evaluation of motion management strategies based on required margins

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Evaluation of motion management strategiesbased on required marginsTo cite this article D Sawkey et al 2012 Phys Med Biol 57 6347

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Phys Med Biol 57 (2012) 6347ndash6369 doi1010880031-915557206347

Evaluation of motion management strategies based onrequired margins

D Sawkey M Svatos and C Zankowski

Varian Medical Systems 3120 Hansen Way Palo Alto CA 94304 USA

E-mail darensawkeyvariancom

Received 13 April 2012 in final form 26 July 2012Published 19 September 2012Online at stacksioporgPMB576347

AbstractStrategies for delivering radiation to a moving lesion each require a marginto compensate for uncertainties in treatment These motion margins havebeen determined here by separating the total uncertainty into componentsProbability density functions for the individual sources of uncertainty werecalculated for ten motion traces obtained from the literature Motion marginsrequired to compensate for the center of mass motion of the clinical treatmentvolume were found by convolving the individual sources of uncertainty Formeasurements of position at a frequency of 33 Hz system latency was thedominant source of positional uncertainty Averaged over the ten motion tracesthe motion margin for tracking with a latency of 200 ms was 46 mm Gatingwith a duty cycle of 33 required a mean motion margin of 32ndash34 mm andtracking with a latency of 100 ms required a motion margin of 31 mm Feasiblereductions in the effects of the sources of uncertainty for example by usinga simple prediction algorithm to anticipate the lesion position at the end ofthe latency period resulted in a mean motion margin of 17 mm for trackingwith a latency of 100 ms 24 mm for tracking with a latency of 200 ms and21ndash22 mm for the gating strategies with duty cycles of 33 A crossovertracking latency of 150 ms was found below which tracking strategies couldtake advantage of narrower motion margins than gating strategies The methodsdescribed here provide a means to guide selection of a motion managementstrategy for a given patient

(Some figures may appear in colour only in the online journal)

Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 30 licence Any further distribution of this work must maintain

attribution to the author(s) and the title of the work journal citation and DOI

0031-915512206347+23$3300 copy 2012 Institute of Physics and Engineering in Medicine Printed in the UK amp the USA 6347

6348 D Sawkey et al

1 Introduction

Target motion can result in dose intended for a lesion being delivered to normal tissue andorgans at risk instead This requires a strategic treatment decision to mitigate the effect ofany anticipated motion in order to preserve the treatment intent Many methods have beenproposed or developed to reduce the dose to normal tissue (Keall et al 2006) includingpausing the treatment beam while the lesion is outside the beam (gating) and moving thebeam to follow the lesion motion (tracking) It can be difficult however to compare theeffectiveness of different strategies and to determine the best strategy for a given patientIn part this stems from the stochastic nature of the events causing the motion Furthermorefactors contributing to the relative effectiveness or ineffectiveness of each treatment strategyare not always apparent prior to treatment Methods to compare motion management strategiesinclude convolving dose distributions calculated for a static patient with the motion (Hugoet al 2007 Engelsman et al 2005) George et al (2008) used a margin formula (Stroom et al1999 van Herk et al 2000) to calculate margins for different motion management strategiesfor a population of patients Recently Sohn et al (2012) used principal component analysisto model the dosimetric consequences of organ motion In the present paper a systematicand quantitative method of comparing motion management strategies based on convolution ofuncertainty probability density functions (PDFs) has been developed This method producesa recommendation of a strategy for a particular patient or a population and allows isolationof the factors contributing to unplanned extraneous dose

Margins were determined for several motion management strategies for a variety ofmotion traces that were previously published In each case a motion margin that accountsfor the motion of the center of mass of the clinical treatment volume (CTV) was calculatedActual treatment margins would include other sources of uncertainty and be larger Foreach motion management strategy treatments of lesions moving according to the motiontraces were simulated For each simulated treatment the motion margin was the minimumvalue such that the entire CTV received 95 of the prescription dose over the course of thetreatment In contrast to the work of van Herk et al (2000) a treatment comprised of onlya few fractions was considered and therefore no distinction was made between random andsystematic uncertainties This lack of distinction between random and systematic uncertaintiesfor few fraction treatments has been noted before (Zhang et al 2012)

In order to determine the motion margin the sources of uncertainty potentially leading toa geometric miss were first considered in isolation Other sources of uncertainty were assumedto be negligible PDFs were generated for each source of uncertainty giving the probabilitiesof displacements between the beam and CTV For some sources of uncertainty PDFs werebased on values taken from the literature For others PDFs were calculated by simulatingtreatment of a CTV moving according to the motion trace

Sources of uncertainty were categorized into a binary tree The first division was betweenthose sources related to treating a moving lesion and those not Sources of uncertainty unrelatedto treating a moving lesion were beyond the scope of this paper For example the ICRU(1999) lists changes in shape and size of the lesion plus mechanical uncertainties of theequipment dosimetric uncertainties transfer set-up errors and human factors Motion-relateduncertainties were divided into localizing the CTV and delivering radiation to the target Inall the motion-related uncertainties were divided into six sources

Complete motion management strategies were studied by combining the individual PDFsby convolution Typical values of parameters were chosen Motion margins were determinedfrom the combined PDF for each motion management strategy for each motion trace and themotion margins for the individual traces were averaged Motion management strategies were

Evaluation of motion management strategies 6349

compared based on the mean motion margins Possible reductions to the individual sources ofuncertainty were discussed These reductions were incorporated into the combined PDF foreach motion management strategy and new motion margins were calculated

It should be noted that this analysis is based on a limited number of motion traces obtaineddirectly from the literature in order to highlight the method itself rather than any particularsource of data The PDFs for the individual sources of uncertainty were chosen as reasonableexamples for particular scenarios and are not meant to be representative of all devices Forapplication in the clinic it is recommended that each clinic use data from their intendedpatient(s) and obtain values specific to their equipment

2 Methods and materials

21 Definitions

Consider a treatment with a C-arm gantry linac with a multi-leaf collimator (MLC) that may ormay not move The methods described here readily generalize to other geometries Considera beamlet of a step-and-shoot fieldmdashthat is the size and shape of the MLC-defined field doesnot change during delivery of the beamlet Extension to sliding window or VMAT treatmentsmay be done by considering multiple beamlets and for different gantry angles lesion motionin different directions is important Consider a rigid CTV that does not rotate but may exhibittranslational motion Suppose that a reference point in the CTV can be precisely definedDefine a coordinate system such that the beam axis is directed along the positive z axisDenote the position of the CTV reference point as x = (x y z) where boldface denotes avector (see figure 1)

Treatment proceeds with simultaneous measurement of the position of a marker Theposition of the CTV is inferred from the position of the marker The inferred position is thetarget to which a radiation beam defined by the MLC is directed Define a reference point inthe beam at coordinates xprime = (xprime yprime z0

prime) where the component in the z direction (along thebeam axis) is arbitrary The CTV and beam may both move so x and xprime are functions of time tMotions in each direction were assumed to be independent In the x direction the differencebetween beam and CTV positions is

x(t) = xprime(t) minus x(t)

x(t) will take a range of values over the beam-on time of the beamlet The probability thatx(t) was between x and x + dx at a particular time is given by P(x)dx where P(x) is the PDFof the motion in the x direction The reference point xprime was chosen such that the center of massof the PDF was zero PDFs were normalized such that their integral was 1

