

SYMPOSIUM  ORIGINAL RESEARCH 



J Pathol Inform 2013,
4:4 
A statistical framework for analyzing hypothesized interactions between cells imaged using multispectral microscopy and multiple immunohistochemical markers
Chris J Rose^{1}, Khimara Naidoo^{2}, Vanessa Clay^{2}, Kim Linton^{3}, John A Radford^{3}, Richard J Byers^{4}
^{1} Centre for Imaging Sciences, Institute for Population Health; The University of Manchester Biomedical Imaging Institute; Manchester Academic Health Science Centre, The University of Manchester, Manchester, United Kingdom ^{2} Central Manchester University Hospitals NHS Foundation Trust; School of Medicine, Faculty of Medical and Human Sciences, The University of Manchester, Manchester, United Kingdom ^{3} Manchester Academic Health Science Centre; Institute of Cancer Sciences, Faculty of Medical and Human Sciences, The University of Manchester; The Christie NHS Foundation Trust, Manchester, United Kingdom ^{4} Manchester Academic Health Science Centre; Central Manchester University Hospitals NHS Foundation Trust; Institute of Cancer Sciences, Faculty of Medical and Human Sciences, The University of Manchester, Manchester, United Kingdom
Date of Submission  21Jan2013 
Date of Acceptance  21Jan2013 
Date of Web Publication  30Mar2013 
Correspondence Address: Chris J Rose Centre for Imaging Sciences, Institute for Population Health; The University of Manchester Biomedical Imaging Institute; Manchester Academic Health Science Centre, The University of Manchester, Manchester United Kingdom
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/21533539.109856
Abstract   
Background: Multispectral microscopy and multiple staining can be used to identify cells with distinct immunohistochemical (IHC) characteristics. We present here a method called hypothesized interaction distribution (HID) analysis for characterizing the statistical distribution of pairwise spatial relationships between cells with particular IHC characteristics and apply it to clinical data. Materials and Methods: We retrospectively analyzed data from a study of 26 follicular lymphoma patients in which sections were stained for CD20 and YY1. HID analysis, using leaveoneout validation, was used to assign patients to one of two groups. We tested the null hypothesis of no difference in KaplanMeier survival curves between the groups. Results: Shannon entropy of HIDs assigned patients to groups that had significantly different survival curves (median survival was 7.70 versus 110 months, P = 0.00750). Hypothesized interactions between pairs of cells positive for both CD20 and YY1 were associated with poor survival. Conclusions: HID analysis provides quantitative inferences about possible interactions between spatially proximal cells with particular IHC characteristics. In follicular lymphoma, HID analysis was able to distinguish between patients with poor versus good survival, and it may have diagnostic and prognostic utility in this and other diseases. Keywords: Cellular interactions, follicular lymphoma, image analysis, immunohistochemical staining, multispectral microscopy
How to cite this article: Rose CJ, Naidoo K, Clay V, Linton K, Radford JA, Byers RJ. A statistical framework for analyzing hypothesized interactions between cells imaged using multispectral microscopy and multiple immunohistochemical markers. J Pathol Inform 2013;4:4 
How to cite this URL: Rose CJ, Naidoo K, Clay V, Linton K, Radford JA, Byers RJ. A statistical framework for analyzing hypothesized interactions between cells imaged using multispectral microscopy and multiple immunohistochemical markers. J Pathol Inform [serial online] 2013 [cited 2018 Nov 21];4:4. Available from: http://www.jpathinformatics.org/text.asp?2013/4/2/4/109856 
Background   
Pathologists use microscopic tissue analysis for diagnosis and prognostication of diseases. This is based on visual recognition of particular patterns of distinct cells indicative of specific or general cellular processes. However, it can be difficult or impossible to disambiguate cells in fixed sections using standard illumination methods. In the context of solid tumors, multiple molecular markersparticularly at the protein level using immunohistochemistrycan be imaged using multispectral microscopy. ^{[1]} This is an imaging technique in which a section is imaged multiple times, each time illuminated using a distinct and narrow range of wavelengths. The result is a "cube" of optical density data or, equivalently, a spectrum of optical densities at each pixel location. This data can be processed to identify regions or cells that are positive for particular markers (e.g., via thresholding of optical densities and other techniques). However, even with sophisticated analysis and visualization tools, it is difficult for expert clinicians to interpret images acquired using more than a few markers. Furthermore, while it is believed that cells with particular immunohistochemical (IHC) profiles may interact to varying degrees of patient detriment, there are few quantitative methods available for investigating these hypotheses. The present paper presents such a method and demonstrates the application of it to a study of follicular lymphoma (FL).
