Vol.:(0123456789) 1 3 Journal of Medical and Biological Engineering https://doi.org/10.1007/s40846-018-0382-1 ORIGINAL ARTICLE Automatic Diabetes Detection from Histological Images of Rats Phrenic Nerve Using Two‑Dimensional Sample Entropy Antonio Carlos da Silva Senra Filho 1  · Juliano Jinzenji Duque 1  · Luiz Eduardo Virgilio Silva 2,3  · Joaquim Cesar Felipe 1  · Valéria Paula Sassoli Fazan 4  · Luiz Otávio Murta Junior 1 Received: 24 July 2017 / Accepted: 12 December 2017 © Taiwanese Society of Biomedical Engineering 2018 Abstract In microscopy, morphological characteristic of the axon are the most common features assessed in histological images of nerves. Although morphometric indexes are widely used to describe histological data, the calculation of those indexes is a highly time-consuming task that demands great manual effort from the specialist. Recently, two-dimensional sample entropy (SampEn2D) was proposed to quantify the degree of irregularity present in an image, based on the spatial patterns of pixels. Here, we propose the use of SampEn2D as a suitable metric for classifying diabetic status of rats from histological images of the phrenic nerve. Microscopy images of three different Wistar rats groups (untreated diabetic (N = 24), insulin-treated dia- betic (N = 9), and non-diabetic control (N = 11)) were analysed. The results show that for the optimal SampEn2D parameters (m = 1, r = 0.1), control rats have significantly (p < 0.01) lower entropy (3.76 ± 0.26) as compared to both insulin-treated (5.09 ± 0.20) and untreated (5.30 ± 0.13) diabetic animals. Performance of SampEn2D for image classification between untreated and control groups was assessed by ROC analysis and area under the ROC curves (AUROC = 0.96). SampEn2D reaches a sensitivity of 87% and specificity of 82% when a threshold of SampEn2D = 4.73 is taken to separate the two assessed groups. In conclusion, SampEn2D method arises as a useful tool in the screening of diabetic rats. The method may be useful to pre-select animals for further morphometric evaluation, reducing the burden of manual processing. Keywords Sample entropy · Regularity · Image processing · Diabetes · Phrenic nerve · Morphometry 1 Introduction Histological images are widely assessed by morphological measurements, which are well-established approaches [1, 2]. On rats, morphometric parameters, e.g., axon diameter and g ratio (a measure of the degree of myelination), have been used to describe diabetes disease evolution and its related effects over the axons [3, 4]. Moreover, the precision obtained with the manual morphometric evaluation makes it the gold standard procedure to evaluate histological altera- tions related to the disease. On the other hand, although the unquestionable value of morphological measurements, their evaluation is highly time-consuming and demands a great manual effort from the specialist. The evolution of diabetes disease causes a general axon deterioration. Such changes can be tracked in histologi- cal images of nerves, where morphometric parameters are affected [1, 4]. However, histological alterations related to diabetes may also change the spatial pattern of pixels, and other metrics which are more sensitive to regularity infor- mation might be useful in this case. Several computational classification approaches have been applied to histological images [5–9], however still requiring some manual pro- cessing by the specialist. Two-dimensional sample entropy (SampEn2D) was recently introduced [10] as an automated * Antonio Carlos da Silva Senra Filho acsenrafilho@usp.br 1 Department of Computing and Mathematics, Faculty of Philosophy, Science and Letters of Ribeirao Preto, University of Sao Paulo, Av. Bandeirantes, 3900 – Monte Alegre, Ribeirao Preto, SP, Brazil 2 Department of Physiology, School of Medicine of Ribeirao Preto, University of Sao Paulo, Ribeirao Preto, SP, Brazil 3 Department of Computer Science, Institute of Mathematics and Computer Science, University of Sao Paulo, Sao Paulo, SP, Brazil 4 Department of Surgery and Anatomy, School of Medicine of Ribeirao Preto, University of Sao Paulo, Sao Paulo, SP, Brazil