Refraction-compensated motion tracking of unrestrained small animals in positron emission tomography

Abstract

Motion-compensated radiotracer imaging of fully conscious rodents represents an important paradigm shift for preclinical investigations. In such studies, if motion tracking is performed through a transparent enclosure containing the awake animal, light refraction at the interface will introduce errors in stereo pose estimation. We have performed a thorough investigation of how this impacts the accuracy of pose estimates and the resulting motion correction, and developed an efficient method to predict and correct for refraction-based error. The refraction model underlying this study was validated using a state-of-the-art motion tracking system. Refraction-based error was shown to be dependent on tracking marker size, working distance, and interface thickness and tilt. Correcting for refraction error improved the spatial resolution and quantitative accuracy of motion-corrected positron emission tomography images. Since the methods are general, they may also be useful in other contexts where data are corrupted by refraction effects.

Introduction

Molecular imaging techniques such as positron emission tomography (PET) are used to study the early stages of neuropsychiatric disorders and other chronic diseases, typically in animal models. Due to the negative impact of uncompensated motion on the image reconstruction, animals undergoing PET imaging are nearly always anaesthetised. However, anaesthesia not only disturbs the underlying biology, it precludes study of an animal’s response to external stimuli or the functional changes occurring as it interacts with its environment. This limits the potential of PET in preclinical investigations. The use of physical restraint (e.g. Javors et al., 2005) is a known stressor for species such as rats and mice (Ohata et al., 1981), therefore allowing animals freedom to move is preferable. This has led to the development of motion compensation techniques, relying on accurate motion measurements, to enable PET imaging of unrestrained awake animals (Kyme et al., 2009, Weisenberger et al., 2008).

Stereo-optical motion tracking is a feasible and accurate way to measure the head pose of awake rodents having limited or full movement (Kyme et al., 2010, Kyme et al., 2009, Weisenberger et al., 2008). Awake rodents imaged in tubes are able to move their heads freely and respond to external stimuli, thus enabling a more diverse range of experiments compared to that possible using anaesthetised subjects. Open-ended tubes (Kyme et al., 2009) allow the head to be tracked directly but animals must be trained to remain near the end of the tube. Enclosed tubes (Weisenberger et al., 2008) have the advantage of confining the animal to the scanner field of view (FOV), however the tube must be transparent to allow tracking of the head by externally placed cameras. In contrast to tubes, a chamber environment is even more appealing for research because of the greater range of animal behaviours possible (Zhou et al., 2010). Of particular research interest is the ability to detect correlations between function and behaviour for a freely moving animal in such an enclosure (Shultz et al., 2011). Similarly to enclosed tubes, a chamber requires transparent walls through which motion tracking can occur.

For both enclosed tubes and chambers, light rays will refract at the surfaces of the transparent walls. This violates a basic assumption of the linear pinhole camera model – that the object point, camera centre and image point are collinear. Failure to account for this is expected to cause errors in pose estimation. However, investigations into the nature, extent and correction of refraction-based error in stereo pose measurements are scant in the literature. Therefore, our goals in this work were to (i) develop and validate a model to accurately predict stereo motion tracking errors caused by refraction at plane-parallel interfaces; (ii) explore the severity of refraction errors as a function of system parameters (e.g. interface thickness and tilt); (iii) derive the refraction error for position measurements of individual points and pose measurements of rigid ensembles of points; (iv) specify the conditions for which correction of refraction error may be necessary in small animal imaging; and (v) formulate and validate a method to accurately correct tracker measurements for refraction-based errors. Although the motivation for this work is awake animal PET, we anticipate that the methods may be applicable in other contexts where objects are tracked through a refractive medium.