Automated HER2 Scoring in Breast Cancer Images Using Deep Learning and Pyramid Sampling

Human epidermal growth factor receptor 2 (HER2) is a critical protein in cancer cell growth that signifies the aggressiveness of breast cancer (BC) and helps predict its prognosis. Accurate assessment of immunohistochemically (IHC) stained tissue slides for HER2 expression levels is essential for both treatment guidance and understanding of cancer mechanisms. Nevertheless, the traditional workflow of manual examination by board-certified pathologists encounters challenges, including inter- and intra-observer inconsistency and extended turnaround times. Here, we introduce a deep learning-based approach utilizing pyramid sampling for the automated classification of HER2 status in IHC-stained BC tissue images. Our approach analyzes morphological features at various spatial scales, efficiently managing the computational load and facilitating a detailed examination of cellular and larger-scale tissue-level details. This method addresses the tissue heterogeneity of HER2 expression by providing a comprehensive view, leading to a blind testing classification accuracy of 84.70%, on a dataset of 523 core images from tissue microarrays. Our automated system, proving reliable as an adjunct pathology tool, has the potential to enhance diagnostic precision and evaluation speed, and might significantly impact cancer treatment planning.

Virtual birefringence imaging and histological staining of amyloid deposits in label-free tissue using autofluorescence microscopy and deep learning

Systemic amyloidosis is a group of diseases characterized by the deposition of misfolded proteins in various organs and tissues, leading to progressive organ dysfunction and failure. Congo red stain is the gold standard chemical stain for the visualization of amyloid deposits in tissue sections, as it forms complexes with the misfolded proteins and shows a birefringence pattern under polarized light microscopy. However, Congo red staining is tedious and costly to perform, and prone to false diagnoses due to variations in the amount of amyloid, staining quality and expert interpretation through manual examination of tissue under a polarization microscope. Here, we report the first demonstration of virtual birefringence imaging and virtual Congo red staining of label-free human tissue to show that a single trained neural network can rapidly transform autofluorescence images of label-free tissue sections into brightfield and polarized light microscopy equivalent images, matching the histochemically stained versions of the same samples. We demonstrate the efficacy of our method with blind testing and pathologist evaluations on cardiac tissue where the virtually stained images agreed well with the histochemically stained ground truth images. Our virtually stained polarization and brightfield images highlight amyloid birefringence patterns in a consistent, reproducible manner while mitigating diagnostic challenges due to variations in the quality of chemical staining and manual imaging processes as part of the clinical workflow.

Multiplexed all-optical permutation operations using a reconfigurable diffractive optical network

Large-scale and high-dimensional permutation operations are important for various applications in e.g., telecommunications and encryption. Here, we demonstrate the use of all-optical diffractive computing to execute a set of high-dimensional permutation operations between an input and output field-of-view through layer rotations in a diffractive optical network. In this reconfigurable multiplexed material designed by deep learning, every diffractive layer has four orientations: 0, 90, 180, and 270 degrees. Each unique combination of these rotatable layers represents a distinct rotation state of the diffractive design tailored for a specific permutation operation. Therefore, a K-layer rotatable diffractive material is capable of all-optically performing up to 4^K independent permutation operations. The original input information can be decrypted by applying the specific inverse permutation matrix to output patterns, while applying other inverse operations will lead to loss of information. We demonstrated the feasibility of this reconfigurable multiplexed diffractive design by approximating 256 randomly selected permutation matrices using K=4 rotatable diffractive layers. We also experimentally validated this reconfigurable diffractive network using terahertz radiation and 3D-printed diffractive layers, providing a decent match to our numerical results. The presented rotation-multiplexed diffractive processor design is particularly useful due to its mechanical reconfigurability, offering multifunctional representation through a single fabrication process.

