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.

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