1. Introduction

Phase-sensitive detection has a long history as a means of increasing contrast in optically transparent biological samples. In the past decade, new insight into biological structures and cellular dynamics provided by quantitative phase contrast imaging modalities has stimulated a proliferation of quantitative phase-sensitive imaging techniques applied to cellular imaging. Optical interferometric techniques such as digital holographic microscopy [1–3], Fourier phase microscopy [4, 5], and Hilbert phase microscopy [6, 7, 8] and their derivatives exploit the intrinsic utility of interferometry for measuring nanoscale differences in optical pathlength. Broadband interferometric techniques such as optical coherence tomography (OCT) [9], optical phase microscopy [10], and white light interferometry [11] are particularly attractive for multi-dimensional phase-sensitive imaging because they exhibit cross-sectional depth selectivity with micron-resolution.

Modern Fourier-domain (FD) OCT systems are distinguished from earlier, time-domain (TD) systems both in implementation and performance. The mechanical limitations imposed on TD systems by the moving reference arm reflector are absent in FD systems, which instead utilize a stationary reference mirror. Furthermore, the principles of Fourier mathematics that govern the conversion of raw interferometric data to cross-sectional depth profiles (A-scans) in FD systems enable the results to be obtained at faster speeds and higher signal-to-noise ratios (SNR) [12–14]. In contrast with its TD counterpart, the non-scanning nature of FD-OCT limits the effect of specular reflection changes as a noise contributor for all depths acquired within a single A-scan to changes occurring during the integration time, which are usually insignificant given the sub-millisecond times typically used. Common-path FD-OCT systems suffer from an inability to simultaneously focus on the reference and sample reflectors, making shot-noise-limited collection nearly impossible. However, the common-path configuration eliminates common-mode noise, resulting in a superior phase stability that makes such systems ideally suited for phase-sensitive imaging in biological samples.

Spectral domain phase microscopy (SDPM) [15] is a common-path, phase-sensitive derivative of FD-OCT that uses the phase information inherent to FD-OCT processing to dynamically resolve sub-wavelength changes in optical pathlength. Because optical pathlength is a function of refractive index and displacement, this single parameter captures information about both dynamic structural and morphological changes in target samples. Previous demonstrations of one-dimensional SDPM, which probed a single spatial location on the lateral surface of the sample, have resolved such dynamic phenomena as cell surface motion during spontaneous beating in embryonic cardiomyocytes and microflow cytoplasmic streaming [16]. SDPM has also been demonstrated as a viable tool for investigating rheological properties of single cells [17].

The ability to visualize dynamic processes at multiple locations on the sample holds promise for providing a more complete understanding of the cellular processes being investigated. To date, two works have extended the principles of SDPM to perform en face high-resolution imaging: spatial variations in optical pathlength have been used to construct metrology contours of imaged samples in much the same way that temporal variations in optical pathlength can produce phase portraits of dynamic events in standard SDPM. Full-field spectral domain phase microscopy (FFSDPM) [18] employs a bulk-optic interferometer to uniformly illuminate the sample and records interferometric information on a two-dimensional charge-coupled device array. A full sweep of the time-encoded-wavenumber swept-source provides the spectral discrimination needed for depth-selectivity. Spectral domain optical coherence phase microscopy (SDOCPM) [19] uses raster scanning of the probe beam of a high-speed, one-dimensional SDPM system to acquire A-scans at various spatial positions across the sample. Both techniques have been demonstrated on static biological samples.

Our present work extends SDPM to perform phase-sensitive cross-sectional imaging of dynamic biological samples. This multi-dimensional SDPM (MD-SDPM) system combines the dynamic sensing capabilities of SDPM with the lateral spatial discrimination demonstrated by FFSDPM and SDOCPM. Here we report on a MD-SDPM system whose one-dimensional capabilities surpass those of the previous SPDM demonstration in boasting a potential fifty-fold increase in time resolution through addition of a custom spectrometer and a two-fold increase in axial resolution through replacement of the source. We also present new results of cardiomyocyte contractile behavior and cytoplasmic streaming using this MD-SDPM system.

2. System design and methods

Our MD-SDPM system, based on the SDOCPM system layout, consisted of a fiber-based Michelson interferometer designed to support broadband light (Fig. 1). A mode-locked Ti: Sapphire laser (Femtolasers, Femtosource) served as the illuminating source (λ₀ ~ 780 nm, Δλ_FWHM ~ 70–90 nm). The imaging optics were fit to the documentation port of an inverted microscope (Zeiss, Axiovert 200) to facilitate biological imaging and concurrent acquisition of video microscopy. The custom-designed spectrometer featured a 2048-pixel, 19 kHz linescan camera (Atmel, AVIVA) with a minimum integration time of 50 μs, which represents a nearly 50-fold time resolution improvement over the first-generation SDPM design. The upper limit on the dynamics of optical pathlength changes that can be captured with this system is set by the phase unwrapping condition at 2π/τ, where t is the longer of the integration period or the wait period between successive scans of the same lateral position; the lower limit is set by the phase sensitivity, which is a function of SNR [15].

