Automated gleason grading on prostate biopsy slides by statistical representations of homology profile

Abstract

Background and Objective:

Gleason grading system is currently the clinical gold standard for determining prostate cancer aggressiveness. Prostate cancer is typically classified into one of 5 different categories with 1 representing the most indolent disease and 5 reflecting the most aggressive disease. Grades 3 and 4 are the most common and difficult patterns to be discriminated in clinical practice. Even though the degree of gland differentiation is the strongest determinant of Gleason grade, manual grading is subjective and is hampered by substantial inter-reader disagreement, especially with regard to intermediate grade groups.

Methods:

To capture the topological characteristics and the degree of connectivity between nuclei around the gland, the concept of Homology Profile (HP) for prostate cancer grading is presented in this paper. HP is an algebraic tool, whereby, certain algebraic invariants are computed based on the structure of a topological space. We utilized the Statistical Representation of Homology Profile (SRHP) features to quantify the extent of glandular differentiation. The quantitative characteristics which represent the image patch are fed into a supervised classifier model for discrimination of grade patterns 3 and 4.

Results:

On the basis of the novel homology profile, we evaluated 43 digitized images of prostate biopsy slides annotated for regions corresponding to Grades 3 and 4. The quantitative patch-level evaluation results showed that our approach achieved an Area Under Curve (AUC) of 0.96 and an accuracy of 0.89 in terms of discriminating Grade 3 and 4 patches. Our approach was found to be superior to comparative methods including handcrafted cellular features, Stacked Sparse Autoencoder (SSAE) algorithm and end-to-end supervised learning method (DLGg). Also, slide-level quantitative and qualitative evaluation results reflect the ability of our approach in discriminating Gleason Grade 3 from 4 patterns on H&E tissue images.

Conclusions:

We presented a novel Statistical Representation of Homology Profile (SRHP) approach for automated Gleason grading on prostate biopsy slides. The most discriminating topological descriptions of cancerous regions for grade 3 and 4 in prostate cancer were identified. Moreover, these characteristics of homology profile are interpretable, visually meaningful and highly consistent with the rubric employed by pathologists for the task of Gleason grading.

1. Introduction

Prostate cancer is the second leading cause of cancer deaths among males, accounting for 7.1% and 3.8% for cancer incidence and mortality, respectively [1]. The Gleason grading system [2] is the most widely used grading scheme for diagnosis and risk stratification of prostate cancer. The Gleason grade is the strongest marker of disease aggressiveness and longer term outcome for prostate cancer. It is significant in that it can help clinicians make appropriate treatment management decisions for prostate cancer patients, i.e. help decide between more aggressive therapy versus active surveillance. In the Gleason grading schema, the regions in the tissue slides are assigned pathological grades from 1 to 5 (worst) based off the observed gland differentiation patterns. Typically the dominant and the secondary most aggressive Gleason patterns are identified and combined to provide the Gleason score. Note that while this can generate scores from 2 to 10, the newest ISUP scheme categorizes the different Gleason score tumors into 5 categories corresponding to the most commonly occurring Gleason scores (3+3, 3+4, 4+3, 4+4 and > 4+4) [3]. The most challenging set of categories to distinguish are grade 3 ( G₃ ) and grade 4 ( G₄ ). This is a task that is time-consuming and typically has the highest degree of inter-reader variability among pathologists. There is thus a need for developing computerized image analysis systems for distinguishing G₃ and G₄.

In recent years, with the rapid development of digital pathology [4], many computational pathology algorithms have been presented for studying digitized histological slides and aiding in problems relating to disease diagnosis, prognosis and prediction of treatment response [5–8]. Bera et al. [8] provided an excellent review of the various categories of feature based approaches in computational pathology, including hand-crafted and deep learning based approaches. In the context of prostate cancer, many approaches have been proposed for both prostate cancer diagnosis and grading [9–15]. Doyle et al. [16] identified cancerous regions on biopsy slides by a boosted Bayesian multi-resolution system. Monaco and Madabhushi [17] used a Markov-random field (MRF) based approach with a class specific weighting approach to identify regions of cancer on surgically resected specimens. In the field of deep learning, Li et al. [11] presented a region-based convolutional neural network framework for simultaneous multi-task epithelial cell detection and Gleason grading. Poojitha and Sharma [15] presented a hybrid architecture with unified deep learning techniques to perform Gleason grading. Two papers in The Lancet Oncology by Ström et al. [18], Bulten et al. [19] used deep learning methods for detection and Gleason grading of prostate cancer in digital images of biopsies.

