Phase-sensitive dynamic micro-optical coherence tomography for high-speed intracellular motion imaging

Abstract

Dynamic optical coherence tomography with micrometer resolution (DμOCT) offers enhanced contrast information by evaluating time-dependent signal fluctuations in images of living tissue. DμOCT’s use has been limited to imaging excised fresh tissue specimens or 3D cell cultures due to the long observation times required, typically ranging from 1.35 to 25 seconds. To reduce the time needed to obtain DμOCT images, we developed a phase-based algorithm that analyzes intracellular motion by measuring phase changes between adjacent B-scans. This approach significantly reduces imaging time to as low as 40.5 ms while providing a quantitative measure of intracellular motion.

Dynamic μOCT (DμOCT) is a cross-sectional imaging modality that enables the visualization of individual cells and intracellular motion as an indicator of metabolic activity [1]. Similar to full-field-based dynamic cell imaging [2], DμOCT analyzes light scattering fluctuations resulting from intercellular motion on a pixel-by-pixel basis [1]. μOCT intensity B-scans acquired from the same tissue plane are acquired over time before applying a fast Fourier transform (FFT) on the intensity data along the time axis. The resulting data are then integrated over three distinct frequency ranges, with each range corresponding to a channel in an RGB color space [3]. In addition to providing information about intracellular motion, this technique dramatically increases image contrast, as demonstrated in different types of living tissue samples [3-5]. All DμOCT image reconstruction methods reported to date utilize OCT image intensity and require serial image acquisition over relatively long times, ranging from 1.35 [3] to 25 seconds [1]. The extended time period over which images must be acquired makes it challenging to use DμOCT on large specimens, capture volumetric images, or use it for applications where high throughput is needed. In this study, we present a novel phase-sensitive DμOCT method for quantifying intracellular motion that requires less data than intensity-based approaches. By analyzing the phase difference between adjacent B-scans, our phase-sensitive DμOCT algorithm enables quantitative dynamic cellular imaging while reducing the imaging time to tens of milliseconds.

The theoretical basis for phase-sensitive DμOCT is the ability of OCT to detect nanometer-level displacements by determining the phase difference, calculated as:

$$\Delta \varphi =\frac{4\pi n\Delta tV}{\lambda },$$ (1)

where $\lambda$ is the smallest wavelength of the system, $n$ is the refractive index of the tissue, $\Delta t$ is the time difference between adjacent B-scans and $V$ is the velocity of the intracellular motion. In analogy to Doppler OCT [6], the frequency can be derived from phase difference using the relationship:

$$f=\frac{\Delta \varphi }{2\pi \Delta t}.$$ (2)

The dynamic range of phase-sensitive DμOCT is the ratio between the maximum and minimum detectable velocity, which is fundamentally limited by the signal-to-noise ratio of the system and is further degraded by positioning errors caused by beam displacement between sequential scans in the lateral direction. The smallest detectable phase difference is limited by the SNR $\Delta {\varphi }_{z,min}={(SNR)}^{-1∕2}$ [7] and defining the minimal detectable frequency $f_{z,min}$ as follows:

$$f_{z,min}=\frac{\Delta {\varphi }_{z,min}}{2\pi \Delta t}.$$ (3)

The maximum detectable frequency $f_{z,max}$ is limited to the range where phase wrapping occurs and is given as:

$$f_{z,max}=\frac{\Delta \varphi }{2\pi \Delta t}\mid \Delta \varphi \mid \le \pi .$$ (4)

Based on this theory, calculation of the phase differences between subsequent DμOCT B-scans can be used to precisely quantify intracellular movements in tissues and represent the information in an HSV image. To achieve this, the phase difference $\Delta \varphi (z,x,t)$ between two adjacent B-scans is computed as:

$$\Delta \varphi (z,x,t)=arg[D(z,x,t)\cdot D^{\ast }(z,x,t+\tau )],$$ (5)

where $D(z,x,t)$ is the complex OCT data at the spatial coordinates $(z,x)$ at the time $t$, and $D^{\ast }(z,x,t+\tau )$ is its complex conjugate at time $t+\tau$.

