Objective: Reconstructing freehand ultrasound in 3D without any external tracker has been a long-standing challenge in ultrasound-assisted procedures. We aim to define new ways of parameterising long-term dependencies, and evaluate the performance. Methods: First, long-term dependency is encoded by transformation positions within a frame sequence. This is achieved by combining a sequence model with a multi-transformation prediction. Second, two dependency factors are proposed, anatomical image content and scanning protocol, for contributing towards accurate reconstruction. Each factor is quantified experimentally by reducing respective training variances. Results: 1) The added long-term dependency up to 400 frames at 20 frames per second (fps) indeed improved reconstruction, with an up to 82.4% lowered accumulated error, compared with the baseline performance. The improvement was found to be dependent on sequence length, transformation interval and scanning protocol and, unexpectedly, not on the use of recurrent networks with long-short term modules; 2) Decreasing either anatomical or protocol variance in training led to poorer reconstruction accuracy. Interestingly, greater performance was gained from representative protocol patterns, than from representative anatomical features. Conclusion: The proposed algorithm uses hyperparameter tuning to effectively utilise long-term dependency. The proposed dependency factors are of practical significance in collecting diverse training data, regulating scanning protocols and developing efficient networks. Significance: The proposed new methodology with publicly available volunteer data and code for parametersing the long-term dependency, experimentally shown to be valid sources of performance improvement, which could potentially lead to better model development and practical optimisation of the reconstruction application.

翻译：目的：在无外部跟踪器的情况下实现自由手超声的三维重建一直是超声引导手术中长期存在的挑战。本研究旨在定义长期依赖关系参数化的新方法，并评估其性能。方法：首先，通过帧序列中的变换位置对长期依赖关系进行编码，通过结合序列模型与多变换预测实现。其次，提出解剖图像内容和扫描协议两种依赖因子，以促进精确重建，并通过分别降低训练方差进行实验量化。结果：1) 在20帧/秒的帧率下，加入长达400帧的长期依赖关系显著提升了重建效果，累计误差相比基线降低高达82.4%。该改进效果依赖于序列长度、变换间隔和扫描协议，但出乎意料地，与使用长短期记忆模块的循环网络无关；2) 减少训练中解剖或协议方差会导致重建精度下降。有趣的是，代表性协议模式带来的性能增益高于代表性解剖特征。结论：所提算法通过超参数调优有效利用长期依赖关系，所提出的依赖因子在收集多样化训练数据、规范扫描协议及开发高效网络方面具有实际意义。意义：本研究提出的新方法（含公开志愿者数据和参数化长期依赖关系的代码）经实验验证可有效提升性能，有望推动重建应用的模型优化与实践改进。