Fourier phase based depth-resolved nanoscale nuclear architecture mapping for cancer detection

Abstract

Quantitative phase imaging (QPI) modality has been widely adopted in a variety of applications ranging from identifying photomask defects in lithography to characterizing cell structure and tissue morphology in cancer. Traditional QPI utilizes the electromagnetic phase of transmitted light to measure, with nanometer scale sensitivity, alterations in the optical thickness of a sample of interest. In our work, the QPI paradigm is generalized to study depth-resolved properties of phase objects with slowly varying refractive index without a strong interface by utilizing the Fourier phase associated with Fourier-domain optical coherence tomography (FD-OCT). Specifically, based on computing the Fourier phase of light back-scattered by cell nuclei, we have developed nanoscale nuclear architecture mapping (nanoNAM) method that quantifies, with nanoscale sensitivity, (a) the depth-resolved alterations in mean nuclear optical density, and (b) depth-resolved localized heterogeneity in optical density of the cell nuclei. We have used nanoNAM to detect malignant transformation in colon carcinogenesis, even in tissue that appears histologically normal according to pathologists, thereby showing its potential as a pathology aid in cases where pathology examination remains inconclusive, and for screening patient populations at risk of developing cancer. In this paper, we integrate all aspects of nanoNAM, from principle through instrumentation and analysis, to show that nanoNAM is a promising, low-cost, and label-free method for identifying pathologically indeterminate pre-cancerous and cancerous cells. Importantly, it can seamlessly integrate into the clinical pipeline by utilizing clinically prepared formalin-fixed, paraffin-embedded tissue sections.

Figure 1

The schema of the FFPE tissue section on the glass slide in nanoNAM.

Figure 2

Model 1: Incremental alterations in mean refractive index for a fixed s = 50 × 10⁶m⁻¹. (A) Simple refractive index profiles with increments of 0.001 in Δn (B) Simulated spectral interference signals. (C) Amplitude of the Fourier transform of the spectral interference signals. (D) Phase of the Fourier transform of the spectral interference signals. (E) drOPD profiles corresponding to the nanoNAM-associated Fourier phase.

Figure 3

Model 2: Incremental alterations in rate-of-change of refractive index for a fixed Δn = 0.001. (A) Simple refractive index profiles with increments of 40 × 10⁶m⁻¹ in s (B) Simulated spectral interference signals. (C) Amplitude of the Fourier transform of the spectral interference signals. (D) Phase of the Fourier transform of the spectral interference signals. (E) drOPD profiles corresponding to the nanoNAM-associated Fourier phase.

Figure 4

Two sets (red and blue) of refractive index model parameters (A) Δn_i, and (B) s_i for modeling their joint effect on refractive index heterogeneity are shown. The two sets for both parameters are plotted as a function of the depth at which they alter the refractive index profile generated using Eq. (7). The heterogeneity is modeled around the physical depth of 4.5 μm.

Figure 5

Model 3: Simulating heterogeneity in refractive index via Eq. (7). The model parameters are shown in Fig. 4. (A) Heterogeneity refractive index models for the two sets of parameters whose average values are shown in the figure legend. (B) Simulated spectral interference signals for the two models (C) Amplitude of the Fourier transform of the spectral interference signals. (D) Phase of the Fourier transform of the spectral interference signals. (E) drOPD profiles corresponding to the nanoNAM-associated Fourier phase.

Figure 6

The schematic of the nanoNAM system. (A) The light path diagram for transmission phase and bright-field imaging. (B) The light path diagram for drOPD mapping. Xe: Xenon lamp; RM: removable mirror; F: field diaphragm; L: lens; BS: beam splitter; OBJ: objective; TL: tube lens; M: mirror; G: transmission grating.

Figure 7

(A) Squared gradient plot versus the axial position of the objective lens at the wavelength of 550 nm. (B) The dependence of the focal-plane shift on the wavelength. Each point was the average value from 20 measurements (orange line), and the error bar indicates standard deviation. Data was then fitted to a fourth-order polynomial (blue line).

Figure 8

Correction for chromatic aberration-induced image distortion. (A) The region of interest on the imaging standard. (B–C) The difference maps between two wavelengths of 510 nm and 674 nm (B) before distortion correction and (C) after distortion correction.

Figure 9

Phase modulation – due to the carrier frequency of the light source – of the Fourier phase associated with the Fourier transform of the spectral interference signal. Ideal phase modulation, given by −2πK_c(z_opl(z)), is depicted in red, while the experimentally-obtained phase modulation is shown in blue. Unwrapped versions of the respective phase modulations are shown.

Figure 10

Demonstration of the depth-resolved capability of drOPD mapping. (A) Bright-field image and (B) transmission quantitative phase map of a 5μm section of HeLa cell block. (C–E) The corresponding drOPD maps of the 5μm section at the optical depth (z_opl) of (C) 1μm, (D) 2μm and (E) 5μm. The dashed lines from the insets illustrate the location of the optical depth with respect to the sample where the thicker bottom layer indicates the glass slide that faces the incoming light. The pseudo color shown in (B) is the integrated optical path length along the axial direction and those in (C–E) are drOPD value. The colorbar represents values in nanometer.

Figure 11

Image registration based on the transmission phase (OPL) images of unstained and H&E-stained tissue. The transmission phase (OPL) images of (A) unstained and (B) stained tissue, as well as (C–D) the overlaid transmission phase images (gray: unstained tissue; green: H&E-stained tissue) (C) before and (D) after image registration.

Figure 12

Reproducibility of mean-drOPD value at a single-nucleus level for ~150 cell nuclei. For each column, the box plot shows the variation of drOPD value for the pairwise difference of the same sample with two different acquisition times (20 ms, 50 ms and 100 ms). The red line indicates 1 nm. The average variation of the single-nucleus mean-drOPD is below 1 nm (red line), as shown in the dark line on each box plot.

Figure 13

Nuclear architecture maps obtained from the three imaging modalities of our optical microscopy system: (A) Bright-field image of an H&E-stained colon tissue, corresponding (B) transmission quantitative phase image and (C) depth-averaged (over the range of range of 1.35 to 3.15μm at a step size of 0.045μm) drOPD maps from an unstained colon tissue section. (D–F) The zoom-in regions of the red boxes in (A–C). (F) The drOPD map at 3 optical depths (central localization z_OPL = 1.35μm, 2.25 μm and 3.15μm) from the unstained colon tissue. The scale bar shows drOPD value in nanometers.

Figure 14

Cancer risk assessment of UC patients: Bright-field image of stained H&E tissue section (from the initial tissue biopsy) from a (A) low-risk UC patient, and (C) a high-risk UC patient. drOPD maps for the same (B) low-risk and (D) high-risk UC patients computed from the same tissue sections as those used for bright-field imaging before staining.

Figure 15

nanoNAM based assessment and quantification of low- and high-risk UC patients. (a) Box plot of cell-level mean drOPD values for each patient. (b) Box plot of patient-level drOPD value for each patient. (c) Probability distribution of cell-level mean drOPD values from all patients in the low-risk and high-risk groups.