This choice in system design was motivated by the time scales of the dynamic cellular phenomena we intended to observe. Hence, image acquisition time was of primary importance. In FFSDPM-based systems, camera frame rate is the most significant limiting factor. Axial spectral sampling resolution and imaging depth improvement scale with the number of distinct spectral acquisition points, but simultaneously increase the effective A-scan acquisition time. Correspondingly, FFSDPM suffers from increased sensitivity to axial motion artifacts. While suitable for static biological specimen, given the current technology such a system is inadequate for imaging samples whose dynamic activity varies on sub-millisecond time scales. In contrast, state-of-the-art SDOCPM technology is sufficient for cellular imaging, but forces a tradeoff between frame rate, lateral resolution, and field-of-view.

 

Fig. 1. MD-SDPM schematic. The system employs a broadband source (Ti:Sapphire laser, λ₀ = 780 nm, Δλ ~ 70–90 nm) and customized spectrometer (19 kHz line rate) that have been fitted to the documentation port of an inverted microscope. Lateral imaging is performed by raster scanning. FC - fiber coupler; L - lens; DP - documentation port; OBJ - objective; TL - tube lens; CS - coverslip; CCD - charge coupled device; θ_x,y - galvonometer mirror scan pair.

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3. Cell experiments

3.1 Cardiac contractility

Isolated myocardial cells from chick embryos were obtained as follows. Fertilized Arbor Acre chicken eggs (Gold Kist Hatchery, Siler City, NC) were incubated at 37°C and 97% humidity, until they reached the required developmental stage [20]. Stage 14 embryo hearts were placed in phosphate-buffered saline (PBS) and dissociated with repeated 4–8 min exposures to PBS containing trypsin (7.5 U/ml, trypsin TL) and/or collagenase (180 U/ml, Worthington, type II), DNAase (11 g/ml, Worthington, DNAase I) and BSA (fatty-acid free, 1 mg/ml) at 37°C. Cells were collected from each digestion and diluted into a bicarbonate-buffered trypsin-inhibiting solution containing 1.8 mM calcium. Cells were pelleted, cultured in DeHaan’s 21212 medium (1.8Mm CaCl₂), and plated in 35 mm petri dishes, from which a small window had been excised and replaced with a glass coverslip attached from below. The dissociated cells remained in growth medium overnight and were maintained in the incubator prior to imaging, which occurred within 48 hours of plating. During imaging, dishes were placed on a temperature-controlled stage that was heated to approximately 37°C, at which temperature spontaneous beating was observed.

The lateral resolution of our system was measured to be less than 2.2 μm using a US Air Force Test Target, which agrees with our expected value of 1.86 μm based on the system optics and the magnification of the microscope objective used (40x magnification, NA = 0.326, depth of field = 27.76 μm). The axial resolution of our system, which depends on the characteristics of the source, ranged from 2.99–3.84 μm in air. Lateral scans (B-scans) were typically 50–100 A-scans in length; the B-scan length and integration time were optimized for each specimen to ensure image frame rates minimally equal to 40 Hz. Interferometric data were linearly resampled in wavenumber prior to applying the Fourier transform to obtain the amplitude and phase A-scans. Phase values at each transverse depth were unwrapped in time using built-in MATLAB unwrapping functions to create dynamic phase portraits for each lateral position sampled. The inter-scan phase stability (that is, the standard deviation of the phase at a single lateral position over the duration of the experiment) measured at the coverslip surface was 2.4nm.

Representative data taken across a lateral line of an isolated, spontaneously beating cell are shown in Fig. 2. The 100-point lateral scan spanned 10.95 μm, and was taken at an integration time of 250 μs. The SNR (given by the ratio of the average signal peak to the standard deviation of the background noise) inside the cell was roughly 22dB. An amplitude B-scan image acquired in the middle of a contraction event appears in Fig. 2(a). The associated phase B-scan image in Fig. 2(b) reveals two domains of different activity in this contracting cell: the left domain takes on negative phase values, while the right domain assumes positive phase values, relative to the phase of each position at time t = 0. Thus, it is clear from the phase B-scan, but not visible in the amplitude B-scan, that the two sides of the cell are moving in opposite directions. Phase portraits taken from two points at the same axial depth (44.9 μm) in each of the two domains support this conclusion as well [Fig. 2(d)]. A movie of the phase B-scans during the first two contraction beats (supplementary material - colorbar indicates phase change in radians) suggests that the contractile activity in the cell originates in the rightmost domain and propagates to the other with a time delay. The delay between the onset of the peaks during the 4 captured beats can be approximated to within the resolution of the system frame duration (25 ms), and ranges from 57.1 ms to 159.8 ms. The average inter-peak delay for the two locations plotted is roughly 105 ms. Both the amplitude and phase B-scans suffer from an artifact of unknown origin in the region below the coverslip reflector.

