The Corrected Inverse-Gaussian: A Tractable First-Hitting-Time Channel Model for Nonstationary Molecular Communication

This paper develops a tractable analytical channel model for first-hitting-time molecular communication (MC) systems under time-varying drift.

While existing studies of nonstationary transport rely primarily on numerical solutions of advection-diffusion equations or parametric impulse-response fitting, they do not provide an explicit analytical description of trajectory-level arrival dynamics at absorbing boundaries.

By adopting a change-of-measure formulation, we reveal a structural decomposition of the first-hitting-time density into a cumulative-drift displacement term and a stochastic boundary-flux modulation factor.

This leads to a closed-form analytical approximation, termed the calibrated Corrected-Inverse-Gaussian (C-IG) density, that advances the stationary-drift IG channel law to deterministic nonstationary drift while preserving O(1) evaluation complexity.

Monte Carlo simulations under both smooth pulsatile and abrupt switching drift profiles confirm that the proposed C-IG model accurately captures complex transport phenomena, including phase modulation, multi-pulse dispersion, and transient backflow--effects that traditionally complicate symbol synchronization and induce severe inter-symbol interference.

The resulting framework provides a physics-informed, computationally efficient MC channel law suitable for system-level analysis and advanced receiver design, such as real-time maximum likelihood detection, in dynamic biological and MC environments.