To eliminate the influence of bulk motion along the optical axis, the magnitude of the phase difference at each point was calculated by subtracting the mean phase difference as follows:

$$\theta (z,x,t)=\mid \Delta \varphi (z,x,t)-\Delta {\varphi }_{mean}(x,t)\mid .$$ (6)

The average phase difference along the depth axis is calculated as:

$$\Delta {\varphi }_{mean}(x,t)=arg\left[\frac{1}{N_z}\sum _{z=1}^{N_z}\Delta \varphi (z,x,t)\right].$$ (7)

where $N_z$ denotes the number of points along the depth axis. In contrast to intensity-based DμOCT approaches, the phase difference provides direct access to depth-dependent scattering velocity at each pixel. To create the DμOCT from these calculations, we adopted and modified the HSV color space method proposed by Scholler et al. [8] assigning a distinct physical property to each channel for meaningful visual interpretation using at least two-phase differences. In the modified version, hue, saturation, and value are represented as follows: hue ($H$) was computed as the mean of the phase differences $\theta (z,x,t)$ over time:

$$H(z,x)=\frac{1}{T}\sum _{t=1}^T\theta (z,x,t),$$ (8)

where $T$ is the number of time frames. A Gaussian filter with a kernel size of 3 pixels was applied to $H$, where the color blue represents small phase differences while red indicates larger differences. The saturation ($S$) represents the phase difference spread relative to the mean and is computed as the inverted coefficient of variation:

$$S(z,x)=-\frac{{\sigma }_{H(z,x)}}{H_{(z,x)}}.$$ (9)

The standard deviation ${\sigma }_{H(z,x)}$ of mean phase difference $\theta (z,x,t)$ is computed as

$${\sigma }_{H(z,x)}=\sqrt{\frac{1}{T-1}\sum _{t=1}^T{[H(z,x,t)-H(z,x)]}^2}.$$ (10)

The value ($V$) is computed as the standard deviation of the principal components from the complex images $D$, across all time frames of each spatial location as follows:

$$V(z,x)=std[PC{A}_{res}(z,x)],$$ (11)

where $PC{A}_{res}$ is the result of the principal component analysis performed on complex μOCT data $D(x,z,:)$ with the number of components limited to the number of time points. Due to the high dynamic range of the μOCT signal, we applied a gamma correction to compress the dynamic range value with $\gamma =0.5$.

Imaging was performed using a previously described compact μOCT system [3]. Briefly, the μOCT system was based on a high-power supercontinuum light source (SuperK Extreme EXR-15 OCT, NKT Photonics, Denmark). The supercontinuum light (400–2000 nm) was optical filtered (SuperK Split, NKT Photonics, Denmark) to a wavelength range of 600–1000 nm and coupled into a 90:10 fiber coupler (TW670R2A2, Thorlabs, US). The fiber carrying 10% of the light was directed through a reflective collimator (RC08APC-P01, Thorlabs, US) into a modular OCT scan head (OCTP, Thorlabs, US). To increase the depth of focus, the fiber tip was equipped with a mirror tunnel-based depth of focus extension [9]. A non-polarizing beam splitter divided the light into reference and sample arms at a 30:70 ratio. In the reference arm, the light traveled through an objective lens (UMPLFLN 10XW Objective, Olympus, US) and was reflected from a mirror through the optical system. In the sample arm, the light was deflected by scanning galvanometers (OCTP, Thorlabs, US), which directed it through a water immersion microscope objective (UMPLFLN 10XW Objective, Olympus, US) onto the tissue. The returned light was coupled into a customized Thorlabs Ganymede unit (GAN621-SP10, Thorlabs, US).

