量化人脑的解剖和功能有着巨大的科学意义和临床必要性。在本项目中，我们创新性地提出“计算解剖学”来定量分析大脑解剖。在计算解剖学中，黎曼流形被用来模拟大脑解剖，从而量化其从整体到局部的各个特征。微分同胚映射被用来联接不同的解剖来实现大脑解剖及功能信息的传递、解析计算解剖之间的距离、以及量化解剖从整体到局部的相对形变。黎曼坐标系、解剖的距离度量、以及微分同胚变换构成了计算解剖学中的测地线定位系统。我们将结合统计分析、概率理论、以及机器学习的方法来实现对计算解剖学理论算法的进一步完善和实际的医学临床应用（包括：分析阿兹海默病对大脑解剖的时空影响机制，提取预测疾病状态的生物指标，统计估计阿兹海默病解剖异常起始时间，量化大脑解剖与认知功能之间的统计关联性，以及设计预防阿兹海默病的非药物性方案）。本项目对阿兹海默病的辅助诊断和预防将带来突破性的发展，所带来的成果对其他脑科疾病也将有着极大的应用潜力。

Quantitative analysis of the human brain’s anatomy and function is of great scientific and clinical importance. In this project, we propose a fundamentally novel framework for quantifying the brain anatomy, called “computational anatomy” or “CA”. In CA, the brain’s anatomy is modeled with smooth Riemannian manifolds so as to quantify the anatomical features both globally and locally. An optimal diffeomorphism, across anatomical systems, is used to transfer anatomical and functional information, to measure the inter-anatomy distance, and to quantify the coarse-to-fine morphological differences between two anatomies. These three elements, the Riemannian coordinates, the inter-anatomy distance metric, and the diffeomorphism together form the geodesic positioning system of brain anatomy. Through combination with statistical analysis methodologies, probability theory, and machine learning technologies, we see tremendous potential in CA. In this project, we will not only advance the algorithmic formulation of CA but also apply it to practical clinical applications. In doing so we aim to address the following clinical questions: 1) How does Alzheimer’s disease (AD) quantitatively affect the brain’s anatomy, both spatially and temporally; 2) What will be a possibly accurate MRI-based biomarker for the prediction of the neuro-degeneration in AD; 3) How can we statistically estimate the onset time of AD, the point at which the anatomy starts to degenerate but not the cognition; 4) What potential is there in effective non-pharmaceutical approaches for preventing or even halting AD. This project aims to bring groundbreaking developments to computer-assisted diagnosis and prognosis of AD. The methodologies developed in this project will also have a powerful applicability in the analysis of other brain disorders.