M Kissick

Confirmation, refinement, and extension of a study in intrafraction motion interplay with sliding jaw motion

The interplay between a constant scan speed and intrafraction oscillatory motion produces interesting fluence intensity modulations along the axis of motion that are sensitive to the motion function, as originally shown in a classic paper by Yu et al. [Phys. Med. Biol. 43, 91-104 (1998)]. The fluence intensity profiles are explored in this note for an intuitive understanding, then compared with Yu et al., and finally further explored for the effects of low scan speed and random components of both intrafraction and interfraction motion. At slow scan speeds typical of helical tomotherapy, these fluence intensity modulations are only a few percent. With the addition of only a small amount of cycle-to-cycle randomness in frequency and amplitude, the fluence intensity profiles change dramatically. It is further shown that after a typical 30-fraction treatment, the sensitivities displayed in the single fraction fluence intensity profiles greatly diminish.

On the impact of longitudinal breathing motion randomness for tomotherapy delivery.

The purpose of this study is to explain the unplanned longitudinal dose modulations that appear in helical tomotherapy (HT) dose distributions in the presence of irregular patient breathing. This explanation is developed by the use of longitudinal (1D) simulations of mock and surrogate data and tested with a fully 4D HT delivered plan. The 1D simulations use a typical mock breathing function which allows more flexibility to adjust various parameters. These simplified simulations are then made more realistic by using 100 surrogate waveforms all similarly scaled to produce longitudinal breathing displacements. The results include the observation that, with many waveforms used simultaneously, a voxel-by-voxel probability of a dose error from breathing is found to be proportional to the realistically random breathing amplitude relative to the beam width if the PTV is larger than the beam width and the breathing displacement amplitude. The 4D experimental test confirms that regular breathing will not result in these modulations because of the insensitivity to leaf motion for low-frequency dynamics such as breathing. These modulations mostly result from a varying average of the breathing displacements along the beam edge gradients. Regular breathing has no displacement variation over many breathing cycles. Some low-frequency interference is also possible in real situations. In the absence of more sophisticated motion management, methods that reduce the breathing amplitude or make the breathing very regular are indicated. However, for typical breathing patterns and magnitudes, motion management techniques may not be required with HT because typical breathing occurs mostly between fundamental HT treatment temporal and spatial scales. A movement beyond only discussing margins is encouraged for intensity modulated radiotherapy such that patient and machine motion interference will be minimized and beneficial averaging maximized. These results are found for homogeneous and longitudinal on-axis delivery for unplanned longitudinal dose modulations.

Modelling simple helically delivered dose distributions

In a previous paper, we described quality assurance procedures for Hi-Art helical tomotherapy machines. Here, we develop further some ideas discussed briefly in that paper. Simple helically generated dose distributions are modelled, and relationships between these dose distributions and underlying characteristics of Hi-Art treatment systems are elucidated. In particular, we describe the dependence of dose levels along the central axis of a cylinder aligned coaxially with a Hi-Art machine on fan beam width, couch velocity and helical delivery lengths. The impact on these dose levels of angular variations in gantry speed or output per linear accelerator pulse is also explored.

The impact of linac output variations on dose distributions in helical tomotherapy

It has been suggested for quality assurance purposes that linac output variations for helical tomotherapy (HT) be within +/-2% of the long-term average. Due to cancellation of systematic uncertainty and averaging of random uncertainty over multiple beam directions, relative uncertainties in the dose distribution can be significantly lower than those in linac output. The sensitivity of four HT cases with respect to linac output uncertainties was assessed by scaling both modeled and measured systematic and random linac output uncertainties until a dose uncertainty acceptance criterion failed. The dose uncertainty acceptance criterion required the delivered dose to have at least a 95% chance of being within 2% of the planned dose in all of the voxels in the treatment volume. For a random linac output uncertainty of 5% of the long-term mean, the maximum acceptable amplitude of the modeled, sinusoidal, systematic component of the linac output uncertainty for the four cases was 1.8%. Although the measured linac output variations represented values that were outside of the +/-2% tolerance, the acceptance criterion did not fail for any of the four cases until the measured linac output variations were scaled by a factor of almost three. Thus, the +/-2% tolerance in linac output variations for HT is a more conservative tolerance than necessary.