Although deep learning based approaches have become very popular in the context of computational pathology [14,20], the black-box nature of these approaches raises questions about interpretability and clinical adoption [21]. Handcrafted features, however, usually leverage intrinsic domain knowledge of pathologists [8]. For pathologists, the degree of glandular differentiation is critical for determining the grade of prostate cancer (see Fig. 1). Mosquera-Lopez et al. [9] in their paper discussed multiple different textural based approaches for detection and grading of prostate cancer. Ali et al. [22] discriminated different grade patterns by nuclear shape-based, architectural and textural features. Farooq et al. [10] presented a computer aided system by combining Gabor and local binary pattern (LBP) based texture features for the grading of prostate cancer. Leo et al. [23] studied stability and discriminability for a wide spectrum of gland texture and shape features for Gleason grading in prostatectomy specimens. Lee et al. [24] presented a co-occurring gland angularity approach to model the extent of gland architectural disorder for the problem of discriminating benign and malignant glands on prostate tissue sections. The features were also shown to be prognostic of the risk of biochemical recurrence on post-prostatectomy specimens. Niazi et al. [25] evaluated luminal and architectural features to discriminate low-grade (Gleason score ≤ 6) and high-grade (Gleason score ≥ 8) prostate cancers. Interestingly, a number of studies have shown that the Gleason grading system is based on architectural patterns [26,27], which suggests that the topological arrangement of the nuclei with respect to the individual glands could harbor grade discriminating information. None of the approaches presented to date, that we are aware of, have explicitly looked at the interplay of cellular and glandular features for the problem of prostate cancer grading.

Fig. 1.

An example of a digital whole slide image with pathologists’ annotations and its samples, which illustrate the degree of gland differentiation among Gleason G₃ and G₄. Left and right are samples of G₃ and G₄ with 160 × 160 pixel at 10x magnification, respectively.

The Homology Profile (HP) algorithm is an algebraic tool for measuring topological features of objects [28]. Given a topological space, the HP algorithm computes numbers of connected components and holes using the structure of that space based on continuous thresholds. These topological features represent the sustained variance in arrangement of objects such as nuclei of glands in different grades of prostate cancer. Nakane et al. [42,43] Recently, Qaiser et al. [29–31] employed the HP algorithm for tumor segmentation by focusing on the connectivity between nuclei.

In this work, we present novel Statistical Representation of Homology Profile (SRHP) features for automated discrimination of Gleason grade patterns G₃ and G₄ from digital pathological tissue images. We employed the HP features to describe topological arrangements of the nuclei with respect to the gland lumen and quantify the degree of gland differentiation in needle biopsy slides of prostate cancer. A supervised machine classifier algorithm was employed in conjunction with the HP features to evaluate the discrimination of the G₃ and G₄ tissue pathology images. In this study, 43 whole slide images of prostate biopsy slides were chosen and we obtained 9597 patches for G₃ and 8679 patches for G₄ grade regions from the slides. A 10-fold cross validation scheme across 18,276 was then utilized for evaluation.

2. Materials and methods

Fig. 2 illustrates the overall flowchart of our approach. The flowchart delineates the image processing, HP feature extraction and classifier modeling modules.

Fig. 2.

(A) The flowchart for our approach for discrimination of G₃ and G₄ prostate cancerous regions. Hematoxylin staining component of the patch is leveraged for HP computation and statistical representation, followed by classifier modeling. (B) The procedure of HP computation. An image is converted to binary images for computing Betti numbers [29], which form variable distributions.

