Tracking 'differential organ motion' with a 'breathing' multileaf collimator: magnitude of problem assessed using 4D CT data and a motion-compensation strategy.

Intrafraction tumour (e.g. lung) motion due to breathing can, in principle, be compensated for by applying identical breathing motions to the leaves of a multileaf collimator (MLC) as intensity-modulated radiation therapy is delivered by the dynamic MLC (DMLC) technique. A difficulty arising, however, is that irradiated voxels, which are in line with a bixel at one breathing phase (at which the treatment plan has been made), may move such that they cease to be in line with that breathing bixel at another phase. This is the phenomenon of differential voxel motion and existing tracking solutions have ignored this very real problem. There is absolutely no tracking solution to the problem of compensating for differential voxel motion. However, there is a strategy that can be applied in which the leaf breathing is determined to minimize the geometrical mismatch in a least-squares sense in irradiating differentially-moving voxels. A 1D formulation in very restricted circumstances is already in the literature and has been applied to some model breathing situations which can be studied analytically. These are, however, highly artificial. This paper presents the general 2D formulation of the problem including allowing different importance factors to be applied to planning target volume and organ at risk (or most generally) each voxel. The strategy also extends the literature strategy to the situation where the number of voxels connecting to a bixel is a variable. Additionally the phenomenon of 'cross-leaf-track/channel' voxel motion is formally addressed. The general equations are presented and analytic results are given for some 1D, artificially contrived, motions based on the Lujan equations of breathing motion. Further to this, 3D clinical voxel motion data have been extracted from 4D CT measurements to both assess the magnitude of the problem of 2D motion perpendicular to the beam-delivery axis in clinical practice and also to find the 2D optimum breathing-leaf strategy. Issues relating to the practical calculation of the strategy, including effects on leaf velocity and effects of different spatial-sampling frequencies, have been investigated, and unattenuated-fluence maps have been produced showing the effects of the differential motion and tracking. It was discovered that large distances between adjacent leaf-ends could cause the tracking to fail when there was tissue motion across the leaf channels. To overcome this problem the use of 'synchronized' leaf trajectories, which ensure that adjacent leaf-ends are always close enough to each other to facilitate tracking, has also been investigated.

A strategy to minimize errors from differential intrafraction organ motion using a single configuration for a 'breathing' multileaf collimator.

Intensity-modulated radiation therapy (IMRT) can be delivered by the 'sliding-leaves' dynamic multileaf collimator (DMLC) technique. Intrafraction organ motion can be accommodated by arranging an identical tracking motion for 'breathing leaves'. However, this is only possible for very specific circumstances such as regular, mathematically parameterizable, rigid-body, density-conserving, one-dimensional translations. In this paper, we investigate what happens when planes of tissue in the line of sight of the MLC have differential motion with respect to the moving leaves. In this situation, there is no solution to the problem and a perfect tracking motion cannot be arranged. However, an iterative minimization-of-errors 'solution' (or strategy) can be found and the technique is presented for this. From this, under certain mathematically simple differential motions it is possible to obtain some elegant algebraic solutions which are presented. In general, however, a lengthy computational minimization is required and results of examples of these are presented.

A prototype rotating slat collimator for single photon emission computed tomography.

A collimator consisting of a series of highly attenuating parallel slats has been constructed and used in conjunction with a gamma-camera to approximately measure planar projections of a given radionuclide distribution. The enlarged solid angle of acceptance afforded by the slat collimator gave rise to an increased geometric efficiency of between 12 and 28 times that observed with a low-energy high-resolution (LEHR) parallel-hole collimator. When the slats rotated over the face of the detector and the camera gantry turned about the object, sufficient projections were acquired to reconstruct a three-dimensional (3-D) image using the inversion of the 3-D radon transform. The noise behavior of an algorithm for implementing this inversion was studied analytically and the resulting relationship has been verified by computer simulation. The substantially improved geometric efficiency of the slat collimator translated to improvements in reconstructed signal-to-noise ratio (SNR) by, at best, up to a factor of 2.0 with respect to standard parallel-hole collimation. The spatial resolution achieved with the slat collimator was comparable to that obtained with a LEHR collimator and no significant differences were observed in terms of scatter response. Accurate image quantification was hindered by the spatially variant response of the slat collimator.

