Biological speckle has a dual character. On one hand, it is a parasitic effect that degrades the contrast of biomedical imaging, and many approaches seek speckle reduction.¹ On the other hand, speckle provides strong statistical information about scattering media and can be used for interferometric imaging of cells.² Dynamic speckle, in particular, has considerable information content. For instance, dynamic speckle can be used to monitor blood flow³ and can assess the health of living tissue using intracellular motion as a fully endogenous imaging contrast agent.⁴ 3-D imaging approaches are particularly important for assessing tissue viability, pharmacological toxicity, and cancer progression,⁵ and can be provided by coherence-domain techniques⁶ and digital holography.⁷ Holography captures high-contrast depth-gated speckle statistics because of broad-field illumination.⁸

We previously used coherence-gated digital holography to capture intracellular motion in 3-D tissue as an imaging contrast agent⁹ based on the statistical fluctuations of dynamic speckle. However, there are many functional causes of subcellular motion, and an overall motility metric does not capture specific functions. In this work, we perform fluctuation spectroscopy on depth-gated dynamic speckle to generate frequency versus time spectrograms of tissue responding to various environmental and pharmacological perturbations. The spectral responses depend on the specific type of perturbation, and these spectral responses can serve as functional fingerprints for tissue-based screening.

Holograms in short coherence digital holography were recorded and reconstructed from the experimental setup shown in Fig. 1 . Lenses L1 and L2 expanded a reference beam, and lens L3 performed the Fourier transform of the object beam. Details of the experimental configuration are discussed in Ref. 9. We used rat osteogenic sarcoma tumor spheroids as the target tissue samples.¹⁰ Multicellular tumor spheroids have approximately spherical geometry that facilitates comparison of structure to function. A typical pseudo-B-scan image is shown in Fig. 1, which is produced from 3-D holographic images of an $800\text{-}\mu \mathrm{m}$ -diam rat tumor spheroid.

To generate frequency versus time spectrograms, we acquired 300 successive digital holograms at two acquisition rates (200 holograms for $20\mathrm{s}$ and 100 holograms for $200\mathrm{s}$ ) every $4\min$ for three hours at a fixed depth. Each digital hologram is acquired from a single frame with an exposure time of $10\mathrm{msec}$ . In frequency versus time spectrograms, the frequency resolution is $0.05\mathrm{Hz}$ for the high frequency band and $0.005\mathrm{Hz}$ for the low frequency band; the time resolution is $4\min$ . Figure 2 shows the cross section image from 200 digital holograms acquired with 10 frames per second for a healthy tumor spheroid. The horizontal axis is the spatial axis and time is vertical. The reconstructed high-contrast speckle shows dynamic character as individual speckle intensities fluctuate strongly.

The two equivalent approaches to time-series analysis of fluctuating speckle are temporal autocorrelation and power spectra. Autocorrelation of holographic speckle yields a first-order heterodyne function,¹¹ because holography uses a reference wave (the coherence gate) that captures the real and imaginary parts of the fluctuating field as the coherence-gated pixel number $i_d^{\left(1\right)}\left(t\right)$ . The autocorrelation function is

where $\tau$ is the time delay among an ensemble of images, and $I_d^{\left(1\right)}\left(\tau \right)$ is the heterodyne correlation function. Our previous motility metric⁹ was defined from the heterodyne correlation function as the normalized standard deviation, or speckle contrast, given byAutocorrelation functions and power spectra are related through a Fourier transform. Although the autocorrelation function and the power spectrum contain identical information, the interpretation of that information is qualitatively different. In particular, the spectral information directly displays the presence of characteristic frequencies that can be related to biophysical processes, such as fluctuating membranes or organelle transport.¹²

The spectral power density of a $600\text{-}\mu \mathrm{m}$ -diam tumor is shown in Fig. 2 for the proliferating shell and the necrotic core. The power spectra exhibit $1∕f^n$ behavior from 0.1 to about $1\mathrm{Hz}$ with an exponent $n$ of 1.7. The shell is significantly more active than the core, but part of the core activity can be ascribed to the shimmering showerglass effect from the dynamic overlying tissue layers. The slopes of the power spectral density show a break above $1\mathrm{Hz}$ , which is likely due to Nyquist sampling.

