Fishbaugh James, Durrleman Stanley, Piven Joseph, Gerig Guido
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah.
Carolina Institute for Developmental Disabilities, University of North Carolina, Chapel Hill, North Carolina.
Proc SPIE Int Soc Opt Eng. 2012 Feb 23;8314. doi: 10.1117/12.911721.
Traditional longitudinal analysis begins by extracting desired clinical measurements, such as volume or head circumference, from discrete imaging data. Typically, the continuous evolution of a scalar measurement is estimated by choosing a 1D regression model, such as kernel regression or fitting a polynomial of fixed degree. This type of analysis not only leads to separate models for each measurement, but there is no clear anatomical or biological interpretation to aid in the selection of the appropriate paradigm. In this paper, we propose a consistent framework for the analysis of longitudinal data by estimating the continuous evolution of shape over time as twice differentiable flows of deformations. In contrast to 1D regression models, one model is chosen to realistically capture the growth of anatomical structures. From the continuous evolution of shape, we can simply extract any clinical measurements of interest. We demonstrate on real anatomical surfaces that volume extracted from a continuous shape evolution is consistent with a 1D regression performed on the discrete measurements. We further show how the visualization of shape progression can aid in the search for significant measurements. Finally, we present an example on a shape complex of the brain (left hemisphere, right hemisphere, cerebellum) that demonstrates a potential clinical application for our framework.
传统的纵向分析首先从离散的成像数据中提取所需的临床测量值，如体积或头围。通常，通过选择一维回归模型（如核回归或拟合固定次数的多项式）来估计标量测量值的连续演变。这种分析类型不仅会为每个测量值生成单独的模型，而且没有明确的解剖学或生物学解释来帮助选择合适的范式。在本文中，我们提出了一个一致的框架，用于通过将形状随时间的连续演变估计为可二次微分的变形流来分析纵向数据。与一维回归模型不同，我们选择一个模型来实际捕捉解剖结构的生长。从形状的连续演变中，我们可以简单地提取任何感兴趣的临床测量值。我们在真实的解剖表面上证明，从连续形状演变中提取的体积与对离散测量值进行的一维回归一致。我们进一步展示了形状进展的可视化如何有助于寻找重要的测量值。最后，我们给出了一个关于大脑形状复合体（左半球、右半球、小脑）的例子，展示了我们框架的潜在临床应用。
