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Motion mitigation in scanned ion beam therapy through 4D-optimization
Physica Medica xxx (2014) 1e8
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Motion mitigation in scanned ion beam therapy through 4D-optimization Christian Graeff Biophysics, GSI Helmholzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 January 2014 Received in revised form 28 March 2014 Accepted 31 March 2014 Available online xxx
The treatment of moving tumors remains challenging, especially with scanned ion beam therapy due to interplay effects and the strong range dependence. This is especially true in the context of radiosurgery with high dose delivered in few or single fractions. Inverse treatment planning on the entire 4D-CT may result in conformal plans inherently adapted to the moving anatomy of the patient. Existing studies on this topic for photon therapy are reviewed, but arguably the benefits for ion beam therapy can be even greater. Compared to the main conformal mitigation technique of beam tracking, 4D-optimization permits a) easier, offline handling of range changes, b) handling of complex motion patterns, and c) improved dose shaping capabilities outside of the target. Different approaches for 4D-optimization in scanned ion beam therapy are proposed and compared, together with delivery methods that provide the necessary synchronization between irradiation and detected patient motion. Potential solutions for the improvement of robustness in 4D-optimization are discussed. A method for delivery of homogenous doses to each motion phase is presented that might be a potential solution for robust conformal dose delivery for future clinical use. In an exemplary lung cancer patient case with a large motion amplitude, 4D-optimization resulted in conformal dose coverage while beam tracking did not. In conclusion, different strategies of 4D-optimization could provide increased OAR sparing and highly conformal dose delivery for targets with complex motion patterns and large amplitudes. Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: Treatment planning 4D-optimization Motion mitigation Intrafractional motion
Introduction Motion mitigation in radiotherapy is a crucial element of treating tumors or also non-malignant diseases of the lung or upper abdomen. Many of these cancers have a high incidence and are associated with high mortality [1]. Recent advances in radiotherapy have led to high local control rates at least for early stage NSCLC or small metastases in the lung [2]. Treatment of atrial fibrillation by radiotherapy is currently under investigation and might offer huge benefits to a large patient population [3,4]. The high doses applied in single or few fractions in these strategies increase the benefit of motion mitigation techniques leading to highly conformal dose distribution. Thus, the normal tissue can be spared more effectively through the use of a smaller PTV that still ensures adequate dose coverage. Also, as fractionation can no
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longer be used to average out dose errors, the necessary precision of such strategies has to be higher. Motion mitigation in scanned particle therapy has to cope with two additional effects in comparison to photon therapy, namely the finite range of the particle beam and the interference between beam scanning and target motion (interplay). The breathing motion can lead to large changes in radiological depth or range, caused for example by the solid tumor moving in and out of a given plane. A failure to consider this effect leads to massive dose errors due to under- and overshooting [5]. On the other hand, the physical dose distribution and biological effectiveness of particles permit for an even stronger sparing of normal tissue, so that this increased complexity can be justified. Several motion mitigation techniques exist, such as rescanning, gating, or beam tracking with different advantages and disadvantages. Also motion reduction techniques such as abdominal compression, breath holding, jet ventilation or irradiation under apnea can be employed just as under photon therapy. Nevertheless, a 4D-optimization strategy might lead to
http://dx.doi.org/10.1016/j.ejmp.2014.03.011 1120-1797/Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Graeff C, Motion mitigation in scanned ion beam therapy through 4D-optimization, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.03.011
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the increased conformity and possibly also robustness required by radiosurgery. 4D treatment plan optimization considers the patient motion explicitly already in the planning stage using a 4D-CT instead of a 3D-CT for planning. In this way, the complex target but also OAR motion can be resolved through inverse treatment planning and can also already include the range changes caused by the motion. This latter part is crucially important for conformal particle therapy [6]. Finally, a prerequisite for 4D-optimization is also a 4D delivery that synchronizes the 4D plan to the actual patient motion during treatment. This synchronization is an integral part of 4D-optimization, needed to fulfill the assumptions on the patient motion made in the planning step. In this paper, existing efforts for 4D treatment planning in photon therapy are presented. For particle therapy, only a few studies has been published yet, but arguably the benefit of 4Doptimization is even greater due to the large dependency on beam range. Besides the theoretical background, also a set of practical realizations for 4D-optimization and scanned beam delivery is presented, exploring also specific delivery methods for particle therapy. Review of 4D-optimization in photon therapy A number of theoretical and practical realizations of 4D-optimized treatment planning has been presented for photon therapy. A principal concept paper by Keall [7] delineated steps for the optimization of an IMRT plan on the entire 4D-CT. This necessitates deformable image registration (DIR) to accumulate dose across all motion phases of the 4D-CT. Keall also gave an outlook on potential delivery schemes using a dynamic multi-leaf collimators (DMLC). The finite velocity and width of the DMLC posed a major obstacle for the synchronized delivery which restrains the dose gradients between motion phases and was investigated by Papiez et al. [8,9]. Several authors also published