Ring filter to locate external boundaries in SPECT using scattered radiation.

A novel form of filter for SPECT is described, in which, after back projection and summation, the reconstructed signal is a measure of the total activity within a ring of specified radius, centre and width. The filter is applied to the problem of using Compton scattered radiation to locate external boundaries. In the simple case of the determination of the radius of a circular scattering body of known centre, the filter output would identify a transition region and define an appropriate threshold as the boundary was crossed. However it can also be applied to locate the boundaries seen in individual SPECT projections and hence trace out the envelope of the scattering body. Monte Carlo simulation based on 99mTc is used to test the performance of the filter in a range of situations, with encouraging results.

The experimental evaluation of a prototype rotating slat collimator for planar gamma camera imaging.

A collimator consisting of a series of parallel slats has been constructed and used in conjunction with a conventional gamma camera to collect one-dimensional projections of the radioisotope distribution being imaged. With the camera remaining stationary, the collimator was made to rotate continuously over the face of the detector and the projections acquired were used to reconstruct a planar image by the theory of computed tomography. The propagation of noise on image reconstruction was largely offset by the increased geometric efficiency that resulted from the enlarged solid angle of acceptance afforded by the slat collimator. For a uniform disc of activity the signal to noise ratio (SNR) at a point in an image reconstructed by convolution and backprojection is shown to be given by [formula:see text] and Q1(xi) is the one-dimensional filter function in Fourier space. Improved noise behaviour was observed for images acquired with the slat collimator compared to those acquired with a low-energy high-resolution (LEHR) collimator for small distributions of activity. Spatial resolution with the slat collimator was approximately equal to that obtained with an LEHR collimator and improved contrast was observed in images of small hot regions.

Monte Carlo modelling of the performance of a rotating slit-collimator for improved planar gamma-camera imaging.

Planar imaging with a gamma camera is currently limited by the performance of the collimator. Spatial resolution and sensitivity trade off against each other; it is not possible with conventional parallel-hole collimation to have high geometric sensitivity and at the same time excellent spatial resolution unless field-of-view is sacrificed by using fan- or cone-beam collimators. We propose a rotating slit-collimator which collects one-dimensional projections from which the planar image may be reconstructed by the theory of computed tomography. The performance of such a collimator is modelled by Monte Carlo methods and images are reconstructed by a convolution and backprojection technique. The performance is compared with that of a conventional parallel-hole collimator and it is shown that higher spatial resolution with increased sensitivity is possible with the slit-collimator. For a point source a spatial resolution of some 6 mm at a distance of 100 mm from the collimator with a x7 sensitivity compared with a parallel-hole collimator was achieved. Applications to bone scintigraphy are modelled and an improved performance in hot-spot imaging is demonstrated. The expected performance in cold-spot imaging is analytically investigated. The slit-collimator is not expected to improve cold-spot imaging. Practical design considerations are discussed.

Image intensity normalisation by maximising the Siddon line integral in the joint intensity distribution space.

This paper presents a novel data-driven method for image intensity normalisation, which is a prerequisite step for any kind of image comparison. The method involves a novel application of the Siddon algorithm that was developed initially for fast reconstruction of tomographic images and is based on a linear normalisation model with either one or two parameters. The latter are estimated by maximising the line integral, computed using the Siddon algorithm, in the 2D joint intensity distribution space of image pairs. The proposed normalisation method, referred to as Siddon Line Integral Maximisation (SLIM), was compared with three other methodologies, namely background ratio (BAR) scaling, linear fitting and proportional scaling, using a large number of synthesised datasets. SLIM was also compared with BAR normalisation when applied to phantom data and two clinical examples. The new method was found to be more accurate and less biased than its counterparts for the range of characteristics selected for the synthesised data. These findings were in agreement with the results from the analysis of the experimental and clinical data.