Patent Publication Number: US-8995740-B2

Title: System and method for multiplexed biomarker quantitation using single cell segmentation on sequentially stained tissue

Description:
FIELD 
     Embodiments relate generally to analysis of digital images, and more particularly, to analysis of digital images of biological tissue samples. 
     BACKGROUND 
     In general, the term segmentation refers to the identification of boundaries of biological units, such as cells, within a digital image. These boundaries separate each individual unit from others. The digital image may be obtained using a microscope. Weak or data driven segmentation algorithms may be used to define cell boundaries. For example, a watershed transform is one image processing technique that has been used for segmenting images of cells. With the watershed transform, a digital image may be modeled as a three-dimensional topological surface, where values of pixels (e.g., brightness or grey level) in the image represent geographical heights. 
     Due to variations in the histology of different tissue types, however, weak segmentation algorithms may not produce an accurate segmentation without significant adaptation and optimization to specific tissue type applications. For example, a weak segmentation algorithm may cause the image to be over-segmented (e.g., what appears as a single cell may actually be only a portion of a cell) or under-segmented (e.g., what appears as a single cell may actually be several different cells in combination). Furthermore, the image may not be properly segmented with a weak segmentation algorithm, in part, because a suitable segmentation parameter for one region of the image may not work well in other regions of the same image. Therefore, a weak segmentation algorithm may not be robust enough for segmentation of large numbers of cells having many morphological variations. 
     There has been previous work performed regarding cell analysis (see, e.g., Lindblad et al.,  Image analysis for automatic segmentation of cytoplasms and classification of rac 1  activation , Cytometry A, 57(1):22-33 (2004); Wahlby et al.,  Sequential immunofluorescence staining and image analysis for detection of large numbers of antigens in individual cell nuclei , Cytometry, 47:32-51 (2002); Parvin et al.,  Biosig: An imaging bioinformatics system for phenotypic analysis , IEEE Transactions on Systems, Man and Cybernetics, Part B, 33:814-824 (2003); Mouroutis et al.,  Robust cell nuclei segmentation using statistical modeling , Bioimaging, Vol, 6:79-911998 (1998); Lin et al.,  A hybrid  3 d watershed algorithm incorporating gradient cues and object models for automatic segmentation of nuclei in confocal image stacks ; Cytometry Part A, 56A(1):23-36 (2003); McCullough et al., 3 D segmentation of whole cells and cell nuclei in tissue using dynamic programming , Biomedical Imaging: From Nano to Macro, ISBI 2007, 4th IEEE International Symposium on, pages 276-279 (2007); Wang et al.,  Novel cell segmentation and online SVM for cell cycle phase identification in automated microscopy , Bioinformatcs, Vol. 24, No. 1, pages 94-101 (2008)). 
     For example, Wang et al. proposed a method for cell segmentation and cycle estimation using an individual channel. In general, such method is based on machine learning methods using support vector machines from segmented images. In Lindblad et al., a method for cell segmentation was generally proposed based on nuclei and cytoplasm markers, where each cell has one nucleus. Nuclei segmentation was performed by selecting a global threshold value, and using the watershed algorithm. Once the nuclei regions were segmented, they were used as seed regions to segment the cytoplasm by applying the watershed algorithm. 
     A method for quantification of sequential immunofluorescence staining was proposed in Wahlby et al. This method is generally based on the quantification of the immunofluorescence staining only in the nuclei, where nuclei segmentation is a semi-automatic process, which involves human intervention. In Mouroutis et al., a statistical method for nuclei segmentation was proposed. This method typically includes defining a likelihood function, and to separate touching nuclei as a mixture of Gaussians distributions. 
     In general, different methods have been proposed for cell segmentation in 3D in confocal imaging, and mainly these methods focus in segmenting the cell nuclei. For example, in Lin et al., a method for 3D nuclei segmentation from confocal stacks was proposed, and the approach generally includes three steps. The first step is a pre-processing step, where noise is removed and segmented using global thresholding. The second step typically separates those nuclei which are touching by applying a 3D watershed algorithm using a gradient-weighted distance transform. The third step is a post-processing step, which is typically used as surface breaker. A method for 3D segmentation of whole cells was reported by McCullough et al. This method is designed to segment the nuclei objects in 3D, where cell boundaries are detected. However, there is no segmentation of 3D cells as a unit. 
     Thus, an interest exists for improved systems and methods for analyzing digital images of biological tissue samples. These and other inefficiencies and opportunities for improvement are addressed and/or overcome by the systems, assemblies and methods of the present disclosure. 
     SUMMARY 
     The present disclosure provides advantageous systems and methods for the analysis of digital images. In exemplary embodiments, the present disclosure provides for improved systems and methods for the analysis of digital images of biological tissue samples. 
     The present disclosure provides for a computer-implemented method for performing hierarchical image segmentation analysis of sub-cellular units in biological tissue, the method including accessing image data corresponding to multi-channel multiplexed image of biological tissue sequentially fluorescent stained to manifest expression levels of a plurality of morphological biomarkers in the biological tissue, performing multi-channel image segmentation analysis on the image data based on the biomarker expression levels to identify locations and configurations of one or more cells in the biological tissue, performing multi-channel image segmentation analysis on the image data based on the biomarker expression levels to identify locations and configurations of one or more sub-cellular morphological units within the one or more cells, rendering, on a visual display device, a hierarchical representation of the one or more cells and the one or more sub-cellular morphological units in the one or more cells. 
     The present disclosure provides for a computer system for performing multi-channel hierarchical image segmentation analysis of sub-cellular units in biological tissue, the computer including a visual display device, a processing device, and a storage device. The processing device is configured to access multi-channel image data corresponding to a multiplexed image of biological tissue sequentially fluorescent stained to manifest expression levels of a plurality of morphological biomarkers in the biological tissue, perform multi-channel image segmentation analysis on the image data based on the biomarker expression levels to identify locations and configurations of one or more cells in the biological tissue, and perform image segmentation analysis on the image data based on the biomarker expression levels to identify locations and configurations of one or more sub-cellular morphological units within the one or more cells. The storage device is configured to store the locations and configurations of the one or more sub-cellular morphological units within the one or more cells. 
     The present disclosure provides for a one or more computer-readable media having encoded thereon one or more computer-executable instructions for performing a method for performing multi-channel hierarchical image segmentation analysis of sub-cellular units in biological tissue, the method including accessing image data corresponding to a multiplexed image of biological tissue sequentially fluorescent stained to manifest expression levels of a plurality of morphological biomarkers in the biological tissue, performing multi-channel image segmentation analysis on the image data based on the biomarker expression levels to identify locations and configurations of one or more cells in the biological tissue, performing multi-channel image segmentation analysis on the image data based on the biomarker expression levels to identify locations and configurations of one or more sub-cellular morphological units within the one or more cells, and rendering, on a visual display device, a hierarchical representation of the one or more cells and the one or more sub-cellular morphological units in the one or more cells. 
     In some embodiments, expression levels of a biomarker in the one or more cellular morphological units at cell level can be automatically determined and expression levels of a biomarker in the one or more sub-cellular morphological units at the level of the sub-cellular morphological units can be automatically determined. 
     In some embodiments, a plurality of biological tissue regions can be automatically grouped based on the expression levels of the biomarker in the sub-cellular morphological units. 
     In some embodiments, an analysis to determine a relationship between expression levels of a biomarker in the one or more sub-cellular morphological units and the configurations of the one or more sub-cellular morphological units can be performed. 
     In some embodiments, the one or more sub-cellular morphological units include one or more nuclei, one or more cytoplasms, and/or one or more membranes. 
     In some embodiments, the one or more sub-cellular morphological units include a membrane or a cytoplasm, and the image segmentation analysis can identifies the membrane or cytoplasm by using a probability map to generate a ring-like structure modeling the membrane or the cytoplasm. 
     In some embodiments, representations of expression levels of a biomarker can be rendered on a visual display device in an overlaid manner on the representations of the one or more cells and the one or more sub-cellular morphological units in the one or more cells. 
