fig1 a shows a contour line 1 of an arteriosclerotic deposit 2 that determines the inner contour 3 of a vessel wall 4 . the contour line 1 can be detected , for example , by introducing a contrast agent into the bloodstream and obtaining an x - ray exposure of the vessel to be examined is produced . examination methods operating with intravascular ultrasound , with which resolutions up to 100 μm can be achieved , are a further possibility . the resolution of the exposure can be further improved using recently developed optical coherence tomography , which achieves resolutions in the range of 10 μm . a first step to determine the fractal dimension of the contour line 1 is shown in fig1 b . in this method step , the contour line 1 has been covered by a rectangular surface 5 that has been divided into quadratic fields 6 . the fields 6 exhibit a length d normalized to the numerical value 1 . it can be seen from fig1 b that the contour line 1 passes through all seven fields 6 . the field division of the area 5 has been refined in fig1 c . the area 5 is henceforth divided into fields 7 that exhibit an edge length with the value d = ½ . in the case of fig1 c , in total n = 23 fields 7 are traversed by the contour line 1 . a further reduction of the field division has been effected in fig1 d and 1e . in fig1 d , the edge length d of the fields 8 exhibits the value ¼ , and in fig1 e the edge length d of the fields 8 exhibits the value ⅛ . it can be seen from fig1 d that the contour line 1 in total passes through n = 61 fields 8 , while the contour line 1 in fig1 e traverses a total number of n = 164 fields 9 . the fractal dimension of the contour line 1 can be determined using fig2 . in fig2 , a dual - logarithmic graph is shown in which the logarithm of the number n of the fields traversed by the contour line 1 is plotted against the edge length d of the fields 6 through 9 . corresponding data points 10 are plotted in fig2 . the fractal dimension of the contour line 1 then results from the slope of a line of best fit 11 placed through the data points 10 . in the case shown in fig2 , a fractal dimension of approximately 1 . 61 results for the contour line 1 . in comparison to the contour line 1 , shown in fig3 a through 3e each show a flatter contour line 12 , the length of which is determined in the fig3 b through 3e at different field sizes via enumeration of the fields 6 through 9 covered by the contour line 12 . lengths of n = 7 , n = 18 , n = 36 and n = 71 respectively result in fig3 b through 3e , whereby the edge lengths of the fields 6 through 9 respectively exhibit the value d = 1 , d = ½ , d = ¼ and d = ⅛ . the result of the enumeration is shown in fig4 . fig4 shows a dual - logarithmic diagram in which the logarithm of the number n of the enumerated fields is plotted against the logarithm of the edge length d of the fields 6 through 9 . data points 13 result to which a line of best fit 14 has been adapted . the slope of the line of best fit 14 is approximately 1 . 19 , such that a fractal dimension of 1 . 19 can be associated with the contour line 12 . with the inventive method , it is possible to associate a numerical value ( in the form of a fractal dimensional value ) characterizing the roughness or complexity of the contour line 1 or 12 with the complexity or roughness of a contour line 1 or 12 . by the association of a fractal dimensional value with a specific contour line , data result for the complexity of the contour lines that are suitable for statistical examinations . in particular , these data lie in an ordered value range that can be divided into identical intervals . the data on ratio scales obtained in this manner are particularly well suited for statistical analyses . it is of particular advantage that the determination of the fractal dimension is independent of the image resolution and independent of the length of the examined contour line 1 or 12 . reproducible , comparable and statistically evaluable numbers thus result . the decision as to whether to use a stent or to conduct catheter - angioplasty to treat the atherosclerosis can then be judged on the basis of reliable clinical studies . the basic components of an apparatus with which a vessel of a patient 15 can be examined is shown in fig5 . an image of an inner contour 3 of a vessel of the patient 15 is acquired using a radiation source 16 and a radiation detector 17 . the image is analyzed in an evaluation unit 18 , and the result is output to a display unit 19 . the inventive method and apparatus are not limited to the determination of a contour line . it is also possible to detect a contour surface using a tomography modality and to detect its fractal dimension , the numerical values of which typically lie between 2 and 3 . it should also be noted that the inventive method and apparatus can be applied not only for arteries , but also to examination for any type of vessels in the body of a patient . although modifications and changes may be suggested by those skilled in the art , it is the intention of the inventor to embody within the patent warranted hereon all changes and modifications as reasonably and properly come within the scope of his contribution to the art .