Optimization of Diffusion MRI With Consideration of the Signal Decay in Biological Tissues

Devising methodology to characterize and optimize acquisition schemes for biological tissues, such as the prostate, that produce model-based synthetic diffusion-weighted images and derived model parameters with predictable SNR improvement.

The averaging effect (AE) in synthetic diffusion-weighted images obtained through fitting of various signal decay models to signals measured over 21 linearly spaced b-values between 0 and $2000s/{\text{mm}}^2$ is determined with analytic expressions. Similarly, the standard deviation of a retrospective 2-point ADC fit based on the synthetic data is analyzed. Furthermore, acquisition schemes that achieve constant SNR or constant AE for synthetic images over the same b-value range are devised by means of numerical optimization using either a custom iterative method or a standard function optimizer. These acquisition schemes are verified by measurements on a phantom with a non-monoexponential diffusion signal decay combined with a bootstrapping approach to increase the number of data samples.

The dependence of AE on model function and parameters is complex. Repeated measurements at specific b-values can boost AE locally, while improvements in ADC uncertainty are particularly pronounced for repetitions of the higher b-value. Optimization of acquisition schemes generally results in discrete b-values, whereby the number of b-values corresponds to the number of model parameters. Results from phantom measurements are in agreement with the theoretical predictions.

The presented analytical calculations and numerical optimizations can be useful to improve acquisition schemes under various experimental conditions and clinical needs.