217.

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Page 68

		1.4.12— More Examples of the Fractal Dimension

		We have already seen that the fractal dimension can be used to measure the branching pattern of the blood vessels in the lung. Fractal dimensions have also been measured for many structures and processes at the molecular, cellular, and organ levels.

		The most commonly used methods for determining these fractal dimensions have been the use of the scaling relationship and the capacity dimension done by box counting.

		Examples where the fractal dimension has been measured include:

		1. The surfaces of proteins, cell membranes, cells of the cornea damaged by infection with the herpes simplex virus, and bacterial colonies;

		2. The branching patterns of one type of lipid within the rest of the lipids in the cell membrane, the arms (dendrites) of nerve cells, and the blood vessels in the eye, heart, and lung;

		3. The distribution in space of the blood flow in the heart, the density of bone and teeth, and the concentration of radioactive tracer in the liver;

		4. The distribution in time of the intervals between the electrical impulses in nerve cells and the opening and closing of ion channels;

		5. The distribution in energy space of the differences in energies of vibration in proteins; and

		6. The concentration dependence of the rates of chemical reactions of protein enzymes.

 

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