Data processing algorithms, including spectrum normalization, Hann-windowing, optimization-based numerical dispersion compensation, and k-space rescaling, were implemented using MATLAB (2024a, MathWorks, US), and image resizing and additionally filtering was done in ImageJ [10]. Freshly excised human cervical biopsies were collected during a consented routine diagnostic procedure. The tissue was placed into culture media and stored on wet ice until imaging. The biopsy was immobilized by pinning to a silicone substrate and immersed in phosphate buffered saline solution. Time between excision and imaging was approximately 45 minutes. During imaging, the system operated at 100,000 A-scans, capturing 96 B-scans at 71 fps. The cervical tissue was imaged over 0.8 × 1 mm² with 1024 × 1024 px². The study was approved by the Institutional Review Board (IRB) of the Massachusetts General Hospital (IRB 2015P000328). Swine esophagus tissue was excised immediately postmortem and measured within 60 minutes of extraction. The tissue was placed on a silicone substrate, immersed in phosphate buffered saline solution, and covered to immobilize it. The imaging system operated at 50,000 A-scans, capturing 96 B-scans at 40 fps. The tissue was imaged over 0.8 × 1.5 mm² with 1024 × 1024 px² resolution. The excision and use of the swine tissue were approved by the Institutional Animal Care and Use Committee of the Massachusetts General Hospital (IACUC 2020N000032). For a quantitative assessment of how reduced frame rates affect the accuracy of our new algorithm for reconstructing HSV images, we analyzed a total of four image series, two of which were from regions with higher activity and two of which were from regions with lower activity, using the imaging parameters described above. Phase-based HSV images were generated using 3, 6, 12, 24, 48, and 96 frames. Each HSV image was separated into its three channels (hue, saturation, and value), and histogram similarity was calculated using the Chi-square metric, comparing each to our initial imaging protocol with 96 frames. To statistically evaluate the deviation of similarity values from the reference (96 frames), we performed a one-sample t-test. The similarity values, ranging from 0 to 100, were tested against the theoretical maximum similarity of 100, allowing the determination of whether reduced frame rates resulted in statistically significant differences in similarity compared to the full-frame reference.

Figure 1 compares standard μOCT imaging of human cervical tissue [Fig. 1(A)] and histology [Fig. 1(B)] with dynamic μOCT (DμOCT) images calculated using our phase-sensitive HSV [Fig. 1(C)] and previously utilized amplitude-based RGB [Fig. 1(D)] algorithms with 96 frames. Histology reveals intermediate cervical epithelial cells and a benign cyst. While grayscale μOCT exhibits limitations in visualizing cellular structures, dynamic imaging significantly enhances contrast and provides intracellular motion information, encoded in false colors. The intensity-based RGB algorithm represents static motion in blue, medium motion in green, and rapid motion in red. Cells exhibiting high intracellular motion appear yellow-red, while less active cells appear green, and the extracellular matrix remains relatively static in blue. In comparison to our phase-sensitive HSV algorithm, both methods display blue for static regions; however, the HSV algorithm offers higher contrast between individual cells. Due to binning in the RGB algorithm, cells appear green to orange, indicating frequencies above 0.74 Hz without clear differentiation. In contrast, the HSV algorithm maps each pixel to a distinct Doppler frequency, enhancing the visibility of individual epithelial cells. Low activity cell membranes appear blue, reflecting signal fluctuations below 0.4 Hz. The structure inside the cyst appears blue-green, indicating activity up to 5 Hz, while the surrounding epithelial cells appear yellow-red, indicating activity up to 15 Hz.

Fig. 1.

Comparison of different DμOCT algorithms applied to μOCT images of freshly excised human cervical tissue: (A) standard μOCT and (B) representative histology compared to DμOCT image calculated with (C) phase-based HSV-method and (D) the intensity-based RGB method and to phase-based DμOCT calculated with (E) 12-frames and (F) 3-frames.

A key advantage of the phase-based algorithm is that it is not limited by the frequency resolution of the image acquisition rate and only limited by the phase sensitivity. Therefore, phase changes representing the intracellular activity can be acquired in a shorter amount of time because fewer frames are needed to calculate the phase-sensitive DμOCT image. Figures 1(E) and 1(F) show phase-sensitive DμOCT images when only 3 frames and 12 frames were used for reconstruction. Although the DμOCT images were only calculated with 3 frames over a total acquisition time of 42 ms, single epithelial cells can be clearly visualized and distinguished from the surrounding structures, including a cyst. In direct comparison with the full 96-frame dataset [Fig. 1(C)], the 3-frame and 12-frame DμOCT image contains more speckle noise. Regardless, the 3- and 12-frame images qualitatively show much higher image contrast compared to that seen in the conventional μOCT image [Fig. 1(A)], enabling the visualization of cellular microstructure that was much closer to that seen in histology from the same specimen.

