  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.
