Cochlear Aqueduct Advection and Diffusion Inferred from Computed Tomography Imaging with a Bayesian Approach.

Abstract

Purpose: Fluid flow and transport of therapeutic agents and pathogenic bacteria into the cochlea has been challenging to study due to its small size and location within bone. We here take advantage of recent non-invasive Computed Tomography (CT) imaging to infer transport parameters in a 1-dimensional advection-diffusion model of the cochlear aqueduct using a Bayesian approach.

Methods: Six male C56BL/6 mice injected with the small molecule tracer iohexol in cisterna magna were scanned every 5 min for 30 min in CT under anesthesia. Using the CT data to set boundary conditions, we solve the advection-diffusion equation for given advection and spatially varying diffusion parameters. The CT data is modeled as normally distributed around the model-predicted concentration. We specify priors for the model unknown parameters and infer their posterior distributions using Bayes' formula and the CUQIpy library. The statistical approach is validated using synthetic data.

Results: The evolution of the concentration of tracer in the cochlear aqueduct is well predicted by the advection-diffusion model using inferred parameters. Though diffusion of the small CT tracer varies along the aqueduct, it is usually near the free diffusion and therefore not likely to be influenced much by membranes or flow. Advection is inferred near zero in most cases. We show how to use these results to calculate transport through the cochlear aqueduct for other animals and molecules.

Conclusion: Free diffusion dominates transport of small molecules in the cochlear aqueduct, which can therefore be effectively approximated using simple 1-dimensional (advection-)diffusion formulas.