 

Fig. 2. (a). Amplitude B-scan captured during a contraction event (t = 625 ms) in the isolated cell shown in b. (b) Scan position indicated by red line (10.95 μm). (c) Corresponding phase B-reveals two domains within the cell moving in opposite directions. Color bar denotes relative phase (in radians). Intensity-based mask applied to phase data suppresses noise and emphasizes cell motion. (1.06 MB) movie acquired over the first two beats. (d) Phase traces of two lateral positions (1.97 μm and 6.02 μm, red and blue, respectively) at the same axial depth (44.9 μm) show different motion between the right and left cell domains. [Media 1]

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A multicellular preparation obtained using the same techniques as for isolated cells was also chosen for observation. Figure 3 shows a cross-sectional scan of a cluster of spontaneously beating Stage 14 ventricular cardiomyocytes taken with a 40x objective. The scan, whose location appears as the red line in Fig. 3(b), spans 52.75 μm. The related B-scan image in Fig. 3(a) represents a single frame from the acquired dataset, which was taken at roughly 12.5 Hz (the integration time was 800 μs and the SNR in the cell was roughly 19 dB). The reflection from the coverslip surface on which the cells are resting is visible as a bright white line at 78 μm. Phase portraits [Fig. 3(c)] are shown for three points from differing lateral positions and depths, whose repeating pattern is indicative of regular beating activity; the timing of these beats correlates with the observed motion of the cells capture by video microscopy.

 

Fig. 3. (a). B-scan, or lateral plane image, of the cell cluster shown in b; (b) Bright field photomicrograph of a ventricular cardiomyocyte cluster from a Stage 14 chick embryo. Red line denotes the position of the scan, which is 52.75 μm in length; (c) Phase portraits corresponding to points from the multi-cell cluster identified in a are marked in white in b. The sampling rate was possibly too low (12.5Hz) to capture any resting period between successive beats, leading to interpretive challenges. Point 1 can be said to be beating out of phase with points 2 or 3, or to be moving in the opposite direction.

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The cell cluster phase portraits illustrate the difficulty of interpreting the relationship between relative phase changes and cell movement, and give deference to the importance of matching the sampling rate with the time-scale of the observed dynamics. Figure 3(c) shows no resolvable rest period between successive beats, which is exacerbated by the low sampling rate. Thus, because the phase data in SDPM and other interferometric-based phase-sensitive techniques are relative, rather than absolute, phase measurements (in the case of SDPM the phase is expressed relative to an initial time point - the first frame of the acquired data), the lack of a sustained resting period between beats for this cluster makes it impossible to assess whether the initial phase corresponds to a point on the crest or valley of the waveform. Typically, negative phase values indicate motion towards and positive phase values motion away from the reference coverslip. However, for the present example one cannot determine, based on the phase portrait alone, whether the sampled points in the cells are moving up or down. That points 2 and 3 are moving synchronously or nearly so, while point 1, which is presumably from a different cell, is beating nearly 180° out of phase, is clear from the phase portrait. This suggests the potential to use SDPM to investigate the timing associated with propagation of contractile activity across multiple cells. An alternative interpretation is that all cells are moving in synch, but that one is moving down during a beat while the others are moving up.

3.2 Cytoplasmic streaming

An Amoeba proteus in spring-water solution was transferred to a coverglass and imaged from below using a 40x microscope objective. B-scan images were acquired by scanning 150 points across an 89.1 μm line nearly perpendicular to cell surface. The integration time per line was 300 μs. Data were linearly resampled to be evenly spaced in wavenumber prior to applying the Fourier transform; phase information was low-pass filtered in time to mitigate speckle noise and to emphasize longer, steady flows. Doppler frequencies were computed by taking the numerical derivative of the unwrapped phase in time (obtained through built-in MATLAB unwrapping functions), as has been previously done [16], at each lateral position. The range of resolvable Doppler flow frequencies for this setup was 0.16 Hz – 139.6 Hz. Note that the flow characteristics reported correspond only to the axial component of the flow.