A phantom model demonstration of tomotherapy dose painting delivery, including managed respiratory motion without motion management

The aim of the study was to demonstrate a potential alternative scenario for accurate dose-painting (non-homogeneous planned dose) delivery at 1 cm beam width with helical tomotherapy (HT) in the presence of 1 cm, three-dimensional, intra-fraction respiratory motion, but without any active motion management. A model dose-painting experiment was planned and delivered to the average position (proper phase of a 4DCT scan) with three spherical PTV levels to approximate dose painting to compensate for hypothetical hypoxia in a model lung tumor. Realistic but regular motion was produced with the Washington University 4D Motion Phantom. A small spherical Virtual Water phantom was used to simulate a moving lung tumor inside of the LUNGMAN anthropomorphic chest phantom to simulate realistic heterogeneity uncertainties. A piece of 4 cm Gafchromic EBT film was inserted into the 6 cm diameter sphere. TomoTherapy, Inc., DQA software was used to verify the delivery performed on a TomoTherapy Hi-Art II device. The dose uncertainty in the purposeful absence of motion management and in the absence of large, low frequency drifts (periods greater than the beam width divided by the couch velocity) or randomness in the breathing displacement yields very favorable results. Instead of interference effects, only small blurring is observed because of the averaging of many breathing cycles and beamlets and the avoidance of interference. Dose painting during respiration with helical tomotherapy is feasible in certain situations without motion management. A simple recommendation is to make respiration as regular as possible without low frequency drifting. The blurring is just small enough to suggest that it may be acceptable to deliver without motion management if the motion is equal to the beam width or smaller (at respiration frequencies) when registered to the average position.

A delivery transfer function (DTF) analysis for helical tomotherapy

The previous theoretical work of a delivery transfer function (DTF) in radiotherapy is expanded to include the unique intensity modulation method of helical tomotherapy. In addition to the collimation of each beamlet, and the Gaussian scatter convolution spreading of the dose that other radiotherapy units have, helical tomotherapy uses 51 small arcs of varying lengths to adjust the intensity. The blurring from these arcs is not taken into account during treatment planning. A theoretical DTF is constructed, and a calculation is performed which includes this unique source motion in relation to the other DTF components. Various typical delivery parameters are used to generate resolution maps for a constant intensity projection. Near the isocenter, the transverse (to a given beam direction) blurring is small but at larger radii (>6 cm), the source blurring dominates over leaf size. For most clinical situations, this inherent source motion blurring is expected to be negligible.

On the making of sharp longitudinal dose profiles with helical tomotherapy

Since the beam width on the helical tomotherapy machine produced by TomoTherapy Inc., is typically a few centimeters in the longitudinal direction (into the bore), the optimizer must choose to have a relatively high intensity local to the inside edge of a tumor or planning treatment volume (PTV) when avoiding an immediately adjacent organ at risk (OAR), either superior or inferior. By using a standalone version of the TomoTherapy dose calculator, a realistic beam is applied to idealized deconvolution schemes including the MATLAB Optimizer Toolbox for a simple one-dimensional PTV with adjacent OARs. The results are compared to a clinical example on the TomoTherapy planning station. It is learned that a Gibbs phenomenon type of oscillation in the dose within the tumor under these special circumstances is not unique to TomoTherapy, but is related to the attempt to form a sharp dose gradient-sharper than the beam profile with typical optimization constraints set to achieve a uniform dose as close as possible to the prescription. The clinical implication is that the Gibbs-induced cold spots force the dose to increase in the PTV if a typical PTV dose-volume constraint is used. It is recommended that the dose prescription be smoothed prior to optimization or the dosimetric goals for an OAR adjacent to the PTV are such that a sharp dose falloff is not demanded, especially if the user reduces the requirements that such an OAR be of both high importance and immediately adjacent to the PTV edge.

PET imaging for the quantification of biologically heterogeneous tumours: measuring the effect of relative position on image-based quantification of dose-painting targets

