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Three-dimensional Reconstruction and Quantification of Tumour Invasion based on Histological Serial SectionsUlf-Dietrich Braumann, Jens-Peer Kuska, Markus LöfflerInterdisciplinary Centre for Bioinformatics University of Leipzig Jens Einenkel, Michael Höckel Department of Gynaecology and Obstetrics University of Leipzig Lars-Christian Horn Institute for Pathology University of Leipzig Cooperation: Regina Scherling, Dept. of Gynaecology and Obstetrics, has carefully accomplished all sectioning and staining essential for this work. Torsten Frohn did the extensive digitisations. The analysis of the three-dimensional (3-D) structure of tumoural invasion fronts is considered the prerequisite for understanding some architectural-functional relationship. The variation range of the invasion patterns in cervical tumours known so far reaches from closed via finger-like to diffusely spreading patterns, which all are supposed to have a different prognostic relevance. However, the real importance of the invasion pattern as an independent prognostic factor is extremely diffucult to evaluate due to varying definitions and parameters. In particular, any of these three-tiered verbal morphological classifications of previous studies were based on single histological sections not only exhibiting a high degree of subjectivity but also providing no real insight into the spatial tumour invasion. Among available modalities, e.g. computed tomography (CT), magnetic resonance imaging (MRI), confocal laser scanning microscopy (CLSM), there is no established 3-D procedure or protocol appropriate for tumour invasion imaging at the same time providing appropriate contrasts, spatial ranges, and resolutions. Therefore, the intention of our work is twofold: to provide reconstructed 3-D tumoural tissue data and then to apply some algorithmic tumour invasion quantification. Resected specimens obtained from patients with cervical cancer (pT1b1 – pT2b) which underwent radical hysterectomy were serially sliced (typ. 10µm, 90-500 slices), stained (haematoxylin-eosin, HE) and digitised (1300×1030 pixels, area 10.45mm×8.28mm=0.865cm˛, pixel size 8.04µm˛). Slicing and staining, however, may induce severe artefacts rarely to avoid, mainly different kinds of distortions. These can be algorithmically treated using a dedicated image processing chain consisting of a coarse-to-fine cascade of image registration algorithms. enising structures. Once binarised, the tumour invasion front within the reconstructed volume is going to be assessed. For the invasion quantification we refer to discrete compactness. This property is considered to be in tight correspondence to those invasion front features pathologists generally are paying attention when verbally assessing 2-D sections in routine – but algorithmically obtained in 3-D. Compactness values within [0,1] do reproducibly quantify tumour invasion without any subjectivity. The procedure was successfully applied to an overall of 13 specimens of squamous cell carcinoma of the uterine cervix. The 3-D reconstructions generally give an excellent insight into the tumour invasion front morphology. Obtained compactnesses for the set of specimens have occurred within an interval between 0.881 (diffuse invasion) and 0.995 (closed invasion, see Fig. 1). What becomes visible is that there is no three-tiered distribution (as the previous studies would have suggested). Interestingly, the numbers occur rather equally distributed within this interval. 
Figure 1: The compactness values of the 3-D reconstructed specimens exhibit a rather homogeneous but not a three-tiered
distribution (as used for the verbal assessments in clinical routine). Dots are labelled with consecutive specimen numbers.
A comparison of a (processed) single section and a 3-D visualisation in Fig. 2 may illustrate how the pathologist can benefit from this first insight into the 3-D morphology of a tumour invasion front within the respective specimen volume. Another interesting outcome is that for all our specimens the tumour invasion has occured ‘per continuitatem’, i.e. no separated tumour islets could be detected.
With the above sketched scheme an objective quantification of the invasion of cervical tumours at cellular resolution based on 3-D reconstructed data could be achieved for the first time. The availability of the 3D compactness numbers as new means for tumour invasion quantification is considered the decisive progress of this work. Correlations with various other parameters of carcinoma of the uterine cervix, e.g. the expression of immunohistochemical markers or the survival period etc. are subject of ongoing investigations.
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