  We model substructure in the protoplanetary disks around DoAr 44 and HD
163296 in order to better understand the conditions under which planets may
form. We match archival millimeter-wavelength thermal emission against models
of the disks' structure that are in radiation balance with the starlight
heating and in vertical hydrostatic equilibrium, and then compare to archival
polarized scattered near-infrared images of the disks. The millimeter emission
arises in the interior, while the scattered near-infrared radiation probes the
disks' outer layers. Our best model of the HD 163296 disk has dust masses
$81\pm 13$ $M_\oplus$ in the inner ring at 68 au and $82^{+26}_{-16}$
$M_\oplus$ in the outer ring at 102 au, both falling within the range of
estimates from previous studies. Our DoAr 44 model has total dust mass
$84^{+7.0}_{-3.5}$ $M_\oplus$. Unlike HD 163296, DoAr 44 as of yet has no
detected planets. If the central cavity in the DoAr 44 disk is caused by a
planet, the planet's mass must be at least 0.5 $M_J$ and is unlikely to be
greater than 1.6 $M_J$. We demonstrate that the DoAr 44 disk's structure with a
bright ring offset within a fainter skirt can be formed by dust particles
drifting through a plausible distribution of gas.