     In some embodiments, a measure of expression levels of a biomarker can be determined. The measure can be specific to at least one of the one or more sub-cellular morphological units in the one or more cells. The measure of the expression levels of the biomarker can be a mean of the expression levels. 
     In some embodiments, the locations and configurations of the one or more sub-cellular morphological units can be determined by imposing topological constraints within the cells. 
     In some embodiments, the plurality of morphological biomarkers include a plurality of biomarkers representative of a single type of sub-cellular morphological unit. 
     In some embodiments, image segmentation analysis is performed on the image data based on the biomarker expression levels and biomarker morphology to identify at least one tissue-based region of interest and a hierarchical representation of the one or more cells, the one or more sub-cellular morphological units in the one or more cells, and the at least one tissue-based region of interest can be rendered on a visual display device. 
     In some embodiments, the one or more sub-cellular morphological units include at least one of cell membranes of the one or more cells, cytoplasms of the one or more cells, and nuclei of the one or more cells and a hierarchical representation of the one or more cells, the at least one tissue-based region of interest, the at least one of the cell membranes of the one or more cells, the cytoplasms of the one or more cells, and the nuclei of the one or more cells can be rendered on a visual display device. 
     In some embodiments, the at least one tissue-based region of interest includes a collection of stromal cells or a collection of epithelial cells. 
     In some embodiments, shapes of the one or more cells based on the image segmentation analysis identifying the locations and the configurations of the one or more cells can be determined and the one or more cells, sub-cellular units based on the shapes of the one or more cells, or sub-cellular units can be ranked. Each ranking can indicate a probability or similarity that cell boundaries, or sub-cellular units of a corresponding cell or sub-cellular unit are correctly identified by the image segmentation analysis. 
     In some embodiments, a pixel of the image data is associated with a single type of sub-cellular morphological unit is provided in the hierarchical representation. In some embodiments, a pixel of the image data with one or more types of sub-cellular morphological unit is provided in the hierarchical representation. In some embodiments, the pixel of the image data with a first probability that the pixel corresponds to the first type of sub-cellular morphological unit and a second probability that the pixel corresponds to the second type of sub-cellular morphological unit is provided in the hierarchical representation. In some embodiments, the pixel of the image data with a first membership value that the pixel corresponds to the first type of sub-cellular morphological unit and a second membership value that the pixel corresponds to the second type of sub-cellular morphological unit in the hierarchical representation. 
     In some embodiments, one or more segmentation-quality metrics can be determined for the one or more cells. 
     In some embodiments, the one or more segmentation-quality metrics for the one or more cells can be rendered on a visual display device in an overlaid manner over the rendering of the one or more cells. 
     In some embodiments, rendering of the multi-channel hierarchical representation of the one or more cells includes only rendering a subset of cells among the one or more cells having segmentation-quality metrics that satisfy one or more predefined segmentation quality criteria. 
     In some embodiments, multi-channel image segmentation analysis can be performed on the image data based on the biomarker expression levels to identify locations and configurations of one or more tissue-types in the biological tissue. 
     Any combination or permutation of embodiments is envisioned. Additional advantageous features, functions and applications of the disclosed systems, assemblies and methods of the present disclosure will be apparent from the description which follows, particularly when read in conjunction with the appended figures. All references listed in this disclosure are hereby incorporated by reference in their entireties. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Features and aspects of embodiments are described below with reference to the accompanying drawings, in which elements are not necessarily depicted to scale. 
       Exemplary embodiments of the present disclosure are further described with reference to the appended figures. It is to be noted that the various steps, features and combinations of steps/features described below and illustrated in the figures can be arranged and organized differently to result in embodiments which are still within the spirit and scope of the present disclosure. To assist those of ordinary skill in the art in making and using the disclosed systems, assemblies and methods, reference is made to the appended figures, wherein: 
         FIGS. 1A-E  depict images/schematics of multiplexing images and joint segmentation, according to exemplary embodiments of the present disclosure; 
         FIG. 2  is a flow diagram illustrating a segmentation process in accordance with exemplary embodiments of the present disclosure; 
         FIGS. 3A-C  depict images of image flattening according to exemplary embodiments of the present disclosure; 
         FIGS. 4A-B  depict other images of image flattening; 
         FIGS. 5A-C  depict images of individual nuclei, membrane and nuclei and membrane 
         FIGS. 6A-C  depict images of nuclei segmentation only from the nuclei channel; 
         FIGS. 7A-B  depict images of membrane detection according to exemplary embodiments of the present disclosure; 
         FIGS. 8A-E  depict images of hierarchical joint segmentation at the sub-cellular level, according to exemplary embodiments of the present disclosure; 
         FIG. 9  depicts the representation and abstraction of an exemplary tissue architecture at the sub-cellular level as a tree data structure; 
         FIG. 10  is an example of the proposed tissue representation depicted in  FIG. 9 ; 
         FIG. 11  is a diagram showing hardware and software components of an exemplary system capable of performing the processes of the present disclosure; 
         FIG. 12  is an exemplary client-server environment for implementing the systems and methods of the present disclosure; 
         FIGS. 13A-F  depicts images of individual cell analysis from Xenograft datasets; 
         FIGS. 14A-F  depict images of the segmentation results of individual cell analysis in the epithelium; 
         FIGS. 15A-I  depict a comparison of Xenograft images and segmentation result images according to exemplary embodiments of the present disclosure; 
         FIGS. 16A-I  depict another comparison of Xenograft images and segmentation result images according to exemplary embodiments of the present disclosure; 
         FIGS. 17A-C  depict images from a prostrate cancer study according to exemplary embodiments of the present disclosure; 
         FIGS. 18A-B  depict images of biomarker quantifications according to exemplary embodiments of the present disclosure; and 
         FIG. 19  depicts an image showing the biomarker quantification and localization at the sub-cellular level, according to exemplary embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure provides advantageous systems and methods for the analysis of digital images. More particularly, the present disclosure provides for improved systems and methods for the analysis of digital images of biological tissue samples. 
     Previous approaches do not account for tissue analysis, grouping and quantification of tissue sections in terms of sub-cellular compartments (e.g., nuclei, membrane and cytoplasm). Such existing approaches focus in nuclei segmentation using information derived from only one channel. In addition, morphological biomarkers that provide structural descriptors of the tissue architecture at the sub-cellular level have not been used to group, quantify and correlate individual and cell populations to discover complex biomarker networks within cell populations. 
     Exemplary embodiments of the present disclosure provide for: i) segmenting, ii) grouping, and iii) quantifying molecular protein profiles of individual cells in terms of sub-cellular compartments (e.g., nuclei, membrane, and cytoplasm). Exemplary embodiments advantageously perform tissue segmentation at the sub-cellular level to facilitate analyzing, grouping and quantifying protein expression profiles of tissue in tissue sections globally and/or locally. Performing local-global tissue analysis and protein quantification advantageously enables, for example, correlation of spatial and molecular configuration of cells with molecular information of different types of cancer. 
     In exemplary embodiments, joint segmentation of cellular entities and their compartments can be performed based on registered sequentially stained fluorescent images. Exemplary embodiments of the present disclosure can take advantage of contextual information expressed in the sequentially stained images to segment and quantify tissue both globally and locally in terms of sub-cellular compartments e.g., nucleus, membrane and cytoplasm. Exemplary embodiments can: (i) impose topological constraints in a hierarchical structure to correctly segment sub-cellular compartments, (ii) group individual cells according to specific criteria, and/or (iii) quantify groups of cells based on corresponding biomarker protein expression at the sub-cellular level. 
     The following definitions of the present disclosure mathematically formalize an “individual cell” as an entity in terms of:
         Compartments: Each individual cell has a substantially semicircular/elliptical shape and it may be composed by none, any or all of the three regions: nuclei, membrane and cytoplasm, and where each region is a sub-cellular compartment.   Hierarchical relationship: For each sub-cellular compartment, the following hierarchy relationship holds: i) the nuclei is at the center of the cell, and is surrounded by the cytoplasm, and ii) the membrane is the located at the border of the cell and surrounds the cytoplasm.       

