Deep Learning of Morphologic Correlations To Accurately Classify CD4+ and CD8+ T Cells by Diffraction Imaging Flow Cytometry.

The two major subtypes of human T cells, CD4+ and CD8+, play important roles in adaptive immune response by their diverse functions. To understand the structure-function relation at the single cell level, we isolated 2483 CD4+ and 2450 CD8+ T cells from fresh human splenocytes by immunofluorescent sorting and investigated their morphologic relations to the surface CD markers by acquisition and analysis of cross-polarized diffraction image (p-DI) pairs. A deep neural network of DINet-R has been built to extract 2560 features across multiple pixel scales of a p-DI pair per imaged cell. We have developed a novel algorithm to form a matrix of Pearson correlation coefficients by these features for selection of a support cell set with strong morphologic correlation in each subtype. The p-DI pairs of support cells exhibit significant pattern differences between the two subtypes defined by CD markers. To explore the relation between p-DI features and CD markers, we divided each subtype into two groups of A and B using the two support cell sets. The A groups comprise 90.2% of the imaged T cells and classification of them by DINet-R yields an accuracy of 97.3 ± 0.40% between the two subtypes. Analysis of depolarization ratios further reveals the significant differences in molecular polarizability between the two subtypes. These results prove the existence of a strong structure-function relation for the two major T cell subtypes and demonstrate the potential of diffraction imaging flow cytometry for accurate and label-free classification of T cell subtypes.

Realistic optical cell modeling and diffraction imaging simulation for study of optical and morphological parameters of nucleus.

Coherent light scattering presents complex spatial patterns that depend on morphological and molecular features of biological cells. We present a numerical approach to establish realistic optical cell models for generating virtual cells and accurate simulation of diffraction images that are comparable to measured data of prostate cells. With a contourlet transform algorithm, it has been shown that the simulated images and extracted parameters can be used to distinguish virtual cells of different nuclear volumes and refractive indices against the orientation variation. These results demonstrate significance of the new approach for development of rapid cell assay methods through diffraction imaging.

Spectrophotometric determination of turbid optical parameters without using an integrating sphere.

Spectrophotometric quantification of turbidity by multiple optical parameters has wide-ranging applications in material analysis and life sciences. A robust system design needs to combine hardware for precise measurement of light signals with software to accurately model measurement configuration and rapidly solve a sequence of challenging inverse problems. We have developed and validated a design approach and performed system validation based on radiative transfer theory for determination of absorption coefficient, scattering coefficient, and anisotropy factor without using an integrating sphere. Accurate and rapid determination of parameters and spectra is achieved for microsphere suspension samples by combining photodiode-based measurement of four signals with the Monte Carlo simulation and perturbation-based inverse calculations. The three parameters of microsphere suspension samples have been determined from the measured signals as functions of wavelength from 400 to 800 nm and agree with calculated results based on the Mie theory. It has been shown that the inverse problems in the cases of microsphere suspension samples are well posed with convex cost functions to yield unique solutions, and it takes about 1 min to obtain the three parameters per wavelength.

Acquisition of cross-polarized diffraction images and study of blurring effect by one time-delay-integration camera.

Blurred diffraction images acquired from flowing particles affect the measurement of fringe patterns and subsequent analysis. An imaging unit with one time-delay-integration (TDI) camera has been developed to acquire two cross-polarized diffraction images. It was shown that selected elements of Mueller matrix of single scatters can be imaged with pixel matching precision in this configuration. With the TDI camera, the effect of blurring on imaging of scattered light propagating along the side directions was found to be much more significant for biological cells than microspheres. Despite blurring, classification of MCF-7 and K562 cells is feasible since the effect has similar influence on extracted image parameters. Furthermore, image blurring can be useful for analysis of the correlations among texture parameters for characterization of diffraction images from single cells. The results demonstrate that with one TDI camera the polarization diffraction imaging flow cytometry can be significantly improved and angular distribution of selected Mueller matrix elements can be accurately measured for rapid and morphology-based assay of particles and cells without fluorescent labeling.

Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer.

Label-free and rapid classification of cells can have awide range of applications in biology. We report a robust method of polarization diffraction imaging flow cytometry (p-DIFC) for achieving this goal. Coherently scattered light signals are acquired from single cells excited by a polarized laser beam in the form of two cross-polarized diffraction images. Image texture and intensity parameters are extracted with a gray level co-occurrence matrix (GLCM) algorithm to obtain an optimized set of feature parameters as the morphological "fingerprints" for automated cell classification. We selected the Jurkat T cells and Ramos B cells to test the p-DIFC method's capacity for cell classification. After detailed statistical analysis, we found that the optimized feature vectors yield accuracies of classification between the Jurkat and Ramos ranging from 97.8% to 100% among different cell data sets. Confocal imaging and three-dimensional reconstruction were applied to gain insights on the ability of p-DIFC method for classifying the two cell lines of highly similar morphology. Based on these results we conclude that the p-DIFC method has the capacity to discriminate cells of high similarity in their morphology with "fingerprints" features extracted from the diffraction images, which may be attributed to subtle but statistically significant differences in the nucleus-to-cell volume ratio in the case of Jurkat and Ramos cells.