ideal 4D-optimized IMRT plans, which did not consider the finite leaf speed or size [10,11]. Ma et al. [12] not only included realistic DMLC motion, but also constrained the motion such that fiducials in the tumor remained visible on MV portal imaging, an important feature for a practical realization of tumor tracking. Zhang et al. [13] published a method for tomotherapy, where the synchronization of the delivery was achieved through the gantry rotation together with breath coaching for the patient [14]. Similarly, arc therapy was investigated where both the gantry rotation as well as the DMLC was used for dose shaping and the synchronization of the delivery. A scheme for the assignment of motion phases to the gantry angle was proposed [15e17]. Only a few papers present an experimental validation of 4Doptimization methods, which might be considered important due to the requirements on synchronized delivery. In a paper on robotic radiosurgery, Schlaefer et al. [18] used the CyberKnife (AccuRay Inc. USA) on a moving 3D target, where 4D-optimized beam tracking lead to improved OAR sparing compared to standard beam tracking in the presence of differential motion. Tewatia et al. showed the possibility of DMLC tracking through synchronized delivery, optimized on a single CT phase [19], and in a later conference proceeding [20] on multiple CT phases where they also showed the influence of plan parameters on the plan quality. In general, the studies found 4D-optimization to deliver highly conformal doses to the target, considerably better than margin strategies [21], in shorter treatment times than gated delivery [10,16,17]. The dose to OARs could be reduced also in comparison to conformal 3D-optimized strategies, though this effect was most pronounced in the case of artificial digital phantoms with a large
differential motion between target and OAR [15e17,22,23]. The reduced dose to normal tissue also in patient studies could be exploited for further dose escalation [17]. Robustness issues were addressed by Nohadani et al. [23] and Chin et al. [17], who both studied the effects of desynchronized delivery, i.e. dose delivered to other but the intended motion phases. In the study of Chin et al., a systematic shift of all beam spots by two motion phases mainly led to a degradation of the GTV dose of up to 10%. Up to 20% of beams could be randomly delivered either two phases too early or too late without compromising plan quality for both target and OARs. Li et al. developed a 4D-optimization method that represented an improvement over standard ITV concepts though dose delivery was not completely conformal to the target. They showed reduced normal tissue doses as well as the robustness of their method by calculating the dose of the original plan on repeat 4D-CTs in a limited number of patients [21]. In summary, a wide array of 4D-optimization techniques for different state-of-the-art photon treatment modalities has been investigated. They show the potential of 4D-optimization for motion compensation and improved dose shaping to spare normal tissue. Robustness and clinical applicability remain an issue for future studies. 4D-optimization in ion beam therapy Rationale for 4D-optimization in ion beam therapy Resulting from the physical characteristics of the particle beam, the dose distribution strongly depends on the correctly assessed water-equivalent range. A range mismatch leads to under- and overshoot and thus usually to target underdosage as well as hot spots in normal tissue. Especially in the lung due to its high density differences, the tumor and thorax motion is associated with large range changes over the motion cycle [24,25]. The 4DCTs do not only contain the anatomic motion but also depict the range changes and are thus even more useful for particle than for photon therapy. Range changes can be mitigated through range-considering ITVs, but this leads to large increases in target volume and thus irradiated normal tissue, even in excess of a geometric ITV as useful for photon therapy [6]. In addition, these range-ITVs are fieldspecific, which makes multifield optimization (intensity modulated particle therapy, IMPT) at least difficult [25]. An advantage of scanned particle therapy is the possibility of fast magnetic deflection of the beam, which allows for flexible motion mitigation techniques. A direct application is beam tracking, where online detected motion vectors are compensated, leading potentially to highly conformal doses [26]. This appealing technology has a number of disadvantages though, which might be overcome by 4D-optimization: The magnetic deflection works only for lateral motion, for range changes moving absorber wedges have to be employed, which is challenging and considerably slower [27]. Even with state-ofthe-art accelerator technology, changing between adjacent energies, equivalent to typically 3e5 mm in range, takes around 80 ms [28]. This is not sufficient for compensation of changes observed in the lung.A 4D-optimized plan includes the motion as well as range changes already, so that an online device for fast range changes is no longer necessary. As such, a hardware solution such as the sliding wedges can be replaced by an offline software solution. The added tracking vector only compensates transitional motion, but cannot adequately deal with more complex motion
Please cite this article in press as: Graeff C, Motion mitigation in scanned ion beam therapy through 4D-optimization, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.03.011
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patterns, which leads to dose errors [29]. In 4D-optimization, any kind of motion can be included in the treatment plan, also rotations or deformations. Finally, the compensation of the tumor motion leads to dose inhomogeneities in tissues of the entry channel with differential motion (‘inverse interplay [30]), as typically seen in the chest wall. As the temporal dose distribution is known for 4D-optimized plans, also the out-of-target dose is known in advance, which could be critical for OAR dose constraints. In principle, for both beam tracking and 4D-optimization possible dose distributions for different motion patterns can be pre-computed to assess robustness. But for tracking, the number of degrees of freedom and uncertainty are considerably higher as every beam spot could be applied to any motion phase, making a realistic assessment more difficult.