Materials and Methods   
Combinatorial Molecular Phenotypes
Given a cube of data from a multiplestained section imaged using multispectral microscopy, we assumed that it is possible to determine whether each cell in a section is positive (1) or negative (0) for each marker and to obtain cells' spatial (x, y) coordinates. This can be achieved, for example, using commercially available software (e.g., Nuance; PerkinElmer Inc., Waltham, MA, USA). Let denote a set of N markers and the positivity of a cell for stain as π_{s} . We adopt the term "combinatorial molecular phenotype (CMP)" from a previous study ^{[2]} that describes the positivity of a cell for all stains in as the binary vector π = (π_{s1}, ..., π_{sn}), where s_{i} denotes the i^{th} stain. For example, a possible CMP for an image stained with three markers may be π = (1, 0, 0). No (x,y) coordinates will be recorded for cells that are negative for all markers in . Therefore, any of 2^{N}1 CMPs may be observed. Each possible CMP can be assigned a unique number according to a suitable binary counting scheme. If the rightmost element of a CMP represents the least significant binary digit and the next rightmost element represents the next least significant digit and so on, then the vectors (0, 1, 0), (1, 0, 0), and (1, 1, 1) can be numbered 2, 4, and 7, respectively. Because this numbering system begins at 1, it is useful for indexing the matrices we introduce later in this paper.
Combinatorial Molecular Phenotype Approximation
Some software can automatically and accurately segment individual cells using full multispectral data. However, less sophisticated software is limited to segmenting regions from particular subbands, giving rise to separate sets of region centroid coordinates for each stain, some of which may encompass multiple cells (i.e., inaccurate segmentation). However, it is possible to use the region centroid coordinatesobtained for each marker independentlyto identify regions that are so sufficiently close that they are likely to correspond to the same cell, and, therefore, to approximate CMPs.
First, regions likely to encompass multiple cells are rejected by discarding those that are larger than the maximum area expected for typical cells. Then, coordinates from different markers that are within a "pairing distance," d _{P}, are combined into a single coordinate to which the appropriate cell CMP is associated. Later in the paper, we have shown how distance d _{P} may be chosen statistically.
Hypothesized Interaction Distributions
We hypothesized that two cellssufficiently close together and with identical or different CMPsmay interact to varying degrees of patient benefit or detriment. We call this a "hypothesized interaction." By extension, we hypothesize that if a particular hypothesized interaction does indeed act in this way, then many such interactions between pairs of cells will have a larger effect on patient outcome.
We formalize the notion of hypothesized interactions and quantify their occurrence by introducing a commutative arrow operator. A particular hypothesized interaction y can be denoted by . The notation can be understood as follows. Consider all possible pairings of cells within a given section, such that no two paired cells are located further than an "interaction distance," d _{I}, from one another. The arrow notation specifies that a proportion, p, of all pairings, are between a cell with CMP number i and another with j. This notation is convenient because it can be used to form graphs, which may aid visualization. Later in this paper, we explain how an optimal value of d _{I} can be chosen statistically.
The proportion p can also be interpreted as a probability. By calculating p for each possible hypothesized interaction, we can define a statistical distribution over them. Let D be a (2^{N} − 1) × (2^{N} − 1) symmetric matrix, whose (i, j) ^{th} element is the probability of observing a cell with CMP number i within a distance d _{I} of a cell with CMP number j. If Y is a random variable that represents a hypothesized interaction, then the statistical distribution of Y can be written as Y ~ D, and we call D a "hypothesized interaction distribution" (HID). [Figure 1] shows an example of HIDs and their graphs.  Figure 1: Example hypothesized interaction distributions and their corresponding graphs
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Scalar Summaries of Hypothesized Interaction Distributions
We are interested in testing the hypothesis that cells of particular "types" may interact to varying degrees of patient benefit or detriment. Specifically, we are interested in investigating whether HIDs facilitate the assignment of patients into groups with good versus poor survival. Taking inspiration from greylevel cooccurrence matrix analysis methodology in the texture analysis literature, ^{[3]} [Table 1] defines three scalar summary statistics that can be used to characterize a HID. Note that the indexing used in the summations accounts for the fact that the upper and lower triangles are symmetric and that only one of these triangles is required to specify the HID (i.e., the elements in one of the triangles sum to unity).