Subwavelength Imaging using a Solid-Immersion Diffractive Optical Processor

Phase imaging is widely used in biomedical imaging, sensing, and material characterization, among other fields. However, direct imaging of phase objects with subwavelength resolution remains a challenge. Here, we demonstrate subwavelength imaging of phase and amplitude objects based on all-optical diffractive encoding and decoding. To resolve subwavelength features of an object, the diffractive imager uses a thin, high-index solid-immersion layer to transmit high-frequency information of the object to a spatially-optimized diffractive encoder, which converts/encodes high-frequency information of the input into low-frequency spatial modes for transmission through air. The subsequent diffractive decoder layers (in air) are jointly designed with the encoder using deep-learning-based optimization, and communicate with the encoder layer to create magnified images of input objects at its output, revealing subwavelength features that would otherwise be washed away due to diffraction limit. We demonstrate that this all-optical collaboration between a diffractive solid-immersion encoder and the following decoder layers in air can resolve subwavelength phase and amplitude features of input objects in a highly compact design. To experimentally demonstrate its proof-of-concept, we used terahertz radiation and developed a fabrication method for creating monolithic multi-layer diffractive processors. Through these monolithically fabricated diffractive encoder-decoder pairs, we demonstrated phase-to-intensity transformations and all-optically reconstructed subwavelength phase features of input objects by directly transforming them into magnified intensity features at the output. This solid-immersion-based diffractive imager, with its compact and cost-effective design, can find wide-ranging applications in bioimaging, endoscopy, sensing and materials characterization.

Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

As an optical processor, a Diffractive Deep Neural Network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through thin optical layers. With sufficient degrees-of-freedom, D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light. Similarly, D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination; however, under spatially incoherent light, these transformations are non-negative, acting on diffraction-limited optical intensity patterns at the input field-of-view (FOV). Here, we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light. Through simulations, we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products, a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination. The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors.

Pyramid diffractive optical networks for unidirectional magnification and demagnification

Diffractive deep neural networks (D2NNs) are composed of successive transmissive layers optimized using supervised deep learning to all-optically implement various computational tasks between an input and output field-of-view (FOV). Here, we present a pyramid-structured diffractive optical network design (which we term P-D2NN), optimized specifically for unidirectional image magnification and demagnification. In this P-D2NN design, the diffractive layers are pyramidally scaled in alignment with the direction of the image magnification or demagnification. Our analyses revealed the efficacy of this P-D2NN design in unidirectional image magnification and demagnification tasks, producing high-fidelity magnified or demagnified images in only one direction, while inhibiting the image formation in the opposite direction - confirming the desired unidirectional imaging operation. Compared to the conventional D2NN designs with uniform-sized successive diffractive layers, P-D2NN design achieves similar performance in unidirectional magnification tasks using only half of the diffractive degrees of freedom within the optical processor volume. Furthermore, it maintains its unidirectional image magnification/demagnification functionality across a large band of illumination wavelengths despite being trained with a single illumination wavelength. With this pyramidal architecture, we also designed a wavelength-multiplexed diffractive network, where a unidirectional magnifier and a unidirectional demagnifier operate simultaneously in opposite directions, at two distinct illumination wavelengths. The efficacy of the P-D2NN architecture was also validated experimentally using monochromatic terahertz illumination, successfully matching our numerical simulations. P-D2NN offers a physics-inspired strategy for designing task-specific visual processors.

Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors

Under spatially-coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number (N) of optimizable phase-only diffractive features is greater than or equal to ~2 Ni x No, where Ni and No refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially-incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially-incoherent monochromatic light, the spatially-varying intensity point spread functon(H) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H(m,n;m',n')=|h(m,n;m',n')|^2, where h is the spatially-coherent point-spread function of the same diffractive network, and (m,n) and (m',n') define the coordinates of the output and input FOVs, respectively. Using deep learning, supervised through examples of input-output profiles, we numerically demonstrate that a spatially-incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N is greater than or equal to ~2 Ni x No. These results constitute the first demonstration of universal linear intensity transformations performed on an input FOV under spatially-incoherent illumination and will be useful for designing all-optical visual processors that can work with incoherent, natural light.