Analysis of diffraction imaging in non-conjugate configurations.

Diffraction imaging of scattered light allows extraction of information on scatterer's morphology. We present a method for accurate simulation of diffraction imaging of single particles by combining rigorous light scattering model with ray-tracing software. The new method has been validated by comparison to measured images of single microspheres. Dependence of fringe patterns on translation of an objective based imager to off-focus positions has been analyzed to clearly understand diffraction imaging with multiple optical elements. The calculated and measured results establish unambiguously that diffraction imaging should be pursued in non-conjugate configurations to ensure accurate sampling of coherent light distribution from the scatterer.

Rapid inverse radiative transfer solver for multiparameter spectrophotometry without integrating sphere.

Significance: Multiparameter spectrophotometry (MPS) provides a powerful tool for accurate characterization of turbid materials in applications such as analysis of material compositions, assay of biological tissues for clinical diagnosis and food safety monitoring. Aim: This work is aimed at development and validation of a rapid inverse solver based on a particle swarm optimization (PSO) algorithm to retrieve the radiative transfer (RT) parameters of absorption coefficient, scattering coefficient and anisotropy factor of a turbid sample. Approach: Monte Carlo (MC) simulations were performed to obtain calculated signals for comparison to the measured ones of diffuse reflectance, diffuse transmittance and forward transmittance. An objective function has been derived and combined with the PSO algorithm to iterate MC simulations for MPS. Results: We have shown that the objective function can significantly reduce the variance in calculated signals by local averaging of an inverse squared error sum function between measured and calculated signals in RT parameter space. For validation of the new objective function for PSO based inverse solver, the RT parameters of 20% Intralipid solutions have been determined from 520 to 1000 nm which took about 2.7 minutes on average to complete signal measurement and inverse calculation per wavelength. Conclusion: The rapid solver enables MPS to be translated into easy-to-use and cost-effective instruments without integrating sphere for material characterization by separating and revealing compositional profiles at the molecular and particulate scales.

Study of low speed flow cytometry for diffraction imaging with different chamber and nozzle designs.

Achieving effective hydrodynamic focusing and flow stability at low speed presents a challenging design task in flow cytometry for studying phenomena such as cell adhesion and diffraction imaging of cells with low-cost cameras. We have developed different designs of flow chamber and sheath nozzle to accomplish the above goal. A 3D computational model of the chambers has been established to simulate the fluid dynamics in different chamber designs and measurements have been performed to determine the velocity and size distributions of the core fluid from the nozzle. Comparison of the simulation data with experimental results shows good agreement. With the computational model significant insights were gained for optimization of the chamber design and improvement of the cell positioning accuracy for study of slow moving cells. The benefit of low flow speed has been demonstrated also by reduced blurring in the diffraction images of single cells. Based on these results, we concluded that the new designs of chamber and sheath nozzle produce stable hydrodynamic focusing of the core fluid at low speed and allow detailed study of cellular morphology under various rheological conditions using the diffraction imaging method.

Analysis of cellular objects through diffraction images acquired by flow cytometry.

It was found that the diffraction images acquired along the side scattering directions with objects in a cell sample contain pattern variations at both the global and local scales. We show here that the global pattern variation is associated with the categorical size and morphological heterogeneity of the imaged objects. An automated image processing method has been developed to separate the acquired diffraction images into three types of global patterns. Combined with previously developed method for quantifying local texture pattern variations, the new method allows fully automated analysis of diffraction images for rapid and label-free classification of cells according to their 3D morphology.

Fast method for inverse determination of optical parameters from two measured signals.

Solving inverse problems requires multiple forward calculations of measured signals. We present a fast method combining graphic processing unit-accelerated Monte Carlo simulations of individual photons and a new perturbation scheme for a 300-fold speedup in comparison to conventional CPU-based approaches. The method allows rapid calculations of the diffuse reflectance and transmittance signals from a turbid sample of absorption coefficient µ(a), scattering coefficient µ(s), and anisotropy factor g based on the principle of correlated sampling. To demonstrate its strong utility, we have applied the method for determining the optical parameters of diluted intralipid samples with satisfactory results.

A novel method of diffraction imaging flow cytometry for sizing microspheres.

