## 4 Discussion
### Applications of the Method  
In this study we showed a proof-of-concept application of our approach for the characterization of fibrosis distribution in the atria of cardiac surgery patients. Fibrosis is acknowledged as a crucial factor in the setting and maintenance of cardiac arrhythmias, promoting the emergence of triggers and the maintenance of reentrant activity [5]. In particular, the type, pattern, and spatial distribution of fibrosis have been connected to different arrhythmic substrates and arrhythmic risks, pointing out the importance of a precise and quantitative description of fibrosis features [5; 6; 7; 25]. Our analysis on atrial samples in cardiac surgery patients pointed out a significantly higher amount of fibrosis in patients with AF (average 14.5%) than in patients without a history of arrhythmia (average fibrosis value of 7.8%). The amount of fibrosis detected in the two populations in our study are in line with values reported in previous histology studies in cardiac surgery [26; 27; 28] and autopsy settings [29], despite minor differences, which may be probably ascribed to differences in extraction sites, processing, staining, and analysis of the specimens. Similarto our results in the control patients, [PERSON] et al. [26] found an average fibrosis content of 15.8% in a large population of open-heart surgery patients without a history of AF. Of note, a considerable variability was present in the population with values ranging from 4% to almost 33%. In patients without previous history of AF, [PERSON] et al. [27] found that the fraction of right atrial fibrosis was 5.3 \(\pm\) 3.8% in patients, who developed post-operative AF, versus 4.3 \(\pm\) 3% in patients who did not, without significant differences between the two populations. Consistently with our comparative results in controls versus AF patients, [PERSON] et al. [29] found that fibrosis extent in post-mortem atrial tissue from patients without significant valvular disease was two- to three-fold higher in patients with (range: 22-28%) than without a history of AF (5-8%). [PERSON] et al. [28] reported greater amounts of interstitial fibrosis in atrial samples from chronic AF patients with respect to SR patients (37% versus 7%). Of note, we reported also a higher variability of fibrosis profile in AF patients, which may be indicative of the formation of a complex 3D substrate supporting wave propagation dynamics [6; 30]. Besides the study of AF, the characterization of fibrosis is crucial in other cardiac diseases, such myocardial infarction and nonischemic cardiomyopathies, where the amount and pattern of fibrosis is associated with the risk of fatal ventricular arrhythmias and sudden cardiac death [5]. Our algorithm may facilitate and speed up histological analysis in animal models of cardiac disease, allowing for instance systematic assessment of fibrotic remodeling in models of ischemic and nonischemic cardiac disease, as well as the characterization of genotype-phenotype relationships in models of genetic cardiomyopathies [16]. Quantitative and accurate assessment of structural substrate formation may be important also in other pathophysiologic conditions, such as hypertension, diabetes, or obesity, where cardiac fibrosis is known to play a key role [2; 3]. In translational research, our method may support the analysis of histological 3D datasets, obtained as series of 2D slices. Whole-heart 3D datasets have been obtained in the rabbit heart, where cardiac histoanatomical organization was shown as a major determinant of heart function [31]. In addition, adult human myocardial slices from small heart biopsies were proposed as a simple, reproducible, and relevant preparation for the study of human cardiac tissue at the multicellular level [32]. Moreover, the method may find application in the validation of noninvasive cardiac imaging techniques for fibrosis quantification, such as late gadolinium enhancement magnetic resonance imaging or T1 mapping [5], for which adequate correlation with the histological gold standard is required.