Background and Objective:Hepatocellular ballooning is an important histological parameter in the diagnosis of nonalcoholic steatohepatitis (NASH), and it is considered to be a morphological pattern that indicates the severity and the progression to cirrhosis and liver-related deaths. There remains uncertainty about the pathological criteria for evaluating the spectrum of non-alcoholic fatty liver disease (NAFLD) in liver biopsies. We introduce persistence images as novel mathematical descriptors for the classification of ballooning degeneration in the pathological diagnosis. Methods:We implemented and tested a topological data analysis methodology combined with linear machine learning techniques and applied this to the classification of tissue images into NAFLD subtypes using Matteoni classification in liver biopsies. Results:Digital images of hematoxylin- and eosin-stained specimens with a pathologist’s visual assessment were obtained from 79 patients who were clinically diagnosed with NAFLD. We obtained accuracy rates of more than 90% for the classification between NASH and non-NASH NAFLD groups. The highest area under the curve from the receiver operating characteristic analysis was 0.946 for the classification of NASH and NAFL2 (type 2 of Matteoni classification), when both 0- and 1-dimensional persistence images were used. Conclusions:Our methodology using persistent homology provides quantitative measurements of the topological features in liver biopsies of NAFLD groups with considerable accuracy.

背景与目的：肝细胞球囊扩张是诊断非酒精性脂肪性肝炎（NASH）的重要组织学参数，被认为是一种指示肝硬化和肝相关死亡的严重性，进展和进展的形态学模式。关于评估肝活检中非酒精性脂肪肝疾病（NAFLD）的病理标准尚不确定。我们介绍了持久性图像作为新型数学描述符，用于病理诊断中气球变性的分类。方法：我们实施并测试了结合线性机器学习技术的拓扑数据分析方法，并将其应用于在肝活检中使用Matteoni分类的组织图像分类为NAFLD亚型。结果：从79名临床诊断为NAFLD的患者中获得了经过病理学家视觉评估的苏木精和曙红染色标本的数字图像。对于NASH和非NASH NAFLD组之间的分类，我们获得了90％以上的准确率。当同时使用0维和1维余辉图像时，对于NASH和NAFL2的分类（Matteoni分类的类型2），来自接收器工作特性分析的曲线下最大面积为0.946。结论：我们使用持续同源性的方法可以相当准确地定量测量NAFLD组肝脏活检中的拓扑特征。