Improved computation of Lagrangian tissue displacement and strain for cine DENSE MRI using a regularized spatiotemporal least squares method

INTRODUCTION: In displacement encoding with stimulated echoes (DENSE), tissue displacement is encoded in the signal phase such that the phase of each pixel in space and time provides an independent measurement of absolute tissue displacement. Previously for DENSE, estimation of Lagrangian displacement used two steps: first a spatial interpolation and, second, least squares fitting through time to a Fourier or polynomial model. However, there is no strong rationale for such a through-time model, METHODS: To compute the Lagrangian displacement field from DENSE phase data, a minimization problem is introduced to enforce fidelity with the acquired Eulerian displacement data while simultaneously providing model-independent regularization in space and time, enforcing only spatiotemporal smoothness. A regularized spatiotemporal least squares (RSTLS) method is used to solve the minimization problem, and RSTLS was tested using two-dimensional DENSE data from 71 healthy volunteers. RESULTS: The mean absolute percent error (MAPE) between the Lagrangian displacements and the corresponding Eulerian displacements was significantly lower for the RSTLS method vs. the two-step method for both x- and y-directions (0.73±0.59 vs 0.83 ±0.1, p < 0.05) and (0.75±0.66 vs 0.82 ±0.1, p < 0.05), respectively. Also, peak early diastolic strain rate (PEDSR) was higher (1.81±0.58 (s-1) vs. 1.56±0. 63 (s(-1)), p<0.05) and the strain rate during diastasis was lower (0.14±0.18 (s(-1)) vs 0.35±0.2 (s(-1)), p < 0.05) for the RSTLS vs. the two-step method, with the former suggesting that the two-step method was over-regularized. DISCUSSION: The proposed RSTLS method provides more realistic measurements of Lagrangian displacement and strain from DENSE images without imposing arbitrary motion models.