 

Fig. 4. MD-SDPM data of A. Proteus cytoplasmic flow, flow directed into the page. (a) B-scan image of mean amplitude overlaid with the mean Doppler frequency shift over 9 s at each pixel for |f _Dopp| > 0.15 Hz. (b) Lateral Doppler frequency and (c) lateral unwrapped phase distribution over time taken from the position corresponding to the dashed horizontal line in a (depth = 48.6 μm). The flow manifests itself as a trend of steadily increasing phase confined within the cell, and is visible in c. (d) Axial M-mode and (e) Doppler frequency distribution over time taken from the position corresponding to the dashed vertical line in a (depth = 74.5 μm).

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Figure 4 shows line scan data taken across a pseudopod whose motion was directed into the plane of the page. An image of the mean amplitude overlaid with the mean Doppler flow frequency over 9 seconds appears in Fig. 4(a), which localizes the flow activity to a small region within the pseudopod. Depth-wise amplitude and Doppler frequency M-scans are given in Figs. 4(d) and 4(e), respectively, for data acquired at lateral position 74.5 μm. Doppler frequency and unwrapped phase M-scans across the full lateral scan are given in Figs 4(b) and 4(c), respectively, for a single depth (48.6 μm). While the position of the pseudopod can be localized in the amplitude M-scan, it is with the phase M-scan that the flow activity, isolated to a sub-region within the pseudopod, first becomes evident. Furthermore, although the lateral demarcation between cell and non-cell is clear in Fig. 4(a), the lack of a similar transition in the phase image of Fig. 4(c) indicates that there is no regional distinction to be found in the flow activity near the cell surface. In contrast with the dramatic phase changes induced by flow, it is clear that the both portion of the pseudopod to the left of the bounded flow and the medium that surrounds it are relatively stationary. The Doppler frequency B-scan shows the relative distribution of flow velocities in the pseudopod, which could be converted to absolute velocities if the angle between the probe and flow direction were accurately known.

4. Discussion

We have shown that MD-SDPM can be used to follow cellular dynamics with time-resolutions appropriate for observing single-cell activity. The ability to view phase activity at different lateral positions can provide insight into site-specific activity within various domains of a cell, or possibly about the coordination of activity across multiple cells. While several well-established phase contrast techniques already enable phase-sensitive detection at multiple lateral positions, SDPM, as with other OCT-derivates, remains distinguished in that it also discriminates cross-sectional depth information. Thus, when combined with lateral detection as demonstrated here, these techniques are capable of resolving three-dimensional phase.

The single-cell contractile behavior we observed in these experiments was rather unexpected, given that the cells were embryonic -- not adult -- cardiomyocytes. While the contractile axis is easily identified in regularly-shaped elongated, rod-like adult cardiomycotyes using various techniques, the spherical shape and small size (10–20 μm diameter) of enzymatically isolated embryonic heart cells prohibits the use of commonly employed techniques like edge-detection and laser diffraction to determine shortening fractions, and visually confounds the location of the force-generating source. A single cross-sectional sequence captured with MD-SDPM showed potential for determining the location of the cell’s contractile source-center; multiple such sequences acquired from different planes could likely assist in localizing and fully characterizing the dynamics of contraction propagation in a single cell.

Previous investigations of locomotive cytoplasmic flow in A. proteus conjectured that it was characteristically laminar [16]. The one-dimensional flow profile combined with the visual appearance of the flow under light microscopy supported the idea of flow channels, that is, areas of flowing cytoplasm bounded by non-flowing cytoplasm. In the current work, the boundedness of the bulk flow as visible in the cross-sectional images lends more evidence to the suggestion of flow channels. The fundamental nature and underlying physical mechanisms of such basic processes as locomotion are of considerable interest in fields ranging from embryology to cancer research.

Future studies with cardiomyocytes may look to correlate the domains of contractile activity with the locations of identifiable organelles, while future work with A. proteus might study the time and transition dynamics of flow, and particularly the convergence and divergence of flow tributaries. The current work acquired time sequences of data sets in two spatial dimensions, which represents a modest step towards a future goal of acquiring four-dimensional datasets (space and time) of cellular activity in real time. We note, however, that one major limitation of this and any single-measurement phase-sensitive technique is an inability to decouple changes in refractive index and displacement, the two parameters which contribute to optical pathlength. Throughout this work we have assumed that the motion signal dominates the phase variations we observe. Future work may seek to perform multiple phase-sensitive measurements to enable accurate tracking of motion in samples subject to changing refractive index. In addition, multi-modality imaging that couples MD-SDPM with other established techniques like fluorescence can lead to a better understanding of the chemo-mechanical coupling dynamics of observed biological phenomena. Combined SD-OCPM and multi-photon fluorescence microscopy have recently been demonstrated [21].