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14 February 2012Using radial NMR profiles to characterize pore size distributions
Extracting information about axon diameter distributions in the brain is a challenging task which provides
useful information for medical purposes; for example, the ability to characterize and monitor axon diameters
would be useful in diagnosing and investigating diseases like amyotrophic lateral sclerosis (ALS)1 or autism.2
Three families of operators are defined by Ozarslan,3 whose action upon an NMR attenuation signal extracts
the moments of the pore size distribution of the ensemble under consideration; also a numerical method is
proposed to continuously reconstruct a discretely sampled attenuation profile using the eigenfunctions of the
simple harmonic oscillator Hamiltonian: the SHORE basis. The work presented here extends Ozarlan's method
to other bases that can offer a better description of attenuation signal behaviour; in particular, we propose the use
of the radial Spherical Polar Fourier (SPF) basis. Testing is performed to contrast the efficacy of the radial SPF
basis and SHORE basis in practical attenuation signal reconstruction. The robustness of the method to additive
noise is tested and analysed. We demonstrate that a low-order attenuation signal reconstruction outperforms a
higher-order reconstruction in subsequent moment estimation under noisy conditions. We propose the simulated
annealing algorithm for basis function scale parameter estimation. Finally, analytic expressions are derived and
presented for the action of the operators on the radial SPF basis (obviating the need for numerical integration,
thus avoiding a spectrum of possible sources of error).