用能量几何框架分析脑瘤患者多模态MRI变化,无需分割也能追踪病灶进展。
Energy-based Tissue Manifolds for Longitudinal Multiparametric MRI Analysis

- 以单次基线扫描构建患者特异性能量曲面,描述组织状态的几何结构。
- 复发病例在影像未显异常前,已出现能量值上升和序列空间位移趋势。
- 适合神经肿瘤长期随访研究,为无监督组织风险追踪提供新方法。
本文提出一种基于患者特异性能量建模的纵向多参数MRI分析几何框架。每个体素用多序列强度向量(T1、T1c、T2、FLAIR、ADC)表示,通过去噪得分匹配训练一个紧凑的隐式神经表示,学习定义在R^d上的能量函数E_θ(𝑢)。该模型仅需一次基线扫描即可生成能量景观,表征组织区域而无需分割标签:局部极小值对应组织盆地,梯度幅值反映接近边界程度,拉普拉斯曲率刻画局部约束结构。重要的是,此基线能量曲面作为固定几何参考,不随随访重训练,用于评估后续扫描相对于初始状态的变化。分析不再依赖解剖分割,而是考察序列向量分布如何在基线能量函数下演化。一例儿科复发病例显示,影像未见明显复发病灶前,能量值持续升高且向原肿瘤相关区域发生方向性位移;另一例稳定病例则始终维持在低能盆地内无系统性漂移。案例证明,患者特异性能量曲面可作为无监督的纵向多参数MRI分析几何基准,为神经肿瘤中基于流形的组织风险追踪奠定基础。
原文摘要 · Abstract (English)
We propose a geometric framework for longitudinal multi-parametric MRI analysis based on patient-specific energy modelling in sequence space. Rather than operating on images with spatial networks, each voxel is represented by its multi-sequence intensity vector ($T1$, $T1c$, $T2$, FLAIR, ADC), and a compact implicit neural representation is trained via denoising score matching to learn an energy function $E_θ(\mathbf{u})$ over $\mathbb{R}^d$ from a single baseline scan. The learned energy landscape provides a differential-geometric description of tissue regimes without segmentation labels. Local minima define tissue basins, gradient magnitude reflects proximity to regime boundaries, and Laplacian curvature characterises local constraint structure. Importantly, this baseline energy manifold is treated as a fixed geometric reference: it encodes the set of contrast combinations observed at diagnosis and is not retrained at follow-up. Longitudinal assessment is therefore formulated as evaluation of subsequent scans relative to this baseline geometry. Rather than comparing anatomical segmentations, we analyse how the distribution of MRI sequence vectors evolves under the baseline energy function. In a paediatric case with later recurrence, follow-up scans show progressive deviation in energy and directional displacement in sequence space toward the baseline tumour-associated regime before clear radiological reappearance. In a case with stable disease, voxel distributions remain confined to established low-energy basins without systematic drift. The presented cases serve as proof-of-concept that patient-specific energy manifolds can function as geometric reference systems for longitudinal mpMRI analysis without explicit segmentation or supervised classification, providing a foundation for further investigation of manifold-based tissue-at-risk tracking in neuro-oncology.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。