We report a novel method of diffraction imaging flow cytometry to measure and analyze size distribution of microspheres. An automated and robust image processing software based on the short-time-Fourier-transform algorithm has been developed to analyze the characteristic and spatially varying oscillations of side scatters recorded as a diffraction image. Our results demonstrate that the new method allows accurate and rapid determination of single microspheres' diameters ranging from 1 to 100 µm. The capacity for analysis of light scattering by two-sphere aggregates has been demonstrated but analytical tools for characterization of aggregates by multiple microspheres remain to be developed.

Deep learning of diffraction image patterns for accurate classification of five cell types.

Development of label-free methods for accurate classification of cells with high throughput can yield powerful tools for biological research and clinical applications. We have developed a deep neural network of DINet for extracting features from cross-polarized diffraction image (p-DI) pairs on multiple pixel scales to accurately classify cells in five types. A total of 6185 cells were measured by a polarization diffraction imaging flow cytometry (p-DIFC) method followed by cell classification with DINet on p-DI data. The averaged value and SD of classification accuracy were found to be 98.9% ± 1.00% on test data sets for 5-fold training and test. The invariance of DINet to image translation, rotation, and blurring has been verified with an expanded p-DI data set. To study feature-based classification by DINet, two sets of correctly and incorrectly classified cells were selected and compared for each of two prostate cell types. It has been found that the signature features of large dissimilarities between p-DI data of correctly and incorrectly classified cell sets increase markedly from convolutional layers 1 and 2 to layers 3 and 4. These results clearly demonstrate the importance of high-order correlations extracted at the deep layers for accurate cell classification.

Machine learning of diffraction image patterns for accurate classification of cells modeled with different nuclear sizes.

Measurement of nuclear-to-cytoplasm (N:C) ratios plays an important role in detection of atypical and tumor cells. Yet, current clinical methods rely heavily on immunofluroescent staining and manual reading. To achieve the goal of rapid and label-free cell classification, realistic optical cell models (OCMs) have been developed for simulation of diffraction imaging by single cells. A total of 1892 OCMs were obtained with varied nuclear volumes and orientations to calculate cross-polarized diffraction image (p-DI) pairs divided into three nuclear size groups of OCMS , OCMO and OCML based on three prostate cell structures. Binary classifications were conducted among the three groups with image parameters extracted by the algorithm of gray-level co-occurrence matrix. The averaged accuracy of support vector machine (SVM) classifier on test dataset of p-DI was found to be 98.8% and 97.5% respectively for binary classifications of OCMS vs OCMO and OCMO vs OCML for the prostate cancer cell structure. The values remain about the same at 98.9% and 97.8% for the smaller prostate normal cell structures. The robust performance of SVM over clustering classifiers suggests that the high-order correlations of diffraction patterns are potentially useful for label-free detection of single cells with large N:C ratios.

Development of a diffraction imaging flow cytometer.

Diffraction images record angle-resolved distribution of scattered light from a particle excited by coherent light and can correlate highly with the 3D morphology of a particle. We present a jet-in-fluid design of flow chamber for acquisition of clear diffraction images in a laminar flow. Diffraction images of polystyrene spheres of different diameters were acquired and found to correlate highly with the calculated ones based on the Mie theory. Fast Fourier transform analysis indicated that the measured images can be used to extract sphere diameter values. These results demonstrate the significant potentials of high-throughput diffraction imaging flow cytometry for extracting 3D morphological features of cells.

Development and evaluation of realistic optical cell models for rapid and label-free cell assay by diffraction imaging.

Methods for rapid and label-free cell assay are highly desired in life science. Single-shot diffraction imaging presents strong potentials to achieve this goal as evidenced by past experimental results using methods such as polarization diffraction imaging flow cytometry. We present here a platform of methods toward solving these problems and results of optical cell model (OCM) evaluations by calculations and analysis of cross-polarized diffraction image (p-DI) pairs. Four types of realistic OCMs have been developed with two prostate cell structures and adjustable refractive index (RI) parameters to investigate the effects of cell morphology and index distribution on calculated p-DI pairs. Image patterns have been characterized by a gray-level co-occurrence matrix (GLCM) algorithm and four GLCM parameters and linear depolarization ratio δL have been selected to compare calculated against measured data of prostate cells. Our results show that the irregular shapes of and heterogeneity in RI distributions for organelles play significant roles in the spatial distribution of scattered light by cells in comparison to the average RI values and their differences among the organelles. Discrepancies in GLCM and δL parameters between calculated and measured p-DI data provide useful insight for understanding light scattering by single cells and improving OCM.

Validity of a closed-form diffusion solution in P1 approximation for reflectance imaging with an oblique beam of arbitrary profile.

