Myocardial Strain Imaging with Tagged MRI Nicholas J. Tustison, Dana Abendschein, Victor G. D´ avila-Rom´ an, and Amir A. Amini CVIA Lab, Campus Box 8086, 660 S. Euclid Ave., Washington University in St. Louis, St. Louis, MO 63110 Abstract A 4-D B-spline model has been created to accurately capture the dynamic motion of the heart from tagged mag- netic resonance imaging (MRI) enabling displacement field reconstruction of myocardial deformation. The 4-D model is allowed to deform based on the location of the tag lines for all frames within the constraints of the model’s spatio- temporal internal energy. From a displacement field, the corresponding long and short axis Lagrangian strain maps are produced. Motion fields from simulated data produced by a cardiac motion simulator are used to create corre- sponding strain images. In addition, strain images pro- duced from porcine data with posterolateral myocardial in- farction are illustrated. 1. Introduction Magnetic resonance tagging methods allow for noninva- sive measurement of intramural heart wall motion by com- bining the high spatio-temporal resolution of MRI with tis- sue tagging techniques. By altering the magnetization of the myocardial tissue with special MR pulses, planes of hy- pointense signal, or tag planes, can be placed orthogonal to the image plane, producing a grid pattern in the short or long-axis image planes. This pattern deforms in conjunc- tion with the myocardial tissue allowing for the extraction of tissue displacement fields and strain. Such measurements are important in understanding the effects of cardiovascular disease on ventricular function [9]. The advantages of tagged MRI have encouraged signifi- cant research in this area [2]. Amini et. al. use a variational approach using thin-plate splines and energy-minimizing coupled B-spline grids to produce a dense continuous mo- tion field in 2-D between two arbitrary frames [1]. Good local strain analysis is produced in [8] by fitting a 3-D fi- nite element model to the tag planes. However, the model requires a large number of model parameters. In [7], 2-D motion fields are calculated and corresponding strain maps are illustrated by exploiting information present in the fre- quency domain of tagged MR images. In this paper, an improved version of the deformable B- spline algorithm described in [6] was used to interpolate tag data. At the conclusion of fitting the 4-D B-spline model, reconstructed tag surfaces, location of tag surface intersec- tions, displacement fields, as well as short and long-axis myocardial strains become available for all time points in the ECG cycle. 2. 4-D B-spline Model The 4-D B-spline model is a time-varying B-spline solid (B-solid) where knot lines and knot planes are temporal functions. The 4-D B-spline model can be expressed as (1) where is the total number of control points specified by and , , , and designate the order of B-spline. The respective periodic B-spline basis func- tions which blend the control points are , , , and . The basis functions for a fourth or- der periodic B-spline and the corresponding knot vector are given in Figure 1. The 4-D fitting process of deforming the knot planes of the B-spline model to interpolate the tag planes for all time frames is formulated as an energy minimization problem numerically solved by the conjugate gradient descent algo- rithm. The total energy of the model is simply the sum of its external and internal energies. An improvement over previous models is the flexibil- ity incorporated into the model to allow additional control points to be inserted into the model for more localized in- terpolation. Since a direct relationship exists between the 1051-4651/02 $17.00 (c) 2002 IEEE