‘Intensity diffusion’ is a better description than ‘partial volume effect’

Dear Sir, The term ‘partial volume effect’ (PVE) has frequently been used in nuclear medicine 3D imaging to describe the effects of blurring of an ideal PET or SPECT activity distribution by a point spread function [1–3] .The term was first introduced as a description of the artefact that arose in CT images when a structure (usually bone) was partially covered by the scanning X-ray beam. The resulting reconstructed image would then show this structure but with an erroneous Hounsfield number assigned to it and often with a distorted form. The concentration of activity can vary significantly within an organ and even within a voxel. It is therefore a lack of precision to talk of the volume that the activity occupies or the ‘tissue fractions’ of the voxel volume [3]. In order to understand all the implications of image formation it is necessary to describe nuclear medicine 3D imaging (SPECT and PET) in a totally different way. One solution is to introduce the term ‘intensity diffusion’ in analogy to the physical process of diffusion. If one deposits a very small volume -a sourceof a diffusible substance (consisting of equal molecules) within a gel the molecules will move randomly so that their concentration form a continuous 3D gaussian distribution with the width (in nuclear medicine the FWHM) depending on time and magnitude of the diffusion coefficient. If there were several small such sources diffusion would lead to a superposition in space of contributions from each of them. Finally, one could image to cut the gel into regular cubes (voxels) and count the molecules within each of them. This is a very close analogy to nuclear medicine 3D imaging although the image is formed as a result of a computer algorithm. The 3D point spread function can be though to act on the activity distribution before the volume is subdivided into voxels of finite size and counts integrated for each of these. This description would explain the lack of counts recovery for small volumes, the ‘spill in’ and ‘spill out’ (3) from/to voxels etc. If one considers an intense point source with a spatial extent of one micrometer there would be no partial volume but still contributions to neighbouring voxels. Description of PET and SPECT imaging as an ‘intensity diffusion’ also serves to explain some phenomena associated with image intensity: The spread of intensity is such that the maximal signal decreases while the total intensity integrated over a larger volume is maintained. This description would also clarify to non-nuclear medicine referring physicians a frequently met misunderstanding: that the low spatial resolution power makes it impossible to detect a source of sub-millimeter size. If the source carries enough activity, it is seen alright but its intensity diffuses into neighbouring voxels. Furthermore, the effects of smoothing with a 3D gaussian filter during reconstruction of a PET image series (as is for instance done on the Siemens Biograph series) may be considered a further diffusion of intensity: Choice of an increasingly wider smoothing filter makes the maximum signal (and thus the SUV) from small tumours decrease (admittedly the noise decreases as well). With good accuracy the resulting width of the point spread function may be calculated exactly as one would calculate the effects of further diffusion of the molecules in the gel: by adding the squares of the FWHM of the intrinsic resolution and gaussian filter to form the square of the resulting system FWHM. Mathematically, the reconstructed image intensity distribution can be described Eur J Nucl Med Mol Imaging (2009) 36:536–537 DOI 10.1007/s00259-008-1032-6