intensity data I(z; x, y; τ, t) of the digitally reconstructed image at the coherence-gated depth z. The two time arguments τ and t correspond to the individual frames of a high frame-rate acquisition and to the long-term response of the tumor tissue, respectively. At a fixed depth, these data constitute a data cube of two spatial dimensions and one time dimension. For image representation in MCI, the normalized standard deviation (also known as temporal speckle contrast) is computed as

Motility contrast imaging provides a measure of the fluctuation magnitudes, but is not specific to fluctuations on different time scales, which are captured by fluctuation spectroscopy. The power spectra of the data are computed through the Fourier transform

2.3.

Autocorrelation Analysis and Multiple Scattering

For a dilute collection of scatterers, the single-scatter coherence-gated speckle intensity from a fixed depth and spatial location (x,y) on the reconstructed image plane has a temporal autocorrelation^{31, 73}

However, living tissue deviates in many important ways from the model of a dilute set of freely diffusing homogeneous particles. First, it is not dilute, but rather consists of a high density of scattering sites with multiple scattering and coherent light propagating up to 12 mean-free paths through the sample. Second, living tissue is highly heterogeneous in the size and density of scattering structures. Third, cells are highly active systems, with active transport inside the cell and active motions of the cell membrane, far from thermal equilibrium that precludes application of the equipartition theorem or the fluctuation dissipation theorem.^{4, 11} Most of the assumptions that are at the basis of Eq. 7 are not valid under these conditions. In spite of this complexity of living tissue, the general phenomenology remains if the parameters are replaced by effective parameters that are related to the properties of the scattering sample.

2.3.2.

Anomalous diffusion

The strong activity of living tissue makes many contributions to the mean-squared displacement Δz ², much of which is active motion of the cytoskeleton driven by molecular motors. However, few components of living tissue are free to move, but are usually constrained. For instance, diffusing particles can be confined within compartments,⁷⁸ and membrane undulations are limited by elastic harmonic potentials.^{79, 80} The simplest extension of free diffusion is called anomalous diffusion^{81, 82} with a mean-squared displacement time dependence given by

Eq. 10

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation} \Delta z^2 (t) = D^* \left({\frac{t}{{t_0 }}} \right)^\beta. \end{equation}\end{document} $$\Delta z^2\left(t\right)=D^{*}{\left(\frac{t}{t_0}\right)}^{\beta }.$$

If β > 1, the diffusion is called super-diffusion and if β < 1, the diffusion is called sub-diffusion. Both super-diffusion and sub-diffusion relate to correlations in the motion of scattering objects. Super-diffusion occurs when there is persistent motion of a particle, as for active transport of vesicles by molecular motors,⁸³ while sub-diffusion occurs if motion is constrained. Constrained diffusion occurs in a compartment or a harmonic potential, which has the time dependence

Eq. 11

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation} \Delta z^2 (t) = \Delta z_{\max }^2 \{ {1 - \exp [ { - ({\Gamma t})^\beta }]}\}, \end{equation}\end{document} $$\Delta z^2\left(t\right)=\Delta z_{\max }^2\left\{1-\exp \left[-{\left(\Gamma t\right)}^{\beta }\right]\right\},$$

where [TeX:] $\Delta z_{\max }^2$ $\Delta z_{\max }^2$ is a maximum averaged value and Γ is a relaxation rate.

As an example, the autocorrelations of coherence-gated intensities from a fresh tumor spheroid are shown in Fig. 3a for the core of the tumor compared with the proliferating shell, and in Fig. 3b for the shell at room temperature compared with the shell at physiological temperature. Each of the autocorrelation data are fit both by the constrained diffusion model of Eq. 11 and by a two-component autocorrelation decay given by

Eq. 12

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation} A_I (\tau) = [ {A_1 e^{ - \left({t/\tau _1 } \right)^\beta } +({1 - A_1 })e^{ - ({t/\tau _2 })^\beta } } ]^2. \end{equation}\end{document} $$A_I\left(\tau \right)={\left[A_1{e}^{-{\left(t/{\tau }_1\right)}^{\beta }}+\left(1-A_1\right)e^{-{\left(t/{\tau }_2\right)}^{\beta }}\right]}^2.$$

Both fits are nearly equally good, with similar anomalous diffusion exponents of β ≈ 0.5. Neither model is strictly correct, but each provides a different perspective on effective fluctuation properties of the tissue. In the case of the two-component decay, characteristic time constants are extracted, while in the case of the single constrained diffusion, a root-mean-squared maximum displacement may be estimated.

