The approximate entropy concept extended to three dimensions for calibrated, single parameter structural complexity interrogation of volumetric images

Abstract

Reconstructive volumetric imaging permeates medical practice because of its apparently clear depiction of anatomy. However, the tell tale signs of abnormality and its delineation for treatment demand experts work at the threshold of visibility for hints of structure. Hitherto, a suitable assistive metric that chimes with clinical experience has been absent. This paper develops the complexity measure approximate entropy (ApEn) from its 1D physiological origin into a three-dimensional (3D) algorithm to fill this gap. The first 3D algorithm for this is presented in detail. Validation results for known test arrays are followed by a comparison of fan-beam and cone-beam x-ray computed tomography image volumes used in image guided radiotherapy for cancer. Results show the structural detail down to individual voxel level, the strength of which is calibrated by the ApEn process itself. The potential for application in machine assisted manual interaction and automated image processing and interrogation, including radiomics associated with predictive outcome modeling, is discussed.