2.1.

Three-Dimensional Tissue Culture

Three different multicellular spheroid tissue growth methods were used for 3-D tissue culture: (1) a Synthecon (Houston, Texas) rotating BR, (2) Corning (Corning, New York) U-bottom (UB) spheroid plates, and (3) 3D Biomatrix (Ann Arbor, Michigan) HD plates. Two cell lines, A2780 (human ovarian cancer) and DLD-1 (human colon adenocarcinoma), were obtained from the American Type Culture Collection (Manassas, Virginia) and grown at 37°C in a humidified 5% ${\mathrm{CO}}_2$ incubator in RPMI-1640 medium supplemented with 10% fetal bovine serum (Atlanta Biologicals, Lawrenceville, Georgia), $100\mathrm{U}/\mathrm{mL}$ of penicillin, and $100\mu \mathrm{g}/\mathrm{mL}$ of streptomycin (Sigma). To grow spheroids in the BR, the cells from a $25\text{-}{\mathrm{cm}}^2$ flask ($\sim 2\times {10}^6\text{cells}$) were placed in a 50-mL capacity rotating drum BR in complete growth medium. The medium was refreshed (30%) every other day until the cells formed spheroids of optimal experimental size (300 to $800\mu \mathrm{m}$ in diameter). Cells were seeded at a concentration of 5000/well in Corning spheroid plates and 5000/drop in the 3D Biomatrix HD plate. Spheroids formed within 24 to 48 h in these plate-based methods.

2.2.

Ex Vivo Tumor Explants

Established cancer cell lines and xenografts have been the mainstay of cancer research for the past several decades. To date, the analysis of drug sensitivity and resistance in both established cancer cell lines and xenografts has been indispensable. However, while testing of compounds in established cancer cell lines is often not predictive of clinical efficacy, corresponding in vivo studies in animals are very expensive and time consuming. Therefore, heightened attention is being paid toward ex vivo analysis of tumor explants due to the greater understanding that cancer therapeutic response is not exclusive to the inherent molecular composition of cancer cells but rather is greatly influenced by the tumor cell microenvironment, a feature that cannot be recapitulated by traditional culturing methods. Ex vivo treatment response analysis could become a standard tool in preclinical and clinical development of cancer therapeutics and is envisioned as a step toward a personalized medicine approach for new therapeutic development strategies.^52,53

Tumor xenografts were generated in nude mice using human ovarian carcinoma cell lines (A2780, SKOV-3). Animal procedures were approved by the Indiana University School of Medicine Animal Care and Use Committee and were in accordance with federal regulations. Female nude mice (nu/nu BALB/c) 7- to 8-weeks old (Harlan, Indianapolis, IN) were subcutaneously injected in the right flank with $2\times {10}^6$ cells or orthotopically injected in one of the ovaries. The mice were euthanized 2 to 4 weeks after the injection and the tumor xenografts removed. Tumor xenografts were diced into $1{\mathrm{mm}}^3$ pieces and immobilized in 96-well cell culture plates in a thin layer of 1% low gel-temperature agarose made up in HEPES buffered RPMI 1640 medium (ATCC, Manassas, Virginia).

2.3.

Biodynamic Imaging

BDI was performed with an optical instrument that captures backscattered light from biological samples and records digital holograms on a CCD Fourier-plane chip. The light source is a continuous-wave low-coherence light source (Superlum, Cork, Ireland) with a 20-mW output intensity at a wavelength of 850 nm and a bandwidth of 15 nm with a coherence length of $\sim 15\mu \mathrm{m}$. The optical section thickness is significantly broadened by multiple scattering with increasing broadening with increasing gated depth. The BDI system is a Mach–Zehnder interferometer shown in Fig. 1. The light path is divided into a signal and reference arm by a polarizing beam splitter with a variable polarizer to adjust the relative intensities in the signal and reference arms. Dynamic light scattering is performed in a back-scatter geometry because the sensitivity to Doppler frequency shifts depends on the momentum transfer vector that selects longitudinal motion along the backscatter direction. The maximum backscattering momentum transfer is given by $q=4\pi n/\lambda$, where $n$ is the refractive index of the tissue and $\lambda$ is the free-space wavelength. The reduced wavelength inside the medium is given by ${\lambda }_{\text{red}}={\lambda }_{\text{free}}/4\pi n$. Assuming a refractive index $n=1.4$ and a free-space wavelength of 840 nm, the reduced wavelength is equal to 50 nm. The light scattered by the living biological sample is collected by a long focal-length lens and transformed to a Fourier plane (FP) where the CCD pixel array is placed. The reference wave is incident on the CCD array at a small angle of 3 deg relative to the signal axis, creating an off-axis digital hologram with a fringe spacing of $25\mu \mathrm{m}$ on the camera chip. A digital hologram is acquired on the FP of the optical imaging system, and this Fourier-domain hologram is transformed using an FFT algorithm into the image domain. The transformation performs two functions: (1) demodulating the spatial carrier frequency represented by the holographic interference fringes and (2) coherence-gating the low-coherence light to a specified depth inside the tissue sample.

