Displacement Error Propagation From Embedded Markers to Brain Strain

Head injury model validation has evolved from against pressure to relative brain-skull displacement, and more recently, against marker-based strain. However, there are concerns on strain data quality. In this study, we parametrically investigate how displacement random errors and synchronization errors propagate into strain. Embedded markers from four representative configurations are used to form unique and nonoverlapping tetrahedrons, triangles, and linear elements. Marker displacements are then separately subjected to up to ±10% random displacement errors and up to ±2 ms synchronization errors. Based on 100 random trials in each perturbation test, we find that smaller strain errors relative to the baseline peak strains are significantly associated with larger element sizes (volume, area, or length; p < 0.05). When displacement errors are capped at the two extreme levels, the earlier "column" and "cluster" configurations provide few usable elements with relative strain error under an empirical threshold of 20%, while about 30-80% of elements in recent "repeatable" and "uniform" configurations are considered otherwise usable. Overall, denser markers are desired to provide exhaustive pairwise linear elements with a range of sizes to balance the need for larger elements to minimize strain error but smaller elements to increase the spatial resolution in strain sampling. Their signed strains also provide unique and unambiguous information on tissue tension and compression. This study may provide useful insights into the scrutinization of existing experimental data for head injury model strain validation and to inform how best to design new experiments in the future.