The reconstruction of physically valid transport fields from subject-specific imaging data is a fundamental challenge in image-based computational modeling due to measurement noise, modeling uncertainties and discretization errors. Without a methodology to construct models that faithfully reflect the underlying physics, mechanistic understanding of complex biological systems is inherently limited. In this work, we address this challenge in the glymphatic system, the brain's waste-clearance network, where cerebrospinal fluid (CSF) is transported through perivascular spaces into the brain parenchyma to facilitate metabolic waste removal. We introduce a computational framework for the high-fidelity reconstruction of subject-specific glymphatic transport fields from spatiotemporal imaging data. The formulation utilizes an advection-diffusion model with a velocity decomposition that imposes mass conservation, enabling the recovery of solenoidal (divergence-free) velocity fields through the solution of a constrained inverse problem. The system is discretized using immersed isogeometric analysis with quadratic B-spline basis functions, providing smooth, high-continuity solutions and inherent regularization of imaging noise. We demonstrate the framework's utility by using contrast-enhanced magnetic resonance imaging of tracer transport in a mouse brain, obtaining spatially varying estimates of CSF velocity, diffusivity, and clearance parameters. Forward simulations using the recovered fields show close agreement with experimental observations, validating the framework's ability to characterize complex transport dynamics while preserving physical integrity. This approach provides a generalizable methodology for the robust inference of physically consistent transport fields from imperfect imaging data, with broad applicability to the image-guided modeling of biological and engineering systems.

翻译：从个体影像数据重建符合物理规律的输运场，是基于影像的计算建模面临的根本性挑战，其原因在于测量噪声、建模不确定性和离散化误差。若缺乏构建忠实反映底层物理机制模型的方法，对复杂生物系统的机理认知将固有地受到限制。在本工作中，我们针对类淋巴系统——大脑的废物清除网络——解决这一挑战，在该系统中，脑脊液经血管周围间隙进入脑实质以促进代谢废物清除。我们提出一个计算框架，用于从时空影像数据高保真重建个体化的类淋巴输运场。该公式采用对流-扩散模型，并引入满足质量守恒的流速分解，从而通过求解约束反问题恢复有源（散度为零）速度场。系统采用基于二次B样条基函数的浸入式等几何分析进行离散化，可生成光滑且高连续性的解，并对影像噪声具有固有正则化作用。我们通过对比增强磁共振成像在小鼠脑中示踪剂输运的应用验证了该框架的实用性，获得了脑脊液流速、扩散率和清除参数的空间变化估计。利用重建场进行正向模拟所得结果与实验观测高度吻合，验证了该框架在保持物理完整性的同时表征复杂输运动力学的能力。该方法为从不完美影像数据中稳健推断符合物理规律的输运场提供了通用性方法论，对生物与工程系统的影像引导建模具有广泛适用性。