Fig. 1

Fourier domain low-coherence digital holography system with a Mach–Zehnder off-axis configuration recording on the FP. The object light backscattered by the target is collected and projected onto the FP at the CCD by lenses L1, L2, and L3 with intermediate image plane and FP.

The coherence-gating role of digital holography creates a full-frame OCT section of the tumor spheroid at a fixed depth. The reconstructed section is highly speckled, which normally is considered to be an undesirable side effect in OCT, but dynamic speckle for our application provides the basis for BDI. BDI captures successive frames at a fixed coherence gate at a frame rate of 25 Hz. In dynamic light scattering, there are two limits related to the characteristic fluctuation frequency depending on the mean speeds of intracellular motions. The Doppler limit corresponds to mean free flight distances longer than the reduced wavelength, for $qv\tau \gg 1$, where $v$ is the intracellular speed and $\tau$ is the persistence time for the transport. The opposite limit is the diffusion limit when $qv\tau \ll 1$. In this limit, the diffusion is still dominated by random flights rather than thermally driven Brownian motion, but the transport is a random walk, driven by active transport such as molecular motors or cytoskeletal restructuring. The diffusion coefficient in this limit is given by $D=v^2\tau$, and the diffusion and Doppler angular frequencies, in the respective limits, are

Living tissue is highly complex, with a wide range of speeds and persistence times. The measured knee frequency (half-width half-maximum of the spectrum) for the fluctuation spectrum scales as

2.4.

Finite-Sampling Effects

A common metric that characterizes tissue health is the normalized standard deviation (NSD), also known as temporal speckle contrast,⁶² that is calculated from the standard deviation of the intensity divided by the average intensity. Large fluctuations in the dynamic speckle images result in high NSD values, and a 2-D map of NSD values gives a visual measure of motility, called motility contrast imaging (MCI). The MCI map displays the NSD from a biological sample as a representation of the activity/health of the sample. A high NSD can indicate vitality of the sample, high proliferation, or it may represent a high overall metabolic rate. For example, 3-D spheroids of known aggressive cancer cell lines with short doubling times and high metabolism typically have a higher NSD value than less aggressive cancers for spheroids of equivalent health. For an exponential probability distribution function of intensities, the standard deviation is equal to the mean, and therefore under ideal sampling $\mathrm{NSD}=1$. However, for finite sampling, the NSD is less than unity and depends on the finite-sampling time as well as on the characteristic persistence times of the subcellular motion. Figure 2 shows the NSD versus the scaling quantity $q^2{v}^2\tau T$ for a set of 100 Monte Carlo simulations using random particle flights with speeds of 0.1 and $1\mu \mathrm{m}/\mathrm{s}$ with persistence times of 0.1 and 1 s. The time $T$ is the total acquisition time, and $\tau$ is the persistence time. The NSD approaches 1 as $q^2{v}^2\tau T\gg 1$ and NSD changes rapidly when $q^2{v}^2\tau T\sim 1$. The condition for $\mathrm{NSD}=0.5$ is $q^2{v}^2\tau T=1$. Because $q$ and $T$ are fixed parameters of the experiment, changes in NSD induced by applied therapies are caused by changes in the $v^2\tau$ product, capturing the influence of the therapy on the physiological motions of the living sample. The common behavior for different velocities and persistence times is described by the relationship

Fig. 2

NSD as a function of the scaling parameter $q^2{v}^2\tau T$, where $q$ is the momentum transfer, $v$ is the organelle speed, and $\tau$ is the persistence time of the random flights. Monte Carlo simulation of flights were performed with 500 frames at 25 fps for $T=20\mathrm{s}$. The NSD data are accumulated from simulations using different organelle velocities and persistence times, demonstrating the scaling relationship between NSD and the transport properties. For $q^2{v}^2\tau T\gg 1$, the NSD approaches unity.