22 Sources of uncertainty

Sources of uncertainty that contribute to the required margins were categorized in figure 2The highest level division was between the sources of uncertainty that relate to deliveringradiation to a moving CTV and those from other sources The sources related to motionwere divided into locating the CTV and hitting the target Sources of uncertainty in locatingthe CTV were divided into the instantaneous measurement of position and the predictionof the position at future times Uncertainties in the instantaneous measurement of positionincluded measuring the position of the marker and correlating the position of the marker withthe position of the CTV Similarly the uncertainties in targeting were divided into those relatedto the instantaneous targeting and those from the latency The uncertainties in instantaneoustargeting included the accuracy of the machine and the residual motion

6350 D Sawkey et al

Figure 1 Definition of the terms and coordinate used The cells to which dose is intended to bedelivered make up the CTV The position of a marker is measured from which the position of thetarget is inferred A beam is directed at the target Reference points (indicated by circles) in theCTV and beam are defined and the difference between the reference points (x) is determined

In total the lowest level of the uncertainty tree has six leaves related to treating a movingCTV These are described individually as follows

221 Instantaneous measurement of position This uncertainty results from the accuracyof which a static measurement of position can be made

222 Correlation between marker and CTV positions The measurement of position isnot necessarily of the CTV itself Rather it could be of an internal or external marker Thisuncertainty accounts for the imperfect correlation between the position of the marker and theposition of the CTV


Figure 2 Classification of sources of uncertainty

223 Prediction of position in between measurements For occasional measurements theposition between measurements is unknown and must be predicted This uncertainty accountsfor the differences between actual and predicted positions

224 Machine accuracy This uncertainty describes the accuracy with which the treatmentmachine can hit a target at a known position and time

225 Residual motion For gated treatments the beam is on for a range of target positionsThis range is considered an uncertainty since the actual instantaneous position may beanywhere within the window of pre-defined range

226 Latency The position at a particular time is measured and the radiation is delivered ata later time The change in position between the two times is expressed as an uncertainty Thisdefinition of latency includes all its components including the latency due to the measurementof position and the latency due to moving the linac or MLCs

23 Motion traces

Ten patient motion traces from the literature were analyzed The published traces were formotion in the thorax in the superiorndashinferior direction and the entire published trace (spanning45ndash90 s) was used Traces were manually digitized using computer monitor and mouse andinterpolated between digitized points to create position values every 10 ms The coordinatesystem was defined such that the end-of-exhale position was more negative than the end-of-inhale position and the time-averaged position was zero

Cervino et al (2011) measured positions of vascular structures in the lungs of healthyvolunteers using cine-MRI with a frame rate of 4 Hz The volunteers were instructed toperform both regular and irregular breathing Four traces from the same volunteer presentedin figures 3(a)ndash(d) were used

Suh et al (2008) extracted position data from patients treated with Cyberknife Synchrony(Accuray Inc Sunnyvale CA) The position of the chest wall was monitored at 32 Hz by usinglight emitting diodes attached to the chest Orthogonal kV images were acquired in a periodof sim30 s The lesion position was inferred from the position of the external marker usingan internalexternal correlation model updated as new kV images were acquired Several of

6352 D Sawkey et al

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Figure 3 The motion traces acquired from the literature Traces (a)ndash(d) are from Cervino et al(2011) (e)ndash(h) are from Yoon et al (2011) and (i) (j) are from Mageras et al (2001) Tracesrepresent the position of the lesion in the superiorndashinferior direction All traces are presented suchthat the end-of-exhale position is negative and the time-averaged position is zero

those motion traces of the lesion were published in Yoon et al (2011) and these were used inthe current work (figures 3(e)ndash(h))

Mageras et al (2001) determined the position of the diaphragm using fluoroscopy Thediaphragm position was used to approximate the lesion position for the purposes of this paperthe diaphragm position was considered to be equivalent to the lesion and CTV positions Twotraces were obtained for the same patient During acquisition of the trace in figure 3(i) thepatient was undergoing free breathing and during acquisition of the trace in figure 3(j) thepatient was undergoing verbally-coached breathing The authors also recorded the position of


Table 1 Characteristics of the motion traces Motion-encompassing margins are margins suchthat the reference point is within the margin 975 of the time neglecting all other sources ofuncertainty Pop std dev stands for lsquopopulation standard deviationrsquo and RMS stands for root meansquare

Position (mm) Velocity (mm sminus1)

Peakndashpeak Motion-encompassing MaximumTrace amplitude RMS amplitude margins magnitude RMS

A 153 44 66 302 72B 368 82 149 415 122C 231 67 102 366 78D 241 58 108 316 63E 182 39 76 342 114F 146 40 66 296 74G 172 39 72 298 48H 150 36 61 341 98I 205 51 94 641 136J 236 80 112 585 167Mean 208 54 91 390 97Pop std dev 63 16 26 117 35

a marker block on the patientrsquos chest over the same time period as the fluoroscopy using theRPM system (Varian Medical Systems Palo Alto CA)

Characteristics of these traces are given in table 1 Over the ten traces the mean peak-to-peak and RMS amplitudes were 208 and 54 mm respectively The mean of the marginsthat would encompass 975 of the motion was 91 mm The velocity at a given timewas calculated as the average over 01 s The mean of the maximum magnitudes of thevelocities was 390 mm sminus1 and the mean of the RMS velocities was 97 mm sminus1

24 Determination of PDFs

Each source of uncertainty was initially considered independently PDFs of the displacementbetween beam and lesion were created as described below assuming other sources ofuncertainty were negligible Note that the values obtained from the literature are not necessarilyrepresentative of any particular patient or treatment method For clinical implementation ofthese methods PDFs specific to the patient and treatment method would need to be determined

241 Instantaneous measurement of position A PDF for determination of position usingCalypso electromagnetic beacons (Varian Medical Systems Palo Alto CA) was used Thevalue was taken from the literature (Balter et al 2005)

242 Correlation between marker and lesion positions The two simultaneous motiontraces of the lesion and an external marker (Mageras et al 2001) were analyzed A model wascreated to relate the lesion position to the marker position Traces were first divided into inhaleand exhale traces based on the direction of motion of the marker For each trace (of a givendirection) a fourth-order polynomial was fit to the lesion position as a function of markerposition Treatment was simulated by inferring the lesion position from the marker positionusing the appropriate fit function The uncertainty PDF was calculated from the differencesbetween the inferred and measured lesion positions over the time period of the motion traces

6354 D Sawkey et al

The same methodology could be used to account for the position of an internal markerrelative to the lesion Although studies (eg Shirato et al (2003)) have shown that markerpositions remain constant from day to day (interfraction) there is little data on the motionon the (intrafraction) time scale of seconds Korreman et al (2006) found that the correlationbetween the position of an internal marker and the position of the lesion was generally goodbut patient dependent Cervino et al (2009) found that the position of the diaphragm could beused as a surrogate for tumor position for most patients with an error at the 95 confidencelevel of 21 mm Smith et al (2011) examined the correlation of tissue motion within the lungand found that the mean distance for an implanted fiducial to correlate with tissue motion washighly patient specific For the simulated treatments in this work using an internal markerthe correlation between internal marker position and lesion position was taken to be a deltafunction This is only realistic for location methods such as fluoroscopy (Li et al 2009) or MRI(Cervino et al 2011) in which the lesion position is determined directly We caution the readerthat for clinical implementation of these methods values appropriate for their measuringtechniques should be used

