The analysis of the three-dimensional (3-D) structure of tumoral invasion fronts of carcinoma of the uterine cervix is the prerequisite for understanding their architectural-functional relationship. The variation range of the invasion patterns known so far reaches from a smooth tumor-host boundary surface to more diffusely spreading patterns, which all are supposed to have a different prognostic relevance. As a very decisive limitation of previous studies, all morphological assessments just could be done verbally referring to single histological sections. Therefore, the intention of this paper is to get an objective quantification of tumor invasion based on 3-D reconstructed tumoral tissue data. The image processing chain introduced here is capable to reconstruct selected parts of tumor invasion fronts from histological serial sections of remarkable extent (90-500 slices). While potentially gaining good accuracy and reasonably high resolution, microtome cutting of large serial sections especially may induce severe artifacts like distortions, folds, fissures or gaps. Starting from stacks of digitized transmitted light color images, an overall of three registration steps are the main parts of the presented algorithm. By this, we achieved the most detailed 3-D reconstruction of the invasion of solid tumors so far. Once reconstructed, the invasion front of the segmented tumor is quantified using discrete compactness.

Background: Malignant growth and invasiveness of cancers is a function of both intratumoral and stromal factors. The accessibility to nutrients, oxygen and growth factors, the stromal composition, and the interference with the immune system all shape the tumor invasion front. A recent study has shown a prognostic difference with respect to different invasion patterns analyzed on histological specimens of cervical cancers. The present study analyzes the spatial organization of a cervical cancer and the relation of the tumor invasion front and the infiltration with CD31 T-cells. Methods: From a cervical squamous cell carcinoma specimen, 84 serial sections were performed and three interleaving series were stained with hematoxylin/eosin and immunohistochemistry directed against the cervical carcinoma biomarker p16INK4a and the T-cell marker CD3. Sections were passed through an image processing chain to obtain a reconstructed and segmented tissue volume. For local tumor invasion front analysis the mean curvature was used, which in turn was related to the respective local minimum tumor to T-cell distance as well to a T-cell originated diffusing substance's concentration at the tumor surface.

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The goal of nonparametric image registration lies in the solution of highly nonlinear partial differential equations. We present a new partial differential equation for the nonlinear image registration that can be used for the registration of images with textured and complex shaped motifs. The new equation allows to control the vortex structure in the registration field. For many image registration problems, the required transformation should not contain vortices. The application field of the new equation is not restricted to biomedical imaging.

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