**1. Introduction**

The spread of Deep Learning (DL) techniques and frameworks has led to a revolution in the medical imaging field. The assessment of organ viability, by donor kidney biopsy examination, is essential prior to transplantation. The traditional evaluation of biopsies was based on the visual analysis by trained pathologists of biopsy slides using a light microscope which is a time consuming and highly variable procedure. The high variability between the observers resulted in poor reproducibility among pathologists, which may cause an inappropriate organ discard. Therefore, the development of new techniques able to objectively and rapidly interpret donor kidney biopsy to support pathologist's decision making is strongly fostered. The increasing availability of whole-slide scanners, which facilitate the digitization of histopathological tissue, led to a new research field denoted as digital pathology and generated a strong demand for the development of Computer-Aided Diagnosis (CAD) systems. As stated in the literature, the application of deep learning techniques for the analysis of Whole-Slide Images (WSIs) has shown significant results and sugges<sup>t</sup> that the integration of DL framework with CAD systems is a valuable solution.

In the realm of digital pathology, several recent studies have proposed CAD systems for glomerulus identification and classification in renal biopsies [1–8]. The eligibility for transplantation of a kidney retrieved from Expanded Criteria Donors (ECD) relies on rush histological examination of the organ to evaluate suitability for transplant [9]. The Karpinski score is based on the microscopic examination of four compartments: glomerular, tubular, interstitial and vascular, in order to assess the degree of chronic injury. For each compartment is assigned a score from 0 to 3 where 0 corresponds to normal histology and 3 to the highest degree of, respectively, global glomerulosclerosis, tubular atrophy, interstitial fibrosis and arterial and arteriolar narrowing [9,10]. The evaluation of global glomerulosclerosis requires detection and classification of all the glomeruli present in a kidney biopsy, distinguishing between healthy (non-sclerotic) and non-healthy (sclerotic) ones.

The two fundamental components that characterize a non-sclerotic glomerulus are the capillary tuft with the mesangium and the Bowman's capsule. The first one is placed inside the glomerulus while the second one is peripheral and has the function to contain the tuft. The space between these two components is called Bowman's space. From a morphological point of view, the non-sclerotic glomerulus generally has an elliptic form. The capillary tuft has a pomegranate form, caused by the contemporary presence of blue points (nuclei of cells), white areas (capillary lumens) and variable amount of regions with similar tonality and different levels of saturation (mesangial matrix). A non-healthy glomerulus, from the point of view of Karpinski's score, is a globally sclerotic glomerulus, namely a glomerulus where capillary lumens are completely obliterated for increase in extracellular matrix and Bowman's space is completely filled by collagenous material. Examples of non-sclerotic and sclerotic glomeruli are depicted in Figure 1.

**Figure 1.** Glomeruli. Top row: non-sclerotic glomeruli. Bottom row: sclerotic glomeruli.

Ledbetter et al. proposed a Convolutional Neural Network to predict kidney function (evaluated as the quantity of primary filtrate that passes from the blood through the glomeruli per minute) in chronic kidney disease patients from whole-slide images of their kidney biopsies [3]. Gallego et al. proposed a method based on the pretrained AlexNet model [11] to perform glomerulus classification and detection in kidney tissue segments [2]. Gadermayr et al. focused on the segmentation of the glomeruli. The authors proposed two different CNN cascades for segmentation applications with sparse objects. They applied these approaches to the glomerulus segmentation task and compared them with conventional fully convolutional networks, coming to the conclusion that cascade networks can be a powerful tool for segmenting renal glomeruli [4]. Temerinac-Ott et al. compared the performance between a CNN classifier and a support-vector machines (SVM) classifier which exploits features extracted by histogram of oriented gradients (HOG) [12] for the task of glomeruli detection in WSIs with multiple stains, using a sliding window approach. The obtained results showed that the CNN method outperformed the HOG and SVM classifier [1]. Kawazoe et al. faced the task of glomeruli detection in multistained human kidney biopsy slides by using a Deep Learning approach based on Faster R-CNN [6]. Marsh et al. developed a deep learning model that recognizes and classifies sclerotic and non-sclerotic glomeruli in whole-slide images of frozen donor kidney biopsies. They used a Fully Convolutional Network (FCN) followed by a blob-detection algorithm [13], based on Laplacian-of-Gaussian, to post-process the FCN probability maps into object detection predictions [8]. Ginley et al. proposed a CAD to classify renal biopsies of patients with diabetic nephropathy [7], using a combination of classical image processing and novel machine learning techniques. Hermsen et al. adopted CNNs, namely an ensemble of five U-Nets, for segmentation of ten tissue classes from WSIs of periodic acid-Schiff (PAS) stained kidney transplant biopsies [14].

The analysis of the literature suggests that main works focused on the glomerular detection task only, without considering the further classification into sclerotic and non-sclerotic [1,2,4,6]. Few papers considered the assessment of global glomerulosclerosis from kidney biopsies [7,8,14].

In our previous works we focused on other kidney biopsies analysis tasks, such as classification of tubules and vessels [15] and classification of non-sclerotic and sclerotic glomeruli [5]. In this work, we propose a CAD system to address the segmentation and the classification tasks of glomeruli, in order to obtain a reliable estimate of Karpinski histological score. The proposed work allowed us to obtain better results than the literature in the classification task.