2.1. Data set and images preprocessing

43 digitized images of prostate biopsy slides stained with Hematoxylin&Eosin (H&E) were used in this study. All these slides including regions of interest with G₃ and G₄ were obtained from UPenn (the Hospital at the University of Pennsylvania). All slides were digitized at 40x magnification and manually annotated by expert pathologists. From the regions of interest annotated by pathologists, image patches of sizes 640 × 640 pixels at 40x magnification were extracted. The grades of these patches were determined according to pathologist based annotation of the regions they were derived from. Since the focus was on evaluating features relating to the topology and connectivity among nuclei rather than features relating to individual nuclei, the patch size was 160 × 160 pixels at 10x magnification. The window slides across each region of interest image row by row from upper left corner to lower right (the step size was fixed at 80 pixels). Then the overlapping image patches of 160 × 160 pixels were employed for feature extraction. We thus obtained 9597 patches for G₃ and 8679 patches for G₄ grade regions from a total of 43 biopsy slides.

H&E staining is the most commonly used method for paraffin sections. The hematoxylin staining makes the chromatin in the nucleus and ribosome in cytoplasm purple-blue and eosin makes the components of cytoplasm and extracellular matrix red. We utilized color deconvolution [32] for separation of the hematoxylin stain. However, on account of high variability of color stain, the fixed stain matrix adopted in Ruifrok et al. [32] is not appropriate. Since we needed an adaptive approach, we employed the color stain estimation approach proposed in Macenko et al. [33] for computing the stain matrix. The estimation method yielded a unique matrix for each image patch, representing the stain matrix for hematoxylin separation. The corresponding stain matrices are shown as follows:

$$\left[\begin{array}{ccc}0.644211& 0.716556& 0.266844\\ 0.092789& 0.954111& 0.283111\end{array}\right]$$ (1)

$$\left[\begin{array}{ccc}0.5155\pm 0.0307& 0.7234\pm 0.0169& 0.4576\pm 0.0205\\ 0.1501\pm 0.0200& 0.7723\pm 0.0308& 0.6149\pm 0.0391\end{array}\right]$$ (2)

where (1) is the original fixed Ruifrok stain matrix [32] and (2) is the average stain matrix obtained via the adaptive estimation method [33]. The first and the second rows in the matrices (1) and (2) refer to hematoxylin and eosin stains, respectively. Separation of hematoxylin stain channel can emphasize the precise location of the individual nuclei and facilitate the computation of the HP features.

2.2. Statistics representation of homology profile (SRHP)

The HP algorithm provides an algebraic tool for measuring and quantifying geometric and topological features of objects and shapes in the topological space [28]. For a two-dimensional image, the HP method involves the calculation of the number of connected components and voids, denoted as b₀ and b₁ to represent the topological features. In this work we employ b₀ and b₁ for measuring the degree of connectivity among the nuclei around glands.

Prior to feature extraction, the H stained image is binarized from $X$ to ${X^{\prime }}_t$ by the application of threshold t, replacing any value in X more than t by 1 and all other values by 0. The resulting image ${X^{\prime }}_t$ can be thought of as filtered representations of the original image X. Betti numbers [29] b₀ and b₁ are then computed based off connected components in ${X^{\prime }}_t$ and ${X^{\prime }}_{255}\backslash {X^{\prime }}_{\mathrm{t}}$, respectively, where ${X^{\prime }}_{255}\backslash {X^{\prime }}_t$ is the complement of ${X^{\prime }}_t$ in ${X^{\prime }}_{255}$ and ${X^{\prime }}_{255}$ is the binarized image from X with a threshold 255. As t gradually changes with respect to the value from 0 to K, the filtered representations ${X^{\prime }}_t$ change dynamically. This makes b₀ and b₁ values increase or decrease. Fig. 3 shows the process of image evolution and the calculation of Betti numbers. In this work, the threshold t range was set from 1 to 255 with an increment of 1 for HP computation. We thus obtain a 510-dimensional (255 × 2) low-level Betti sequence vector which represents the image patch.

Fig. 3.

