Can OCT be sensitive to nanoscale structural alterations in biological tissue?

Exploration of nanoscale tissue structures is crucial in understanding biological processes. Although novel optical microscopy methods have been developed to probe cellular features beyond the diffraction limit, nanometer-scale quantification remains still inaccessible for in situ tissue. Here we demonstrate that, without actually resolving specific geometrical feature, OCT can be sensitive to tissue structural properties at the nanometer length scale. The statistical mass-density distribution in tissue is quantified by its autocorrelation function modeled by the Whittle-Matern functional family. By measuring the wavelength-dependent backscattering coefficient µb(λ) and the scattering coefficient µs, we introduce a technique called inverse spectroscopic OCT (ISOCT) to quantify the mass-density correlation function. We find that the length scale of sensitivity of ISOCT ranges from ~30 to ~450 nm. Although these sub-diffractional length scales are below the spatial resolution of OCT and therefore not resolvable, they are nonetheless detectable. The sub-diffractional sensitivity is validated by 1) numerical simulations; 2) tissue phantom studies; and 3) ex vivo colon tissue measurements cross-validated by scanning electron microscopy (SEM). Finally, the 3D imaging capability of ISOCT is demonstrated with ex vivo rat buccal and human colon samples.

Computation of tightly-focused laser beams in the FDTD method.

We demonstrate how a tightly-focused coherent TEMmn laser beam can be computed in the finite-difference time-domain (FDTD) method. The electromagnetic field around the focus is decomposed into a plane-wave spectrum, and approximated by a finite number of plane waves injected into the FDTD grid using the total-field/scattered-field (TF/SF) method. We provide an error analysis, and guidelines for the discrete approximation. We analyze the scattering of the beam from layered spaces and individual scatterers. The described method should be useful for the simulation of confocal microscopy and optical data storage. An implementation of the method can be found in our free and open source FDTD software ("Angora").

Open source software for electric field Monte Carlo simulation of coherent backscattering in biological media containing birefringence.

ABSTRACT. We present an open source electric field tracking Monte Carlo program to model backscattering in biological media containing birefringence, with computation of the coherent backscattering phenomenon as an example. These simulations enable the modeling of tissue scattering as a statistically homogeneous continuous random media under the Whittle-Matérn model, which includes the Henyey-Greenstein phase function as a special case, or as a composition of discrete spherical scatterers under Mie theory. The calculation of the amplitude scattering matrix for the above two cases as well as the implementation of birefringence using the Jones N-matrix formalism is presented. For ease of operator use and data processing, our simulation incorporates a graphical user interface written in MATLAB to interact with the underlying C code. Additionally, an increase in computational speed is achieved through implementation of message passing interface and the semi-analytical approach. Finally, we provide demonstrations of the results of our simulation for purely scattering media and scattering media containing linear birefringence.

Alternate formulation of enhanced backscattering as phase conjugation and diffraction: derivation and experimental observation.

Enhanced backscattering (EBS), also known as weak localization of light, is derived using the Huygens-Fresnel principle and backscattering is generally shown to be the sum of an incoherent baseline and a phase conjugated portion of the incident wave that forms EBS. The phase conjugated portion is truncated by an effective aperture described by the probability function P(s) of coherent path-pair separations. P(s) is determined by the scattering properties of the medium and so characterization of EBS can be used for metrology of scattering materials. A three dimensional intensity peak is predicted in free space at a point conjugate to the source and is experimentally observed.

Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method.

Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially coherent and unpolarized illumination. The scattering of light from the sample is calculated using the finite-difference time-domain (FDTD) numerical method. Geometrical optics principles are applied to the scattered light to obtain the intensity distribution at the image plane. Multilayered object spaces are also supported by our algorithm. For the first time, numerical FDTD calculations are directly compared to and shown to agree well with broadband experimental microscopy results.

Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media.

A rigorous error analysis is presented for the scattering coefficient of biological random continuous media in the Born (or single-scattering) approximation. The analysis is done in two dimensions (2-D) for simplicity of numerical computation. Scattering coefficients of various tissue-like random media are numerically calculated via statistical finite-difference-time-domain analysis. The results are then checked against analytical formulas for the scattering coefficient in the Born approximation. The validity ranges for the correlation length and the refractive index fluctuation strength of the medium are clearly identified. These 2-D results show promise for future 3-D investigations.

Nonscalar elastic light scattering from continuous random media in the Born approximation.

A three-parameter model based on the Whittle-Matérn correlation family is used to describe continuous random refractive-index fluctuations. The differential scattering cross section is derived from the index correlation function using nonscalar scattering formulas within the Born approximation. Parameters such as scattering coefficient, anisotropy factor, and spectral dependence are derived from the differential scattering cross section for this general class of functions.

Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis.

Existing optical imaging techniques offer us powerful tools to directly visualize the cellular structure at the microscale; however, their capability of nanoscale sensitivity is restricted by the diffraction-limited resolution. We show that the mesoscopic light transport theory analysis of the spectra of partial waves propagating within a weakly disordered medium, such as biological cells [i.e., partial wave spectroscopy (PWS)] quantifies refractive index fluctuations at subdiffractional length scales. We validate this nanoscale sensitivity of PWS using experiments with nanostructured models. We also demonstrate the potential of this technique to detect nanoscale alterations in cells from patients with pancreatic cancer who are otherwise classified as normal by conventional microscopic histopathology.

Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells.

Recently, there has been a major thrust to understand biological processes at the nanoscale. Optical microscopy has been exceedingly useful in imaging cell microarchitecture. Characterization of cell organization at the nanoscale, however, has been stymied by the lack of practical means of cell analysis at these small scales. To address this need, we developed a microscopic spectroscopy technique, single-cell partial-wave spectroscopy (PWS), which provides insights into the statistical properties of the nanoscale architecture of biological cells beyond what conventional microscopy reveals. Coupled with the mesoscopic light transport theory, PWS quantifies the disorder strength of intracellular architecture. As an illustration of the potential of the technique, in the experiments with cell lines and an animal model of colon carcinogenesis we show that increase in the degree of disorder in cell nanoarchitecture parallels genetic events in the early stages of carcinogenesis in otherwise microscopically/histologically normal-appearing cells. These data indicate that this advance in single-cell optics represented by PWS may have significant biomedical applications.

Generation of an incident focused light pulse in FDTD.

A straightforward procedure is described for accurately creating an incident focused light pulse in the 3-D finite-difference time-domain (FDTD) electromagnetic simulation of the image space of an aplanatic converging lens. In this procedure, the focused light pulse is approximated by a finite sum of plane waves, and each plane wave is introduced into the FDTD simulation grid using the total-field/scattered-field (TF/SF) approach. The accuracy of our results is demonstrated by comparison with exact theoretical formulas.