The time traces of the fluctuating intensities are transformed into the frequency domain as a spectral power density denoted by $S(\omega )$. The measured power spectrum is a function of the frame rate of the acquisition and exposure time of the shutter. In particular, the Nyquist theorem states that the highest frequency that can be resolved is $f_{\max }=\mathrm{fps}/2$, where fps stands for frames per second. In addition, during the data acquisition, the detection bandwidth is set by the exposure time as $f_{\mathrm{BW}}=1/(2t_{\exp })$, where $t_{\exp }$ is the exposure time that “freeze-frames” motion, like a strobe, between the Nyquist frequency and the detection bandwidth. The integral of the spectral power between the Nyquist frequency and the detection bandwidth appears as a baseline at the Nyquist frequency. This is called the Nyquist floor and is not, in general, a noise floor but contains information about fast vesicle motions with frequencies up to $f_{\mathrm{BW}}$. The spectrum also has a noise floor that can contribute to the integral, but this contribution is usually small relative to the Nyquist floor in active tissues.

3.1.

Biodynamic Growth Characterization

A selection of representative power spectra is shown in Fig. 3 for BR, HD, and UB plate spheroids as well as living biopsies. In Fig. 3(a), the HD spheroids have the highest knee frequency because they are more active than the other two growth methods. Figure 3(b) shows the spectra of a mouse ovarian xenograft biopsy and a human esophageal biopsy compared with tumor spheroids from a BR. The NSD of the tumor biopsies have mean values around 0.8, which are similar to values for the BR sample, and the power spectra have similar knee frequencies around 0.05 Hz. The similarity between the biopsies and the BR tumor spheroids provides support for the conclusion that the BR sample performance is closer to the biopsy than the HD and UB methods. This could reflect the longer culture period in the BR, enabling the formation of extracellular matrix (ECM), and denser cellular adhesions,⁶³ rendering BR-grown spheroids more similar to in vivo grown tumors.

Fig. 3

(a) The measured fluctuation power spectra of A2780 and DLD-1 spheroids for three growth techniques: BR, bioreactor (red); UB, U-bottom (blue); and HD, hanging drop (green). The data are plotted on double ${\log }_{10}$. The knee frequencies are in the range of 0.02 to 0.03 Hz. The slope parameters are around $-1.5$ to $-1.7$, and the dynamic range is $\sim 1000:1$. The tumors from the BR have lower knee frequencies than tumors from the HD method. (b) Mouse (red) and human esophageal biopsies (blue) have lower dynamic range relative to the spectra of A2780 (green) and DLD-1 (black) tumor spheroids obtained from the BR.

Motility contrast images (MCI) of the A2780 and DLD-1 cell lines under the three growth methods are shown in Fig. 4(a). The NSD increases from the BR to UB to HD for each cell line. An averaged NSD of 0.79 for BR DLD and 0.82 for BR A2780, and a higher NSD of 0.9 for the HD DLD and A2780 spheroids were measured. The BR usually takes several weeks to grow tumor spheroids to the optimal size, which allows it to develop more ECM and complex cellular adhesions than the other methods.⁶⁴ Conversely, the UB and HD methods take 1 to 2 days to accomplish the growth, and hence they tend to be looser aggregates of cells. It is typical for the BR spheroids to have low motility in the core of the spheroid because the cells in the core area have been exposed to lower oxygen and nutrients for a longer period of time, which can be seen from the MCI of the BR-grown A2780 spheroid in Fig. 4(a). Unlike the BR spheroids, the UB and HD spheroids tend to be more uniform because the cells are less dense, and nutrients can be transported more easily from the outer environment into the spheroids.^49,65–67

Fig. 4

(a) MCI of A2780 and DLD-1 spheroids for three different growth methods: BR, bioreactor; UB, U-bottom; and HD, hanging-drop, and compared with ovarian tumor xenografts. The color scale ranges from 0.6 to 1. The BR spheroids have lower NSD in the core area because the BR spheroids are tighter and denser. UB and HD spheroids have higher NSD because of lower adhesions. (b) Bar chart of knee frequency and (c) NSD of spheroids and biopsies. BR spheroids have a large variability. HD spheroids have the most uniform properties.

