基于几何热扩散的MRI脑皮层形态特征抽取与鉴别回归分析研究

Cortical morphologic measurement in magnetic resonance imaging (MRI) is an important technique in the field of studying Alzheimer's . Most previous measurements for describing the cortical complex morphological characteristics are not sufficiently accurate on its own to serve as an absolute diagnostic criterion. It's hard to extract the low-dimensional discriminative representations from the high-dimensional cortical complex morphological characteristics. And we are short of the local structural differences quantitative assessment methods for the clinical diagnosis of AD at the different cognitive impairment stages. To overcome these problems, the main issue of this project focuses on the theory and related algorithm of the complex morphology description and assessment for MRI cortical atrophy. The main contributions will be made as follows. Firstly, we will construct an optimized tetrahedral mesh that matches the MR image based on the geometric fusion implicit surface property metric and the harmonic function minimization regularization model. Secondly, by incorporating the vibration mode characterization system of the complex manifold and the spatial location information, we will propose the heat kernel morphology measurement driven by the partial structure of the MRI data. Thirdly, by combining the compact property intra-class and the alienation property inter-class of the linear classifier, we will propose the optimal sparse representation of the projection direction in the classification space and construct the low-dimensional nature representation method from the MRI high-dimensional morphological characteristics based on the jointly sparse reconstruction and classification in the projection vector space. And the risk assessment strategy will be constructed for the individual from MCI to AD. Finally, by using the common structure maintenance property under the metric of nuclear norm, we will propose the matrix low rank evaluation method and related efficient numerical optimization algorithms for discriminating the local structural differences between the different groups. The research will establish the solid fundamentals for solving the three dimension mesh modeling, feature measurement, and high-dimensional signal understanding problems.

磁共振成像(MRI)脑皮层形态度量是研究阿尔茨海默症(AD)的重要手段。项目拟针对目前缺乏有针对性的脑皮层复杂形态特征描述方法以及高维信息的低维本质分类表达与局部结构差异评估等问题，研究MRI脑皮层萎缩复杂形态的描述与评估理论和算法。主要研究内容为：利用几何融合隐式表面属性度量与调和能量最小化正则模型，建立形态保持与结构优化的四面体网格模型；结合黎曼流形下的振动模式表征系统和位置信息，提出局部结构驱动的热核扩散形态表征测度；融合线性分类器类内紧致、类间疏远的特性，以及分类空间投影方向的优化稀疏表示，提出联合稀疏重建与鉴别分类的脑皮层低维本质表征方法，以及构建认知障碍个体转化AD的风险评估策略;利用核范数度量下的共性结构保持特性，提出基于脑皮层局部萎缩的矩阵低秩量化评估方法以及相应的高效数值优化方法。项目的研究成果有望为生物医学领域的三维网格建模、特征度量、高维信息感知提供基础支撑。

随着人口老龄化的加剧，AD的防治已经成为当今医学领域研究的重大公共卫生问题。为了加快研发有效的AD防治疗法，迫切需要构建一种与AD病情关联度紧密的脑皮层形态表征方法以及AD病情影响下所导致的脑皮层局部萎缩的量化评估算法和理论。用以评估早期AD干预疗法的效果，提升医疗机构的诊疗水平。同时也是促进AD防治走向智能化、精准化，有效解决老龄化社会突出健康问题的重要途径。.基于此，本项目构建了一套与AD病情关联度紧密的脑皮层形态表征体系以及AD病情影响下所导致的脑皮层局部萎缩的量化评估算法和理论。研究内容包括提出了基于脑皮层MRI影像数据的四面体网格优化生成模型，该模型能够在准确地表征脑皮层复杂的几何拓扑结构的同时保证稳健的四面体结构；提出了基于三维稳恒场热流场线的形态特征提取模型，从而高精度确定脑皮层的厚度特征；提出了基于低秩主成分分解以及AD形态相似性统计模型的单变量神经退行性生物标志（UNB）生成模型，可以精确表征个体受AD影响所导致的形态变化；建立了基于生存分析模型的AD转化风险以及生存概率差异的统计分析框架，可以预测分析MCI个体AD病情发展趋势。.通过研究相关算法背后的核心科学问题，突破目前UNB在感知受AD影响的形态变化方面存在灵敏度和鲁棒性较弱的缺陷，精确揭示AD病情导致的本质形态变化，有效推进计算神经影像学在临床诊断和预后的应用，提升MRI影像分析技术的国产自主研发水平。