  The distribution of energy dose from Lu$^{177}$ radiotherapy can be estimated
by convolving an image of a time-integrated activity distribution with a dose
voxel kernel (DVK) consisting of different types of tissues. This fast and
inacurate approximation is inappropriate for personalized dosimetry as it
neglects tissue heterogenity. The latter can be calculated using different
imaging techniques such as CT and SPECT combined with a time consuming
monte-carlo simulation. The aim of this study is, for the first time, an
estimation of DVKs from CT-derived density kernels (DK) via deep learning in
convolutional neural networks (CNNs). The proposed CNN achieved, on the test
set, a mean intersection over union (IOU) of $= 0.86$ after $308$ epochs and a
corresponding mean squared error (MSE) $= 1.24 \cdot 10^{-4}$. This
generalization ability shows that the trained CNN can indeed learn the
difficult transfer function from DK to DVK. Future work will evaluate DVKs
estimated by CNNs with full monte-carlo simulations of a whole body CT to
predict patient specific voxel dose maps.
