# A Method for Unsupervised Semi-Quantification of Inmunohistochemical Staining with Beta Divergences

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Methods

#### 3.1. Stain Separation

#### 3.1.1. Preliminary Separation Step

#### 3.1.2. Final Separation Step

#### 3.2. Feature Extraction

#### 3.3. Prediction of the Scores

## 4. Results and Discussion

#### 4.1. Data Description

#### 4.2. Stain Separation Results

#### 4.3. Prediction of the Scores Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

IHC | Immunohistochemistry |

RGB | Red–Green–Blue |

DAB | 3,3′-Diaminobenzidine |

H | Hematoxylin |

CD | Color Deconvolution |

NMF | Non-Negative Matrix Factorization |

SNMF | Sparse Non-Negative Matrix Factorization |

KL | Kullback–Leibler |

IS | Itakura–Saito |

OD | Optical Density |

ED | Eigendecomposition |

## References

- van der Loos, C.M. Multiple immunoenzyme staining: Methods and visualizations for the observation with spectral imaging. J. Histochem. Cytochem. Off. J. Histochem. Soc.
**2008**, 56, 313–328. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kitaya, K.; Yasuo, T. Inter-observer and intra-observer variability in immunohistochemical detection of endometrial stromal plasmacytes in chronic endometritis. Exp. Ther. Med.
**2013**, 5, 485–488. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Meyerholz, D.K.; Beck, A.P. Fundamental Concepts for Semiquantitative Tissue Scoring in Translational Research. ILAR J.
**2018**, 59, 13–17. [Google Scholar] [CrossRef] [PubMed] - Fedchenko, N.; Reifenrath, J. Different approaches for interpretation and reporting of immunohistochemistry analysis results in the bone tissue—A review. Diagn. Pathol.
**2014**, 9, 221. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Aeffner, F.; Wilson, K.; Martin, N.T.; Black, J.C.; Hendriks, C.L.L.; Bolon, B.; Rudmann, D.G.; Gianani, R.; Koegler, S.R.; Krueger, J.; et al. The Gold Standard Paradox in Digital Image Analysis: Manual Versus Automated Scoring as Ground Truth. Arch. Pathol. Lab. Med.
**2017**, 141, 1267–1275. [Google Scholar] [CrossRef] [Green Version] - Bankhead, P.; Fernández, J.; McArt, D.G.; Boyle, D.P.; Li, G.; Loughrey, M.B.; Irwin, G.W.; Harkin, D.P.; James, J.A.; McQuaid, S.; et al. Integrated tumor identification and automated scoring minimizes pathologist involvement and provides new insights to key biomarkers in breast cancer. Lab. Investig.
**2018**, 98, 15–26. [Google Scholar] [CrossRef] [Green Version] - Varghese, F.; Bukhari, A.B.; Malhotra, R.; De, A. IHC Profiler: An Open Source Plugin for the Quantitative Evaluation and Automated Scoring of Immunohistochemistry Images of Human Tissue Samples. PLoS ONE
**2014**, 9, e96801. [Google Scholar] [CrossRef] [Green Version] - Loughrey, M.B.; Bankhead, P.; Coleman, H.G.; Hagan, R.S.; Craig, S.; McCorry, A.M.B.; Gray, R.T.; McQuaid, S.; Dunne, P.D.; Hamilton, P.W.; et al. Validation of the systematic scoring of immunohistochemically stained tumour tissue microarrays using QuPath digital image analysis. Histopathology
**2018**, 73, 327–338. [Google Scholar] [CrossRef] [Green Version] - Mane, D.R.; Kale, A.D.; Belaldavar, C. Validation of immunoexpression of tenascin-C in oral precancerous and cancerous tissues using ImageJ analysis with novel immunohistochemistry profiler plugin: An immunohistochemical quantitative analysis. J. Oral Maxillofac. Pathol.
**2017**, 21, 211–217. [Google Scholar] [CrossRef] [Green Version] - Crowe, A.R.; Yue, W. Semi-quantitative Determination of Protein Expression using Immunohistochemistry Staining and Analysis: An Integrated Protocol. Bio-Protoc.
**2019**, 9, e3465. [Google Scholar] [CrossRef] - Ruifrok, A.C.; Johnston, D.A. Quantification of histochemical staining by color deconvolution. Anal. Quant. Cytol. Histol.
**2001**, 23, 291–299. [Google Scholar] [PubMed] - Macenko, M.; Niethammer, M.; Marron, J.S.; Borland, D.; Woosley, J.T.; Guan, X.; Schmitt, C.; Thomas, N.E. A method for normalizing histology slides for quantitative analysis. In Proceedings of the 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Boston, MA, USA, 28 June–1 July 2009; pp. 1107–1110. [Google Scholar] [CrossRef]
- Anghel, A.; Stanisavljevic, M.; Andani, S.; Papandreou, N.; Rüschoff, J.; Wild, P.; Gabrani, M.; Pozidis, H. A High-Performance System for Robust Stain Normalization of Whole-Slide Images in Histopathology. Front. Med.