Cost function for 4D-optimization The 4D-optimization problem can be solved by minimizing the cost function given in equation (1), given as the squared difference between prescribed dose Dpre and actual dose Dact. Only overdose is counted for OARs, which are assigned a specific weighting factor w. The actual dose depends on the particle numbers N assigned to each beam spot j in each motion phase k. The voxels i are transformed to each motion phase k of the 4D-CT phases by deformable image registration (DIR). Then, the factor cijk is calculated, which describes the contribution of each beam spot j in motion phase k to the given voxel. The resulting dose matrix containing all cijk therefore already includes the target motion and the correct ranges.
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This cost function is a 4D adaptation of the existing 3D implementation of TRiP [31]. m X v h i2 X ! ! i Dik E N ¼ pre N k Dact k¼1 i¼1
þ wOAR
m OAR i2 X Xh ! i Dik ; pre N k Dact þ
k¼1 i¼1
r ! ! X cijk Njk ; Dik act N k ¼ RBE cijk ; N k
½Aþ ¼
(1)
j¼1
AcA > 0 0 otherwise
The non-linear RBE is calculated using the local effect model (LEM) [32]. It depends on the mixed field irradiation of all beam spots from all fields in all motion phases contributing to a voxel. Therefore, it is not possible to warp the dose from one phase to another; rather all beam spot contributions have to be collected in one reference phase. Workflow The general workflow for creating and delivering plans either for 3D or 4D-optimization as well as 4D-dose recalculation is shown in Fig. 1. Both flowcharts are independent of the specific motion mitigation method used, but illustrate some fundamental differences. The workflow for 4D-dose calculation is adapted from Richter et al. [33]. Both start from treatment planning, respectively on a 3D-CT and a 4D-CT. The 4D-dose calculation in both cases
Figure 1. Workflow for both 3D (top) and 4D (bottom) treatment planning as well as delivery and dose recalculation for a moving target. A major difference is the inclusion of the 4D-CT for 4D-optimization and the resulting change of ‘temporal correlation’ from an output of to an input for dose delivery.