243 Prediction of position between measurements For each motion trace a virtual setof measurement data was created by extracting positions at times corresponding to a givenmeasurement frequency for the example treatment scenarios These positions represented theresults of the would-be measurements of position A prediction function was fit to a subset ofthe virtual measurement data and used to predict the position between the last measurementin the subset and the next virtual measurement The length of time over which the fit wasmade was denoted the fit interval A sine function was used as the simple prediction functionEach fit was offset such that the fit function coincided with the last data point in the subset ofvirtual measurements A PDF was formed for each motion trace from the differences betweenpredicted and actual positions at times between measurements over the motion trace

Measurement frequencies from 1 to 33 Hz were considered Fit intervals in the range of1 to 10 s were considered For each measurement frequency and motion trace the fit intervalthat resulted in the lowest margin was used

This method is independent of the means of measurement (whether the position is derivedfrom electromagnetic beacons kV or MV imaging etc) depending only on the frequencywith which it is undertaken Estimation of the lesion position in between measurements isnot straightforward It could be done for instance prior to treatment by analyzing high-frequency trajectory data from the cone-beam CT projections Alternatively the PDF couldbe based on literature values for the same technique with similar motion traces For hightemporal resolution techniques such as Calypso where the position information is essentiallycontinuous the location of the lesion between measurements is not known exactly but of lesssignificance since less biological motion is possible in very short intervals

244 Machine accuracy The end-to-end spatial accuracy of the TrueBeam (Varian MedicalSystems) system was taken from published experimental measurements (Wang et al 2012)and converted to a PDF

245 Residual motion The uncertainty from residual motion was a function of the dutycycle For a given duty cycle the motion margin was defined as the minimum range of allowedmotion such that the desired duty cycle was obtained The center of the gating window was afree parameter The motion margin was determined by first numerically calculating the dutycycle for every combination of motion margin and center of gating window For a given duty


cycle the center of the gating window that resulted in the smallest motion margin was selectedThis margin was defined as the motion margin for that duty cycle

Baseline correction (DrsquoSouza et al 2005 Pepin et al 2011a) was applied to all motiontraces (Korreman et al 2008) If it were not the relation between duty cycle and motionmargin would be ill-defined in the presence of baseline drift Between each pair of end-of-exhale positions the baseline was defined as the line containing the previous two end-of-exhalepositions The baseline was subtracted from the position data End-of-exhale positions weredefined as times in the motion trace where the position was more negative than in the followingor preceding second

246 Latency The latency τ L was defined as the difference between the time to whichthe measurement of position corresponded (ie the time the measurement was taken) and thetime at which radiation could be delivered based on that measurement information (the time arealigned beam was delivered) This definition of latency includes the time required for imageacquisition and processing plus any repositioning of linac components for beam deliveryThus the latency is essentially machine dependent and must be estimated for each specificdelivery scenario (eg a TrueBeam delivery using couch tracking guided by Calypso beaconswould be expected to have a different latency than a Clinac delivery with MLC tracking guidedby 1 Hz kV images) The uncertainty PDF was formed from the differences of actual targetpositions (from the motion trace) as measured at times t and t + τ L for t spanning the motiontrace Latencies from 005 to 05 s were considered These values span a range of publishedvalues (Hoogeman et al 2009 Depuydt et al 2011 Sawant et al 2009 2010 Jin and Yin 2005)measured for example by continuous MV imaging of both a radiopaque object and the MLC

25 Combining uncertainties

Individual sources of uncertainty were combined to form the positional uncertainty for differentmotion management strategies PDFs were combined by convolution

26 Determination of motion margins

Motion margins were calculated from the requirement that the minimum dose to the CTVbe 95 of the prescription dose Neglecting scatter this was equivalent to requiring thatthe reference point of the CTV be within the margin of the reference point of the radiationbeam 95 of the time It was assumed that there was motion in two orthogonal directionscontributing to the margins For simplicity it was assumed that for each direction the referencepoint of the CTV was required to be within the margin of the reference point of the radiationbeam (095)12 = 0975 of the treatment time The motion margin was the minimum valueencompassing 975 of the area of the PDF and was determined by numerical integration

3 Results

31 Components of the uncertainty

311 Instantaneous measurement of position Values for the uncertainty usingelectromagnetic beacons were used For one system the differences between measurementsof the positions of the beacons relative to the position of the array and the known positionswere found to be described by a mean of 04 mm and a standard deviation of 04 mm(Balter et al 2005) This was conservatively approximated as a Gaussian distribution with

6356 D Sawkey et al

standard deviation 08 mm centered on zero It was assumed that the position of the arraycould be measured sufficiently accurately that the uncertainty was negligible compared to theuncertainty of measuring the beacon positions

312 Correlation between marker and CTV positions Simultaneous traces of the markerand CTV (Mageras et al 2001) are shown in figures 4(a) (b) During acquisition of thedata in figure 4(a) breathing was coached during acquisition of the data in figure 4(b)the patient was free breathing Figures 4(c) (d) are plots of marker position versus CTVposition The data points were divided into inhale and exhale Hysteresis was evident nearthe end-of-exhale position while breathing was coached and over the full trace while freebreathing The polynomial fits to the data are shown The residuals between the inferred andthe measured CTV positions as a function of time are shown in figures 4(e) (f) For coachedbreathing most of the points were within 1 mm of zero but there were occasional spikes ofup to 7 mm magnitude These typically occurred right at the transition between inhale andexhale or vice versa For some transitions the marker began to move either before or after thediaphragm While free breathing there was an additional variation in the baseline of plusmn 1 mmthat correlated with the baseline drift in the motion trace The PDFs constructed from theresiduals are shown in figures 4(g) (h) The margin required to account for the imperfectcorrelation between measured and inferred CTV positions was 30 mm for coached breathingand 33 mm for free breathing

As with all the data presented in this work the values may or may not be applicable toa given patient The correlation between the positions of an external marker and the lesion isnotably variable see for example Keall et al (2006) for a list of studies showing a large rangeof correlations For clinical implementation it is recommended that values specific to a givenpatient are obtained and updated throughout treatment

313 Prediction of position in between measurements Margins required to account for thechange of CTV position between measurements are shown in figure 5 for the ten motion tracesMargins are plotted against the inverse of measurement frequency For high measurementfrequencies the margins approached zero On decreasing the measurement frequency themargins increased nearly linearly with the measurement period The rate of increase wasdifferent for each motion trace and ranged from 5 to 18 mm sminus1 The mean margin wasdescribed by a line with slope 87 mm sminus1 At a measurement frequency of 2 Hz the marginsranged from 23 to 72 mm with a mean of 43 mm At 16 Hz the margins ranged from 03 to13 mm with a mean of 06 mm

The traces that were outliers were characterized by similar features Motion traces thatrequired the largest margins included (i) (j) and (b) The first two of these traces wereregular but showed a large asymmetry between inhale and exhale The prediction algorithmwas therefore not able to accurately predict the position of an inhale peak say based onthe position of the previous end-of-exhale peak Trace (b) had highly inconsistent breathingamplitudes The prediction algorithm predicted one breathing cycle to be similar to the previousone and therefore did poorly when the amplitudes varied Motion traces that were predictedwell were symmetric with regard to inhaleexhale and had consistent amplitude from cycleto cycle Examples were traces (a) and (f)

