Isotropic sampling of tensor-encoded diffusion MRI

The purpose of this study is to develop a method for selecting uniform wave vectors for double diffusion encoding (DDE) to improve the accuracy and reliability of diffusion measurements.

The method relies on identifying orthogonal wave vectors with rotations, and representing these rotations as points on a three-dimensional sphere in four dimensions using quaternions. This enables an electrostatic repulsion algorithm to achieve a uniform distribution of these points. The optimal points are then converted back into orthogonal wave vectors (or rotations).

The method was validated by comparing the distribution of directions to those generated by uniform sampling and by evaluating the error in the powder-averaged signal for various models. Our results demonstrate that the electrostatic repulsion approach effectively achieves a uniform distribution of wave vectors.

The proposed method provides a systematic way to generate uniform diffusion directions suitable, for example, for DDE, enhancing the precision of diffusion measurements and reducing potential bias in experimental results. The method is also capable of generating uniform sets of B-tensors, and is thus applicable for general free waveform encoding.