Enhanced spectral response in frequency-dependent diffusion measurements using a linear encoding model.

Abstract

Purpose: To devise a more comprehensive quantitative representation for spectral encodings in frequency-dependent diffusion measurements for improved estimation of D(ω).

Theory and methods: Whereas a spectral diffusion measurement is typically represented by a Dirac delta function at a single attributed frequency, spectral response is represented here by the encoding power in |Q(ω)|² over a set of contiguous frequency intervals. Using this representation paradigm, a linear encoding model is formulated wherein diffusivity over each interval can be estimated by inverting the encoding process from a set of measurements. This strategy was validated in in vivo human brain imaging experiments evaluating D(ω) up to 50 Hz over 10-Hz intervals using high-performance gradients. The employed spectral encodings were selected using an accompanying framework devised to ensure robust encoding performance given the chosen frequency intervals. Additionally, simulated measurements were carried out to compare the performance in estimating D(ω) using the proposed encoding model versus using single-frequency attribution in relation to the form of D(ω) and the width of frequency intervals.

Results: In vivo D(ω) determined using the proposed encoding strategy were found to increase with increasing frequency and could be mapped to spectral responses more spectrally selective than those characteristic of single-frequency attribution. In turn, simulated measurements demonstrated that the linear encoding model permitted D(ω) estimation with improved accuracy, especially for more nonlinear D(ω), at the expense of reduced precision, particularly for narrower frequency intervals.

Conclusion: By devising a more holistic representation paradigm for frequency-dependent diffusion measurements, D(ω) can be recovered with higher fidelity.