The procedure of binary image evolution and calculation of the Betti numbers. The H staining component image is binarized using different threshold values (40, 100 and 150). Connected components b₀ and white voids b₁ are indicated via blue dots and red stars, respectively.

There are many methods to characterize and evaluate the 510-dimensional feature vector corresponding to an image patch. One approach is to measure the distance between the testing patch and an exemplar patch identified via a Convolutional Neural Network using the symmetric Kullback-Leibler Divergence [29]. However, this approach tends to rely heavily on the choice of exemplars. On account of the significant morphologic heterogeneity within individual grades, let alone between G₃ and G₄ [34], identifying exemplars to represent G₃ and G₄ is non-trivial. We utilized the classical statistical method [35] to re-characterize the 510-dimensional feature vector and use it to discover the regularity of data.

The two 255 successive Betti numbers can be viewed as 2 discrete probability distributions Y₀ , Y₁. Y₀, Y₁ can be viewed in terms of (1) the centralized trend of distribution, (2) the degree of dispersion and (3) the shape [36]. The central trend is a typical description of a probability distribution. The most common measures of central tendency are the mean, median and mode. Dispersion is the extent to which a distribution is stretched or squeezed. Examples of dispersion measures include standard deviation, range, mean absolute deviation, and coefficient of variation. Moreover, quantitative measures such as skewness and kurtosis are descriptive of the shape of a distribution. We utilized the mean and median statistics for describing central tendency and, standard deviation, range and coefficient of variation to represent the dispersion of distributions Y₀, Y₁. Consequently, a total of 7 measures of statistics are employed for Y₀, Y₁ and ratio of Y₁ to Y₀. The 510-dimensional feature of each image patch were expressed in terms of 21 different statistical measures.

2.3. Classifier modeling

A machine learning classifier was built to evaluate the SRHP features. We utilized the weighted k nearest neighbor (wKNN) classifier with an exhaustive search algorithm and the Euclidean distance metric for sample grading and feature modeling. The wKNN algorithm assigns weight vectors $W\in R^{1\times K}$ for the K nearest neighbors. The j^th weight value for the i^th sample is defined as:

$$W_{ij}=\frac{1}{{\sum }_{n=1}^N{\left({\chi }_i^n-x_j^n\right)}^2}j\in \left\{1,\dots ,K\right\}$$ (3)

where $x_i^n$ is the n^th feature value of the i^th sample for testing. $x_j^n$ denotes the n^th dimension feature value of the j^th sample amongst the K nearest neighbors from the training set. N represents the number of features, which is 21 in this study. Prior to the application of wKNN, the features are normalized by the mean and standard deviation of samples in the training set.

3. Experimental designs and comparative strategies

In order to demonstrate the effectiveness of our SRHP approach for discriminating G₃ and G₄ image patterns, the experiments described below were conducted.

3.1. Evaluation of SRHP approach

The aim of this experiment was to evaluate the effectiveness of our SRHP approach for discriminating G₃ and G₄ patterns at both the image patch- and slide-levels, respectively. We adopted a 10-fold cross validation scheme involving 18,276 representative patches from 43 biopsy slides for evaluation.

In these experiments, we compared the performance of the SRHP approach with other extant state-of-the-art methods [12,22,37]. A brief description of these approaches is summarized below:

• End-to-end supervised learning method, MobileNet [38], which Arvaniti et al. [12] adopted for 4-class Gleason grading (benign, grade 3, 4 and 5) directly on prostate cancer tissue micro-array images. We abbreviate this Deep Learning for Gleason Grading approach as DLGg. It is worth noting that we employed the pre-trained model on our dataset.

• End-to-end unsupervised learning method, stacked sparse autoencoder algorithm (SSAE) presented by Xu et al. [37]. The method was used for nuclei detection on pathological images. The stacked sparse autoencoder was employed for classifying individual candidate locations as nuclei or not via a sliding window scheme.

• Traditional handcrafted features including nuclear morphological, architectural and textural features, denoted collectively as MATF. These features were employed by Ali et al. [22] for distinguishing G₃ and G₄ patterns of prostate cancer.

