  The goal of this paper is to investigate the validity of a hybrid
embedded/homogenized in-silico approach for modeling perfusion through solid
tumors. The rationale behind this novel idea is that only the larger blood
vessels have to be explicitly resolved while the smaller scales of the
vasculature are homogenized. As opposed to typical discrete or fully-resolved
1D-3D models, the required data can be obtained with in-vivo imaging techniques
since the morphology of the smaller vessels is not necessary. By contrast, the
larger vessels, whose topology and structure is attainable non-invasively, are
resolved and embedded as one-dimensional inclusions into the three-dimensional
tissue domain which is modeled as a porous medium. A sound mortar-type
formulation is employed to couple the two representations of the vasculature.
We validate the hybrid model and optimize its parameters by comparing its
results to a corresponding fully-resolved model based on several well-defined
metrics. These tests are performed on a complex data set of three different
tumor types with heterogeneous vascular architectures. The correspondence of
the hybrid model in terms of mean representative elementary volume blood and
interstitial fluid pressures is excellent with relative errors of less than 4%.
Larger, but less important and explicable errors are present in terms of blood
flow in the smaller, homogenized vessels. We finally discuss and demonstrate
how the hybrid model can be further improved to apply it for studies on tumor
perfusion and the efficacy of drug delivery.
