Model fitting in two dimensions to small angle diffraction patterns from soft tissue

In our research programme small angle x-ray scattering (SAXS) is used to provide information on the axial arrangement of collagen molecules as well as data about the state of other components of the extra cellular matrix (ECM) in human tissues. Derivation of parameters to describe and simplify the data is required for much of the SAXS patterns analysis. A method is presented here to achieve function fitting to collagen diffraction peaks along with a representation of the underlying diffuse scatter. A simple model was used which proved reliable in fitting a variety of 2D diffraction patterns. The logarithm of the scatter intensity over the area of the scatter image was taken to reduce the range and improve fitting accuracy. Our model was then used to fit the log data. The model consisted of a radial exponential diffuse scatter component added to a specified number of Gaussian peaks. In 2D the peak model is toroidal, each component being rotated about a common specified centre. Initial search parameters from a 1D averaged sector were supplied to the iterative 2D fitting routine. With the aid of data weighting and basic wavelet filtering, successful and reliable fitting of a specified 2D model to real data is achievable. The process is easily automated. Multiple SAXS patterns can be fitted without operator intervention. As described the model is simple enough to converge rapidly and yet allows image data to be parameterized to a form suitable for extracting the requisite information. The fitting method is flexible enough to be extended to achieve a more comprehensive and complex pattern fitting in two dimensions if this turns out to be necessary. It is our intention to implement orientation distribution functions in the near future by including an angular scaling factor.