  We consider biotransport in tumors with uncertain heterogeneous material
properties. Specifically, we focus on the elliptic partial differential
equation (PDE) modeling the pressure field inside the tumor. The permeability
field is modeled as a log-Gaussian random field with a prespecified covariance
function. We numerically explore dimension reduction of the input parameter and
model output. Truncated Karhunen--Lo\`{e}ve (KL) expansions are used to
decompose the log-permeability field, as well as the resulting random pressure
field. We find that although very high-dimensional representations are needed
to accurately represent the permeability field, especially in presence of small
correlation lengths, the pressure field is not very sensitive to high-order KL
terms of the input parameter. Moreover, we find that the pressure field itself
can be represented accurately using a KL expansion with a small number of
terms. These observations are used to guide a reduced-order modeling approach
to accelerate computational studies of biotransport in tumors.
