Abdominal aortic aneurysms (AAAs) are progressive dilatations of the abdominal aorta that, if left untreated, can rupture with lethal consequences. Imaging-based patient monitoring is required to select patients eligible for surgical repair. In this work, we present a model based on implicit neural representations (INRs) to model AAA progression. We represent the AAA wall over time as the zero-level set of a signed distance function (SDF), estimated by a multilayer perception that operates on space and time. We optimize this INR using automatically extracted segmentation masks in longitudinal CT data. This network is conditioned on spatiotemporal coordinates and represents the AAA surface at any desired resolution at any moment in time. Using regularization on spatial and temporal gradients of the SDF, we ensure proper interpolation of the AAA shape. We demonstrate the network's ability to produce AAA interpolations with average surface distances ranging between 0.72 and 2.52 mm from images acquired at highly irregular intervals. The results indicate that our model can accurately interpolate AAA shapes over time, with potential clinical value for a more personalised assessment of AAA progression.

翻译：腹主动脉瘤（AAA）是腹主动脉的进行性扩张，若不治疗，可能破裂并导致致命后果。基于影像的患者监测是选择适合手术修复患者的关键。本研究提出一种基于隐式神经表示（INRs）的模型，用于建模AAA的进展。我们将随时间变化的AAA壁表示为符号距离函数（SDF）的零水平集，该函数由作用于空间和时间维度的多层感知器估计。利用纵向CT数据中自动提取的分割掩膜优化该INR。该网络以时空坐标为条件，可在任意时刻以任意所需分辨率重建AAA表面。通过对SDF空间和时间梯度的正则化处理，确保AAA形状的合理插值。我们验证了该网络在高度不规则时间间隔获取的图像间生成AAA插值的能力，其平均表面距离介于0.72至2.52毫米之间。结果表明，我们的模型能够精确插值随时间变化的AAA形状，对AAA进展的个性化评估具有潜在临床价值。