The fractal dimension may be a useful morphometric discriminant in histopathology

The hypothesis is presented that fractal geometry, and the fractal dimension in particular, is likely to be a more useful method of image analysis in histopathology than the use of regular Euclidean geometry. The concept of the fractal dimension is described and it is suggested that many human tumours have a fractal structure over a wide range of scales. It is postulated that the fractal dimension will be useful in discriminating between different diagnostic categories and may also allow more precise prognostic stratification within single diagnostic groups.

[1]  R. Glenny,et al.  Fractal properties of pulmonary blood flow: characterization of spatial heterogeneity. , 1990, Journal of applied physiology.

[2]  A. G. Flook.  The use of dilation logic on the quantimet to achieve fractal dimension characterisation of textured and structured profiles , 1978 .

[3]  J. Jass,et al.  Reporting colorectal cancer. , 1987, Journal of clinical pathology.

[4]  C Wittekind,et al.  Computerized morphometric image analysis of cytologic nuclear parameters in breast cancer. , 1987, Analytical and quantitative cytology and histology.

[5]  T. N. James,et al.  The spectrum of diseases of small coronary arteries and their physiologic consequences. , 1990, Journal of the American College of Cardiology.

[6]  Heinz-Otto Peitgen,et al.  The science of fractal images , 2011 .

[7]  H Strickland,et al.  Fractal Modeling of Biological Structures , 1987, Annals of the New York Academy of Sciences.

[8]  C. Dukes,et al.  The classification of cancer of the rectum , 1980 .

[9]  J. Baak,et al.  Borderline or malignant ovarian tumour? A case report of decision making with morphometry. , 1984, Journal of clinical pathology.

[10]  Peter Pfeifer,et al.  Molecular fractal surfaces , 1984, Nature.

[11]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[12]  Lars Håkanson,et al.  The length of closed geomorphic lines , 1978 .

[13]  B. Mandelbrot,et al.  Fractal character of fracture surfaces of metals , 1984, Nature.

[14]  Baak Jp,et al.  The principles and advances of quantitative pathology. , 1987 .

[15]  Gundula Schaumburg-Lever,et al.  Histopathology of the skin , 1975 .

[16]  M. Goodchild.  Fractals and the accuracy of geographical measures , 1980 .

[17]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[18]  Stephen Wilson,et al.  The Beauty of Fractals: Images of Complex Dynamical Systems by Heinz Otto Peitgen, Peter Richter (review) , 2017 .

[19]  B. West.  Physiology in Fractal Dimensions , 1990 .

[20]  P. Meakin,et al.  A new model for biological pattern formation. , 1986, Journal of theoretical biology.

[21]  T. Stephenson.  Quantitation of the nucleus. , 1990, Current topics in pathology. Ergebnisse der Pathologie.

[22]  R. Laing,et al.  Feasibility of new prognostic classification for rectal cancer. , 1988, Journal of clinical pathology.

[23]  A. Goldberger,et al.  Beyond the principle of similitude: renormalization in the bronchial tree. , 1986, Journal of applied physiology.

[24]  J. Baak,et al.  Discrimination of hyperplasia and carcinoma of the endometrium by quantitative microscopy–a feasibility study , 1981, Histopathology.

[25]  David L. Page,et al.  Diagnostic Histopathology of the Breast , 1988 .

[26]  Chaos: to see a world in a grain of sand and a heaven in a wild flower. , 1990, Archives of dermatology.

[27]  P. Burrough.  Fractal dimensions of landscapes and other environmental data , 1981, Nature.

[28]  J. Lawton,et al.  Fractal dimension of vegetation and the distribution of arthropod body lengths , 1985, Nature.

[29]  G. Diamond,et al.  Fascinating rhythm: a primer on chaos theory and its application to cardiology. , 1990, American heart journal.

[30]  C Javanaud,et al.  The application of a fractal model to the scattering of ultrasound in biological media. , 1989, The Journal of the Acoustical Society of America.