Please cite this article in press as: Graeff C, Motion mitigation in scanned ion beam therapy through 4D-optimization, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.03.011
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requires a 4D raster treatment plan (RST), which describes which beam spots were delivered to which 4D-CT motion phase. In case of the 3D-optimized plans, the 4DRST is a result of correlating the dose delivery timing to a motion surrogate. This means that the 4D-dose distribution is essentially unknown during treatment planning, though it can be simulated before delivery using calculated delivery times. In contrast, the 4D-optimization directly results in a 4DRST; the 4D-dose distribution is thus known. Consequently, the vector fields from DIR are an integral part of the optimization, though not in case of uniform doses to each motion phase, see the next section. Treatment planning also has to provide a prescription for the synchronization of the 4DRST delivery relative to patient motion. The additional task of the 4D treatment control system (TCS) is to realize this synchronization. Again in both cases, the 4D dose can be recalculated using measured delivery data including particle numbers, exact positions, and timing of each beam spot, as well as patient motion monitoring. Realizations of 4D-optimization Different approaches resulting in a deliverable treatment plan are feasible; an overview is given in Table 1. The straightforward approach is to create a set of identical 3DRST geometries, one for each motion phase k, in the following RSTk. The particle numbers can then be optimized following equation (1). This full 4D-optimization approach leads to very large problem sizes, especially if also multiple fields are optimized simultaneously. Due to the high number of beam spots, the dose can be shaped effectively, delivering different dose distributions to each motion phase. This can be exploited for OAR sparing in case of differential motion between target and OARs [34]. Alternatively, the treatment time especially for systems with a long energy change (3.2 s at GSI) could be reduced by exploiting range changes over the motion cycle. The overall needed number of iso-energy slices (IES) could be reduced by irradiating distal target regions in motion phases where the entry channel has a low radiological path length and vice versa. Heuristic solutions Adequate dose coverage is also possible with a lower number of beam spots, provided they are selected such that a suitable 4D dose can be realized. This is not trivial: if beam spots are distributed randomly from a 3DRST to each motion phase, dose coverage is in general not possible. A kind of interplay pattern will result from different beam spots covering identical locations of the moving target. Feasible distributions can be achieved by using a beam tracking plan as basis, and re-optimizing particle numbers after application
of a chosen set of tracking vectors. This approach uses the same number of beam spots as a 3D plan, but each spot is assigned to a specific motion phase. The treatment control system has to ensure the synchronized delivery to a measured motion surrogate during delivery using fast gating for each motion phase; it was therefore named ‘multigating’ [35]. Another option is to let each RSTk cover only a subsection of the target (4D-sectors). Through simultaneous optimization, the sum of the RSTk leads to a homogenous dose. The number of beam spots as well as the steepness of the dose gradients can be controlled through an overlap factor of the individual RSTk. Computation time and number of beam spots can be reduced to about 30% of full 4Doptimization without compromising target coverage [36]. Using the arrangement of the target sections relative to the main motion direction, an efficient means of dose shaping is possible. Also the sections could be arranged to exploit range differences between motion phases to reduce the overall number of IES, similar as for the full 4D-optimization. The layout of the sectors is currently done manually, but could also be automated with respect to the different stated criteria.
Uniform dose to each motion phase In case that either no differential motion is present or OAR sparing through optimization over all motion phases is not necessary, it is also possible to optimize treatment plans for each motion phase separately to a uniform dose. For each phase, the full dose constraints can be used, leading to a set of beam weights Nk. Similar to rescanning, the particle numbers for each motion phase are then weighted by their duration tk relative to the complete motion period T, resulting in the final beam weights Nk0 . The single RSTk thus deliver a uniform dose to each phase. This 4D-rescanning (or also single phase uniform dose, SPUD) approach has an improved robustness due to the lacking dose gradients between motion phases. Random, periodic errors are reduced similar as in rescanning, for example interplay due to residual motion within motion phases. The optimization problem also becomes much more tractable when m plans can be computed separately according to equation (2). For individual field optimization (SFUD), each field is optimized to the full target dose, and particles numbers are weighted also by the number of fields f. For IMPT, all fields in a single phase can be optimized to the target dose, and f is set to 1 in equation (2). v h i2 X ! ! i Dik Ek N k ¼ pre N k Dact i¼1
þ wOAR Table 1 Overview of the presented 4D-optimization techniques. Problem size shows the approximate increase of the size of the dose matrix in the cost function. With the exception of the 4D-ITV, this is proportional to the number of delivered beam spots. Modality
RST Motion Problem Characteristics monitoring size
4D-ITV
3D No
2.m
4D-multigating 3D Yes
1
4D-sectors
m/4
4D Yes
4D-rescanning 4D Yes
m1
Full 4D4D Yes optimization
m
Range-sensitive ITV for multifield optimization, enlarged VOI Based on beam tracking, difficult timing, only small changes to TCS Irradiate subset of CTV in each phase, limited dose shaping & problem size Uniform dose to phases: robust due to lack of gradients, no DIR for optimization Huge problem size, dose shaping & OAR sparing possible
! t ! Nk0 ¼ k Nk fT
OAR Xh i¼1
i2 ! i Dik ; pre N k Dact
(2)
þ
The drawback of this method is that no additional dose shaping is possible, and the motion can also not be exploited to reduce the number of iso-energy slices. Sparing of OARs can be achieved similar to standard IMPT by weighting the fields. In this case, the resulting gradients between the fields do not necessarily match for each motion phase, partially negating the stated benefit for robustness. The weighting factor for the particle numbers especially for SFUD can be high. A lower limit (typically 5000) for the final particle number in each beam spot is necessary to permit dose monitoring. During the optimization, this limit thus has to be set higher accordingly, which might be difficult for low fraction doses. This method is therefore especially suited to hypofractionation and radiosurgery.
