Strain Measurements Through Optimized Particle Tracking in Volumetric Images: Methodology and Error Assessment

An optimized particle tracking methodology using rigid spherical markers embedded within a material is developed for use with volumetric images. Using synthetic volumetric images with additive Gaussian intensity pattern noise in both the undeformed and deformed states, numerical simulations are performed to quantify the positional errors that accumulate at each marker position during the optimal tracking process. To quantify the positional errors, Monte Carlo simulations are performed to obtain the marker position variability for a range of key parameters including marker radius, image intensity noise level and marker spacing. Using theoretical analyses to quantify strain metric variability, results show that (a) without intensity noise, there is a “sinusoidal” bias trend for sub-voxel displacement that is maximum at 0.4 and 0.6 sub-voxel positions; (b) with intensity noise up to 10 %, the standard deviation range is a non-linear function of marker radius, decreasing to 0.03 voxels when the marker radius is 9 voxels and rising to 0.25 voxels for markers with a radius of 1 voxel; (c) standard deviation in the line strain is approximately 2σ_C /L where σ_C is the standard deviation in marker centroid position and L is the distance between markers; and (d) the standard deviation in shear strain is approximately 8σ_C /L.