The values of hyper-parameters were set based off the specifications in the original publications where the methods were first introduced.

3.2. Statistical features analysis

The aim of this experiment was to analyze the effectiveness of all 21 statistical features for discriminating G₃ and G₄ patterns. We also compared different feature permutation schemes in terms of connected components (b₀ ), voids (b₁ ) and the ratio of b₁ to b₀ (denoted as b ).

3.3. Sensitivity analysis

The aim of this experiment was to evaluate the sensitivity of our model to the H stain separation scheme and hyper-parameters K values. Specifically we sought to evaluate (1)how the HP features extracted from the H channel alone compared to the features extracted from the original RGB images and also to assess (2) how the classifier performed across K different values.

3.4. Performance evaluation

The performance of our SRHP approach and comparative strategies were evaluated in terms of Area Under Curve value (AUC), Accuracy (ACC), Recall (REC), Precision (PRC), Specificity (SPC) and F1 score [37]. We employed a 10-fold cross validation scheme and reported the average values for the performance metrics on the models.

4. Results

4.1. Evaluation of SRHP at the image patch-level

We compared the performance of our approach and the comparative strategies listed in Table 1 in terms of AUC, Accuracy, Recall, Precision, Specificity, and F1 score measurements. The reported performance measures were averaged across 10-fold cross validation and the results are reported in Table 1. The results show that the SRHP approach outperforms three other comparative methods and achieves the highest AUC of 0.96, accuracy of 89.02% and an F1 score of 0.89. The results suggest that the SRHP approach is more accurate at differentiating G₃ and G₄ tissue as compared to traditional handcrafted cellular features. Also, our approach outperforms the end-to-end DLGg and SSAE methods. This further reinforces the effectiveness of our SRHP approach for distinguishing G₃ and G₄ grades.

Table 1.

Quantitative evaluation results of our SRHP algorithm against comparative methods at the patch-level in terms of AUC, Accuracy, Recall, Precision, Specificity, and F1 score. The results are averaged across multiple runs of 10 fold cross validation (The best results are shown in bold).

Patch-level	AUC	Accuracy	Recall	Precision	Specificity	F1 Score
DLGg	0.91	85.04%	0.72	0.90	0.94	0.80
SSAE	0.79	72.07%	0.65	0.73	0.79	0.69
MATF	0.94	86.41%	0.84	0.87	0.89	0.85
SRHP	0.96	89.02%	0.94	0.84	0.84	0.89

4.2. Evaluation of SRHP at the image slide-level

Table 2 illustrates the results of quantitative evaluation of SRHP and comparative strategies at the slide-level in terms of AUC, Accuracy, Recall, Precision, Specificity, and F1 score. The SRHP approach is evaluated on a per slide basis. Noting that only 20 slides include both G₃ and G₄ regions, the evaluation results reported were averaged across these 20 slides. We can see from Table 2 that our SRHP still achieves better performance compared to the other methods at the slide-level in terms of all performance metrics. This again reinforces the effectiveness of our HP features. Standard deviation in the performance metrics across slides are also reported. The relatively small standard deviation in the performance metrics appears to suggest robustness of our approach across different slide images.

Table 2.

Results of quantitative evaluation of features robustness of our SRHP algorithm against comparative methods at the slide-level in terms of AUC, Accuracy, Recall, Precision, Specificity, and F1 score. The results are averaged across 20 slides, which includes both G₃ and G₄ regions on the same slide. We also report standard deviations in performance metrics across slides (The best results are indicated in bold).

