Department of Radiation Oncology, University of Minnesota, 420 Delaware St. SE, Minneapolis, MN, MMC-494, USA.
Med Phys. 2019 Sep;46(9):4021-4036. doi: 10.1002/mp.13698. Epub 2019 Jul 26.
Cerenkov photons are generated by high-energy radiation used in external beam radiation therapy (EBRT). This study expands upon the Cerenkov light dosimetry formula previously developed to relate an image of Cerenkov photons to the primary beam fluence. Extension of this formulation allows for deconvolution to be performed on images acquired from curved geometries.
The integral equation, which represented the formation of Cerenkov photon image from an incident high-energy photon beam, was expanded to allow for space-variance of the convolution kernel called as the Cerenkov scatter function (CSF). The GAMOS (Geant4-based Architecture for Medicine-Oriented Simulations) Monte Carlo (MC) particle simulation software was used to obtain the CSF for different incident beam angles. The image of a curved surface was first projected to a flat plane by using a perspective correction method. Then, the planar image was partitioned into small segments (or blocks), where a CSF corresponding to a specific beam incident angle was applied for deconvolution. The block size and the margin around the block were optimized by studying the effects of those parameters on the deconvolution accuracy for a test image. We evaluated three deconvolution techniques: Richardson-Lucy, Blind, and Total Variation minimization (TV/L2) algorithms, to select the most accurate method for the current applications.
Analysis of deconvolution algorithms showed that the TV/L2 method provided the most accurate solution to the deconvolution problem for Cerenkov imaging. Optimization of space-variant deconvolution parameters showed that including a margin that is at least 42.9% of the image width provided the most accurate product image. There was no optimal size for the deconvolution area and should be chosen based on the presence of unique CSF kernels within an image. Space-variant deconvolution improved measured field size in Cerenkov photon images by 7.37%, as compared with 1.74% by space-invariant deconvolution. Space-variant deconvolution improved measured penumbra by 99.3%, as compared with 76.7% by space-invariant deconvolution. Space-variant deconvolution introduced artifacts in flat regions of the beam. Artifacts were avoided through selective space-variant deconvolution in only the penumbra region.
Primary photon fluence distributions of a curved surface can be obtained by using space-variant deconvolution methods in Cerenkov light dosimetry. The TV/L2 algorithm is the best method for deconvolution of Cerenkov photon images from an open-field beam derived from either a flat or curved surface. The partition size chosen for space-variant deconvolution should be at least six times the full width at half maximum (FWHM) of the corresponding scatter kernel used in deconvolution. Space-variant deconvolution is necessary if the incident beam angle difference is larger than 6 between regions of an image.
切伦科夫光子是由外部束放射治疗（EBRT）中使用的高能射线产生的。本研究扩展了先前开发的用于将切伦科夫光子图像与初级射束通量相关联的切伦科夫光剂量学公式。该公式的扩展允许对从弯曲几何形状获得的图像进行反卷积。
表示由入射高能光子束形成切伦科夫光子图像的积分方程，被扩展为允许卷积核（称为切伦科夫散射函数（CSF））的空间变化。GAMOS（基于 Geant4 的面向医学模拟的架构）蒙特卡罗（MC）粒子模拟软件用于为不同的入射束角获得 CSF。首先通过使用透视校正方法将曲面的图像投影到平面上。然后，将平面图像分成小片段（或块），在该小片段中应用与特定入射束角相对应的 CSF 进行反卷积。通过研究这些参数对测试图像反卷积精度的影响，对块大小和块周围的边缘进行了优化。我们评估了三种反卷积技术：Richardson-Lucy、盲和总变分最小化（TV/L2）算法，以选择当前应用的最准确方法。
反卷积算法的分析表明，TV/L2 方法为切伦科夫成像的反卷积问题提供了最准确的解决方案。对空间变化反卷积参数的优化表明，包括至少为图像宽度的 42.9%的边缘提供了最准确的乘积图像。反卷积区域没有最佳尺寸，应根据图像中存在的独特 CSF 内核来选择。与空间不变反卷积相比，空间变化反卷积将切伦科夫光子图像中的测量场尺寸提高了 7.37%。与空间不变反卷积相比，空间变化反卷积将测量半影提高了 99.3%。空间变化反卷积在射束的平坦区域中引入了伪影。通过仅在半影区域选择性地进行空间变化反卷积，可以避免伪影。
可以通过在切伦科夫光剂量学中使用空间变化反卷积方法来获得曲面的初级光子通量分布。TV/L2 算法是从平面或曲面衍生的开放场束中反卷积切伦科夫光子图像的最佳方法。对于反卷积使用的散射核的半高全宽（FWHM）的至少六倍，应选择用于空间变化反卷积的分区大小。如果图像区域之间的入射束角差大于 6 ，则需要空间变化反卷积。
