Applications of deep-learning (DL) algorithms in digital pathology have been in great interest in recent years [1]. For applications related to digital pathology (for example, in the case of designing applications for TILs-scoring, as will be discussed shortly), segmentation is often a major stage. For example, it is shown that tumor-infiltrating lymphocytes (TILs) are important in cancer prognosis [2]. In clinical practice, pathologists’ visual assessment of TILs in biopsies and surgical resections of human epidermal growth factor receptor-2 positive (HER2+) and triple-negative breast cancers (TNBC) results in a quantitative score (TILs-score). Advances in ML algorithms in digital pathology pave the way for designing algorithms to automatically generate TILs-scores using whole slide images (WSIs). However, to design an automated TILs-scoring algorithm, the first stage is to design a segmentation algorithm to segment the tissue into tumoral and tumor-associated stromal regions. In later stages, a detection algorithm is also designed to detect “Lymphocytes” in the stromal regions. Based on the outputs of these segmentation and detection algorithms, a TILs-score, as a quantitative biomarker can be calculated automatically [3]. Hence, segmentation algorithms play a major role in a DL-based application in digital pathology.
With the segmentation annotations (in the form of segmentation masks) manually delineated by expert clinicians, a DL algorithm could be trained to automatically segment the tissue into tumoral and stromal regions. However, it is very burdensome and even infeasible to obtain segmentation annotations in the entire tissue regions of a WSI. This is due to the sheer size of WSIs in digital pathology applications in the range of 100,000 pixels in each of the two dimensions. Hence, a common practice is to select several regions of interests (ROIs) for segmentation annotations. As a result, segmentation annotations are obtained across several whole slide images, each containing several ROIs annotated in different locations.
One example is shown in the figure below wherein three ROIs in a single WSI are annotated by expert clinicians to train/test a segmentation algorithm.
Figure 1. Left hand side shows the entire whole slide image usually with a size on the order of 100,000 by 100,000 pixels. Three selected ROIs are chosen and annotated. One ROI is shown on the right-hand side with the segmentation mask highlighting different tissue regions (image courtesy: https://tiger.grand-challenge.org).
After training a segmentation algorithm, these algorithms should be properly evaluated. As discussed previously, providing segmentation annotations in the entire tissue region of a whole slide image is not feasible. Instead, several ROIs are annotated. It is critically important to have proper test methodologies for aggregation when evaluating the performance of segmentation algorithms in digital pathology applications.
Note: We assume that the segmentation reference standard is already obtained through an established method in selected ROIs across a set of whole slide images and we only focus on evaluating the performance of these segmentation algorithms as compared to the reference standard annotations.
References
- Janowczyk A, Madabhushi “A. Deep learning for digital pathology image analysis: A comprehensive tutorial with selected use cases”. J Pathol Inform. 2016; 7:29. Jul 26, 2023.
- C. Denkert et al., “Tumour-infiltrating lymphocytes and prognosis in different subtypes of breast cancer: a pooled analysis of 3771 patients treated with neoadjuvant therapy”, The Lancet Oncology, 19, 2018, 40-50.
- Arian Arab, et. al., “Effect of color normalization on deep learning segmentation models for tumor-infiltrating lymphocytes scoring using breast cancer histopathology images”. Proc. SPIE 12471, Medical Imaging 2023: Digital and Computational Pathology, 124711H, April 6, 2023.
We briefly describe the methods in this tool to evaluate performance of segmentation algorithms applied to digital pathology whole slide image applications.
We assume that the test dataset contains N WSIs from N patients with one WSI per patient (i=1,2, ...N, where i is the index of the ith WSI and N is the total number of WSIs). Each WSI contains a number of ROIs annotated (M1, M2, M3, … where Mi is the number of ROIs annotated for the ith WSI, the total number of ROIs annotated across the entire set of WSIs is M= ∑Mi). For each ROI, a reference segmentation mask is obtained. The reference segmentation masks will be compared to the algorithm-generated segmentation masks. If the segmentation algorithm is designed to segment the tissue into C classes, for each ROI, a C×C confusion matrix can be obtained, and a Dice score for each of the C class labels can be found (cmij refers to the confusion matrix of the jth ROI of the ith whole slide image).
