Zhang Xiaoxi, Johnson Timothy D, Little Roderick J A, Cao Yue
Pfizer Inc., New York, NY 10017.
J R Stat Soc Ser C Appl Stat. 2010 Nov 1;59(5):821-838. doi: 10.1111/j.1467-9876.2010.00718.x.
This work is motivated by a quantitative Magnetic Resonance Imaging study of the differential tumor/healthy tissue change in contrast uptake induced by radiation. The goal is to determine the time in which there is maximal contrast uptake (a surrogate for permeability) in the tumor relative to healthy tissue. A notable feature of the data is its spatial heterogeneity. Zhang, Johnson, Little, and Cao (2008a and 2008b) discuss two parallel approaches to "denoise" a single image of change in contrast uptake from baseline to one follow-up visit of interest. In this work we extend the image model to explore the longitudinal profile of the tumor/healthy tissue contrast uptake in multiple images over time. We fit a two-stage model. First, we propose a longitudinal image model for each subject. This model simultaneously accounts for the spatial and temporal correlation and denoises the observed images by borrowing strength both across neighboring pixels and over time. We propose to use the Mann-Whitney U statistic to summarize the tumor contrast uptake relative to healthy tissue. In the second stage, we fit a population model to the U statistic and estimate when it achieves its maximum. Our initial findings suggest that the maximal contrast uptake of the tumor core relative to healthy tissue peaks around three weeks after initiation of radiotherapy, though this warrants further investigation.
这项工作的动机来自于一项定量磁共振成像研究，该研究旨在观察放疗引起的肿瘤/健康组织对比剂摄取的差异变化。目标是确定肿瘤相对于健康组织中对比剂摄取量最大（作为通透性的替代指标）的时间。数据的一个显著特征是其空间异质性。张、约翰逊、利特尔和曹（2008年a篇和2008年b篇）讨论了两种并行的方法，用于对从基线到一次感兴趣的随访期间对比剂摄取变化的单幅图像进行“去噪”。在这项工作中，我们扩展了图像模型，以探索肿瘤/健康组织对比剂摄取随时间在多幅图像中的纵向变化情况。我们拟合了一个两阶段模型。首先，我们为每个受试者提出一个纵向图像模型。该模型同时考虑了空间和时间相关性，并通过在相邻像素之间以及随时间借用强度来对观察到的图像进行去噪。我们建议使用曼-惠特尼U统计量来总结肿瘤相对于健康组织的对比剂摄取情况。在第二阶段，我们对U统计量拟合一个总体模型，并估计其何时达到最大值。我们的初步研究结果表明，肿瘤核心相对于健康组织的最大对比剂摄取量在放疗开始后约三周达到峰值，不过这还有待进一步研究。
