Wilkinson S J, Rogers K D, Hall C J
Department of Materials and Medical Sciences, Cranfield University, Shrivenham, Swindon, Wiltshire SN6 8LA, UK.
Phys Med Biol. 2006 Apr 7;51(7):1819-30. doi: 10.1088/0031-9155/51/7/013. Epub 2006 Mar 21.
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.
在我们的研究项目中，小角X射线散射（SAXS）用于提供有关胶原蛋白分子轴向排列的信息，以及关于人体组织细胞外基质（ECM）其他成分状态的数据。SAXS模式分析的大部分工作都需要推导参数来描述和简化数据。本文提出了一种方法，用于实现对胶原蛋白衍射峰的函数拟合以及对潜在漫散射的表示。使用了一个简单模型，该模型在拟合各种二维衍射模式时证明是可靠的。取散射图像区域上散射强度的对数以减小范围并提高拟合精度。然后用我们的模型拟合对数数据。该模型由一个径向指数漫散射分量加上指定数量的高斯峰组成。在二维中，峰模型是环形的，每个分量围绕一个共同的指定中心旋转。将一维平均扇区的初始搜索参数提供给迭代二维拟合程序。借助数据加权和基本小波滤波，可以将指定的二维模型成功且可靠地拟合到实际数据。该过程易于自动化。多个SAXS模式可以在无需操作员干预的情况下进行拟合。如前所述，该模型足够简单，能够快速收敛，同时允许将图像数据参数化为适合提取所需信息的形式。如果有必要，该拟合方法足够灵活，可以扩展以实现二维中更全面和复杂的模式拟合。我们打算在不久的将来通过纳入角度缩放因子来实现取向分布函数。
