  Solute transport is modeled using mixture theory, applied to the nanoparticle
accumulation and concentration decay in the tissue space for different vascular
configurations. 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. 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. Co-current flow direction between two adjacent vessels led to
nonhomogeneous nanoparticle distribution for larger particle sizes in the
tissue space, while smaller particles (0.1 kDa and 3 kDa) showed the propensity
to get trapped locally in the tissue during counter-current flow. 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 concertation 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, T_peak^* = 0.027+/-0.018,
irrespective of the solute size, tissue architecture, and microvessel flow
direction. This suggests that if indeed such a universal time scale holds, the
knowledge of this 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.