The ability of DμOCT to visualize structures that are typically not visible in conventional OCT is further demonstrated in freshly excised swine esophagus (Fig. 2). In this image, signal fluctuations are a bit lower up to 7 Hz. The DμOCT images [Figs. 2(A)-2(C)] reveal that high-frequency motion is less prominent in the squamous cell epithelium of the esophagus compared to the cervical epithelium. In detail, the images show areas of low-frequency motion in the most superficial layer, which aligns with our expectations for mature stratified epithelium. Beneath the stratified epithelium, an increase in frequency and contrast is observed, allowing the identification of individual squamous cells. Near the basal membrane, cell nuclei become more visible due to differences in activity. These findings are consistent with the familiar pattern of squamous epithelial cell maturation and align well with corresponding histology [Fig. 2(D)]. The same patterns are clearly visible in images calculated from the full 96-frame dataset [Fig. 2(A)], the 12-frame [Fig. 2(B)], and 3-frame [Fig. 2(C)] datasets. However, the ability to resolve individual cells and distinguish cell nuclei decreases as the number of frames is reduced. This effect is more pronounced in the esophageal images compared to those from the cervical tissue biopsy.

Fig. 2.

Imaging of swine esophagus tissue. DμOCT image calculated with the phase-sensitive HSV method, using (A) 96-frames, (B) 12-frames, (C) 3-frames compared to (D) representative histology.

Chi-square similarity analysis was used to quantify how the algorithm performed as a function of frames used in the reconstruction (Fig. 3). For the hue channel, which represents the frequency of the intracellular motion information, the similarity metric was lowest at three frames (91.9% ± 7.2%) and increased logarithmically reaching 99.1% ± 0.9% at 48 frames. However, no statistically significance difference was observed between the hue channel calculated with reduced number of frame images compared to the 96-frame reconstruction. The saturation and value channels, which reflect variations in the phase difference and image contrast, respectively, exhibited lower initial similarity values when using three frames (86.7% ± 2.6% for saturation and 66.1% ± 19.9% for value). Still, both channels approached 90% similarity when calculated with 12 frames. The statistical analysis shows that all the saturation channels calculated with the reduced frame rate were significantly different from the baseline image calculated with 96 frames. For the value channel, images calculated with 3 and 6 frames were statistically significantly different, while the ones calculated with 12, 24, and 48 were not.

Fig. 3.

Chi-square similarity analysis of reduced frame rate DμOCT images using 3, 6, 12, 24, and 48 frames, compared to the reference 96-frame dataset. Statistically significant differences are indicated by *p < 0.05.

In contrast to previous methods, which relied on phase differences to image intracellular motion but were limited to thin samples and long measurement times, and limited morphological contrast [11], or focused on measuring fast-moving cilia on the epithelial surface [12], our approach uses phase differences to extract intracellular activity and combines this information with the standard deviation assembled in an HSV image to create high-contrast images in scattering tissue. In dynamic imaging data shown here, the phase-based approach qualitatively produces equivalent contrast compared to intensity-based methods. However, speckle noise continues to limit the contrast in a similar manner. AI-based speckle suppression applied to the value channel of the HSV image may help overcome current contrast limitations, when using only a few frames. Another key advantage of our method is its ability to resolve motion components between 1 and 5 Hz using only three B-scans (40.5 ms), achieving video-rate imaging. This speed outperforms intensity-based frequency analysis methods, which require at least 250 ms to resolve 1 and 5 Hz motion, since it is not constrained by the frequency resolution of the Fourier analysis. In addition, phase differences between neighboring B-scans are calculated, which reduces the requirements for long-term phase stability for the intracellular information, even when using tens of frames. In contrast to frequency-based methods, which require stability over the full acquisition time, our method requires stability of only two consecutive B-scans, which minimizes impact of mechanical drift, thermal expansion, and vibration artifacts. This speed advantage allows real-time visualization and rapid scanning of the most relevant field of interest. It also holds potential as an alternative to techniques like fluorescence lifetime imaging (FLIM) [13], which probe intracellular metabolism and dynamics. These methods, while effective, may require exogenous dyes and are limited by photobleaching, shallow imaging depth, and the need for high-NA optical lenses.

One limitation of phase-based dynamic imaging is SNR-dependent phase noise, which reduces sensitivity to low-frequency motion. This noise can be problematic when conducting phase-based dynamic imaging deep within tissues. Extended depth of focus approaches [9] can partially mitigate this issue by increasing SNR at depth while preserving high spatial resolution. Other methods to improve depth-dependent SNR like tissue clearing [14] could also be of benefit.

In conclusion, we present a novel phase-sensitive approach for DOμCT imaging that achieves image quality and contrast comparable to established methods. Moreover, the significant reduction in imaging time per frame opens new possibilities for a variety of new dynamic μOCT applications.

Data availability.

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.