Fourier analysis of the shape of normal and transformed epithelial cells derived from human transitional epithelium

Abstract

The aim of this paper is to show the possibility of objective mathematical description of changes occurring in the shape of cells in the process of transformation. The evaluation of the changes in cell shape of the chosen cell lines differing in transformation grade was performed by the use of Fourier analysis of the shape. Any two-dimensional contour can be described with specific accuracy in a mathematical manner using the closed form Fourier series of cosines. The components forming the analysed shape, called harmonics, are independent and uncorrelated measures of their contribution to the total shape. The shape of each cell can be represented by the spectrum of harmonic amplitudes. To quote the paper by Healy-Williams and Williams (1981): "The observed shape is partitioned into series, where gross shape, as elongation or triangularity, is measured by the harmonic amplitudes of the lower harmonic order and increasingly fine scaled surface sculpture is measured at higher orders". The statistically evaluated results allow the objective comparison of the cell shapes of several compared cell lines differing in transformation grades. Malignant transformation is supposed to be a multistep process. The different grades of transformation could be defined by several parameters as changes in the morphology of the cells, their ability to compete with fibroblasts, their life span, their angiogenic potency, their invasiveness in vitro and their tumorigenicity in nude mice. In this paper several human urothelial cell lines of normal and tumor origin differing in their transformation grade (TGr I-III) were compared by the use of Fourier analysis of their shape. TGr I cultures have finite life span but do not need intermittent collagenase treatment to prevent fibroblast overgrowth. TGr II cultures acquire infinite growth potential, here defined as capacity to survive at least 70 passages. They are neither tumorigenic nor invasive. TGr III cultures show infinite growth transformation, increased angiogenicity and ability to invade normal host tissue in vitro. They produce progressively growing tumors in nude mice. The following human uroepithelial cell lines differing in the degree of transformation were studied and compared by statistical evaluation of the harmonic amplitudes describing mathematically the cell shape: Two cell lines derived from human transitional cell carcinoma (TCC): 1. Hu 1703S classified as TGr I, 2. Hu 1703He classified as TGr III. It was found that these two cell lines differ in all harmonics. Two cell lines derived from morphological normal human bladder epithelium: 3. HCV-29 classified as TGr II.(ABSTRACT TRUNCATED AT 400 WORDS)