T1 fast acquisition relaxation mapping (T1-FARM): an optimized reconstruction.

Maps of spin lattice relaxation time (T1) can be reconstructed directly from magnetic resonance imaging (MRI) k-space data measured with very short data acquisition times, e.g., a data set for a 128 x 128 T1 map can be acquired in less than 3 s using gradients with 10-T/m/s slew rate. In principle, this approach could be extended to quantitate other MRI parameters but current use is limited by the lack of precise, accurate and fast reconstruction. Using theoretical calculations, computer simulations, and experiments we have optimized a parametric reconstruction method using a Leverberg-Marquardt (L-M) algorithm and compared it to the quasi-Newton method originally used. We have found significant improvement using the L-M method provided T1 is solved for directly without linearization. Reconstruction time was reduced by a factor of 60. Computer simulations show that the method has acceptable accuracy even in signals with 5% noise. Optimization included the investigation of the signal-to-noise (S/N) of each k-space data point and its impact on relative error of the reconstruction. This result indicates that rectangular k-space data could be collected for further reduction of data acquisition times. Determination of T1 maps by direct parametric reconstruction of k-space data appears feasible and may stimulate further application of quantitative MRI.