Dynamics Optical Coherence Tomography (dOCT)

 

This project was completed as a prerequisite for the conferral of a Master of Science degree in Physics from the University of Waterloo in the year 2023.

 

Optical Coherence Tomography (OCT) is a non-invasive imaging technique renowned for its rapidity and micron-level resolution, applicable in both ex-vivo and in-vivo scenarios. This technology is immensely valuable in the diagnosis and detection of ocular diseases such as glaucoma, diabetic retinopathy, cancer, and age-related macular degeneration. OCT operates on the principle of interferometry, utilizing ultra-broadband laser pulses and the interference of reflected light from the sample with a reference mirror to generate interference fringes.Significant advancements in resolution have been achieved with OCT, showcasing superior performance in both axial and lateralresolutions compared to alternative imaging techniques. The enhanced resolution of OCT significantly contributes to the precision and clarity of medical imaging, elevating its importance in the field.

OCT is typically implemented in two primary modes: Time Domain OCT (TD-OCT) and Spectral Domain OCT (SD-OCT). SD-OCT further divides into Fourier Domain OCT (FD-OCT) and Swept Source OCT (SS-OCT). The choice of scanning method and light direction results inthree variations: point scanning OCT, line scanning OCT, and full-field OCT.

Dynamic OCT (dOCT) represents a thrilling progression in medical imaging, providing instantaneous visualization of dynamic processes within tissues and extracting data from moving cellular structures. It functions by directly analyzing the temporal fluctuations of reflected intensity from an object in motion into the camera.

While Traditional OCT offers valuable insights into tissues and the layers of the eye with sub-micrometer (1μm) resolution, it lacks the capability to capture information from live cells. In contrast, dOCT enhances the capabilities of traditional OCT by furnishing real-time, time-resolved imaging. This enables it to capture and depict dynamic processes and changes occurring within tissues and organs, including phenomena such as blood flow, motion, and tissue deformation.

dOCT proves to be indispensable for investigating vascular dynamics, such as blood flow in the retina or coronary arteries.

Two significant methodologies arise in dynamic imaging: logarithmic intensity variance (LIV) and Fast Fourier Transform (FFT). These strategies serve as potent instruments for deciphering the temporal complexities of cellular behavior within a given biological context.

The LIV technique entails a meticulous examination of the intensity fluctuations displayed by individual pixels over a specified duration. By closely tracking changes in pixel intensity over time, LIV enables the identification and characterization of cellular motion. This method excels at capturing subtle variations and modifications in intensity, rendering it a valuable tool for discerning dynamic cellular processes.

In contrast, the FFT approach employs a different tactic by utilizing the Fast Fourier Transform to uncover the temporal properties of pixel intensities. This method entails transforming the intensity profile of each pixel across the temporal domain into its frequency constituents. Through the FFT procedure, distinctive frequency patterns emerge, offering insights into the periodic or rhythmic elements within the cellular dynamics under investigation. The FFT method is particularly adept at identifying repetitive patterns or oscillations in intensity data, providing a unique perspective on the temporal dynamics of the biological system.

In essence, these two methods, LIV and FFT, serve as indispensable tools in dynamic imaging, each presenting a distinct approach to unraveling the nuanced temporal behaviors of cells. Their utilization furnishes researchers with valuable insights into the intricate and ever-changing world of cellular motion and activity.

The Principle of LIV

In dOCT differs from traditional OCT as it doesn't involve the modulation of a reference signal; instead, it relies solely on movements within the sample to induce signal modulation. Specifically, dOCT captures a time-dependent interferometric back-scattered signal superimposed on a static (stationary) signal. Apelian et al. [17] utilized standard deviation (STD) to generate dynamic images. By repetitively imaging the same spot over time, time-series images are acquired for analysis. They employed a D-FFOCT system for imaging, represented by the equation:

\begin{equation}\label{equ1}
I(x,y,z)=I_0(x,y,z)+\alpha(x,y,z)\cos \phi(x,y,z)
\end{equation}

Where:

  • \(I\): Intensity received on the camera
  • \(x, y, z\): Spatial coordinates
  • \(I_{0}\): Originating from the reference signal and stationary back-scattered light inside and outside the coherence gate
  • \(\alpha\): Amplitude of the signal
  • \(\phi\): Phase of the back-scattered signal as it interferes with the reference signal.

When there's relative (three-dimensional) motion among scatterers, such as the Brownian motion of subcellular structures, the phase can be split into a combination of a global and a relative component:

\begin{equation}\label{equ2}
\phi(t)=\frac{2 \pi (\Delta(t)+\delta(t))}{\lambda}
\end{equation}

Here, \(\Delta(t)\) signifies the overall displacement of scatterers along the optical axis, and \(\delta(t)\) indicates the effective distance corresponding to phase changes introduced by the relative displacements among scatterers.

If the fluctuations of \(\delta(t)\) occur rapidly compared to the capture time \(T\) of the camera, and if \(\Delta(t)\) changes gradually compared to \(T\), then the recorded value of \(\delta(t)\) on the camera will be insignificant compared to \(\Delta(t)\), and the global motion will be predominant.

Data processing entails computing the standard deviation (STD) of the signal over time to diminish signals originating from stationary structures while accentuating dynamic scatterers. Although weakly scattering structures like cells exhibit substantially lower signal amplitudes compared to strongly scattering structures, dOCT can unveil the most dynamic components within the sample.

\begin{equation}\label{equ3}
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \left( I(x, y, t_i) - \langle I(x, y) \rangle \right)^2}
\end{equation}

 

The signal's characteristics may be influenced by both axial \((z)\) and transverse \((x, y)\) sensitivity to displacement. Axially, minimal motion corresponds to a transition from the cosine function's minimum to its maximum, with this sensitivity being more pronounced than in the \(x\) and \(y\) directions.

The processed data employing the logarithm of intensity and the standard derivation of intensities. The procedure is defined as:

\begin{equation}\label{equ4}
I_{dB}(x, z, t_i) \equiv 10 \log I(x, z, t_i) = 10 \log I_D(x, z, t_i) + 10 \log I_S(x, z)
\end{equation}

Where the logarithm base is 10, the Logarithmic Intensity Variance (LIV) is calculated as the time variance of \(I_{dB}\):

\begin{equation}\label{equ5}
LIV(x, z, t_i) = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} [I_{dB}(x, y, t_i) - \langle I_{dB}(x, y) \rangle_{t_i} ]^2}
\end{equation}
​

Here, \(<>\) denotes the average over \(t_i\)​.

As per the equation, the LIV exclusively responds to the dynamic portion of the OCT signal, remaining unaffected by the magnitude of the static component. Notably, the LIV solely detects changes in the magnitude of the OCT signal and does not respond to the temporal rate or speed of the dynamics.

\begin{equation}\label{equ}
\varepsilon(r,z,\tau)=\varepsilon_0(z)-\frac{r^2}{r_0^2}\varepsilon_r-\frac{\tau^2}{\tau_0^2}\varepsilon_\tau,
\end{equation}