     As used herein, the term “morphological unit” refers to different cellular or sub-cellular structures, including, for example, nuclei, cytoplasm, and membrane. 
     As discussed further below, the exemplary systems/methods of the present disclosure include a hierarchical top-down approach to cell segmentation. In one exemplary embodiment of the top-down approach, first, individual single cell boundaries are segmented, and then individual sub-cellular compartments are imposed with topological constraints within the cell, so that hierarchical relationships are valid. 
     In exemplary embodiments, multi-channel segmentation processes can be performed using multiplexed images of biological tissue. In general, a multiplexed image typically consists of “N” number of channels of the same tissue section, where each channel provides a detailed and unique protein expression profile of the tissue of interest, thereby describing, for example, both the morphology and molecular composition of cancer tumors. Thus, local tissue quantification at both the molecular and morphological level is possible by applying image analysis methods to multiplexed imaging in tissue micro-arrays. 
     Some of the problems of individual cell analysis of tissue in multiplexed imaging can include the following challenges associated with individual cell segmentation, grouping and quantification as follows:
         Individual cell segmentation challenges can include: i) finding the association rule that maps every pixel in the multiplexing image to each individual cell, ii) finding the association rule of each pixel within the sub-cellular compartments corresponding to each individual cell (e.g., the association rule of each pixel and the nuclei, membrane and cytoplasm for a given cell), iii) finding a membership function that maps every pixel within the sub-cellular compartments corresponding to each individual cell (e.g., the membership function of each pixel and the nuclei, membrane and cytoplasm for a given cell)   One challenge of cell grouping is association among individual cells according to a given rule. For example, grouping rules can be according to: i) spatial relations (e.g., cells that belong to the epithelium region, or tissue organs), ii) morphological relationships among cells (e.g., cells that are circular versus cells that resemble ellipses), and/or iii) image segmentation quality, where those that are based on inclusion-exclusion rules (e.g., cells for which the membrane is surrounding the complete cell border).   One challenge of individual cell quantification is the measure of the protein expression locally and globally in terms of the sub-cellular compartments. That is, for every pixel, a given value of the protein expression is assigned according to the contextual information of the sub-cellular compartments.       

     Other challenges towards individual cell analysis are the following:
         Variation in cell morphology. Individual cells are three-dimensional objects, and once samples are obtained as serial fluorescent tissue sections, cells are then described by the two-dimensional projection of the cell. Depending on the serial section, individual cells are not regular circular objects, but rather can have elliptical shapes.   Absence of nuclei. Individual cells may not have a nucleus well defined or present at all, given that some tissue samples have a thickness of about 5 mm. In this regard, cells that are not cut correctly by the middle, the two dimensional image may not intersect the cell-nuclei, and still the region can define an individual cell. This is due to orientation of the cut with respect to the cell.   Noise. Image noise can affect the quality of the image at the global and/or local level. In addition, the non-uniform distribution of the fluorescent dyes and the effects of auto-fluorescence of the tissue may produce regions which contain high levels of artifacts.       

     It is noted that one purpose of tissue multiplexing imaging is not to capture the entire bandwidth of the signal (similar to satellite imaging) but rather, to capture substantially all available contextual information with the means of molecular fluorescent probes that label specific cellular compartments or tissue organs (blood vessels, etc.). 
     An example of contextual information is the intracellular spatial relations of sub-cellular compartments, where the nucleus is the cell&#39;s center, the membrane is at the cell&#39;s border, and the cytoplasm is between the membrane and the nuclei. Also, it should be noted that information of additional channels can be integrated. For example, by integrating protein markers that bind to specific tissue types such as blood vessels, this can provide unique and relevant information to group individual cells for tissue architecture analysis. 
     Multiplexed Imaging 
     Given “Z” number of distinct channels, the channels can be grouped as structural and morphological protein markers, so that there are “P” and “M” number of protein and morphological channels, respectively. The original number of “Z” channels can then be expressed as: Z=P+M. The compound image T can be defined as the vector-value function with Z number of channels or features as:
 
 T ( x,y )=[ I   1 ( x,y ), . . . , I   N ( x,y )],( x,y )εΩ.
 
     Then T can be written in terms of the individual channels as:
 
 T=[T   Structural   ;T   Protein   ]=[I   1   , . . . ,I   m   ;I   1   , . . . ,I   n ].
 
     The morphological channels T Structural  consist of three or more different channels that provide structural information of the tissue in terms of: nuclei: T Structural   Nuc , membrane: T Structural   Memb , and cytoplasm: T Structural   Cyt  and they can be written as the vector value function: 
                     T   Structural     =       ⁢     [       T   Structural   Nuclei     ;     T   Structural   Membrane     ;     T   Structural   Cytoplasm       ]                   =       ⁢     [       I   1   N     ,   …   ⁢           ,       I   p   N     ;     I   1   M       ,   …   ⁢           ,       I   q   M     ;     I   1   C       ,     …   ⁢           ⁢     I   r   C         ]       ,               
where p+q+r=m
 
     Similarly, the vector value function T Protein  can be written in terms of the protein channels: T Protein =[I 1 , . . . , I n ]. 
     Multi-Channel Segmentation 
     In exemplary embodiments, g N , g M , g C  are different vector-value functions which map the corresponding nuclei, membrane and cytoplasm channels into a single channel. For example, g N (T Structural   Nuclei ), g M (T Structural   Membrane ), g C (T Structural   Cytoplasm ) are scalar value images and each mapping g i , i={N, M, C} is defined as a flattening function and its purpose is to enhance the morphological structures from different channels. 
     Next, a compartmental channel image T Compartments  is formed, capturing the most relevant structural information within the image, and it can be written as:
 
 T   Compartments   =[g   N ( T   Structural   Nuclei ), g   M ( T   Structural   Membrane ), g   C ( T   Structural   Cytoplasm )]
 
     Note that, g M  enhances the overall membrane from different membrane markers such as: NaKATP, pCad, and Keratin. Similarly g C  enhances the cytoplasm and g N  the nuclei. Then T Compartments  is a three-channel image containing the optimal structural representation of the tissue architecture. 
       FIGS. 1A-E  depict images/schematics of multiplexing images and joint segmentation, according to exemplary embodiments of the present disclosure.  FIG. 1A  depicts a tissue core with different degrees of cancer. In  FIGS. 1B-D , the images corresponding to T Compartments  (derived from the structural markers) and the corresponding ƒ Segmentation  function which maps the corresponding pixels into nuclei, membrane and cytoplasm are shown. In  FIG. 1E , schematics corresponding to different protein markers T Protein  for the same tissue spot is shown. 
     As such,  FIG. 1  presents images of a tissue sample with the corresponding optimal structural T Compartments  and protein markers T Protein . Optimal structural markers T Compartments  are shown in different colors represented by cross-hatching in  FIG. 1  (e.g., orange/red, green and blue), and represent membrane structures  104 , cytoplasm structures  102  and nuclei structures  100 , respectively. Protein markers T Protein  are shown in  FIG. 1E . 
     Individual cell segmentation and quantification is thereby formulated as a multi-channel segmentation problem, where each individual cell is associated with three classes: 1) membrane, 2) cytoplasm, and 3) nuclei (as depicted in  FIG. 1D ). 
     Given the set of cell labels: Cell_Labels:={ln=nuclei, lm=membrane, lc=cytoplasm, lb=background}, the cell segmentation problem can be formulated as finding the function ƒ segmentation  which is defined as:
 
ƒ Segmentation ( T   Compartments ( x,y ))=[ n cell, ln,lm,lc,lb ], and  ln+lm+lc+lb= 1,
 
where ncell is the specific cell number, and liε[0,1], i={n,m,c,b} are the affinity values for the pixel (x, y).
 
