Analysis of collagen fibril diameter distribution in connective tissues using small-angle X-ray scattering

Analysis of the diameters of collagen fibrils provides insight into the structure and physical processes occurring in the tissue. This paper describes a method for analyzing the frequency distribution of the diameters of collagen fibrils from small-angle X-ray scattering (SAXS) patterns. Frequency values of fibril diameters were input into a mathematical model of the form factor to calculate the equatorial intensity which best fits the experimentally derived data from SAXS patterns. A minimization algorithm utilizing simulated annealing (SA) was used in the fitting procedure. The SA algorithm allowed for random sampling of the frequency values, and was run iteratively to build up an optimized frequency distribution of fibril diameters. Results were obtained for collagen samples from sheep spine ligaments. The mean fibril diameter value obtained from this data-fitting method was 73 nm±20 nm (S.D.). From scanning transmission electron microscopy, the mean diameter was found to be 69 nm±14 nm (S.D.). The good agreement between the two methods demonstrates the reliability of the SAXS method for the tissue examined. The non-destructive nature of this technique, as well as its statistical robusticity and capacity for large sampling, means that this method is both quick and effective.