Abstract
Optimising the shape of a generalised gradient waveform (GEN) in diffusion-weighted MR has been shown to, in theory, greatly increase sensitivity to pore size. The broad class of optimised shapes takes simple oscillatory forms. To speed up convergence of the optimisation, improve computation times and make the waveforms more practical, here we explore various oscillatory waveforms constructed from trapezoidal and sinusoidal shapes and compare their performance with the optimised GEN waveform. The oscillating waveforms are optimised to maximise sensitivity to parameters, such as axon radius, intra-cellular volume fraction and diffusion constants, of a simple white matter model. Simulation experiments find that all oscillating waveforms we tried perform significantly better than the original generalised waveform due to the improved convergence of the optimisation. Differences among the oscillating shapes however are very small and although a truncated sinusoidal waveform consistently gives the lowest cost function, no significant difference in the estimated model parameters was found. Therefore the simplest choice, i.e. the trapezoidal parametrisation, seems sufficient for most practical purposes.
Highlights
Diffusion-weighted Magnetic Resonance (MR) can provide insight into pore morphology and fluid transport [1] and is useful for studying porous structures such as sandstone rocks, catalysts or biological tissues [2,3,4]
We have shown that optimised generalised gradient waveforms (GEN) provide much better sensitivity to pore sizes than rectangular pulses such are those in standard diffusion sequences [11,13]
Protocols of simple oscillating waveform-shapes optimised for pore size estimation via a simple white matter model produce similar components of frequency and amplitude as GEN protocols
Summary
Diffusion-weighted Magnetic Resonance (MR) can provide insight into pore morphology and fluid transport [1] and is useful for studying porous structures such as sandstone rocks, catalysts or biological tissues [2,3,4]. We focus on biomedical imaging where diffusion MRI offers the potential to map microstructural features in tissue [5,6,7]. We have shown that optimised generalised gradient waveforms (GEN) provide much better sensitivity to pore sizes than rectangular pulses such are those in standard diffusion sequences [11,13]. This is because the optimisation in [11,13] discretises a general waveform and varies each point independently. The search space is high-dimensional (hundreds of degrees of freedom) so convergence to the optimal configuration is slow and in practice the global minimum is difficult to find
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