     It is noted that this formulation allows assigning each pixel (x, y)εI C  to the unique cell and the specific compartments. One advantageous case of the previous formulation is binary segmentation. In addition, information contained in the different channels T Compartments  is complementary with respect to each other, and it is used by the segmentation function ƒ Segmentation  (T Compartments ). An example of such used is specific cell morphological configuration. 
     Multi-Channel Quantification 
     Quantifying of the protein channels T Protein  given segmentation function ƒ seg  relates to measure the strength of the protein expression not only at the pixel level, but in a sub-cellular level across the identified cells. It is defined by the function ƒ Quantification  as follows:
 
ƒ Quantification (ƒ Segmentation ( T   Compartments ), T   Protein )=[ n cell, q   nuc   ,q   memb   ,q   cyt ],
 
where ƒ Quantification  is a function that maps the values from the protein image T Protein  at the specific cell, and at the sub-cellular compartments defined by ƒ Segmentation . An example of functions for ƒ Quantification  can be the mean, and standard deviation among others. In addition, ƒ Quantification  can represent probability distributions of the protein with respect to a given compartment.
 
     EXAMPLES 
     The present disclosure will be further described with respect to the following examples; however, the scope of the disclosure is not limited thereby. 
     Materials 
     Images were acquired with an Olympus Microscope from: i) a representative dataset of tissue samples with different degrees of prostate cancer, and ii) Xenograft images. Typical Biomarkers of interest include, without limitation: DAPI, CFP3, S6, pS6, DAPI, CFP4, Glu1, pCad, CFP5, pCREB, Ki67, pS6235, CFP6, AF_pCREB, AF_Ki67, CFP7, FOXO3a, NaKATP, CFP8, pAkt, Keratin, CFP9, and pGSK3beta. 
     Structural makers include: T Structural ={DAPI, S6, pCad, NaKATP, Keratin}, while the rest are protein makers T Protein . 
     Method Overview 
     As noted above, the following definitions of the present disclosure mathematically formalize an “individual cell” as an entity in terms of: (i) compartments: each individual cell has a substantially semicircular/elliptical shape and is composed by three regions: nuclei, membrane and cytoplasm, and where each region is a sub-cellular compartment; and (ii) hierarchical relationship: for each sub-cellular compartment, the following hierarchy relationship holds: a) the nuclei is at the center of the cell, and is surrounded by the cytoplasm, and b) the membrane is the located at the border of the cell and surrounds the cytoplasm. The systems/methods of the present disclosure include a hierarchical top-down process ( FIG. 2 ). In the top-down process, first, individual single cell boundaries are segmented, and then individual sub-cellular compartments are imposed with topological constraints within the cell, so that hierarchical relationships are valid. 
       FIG. 2  is a flow diagram illustrating a top-down segmentation process  200  in accordance with exemplary embodiments of the present disclosure. In exemplary embodiments, multiplexed images of biological tissue can be retrieved from memory (e.g., non-transitory computer-readable media). The digital image may be obtained, for example, using a microscope and a camera. The target biological units in the digital image may include, but are not necessarily limited to, cells and/or sub-cellular compartments. Exemplary target cells may include, for example, i) epithelial cells and/or stromal cells, or ii) necrotic cells. The term biological unit, as used herein, refers to discrete biological structures and portions, components or combinations of biological structures in the digital image. 
     In step  202 , a multiplexed digital image of biological tissue is enhanced to integrate information from different protein channels. In step  204 , individual cell segmentation is performed to discriminate between individual cells. For example, exemplary embodiments can identify individual cell by detecting the border or boundary of the individual cells. In some embodiments, supervised or unsupervised shape ranking and/or support vector segmentation can be used to identify cell borders in the digital image. In some embodiments, tissue segmentation can be performed in the flattened image to discrimination between different tissue types before step  204 . For example, tissue segmentation can be implemented to discriminate between, and classify cells as, epithelial cells, stromal cells, and/or necrotic cells. 
     In step  206 , sub-cellular compartment segmentation is performed to discriminate between and classify different sub-cellular compartments. For example, exemplary embodiments can identify and classify sub-cellular compartments as nuclei, membrane, and/or cytoplasm. 
     In step  208 , a hierarchical representation of the identified sub-cellular compartments is generated using a spatial order within the cell compartments. The hierarchical representation can include an expected location of the nuclei, cytoplasm, and membrane with respect to each other. In step  210  cells are grouped based on characteristics of the individual cells as determined based on the segmentation steps above. For example, cells can be grouped according to protein profile expression and/or according to spatial and/or morphological rules. With respect to the latter, the grouping of cells can be used to discriminate between, and classify cells as, epithelial cells, stromal cells, and/or necrotic cells. In step  212 , a hierarchical representation of the tissue architecture is generated. The hierarchical representation can include images, graphics, and/or text to illustrate a hierarchy of the biological tissue in the digital image. The hierarchy relates to the relationships between the biological units in the image and can include levels, such as, a tissue level, cellular level, and/or a sub-cellular level. For example, in certain embodiments, a tree data structure can be generated, which can be rendered as in a graphical form, as described in more detail below. 
     Image Enhancement of Structural Markers 
     Image enhancement improves the imaging quality of a specific compartment by integrating information from different protein channels with respect to the same sub-cellular compartment so that important information from different channels enhances the overall image specific marker. In one embodiment, image flattening can be defined as a linear transformation, for which each channel in a composite image has a different mixing factor contributing to the overall enhanced image. The enhancement function for the membrane and cytoplasm markers can be expressed mathematically as: 
                   g   M     ⁡     (     T   Structural   Membrane     )       =         α   1     ⁢     I   1   M       +       α   2     ⁢     I   2   M       +   …   +       α   p     ⁢     I   p   M           ,     
     ⁢       such   ⁢           ⁢   that   ⁢           ⁢       ∑   i             ⁢           ⁢     α   i         =   1     ,     
     ⁢         g   C     ⁡     (     T   Structural   Cytoplasm     )       =         β   1     ⁢     I   1   C       +       β   2     ⁢     I   2   C       +   …   +       β   q     ⁢     I   q   C           ,     
     ⁢       such   ⁢           ⁢   that   ⁢           ⁢       ∑   i             ⁢           ⁢     β   i         =   1     ,         
where α i , β i  are the corresponding mixing factors. The overall energy of the system is preserved by constraining the sum of the corresponding mixing factors to one. Averaging is a particular case of image enhancement transformation.
 