The constrained-diffusion model is used to estimate the maximum root-mean-squared displacement from the data in Fig. 3 that were obtained at a depth of approximately 1.5 mean transport lengths for three mean transport lengths double-pass. Accounting for this factor of three from multiple scattering, the maximum root-mean-squared displacement of shell and the core are Δz _max = 65 and 25 nm, respectively. The fluctuation amplitudes of the tissue in the inactive core of the tumor spheroid are consistent with thermal membrane undulations, while the proliferating outer shell is much more active and far from equilibrium.^{84, 85} Because of multiple scattering and the complexity of intra-tissue motions, these values must be viewed as effective values. However, these values can be compared to thermal undulation amplitudes of cell membranes that have values near 30 nm (Ref. 86) that are smaller than the values measured in the proliferating tissue, but are comparable with the values measured in the core. For the comparison between room and physiological temperatures in Fig. 3b, the maximum root-mean-squared displacement increases by 40%, even though the thermodynamic temperature rise alone for membrane undulations is expected to be only 2%. These interpretations are consistent with active and energetic processes of the cell dominating intracellular motions in the proliferating shell far from thermodynamic equilibrium.

Fig. 3

Temporal autocorrelation functions of the holographically-gated intensity fluctuations from tumor spheroids. (a) Comparison of the shell and the core at 37°C. (b) Comparison of the shell at room temperature compared with physicological temperature. The solid curve is the two-component fit. The dashed curve is the constrained diffusion fit.

The two-component model can be used to extract characteristic fluctuation times from the data in Fig. 3. In Fig. 3a, the shell has two time constants τ₁ = 2 s and τ₂ = 50 s, while the core has τ₁ = 1.2 s and τ₂ = 50 s. The main difference in the behavior in this case is in the relative contributions, with the short-time component comprising a much larger fraction in the shell than in the core. Similarly, for the shell temperature effects, the room temperature values from the fits in Fig. 3b are τ₁ = 2.8 s and τ₂ = 50 s, while the physiological temperature data have τ₁ = 1.5 s and τ₂ = 36 s. These times lead to characteristic knee frequencies that appear in the power spectra discussed in Sec. 2.4.

2.4.

Fluctuation Spectra

The autocorrelation functions are related to the spectral power densities through the Wiener-Khintchine theorem as

In the case of dynamic light scattering under heterodyne detection conditions, the power spectrum is

An example of a spectral power density is shown in Fig. 4a for the same data as in Fig. 3a for the shell and core of a fresh tumor spheroid. The shell data have a clear knee frequency around 0.1 Hz, followed by [TeX:] $1/f^{\beta ^\prime + 1}$ $1/f^{{\beta }^{\prime }+1}$ behavior at a higher frequency with and exponent β^′ ≈ 0.4. The necrotic core has a less distinct, but lower, knee frequency with a lower exponent β^′ ≈ 0.2. Both spectra have similar noise floors at the Nyquist frequency of 5 Hz. The detection bandwidth for these data is f_B = 16 Hz, so part of the noise floor is caused by higher-frequency motions that are “freeze-framed” by the 10 msec acquisition speed of the camera. Motion in the living tissue up to 16 Hz is captured by the fast exposure, even though the frequencies are not resolved. The dependence of the noise floor on exposure time can provide an indication of the amount of high-frequency dynamics in the scattered light. The power spectra in Fig. 4b are for the shell at room and physiological temperatures. The characteristic frequencies shift higher for the warmer case, with a higher Nyquist floor reflecting higher frequency content between 5 and 16 Hz.

Fig. 4

Power spectra for the data of Fig. 3. (a) The power spectrum of the shell compared with the core at 37°C. (b) The power spectrum of the shell at 37°C compared with 24°C.

2.5.

Fluctuation Differential Spectrograms

When perturbations are applied to a living tissue sample, the response of the tissue dynamics can be subtle, but consistent. Because both the autocorrelation and spectral density functions span a wide dynamic range over several orders of magnitude, small changes in dynamics are de-emphasized in logarithmic plots. To capture the time course of subtle changes in tissue dynamics requires a differential relative measure, which we take to be the differential relative spectrum

This differential spectrogram is a two-dimensional function of frequency and time at fixed depth z, that captures the changes in the spectral power density as a function of time normalized by an appropriate spectral density, usually taken as the spectrum prior to the perturbation. The differential spectrogram shows positive and negative deviations from the nominal values across a wide frequency range.