For tissue responding to stimuli, such as temperature and osmolarity changes or response to drugs, the key property of the spectral power density is its relative change in response to the stimulus. The normalized spectral difference for a time series is given by

where $S_0(\omega ,t_0)$ is the starting spectral power density at the beginning time $t_0$ of the experiment, and $S(\omega ,t)$ is the time development of the spectral power density. The normalized power spectrum of a $450\text{-}\mu \mathrm{m}$ -diam tumor responding to a dose of $1\mu \mathrm{g}∕\mathrm{ml}$ of nocodazole, an antitubulin cytoskeletal drug, is shown in Fig. 2 at the selected times after the application of the drug. The differential relative spectral change is shown in Fig. 2 as a function of time for the selected frequencies. The higher frequencies change relatively less than the lower frequencies in response to nocodazole.

The tissue response contained in $D(\omega ,t)$ can be represented as a spectrogram, showing the relative change in the spectrum as a function of time. Examples of several spectrograms are shown in Fig. 3 . These spectrograms track the changes of the intracellular motion in living tumors responding to temperature changes, osmolarity changes, and to nocodazole. The spectral difference in response to changes in temperature is shown in Fig. 3 as the temperature increased from $24\text{to}37°\mathrm{C}$ and then decreased to $24°\mathrm{C}$ . The spectral weight shifts to higher frequencies with increasing temperature.

Osmolarity has a strong effect on the exchange of water into cells and tissue. Hypotonic conditions lead to strong cellular swelling, or edema, and possibly cell lysis, while hypertonic conditions dessicate the cells and cause them to contract. We monitored the change in the relative spectral density as we changed the osmolarity of the growth medium around the tumors. Isotonic conditions are $310\mathrm{mOsm}$ . The results of hypotonic conditions $\left(200\mathrm{mOsm}\right)$ are shown in Fig. 3. The lower frequencies show weak suppression, while the upper frequencies show initial enhanced motion that slowly relaxes over $180\min$ . The hypertonic condition $\left(400\mathrm{mOsm}\right)$ is shown in Fig. 3. The hypertonic effects on the spectrogram are opposite the hypotonic, stronger, and last longer. Cellular swelling increases the cell volume, decreases the density of intracellular constituents, and facilitates intracytosol motion. This leads to increases in motion in the higher frequencies of Fig. 3. On the other hand, dessication of the cytosol under hypertonic conditions shrinks the cell volume and increases the density of intracellular constituents, significantly impeding motion. However, membrane vesicles may still be active to reestablish stasis.

The tissue response to the antitubulin drug nocodazole shows very strong suppression in motion in the middle frequency range between $0.02\text{to}1\mathrm{Hz}$ , but with enhancement at ultralow frequency below $0.01\mathrm{Hz}$ . The strongest effect of nocodazole on intracellular motion is the reduction of microtubules in the cytosol that provides fewer pathways for organelle transport corresponding to strong suppression of frequencies above $0.02\mathrm{Hz}$ . This same frequency range showed enhanced motion at physiological temperatures relative to room temperature. Low cellular metabolism at room temperature would have slower organelle transport.

These differences in the tissue response reflect the specific actions of the perturbations on the tissue. Increasing temperature increases metabolic activity and increases membrane fluidity, reflected in the preferential enhancement of frequencies around $1\mathrm{Hz}$ at physiological temperatures relative to room temperature. Conversely, osmotic hypotonicity induces tension on the cell membrane, increasing the effective undulation frequency while reducing damping, reflected in the enhanced fluctuations across the spectral range of Fig. 3, with opposite effects for hypertonicity. In contrast, the antitubulin action of nocodazole decreases the number of microtubules in the cells and therefore specifically inhibits organelle motion, reflected in the strong suppression of the midfrequency fluctuations. These spectral cues allow a tentative identification of the low frequencies as part of the $1∕f$ spectrum of membrane undulations (up to $0.1\mathrm{Hz}$ ), while the higher frequency originates with active organelle transport. This spectral range assignment is consistent with Ref. 13.

In conclusion, we apply speckle fluctuation spectroscopy to dynamic speckle obtained using coherence-gated digital holography on living tumor spheroids. By defining a relative spectral response to perturbations, we generate spectrograms of the tissue responding to temperature changes, osmolarity changes, and to the antitubulin drug nocodazole. Different spectral ranges increase or decrease, depending on the perturbation, providing insight into the different cellular functions that contribute to different spectral ranges. The striking changes in the responses to various perturbations provide a means to develop spectrogram fingerprints that can be used to identify the effects of drugs on cellular activity. Therefore, the spectrograms define the specificity of motility-contrast imaging to different perturbations and to different functional responses. These signatures and their specificity may open the door to broad compound screening applications.