  Recent studies have confirmed cardiovascular diseases remain responsible for
highest death toll amongst non-communicable diseases. Accurate left ventricular
(LV) volume estimation is critical for valid diagnosis and management of
various cardiovascular conditions, but poses significant challenge due to
inherent uncertainties associated with segmentation algorithms in magnetic
resonance imaging (MRI). Recent machine learning advancements, particularly
U-Net-like convolutional networks, have facilitated automated segmentation for
medical images, but struggles under certain pathologies and/or different
scanner vendors and imaging protocols. This study proposes a novel methodology
for post-hoc uncertainty estimation in LV volume prediction using It\^{o}
stochastic differential equations (SDEs) to model path-wise behavior for the
prediction error. The model describes the area of the left ventricle along the
heart's long axis. The method is agnostic to the underlying segmentation
algorithm, facilitating its use with various existing and future segmentation
technologies. The proposed approach provides a mechanism for quantifying
uncertainty, enabling medical professionals to intervene for unreliable
predictions. This is of utmost importance in critical applications such as
medical diagnosis, where prediction accuracy and reliability can directly
impact patient outcomes. The method is also robust to dataset changes, enabling
application for medical centers with limited access to labeled data. Our
findings highlight the proposed uncertainty estimation methodology's potential
to enhance automated segmentation robustness and generalizability, paving the
way for more reliable and accurate LV volume estimation in clinical settings as
well as opening new avenues for uncertainty quantification in biomedical image
segmentation, providing promising directions for future research.
