Exact solutions for heat transfer and nanoparticle extravasation across microvessel walls within biological tissues

Purpose The purpose of this study is to investigate the coupled transport mechanisms of heat and nanoparticles (NPs) in a horizontally oriented microvessel embedded in thermally active biological tissue, with the aim of identifying the factors that govern heat dissipation and NP delivery to surrounding tissues, particularly in the context of thermal therapy and tumour targeting. The specific objective of this study is to derive closed-form analytical solutions for NP extravasation and heat flux, thereby addressing the limitations of existing numerical and oversimplified analytical models. Design/methodology/approach The study uses asymptotic analysis to derive analytical solutions for blood velocity and pressure in a microvessel with a small radius. This approach simplifies the NP and heat transport equations into two ordinary differential equations, which are then solved analytically to examine NP extravasation and thermal interactions across the microvessel wall. Findings The results indicate a decrease in NP concentration along the microvessel axial direction due to leakage into surrounding tissue. Simultaneously, blood temperature increases due to heat transfer from the tissue. The study derives mathematical expressions for heat and NP fluxes through the vessel walls, offering valuable estimates for NP delivery to tumours and heat loss through tumour vasculature. Originality/value This research provides novel analytical expressions for heat and NP transport in biologically relevant microvascular environments, highlighting the critical role of vessel-tissue interactions in optimizing thermal therapies. The findings contribute to the development of more effective strategies for targeted NP delivery and thermal regulation in medical treatments.