A Hybrid 1D-3D Fractional Transport and Non-Fourier Bioheat Model for Hyperthermia Enhanced Drug Delivery in Cerebral Microcirculation

Abstract

Fractional-order models provide a powerful framework for capturing anomalous transport, memory, and nonlocal interactions in biological microvascular networks. This study presents a hybrid 1D-3D model of cerebral drug transport under mild hyperthermia, coupling fractional intravascular dynamics with non-Fourier tissue bioheat. The vascular network is represented as a directed 1D graph, where advection, diffusion, and reactive exchange obey Caputo-Fabrizio time-fractional and Riesz space-fractional laws, linked through Robin-type mass and heat transfer to surrounding 3D tissue governed by a Cattaneo-Vernotte bioheat equation. Thermal feedback modifies permeability and perfusion, yielding a two-way thermo-chemical coupling. The explicit fractional scheme employs exponential-memory updates for Caputo-Fabrizio derivatives and symmetric Grönwald-Letnikov sums for nonlocal spatial fluxes while preserving global conservation. Simulations on an arteriole-capillary-venule network show that increasing fractional order α sharpens pulse dispersion and delays washout; higher temperature enhances vascular-tissue exchange and accelerates equilibration; and dual-phase-lag relaxation mitigates nonphysical heat spikes near vessel walls. The framework unifies anomalous vascular transport, temperature-sensitive physiology, and network geometry into a scalable model suitable for hyperthermia-optimized brain drug delivery and parameter calibration from imaging data.