Fractal Dimensions and Dendritic Branching of Neurons in the Somatosensory Thalamus
The investigation and modelling of irreversible growth phenomena has become a topic of considerable interest in the last decade, stimulated by the introduction of the concept of fractality by B.B. Mandelbrot. This concept provides a quantitative framework to study in particular biological growth phenomena of complex shapes, such as the branching structures of trees, of bronchial trees and of blood vessels. Recently, it was shown that the shapes of 2-dimensional retinal neurons are fractal objects, and hence may be characterized by their fractal dimension D = 1.68±0.15 (Caserta et al., 1990). The authors proposed an explanation of certain stages of neuronal development by a diffusion-limited particle-cluster aggregation (DLA) model, which predicts in 2-dimensional space D = 1.70 ± 0.1.
KeywordsFractal Dimension Dendritic Tree Bronchial Tree Dendritic Branch Branch Order
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- Kniffki, K.-D., Chialvo, D., Vahle-Hinz, C., Apkarian, A.V. Fractal dimensions of neurons located in the cat’s thalamic ventrobasal complex (VB) and its ventral periphery (VB vp). Soc. Neurosci. Abstr. 16: 622 (1991).Google Scholar
- Kniffki, K.-D., Vahle-Hinz, C., Block, A., von Bloh, W., Schellnhuber, HJ. Fractal scaling characteristics of 3-dimensional thalamic neurons. In preparation (1993).Google Scholar
- Mandelbrot, B.B. The fractal geometry of nature. Freeman, New York (1983).Google Scholar
- Schierwagen, A., Grantyn, R. Quantitative morphological analysis of deep superior colliculus neurons stained intracellularly with HRP in the cat. J. Hirn-forsch. 27: 611–623 (1986).Google Scholar
- Takayasu, H. Fractals in the physical sciences. Manchester University Press, Manchester and New York (1990).Google Scholar
- Vahle-Hinz, C., Pawlak, M., Kniffki, K.-D. Morphology of neurons in the ventral periphery of the thalamic ventrobasal complex (VB vp) of the cat. J. Comp. Neurol. (in press, 1993).Google Scholar