1 Small animal imaging with multi-pinhole SPECT Johan Nuyts Nuclear Medicine, Katholieke Universiteit Leuven, Belgium Kathleen Vunckx Nuclear Medicine, Katholieke Universiteit Leuven, Belgium Michel Defrise Nuclear Medicine, Vrije Universiteit Brussel, Belgium Christian Vanhove Nuclear Medicine, Vrije Universiteit Brussel, Belgium correspondence: Johan Nuyts Nuclear Medicine, UZ Gasthuisberg Herestraat 49, B3000 Leuven, Belgium e-mail: Johan.Nuyts@uz.kuleuven.be tel: +32 16 34 37 15 fax: +32 16 34 37 59 Abstract—With Single Photon Emission Computed Tomography (SPECT), images of minute concentrations of tracer molecules can be acquired, allowing in vivo molecular imaging. For human imaging, the SPECT system has a modest spatial resolution of 5 to 15 mm, a large field of view and a high sensitivity. Using multi-pinhole SPECT, one can trade in field of view for resolution with preserved sensitivity, which enables the implementation of a small animal SPECT system with an improved resolution, currently ranging from 0.3 to 2 mm, in a much smaller field of view. The unconventional collimation and the more stringent resolution requirements pose problems that are not present in clinical SPECT imaging. This paper discusses how these problems can be solved to implement microSPECT imaging on a rotating gamma camera. keywords: SPECT, microSPECT, pinhole, tomography, cal- ibration, system matrix, maximum-likelihood, maximum-a- posteriori estimation I. I NTRODUCTION In the last decade, small animal SPECT imaging has made considerable progress, driven by the demands from medical and biological research. Several approaches have been fol- lowed to implement small animal SPECT imaging. Some groups converted a clinical gamma camera into a microSPECT system using new collimators and software, others built a whole new system dedicated to high resolution imaging of a small object [1]. Most systems rely on pinhole collimation, although other collimators are being considered, including rotating slit-slat collimators [2], translating slit collimators acquiring linograms [3] and rotating slat collimators [4], [5]. All these collimators scan along converging projection lines resulting in zoomed projections along one or two dimensions, which creates better usage of the available detectors. This work is supported by F.W.O. grant G.0569.08, by IAP-grant P6/38 and by MOSAIC, the K.U.Leuven Molecular Small Animal Imaging Center (KUL EF/05/08). In this paper, only multi-pinhole SPECT is considered. Many different system designs have been proposed, ranging from systems based on a rotating gamma camera [6]–[8], a station- ary camera with rotating collimator [9] or a completely station- ary camera [10]–[12]. We focus on multi-pinhole SPECT using a rotating gamma-camera, although part of what is presented here also holds for stationary systems. For accurate reconstruction, the projector and backprojector must be based on an accurate model for the system geometry. This can be determined in several ways. The most straight- forward one is to scan a small point source through the field-of-view, and directly measure the corresponding point spread function for each of the pinhole apertures [10]–[12]. This approach is slow and requires sophisticated positioning tools, but is highly accurate and directly measures the entire system matrix. It is probably best suited for stationary systems, because they are expected to have a more stable system matrix. In contrast, rotating systems, in particular those based on a clinical gamma camera, have many degrees of freedom and hence can use different system matrices for different scans. For those systems, an easier method to determine the system matrix is useful. In the next section, different approaches for modelling the system matrix are discussed. Finally, an ap- proach to compare the effects of a particular choice of system design parameters on the resolution and noise characteristics of the reconstructed images is discussed. II. SYSTEM MATRIX MODEL Single or multi pinhole SPECT projections using a rotating gamma camera provide incomplete tomographic information [13]. However, in practice, good reconstructions can be ob- tained with maximum likelihood (ML) or maximum a posteri- ori (MAP) reconstruction. The algorithms use a discrete model to represent the unknown tracer distribution and the acquired projections; the relation between the two can be written as Y = AX or y i =  j a ij x j , (1) where Y is a I × 1 matrix containing the measured counts y i in the detector elements i =1 ...I , X is J ×1 matrix with the reconstruction values x j , and A is the I × J system matrix. Its element a ij is the expected amount of photons contributed by a unit of activity at position j to the measurement at detector