314 Machine accuracy Wang et al (2012) measured the end-to-end targeting accuracyof the TrueBeam dose delivery by delivering dose to a phantom with embedded film Fornine treatment plans they found that the maximum magnitude of geometric displacement in


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Figure 4 Determination of the correlation PDF Left side (a) (c) (e) (g) are for a patient undergoingcoached breathing Right side (b) (d) (f) (h) are for the same patient undergoing free breathingPlots (a) (b) show the positions of the CTV and marker as functions of time Plots (c) (d) showthe CTV position as a function of marker position separated into inhale (blue) and exhale (red)The polynomial fits to the data are shown as lines Plots (e) (f) show the residuals of the fit Plots(g) (h) show the PDFs constructed from the residuals

6358 D Sawkey et al

0 02 04 06 08 11measurement frequency [s]

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Figure 5 Margins for the ten individual traces plus the mean due to predicting the CTV positionin between measurement times The uncertainty due to prediction was considered in isolation

three dimensions between the measured dose and the planned dose was lt09 mm With theassumption that the targeting uncertainty involved uncertainties in two orthogonal directionsadded in quadrature the maximum magnitude of displacement in one direction was 06 mm(ie 09 mm

radic2) Further assuming that this value represented the 2σ value of a Gaussian

distribution the PDF for the machine accuracy was taken to be a Gaussian with σ = 03 mmThis is a conservative estimate for this quantity because the end-to-end test included moresources of uncertainty than machine accuracy

315 Residual motion The PDFs of the CTV positions for the ten traces are shownin figure 6 with and without baseline correction Consider first the PDFs with no baselinecorrection Most of the PDFs were characterized by a large peak at the end-of-exhale positionThe amplitude of the peak varied and was a maximum of 40 mmndash1 for trace (a) Several ofthe traces also showed a smaller peak at the inhale position The shapes of the peaks variedand for several traces there were multiple peaks at end-of-exhale Trace (e) which showeda pronounced baseline drift in the motion trace was alone in not showing an end-of-exhalepeak After correcting for baseline drift most PDFs (shown in red) were largely unchangedThe exception was trace (e) for which end-of-exhale and end-of-inhale peaks were visible inthe PDF only after baseline correction

Required margins due to residual motion for the ten baseline-corrected motion tracesare shown in figure 7 as a function of duty cycle For duty cycles below 30ndash40 marginswere proportional to the duty cycle The constant of proportionality ranged from 001 to0045 mm with mean 0025 mm For duty cycles above 40ndash50 the relation betweenmargin and duty cycle was again linear with slopes in the range of 008 to 024 mm andmean 012 mm At a duty cycle of 33 the margins ranged from 06 to 16 mm with a


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Figure 6 PDFs of the motion traces with (red) and without (blue) baseline correction

mean of 10 mm At a duty cycle of 50 the margins ranged from 14 to 30 mm with mean23 mm

At low duty cycles the outlier with highest margins was (d) This trace was characterizedby a constantly moving CTV at exhale The end-of-exhale peak in the PDF and thereforethe margin was wide The motion traces with the narrowest margins were (a) and (c)These traces had consistent end-of-exhale positions during which the CTV was stationaryand large amplitude narrow peaks in the motion PDFs at end-of-exhale At high duty cycles(g) had narrow margins compared to the other traces This motion trace was inconsistent butshowed both long times at the end-of-exhale position and a small breathing amplitude

6360 D Sawkey et al

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Figure 7 Margins due to duty cycle for a gated treatment Other sources of uncertainty wereneglected

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Figure 8 Margins due to latency considered in isolation

316 Latency Margins resulting from latency for the ten motion traces are shown in figure 8for latencies in the range of 005 to 05 s For small latencies the margins were proportionalto the latency The slopes ranged from 13 to 45 mm sminus1 with mean 24 mm sminus1 The curvesflattened slightly at latencies approaching 05 s At a latency of 005 s the margins ranged


from 06 to 26 mm and had a mean of 12 mm At a latency of 02 s the margins ranged from23 to 76 mm with a mean value of 41 mm

Traces which were outliers had similar features The traces with the largest marginswere (i) (j) and (b) These traces all had the largest maximum and RMS velocities Theformer two traces had long times at end-of-exhale relative to the breathing period andlarge amplitudes of motion resulting in large velocities The latter trace had occasional largeamplitude inhalations during which the lesion moved rapidly The trace with the smallestmargins (g) had the smallest RMS velocity and nearly the smallest maximum velocity Italso had a small breathing amplitude and long periods of time at end-of-exhale

32 Combined uncertainties for different motion management strategies

Five motion management scenarios were considered

321 Tracking with latency 200 ms Suppose that the patient has electromagnetic beaconsimplanted internally and that the correlations between the CTV positions and those inferredfrom the beacons can be described as a delta function There is no residual motion because thisis not a gating strategy Suppose that the latency is 200 ms a value consistent with measuredvalues on the Trilogy (Sawant et al 2010) For each trace the combined uncertainty is theconvolution of the uncertainty for measurement accuracy prediction machine accuracy andlatency

The motion margins calculated from the resultant motion PDF are shown in figure 9(a)for each motion trace At high measurement frequencies the margins reached a plateau atnon-zero values The values ranged from 30 to 80 mm and had a mean value of 46 mmThese values were within 07 mm of the values solely resulting from the latency of 200 ms(figure 8) As the measurement frequency decreased the margins at first were nearly constantthen began to increase near 10 Hz At a measurement frequency of 2 Hz the margins rangedfrom 39 to 100 mm and had a mean value of 61 mm At 1 Hz the mean of the motionmargins was 93 mm

322 Tracking with latency 100 ms Suppose that the same tracking strategy as above isapplied but with a latency of 100 ms This value is near the value for the Cyberknife (Accuray)system Motion margins are shown in figure 9(b) At high measurement frequencies the motionmargins for each trace ranged from 22 to 49 mm and had a mean of 31 mm Motion marginsincreased as the measurement frequency decreased At 2 Hz the mean of the motion marginswas 52 mm and at 1 Hz the mean was 86 mm

323 Gating with an internal marker 33 duty cycle and latency 100 ms Consider agating strategy with an implanted beacon Suppose that the latency is 100 ms lower than thatfor tracking because the linac is not required to move A duty cycle of 33 with baselinesubtraction is used The uncertainty is the convolution of the individual uncertainties formeasurement accuracy prediction latency machine accuracy and residual motion

Motion margins are shown in figure 9(c) for each motion trace For a measurementfrequency of 33 Hz the margins ranged from 24 to 52 mm with mean 34 mm The meanvalue was 1 mm greater than that for a latency of 100 ms considered in isolation On decreasingthe measurement frequency the motion margins were nearly constant until 10 Hz At lowerfrequencies the motion margins increased At a measurement frequency of 2 Hz the motionmargins ranged from 35 to 83 mm with mean 54 mm At 1 Hz the mean of the motionmargins was 87 mm

6362 D Sawkey et al

0 02 04 06 08 1

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argi

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(c) (d) (e)