Slide-level	AUC	Accuracy	Recall	Precision	Specificity	F1 Score
DLGg	0.93 ± 0.13	89.35% ± 0.14	0.80 ± 0.25	0.82 ± 0.20	0.91 ± 0.13	0.78 ± 0.21
SSAE	0.62 ± 0.18	71.31% ± 0.12	0.42 ± 0.30	0.48 ± 0.36	0.73 ± 0.21	0.53 ± 0.25
MATF	0.94 ± 0.01	86.45% ± 0.02	0.84 ± 0.03	0.87 ± 0.05	0.89 ± 0.03	0.85 ± 0.03
SRHP	0.99 ± 0.01	98.75% ± 0.01	0.97 ± 0.03	0.93 ± 0.12	0.98 ± 0.02	0.95 ± 0.09

Fig. 4 shows the scatter plot for each slide in terms of AUC and accuracy for the 4 different methods considered in our experimental design. The performance metrics for each method is shown in a different color. Each point represents the results on a per slide basis, and the DLGg, SSAE, MATF and the SRHP approaches are represented via the blue, black, green and red colors, respectively. It is clear that our SRHP method achieves more accurate and robust results compared to the other approaches, note that the red elements aggregate towards the extreme north-east corner, reflecting an accuracy and AUC of almost 100%. It not only reinforces the effectiveness of HP features, but also illustrates the robustness of our approach.

Fig. 4.

Scatter plot of each slide in terms of AUC and accuracy measurements across different approaches. Each point represents the evaluation result of a slide, where blue, black, green and red colors represent DLGg, SSAE, MATF, and the SRHP methods, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

4.3. Statistical features analysis

Box-plots of statistical features are illustrated in Fig. 5(a), and the feature indices corresponding to b (b₁/b₀), b₀ and b₁ are shown in Fig. 5(b). The box-plots of 21 features illustrate their strong discriminability for the grading task.

Fig. 5.

(a) Box-plots of all 21 statistical features for the G₃ and G₄ grading task. Each box represents one HP feature which has been normalized. (b) Illustration of the feature indices corresponding to statistical features in (a) in terms of b (b₁/b₀), b₀ and b₁ .

Fig. 6 shows results of different combinations of features in terms of connected components (b₀ ), voids ( b₁ ) and the ratio of b₁ to b₀ (b). It is apparent that the combination of all features achieves the best result averaged across 10-fold cross validation, reinforcing the effectiveness of the HP features. We can also see that the b₁ statistic performs better compared to the b₀ features. This trend is in concordance with the clinical grading criteria that the degree of gland differentiation plays a more critical role in Gleason grading, compared to variation of the number of nuclei. The results suggest that HP features can quantitatively capture the topological arrangement and degree of differentiation around prostate cancer glands.

Fig. 6.

Results of quantitative evaluation of different feature combinations in terms of connected components (b₀) , voids (b₁), the ratio of b₁ to b₀ (b), and all.

4.4. Sensitivity analysis

The results of sensitivity analysis of our SRHP approach as a function of stain separation and the K value hyper-parameter are illustrated in Table 3 and Fig. 7, respectively. From Table 3 we can observe that the features perform better on the H stain compared to the original RGB image.

Table 3.

Quantitative evaluation results of sensitivity analysis for our SRHP approach in terms of H stain separation as compared to that of original RGB images. The results of RGB and H stain show the performances based on HP features extracted from raw RGB images and hematoxylin channels, respectively.

Channel	AUC	Accuracy	Recall	Precision	Specificity	F1 Score
RGB	0.9479	87.33%	0.9011	0.8443	0.8478	0.8718
H stain	0.9612	89.02%	0.9442	0.8435	0.8413	0.8910

Fig. 7.

Sensitivity analysis of the SRHP approach across different hyper-parameter K values as assessed in terms of AUC, Accuracy, Recall, Precision, Specificity and F1 Score of a wKNN classifier, where K ranges from 3 to 20.

Fig. 7 shows performance results for the HP features as a function of the hyper-parameter K in conjunction with a wKNN classifier. We can observe from these results that the model yields stable performance across a spectrum of K values (3 to 20). This in turn appears to suggest that our SRHP algorithm is relatively robust to the spectrum of hyper-parameter K values.

5. Discussion

Although our SRHP approach achieved excellent results in discriminating G₃ and G₄ pattern tissue biopsy images, the representative regions of interest were manually selected via an expert’s annotations of biopsy slides. To demonstrate the feasability of automated grading on the prostate whole biopsy slide, we performed the automated grading on a slide-level.

