Optimized Gradient Waveforms for Tensor-Valued Diffusion MRI Under Time-Dependent Diffusion Using Double-Isotropic...

Spherical and linear b-tensor encoding (STE and LTE) enables quantification of microscopic diffusion anisotropy and diffusional variance. However, such waveforms are often variably sensitive to time-dependent diffusion, causing rotational variance and spectral mismatch. We propose double-isotropic matched encoding (DIME), which enforces isotropy in diffusion- and restriction-weighting tensors ( $B$ and $M$ ) and STE/LTE pairs matched in restriction sensitivity.

DIME uses trapezoidal pulses, optimized to yield isotropic $B$ and $M$ while generating a spectrally matched LTE. The design ensures concomitant gradient balance and constrains peripheral and cardiac nerve stimulation. Rotational invariance and spectral matching were assessed by simulations in ideal and realistic substrates at 80 and 200 mT/m via CV across rotations and STE/LTE mean diffusivity (MD). DIME was compared to numerically optimized waveforms (NOWs).

DIME had the lowest rotational variance and best spectral matching. In cylinders, the median (IQR) CV was 2.0% (1.5%-3.3%) and 1.7% (1.2%-2.7%) at 80 and 200 mT/m, versus 2.5% (1.8%-4.1%) and 2.0% (1.4%-3.5%) for NOW. In spheres, the maximum MD mismatch ( $\Delta$ MD) was 0.08 versus $0.52\mu m^2/\text{ms}$ for NOW. In realistic substrates, DIME was superior ( $\Delta$ MD =  $0.01\pm 0.01$ ) compared to NOW ( $-0.16\pm 0.10\mu m^2/\text{ms}$ ). DIME increased encoding duration by 13-22 ms.

By controlling both $B$ and $M$ , DIME improves STE rotational invariance and reduces spectral mismatch under time-dependent diffusion, enabling more reliable tensor-valued encoding tailored to hardware and nerve stimulation constraints.