  Dopamine transporter (DAT) imaging is commonly used for monitoring
Parkinson's disease (PD), where striatal DAT uptake amount is computed to
assess PD severity. However, DAT imaging has a high cost and the risk of
radiance exposure and is not available in general clinics. Recently, MRI patch
of the nigral region has been proposed as a safer and easier alternative. This
paper proposes a symmetric regressor for predicting the DAT uptake amount from
the nigral MRI patch. Acknowledging the symmetry between the right and left
nigrae, the proposed regressor incorporates a paired input-output model that
simultaneously predicts the DAT uptake amounts for both the right and left
striata. Moreover, it employs a symmetric loss that imposes a constraint on the
difference between right-to-left predictions, resembling the high correlation
in DAT uptake amounts in the two lateral sides. Additionally, we propose a
symmetric Monte-Carlo (MC) dropout method for providing a fruitful uncertainty
estimate of the DAT uptake prediction, which utilizes the above symmetry. We
evaluated the proposed approach on 734 nigral patches, which demonstrated
significantly improved performance of the symmetric regressor compared with the
standard regressors while giving better explainability and feature
representation. The symmetric MC dropout also gave precise uncertainty ranges
with a high probability of including the true DAT uptake amounts within the
range.