       FIGS. 3A-C  depict examples where the transformed enhanced image captures the whole tissue morphology globally and locally. In this case, the structural markers correspond to membrane markers, where high protein content is localized in the cell membrane (e.g., these markers enhance the cell border).  FIG. 3A  depict Na/K ATPase  202 .  FIG. 3B  depict P-cadherin  204 .  FIG. 3C  depict a color image that is a composite of the two protein markers: Na/K ATPase  202  (as shown in  FIGS. 3A and 3C ) and P-cadherin  204  (as shown in  FIGS. 3B and 3C ). 
     Different image artifacts can be recovered by applying the enhanced image transformation. For example,  FIG. 3A  shows a region with an image artifact  300 , and  FIG. 3B  presents the corresponding region with no artifacts after enhancement.  FIG. 3C  shows how these markers provide information needed to recover such artifacts. 
     As such, structural markers T Structural  corresponding to Na/K ATPase  302  and P-cadherin  304  are shown in  FIGS. 3A and 3B , respectively. A composite image from the corresponding protein markers is shown in  FIG. 3C . It is noted that by combining different markers, cases where image artifacts may exist can be corrected (e.g.,  FIG. 3C ). 
       FIG. 4A  depicts a composite color image of two membrane protein markers: Na/K ATPase  404  (e.g., cross-hatching to represent pure red) and P-cadherin  402  (e.g., cross-hatching to represent pure green), respectively.  FIG. 4B  shows the corresponding transformed image g M (T Structural   Membrane ) as the result of the enhancement process. The result of the image enhancement is an image that integrates the morphological information of both markers: Na/K ATPase  404  and P-cadherin  402 . Here, the combination of both protein markers delineates the epithelial cell membranes. 
     Cell Border Detection (Cell Segmentation) 
     In one exemplary embodiment, cell segmentation can follow a top-down approach, where cells are first detected as a unit, and then, sub-cellular compartments are detected based on hierarchical constraints as discussed in more detail below. One challenge of segmenting each cell can be posed as detecting individual cell borders. The challenge in detecting cell borders is that there can be no clear and well defined boundary among cells, and cells must not overlap with each other. In the case where cells touch each other, there must exist a minimum distance of “one unit or pixel.” 
     In one embodiment, individual cell borders can be detected based on the transformed enhanced image g M (T Structural   Membrane ) described herein. Using the transformed enhanced image, regions that correspond to local maxima also correspond to the “optimal” separation of two cells, while regions that correspond to local minima, correspond to the nuclei region. To identify the regions, a variation of a watershed algorithm can be implemented, where regions of local minima are used as regions to delineate the cell borders by applying the watershed algorithm (see, e.g., Soille,  Morphological Image Analysis , Springer-Verlag, Heidelberg, 2nd edition (2003)). Using this approach, regions of local maxima correspond to cell borders. Other examples of detecting individual cell borders are discussed in more detail in co-pending U.S. patent application Ser. Nos. 13/666,343 and 13/657,255, filed on Nov. 1, 2012, Oct. 22, 2012, respectively, the disclosure of which is incorporated by reference herein. 
     Nuclei Candidate Generation (Sub-Cellular Segmentation) 
     In the context of individual cell segmentation in terms of sub-cellular compartments, a candidate nucleus is generated from the DAPI channel itself, and then, to correctly separate corresponding nuclei, a novel method, which penalizes the cell border estimated from the membrane marker, is used. 
       FIGS. 5A-C  depict examples of typical tissue where cells are touching each other.  FIG. 5A  depicts a DAPI channel of nuclei and membrane,  FIG. 5B  depicts an enhanced image of nuclei and membrane, and  FIG. 5C  depicts a composite image of nuclei  502  and membrane  504 .  FIG. 5A  presents the case where cells are poorly differentiated from the DAPI channel. Note that three cells: A, B, and C overlap with respect to each other (e.g., nuclei corresponding to cells A and B are overlapping with each other, making the difference of cells A and B difficult—similarly for cells B and C).  FIG. 5B  shows the same region with respect to the membrane channel. Note that cell discrimination is more evident as compared with the DAPI channel.  FIG. 5C  shows a composite of both, nuclei  502  and membrane channels  504  using cross-hatching to representing blue and red, respectively. 
     In this step, two alternative methods for nuclei candidate generation are presented. The first method is based on detection of blob-like objects from a curvature metric constrained to a shape template, see Methods for segmenting objects in Images, International Application Number: PCT/SE2011/050407]. The second method is based on Wavelet Analysis (Padfield et al.,  Spatiotemporal cell segmentation and tracking for automated screening , Biomedical Imaging: From Nano to Macro, ISBI 2008, 5th IEEE International Symposium, 376-379 (2008)). 
     The wavelet analysis approach decomposes the images into different frequency channels, then de-noises the images in the wavelet coefficient space, and recombines relevant levels to yield segmented objects. Wavelets have several advantages for this application: they decompose the image in both the spatial and frequency domain enabling effective scale-space analysis, the calculation of wavelets across multiple scales is fast and computationally efficient, and the number of parameters can be limited or completely eliminated. 
     To de-noise the images and segment the objects, an algorithm is utilized based on the shift-invariant wavelet frames transformation of the image, as well as the filtering of non-salient wavelet coefficients. Wavelet frames are identical to the standard wavelet transform except that the decimation operation at each level is omitted. Prior research demonstrates that the wavelet frames transform is robust to local noise variations and discards low frequency objects in the background. To de-noise the images in the wavelet coefficient space, the signal term is approximated by thresholding the image stack with an Amplitude-scale-invariant Bayes Estimator (ABE) using Jeffreys&#39; non-informative prior as an estimate of the significance of wavelet coefficients. In order to further reduce noise and enhance objects that extend across multiple resolutions, a correlation stack is computed, which is the multiplication of a subset of the de-noised wavelet coefficients corresponding to the selected scales. 
     One of the advantages of the wavelet-based method for de-noising and segmentation is how it naturally represents objects at different scales. The selection of which scales to combine can be determined from the resolution of the images and the approximate expected object size. The subset of the channels used for the correlation stack are chosen to correspond with the scales at which the objects appear, thus ignoring scales containing only noise and those containing only low-frequency background information. The segmentation is then obtained as the extraction of connected regions in the correlation stack for coefficients greater than zero. Since the correlation stack emphasizes the frequencies corresponding to the objects, little post-processing is necessary to yield consistent filled shapes. This algorithm can detect objects even in the presence of relatively low contrast-to-noise and in the presence of slowly varying backgrounds (e.g., see  FIG. 6B ).  FIGS. 6A-6C  depict: (i) an original image ( FIG. 6A ), (ii) nuclei segmentation based on the wavelets based approach ( FIG. 6B ), and (iii) nuclei segmentation based on the shape-analysis based approach ( FIG. 6C ). 
     The shape analysis approach assumes that nuclei cells have smooth but irregular convex shape such as a deformed ellipsoid. The method generally operates in two main steps. First, a watershed algorithm is used to find the cell nuclei regions. Watershed uses seed points that correspond to local minimum, where each seed point is found by applying morphological operations. In the second step, regions are merged. Merging criteria is a function of the magnitude of the gradient, the distance transform and the perimeter ratio of two neighboring nuclei (see, e.g.,  FIG. 6C ). 
     Membrane and Cytoplasm Detection (Ring Model Based Detection) (Sub-Cellular Segmentation) 
       FIG. 7A  depicts an image corresponding to the transformed structural marker g M (T Structural   Membrane ). In  FIG. 7A , it can be observed that the membrane  702  exhibits a tubular-like morphology, and regions corresponding to local maxima are in the substantial center or medial axis of the membrane  702 , while regions corresponding to local minima are the center of each individual nuclei. In general, structural markers corresponding to the membrane and cytoplasm reach a maximum protein expression in the center of the membrane and cytoplasm respectively, while reaching a minimum protein expression in the stroma and nuclei regions, making them suitable to the local and global shape of the membrane and cytoplasm. In exemplary embodiments, the advantageous approaches of the present disclosure include proposing a shape model for the individual membrane and cytoplasm, where the shape model corresponds to the geometrical model of a two-dimensional image with variations in diameter.  FIG. 7B  shows an image depicting the probability map of the detected membrane  702 . 
     One proposed approach of the present disclosure detects both membrane and cytoplasm with different thickness. In exemplary embodiments, this approach is model based and performs analysis at different scales. It is inspired in the geometrical model of a two-dimensional ring, where the scale factor corresponds to the radius of the ring, and the center of the two dimensional ring reaches values that are close to one, while the border of the ring reaches values close to zero. 
     Let 0≦λ 1 (x, y)≦λ 2 (x, y) be the ordered eigenvalues of the Hessian matrix at a specific scale. A measure for ring-like structures can then be defined by constructing a probability map, where values with maxima probability are assigned to the medial axis of the two-dimensional ring as: 
     
       
         
           
             
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     In the above equation, r min , r min  are the minimum and maximum radius of the two dimensional ring, and λ 1   r , λ 2   r  are the eigenvalues of the Hessian matrix at the scale r, and g: λ 1   r ×λ 2   r →[0,1] is the function subject to the following constraint: 
                 lim     x   →   ∞       ⁢           ⁢     g   ⁡     (   x   )         =   1                     lim     x   →   1       ⁢           ⁢     g   ⁡     (   x   )         =   0     ,         
where
 
               x   =            λ   1       λ   2              ,         
that is, x is the ratio of the eigenvalues, and g penalizes when they are equal and assigns values of one when the ratio is large.
 
