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		1.4.11— Example of the Fractal Dimension: Blood Vessels in the Lungs

		Many parts of the body have fractal structures. The fractal dimension can be used to measure the differences between normal structures and those altered by disease.

		Laboratory rats that are brought up breathing less oxygen or more oxygen than is found in normal air have higher blood pressure in the blood vessels in the lungs. X-ray images can be taken of these blood vessels. We digitized these images and used the box counting method to determine the fractal dimension of these blood vessels.

		We found that the fractal dimension of the blood vessels in the normal lungs was 1.65. We also found that the fractal dimension of the blood vessels in the abnormal lungs was 1.53 and 1.43. That is, the fractal dimension was lower in the abnormal lungs. The fractal dimension tells us how many additional branches are found as smaller blood vessels are examined. Thus there were fewer, finer branches in the blood vessels from the abnormal lungs. The fractal dimension is one way to measure the differences between these normal and abnormal lungs.

 

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