**2019**, 6, 193. [Google Scholar] [CrossRef] [PubMed] - Salvi, M.; Michielli, N.; Molinari, F. Stain Color Adaptive Normalization (SCAN) algorithm: Separation and standardization of histological stains in digital pathology. Comput. Methods Programs Biomed.
**2020**, 193, 105506. [Google Scholar] [CrossRef] [PubMed] - Pérez-Bueno, F.; Vega, M.; Sales, M.A.; Aneiros-Fernández, J.; Naranjo, V.; Molina, R.; Katsaggelos, A.K. Blind color deconvolution, normalization, and classification of histological images using general super Gaussian priors and Bayesian inference. Comput. Methods Programs Biomed.
**2021**, 211, 106453. [Google Scholar] [CrossRef] - Gavrilovic, M.; Azar, J.; Lindblad, J.; Wahlby, C.; Bengtsson, E.; Busch, C.; Carlbom, I. Blind color decomposition of histological images. IEEE Trans. Med Imaging
**2013**, 32, 983–994. [Google Scholar] [CrossRef] - Geijs, D.J.; Intezar, M.; van der Laak, J.A.W.M.; Litjens, G.J.S. Automatic color unmixing of IHC stained whole slide images. In Proceedings of the SPIE Medical Imaging 2018: Digital Pathology, Houston, TX, USA, 10–15 February 2018; Volume 10581. [Google Scholar] [CrossRef]
- Trahearn, N.; Snead, D.; Cree, I.; Rajpoot, N. Multi-class stain separation using independent component analysis. In Proceedings of the SPIE Medical Imaging 2015: Digital Pathology, Orlando, FL, USA, 21–26 February 2015; Gurcan, M.N., Madabhushi, A., Eds.; International Society for Optics and Photonics: Bellingham, WA, USA, 2015; Volume 9420, pp. 113–123. [Google Scholar] [CrossRef]
- Carey, D.; Wijayathunga, V.; Bulpitt, A.; Treanor, D. A novel approach for the colour deconvolution of multiple histological stains. In Proceedings of the 19Th Conference of Medical Image Understanding and Analysis, Lincoln, UK, 15–17 July 2015; pp. 156–162. [Google Scholar]
- Rabinovich, A.; Agarwal, S.; Laris, C.A.; Price, J.H.; Belongie, S. Unsupervised Color Decomposition of Histologically Stained Tissue Samples. In Proceedings of the 16th International Conference on Neural Information Processing Systems (NIPS’03), Whistler, BC, Canada, 9–11 December 2003; MIT Press: Cambridge, MA, USA, 2003; pp. 667–674. [Google Scholar]
- Vahadane, A.; Peng, T.; Sethi, A.; Albarqouni, S.; Wang, L.; Baust, M.; Steiger, K.; Schlitter, A.M.; Esposito, I.; Navab, N. Structure-Preserving Color Normalization and Sparse Stain Separation for Histological Images. IEEE Trans. Med. Imaging
**2016**, 35, 1962–1971. [Google Scholar] [CrossRef] - Van Eycke, Y.R.; Allard, J.; Salmon, I.; Debeir, O.; Decaestecker, C. Image processing in digital pathology: An opportunity to solve inter-batch variability of immunohistochemical staining. Sci. Rep.
**2017**, 7, 42964. [Google Scholar] [CrossRef] [Green Version] - Li, X.; Plataniotis, K.N. A Complete Color Normalization Approach to Histopathology Images Using Color Cues Computed From Saturation-Weighted Statistics. IEEE Trans. Biomed. Eng.
**2015**, 62, 1862–1873. [Google Scholar] [CrossRef] - Geread, R.S.; Morreale, P.; Dony, R.D.; Brouwer, E.; Wood, G.A.; Androutsos, D.; Khademi, A. IHC Color Histograms for Unsupervised Ki67 Proliferation Index Calculation. Front. Bioeng. Biotechnol.
**2019**, 7, 226. [Google Scholar] [CrossRef] - Ghoshal, B.; Hikmet, F.; Pineau, C.; Tucker, A.; Lindskog, C. DeepHistoClass: A Novel Strategy for Confident Classification of Immunohistochemistry Images Using Deep Learning. Mol. Cell. Proteom.