Data class-specific all-optical transformations and encryption

Diffractive optical networks provide rich opportunities for visual computing tasks since the spatial information of a scene can be directly accessed by a diffractive processor without requiring any digital pre-processing steps. Here we present data class-specific transformations all-optically performed between the input and output fields-of-view (FOVs) of a diffractive network. The visual information of the objects is encoded into the amplitude (A), phase (P), or intensity (I) of the optical field at the input, which is all-optically processed by a data class-specific diffractive network. At the output, an image sensor-array directly measures the transformed patterns, all-optically encrypted using the transformation matrices pre-assigned to different data classes, i.e., a separate matrix for each data class. The original input images can be recovered by applying the correct decryption key (the inverse transformation) corresponding to the matching data class, while applying any other key will lead to loss of information. The class-specificity of these all-optical diffractive transformations creates opportunities where different keys can be distributed to different users; each user can only decode the acquired images of only one data class, serving multiple users in an all-optically encrypted manner. We numerically demonstrated all-optical class-specific transformations covering A-->A, I-->I, and P-->I transformations using various image datasets. We also experimentally validated the feasibility of this framework by fabricating a class-specific I-->I transformation diffractive network using two-photon polymerization and successfully tested it at 1550 nm wavelength. Data class-specific all-optical transformations provide a fast and energy-efficient method for image and data encryption, enhancing data security and privacy.

Deep Learning-enabled Virtual Histological Staining of Biological Samples

Histological staining is the gold standard for tissue examination in clinical pathology and life-science research, which visualizes the tissue and cellular structures using chromatic dyes or fluorescence labels to aid the microscopic assessment of tissue. However, the current histological staining workflow requires tedious sample preparation steps, specialized laboratory infrastructure, and trained histotechnologists, making it expensive, time-consuming, and not accessible in resource-limited settings. Deep learning techniques created new opportunities to revolutionize staining methods by digitally generating histological stains using trained neural networks, providing rapid, cost-effective, and accurate alternatives to standard chemical staining methods. These techniques, broadly referred to as virtual staining, were extensively explored by multiple research groups and demonstrated to be successful in generating various types of histological stains from label-free microscopic images of unstained samples; similar approaches were also used for transforming images of an already stained tissue sample into another type of stain, performing virtual stain-to-stain transformations. In this Review, we provide a comprehensive overview of the recent research advances in deep learning-enabled virtual histological staining techniques. The basic concepts and the typical workflow of virtual staining are introduced, followed by a discussion of representative works and their technical innovations. We also share our perspectives on the future of this emerging field, aiming to inspire readers from diverse scientific fields to further expand the scope of deep learning-enabled virtual histological staining techniques and their applications.

Virtual stain transfer in histology via cascaded deep neural networks

Pathological diagnosis relies on the visual inspection of histologically stained thin tissue specimens, where different types of stains are applied to bring contrast to and highlight various desired histological features. However, the destructive histochemical staining procedures are usually irreversible, making it very difficult to obtain multiple stains on the same tissue section. Here, we demonstrate a virtual stain transfer framework via a cascaded deep neural network (C-DNN) to digitally transform hematoxylin and eosin (H&E) stained tissue images into other types of histological stains. Unlike a single neural network structure which only takes one stain type as input to digitally output images of another stain type, C-DNN first uses virtual staining to transform autofluorescence microscopy images into H&E and then performs stain transfer from H&E to the domain of the other stain in a cascaded manner. This cascaded structure in the training phase allows the model to directly exploit histochemically stained image data on both H&E and the target special stain of interest. This advantage alleviates the challenge of paired data acquisition and improves the image quality and color accuracy of the virtual stain transfer from H&E to another stain. We validated the superior performance of this C-DNN approach using kidney needle core biopsy tissue sections and successfully transferred the H&E-stained tissue images into virtual PAS (periodic acid-Schiff) stain. This method provides high-quality virtual images of special stains using existing, histochemically stained slides and creates new opportunities in digital pathology by performing highly accurate stain-to-stain transformations.