Gaussian Process With Physical Laws For 3d Cardiac Modeling

This paper introduces some physical laws into a Gaussian process for a statistical three-dimensional (3D) cardiac computational model. The 3D cardiac shape modeling is still challenging, since it involves personality and diversity. However, in spite of such variety, the heart shape must be ruled by some physical laws, which should be an important clue for the statistical shape estimation. Specifically, we introduce the Frank-Starling laws into the Gaussian process as a linear constraint, whose resulting process also follows a Gaussian process. For demonstration, we apply our model into the pipeline that estimates the heart shape from cardiovascular magnetic resonance (CMR) imaging, by combining it with the deep neural networks-based anatomical segmentation of CMR imaging.