Determination of optical parameters of turbid media from reflectance image data is an important class of inverse problems due to its potential for noninvasive characterization of materials and biological tissues, which demands rapid modeling tools to generate calculated images. We treat the problem of reflectance imaging with homogeneous semi-infinite turbid media as a boundary-value problem of diffusion type in the P1 approximation to the radiative transfer equation. A closed-form solution has been obtained for an oblique incident beam of arbitrary profile and its accuracy has been examined against a Monte Carlo method and measured data. We find that the diffusion solution provides a sufficiently accurate tool to rapidly calculate reflectance images for samples of large or moderate scattering albedo illuminated by a beam of arbitrary profile as long as the anisotropy factor remains less than 0.7 and single scattering albedo larger than 0.8. The closed-form solution can thus be used as a part of a forward modeling toolbox to determine optical parameters from reflectance image data in combination with other method such as the Monte Carlo simulation.

Quantitative characterization of turbidity by radiative transfer based reflectance imaging.

A new and noncontact approach of multispectral reflectance imaging has been developed to inversely determine the absorption coefficient of µ a , the scattering coefficient of µs and the anisotropy factor g of a turbid target from one measured reflectance image. The incident beam was profiled with a diffuse reflectance standard for deriving both measured and calculated reflectance images. A GPU implemented Monte Carlo code was developed to determine the parameters with a conjugate gradient descent algorithm and the existence of unique solutions was shown. We noninvasively determined embedded region thickness in heterogeneous targets and estimated in vivo optical parameters of nevi from 4 patients between 500 and 950nm for melanoma diagnosis to demonstrate the potentials of quantitative reflectance imaging.

Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers.

We compare the discrete dipole approximation (DDA) and the finite difference time domain (FDTD) method for simulating light scattering of spheres in a range of size parameters x up to 80 and refractive indices m up to 2. Using parallel implementations of both methods, we require them to reach a certain accuracy goal for scattering quantities and then compare their performance. We show that relative performance sharply depends on m. The DDA is faster for smaller m, while the FDTD for larger values of m. The break-even point lies at m = 1.4. We also compare the performance of both methods for a few particular biological cells, resulting in the same conclusions as for optically soft spheres.

Angle-resolved Mueller matrix study of light scattering by B-cells at three wavelengths of 442, 633, and 850 nm.

Angle-resolved signals of polarized light scattered by biological cells provide rich information on cell morphology. Quantitative study of these signals can lead to new methods to develop and improve high-throughput instrumentation for cell probing such as scattering-based flow cytometry. We employ a goniometer system with a photoelastic modulation scheme to determine selected Mueller matrix elements of B-cell hydrosol samples. The angular dependence of S(11), S(12), and S(34) is determined from the scattered light signals between 10 and 160 deg at the three wavelengths 442, 633, and 850 nm. A finite-difference, time-domain (FDTD) method and coated-sphere model are used to investigate the effect of nuclear refractive index on the angle-resolved Mueller elements at different wavelengths using the 3-D structures of selected B cells reconstructed from confocal images. With these results, we demonstrate the value of the light-scattering method in obtaining the cell morphology information.

Numerical study of reflectance imaging using a parallel Monte Carlo method.

Reflectance imaging of biological tissues with visible and near-infrared light has the significant potential to provide a noninvasive and safe imaging modality for diagnosis of dysplastic and malignant lesions in the superficial tissue layers. The difficulty in the extraction of optical and structural parameters lies in the lack of efficient methods for accurate modeling of light scattering in biological tissues of turbid nature. We present a parallel Monte Carlo method for accurate and efficient modeling of reflectance images from turbid tissue phantoms. A parallel Monte Carlo code has been developed with the message passing interface and evaluated on a computing cluster with 16 processing elements. The code was validated against the solutions of the radiative transfer equation on the bidirectional reflection and transmission functions. With this code we investigated numerically the dependence of reflectance image on the imaging system and phantom parameters. The contrasts of reflectance images were found to be nearly independent of the numerical aperture (NA) of the imaging camera despite the fact that reflectance depends on the NA. This enables efficient simulations of the reflectance images using an NA at 1.00. Using heterogeneous tissue phantoms with an embedded region simulating a lesion, we investigated the correlation between the reflectance image profile or contrast and the phantom parameters. It has been shown that the image contrast approaches 0 when the single-scattering albedos of the two regions in the heterogeneous phantoms become matched. Furthermore, a zone of detection has been demonstrated for determination of the thickness of the embedded region and optical parameters from the reflectance image profile and contrast. Therefore, the utility of the reflectance imaging method with visible and near-infrared light has been firmly established. We conclude from these results that the optical parameters of the embedded region can be determined inversely from reflectance images acquired with full-field illumination at multiple incident angles or multiple wavelengths.