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Colorectal cancer (CRC) is a major cause of cancer mortality; loss of the Apc gene is an early step in the formation of CRC. A new computational model of the colonic crypt has been developed to simulate the effects of Apc loss. The model includes a region of flat mucosa, which has not previously been considered in the context of Apc loss. The model suggests that Apc loss confers a survival advantage at the crypt mouth which may be a previously unknown method of mutation fixation.

Colons of young adult Sprague-Dawley rats are embedded in paraffin, cut, and stained with Feulgen. The sections are scanned with a Quantimet-system 23 image analyzer under PDP - 11 34 computer control. Each crypt is digitized into 192 × 700 8-bits pixels. The images are stored on magnetic tapes and processed on a PDP - 15 76 computer providing the necessary features for interactive image analysis. The epithelium of each crypt image is separated, and the cells are ordered and numbered according to their position in relation to crypt origin. The location of mitotic figures is also recorded. The progenitor region outer boundary is estimated with the aid of life table analysis. The program also computes the average crypt length and the progenitor/functional ratio, and estimates the epithelial cell production rate.

An adequate neoplastic grading system should provide a framework for a precise expression of cell turnover and differentiation. The grading system proposed herewith is applicable to all tissue pathologies associated with changes in cell turnover and differentiation, including neoplasia. It is illustrated on rapidly proliferating tissues known as continuous replicators e.g. the colon crypt epithelium. The enterocyte starts its existence at crypt bottom, during a stem cell division whereupon it gradually advances outward, differentiating as it goes. The typical path covered by the cell, denominated as tissue radius summarizes its life history. The cell is viewed as a point advancing on the radius in a rectlinear motion, defined by two variables: Distance from radius origin ‘x’, defined as the cell location number separating it from origin, and its velocity v(x) defined as the cell location number it covers per unit of time. The path the cell covers is represented by a trajectory in a two dimensional Galilean geometry. The cell's transition from state to state is defined by two transformations: Displacement and shear. Each continuous replicator is represented by a typical trajectory which differs in different pathologies. Neoplastic progression in the continuous replicator may be expressed as a trajectory in the Galilean geometry, which serves also for a unique grading of neoplasia.