Applied sciences Article  
Model-Based Approach for the Semi-Automatic Analysis of Collagen Birefringence in Polarized Light Microscopy  
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where its effects depend not only on the amount, but also on the texture and spatial distribution of fibrosis [5; 6; 7]. A quantitative and detailed description of fibrosis/collagen spatial distribution in cardiac tissue is thus fundamental for a complete understanding of cardiac arrhythmia mechanisms and structure-function relation, and for the optimization of therapeutic approaches [5].  
Histological morphometric evaluation of tissue samples remains the gold standard for cardiac tissue characterization and collagen assessment. Polarized light microscopy (PLM) is commonly used to analyze these samples, since collagen is optically anisotropic and intrinsically birefringent (i.e., its refractive index depends on the polarization and propagation direction of the incident light), appearing bright when viewed in polarized light [8; 9; 10]. The birefringence characteristics of collagen can be enhanced by specific staining procedures, such as picrosirius red staining. Picrosirius red is an anionic dye, which can stably bind along cationic collagen fibers and provide additional birefringence by virtue of its anisotropic molecular organization [11; 12; 13].  
Subsequent quantification of collagen from PLM images is traditionally performed by manual stereology approaches [14], which are however strictly dependent on the skills of the operator and can be particularly time consuming when a large number of sections need to be processed. On the other hand, extrinsic variability factors, related to either the realization and processing of tissue slices or to limitation in the microscope set-up and imaging sessions can produce artifacts and further affect the quantification of collagen content.  
Few methods for the semi-quantitative and/or semi-automatic estimation of collagen content in histological sections have been previously proposed [9; 10; 15; 16; 17; 18; 19], but there is still a lack of rigorous computational approaches, which should couple objective and fast quantification of collagen with control of confounding factors.  
Based on these considerations, in this paper, we propose a model-based semi-automatic analysis framework for the quantification of collagen content from PLM images of histological tissue sections. The framework combines the information in bright-field and dark-field polarized light images to perform a semi-automatic segmentation of cardiac tissue from the background and of collagen from cardiac tissue, providing the collagen fraction as an output. The user tasks are limited to the initial choice of a segmentation threshold on a limited number of sections, the supervision of the processing, and the final check of segmentation results, with significant reduction of processing time. In addition, the framework is enforced by an underling physical model of polarized light-sample interaction and birefringence signal production, which reduces the effects of confounding factors, such as variability in tissue slice thickness, illumination spatial inhomogeneity, and temporal variability of the light source. As a proof-of-concept application, we applied our method to human cardiac tissue samples and showed its capability to point out differences in fibrosis content and distribution in patients with different cardiac rhythms, i.e., patients with and without atrial fibrillation (AF).