Figure 9 Margins for five treatment strategies The margins incorporate all the motion-relatedsources of uncertainty discussed in the paper (a) Tracking with 200 ms latency (b) Tracking with100 ms latency (c) Gating using an internal marker a 33 duty cycle and 100 ms latency (d)Gating using an external marker a 33 duty cycle and no latency (e) Gating using an internalmarker a 50 duty cycle and 100 ms latency

324 Gating with an external marker duty cycle 33 and negligible latency Supposethat a gating strategy is used with an external marker The latency results from measuringthe position of the external marker and holding the beam it was assumed to be zero Aduty cycle of 33 with baseline correction is used The uncertainty is the convolution of theuncertainties in measurement accuracy prediction machine accuracy residual motion andcorrelation A difficulty was that correlations were only available for two of the motion tracesThe two correlation PDFs were similar therefore one was used as the correlation PDF for allthe motion traces The correlation PDF for trace (j) was narrower than for trace (i) Howeveras discussed in section 4 the correlation PDFs could be improved Therefore the correlationPDF for trace (j) was taken to be representative and used for all the traces

The resulting motion PDFs led to motion margins shown in figure 9(d) For highmeasurement frequencies the motion margins clustered at a mean value of 32 mmThe minimum and maximum values were 31 and 34 mm respectively On decreasingthe measurement frequency the motion margins first remained nearly constant then ata measurement frequency near 5ndash10 Hz the motion margins increased At measurementfrequencies of 2 and 1 Hz the means of the motion margins were 53 and 86 mm respectively

325 Gating with an internal marker a 50 duty cycle and latency 100 ms For gating withan internal marker as described in subsection 323 but with an increased duty cycle of 50the motion margins were increased (shown in figure 9(e)) At high measurement frequencies


Figure 10 Comparison of the means of the margins for the different treatments consideredpreviously (solid lines) Shaded areas represent the values one standard deviation from the meanand are shown for tracking with 200 ms latency (red) and gating from an external marker (blue) Thehorizontal line (magenta) represents margins for a motion-encompassing strategy only accountingfor the motion of the CTV Dashed lines represent margins for the different motion managementstrategies taking into account reductions in the individual sources of uncertainty as discussed inthe discussion

the motion margins ranged from 28 to 57 mm with a mean of 40 mm At measurementfrequencies of 2 and 1 Hz the means of the motion margins were 57 and 90 mm respectively

33 Comparisons of different motion management strategies

The mean motion margins for the five motion management strategies considered above areplotted as lines in figure 10 The motion margins for the gating strategies with a duty cycleof 33 with either the external or internal marker were similar to those for tracking with a100 ms latency over the range of measurement frequencies The mean of the motion marginswas 3 mm at a measurement frequency of 33 Hz For tracking with a latency of 200 ms themean motion margin was 46 mm at 33 Hz For internal gating with a duty cycle of 50the motion margin was 40 mm at 33 Hz These values were intermediate between those fortracking with a latency of 200 ms and those for either tracking with a latency of 100 ms oreither gating strategy with a duty cycle of 33 At 1 Hz all the strategies required motionmargins near 9 mm

These motion margins at measurement frequencies greater than 1 Hz were lower thanthose for a motion-encompassing strategy At a minimum motion-encompassing marginsneed to account for the motion of the CTV during the motion trace Averaged over the tentraces the margin required such that the CTV was in the beam 975 of the time was 91 mmThis value is shown as a magenta line in figure 10 It intersects the curves for the various

6364 D Sawkey et al

motion management strategies near a measurement frequency of 1 Hz At 33 Hz the motion-encompassing margins were 2ndash3 times those for the various motion management strategies

The standard deviations of the distributions of motion margins for the ten traces are shownas shaded areas for tracking with a latency of 100 ms and gating with an external marker Thestandard deviation for the external gating strategy was low at high measurement frequenciesbecause the same correlation uncertainty was used for each trace The difference between themean motion margins for the different strategies at a measurement frequency of 33 Hz was onestandard deviation of the tracking results At 1 Hz the differences in mean motion marginsfor the different strategies were much less than one standard deviation

The curves representing the mean motion margins can be characterized At highmeasurement frequencies latency was a dominant source of uncertainty For tracking with alatency of 200 ms almost all of the motion margin resulted from latency On reducing thelatency to 100 ms other sources of uncertainty such as the measurement accuracy and forgating the residual motion and the correlation between internal and external positions becomeimportant As the measurement frequency was reduced the prediction uncertainty becamemore important At 1 Hz it was the dominant source of uncertainty

4 Discussion

Uncertainties that have a strong contribution to the required motion margins are discussedas to how they could be improved and the amount of improvement that could be expectedThe improved PDFs of the individual sources of uncertainty were combined to determine therequired motion margins after reducing the individual sources of uncertainty

41 Reduced uncertainty from latency

The largest contribution to the motion margins at high measurement frequencies was thelatency Several methods were considered to reduce the uncertainty due to latency

(1) System latency could be reduced To some extent the latency is a design decision onthe part of the manufacturer Discussion of the tradeoffs and possible decrease in latencyis beyond the scope of this paper Reductions in motion margins due to latency can bedetermined from figure 8

(2) The position at the end of the latency period could be predicted The analysis above was aworst-case situation where the change in position over the latency time was considered asthe uncertainty However this uncertainty could be reduced if the position was predictedTo set a bound for this value positions after the latency period were predicted using thealgorithm described above for predictions between measurement points For a latency of200 ms the margins required due to differences between actual and predicted positionsaveraged over the ten motion traces were 30 mm a 28 improvement over the valuewithout prediction

(3) More accurate prediction algorithms could be used However published works have notshown a large improvement over the value determined here Sharp et al (2004) studiedadaptive neural networks Kalman filtering and linear prediction and compared to noprediction They found that predicting the position reduced the RMS difference in 3Dpositions for a latency of 200 ms and measurement frequencies between 10 and 30 Hzby 33 Murphy and Dieterich (2006) used adaptive neural networks and linear adaptivefiltering to predict the position of an external marker For latency of 200 ms the RMS errordifference in position was 40 of the RMS position of the marker block (averaged over


ten traces) The traces considered in the present work had a mean RMS position of 54 mmScaling the results of Murphy and Dieterich to the RMS CTV displacements in this workleads to an RMS difference in position of 22 mm Assuming a Gaussian distribution ofdifferences this value is equivalent to a required margin of 48 mm (to ensure accuratetargeting 975 of the time) This required margin is greater than that obtained in thepresent work with a sinusoidal prediction Vedam et al (2004) used sinusoidal predictionand an adaptive filter For a latency of 200 ms and a lesion with an RMS position of36 mm (free breathing) they found that the RMS difference in positions was reducedfrom 12 mm (using no prediction) to 11 mm with sinusoidal prediction and 08 mm withadaptive filter prediction Scaling to the present RMS lesion position resulted in a meanmargin of 27 mm (for 975 targeting accuracy) This is close to the value of 30 mmreported here using a sine prediction It appears that the maximum expected reduction inPDF width through better prediction algorithms is 10

The above prediction functions were based on the measured positions as a functionof time More information is available In particular incorporating the velocity into theprediction may increase the accuracy

(4) The sine fit performed the worst at transitions between inhale and exhale and vice versaIt might be possible to reduce the residuals at these points Possibilities include usinga better prediction algorithm reducing dose rate at these times coaching the patient inbreathing patterns or obtaining a signal from the patient The improvement using betterpredictions might already be accounted for in the better predictions discussed above