     It is noted that to detect the ring having a variable radius, a multi-scale analysis is performed, thereby ensuring that the probability values are assigned with respect to the range of expected radius values. Then, the maximum probability across scales corresponds to the radius of the two-dimensional ring. 
     Hierarchical Representation from the Model Based Topological Constraints 
     Hierarchical representation of sub-cellular compartments assigns spatial order within the cell compartments as depicted in  FIG. 1 . The hierarchical model is constrained so that sub-cellular regions are competing with each other and have a predetermined precedence so that they maximize the probability of the specific localization. 
     As discussed in more detail below,  FIG. 8A  depicts an original multi-channel image, with the nuclei  802 , cytoplasm  806  and membrane  804 , which are represented using cross-hatching corresponding to the blue, green and red channel, respectively.  FIG. 8B  depicts the probability map that corresponds to the detected cytoplasm based on the ring-based model.  FIG. 8C  depicts the probability map that corresponds to the detected membrane based on the ring-based model.  FIG. 8D  depicts the hierarchical segmentation with a non-overlapping rule, and  FIG. 8E  depicts the hierarchical segmentation with an overlapping rule. 
       FIG. 8A  depicts a composite image of three channels: nuclei  802  (blue), membrane  804  (red), and  806  cytoplasm (green). In this example it is evident that the structural markers overlap and this ambiguity can be modeled by the segmentation function ƒ seg (I C (x, y))=[ncell, ln, lm, lc, lb], and assigning a label (or membership) value to the specific compartment. 
       FIG. 8B  represents the probability map of the detected cytoplasm. It is noted that the probability values are maximum in the center of the membrane where there is a variable radius. Similarly, the probability map of the membrane is presented in  FIG. 8C . It is noted that the membrane is localized towards the cell border, while the cytoplasm is localized closer to the nucleus. This information is incorporated in a cost function, which maximizes the probability of the hierarchical localization of the sub-cellular compartments. 
     The topological constraints that follow the detection of the compartments are as follows: the method can prioritize sub-cellular regions according to different hierarchical combinations of the sub-cellular compartments. Example of sub-cellular prioritization are the following: 1) membrane, versus the rest of the regions: membrane has more priority than cytoplasm and nuclei, and nuclei has more priority than cytoplasm, 2) membrane, versus the rest of the regions: membrane has more priority than cytoplasm and nuclei, and cytoplasm has more priority than nuclei. 
       FIG. 8D  depicts the result of the hierarchical segmentation, where the red region corresponds to the detected membrane within the cell. The green region corresponds to the detected cytoplasm, and the detected nuclei is blue, while the background is in black. In this case, each pixel gets assigned a unique label: liε[0,1], i={n,m,c,b}.  FIG. 8E  depicts the case where pixels belong to different compartments, according to whether they overlap or not. The an intersection of the detected membrane and cytoplasm is shown in  FIG. 8E , and in this case, the weights are assigned evenly. 
     Cell Grouping 
     In exemplary embodiments, cell grouping includes identifying individual cells that follow a specific pattern or criteria. In general, there are two main criteria for cell association. The first is grouping according to different protein profile expressions (e.g., the clustering of individual cells according to their specific protein profiles). The second is grouping according to spatial and morphological rules (e.g., cells that belong to the epithelium and stroma). 
     Hierarchical Graph Based Representation 
       FIG. 9  depicts the representation and abstraction of an exemplary tissue architecture  900  at the sub-cellular level as a tree data structure. The first level  902  of abstraction is the segmentation of the tissue in terms of epithelium and stroma. It is noted that epithelium cells typically are associated with different degrees of cancer. The second level  904  of abstraction is the identification of different groups or sub-populations of individual cells (e.g., cells that belong to different glands, cells that belong to red blood cells, among other criteria, etc.). In general, for each group or sub-population, there are spatial, morphological and/or protein expression rules. The third level  906  of abstraction is the representation of the tissue at the sub-cellular level in which each individual cell is expressed in terms of sub-cellular compartments (e.g., individual cell segmentation in terms of nuclei, membrane and cytoplasm). 
       FIG. 10  is an example of the proposed tissue representation depicted in  FIG. 9 . In  FIG. 10 , the tissue architecture  1000  is composed of lobes (e.g., epithelium cells) and stroma regions. The association rule is defined by the cells that are in the end secretory parts of the main prostatic glands. 
       FIG. 10  depicts the lobules  1  of the main prostatic glands  1010 , the end secretory parts  2  of the main prostatic glands, and the stroma  3  composed from smooth muscle cells and/or connective tissue. In  FIG. 10 , leafs (terminal nodes) represent single cells, and nodes represent relevant anatomical structures. For each of the single cells the cellular compartments are specified in terms of nucleus, cytoplasm and associated membrane. 
     Exemplary Computing Device Programmed to Implement Exemplary Embodiments 
     Systems and methods disclosed herein may include one or more programmable processing units having associated therewith executable instructions held on one or more non-transitory computer readable media, RAM, ROM, hard drive, and/or hardware. In exemplary embodiments, the hardware, firmware and/or executable code may be provided, for example, as upgrade module(s) for use in conjunction with existing infrastructure (for example, existing devices/processing units). Hardware may, for example, include components and/or logic circuitry for executing the embodiments taught herein as a computing process. 
     The term “computer-readable medium,” as used herein, refers to a non-transitory storage hardware, non-transitory storage device or product or non-transitory computer system memory that may be accessed by a controller, a processor, a microcontroller, a computational system or a module of a computational system to encode thereon computer-executable instructions or software programs. The “computer-readable medium” may be accessed by a computational system or a module of a computational system to retrieve and/or execute the computer-executable instructions or software programs encoded on the medium. The non-transitory computer-readable media may include, but are not limited to, one or more types of hardware memory, non-transitory tangible media (for example, one or more magnetic storage disks, one or more optical disks, one or more USB flash drives), computer system memory or random access memory (such as, DRAM, SRAM, EDO RAM) and the like. 
       FIG. 11  is a diagram showing hardware and software components of an exemplary system  1100  capable of performing the processes described herein. The system  1100  includes a computing device  1102 , which can include a storage device  1104 , a network interface  1108 , a communications bus  1116 , a central processing unit (CPU)  1110 , e.g., a microprocessor, and the like, a random access memory (RAM)  1112 , and one or more input devices  1114 , e.g., a keyboard, a mouse, and the like. The computing device  1102  can also include a display  1120 , e.g., a liquid crystal display (LCD), a cathode ray tube (CRT), and the like. The storage device  1104  can include any suitable, computer-readable storage medium, e.g., a disk, non-volatile memory, read-only memory (ROM), erasable programmable ROM (EPROM), electrically-erasable programmable ROM (EEPROM), flash memory, field-programmable gate array (FPGA), and the like. The computing device  1102  can be, e.g., a networked computer system, a personal computer, a smart phone, a tablet, and the like. 
     In exemplary embodiments, exemplary embodiments of an engine  1150  programmed to implement one or more processes described herein, can be embodied as computer-readable program code stored on one or more non-transitory computer-readable storage device  1104  and can be executed by the CPU  1110  using any suitable, high or low level computing language, such as, e.g., Java, C, C++, C#, .NET, Python, and the like. Execution of the computer-readable code by the CPU  1110  can cause CPU  1110  to implement an exemplary embodiment of one or more processes described herein. 
     For example, the engine  1150  programmed and/or configured to perform hierarchical image segmentation analysis. In one embodiment the engine  1150  can be programmed and/or configured to implement an embodiment of the process described with respect to  FIG. 2  and can generate a graphical or textual representation of the tissue architecture (e.g.,  FIGS. 9 and 10 . 
