Exact analytical PGSE signal for diffusion confined to a cylindrical surface using a spectral Laplacian formalism
The study derives an exact analytical expression for the diffusion MRI signal of diffusion confined to a cylindrical surface under finite rectangular PGSE gradients, using a spectral matrix formalism of the Laplace operator. The resulting signal, expressed as a product of non‑commuting matrix exponentials, is valid for arbitrary gradient durations and separations and was validated against Monte Carlo simulations. Accelerated implementations based on Strang splitting and Gauss‑Legendre quadrature were developed, offering large speed‑ups while maintaining controllable errors.
The study derives an exact analytical expression for the diffusion MRI signal of diffusion confined to a cylindrical surface under finite rectangular PGSE gradients, using a spectral matrix formalism of the Laplace operator. The resulting signal, expressed as a product of non‑commuting matrix exponentials, is valid for arbitrary gradient durations and separations and was validated against Monte Carlo simulations. Accelerated implementations based on Strang splitting and Gauss‑Legendre quadrature were developed, offering large speed‑ups while maintaining controllable errors.
It provides an approximation‑free reference for evaluating faster signal approximations and supports large‑scale model evaluations, which is relevant for Swiss AI research in medical imaging and computational modeling.
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