In total a reduction in the width of the PDF due to latency of 50 might be expected for afixed latency This value is derived from the sum of 30 due to predicting the lesion positionwith a sine function 10 from use of a better prediction algorithm and 10 from otherimprovements

42 Better prediction between measurements

At low measurement frequencies much of the motion margin resulted from predicting positionsin between measurements Improvements in prediction are similar to those discussed above inthe context of latency Sharp et al (2004) found that at a measurement frequency of 1 Hz anda latency of 200 ms the RMS difference between measured and predicted positions could bereduced from 7 to 5 mm by using an adaptive neural network prediction algorithm (compared tono prediction) That represents a 30 improvement a value comparable to that obtained abovefor predicting the position at the end of the latency period using a sine function This suggeststhat further improvements in the prediction algorithm are likely to have only a small effectPerhaps as for the case of predicting the position after a latency period a 10 improvementin the PDF due to prediction between measurement points can be obtained

43 Better correlation model

In treatments where the position of an external marker is measured an improvement inthe model relating the position of the marker to the position of the CTV would reduce themotion margins The correlation model used in this work produced the largest differencesbetween measured and inferred CTV positions at the transitions between inhale and exhaleand vice versa These differences occurred when either the CTV or the marker began to movebefore the other The amount of improvement possible was estimated by removing the spikes atthe transitions of the difference plot in figure 4 For trace (j) the required margins were reducedto 14 mm from 30 mm As in the case of predictions discussed above this improvement

6366 D Sawkey et al

could be implemented by use of a prediction algorithm capable of predicting the transitionsor a system of coaching or signaling which provides advance knowledge of the transitions orholding the beam when the marker position approaches a transition

Combining monitoring the external marker with occasional measurements of an internalfiducial position might also reduce the correlation uncertainty Cho et al (2010) studied theeffectiveness of correlation models that were updated based on occasional kV imaging Theyfound that for images acquired at frequencies down to 01 Hz the standard deviation of thedifferences between predicted and actual marker positions in one dimension was 05 mm Thisis equivalent to a margin of 11 mm 30 less than the value of 14 mm obtained above Thevalue of 14 mm was used in the analysis as a conservative value

44 Reduced residual motion

The margins could be reduced by decreasing the duty cycle There would only be animprovement in the motion margins for certain cases namely those not dominated by theuncertainty from latency A decrease in the duty cycle with other parameters held constantwould increase treatment time As shown in figure 7 below a duty cycle of 33 the motionmargins were proportional to the duty cycle Alternatively the dose rate could be increasedfor example by removing the flattening filter (Cho et al 2011) Conversely increasing the dutycycle had a larger effect on the motion margins The plot of mean margin versus duty cycle infigure 7 had a positive second derivative near a duty cycle of 40 Increasing the duty cyclefrom 33 to 50 increased the mean margin from 10 to 23 mm A duty cycle of 33 appearsto be a reasonable compromise

45 Measurement accuracy

The uncertainty used for the measurement of position using Calypso beacons was a worst-casevalue More typical values were about half the magnitude A reasonable estimate of the PDFresulting from uncertainties in measurement of position is a Gaussian with σ of 04 mm

46 Combined improvements

An estimation of the reduction in motion margins that could be obtained by implementingthe above improvements was made by scaling the individual PDFs determined in section 3(results) by the values discussed above The same treatment options as presented in the resultswere considered with the new PDFs for each trace Mean motion margins were lower thanthose obtained previously and are plotted in figure 10 At a measurement frequency of 33 Hzthe lowest motion margin was 17 mm obtained with tracking with a latency of 100 msGating based on an external marker required a motion margin of 22 mm and gating with aninternal marker and a latency of 100 ms required motion margins of 21 mm Tracking witha latency of 200 ms had motion margins of 24 mm and gating based on an internal markerwith a duty cycle of 50 required a motion margin of 30 mm The tracking strategies wereimproved by 50 and the gating strategies by 33 The only change in the relative rankingof the strategies was that tracking with a latency of 200 ms required narrower motion marginsthan gating with a 50 duty cycle At a measurement frequency of 1 Hz all the motionmanagement strategies required motion margins between 7 and 8 mm

With the reductions in uncertainties the gated strategies required motion margins at highmeasurement frequencies that were between those for tracking with a latency of 100 ms andthose for tracking with a latency of 200 ms This suggests that the crossover latency was150 ms below which the motion margins for tracking were narrower than those for gating


This was perhaps an overestimate because reductions in the latency for tracking strategiesmight also lead to reductions in the latency for gating strategies

5 Conclusions

Five motion management strategies were compared by dividing the uncertainty in targetingaccuracy into its components Mean margins required to account for the center of mass motionof the CTV were determined At high measurement frequencies tracking with a latency of100 ms was found to require the narrowest motion margins of 31 mm and tracking with alatency of 200 ms required the largest motion margins of 46 mm Gating with a duty cycleof 33 and using either an internal or external marker required motion margins of 33 plusmn01 mm With a duty cycle of 50 the value for internal gating increased to 40 mm Thesevalues were less than the 91 mm required to account for the motion of the CTV with a motion-encompassing strategy At a measurement frequency of 1 Hz motion margins required for allthe strategies were near 9 mm

At high measurement frequencies latency was an important source of uncertainty It waslarger than the positional uncertainty related to residual motion and therefore gated strategiesrequired the same or narrower motion margins than tracking strategies Improvements couldbe made to the individual sources of uncertainty The effects of latency could be reduced byvarious means including predicting the CTV position at the end of the latency period Theseimprovements could reduce the margins required to account for a given latency by 50 Ifthese improvements and ones to the other sources of uncertainty were to be implementedmotion margins for the five motion management strategies would decrease Tracking witha latency of 100 ms would have the lowest motion margin at 17 mm The two trackingstrategies and the two gating strategies with duty cycles of 33 would all require motionmargins in the region 20 plusmn 04 mm Gating with a 50 duty cycle would require motionmargins of 30 mm The only change in the relative rankings would be for the two with thewidest motion margins namely tracking with 200 ms latency and gating with a 50 dutycycle In this case tracking with 200 ms latency would have a narrower motion margin

For tracking strategies to have narrower motion margins than gating strategies the latencymust be reduced to below 150 ms With a latency of 200 ms the gating strategies had narrowermargins Even with the potential reductions in the effects of latency the gating strategieswith duty cycles of 33 had narrow margins than tracking Latencies near 100 ms or lowerare measured on commercially-available tracking systems (Pepin et al 2011b Depuydt et al2011) At latencies above 150 ms gating strategies require equal or narrower motion marginsthan tracking strategies

By using the type of data and analysis presented in this work the decision of a motionmanagement strategy can be tailored to a particular patientrsquos motion and a particular machinersquosdelivery characteristics in arriving at a data-driven optimal strategy which maintains a highprobability of target coverage while minimizing extraneous dose outside the target In thismanner a final decision for motion management strategy may be made by the clinician afterevaluating the pros and cons of the various available approaches for each specific patient andtreatment scenario

References

Balter J M Wright J N Newell L J Friemel B Dimmer S Cheng Y Wong J Vertatschitsch E and Mate T P 2005Accuracy of a wireless localization system for radiotherapy Int J Rad Oncl Biol Phys 61 933ndash37 (availableat httpwwwredjournalorgarticleS0360-3016(04)02839-1abstract)