     The engine  1150  can be programmed and/or executed to access image data from data storage (e.g., a non-transitory computer-readable medium). The image data can correspond to a multiplexed image of biological tissue that has been sequentially fluorescent stained to manifest expression levels of a plurality of morphological biomarkers in the biological tissue. In some embodiments, the morphological biomarkers include biomarkers representative of a single type of sub-cellular morphological unit. 
     The engine  1150  can be programmed and/or configured to determine a measure of expression levels of a biomarker. The measure can be specific to at least one of the one or more sub-cellular morphological units in the one or more cells and can be a mean of the expression levels. The engine  1150  can be programmed and/or configured to perform an image segmentation analysis on the image data based on the biomarker expression levels. The analysis can be used to identify locations and configurations of one or more cells in the biological tissue. For example, the engine  1150  can be programmed to detect individual cell boundaries in the image data using, for example, supervised shape ranking, unsupervised shape ranking, and/or support vector segmentation. The analysis can also be used to identify locations and configurations of one or more sub-cellular morphological units (e.g., nuclei, cytoplasm, and/or membrane) within the one or more detected/identified cells. For example, the engine  1150  can be programmed and/or configured to detect/identify by imposing topological constraints and/or using a probability map to generate a ring-like structure modeling the membrane or the cytoplasm. The expression levels of a biomarker in the one or more sub-cellular morphological units can be automatically determined by the engine  1150  at the level of the sub-cellular morphological units. In some embodiments, the engine  1150  can be programmed and/or configured to perform image segmentation analysis on the image data based on the biomarker expression levels to identify at least one tissue-based region of interest (e.g., a collection of stromal cells or a collection of epithelial cells). The biological tissue sections can be grouped by the engine  1150  based on the expression levels of the biomarker in the sub-cellular morphological units. 
     In exemplary embodiments, the engine  1150  can be programmed and/or configured to perform an analysis to determine a relationship between expression levels of a biomarker in the one or more sub-cellular morphological units and the configurations of the one or more sub-cellular morphological units. 
     The engine  1150  can be programmed to render representations of biological units on the display  1120 . As one example, the engine  1150  can be programmed and/or configured to render a hierarchical representation of one or more cells, one or more sub-cellular morphological units in the one or more cells, and/or at least one tissue-based region of interest. In some embodiments, pixels of the image data can be associated with a single type of sub-cellular morphological unit in the hierarchical representation using hard segmentation for which each pixel belongs to either: 1) nuclei, 2) membrane, 3) cytoplasm as described herein. In some embodiments, pixels of the image data can be associated with one or more types of sub-cellular morphological unit in the hierarchical representation using soft segmentation for which a pixel can belong to one or more sub-cellular compartments (e.g., nuclei, membrane, cytoplasm). In some embodiments, a pixels of the image data has a first probability that the pixel corresponds to the first type of sub-cellular morphological unit and a second probability that the pixel corresponds to the second type of sub-cellular morphological unit in the hierarchical representation using probability-based segmentation where each pixel has a probability of belonging to either to the nuclei, membrane and cytoplasm. In some embodiments, a pixel of the image data has a first membership value that the pixel corresponds to the first type of sub-cellular morphological unit and a second membership value that the pixel corresponds to the second type of sub-cellular morphological unit in the hierarchical representation. 
     As another example, the engine  1150  can be programmed and/or configured to render representations of expression levels of a biomarker in an overlaid manner on the representations of the one or more cells and the one or more sub-cellular morphological units in the one or more cells. 
     In some embodiments, the engine  1150  can be programmed and/or configured to determine one or more segmentation-quality metrics for the one or more cells. The engine  1150  can render the one or more segmentation-quality metrics for the one or more cells on a display in an overlaid manner over the rendering of the one or more cells. In some embodiments, only a subset of cells among the one or more cells having segmentation-quality metrics that satisfy one or more predefined segmentation quality criteria are rendered. Examples of criteria include morphological measurement of the cell such as cell size, elongation, shape and morphological measurements of the sub-cellular compartments such membrane, cytoplasm and nuclei area. 
     The network interface  1108  can include, e.g., an Ethernet network interface device, a wireless network interface device, any other suitable device which permits the computing device  1102  to communicate via the network, and the like. 
     The CPU  1110  can include any suitable single- or multiple-core microprocessor of any suitable architecture that is capable of implementing and/or running the disclosed processes, e.g., an Intel processor, and the like. The random access memory  1112  can include any suitable, high-speed, random access memory typical of most modern computers, such as, e.g., dynamic RAM (DRAM), and the like. 
     Exemplary Client-Server Environment to Implement Exemplary Embodiments 
     System and methods disclosed herein can be implemented in a client-server environment.  FIG. 12  is an exemplary client-server environment  1200  for implementing the systems and methods disclosed herein. The computing system  1200  includes servers  1210 ,  1211 ,  1212  operatively coupled to clients  1220 ,  1221 ,  1222 , via a communication network  1250 , which can be any network over which information can be transmitted between devices communicatively coupled to the network. For example, the communication network  1250  can be the Internet, Intranet, virtual private network (VPN), wide area network (WAN), local area network (LAN), and the like. The environment  1200  can include repositories or databases  1230 ,  1231 , which can be operatively coupled to the servers  1210 - 1212 , as well as to clients  1220 - 1222 , via the communications network  1250 . The servers  1210 - 1212 , clients  1220 - 1222 , and databases  1230 ,  1231  can be implemented as computing devices. Those skilled in the art will recognize that the databases  1230 ,  1231  can be incorporated into one or more of the servers  1210 - 1212  such that one or more of the servers can include databases. 
     In some embodiments, embodiments of the engine  1150  and/or segmentation processes described herein can be implemented by a single device, such as server  1210  or client  1220 . In some embodiments, portions of the engine  1150  and/or segmentation processes described herein can be implemented using different devices (e.g., servers, clients, databases) in the communication network  1250  such that one or more of the devices can be programmed and/or configured to implement one or more steps of the segmentation processes. For example, in one embodiment, the multiplexed digital images can be store in the database  1230  and the engine and/or segmentation processes described herein can be executed by the server  1210 . A user can access the server  1210  via the client device  1220  to execute the engine and/or segmentation processes described herein. The server  1210  can access the multiplexed images from the database  1230  and can perform an embodiment of the processes described herein to output a hierarchical representation of the biological tissue in the multiplexed image, which can be store, for example, in the database  1231 . 
     Experimental Results 
     The results of the individual cell analysis in multiplexed images from both Xenograft models and colon tissue samples are presented below. The exemplary systems/methods of the present disclosure have been applied in at least three thousand images, including images of colon cancer and Xenograft models. The results have also been compared to commercial software. 
       FIG. 13  depicts the results of segmentation of the individual structural markers T Compartments .  FIGS. 13A-C  depict images corresponding to the nuclei ( FIG. 13A ), membrane ( FIG. 13B ), and cytoplasm ( FIG. 13C ).  FIGS. 13D-F  show an overlay of the raw data  1302  (using cross-hatching to represent the color blue) and the detected compartments  1304  (using cross-hatching to represent the color green). 
     More particularly,  FIGS. 13A-C  depict nuclei, membrane and cytoplasm images corresponding from Xenograft datasets, respectively.  FIGS. 13D-F  depict overlays of the segmented nuclei, membrane and cytoplasm (green), with the corresponding image channel (blue), and red lines being the cell boundaries. 