The average NSD values and knee frequencies are shown in Figs. 4(b) and 4(c). The sample numbers for these data are A2780: BR $N=11$, UB $N=8$, and HD $N=7$; DLD1: BR $N=6$, UB $N=10$, and HD $N=5$. The BR method has the smallest average NSD and knee frequencies, and the HD method has the highest average NSD values and knee frequencies. On the other hand, the BR samples have large sample-to-sample variability with varying spheroid metabolic and physiological activity. The variation is diverse because of the long duration of the BR growth. In the same batch, some spheroids may be actively growing, while others may be dying out. The HD method produces spheroids with higher NSD and knee frequencies with smaller variability. Figures 5(a) and 5(b) show the relation between NSD versus knee frequency and NSD versus backscattering brightness. The HD and UB growth techniques produce homogeneous spheroids, and the knee frequency and NSD tend to be high. Unlike HD and UB growth techniques, the BR growth technique produces spheroids with a wide variation. In Fig. 5(a), the NSD and knee frequency vary from 0.6 to 0.9, and 0.01 to 0.1, respectively. A similar trend occurs in the backscattering brightness in Fig. 5(b). Spheroids from HD and UB plates have low backscattering brightness. BR spheroids have higher backscattering brightness because the BR spheroids are structurally heterogeneous. Spheroids from HD and UB techniques are more uniform, but have low ECM and low adhesion density. Therefore, HD and UB plates are good for high-viability and high-uniformity requirements in drug screening, whereas the BR growth is more suitable for experiments that are dependent upon more developed ECM and cell junctions.

Fig. 5

NSD correlated against other properties of the tissue. (a) NSD versus knee frequency of the fluctuation power spectrum for A2780 and DLD-1 spheroids. (b) NSD versus BB for A2780 and DLD-1 spheroids. The BR samples have higher BB because they are more optically heterogeneous. UB and HD spheroids are more transparent. The HD method produces the most uniform tumor spheroid properties.

3.2.

Biodynamic Drug Response

When a drug is applied to a sample, or the environmental conditions change, the relative power density at different frequencies is altered. This change is captured through the differential relative spectral power density defined as

Fig. 6

(a) Paclitaxel time-frequency dose-response averaged spectrograms of A2780 and DLD-1 for three growth methods (BR, bioreactor; UB, U-bottom plate; and HD, hanging drop). The 4-h baseline is under the control medium (DMSO carrier), and $10\mu \mathrm{M}$ paclitaxel was added at $t_0=0$. Red and blue colors correspond to increase or decrease in the differential power density, respectively. The response of the paclitaxel shows mid-frequency suppression from inhibited mitosis. The right-most graphs are the averaged responses from control media. (b) Bar chart of three biodynamic biomarkers: QDIP, SDIP, and APOP that capture symmetric and asymmetric frequency patterns, respectively, and apoptotic behavior. (c) Format for the time-frequency spectrograms.

The drug-response spectrograms exhibit recognizable features that occur in characteristic frequency ranges at characteristic times after a dose is applied. There are many ways that the time-frequency plane can be partitioned and quantified into a feature vector. For the spectrograms in Fig. 6(a), we quantified three feature metrics called SDIP, QDIP, and APOP. The two features SDIP and QDIP are obtained by multiplying the spectrograms by linear masks that represent red shifted (spectral weight moving to lower frequencies) and mid-enhanced (increased spectral weight in central frequencies, and decreased spectral weight at high and low frequencies) frequency patterns, respectively. The feature APOP is a nonlinear mask that measures combined enhanced low frequencies and enhanced high frequencies that captures organelle transport and blebbing processes during apoptosis.⁵⁸ The three biodynamic biomarkers are shown in Fig. 6(b) for the two cell lines and three growth methods. The biomarkers are consistent between the A2780 and DLD-1 cell lines for the HD and UB growth. However, the SDIP biomarker for the BR-grown samples have different signs between the two cell lines. Here again the HD and UB techniques show better homogeneity and similarities between these growth techniques, but the BR samples are less consistent. This is an important conclusion for researchers seeking to perform consistent drug screens in 3-D tissue.