Quantitative imaging of tumours represents the foundation of customized therapies and adaptive patient care. As such, we have investigated the effect of patient positioning errors on the reproducibility of images of biologically heterogeneous tumours generated by a clinical PET/CT system. A commercial multi-slice PET/CT system was used to acquire 2D and 3D PET images of a phantom containing multiple spheres of known volumes and known radioactivity concentrations and suspended in an aqueous medium. The spheres served as surrogates for sub-tumour regions of biological heterogeneities with dimensions of 5-15 mm. Between image acquisitions, a motorized-arm was used to reposition the spheres in 1 mm intervals along either the radial or the axial direction. Images of the phantom were reconstructed using typical diagnostic reconstruction techniques, and these images were analysed to characterize and model the position-dependent changes in contrast recovery. A simulation study was also conducted to investigate the effect of patient position on the reproducibility of PET imaging of biologically heterogeneous head and neck (HN) tumours. For this simulation study, we calculated the changes in image intensity values that would occur with changes in the relative position of the patients at the time of imaging. PET images of two HN patients were used to simulate an imaging study that incorporated set-up errors that are typical for HN patients. One thousand randomized positioning errors were investigated for each patient. As a result of the phantom study, a position-dependent trend was identified for measurements of contrast recovery of small objects. The peak contrast recovery occurred at radial and axial positions that coincide with the centre of the image voxel. Conversely, the minimum contrast recovery occurred when the object was positioned at the edges of the image voxel. Changing the position of high contrast spheres by one-half the voxel dimension lead to errors in the measurement of contrast recovery values which were larger than 30%. However, the magnitudes of the errors were found to depend on the size of the sphere and method of image reconstruction. The error values from standard OSEM images of the 5 mm diameter sphere were 20-35%, and for the 10 mm diameter sphere were 5-10%. The position-dependent variation of contrast recovery can result in changes in spatial distribution within images of heterogeneous tumours. In experiments simulating random set-up errors during imaging of two HN patients, the expectation value of the correlation was approximately 1.0 for these tumours; however, Pearson correlation coefficient values as low as 0.8 were observed. Moreover, variations within the images can drastically change the delineation of biological target volumes. The errors in target delineation were more prominent in very heterogeneous tumours. As an example, in a pair of images with a correlation of 0.8, there was a 36% change in the volume of the dose-painting target delineated at 50%-of-max-SUV (ROI(50%)). The results of these studies indicate that the contrast recovery and spatial distributions of tracer within PET images are susceptible to changes in the position of the patient/tumour at the time of imaging. As such, random set-up errors in HN patients can result in reduced correlation between subsequent image-studies of the same tumour.

Task Group 76 Report on 'The management of respiratory motion in radiation oncology' [Med. Phys. 33, 3874-3900 (2006)].

