Quantifying heterogeneity in dynamic contrast-enhanced MRI parameter maps

Simple summary statistics of Dynamic Contrast-Enhanced MRI (DCE-MRI) parameter maps (e.g. the median) neglect the spatial arrangement of parameters, which appears to carry important diagnostic and prognostic information. This paper describes novel statistics that are sensitive to both parameter values and their spatial arrangement. Binary objects are created from 3-D DCE-MRI parameter maps by "extruding" each voxel into a fourth dimension; the extrusion distance is proportional to the voxel's value. The following statistics are then computed on these 4-D binary objects: surface area, volume, surface area to volume ratio, and box counting (fractal) dimension. An experiment using 4 low and 5 high grade gliomas showed significant differences between the two grades for box counting dimension computed for extruded v(e) maps, surface area of extruded K(trans) and v(e) maps and the volume of extruded v(e) maps (all p < 0.05). An experiment using 18 liver metastases imaged before and after treatment with a vascular endothelial growth factor (VEGF) inhibitor showed significant differences for surface area to volume ratio computed for extruded K(trans) and v(e) maps (p = 0.0013 and p = 0.045 respectively).