Collaborative Research: Multidimensional Curve Estimation for Diffusion MRI

合作研究：扩散 MRI 的多维曲线估计

• 批准号: 1208238
• 负责人: Lyudmila Sakhanenko
• 金额: $ 6.16万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1208238&HistoricalAwards=false
• 关键词: Collaborative; Research; Multidimensional; Curve; Estimation

Integral curves are natural models for a variety of biological phenomena, from neuron fibers in brain imaging data to jet streams in atmospheric data. Traditionally they have been modeled as solutions to differential equations defined on fields of direction vectors that are observed with noise in a 3D domain. But advances in imaging technology now provide much more complex directional information--functions defined on the 3D sphere-at each location in the domain. Integral curves traced from this enhanced directional data have the potential to dramatically increase our understanding of biological phenomena such as brain connectivity, but the statistical properties of integral curve estimators for this cutting-edge data are not well understood. Therefore in this project the investigators will provide a solid theoretical foundation for integral curve estimation in 3D fields of complex directional data and apply it to large corpuses of real data sets from ongoing scientific studies. The primary plan will be to model directional data locally using high-order supersymmetric tensors, and pose integral curve estimation in terms of ODEs defined on the field of their pseudo-eigenvectors. The investigators will show that the proposed integral curve estimators enjoy optimal convergence rates in a minimax sense, and prove that balloon estimators of the pseudo-eigenvector fields will lead to improved convergence. Then integral curve estimators will be linked to accompanying random processes to allow construction of uniform confidence bands around point estimates for curves; and adaptive estimation of these confidence bands will be explored to make them practically useful. The investigators will then study whether estimation may be improved further by selecting arbitrary 3D measurement locations, possibly using enhanced imaging techniques. Finally, a test for branching of integral curves will be constructed, for example at locations where axon fibers diverge or cross.The proposed work has the potential to dramatically increase the usefulness of diffusion magnetic resonance imaging (MRI) data, a technology with tremendous potential to probe the "wiring diagram" of the brain-- its connectivity-- in living people. Currently, brain connectivity measurements are widely regarded as brittle, complicated, and difficult to validate. For each individual receiving a diffusion MRI scan, the investigators will estimate curves describing the trajectories of axon fibers, the electrical "wires" of the brain. These fibers connect brain regions into distributed networks that give rise to thought; the evolution of this brain wiring in response to normal development, gene expression, aging, disease, drugs, and environmental factors is of primary interest to a broad swath of neuroscience. Simply providing scientific end-users with a sense of whether or not they should believe the estimated fiber trajectories provided to them by computer programs will greatly enhance their ability to make confident decisions about relations between such trajectories and other scientific data. In addition, the proposed methodology is also relevant in meteorology. There, isolines, fronts, jetstreams, and pressure troughs in weather data can be modeled by similar curve trajectories that can be used to enhance existing weather maps. Finally, this proposal has an exciting educational impact. The investigators, a statistician and a computer scientist with neuroscience training, envision building an interdisciplinary team of promising young researchers in statistics and neuroimaging who gain exposure to both the mathematical and neuroscience aspects of curve estimation through joined group meetings, graduate courses, and web resources related to theory and applications. This unique cross-pollination will prepare the trainees to contribute to the broadly interdisciplinary research teams that are ascendant in the sciences.

积分曲线是多种生物现象的自然模型，从脑成像数据中的神经元纤维到大气数据中的急流。传统上，它们被建模为微分方程的解，微分方程定义在方向矢量场上，这些方向矢量场在三维域中观察到噪声。但是，成像技术的进步现在提供了更复杂的方向信息——在三维球体上定义的功能——在域中的每个位置。从这种增强的定向数据中追踪到的积分曲线有可能极大地增加我们对大脑连接等生物现象的理解，但是对于这种前沿数据的积分曲线估计器的统计特性还没有得到很好的理解。因此，在这个项目中，研究者将为复杂方向数据的三维领域的积分曲线估计提供坚实的理论基础，并将其应用于正在进行的科学研究的大量真实数据集。主要计划是使用高阶超对称张量局部建模方向数据，并根据在其伪特征向量场上定义的ode提出积分曲线估计。研究人员将证明所提出的积分曲线估计在极小极大意义上具有最优的收敛速率，并证明伪特征向量场的气球估计将导致改进的收敛性。然后，将积分曲线估计与伴随的随机过程联系起来，以允许在曲线的点估计周围构建均匀的置信带；并将探讨这些置信带的自适应估计，使其在实际应用中发挥作用。然后，研究人员将研究是否可以通过选择任意3D测量位置进一步改进估计，可能使用增强的成像技术。最后，将构建积分曲线分支的测试，例如在轴突纤维分叉或交叉的位置。这项提议的工作有可能极大地增加扩散磁共振成像（MRI）数据的有用性，这是一项具有巨大潜力的技术，可以探测活人大脑的“接线图”——它的连通性。目前，大脑连接测量被广泛认为是脆弱、复杂和难以验证的。对于每个接受弥散性核磁共振扫描的个体，研究人员将估计描述轴突纤维（大脑的电线）轨迹的曲线。这些纤维将大脑区域连接成分布式网络，从而产生思考；在正常发育、基因表达、衰老、疾病、药物和环境因素的影响下，这种大脑线路的进化是神经科学广泛领域的主要兴趣所在。简单地向科学最终用户提供他们是否应该相信计算机程序提供给他们的估计纤维轨迹的感觉，将大大提高他们对这些轨迹与其他科学数据之间的关系做出自信决策的能力。此外，所提出的方法也适用于气象学。在那里，天气数据中的等值线、锋面、急流和低压槽可以通过类似的曲线轨迹来建模，这些曲线轨迹可以用来增强现有的天气图。最后，这个建议有一个令人兴奋的教育影响。研究人员，一位统计学家和一位受过神经科学训练的计算机科学家，设想建立一个跨学科的团队，由统计学和神经成像领域有前途的年轻研究人员组成，他们通过参加小组会议、研究生课程和与理论和应用相关的网络资源来接触曲线估计的数学和神经科学方面。这种独特的交叉授粉将使受训者为在科学领域处于优势地位的广泛跨学科研究团队做出贡献。