An example of shell and core spectrograms for a tumor spheroid held in culture for 18 h are shown in Fig. 5. The spectral frequency is along the y-axis and spans three decades of dynamic range. Time is along the x-axis for this 18 h experiment. The baseline is set prior to t = 0 and is used as the quantity in the denominator of Eq. 16 for normalization. The change in the spectral content is plotted in false color, with deep red equal to 70% enhancement and deep blue equal to 70% inhibition. The response occurs in approximately three frequency bands that distinctly show different behaviors: low-frequency (0.005 to 0.1 Hz), mid-frequency (0.1 to 1 Hz), and high-frequency (1 to 5 Hz). The proliferating shell shows enhancements in the third frequency band after about an hour in medium, while the core shows nearly an opposite response. At low frequencies, the shell is mostly unchanged until a strong onset at about 18 h, while the core shows enhanced low frequencies for most of the duration of the experiment.

Fig. 5

Differential spectrograms for the proliferating shell and inner core. The frequency range is composed of roughly three bands that span three decades: band 1 from 0.005 to 0.05 Hz, band 2 from 0.05 to 0.5 Hz, and Band 3 from 0.5 Hz and higher.

To interpret spectrograms, it is necessary to establish a correspondence of the frequencies observed in DLS with frequencies (and velocities and diffusion coefficients) obtained from the literature that are connected with specific biological targets and mechanisms. The lowest frequency in our experimental spectrograms is 0.005 Hz and the highest frequency is 5 Hz. We use the general relationships for single backscattering under heterodyne (holographic) detection: q ² D = ω_D for diffusion and qv = ω_d for directed transport, where D is the diffusion coefficient and v is a directed speed. The smallest and largest frequencies that can be captured in the experiments define the physical ranges for directed transport and diffusion, respectively, which are [TeX:] $0.002 < v < 2\,\mu {\rm m}/\sec$ $0.002<v<2\mu \mathrm{m}/\sec$ , and [TeX:] $8x10^{-5} < D < 0.08 \,\mu {\rm m}^2 /\sec$ $8x{10}^{-5}<D<0.08\mu {\mathrm{m}}^2/\sec$ .

The velocity range is well within the range of intracellular motion in which molecular motors move organelles at speeds of microns per second.^{30, 89, 90, 91, 92} Diffusion of very small organelles, as well as molecular diffusion, are too fast to be resolved by our maximum frame rate of 10 fps. Membrane undulations are a common feature of cellular motions, leading to the phenomenon of flicker.^{86, 93, 94, 95, 96} The characteristic frequency for membrane undulations tends to be in the range around 0.01 to 0.1 Hz.^{86, 91, 97} Results from the literature are summarized in Fig. 6. The graph is not exhaustive, and the size axis is only approximate. But the graph captures the general connection of spatial scale with temporal scale. Experiments on vesicles and the cytoplasm give the highest backscatter frequencies generally above 1 Hz and extending to tens of Hz. Larger mitochondria and organelles have slightly lower backscattering frequencies, but these are still in the range of band 3 frequencies of TDS. Membrane motions are much slower, coinciding with the frequencies of band 1 in TDS. This spatial-temporal trend is only semi-quantitative, but it provides a general principle that may help disentangle the mixtures of frequencies that arise from multiple dynamic light scattering mechanisms.

Fig. 6

QELS dynamic backscatter frequencies for λ = 840 nm calculated from mobility experiments in the literature from Refs. 30, 86, 89, 90, 91, 92, 97, and 98. The sizes are only approximate to show a general trend of lower frequencies for larger motions.

4.1.

Temperature and Heat Shock

The thermal experiment is shown in Fig. 8 over a course of 6 h. The temperature increased from 24 to 37°C, then up to 43°C (which is lethal to cells for long exposure times) and returned to physiological 37°C. The motility contrast image at the mid-section is shown in Fig. 8a. Heating to physiological temperature from room temperature is accompanied by a large increase in the speckle contrast (temporal activity). The spectrograms of the outer shell and the core are shown in Figs. 8b, 8c, respectively. The frequency range spans from 0.005 to 5 Hz. The baseline at 24°C is flat, then there is significant increase in the higher frequencies as the temperature rises to 37 and then to 43°C. Once at 43°C, the enhancement in high frequency motion begins to decay as the cells are stressed by the excessive heat. An important observation in this experiment is the behavior after the tissue is returned to the physiological 37°C temperature. The spectrogram shows clear differences post- to pre-heat-stress. In particular, there is an increase in the low frequencies at late times, which might be indicative of blebbing induced by heat shock. The proliferating shell shows a late strong high-frequency enhancement that is missing in the core. The high frequencies in the proliferating shell may be associated with apoptosis, while the hypoxic core undergoes necrosis in response to the heat shock. These data illustrate the differences that appear in the response spectrograms between the outer shell and the inner core, which are primarily distinguished by their initial metabolic activity and susceptibility to stress. If the high-frequency versus low-frequency differences between the shell and the core are caused by the differences between apoptosis and necrosis, then tissue dynamics spectroscopy would provide a fully endogenous way to probe this difference.