Firstly, we tiled one whole biopsy slide for detection of the regions of cancer. The patch size was 160 × 160 pixels at 10x magnification. The window slides across the whole biopsy slide row by row from upper left corner to lower right (the step size was fixed at 80 pixels). Then the overlapping image patches of 160 × 160 pixels were employed for feature extraction. We adopted the OTSU algorithm [39] for background filtering and AlexNet [40] for identifying the cancerous patches. This AlexNet classifier was trained explicitly to distinguish benign from malignant image regions. Patches identified as being malignant by the AlexNet classifier were then utilized for discrimination of G₃ and G₄ image patches via our SRHP algorithm. Eventually, we stitched together the patch-level prediction assignments into a single contiguous whole image, which included background, benign, G₃ and G₄ regions.

Fig. 8 shows the probability map for regions of cancer on a single biopsy slide, obtained by stitching together the AlexNet prediction results of multiple individual image patches. All malignant regions identified were also qualitatively evaluated by comparing the results with the interpretations of expert pathologists. As can be observed from Fig. 8(b), two region of interests have been magnified to better illustrate the regions of malignancy identified by the classifier. Interestingly, the classifier was also able to identify those regions as malignant that were initially missed by the expert pathologist on the initial inspection of the slide image. We also found that marginal glandular areas with a proliferation of nuclei were more likely to be detected as being cancerous. Fig. 9 illustrates the process of automated discrimination of G₃ and G₄ image patches using our SRHP approach on the whole slide biopsy images.

Fig. 8.

(a) Original whole slide image where pathologist’s annotations of G₃ and G₄ patterns are delineated by green and blue contours, respectively. (b) The corresponding probability map generated by the SRHP approach reveals the regions identified as being malignant on whole biopsy slide images. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 9.

Illustration of SRHP approach for discriminating G₃ from G₄ patterns on a needle biopsy core image. (a) Original biopsy whole slide image with a pathologist’s annotations of G₃ and G₄ regions. (b) The prediction results for G₃ and G₄ regions and the results of the SRHP approach are shown in false-color, where white, blue, green and red colors represent assignments of background, benign, G₃ and G₄ , respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The confusion matrix of errors for the G₃ and G₄ grading for our SRHP approach is presented in Table 4, where specificity, sensitivity, and accuracy are also listed. The SRHP approach can identify G₄ patterns better as compared to G₃ regions, which is consistent with the qualitative results. As illustrated in Fig. 9, our approach fails to identify some G₃ regions which are atypical [34].

Table 4.

Confusion matrix of G₃ and G₄ grading for mis-classification analysis for the SRHP approach, where specificity, sensitivity and accuracy are also reported.

Confusion Matrix	(Target) G3	(Target) G4	-
(Output) G3	8117	476	0.9446
(Output) G4	1480	8203	0.8472
-	(Specificity) 0.8458	(Sensitivity) 0.9452	(Accuracy) 0.8930

6. Conclusions

In this work, we presented a Statistical Representation of Homology Profile (SRHP) approach to capture the topological arrangement and degree of connectivity among nuclei around gland lumen in prostate cancer. The SRHP approach was evaluated at both patch-level as well as at the slide image level. Quantitative evaluation results show that our SRHP approach performed compellingly compared to other supervised / unsupervised learning algorithms (DLGg, SSAE) and handcrafted cellular features approaches (MATF). Extensive experimental results appear to suggest that the SRHP approach could potentially serve as a decision support aid for discriminating G₃ from G₄ prostate cancer grade regions. One limitation of our approach was that we have also not evaluated the ability of this approach to deal with co-occurring cribriform patterns. In the updated grading guidelines, these cribriform patterns occupy a significant role [41].

In summary, we presented a new feature representation approach (SRHP: Statistical Representation of Homology Profile) for the task of discrimination of G₃ from G₄ grade regions on biopsy slides. We presented a new class of computational histological image features which capture the topological arrangement of nuclei with respect to the gland lumen. Thus unlike black box approaches, the new computational pathology features are not just discriminating but also interpretable and intuitive.