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Cervino L I Chao A K Y Sandhu A and Jiang S B 2009 The diaphragm as anatomic surrogate for lung tumor motionPhys Med Biol 54 3529ndash41

Cervino L I Du J and Jiang S B 2011 MRI-guided tumor tracking in lung cancer radiotherapy Phys MedBiol 56 3773ndash85

Cho B Poulsen P R and Keall P J 2010 Real-time tumor tracking using sequential kV imaging combinedwith respiratory monitoring a general framework applicable to commonly used IGRT systems Phys MedBiol 55 3299ndash316

Cho W Kielar K N Mok E Xing L Park J-H Jung W-G and Suh T-S 2011 Multisource modeling of flattening filterfree (FFF) beam and the optimization of model parameters Med Phys 38 1931ndash42

Depuydt T et al 2011 Geometric accuracy of a novel gimbals based radiation therapy tumor tracking system RadiotherOncol 98 365ndash72

DrsquoSouza W D Naqvi S A and Yu C X 2005 Real-time intra-fraction-motion tracking using the treatment couch afeasibility study Phys Med Biol 50 4021ndash33

Engelsman M Sharp G C Bortfeld T Onimaru R and Shirato H 2005 How much margin reduction is possible throughgating or breath hold Phys Med Biol 50 477ndash90

George R Suh Y Murphy M Williamson J Weiss E and Keall P 2008 On the accuracy of a moving average algorithmfor target tracking during radiation therapy treatment delivery Med Phys 35 2356ndash65

Hoogeman M Prevost J-B Nuytens J Poll J Levendag P and Heijman B 2009 Clinical accuracy of the respiratorytumor tracking system of the Cyberknife assessment by analysis of log files Int J Radiat Oncol BiolPhys 74 297ndash303

Hugo G D Yan D and Liang J 2007 Population and patient-specific target margins for 4D adaptive radiotherapy toaccount for intra- and inter-fraction variation in lung tumour position Phys Med Biol 52 257ndash75

International Commission on Radiation Units and Measurements 1999 Prescribing recording and reporting photonbeam therapy Report 62 wwwicruorg

Jin J-Y and Yin F-F 2005 Time delay measurement for linac based treatment delivery in synchronized respiratorygating radiotherapy Med Phys 32 1293ndash6

Keall P J et al 2006 The management of respiratory motion in radiation oncology report of AAPM Task Group 76Med Phys 33 3874ndash900

Korreman S Mostafavi H Le Q-T and Boyer A L 2006 Comparison of respiratory surrogates for gated lungradiotherapy without internal fiducials Acta Oncol 45 935ndash42

Korreman S S Juhler-Noslashttrup T and Boyer A L 2008 Respiratory gated beam delivery cannot facilitate marginreduction unless combined with respiratory correlated imaged guidance Radiother Oncol 86 61ndash8

Li R Lewis J H Cervino L I and Jiang S B 2009 A feasibility study of markerless fluoroscopic gating for lung cancerradiotherapy using 4DCT templates Phys Med Biol 54 N489ndash500

Mageras G S Yorke E Rosenzweig K Braban L Keatley E Ford E Leibel S A and Ling C C 2001 Fluoroscopicevaluation of diaphragmatic motion reduction with a respiratory gated radiotherapy system J Appl Clin MedPhys 2 191ndash200

Murphy M J and Dieterich S 2006 Comparative performance of linear and nonlinear neural networks to predictirregular breathing Phys Med Biol 51 5903ndash14

Pepin E W Wu H and Shirato H 2011a Dynamic gating window for compensation of baseline shift in respiratory-gatedradiation therapy Med Phys 38 1912ndash8

Pepin E W Wu H Zhang Y and Lord B 2011b Correlation and prediction uncertainties in the CyberKnife Synchronyrespiratory tracking system Med Phys 38 4036ndash44

Sawant A Dieterich S Svatos M and Keall P 2010 Failure mode and effect analysis-based quality assurance fordynamic MLC tracking systems Med Phys 37 6466ndash79

Sawant A Smith R L Venkat R B Santanam L Cho B Poulsen P Cattell H Newell L J Parikh P and Keall P J2009 Toward submillimeter accuracy in the management of intrafraction motion the integration ofreal-time internal position monitoring and multileaf collimator target tracking Int J Radiat Oncol BiolPhys 74 575ndash82

Sharp G C Jiang S B Shimizu S and Shirato H 2004 Prediction of respiratory tumour motion for real-time image-guided radiotherapy Phys Med Biol 49 425ndash40

Shirato H et al 2003 Feasibility of insertionimplantation of 20 mm-diameter gold internal fiducial markers forprecise setup and real-time tumor tracking in radiotherapy Int J Radiat Oncol Biol Phys 56 240ndash7

Smith R L Yang D Lee A Mayse M L Low D A and Parikh P J 2011 The correlation of tissue motion within thelung implications on fiducial based treatments Med Phys 38 5992ndash7

Sohn M Sobotta B and Alber M 2012 Dosimetric treatment course simulation based on a statistical model ofdeformable organ motion Phys Med Biol 57 3693ndash709

Stroom J C de Boer H C J Huizenga H and Visser A G 1999 Inclusion of geometrical uncertainties in radiotherapytreatment planning by means of coverage probability Int J Rad Oncol Biol Phys 43 905ndash19


Suh Y Dieterich S Cho B and Keall P J 2008 An analysis of thoracic and abdominal tumour motion for stereotacticbody radiotherapy patients Phys Med Biol 53 3623ndash40

van Herk M Remeijer P Rasch C and Lebesque J V 2000 The probability of correct target dosage dose-populationhistograms for deriving treatment margins in radiotherapy Int J Radiat Oncol Biol Phys 47 1121ndash35

Vedam S S Keall P J Docef A Todor D A Kini V R and Mohan R 2004 Predicting respiratory motion for four-dimensional radiotherapy Med Phys 31 2274ndash83

Wang L Kielar K N Mok E Hsu A Dieterich S and Xing L 2012 An end-to-end examination of geometry accuracyof IGRT using a new digital accelerator equipped with onboard imaging system Phys Med Biol 57 757ndash69

Yoon J-W Sawant A Suh Y Cho B-C Suh T-S and Keall P 2011 Experimental investigation of a movingaveraging algorithm for motion perpendicular to the leaf travel direction in dynamic MLC target trackingMed Phys 38 3924ndash31

Zhang Q Chan M Song Y and Burman C 2012 Three dimensional expansion of margins for single-fraction treatmentsstereotactic radiosurgery brain cases Int J Med Phys Clin Eng Radiat Oncol 1 15ndash22

1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

OPEN ACCESSIOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY

Phys Med Biol 57 (2012) 6347ndash6369 doi1010880031-915557206347

Evaluation of motion management strategies based onrequired margins

D Sawkey M Svatos and C Zankowski

Varian Medical Systems 3120 Hansen Way Palo Alto CA 94304 USA

E-mail darensawkeyvariancom

Received 13 April 2012 in final form 26 July 2012Published 19 September 2012Online at stacksioporgPMB576347