**2021**, 20, 100140. [Google Scholar] [CrossRef] - Bencze, J.; Szarka, M.; Kóti, B.; Seo, W.; Hortobágyi, T.G.; Bencs, V.; Módis, L.V.; Hortobágyi, T. Comparison of Semi-Quantitative Scoring and Artificial Intelligence Aided Digital Image Analysis of Chromogenic Immunohistochemistry. Biomolecules
**2022**, 12, 19. [Google Scholar] [CrossRef] [PubMed] - Uhlén, M.; Fagerberg, L.; Hallström, B.M.; Lindskog, C.; Oksvold, P.; Mardinoglu, A.; Sivertsson, Å.; Kampf, C.; Sjöstedt, E.; Asplund, A.; et al. Proteomics. Tissue-based map of the human proteome. Science
**2015**, 347, 1260419. [Google Scholar] [CrossRef] [PubMed] - Uhlen, M.; Zhang, C.; Lee, S.; Sjöstedt, E.; Fagerberg, L.; Bidkhori, G.; Benfeitas, R.; Arif, M.; Liu, Z.; Edfors, F.; et al. A pathology atlas of the human cancer transcriptome. Science
**2017**, 357, eaan2507. [Google Scholar] [CrossRef] [Green Version] - Choudhury, K.R.; Yagle, K.J.; Swanson, P.E.; Krohn, K.A.; Rajendran, J.G. A robust automated measure of average antibody staining in immunohistochemistry images. J. Histochem. Cytochem. Off. J. Histochem. Soc.
**2010**, 58, 95–107. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ram, S.; Vizcarra, P.; Whalen, P.; Deng, S.; Painter, C.L.; Jackson-Fisher, A.; Pirie-Shepherd, S.; Xia, X.; Powell, E.L. Pixelwise H-score: A novel digital image analysis-based metric to quantify membrane biomarker expression from immunohistochemistry images. PLoS ONE
**2021**, 16, e0245638. [Google Scholar] [CrossRef] [PubMed] - Samek, W.; Blythe, D.; Müller, K.R.; Kawanabe, M. Robust Spatial Filtering with Beta Divergence. In Proceedings of the Advances in Neural Information Processing Systems, Lake Tahoe, NV, USA, 5–10 December 2013; Burges, C.J.C., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K.Q., Eds.; Curran Associates, Inc.: Red Hook, NY, USA, 2013; Volume 26. [Google Scholar]
- Jolliffe, I. Principal Component Analysis; Springer Series in Statistics; Springer: Berlin/Heidelberg, Germany, 2002. [Google Scholar]
- Cichocki, A.; Zdunek, R.; Amari, S.i. Csiszár’s Divergences for Non-negative Matrix Factorization: Family of New Algorithms. In Proceedings of the Independent Component Analysis and Blind Signal Separation, Charleston, SC, USA, 5–8 March 2006; Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S., Eds.; Springer: Berlin/Heidelberg, Germany, 2006; pp. 32–39. [Google Scholar]
- Cichocki, A.; Cruces, S.; Amari, S.i. Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization. Entropy
**2011**, 13, 134–170. [Google Scholar] [CrossRef] - Leplat, V.; Gillis, N.; Févotte, C. Multi-resolution beta-divergence NMF for blind spectral unmixing. Signal Process.
**2022**, 193, 108428. [Google Scholar] [CrossRef] - Cichocki, A.; Amari, S.I. Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities. Entropy
**2010**, 12, 1532–1568. [Google Scholar] [CrossRef] [Green Version] - Cichocki, A.; Zdunek, R.; Phan, A.H.; Amari, S.I. Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-Way Data Analysis and Blind Source Separation; John Wiley & Sons: Hoboken, NJ, USA, 2009. [Google Scholar]
- Sarmiento, A.; Fondón, I.; Durán-Díaz, I.; Cruces, S. Centroid-Based Clustering with AB-Divergences. Entropy
**2019**, 21, 196. [Google Scholar] [CrossRef] [Green Version] - Bodineau, C.; Tomé, M.; Courtois, S.; Costa, A.S.H.; Sciacovelli, M.; Rousseau, B.; Richard, E.; Vacher, P.; Parejo-Pérez, C.; Bessede, E.; et al. Two parallel pathways connect glutamine metabolism and mTORC1 activity to regulate glutamoptosis. Nat. Commun.
**2021**, 12, 4814. [Google Scholar] [CrossRef] - Landis, J.R.; Koch, G.G. The Measurement of Observer Agreement for Categorical Data. Biometrics
**1977**, 33, 159–174. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Examples of different immunolabeling intensities in IHC images with a magnification of 20×: (