Fig. 8

Thermal response for an increase in temperature from 24°C to 37°C and then to 43°C. (a) Motility contrast image of a 400-μm diameter tumor; (b) and (c) differential spectral power densities for the shell and core, respectively.

4.2.

Osmolarity

Osmolarity has a strong effect on the uptake of water into cells and tissue. Hypotonic conditions lead to strong cellular swelling (edema) and possibly lysis, while hypertonic conditions desiccate the cells and cause them to contract. The refractive index of the cells decrease with swelling and produce less light scattering, which appears as a weaker backscattered signal. The overall brightness of the backscattered signal from the tumor spheroids is normalized out by our analysis and does not contribute to the frequency changes in the differential relative spectrograms. We monitored the change in the relative spectral density as we changed the osmolarity of the growth medium at 24°C and at physiological temperature 37°C, as shown in Fig. 9.

Fig. 9

Response of the relative spectral power to changes in osmolarity of the proliferating shell at 24°C and 37°C. The osmolarity is changed from isotonic (300 Osm) at t = 0. The hypotonic osmolarities of 200 and 150 mOsm induces swelling of the tumors. The hypertonic solutions of 400 and 500 mOsm cause tumor dessication and shrinkage.

At room temperature, the osmolarity was changed to 200 or 400 mOsm from isotonic conditions of 310 mOsm. The hypotonic condition caused an initial increase in high and mid frequencies, followed by a relaxation back to normal behavior. This transient effect is likely caused by the cell re-establishing homeostasis after the osmotic shock. For hypertonic conditions with cell shrinkage, there is inhibition of the high frequencies and a significant increase in the low frequencies with no relaxation back to homeostasis. The suppression of high frequencies is associated with inhibited motions, possibly due to increased intracellular viscosity, while the enhanced low frequencies may be associated with cell shape changes as the cells desiccate.

At physiological temperature 37°C, the initial transients are similar to those at room temperature, but both the hypo- and hyper-tonic initial responses rapidly decay (within minutes) and are followed by a much stronger long-term behavior. For the long-term hypotonic condition (cell swelling), the low frequencies are significantly enhanced, while for the long-term hypertonic condition (cell shrinkage), the high frequencies are enhanced. The initial transient responses may be understood in terms of cell swelling and shrinking, which are similar to the room temperature response. Desiccation of the cytosol under hypertonic conditions shrinks the cell volume, increases the viscosity, and increases the density of intracellular constituents, significantly impeding motion. This is reflected in the initial increase of the low frequencies. The most dramatic difference between room and physiological temperatures is the high-frequency enhancement under cell desiccation at physiological temperature, which is absent at room temperature. Membrane vesicles would still be active as the cell tries to reestablish stasis, and might be associated with the high-frequency increase for the hypertonic condition at long times. Cell shrinkage is also associated with the loss of cell-cell contacts, and the high frequency content may be the rapid retraction of cell membrane after the contact is lost.

4.3.

Response to pH

The pH of the growth medium is an important factor in tissue stasis. For instance, when CO₂ increases above 5% in the gas over the growth medium, this causes acidification of the growth medium and decreased viability of the cells and tissues. In addition, many solid tumors have acidic microenvironments, with the largest acidity in the center of the tumors (associated with the maximum hypoxia). Tumors responding to pH of 6 (acidic) and pH of 8 (basic) growth medium are shown in Fig. 10. The acidic conditions slow down the intracellular motions in both the shell and core, but with significantly more suppression in the core. This strong core response may be from the additive effects of the applied low pH to the naturally acidic core of the tumor spheroid. Conversely, the basic conditions enhance the higher frequencies in the shell of the tumor spheroid. There is a relatively mild response in the core, and no enhanced high frequencies, possibly because of the compensation of the internal acidity by the applied basic conditions.

Fig. 10

Spectrogram fingerprints for response to (a) acidic (pH = 6) and (b) basic (pH = 8) conditions for proliferating shell and hypoxic core. The motility contrast images for the tumors are on the left.