AbstractStrategies for delivering radiation to a moving lesion each require a marginto compensate for uncertainties in treatment These motion margins havebeen determined here by separating the total uncertainty into componentsProbability density functions for the individual sources of uncertainty werecalculated for ten motion traces obtained from the literature Motion marginsrequired to compensate for the center of mass motion of the clinical treatmentvolume were found by convolving the individual sources of uncertainty Formeasurements of position at a frequency of 33 Hz system latency was thedominant source of positional uncertainty Averaged over the ten motion tracesthe motion margin for tracking with a latency of 200 ms was 46 mm Gatingwith a duty cycle of 33 required a mean motion margin of 32ndash34 mm andtracking with a latency of 100 ms required a motion margin of 31 mm Feasiblereductions in the effects of the sources of uncertainty for example by usinga simple prediction algorithm to anticipate the lesion position at the end ofthe latency period resulted in a mean motion margin of 17 mm for trackingwith a latency of 100 ms 24 mm for tracking with a latency of 200 ms and21ndash22 mm for the gating strategies with duty cycles of 33 A crossovertracking latency of 150 ms was found below which tracking strategies couldtake advantage of narrower motion margins than gating strategies The methodsdescribed here provide a means to guide selection of a motion managementstrategy for a given patient

(Some figures may appear in colour only in the online journal)

Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 30 licence Any further distribution of this work must maintain

attribution to the author(s) and the title of the work journal citation and DOI

0031-915512206347+23$3300 copy 2012 Institute of Physics and Engineering in Medicine Printed in the UK amp the USA 6347

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References


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1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

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21 Definitions








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(g) (h)


6358 D Sawkey et al


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6362 D Sawkey et al

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6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References





21 Definitions








6350 D Sawkey et al











23 Motion traces




6352 D Sawkey et al

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6356 D Sawkey et al








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inhaleexhale

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10

15

0 10 20 30 40Time [s]

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6362 D Sawkey et al

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6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

6350 D Sawkey et al











23 Motion traces




6352 D Sawkey et al

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6354 D Sawkey et al















3 Results



6356 D Sawkey et al








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CT

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m]

inhaleexhale

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-5

0

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15

0 10 20 30 40Time [s]

-6

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Res

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m]

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-6 -4 -2 0 2 4 6

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PD

F [

mm

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6358 D Sawkey et al


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6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References







23 Motion traces




6352 D Sawkey et al

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Pos

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6354 D Sawkey et al















3 Results



6356 D Sawkey et al








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ositi

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m]

inhaleexhale

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15

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-6

-4

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4

6

Res

idua

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m]

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-2

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4

-6 -4 -2 0 2 4 6

Displacement [mm]

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80

PD

F [

mm

]

-4 -2 0 2 4 60

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6358 D Sawkey et al


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6362 D Sawkey et al

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6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

6352 D Sawkey et al

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6354 D Sawkey et al















3 Results



6356 D Sawkey et al








0 10 20 30 40Time [s]

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CT

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ositi

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inhaleexhale

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-5

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0 10 20 30 40Time [s]

-6

-4

-2

0

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4

6

Res

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m]

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4

-6 -4 -2 0 2 4 6

Displacement [mm]

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PD

F [

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(a) (b)

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6358 D Sawkey et al


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6362 D Sawkey et al

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6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References












6354 D Sawkey et al















3 Results



6356 D Sawkey et al








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CT

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inhaleexhale

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Res

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m]

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Displacement [mm]

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80

PD

F [

mm

]

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6358 D Sawkey et al


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(a) (b)

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6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References









3 Results



6356 D Sawkey et al








0 10 20 30 40Time [s]

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-5

0

5

10

15

CT

V p

ositi

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inhaleexhale

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-5

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5

10

15

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-6

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-2

0

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4

6

Res

idua

l [m

m]

0 10 20 30 40

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-2

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4

-6 -4 -2 0 2 4 6

Displacement [mm]

0

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60

80

PD

F [

mm

]

-4 -2 0 2 4 60

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(a) (b)

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(g) (h)


6358 D Sawkey et al


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-5 0 5 100

5

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PD

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]

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10

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30

-5 0 5 100

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6362 D Sawkey et al

0 02 04 06 08 1

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12

0 02 04 06 08 1


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(a) (b)

(c) (d) (e)











6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

6356 D Sawkey et al








0 10 20 30 40Time [s]

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Pos

ition

[mm

]CTVmarker

0 10 20 30 40

0

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20


-10

-5

0

5

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15

CT

V p

ositi

on [m

m]

inhaleexhale

-5 0 5 10

-5

0

5

10

15

0 10 20 30 40Time [s]

-6

-4

-2

0

2

4

6

Res

idua

l [m

m]

0 10 20 30 40

-4

-2

0

2

4

-6 -4 -2 0 2 4 6

Displacement [mm]

0

20

40

60

80

PD

F [

mm

]

-4 -2 0 2 4 60

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(a) (b)

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6358 D Sawkey et al


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-5 0 5 100

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PD

F [

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]

-5 0 50

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-5 0 5 100

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30

-5 0 5 100

5

10

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20


0

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(a) (b)

(c) (d)

(e) (f)

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(i) (j)




6360 D Sawkey et al

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6362 D Sawkey et al

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6364 D Sawkey et al




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6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References


0 10 20 30 40Time [s]

0

10

20

Pos

ition

[mm

]CTVmarker

0 10 20 30 40

0

10

20


-10

-5

0

5

10

15

CT

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ositi

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m]

inhaleexhale

-5 0 5 10

-5

0

5

10

15

0 10 20 30 40Time [s]

-6

-4

-2

0

2

4

6

Res

idua

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m]

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-4

-2

0

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-6 -4 -2 0 2 4 6

Displacement [mm]

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6358 D Sawkey et al


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-5 0 5 10 150

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[mm

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6362 D Sawkey et al

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argi

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abcdefg

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8

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(a) (b)

(c) (d) (e)











6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

6358 D Sawkey et al


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[mm

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abcdefg

hij

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30


0 10 20 300

10

20

-5 0 5 10 150

10

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30

40

-5 0 5 10 150

5

10

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-5 0 5 100

5

10

15

PD

F [

mm

]

-5 0 50

5

10

15

20

25

-5 0 5 100

10

20

30

-5 0 5 100

5

10

15

20


0

5

10

15

20

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-10 -5 0 5 10 150

10

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6362 D Sawkey et al

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2

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8

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(a) (b)

(c) (d) (e)











6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References


-5 0 5 100

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10

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40

-5 0 5 10 150

5

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5

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PD

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5

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5

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0

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6362 D Sawkey et al

0 02 04 06 08 1

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0 02 04 06 08 10

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8

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0 02 04 06 08 1


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(a) (b)

(c) (d) (e)











6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

6360 D Sawkey et al

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6362 D Sawkey et al

0 02 04 06 08 1

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12

0 02 04 06 08 10

2

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8

10

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0 02 04 06 08 1


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(a) (b)

(c) (d) (e)











6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References











6362 D Sawkey et al

0 02 04 06 08 1

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argi

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8

10

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0 02 04 06 08 1


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(a) (b)

(c) (d) (e)











6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References







6364 D Sawkey et al




4 Discussion
















6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References










6366 D Sawkey et al












5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References



5 Conclusions





References


6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

6368 D Sawkey et al



































1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References








1 Introduction


21 Definitions


23 Motion traces




3 Results




4 Discussion







5 Conclusions

References

evaluation of motion management strategies based on required margins

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