       FIGS. 14A-F  depict images of the segmentation results of individual cell analysis in the epithelium.  FIG. 14A  corresponds to the image T Compartments , where nuclei  1406 , membrane  1402  and cytoplasm  1404 , which are represented using cross-hatching correspond to the blue, green and red channel, respectively.  FIG. 14B  corresponds to the membrane channel, and  FIG. 14C  corresponds to the detected cells.  FIGS. 14E and 14F  depict the probability maps corresponding to the membrane and cytoplasm, respectively.  FIG. 14C  depicts the results of the segmentation at sub-cellular level, where pixels are uniquely associated with a compartmental marker. Nuclei  1406 , membrane  1404  and cytoplasm  1402  ( FIG. 14C ). 
     More particularly,  FIG. 14A  depicts the original image corresponding to subjects from prostrate cancer, with the nuclei  1406  (e.g., using cross-hatching to represent the color blue), membrane  1404  (e.g., using cross-hatching to represent the color green) and cytoplasm  1402  (e.g., using cross-hatching to represent the color red) channels overlaid.  FIG. 14C  depicts detected cell compartments by applying the watershed algorithm, with each color representing an individual cell. 
     The results of segmentation methods of the present disclosure were compared with those obtained using a customized analysis pipeline utilizing the software Definiens© (Definiens, 2009), where both algorithms were used to segment tissue images in sub-cellular compartments: i) nuclei, ii) membrane, and iii) cytoplasm. The set of images correspond to Xenograft studies. 
     An exemplary Xenograft study included 13 subjects, and there was an average of 10 images per subject. As discussed below,  FIGS. 15A-I  and  16 A-I were selected as representative samples, where oversaturation was typically present in these datasets. In general, the images of  FIGS. 15A-I  are less over-saturated as compared to the images in  FIGS. 16A-I . 
       FIGS. 15A-C  depict the channels corresponding to nuclei, membrane and cytoplasm. More particularly,  FIGS. 15A-C  show Xenograft images corresponding to the nuclei, membrane and cytoplasm. Images corresponding to  FIGS. 15D-F  are the segmentation results according to exemplary embodiments of the present disclosure. 
     To visually compare the segmentation from both algorithms, the segmentation results were color-coded in color images (represented using cross-hatching), and where segmentation results according to the systems/methods of the present disclosure would appear in red, while the results using Definiens©—would appear in green, and regions would appear in yellow are where both algorithms coincide ( FIGS. 15D-F ). Similarly, images in  FIGS. 16A-I  show the results of both segmentation algorithms. 
       FIG. 15G  depicts raw data from the study.  FIG. 15H  depicts single cell segmentation according to systems/methods of the present disclosure and in terms of non-overlapping sub-cellular compartments: nuclei  1502  (e.g., using cross-hatching to represent the color blue), membrane  1506  (e.g., using cross-hatching to represent the color red), and cytoplasm  1504  (e.g., using cross-hatching to represent the color green).  FIG. 15I  depicts single cell Definiens segmentation: nuclei  1502  (e.g., using cross-hatching to represent the color blue) and membrane  1506  (e.g., using cross-hatching to represent the color green), with the cytoplasm mask not overlaid in this image (see  FIG. 15F ). 
     As noted, images in  FIGS. 16A-I  show the results of both segmentation algorithms. More particularly,  FIGS. 16A-C  show Xenograft images corresponding to the nuclei, membrane and cytoplasm. Images corresponding to  FIGS. 16D-F  are the segmentation results according to exemplary embodiments of the present disclosure. To visually compare the segmentation from both algorithms, the segmentation results were color-coded in the color images, and where segmentation results according to the systems/methods of the present disclosure would appear in red, while the results using Definiens© would appear in green, and regions would appear in yellow are where both algorithms coincide ( FIGS. 16D-F ).  FIG. 16G  depicts raw data from the study.  FIG. 16H  depicts single cell segmentation according to systems/methods of the present disclosure and in terms of non-overlapping sub-cellular compartments: nuclei  1602  (e.g., using cross-hatching to represent the color blue), membrane  1606  (e.g., using cross-hatching to represent the color red), and cytoplasm  1604  (e.g., using cross-hatching to represent the color green).  FIG. 16I  depicts single cell Definiens segmentation: nuclei  1602  (e.g., using cross-hatching to represent the color blue) and membrane  1606  (e.g., using cross-hatching to represent the color green), with the cytoplasm mask not overlaid in this image (see  FIG. 16F ). 
     In general, both algorithms significantly disagreed over saturated regions. More specifically, Definens© tended to over segment regions, while the systems/methods of the present disclosure advantageously provided a robust segmentation. For example, the membrane image of  FIG. 16B  displayed significant over-saturation, thus making it evident in the results obtained by the Definens© software as shown in  FIG. 16I . The results of the membrane segmentation using the systems/methods of the present disclosure are shown  FIG. 16H , and it is noted how the segmented membrane  1606  (using cross hatching to represent the color red) is not over estimated when intensity saturation is present. 
     FIG.  17 AC displays the results from the tissue section corresponding to colon cancer.  FIG. 17A  depicts the DAPI channel.  FIG. 17B  displays the images corresponding to the structural markers T Compartments . It is noted that that nuclei images overlap each other, and the protein expression in the membrane is less significant than the protein expression in the cytoplasm.  FIG. 17C  shows the segmentation results of the systems/methods of the present disclosure, and the nuclei are correctly separated and the membrane detection is correctly detected in the cell borders. 
     More particularly and with reference to  FIGS. 17A-C , it is noted that  FIG. 17A  displays the nuclei channel.  FIG. 17B  displays an overlay of the morphological channels: nuclei  1702  (e.g., using cross-hatching to represent the color blue), membrane  1706  (e.g., using cross-hatching to represent the color red) and cytoplasm  1704  (e.g., using cross-hatching to represent the color green).  FIG. 17C  shows the results of an exemplary single cell segmentation algorithm according to the present disclosure, where the segmented compartments are: nuclei  1702  (e.g., using cross-hatching to represent the color blue), membrane  1706  (e.g., using cross-hatching to represent the color red) and cytoplasm  1704  (e.g., using cross-hatching to represent the color green). 
       FIGS. 18A and 18B  depict overlays  1800  and  1850 , respectively, of the results of the segmentation with the corresponding protein expression. Stated another way,  FIGS. 18A-B  show biomarker expression overlays with the segmented cell showing nuclei  1802 , membrane  1806  and cytoplasm  1804  using cross-hatching to distinguish the structures. In this case, pGSK protein expression ( FIG. 18A ) and Keratin protein expression ( FIG. 18B ) are shown. It is noted that quantification is performed in the sub-cellular compartments per cell, where each cell is assigned a unique number. 
       FIG. 19  depicts an image  1900  of the segmented cells in the overall tissue.  FIG. 19  is an image showing the results of the segmentation at the sub-cellular level. Each cell is localized in the x-y plane with the corresponding compartments. Detail statistics  1902  per cell are quantified with respect to each cell for every protein. A text file (not shown) can provide a matrix that quantifies the protein expression. More particularly, data can be exported in a text file or the like, where detail statistics  1902  of the protein are estimated in the compartments. 
     Although the systems, assemblies and methods of the present disclosure have been described with reference to exemplary embodiments thereof, the present disclosure is not limited to such exemplary embodiments and/or implementations. Rather, the systems, assemblies and methods of the present disclosure are susceptible to many implementations and applications, as will be readily apparent to persons skilled in the art from the disclosure hereof. The present disclosure expressly encompasses such modifications, enhancements and/or variations of the disclosed embodiments. Since many changes could be made in the above construction and many widely different embodiments of this disclosure could be made without departing from the scope thereof, it is intended that all matter contained in the drawings and specification shall be interpreted as illustrative and not in a limiting sense. Additional modifications, changes, and substitutions are intended in the foregoing disclosure. Accordingly, it is appropriate that the claims be construed broadly and in a manner consistent with the scope of the disclosure. 
     Exemplary flowcharts are provided herein for illustrative purposes and are non-limiting examples of methods. One of ordinary skill in the art will recognize that exemplary methods may include more or fewer steps than those illustrated in the exemplary flowcharts, and that the steps in the exemplary flowcharts may be performed in a different order than the order shown in the illustrative flowcharts.