  $^{18}$F-Fluoromisonidazole ($^{18}$F-FMISO) is a highly promising positron
emission tomography radiopharmaceutical for identifying hypoxic regions in
solid tumors. This research employs spatiotemporal multi-scale mathematical
modeling to explore how different levels of angiogenesis influence the
transport of radiopharmaceuticals within tumors. In this study, two tumor
geometries with heterogeneous and uniform distributions of capillary networks
were employed to incorporate varying degrees of microvascular density. The
synthetic image of the heterogeneous and vascularized tumor was generated by
simulating the angiogenesis process. The proposed multi-scale spatiotemporal
model accounts for intricate physiological and biochemical factors within the
tumor microenvironment, such as the transvascular transport of the
radiopharmaceutical agent, its movement into the interstitial space by
diffusion and convection mechanisms, and ultimately its uptake by tumor cells.
Results showed that both quantitative and semi-quantitative metrics of
$^{18}$F-FMISO uptake differ spatially and temporally at different stages
during tumor growth. The presence of a high microvascular density in uniformly
vascularized tumor increases cellular uptake, as it allows for more efficient
release and rapid distribution of radiopharmaceutical molecules. This results
in enhanced uptake compared to the heterogeneous vascularized tumor. In both
heterogeneous and uniform distribution of microvessels in tumors, the diffusion
transport mechanism has a more pronounced than convection. The findings of this
study shed light on the transport phenomena behind $^{18}$F-FMISO
radiopharmaceutical distribution and its delivery in the tumor
microenvironment, aiding oncologists in their routine decision-making
processes.
