Fully 4-D dynamic cardiac SPECT image reconstruction using spatiotemporal B-spline voxelization

We developed fully 4-D penalized least-squares reconstruction methods that use overlapping multiresolution B-splines to represent radiopharmaceutical distributions that vary smoothly in space and time in human dynamic cardiac SPECT images. This approach does not require segmentation, and improves signal-to-noise and increases computational efficiency compared to methods based on small, non-overlapping cube-shaped voxels and rectangular time windows. The support of spatial B-splines was extended into the time dimension to obtain estimates of time-activity curves directly from projections for a human dynamic Tc-99m-sestamibi cardiac SPECT/CT study. Projection data were acquired in 1-sec time frames with an angular step of 5 deg per frame on a GE millennium VH Hawk-eye SPECT/CT scanner. Attenuation and depth-dependent collimator response were modeled, but not scatter. The 4-D B-splines were piecewise trilinear in space and piecewise quadratic in time. The splines were organized on a 3-D spatial grid that provided uniform sampling of 17.7 mm in each dimension, and on a 1-D temporal grid that provided nonuniform sampling intervals of 0-4, 4-15, 15-48, and 48-144 sec during the first two gantry rotations. The use of nonuniform time sampling with 4-D B-splines that varied quadratically in time yielded smooth time-activity curves that captured the relatively fast rise and fall of tracer in the right and left blood chambers, as well as uptake and retention of tracer in the left ventricular myocardium. These methods can also be applied to dynamic PET.