**a**) very low positivity or negative (1+), (

**b**) low positivity (2+), (

**c**) mild positivity (3+), (

**d**) moderate positivity (4+), and (

**e**) strong positivity (5+). The protein was visualized by DAB chromogen and nuclear counterstain with hematoxylin.

**Figure 2.**Example of IHC images where there is a discrepancy in the score assigned by the observers. In (

**a**), the image has been annotated as 1+ or 2+, in (

**b**), the image has been annotated as 3+ or 4+, and in (

**c**) the image has been annotated as 4+ or 5+.

**Figure 3.**Stain separation results of the reference image ${\mathbf{Y}}_{5+}$ obtained with eigendecomposition method: (

**a**) Original IHC image (

**b**) H-plane estimated (

**c**) DAB-plane estimated.

**Figure 4.**Example of stain separation in an IHC image with a high-intensity level: (

**a**) Original image, (

**b**) Preliminary stain separation and (

**c**) Final stain separation.

**Figure 5.**Example of stain separation in an IHC image with a low-intensity level: (

**a**) Original image, (

**b**) Preliminary stain separation, and (

**c**) Final stain separation.

**Figure 6.**Correlation between some features based on the DAB staining plane and the score annotated by one expert for all the images in the dataset. The features examined are: (

**a**) ATM score, (

**b**) Pix-H score, and (

**c**) 1-norm of the DAB stain concentration vector obtained in the NMF decomposition of the OD image. Similar results are obtained with the scores of the other observers.

**Figure 7.**Scatter plot of the extracted features and the scores: (

**a**) calculated as the median value of the annotations of observers, (

**b**) predicted by our method.

K-Means with Euclidean Distance | K-Means with Beta Divergence | |
---|---|---|

Observer #1 | 93.61 | 94.58 |

Observer #2 | 75.53 | 76.60 |

Observer #3 | 86.17 | 87.23 |

Observer #4 | 89.36 | 90.43 |

Mean | 86.17 | 87.23 |

**Table 2.**Pairwise inter-observer reliability of semi-quantitative scoring by four observers and the proposed score. Crosstabs contain the Cohen’s kappa values, $\kappa $ (orange background), and the strength of agreement (blue background) between two different observers.

Observers | Observer #1 | Observer #2 | Observer #3 | Observer #4 | Predicted |
---|---|---|---|---|---|

Observer #1 | 0.7672 | 0.8503 | 0.8906 | 0.9315 | |

Observer #2 | Good | 0.7810 | 0.6850 | 0.6979 | |

Observer #3 | Very good | Good | 0.7054 | 0.8364 | |

Observer #4 | Very good | Good | Good | 0.8765 | |

Predicted | Very good | Good | Very good | Very good |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sarmiento, A.; Durán-Díaz, I.; Fondón, I.; Tomé, M.; Bodineau, C.; Durán, R.V.
A Method for Unsupervised Semi-Quantification of Inmunohistochemical Staining with Beta Divergences. *Entropy* **2022**, *24*, 546.
https://doi.org/10.3390/e24040546

**AMA Style**

Sarmiento A, Durán-Díaz I, Fondón I, Tomé M, Bodineau C, Durán RV.
A Method for Unsupervised Semi-Quantification of Inmunohistochemical Staining with Beta Divergences. *Entropy*. 2022; 24(4):546.
https://doi.org/10.3390/e24040546

**Chicago/Turabian Style**

Sarmiento, Auxiliadora, Iván Durán-Díaz, Irene Fondón, Mercedes Tomé, Clément Bodineau, and Raúl V. Durán.
2022. "A Method for Unsupervised Semi-Quantification of Inmunohistochemical Staining with Beta Divergences" *Entropy* 24, no. 4: 546.
https://doi.org/10.3390/e24040546