Distribution "peakiness" is characterized in different ways by D _{E} and H(D); D_{max} characterizes the degree to which the most common hypothesized interaction occurs. Shannon entropy, H(D), measures the expected information (in bits) required to transmit a randomly chosen hypothesized interaction, drawn from the distribution D, over an idealized channel. Hypothesized interactions associated with uniform distributions require more information than those from nonuniform distributions.
Assigning Patients to Groups for Survival Analysis
Given a vector of values of a particular summary statistic (e.g., D _{max} ) for n patients, γ = (γ _{1} , …, γ_{n}), we can choose an optimal threshold, ,on that statistic that best assigns patients to groups on the basis of survival via the optimization
Here, the i^{th} element of the vector s is the survival time for the i^{th} patient and the function g_{γΤ} returns a vector whose i^{th} element is the group assignment of the i^{th} patient resulting from the application of threshold γ_{T} to the i^{th} element of the vector γ. The objective function χ^{2} computes the value of the χ^{2} statistic associated with the null hypothesis that the survival curves arising from the group assignments are equal; ^{[4]} high values of χ^{2} have corresponding low P values.
Selecting Optimal Pairing and Interaction Distances
The distances d _{I} and d _{P} may in principle be selected by the investigator, for example, by drawing upon expert clinical knowledge. However, this approach is subjective and we therefore proposed an objective method. Optimal values can be chosen statistically via the optimization
This is a modification of equation 1, where γ(d _{I}, d _{P}) returns a vector of summary statistics for HIDs computed using distances d _{I} and d _{P}.
Application in Follicular Lymphoma
The aims of this experiment were to demonstrate the application of HID analysis to data from multispectral microscopy of multiplestained tissue sections from a sample of FL patients and to evaluate the method's ability to identify patient groups that differ in survival.
Twenty six archived human lymph nodes from patients (16 male, 10 female, aged 3677 years, mean 55 years) with a diagnosis of FL were collected at initial diagnosis, prior to the treatment. Written informed consent and local research ethics committee approval were obtained. The material was routinely processed by fixation in formalin and paraffin embedding. Clinical data and up to 14 years of followup and survival data were available for each sample (19 dead, 7 alive; median time to death 32 months; range 2170 months; 171 months followup in all patients alive at the end of the study period). Paraffinembedded sections from these cases were reviewed by two pathologists.
Duplex quantum dotbased immunofluorescence was used to colocalize YY1 with CD20 using a duplex QDIF protocol. ^{[5]} Briefly, tissue sections were subjected to antigen retrieval by microwave heating in TrisEDTA buffer and incubated with YY1 monoclonal primary antibody (Santa Cruz Biotechnology, Santa Cruz, CA, USA) diluted 1:50 (v/v) in 1:10 (v/v) goat serum overnight at 4°C. Secondary detection was performed using a goat antimouse secondary antibody diluted 1:250 (v/v) in 1:10 (v/v) goat serum, followed by 655 nm quantum dot solution (Invitrogen, Carlsbad, CA, USA) (1:50 (v/v) in 1:10 (v/v) goat serum). Sections were washed and incubated with Avidin solution followed by incubation with Biotin solution (Vector Laboratories, Burlingame, CA, USA). An antiCD20 monoclonal primary antibody (Dako, Glostrup, Denmark) diluted 1:50 (v/v) in 1:10 (v/v) goat serum was then applied for 1 hour at room temperature. Secondary detection was performed using the same protocol as for YY1 with the exception of use of a 605 nm quantum dot solution (Invitrogen) diluted 1:50 (v/v) in 1:10 (v/v) goat serum. Finally, sections were rinsed and mounted in polyvinyl mounting medium with DABCO (SigmaAldrich, St. Louis, MO, USA) and sealed with clear nail varnish.
