Novel 2D displacement estimation in rotating and shearing structures using free-shape kernels of radio frequency data

This fundamental study examines the feasibility of measuring rotation and the performance of strain estimation in shearing and rotating structures using three different RF-based methods. Linear array data of a homogeneous block phantom were simulated using Field II©. The block was subjected to a shear strain of 2.0, 4.0 and 6.0% in combination with an applied load equivalent to 0.0, 1.0 and 2.0% vertical strain. Secondly, simulations in which the block was rotated over a range of 0.5° to 5.0° and 10° (with again 0.0 - 2.0% vertical strain) were performed. Displacements were estimated using a coarse-to-fine strain algorithm with sub-sample aligning and stretching of data using 1D and 2D pre-compression kernels (`rigid-1D´ and `rigid-2D´, respectively). A different approach was developed in which the search area was not limited to a box-shaped 2D region: Axial displacements were used to deform the kernel in the axial direction freely, resulting in shapes such as parallelograms (`free-2D´). All three methods were applied to the simulated data and the displacements, strains and rotations were estimated. The study revealed that `free-2D´ outperformed the other methods, especially for large shear strains or rotation angles. The variance decreased by a factor 4 to 5. Rotations were measured up to 4.0 - 5.0°. The measured angles were slightly underestimated, especially below the focus. The precision of the strain estimates decreased with increasing rotation angles. Again, the precision was enhanced when using the `free-2D´ method. In conclusion, the proposed `free-shape´ 2D method enhances the measurement of (shear) strains and rotation. Experimental validation of the new method still has to be performed.