Harmonic phase interference for the detection of tag line crossings and beyond in homogeneous strain analysis of cardiac tagged MRI data

Homogenous strain analysis (HSA) was developed to evaluate regional cardiac function using tagged cine magnetic resonance images of heart. Current cardiac applications of HSA are however limited in accurately detecting tag intersections within the myocardial wall, producing consistent triangulation of tag cells throughout the image series and achieving optimal spatial resolution due to the large size of the triangles. To address these issues, this article introduces a harmonic phase (HARP) interference method. In principle, as in the standard HARP analysis, the method uses harmonic phases associated with the two of the four fundamental peaks in the spectrum of a tagged image. However, the phase associated with each peak is wrapped when estimated digitally. This article shows that special combination of wrapped phases results in an image with unique intensity pattern that can be exploited to automatically detect tag intersections and to produce reliable triangulation with regularly organized partitioning of the mesh for HSA. In addition, the method offers new opportunities and freedom for evaluating myocardial function when the power and angle of the complex filtered spectra are mathematically modified prior to computing the phase. For example, the triangular elements can be shifted spatially by changing the angle and/or their sizes can be reduced by changing the power. Interference patterns obtained under a variety of power and angle conditions were presented and specific features observed in the results were explained. Together, the advanced processing capabilities increase the power of HSA by making the analysis less prone to errors from human interactions. It also allows strain measurements at higher spatial resolution and multi-scale, thereby improving the display methods for better interpretation of the analysis results.