Mixture theory modeling for characterizing solute transport in breast tumor tissues

Tumor numerical models have been used to quantify solute transport with a single capillary embedded in an infinite tumor expanse, but measurements from different mammalian tumors suggest that a tissue containing a single capillary with an infinite intercapillary distance assumption is not physiological. The present study aims to investigate the limits of the intercapillary distance within which nanoparticle transport resembles solute extravasation in a breast tumor model as a function of the solute size, the intercapillary separation, and the flow direction in microvessels.

Solute transport is modeled in a breast tumor for different vascular configurations using mixture theory. A comparison of a single capillary configuration (SBC) with two parallel cylindrical blood vessels (2 BC) and a lymph vessel parallel to a blood vessel (BC_LC) embedded in the tissue cylinder is performed for five solute molecular weights between 0.1 kDa and 70 kDa. The effects of counter flow (CN) versus co-current flow (CO) on the solute accumulation were also investigated and the scaling of solute accumulation-decay time and concentration was explored.

We found that the presence of a second capillary reduces the extravascular concentration compared to a single capillary and this reduction is enhanced by the presence of a lymph vessel. Varying the intercapillary distance with respect to vessel diameter shows a deviation of 10-30% concentration for 2 BC and 45-60% concentration for BC_LC configuration compared to the reference SBC configuration. Finally, we introduce a non-dimensional time scale that captures the concentration as a function of the transport and geometric parameters. We find that the peak solute concentration in the tissue space occurs at a non-dimensional time, $$ = 0.027 ± 0.018, irrespective of the solute size, tissue architecture, and microvessel flow direction.

This work suggests that the knowledge of such a unique non-dimensional time would allow estimation of the time window at which solute concentration in tissue peaks. Hence this can aid in the design of future therapeutic efficacy studies as an example for triggering drug release or laser excitation in the case of photothermal therapies.