Incompressible Deformation Estimation Algorithm (IDEA) From Tagged MR Images
Measuring the 3D motion of muscular tissues, e.g., the heart or the tongue, using magnetic resonance (MR) tagging is typically carried out by interpolating the 2D motion information measured on orthogonal stacks of images. The incompressibility of muscle tissue is an important constraint on the reconstructed motion field and can significantly help to counter the sparsity and incompleteness of the available motion information. Previous methods utilizing this fact produced incompressible motions with limited accuracy. In this paper, we present an incompressible deformation estimation algorithm (IDEA) that reconstructs a dense representation of the 3D displacement field from tagged MR images and the estimated motion field is incompressible to high precision. At each imaged time frame, the tagged images are first processed to determine components of the displacement vector at each pixel relative to the reference time. IDEA then applies a smoothing, divergence-free, vector spline to interpolate velocity fields at intermediate discrete times such that the collection of velocity fields integrate over time to match the observed displacement components. Through this process, IDEA yields a dense estimate of a 3D displacement field that matches our observations and also corresponds to an incompressible motion. The method was validated with both numerical simulation and in vivo human experiments on the heart and the tongue.