Areas positive for YY1 or CD20 expression were identified by spectral imaging using a LeitzDiaplan fluorescence microscope and a Nuance spectral analyzer. Image cubes were collected and subjected to spectral unmixing using Nuance software version 2.4.2 to generate 2D intensity distributions of YY1 and CD20 positivity; up to five images from different portions of each specimen were taken to help ensure that inferred characteristics were representative. Composite images taken of sections double stained for YY1 and CD20 were unmixed using spectra for 605 nm and 655 nm quantum dots and the resultant 2D intensity maps for each of YY1 and CD20 thresholded to generate biologically relevant positive regions of interest; regions of interest were at least 100 pixels in area. Region centroid coordinates, region area, maximum intensity, and average intensity were exported to Excel (Microsoft Corporation, Redmond, WA, USA). All images were captured at a total magnification of ×400 with standardized and uniform image illumination and magnification such that all images captured were directly comparable in terms of intensity and scale.
Very large regionsrepresenting incorrect discrimination between distinct cellswere rejected by discarding regions with area greater than 200 pixels. The topology of the χ^{2} function (equation 2) for each summary statistic was estimated via thin plate spline interpolation ^{[6]} of values of χ^{2} function computed on a regular 14 × 24 grid of (d _{I}, d _{P}) values. The χ^{2} function is computationally expensive to compute and tends to have multiple maxima. We therefore selected optimal values of d _{I} and d _{P} for each summary statistic by inspecting contour plots, favoring maxima near (d _{I}, d _{P}) = (0, 0). Approximate CMPs, HIDs, and their summary statistics were constructed for each image. Each patient was represented by the median of each summary statistic, taken over all images acquired for the patient. Finally, KaplanMeier survival curves were estimated using leaveoneout validation: at the i^{th} iteration, the i^{th} patient was left out of the analysis and an optimal threshold for each summary statistic calculated for the leftin patients (equation 1); this threshold was used to allocate the leftout patient to one of two groups. Software was implemented in R version 2.13.0. ^{[7]}
Results   
[Figure 2] shows the topology of the objective function (equation 2) for H(D) under the constraint that d _{P} < d _{I} (as we must pair regions before considering that paired regions may interact). [Table 2] shows the results of the leaveoneout survival analyses and the used. There was a statistically significant difference between the survival curves defined by the summary statistic H(D), but not for D_{max} and D _{E}; the P value for H(D) would survive Bonferroni correction for multiple comparisons at the α = 0.05 significance level. KaplanMeier survival curves for H(D)estimated via leaveoneout validationare shown in [Figure 3]. Median survival for the two groups is approximately 7.70 and 110 months. Low H(D) ("peaky" distributions) were associated with poor survival and these peaks were often observed for hypothesized interactions between cells that were positive for both YY1 and CD20. [Figure 1] shows example HIDs and their graphs for patients with poor (D_{1} ) versus good (D_{2} ) survival.  Figure 2: Contour plot showing the value of the χ^{2} test statistic as a function of pairing distance d _{P} and interaction distance d _{I} for the summary statistic D_{max}
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 Figure 3: Survival curves— estimated using leaveoneout validation— for groups defined by thresholding H(D). The curves are statistically significantly different ( P = 0.00750)
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 Table 2: Leaveoneout analysis results. Optimal values of d_{I} and d_{P}, and the resulting P values. The statistically significant (P < 0.05) result for H (D) would survive Bonferroni correction
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Conclusions   
We have developed a statistical framework to represent potential interactions between proximal cells. The method defines a statistical distribution over "hypothesized interactions"a pairing of cells with particular combinations of IHC characteristics, located within a given distance of one another. These distributions can be represented in matrix and graphical forms. Relatively simple scalar summaries of these distributions can be used to assign patients to groups that may differ in terms of survival, and the distributions themselves can be inspected to identify possible cellular interactions that are associated with short versus long survival.
HID analysis of retrospective data from a study of FL showed that Shannon entropy, H(D), was able to assign patients to groups with significantly different survival curves. Our results suggest that cells that are positive for both YY1 and CD20 may interact to patient detriment. This result is consistent with our understanding of the biology of these cells, but existing analysis tools do not allow testing of this hypothesis.
One limitation of this work is the visual (albeit quantitative and objective) selection of distances d _{P} and d _{I} prior to, and outside of, the leaveoneout analysis. Unfortunately, the high computational cost of evaluating the χ^{2} functionand the fact that the function tends to have multiple maximamade automated selection infeasible within the scope of this work. Future research should address this problem.
In conclusion, HID analysis provides a largely automated quantitative method for making inferences about possible interactions between proximal cellsin terms of their IHC characteristics as measured using multispectral microscopy and multiple IHC markerswith potential value for diagnosis and prognosis.
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[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2]
