Niels Buhl | Searcharxiv

arXiv2021

Analytic determination of lung microgeometry with gas diffusion magnetic resonance

Through inhalation of, e.g., hyperpolarized $^3$He, it is possible to acquire gas diffusion magnetic resonance measurements that depend on the local geometry in the vast network of microscopic airways that form the respiratory zone of the human lung. Here, we demonstrate that this can be used to determine the dimensions (length and radius) of these airways noninvasively. Specifically, the above technique allows measurement of the weighted time-dependent diffusion coefficient (also called the apparent diffusion coefficient), which we here derive in analytic form using symmetries in the airway network. Agreement with experiment is found for the full span of published hyperpolarized $^3$He diffusion magnetic resonance measurements (diffusion times from milliseconds to seconds) and published invasive airway dimension measurements.

physics.bio-ph↗

arXiv2018

Different approach to the modeling of nonfree particle diffusion

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore networks to general geometric domains can be considered and that the (free random walk) central limit theorem can be generalized to cover also the nonfree case. The latter gives rise to a continuum-limit description of the diffusive motion where the effect of partially absorbing barriers is accounted for in a natural and non-Markovian way that, in contrast to the traditional approach, quantifies the absorptivity of a barrier in terms of a dimensionless parameter in the range 0 to 1. The generalized theorem gives two general analytic expressions for the continuum-limit propagator: an infinite sum of Gaussians and an infinite sum of plane waves. These expressions entail the known method-of-images and Laplace eigenfunction expansions as special cases and show how the presence of partially absorbing barriers can lead to phenomena such as line splitting and band gap formation in the plane wave wave-number spectrum.

cond-mat.stat-mech↗