For a C-class segmentation task, by comparing the reference standard annotations to the algorithm’s outputs, a confusion matrix of dimensions C×C can be obtained. From the confusion matrix, for each class, a Dice score can be calculated. In a one-versus-the-rest approach, a class is defined as positive and the rest as negative, and a 2×2 confusion matrix can be obtained for each of the C classes. From the 2×2 confusion matrix, a Dice score for the positive class can be obtained (TP, FP, FN, and TN are obtained by comparing the algorithm’s predictions and the ground truth labels at the pixel level):
For each of the class labels, a Dice score can be obtained. If the reference standard annotations contain the positive class, a Dice score is obtained; otherwise, a Dice score is not assigned for that specific class (NaN).
For example, an ROI in a single WSI is shown below. The segmentation annotations contain three different class labels (C=3, with label values of 0, 1, and 2). As a result, three Dice scores for each of the class labels are obtained:
As another example, three ROIs in a single whole slide image, along with the reference standard annotations and the algorithm’s predictions are shown in the figure below. As can be seen, for each of the ROIs, a confusion matrix can be obtained and since this is a 3-class segmentation task, for each of the class labels and for each of the ROIs a Dice score can be obtained:
As can be seen from the figure above, for the first ROI, the reference standard annotations contain all the three class labels and hence three Dice scores are obtained for each of the three class labels (Dice scores of 0.0138, 0.8636, 0.8358).
For the second ROI, since two of the class labels are absent in the reference standard annotations, for these classes, Dice scores are not assigned (“NaN” values). A Dice score of 0.4797 is obtained for the class shown with the red mask.
For the third ROI, since one of the class labels is absent in the reference standard annotation, a Dice score is not assigned for that class ("NaN" value) and Dice scores of 0.9189 and 0.9445 are obtained for the other two classes.
We discuss three methods of obtaining a Dice score for the entire set of whole slide images.
In the first method, we aggregate all the confusion matrices across all the ROIs and across all the WSIs to obtain one confusion matrix (CM, Equation 1). From this confusion matrix, CM , a Dice score can be obtained. This method weighs all the pixels across all the ROIs and across all the whole slide images equally when aggregating all the confusion matrices (cmij) into a single confusion matrix (CM):
Here, FDICE (CM) is the Dice values obtained from the confusion matrix (CM).
In the second method, we first calculate a Dice score for each of the ROIs (Diceij is the Dice score of the jth ROI of the ith WSI obtained from the confusion matrix cmij). We then average all the Dice scores across all the ROIs in all the WSIs . This method weighs all the ROIs across all the WSIs equally, Equation 2:
In the third method, we first calculate a Dice score for each WSI (Dicei is the Dice score of the ith whole slide image). We then average all the Dice scores across all WSIs. This method weighs all the WSIs equally, Equation 3:
However, a Dice score for the whole slide image can be obtained in two different ways: firstly, by weighing all the pixels across an entire whole slide image equally, Equation (3a), and secondly, by weighing all the ROIs across an entire whole slide image equally, Equation (3b):
To calculate confidence intervals we use the bootstrap method. To obtain one bootstrap sample, we randomly sample N WSIs with replacement from the original pool of the N WSIs in the test dataset. Each time we select a WSI from the pool of the N whole slide images, all the ROIs of that slide is also selected. As a result, the three methods discussed above could be used to obtain Dice scores for the bootstrapped samples as well. We repeat this bootstrap sampling k times (e.g., k = 5000). From the distribution of Dice scores across these k samples, lower and upper bounds of confidence interval at different confidence levels could be obtained.
Inputs/Outputs requirements to the software tool as well as each of the functions within the software tool are described in the "User Manual.pdf" document. Please refer to this document for a full descirpiton of the software tool and its usage.
The "run-example.py" function wihtin the "example" folder, contains an example code how to use the software tool to generate Dice score point-estimates as well as confidence intervals for a set of WSIs annotated across several ROIs.
The software package has been tested with Python 3.#.#. Required packages include “NumPy”, “Matplotlib” and “tqdm” that can be installed as follows:
pip install numpy matplotlib tqdm
For any questions/suggestions/collaborations, please contact Arian Arab either via this GitHub repo or via email ([email protected]).
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