To the Editor, In 2006, the AAPM Task Group 76, on respiratory motion in radiation oncology, produced a generally very useful report.1 Mostly in Sec. V.C of this report, an “interplay” issue between motion from the MLC leaves in dynamic IMRT (such as sliding jaw, tomotherapy, and types of VMAT, for example) and organ (or tumor) motion is considered. However, the clinical implications for such interplay, or perhaps more precisely termed “interference,” are somewhat minimized based mainly on fraction averaging considerations. These implications are specifically minimized in the discussion of the effects of the 5 mm criterion that is to be used for the central decision of whether motion management should be used. We believe that this criterion should be expanded to include a consideration of the frequency coherence between the fluence modulation and the tumor motion. The fluence modulation pattern is unique to any particular modality and may vary between treatment plans. The current 5 mm criterion includes only the tumor motion amplitude; essentially, it is based on the assumption that this factor always dominates, and it may not have been evidence-based to a high enough degree. In addition, the effects of fractionation are very likely to reduce dose errors, but as stated in Sec. V.C,1 one should not rely on fractionation alone. Evidence for a potentially dominant role for frequency dependence comes from recently published helical tomotherapy2 experiments. In Fig. 4 of Chaudhari et al.,3 there is a breathing motion displacement graph with each breathing cycle depicted along with the “moving average.” The moving average is nothing more than the low frequency component (“drift”) of the breathing. That drift, about 5 mm in extent for the 15 mm scaling overall, leads to a significant dose error3 (>10%) in Fig. 5. However, the much larger and much higher frequency, main breathing displacement of 15 mm leads to very small dose errors within the PTV (note that the shift in Fig. 5 must have been due to the registration at a position other than the time average of the motion). The reason why these low frequency drifts have such a big effect is because the power spectrum of the total motion is overlapping the response function for interference with the tomotherapy couch movement through the beam (see Fig. 1 of Kissick et al.4). When the breathing motion through the tomotherapy beam is made regular and without drifts such that the motion probability distribution function is invariant in time, then one will simply get blurring (see Fig. 12 of Kissick et al.4). This result demonstrates that only blurring is possible when the frequencies of the MLCs are very different than the frequencies of the tumor motion. The 1 cm motion of that Fig. 12 created no noticeable dose errors relative to the 2.5 cm beam smearing that happens without motion. This is direct evidence that the amplitude of the tumor motion alone cannot always predict whether a large dose error will occur—one also needs to consider the interaction with the frequency or time behavior of the fluence modulation. While this work was done experimentally using helical tomotherapy, all dynamic IMRT will have this issue. Another way to look at this issue is to refer to the often reproduced Fig. 1 in Bortfeld et al.5 The two phases (two stars) in the figure would get the same dose difference even if the tumor motion amplitude was made either smaller or larger. By contrast, if the frequency of the voxel movement was either very fast or very slow compared to the leaf motion, then there would be much less dose difference between the stars; therefore, no phase dependence and no interference, only blurring. In Fig. 3 of Kissick et al.,6 one can see the effect of interference diminish from Figs. 3(f)–3(d) as the beam width divided by the couch velocity becomes much longer than the breathing period. One can also see that the blurring increases to its maximum [edge behavior of Fig. 3(d)] as the interference and phase dependence diminish. Therefore, theoretically, we also see that the dose error depends not only on the amplitude of the tumor motion, but it can easily be dominated by the frequency dependence near interference. Unfortunately, for simplicity, the time dependence of the dose rate is neglected in Bortfeld et al.,5 which means no analytical interference calculation is possible to properly simulate a dynamic IMRT situation like their illustration of Fig. 1 [see Sec. II.B after Eq. (8)]. The following argument should extend beyond helical tomotherapy into all forms of dynamic IMRT. The dose D at a voxel at position x can be formulated as a beamlet-filtered dwell time (fluence), D(x)=∫−∞∞T(x′)B(x−x′)dx′, (1) and the T is the total “dwell time” (units of fluence) convolved with the beamlet profile B. T(x′)=∫0∞R(t)δ(x′−xmotion(t))dt, (2) where the time-dependent modulation is R(t) and inside the Dirac delta function is the time-dependent tumor motion displacement function, xmotion(t). This formulation is simply a generalization from the original investigation on this topic [see Eq. (7) of Yu et al.7]. A key feature for a relatively high frequency tumor motion is that the total dwell time stays nearly constant from voxel to voxel in the PTV, as is the case with nearly regular breathing in helical tomotherapy. The frequencies at which blurring becomes interference will vary from one IMRT modality to another, but the same physics principles will apply to any dynamic IMRT modality. The specific criteria of tumor motion amplitude and frequency for when motion management should be used or not will therefore also vary from one modality to another. The dose error is therefore related to the tumor motion amplitude by the time-integral relation of Eq. 2 above and is further filtered by the (nonisotropic) beamlet profile of Eq. 1. The modulation as an explicit function of time in Eq. 2 should be assumed to be important unless shown otherwise. We therefore are suggesting a focused update to the TG-76 report to include a criterion for the use of motion management techniques with dynamic IMRT that better includes the effects of frequency similarity and difference between MLC leaves and other modulation motions and tumor motion. Perhaps other issues with the this criterion could be addressed as well such as for how long one should observe the intrafraction motion in order to parametrize it and if various parts of the tumor can all use the same criterion. One straightforward approach, potentially useful for the clinic, may be to suggest a motion delivery quality control and assurance check specific to each device (or type of device) and each patient’s motion (or type of motion) to make sure interference effects such as those reported3 do not occur. We suggest that the treatment keep the machine’s fundamental motion frequencies separate from the patient’s fundamental tumor motion frequencies. T. Rockwell Mackie has ownership interests in TomoTherapy, Inc., which is commercializing helical tomotherapy. This work was supported by United States National Institutes of Health, National Cancer Institute Grant No. K25 CA119344.

Low dose fraction behavior of high sensitivity radiochromic film

A high sensitivity (HS) model of radiochromic film is receiving increasing use. The films linear sensitometric response in the range of 0.5-40 Gy would make this film an ideal candidate for complex dosimetry applications that require tissue equivalence. This study investigates the potential use for clinical dosimetry of typical radiotherapy fractions at relatively low doses (0.5-5 Gy). The experiment involved exposing 25 pre-exposed pieces of HS film to five equal fractions of doses from 0.5 to 5 Gy 24 hours apart. The cumulative dose for each film was carefully monitored and optical density measurements were used as the sole determination of film response to dose. The average behavior of the various fractionation schemes was roughly consistent with previous observations of the MD-55 radiochromic film with about twice the overall sensitivity as expected. However, at low doses and low dose increments, unexpected variations beyond a well-documented low dose nonlinearity were observed. These unexpected variations may indicate complex polymer kinetics at low doses. This type of film would require extra care beyond that described in TG-55 for accurate use at low doses or low dose fraction schemes.