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C. Graeff / Physica Medica xxx (2014) 1e8
A big advantage of this method is that DIR is not needed during treatment plan optimization, but only to propagate contours from a reference phase, which can be verified comparably easy. The DIR is a major potential source of errors, so that removing it at least from the planning stage also increases the robustness. It is still needed to judge total doses to normal tissue through 4D-dose calculation, though total dose constraints are guaranteed as they were observed in every optimization for each motion phase. IMPT for ITV irradiation The irradiation of an ITV can be considered a special case of a possible application for 4D-IMPT-optimization. Due to the necessary consideration of range changes, a valid ITV for ion beam therapy is field-specific [6,24]. This makes multifield optimization challenging. A solution to this problem is to include the range variations in the treatment planning itself, by optimizing a single 3DRST on each motion phase. The RST has to be large enough to cover the target propagated to each motion phase. In contrast to equation (1), equation (3) thus does not show a motion phase specific beam spot ! weight vector N k.
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The second delivery concept addresses this inherent drawback by introducing a flexible sequence of beam spots taken from any of the RSTk to be irradiated. The TCS selects unirradiated beam spots from one RSTk depending on the current detected motion phase. In contrast to beam tracking, it is now known in which motion phase a beam spot will be irradiated, but no longer when this will be. The increased flexibility basically eliminates the timing uncertainty of the first approach, making a smooth, efficient irradiation more likely. The beam only needs to be gated when the RSTk for the current beam energy was already completely irradiated. Even this drawback could be reduced in systems with a short time for energy changes such as at PSI or NIRS, by also including adjacent IES in the sequence. This second approach can be used for any of the proposed strategies resulting in a 4DRST. An exemplary treatment planning study Methods
The result of this optimization is thus a treatment plan that fulfills the dose requirements independently of the motion phase. It can therefore be irradiated as any standard treatment plan, but has to be combined with rescanning to compensate interplay effects. This equation can be directly used for multifield optimization, with the known benefits for OAR sparing. A heuristic solution leading to a smaller problem size was proposed by Graeff et al. [25].
To show the feasibility of the presented methods, a four field treatment plan modeled on clinical plans from NIRS [38] was computed on single lung cancer patient with a 4D-CT provided by MDACC, Houston, TX. All motion phases were registered (DIR) to the end-exhale phase using Plastimatch [39]. Fields were optimized individually to a uniform dose (SFUD) or for selected methods also simultaneously (IMPT) to a single fraction total dose of 17.7 Gy (RBE) according to LEM IV [40]. For the computation of the 4D-optimized plans, ideal motion monitoring as well as the reproducibility of the 4D-CT were assumed resulting in a perfectly synchronized delivery. For comparison, a static reference irradiation on the end-exhale reference phase, an interplay case of the same static plan applied to the 4D-CT and a beam tracking plan were also simulated. DVH parameters were evaluated: V95 for dose coverage, V107 for overdose, D5-D95 for homogeneity and the conformity number CN.
Delivery
Results
To fulfill the assumed distribution of beam spots to motion phases, the delivery has to be synchronized to the patient motion. Motion monitoring is therefore an essential part of the delivery. The irradiation should also be efficient with a high duty cycle for short treatment times. Two methods were investigated as add-ons to the existing TCS implemented at GSI Cave M. Details and results of feasibility experiments can be found in Refs. [35,36]. The first one was designed for the 4D-optimized tracking (multigating) strategy and is comparably close to the original TCS for beam tracking. As the RST retains the number as well as the sequence of beam spots, the TCS keeps the synchronization to the measured patient motion through fast gating. Beam spots are only irradiated to their designated motion phase; it is a part of the treatment planning to provide a sequence of beam spots that permit a high duty cycle irradiation. This in essence means that during planning, the required time for irradiating the spots and the breathing period have to be roughly known. In practice, each motion phase is assigned a lower irradiation time as expected, so that the spot sequence is more likely to be synchronized to the breathing motion. A failure to complete the assigned spots with one motion phase leads to a gate over a whole breathing cycle, elongating the treatment time. The distribution of beam spots in a sequence likely to be smoothly irradiated is non-trivial due to the uncertainties involved, even without considering the spill pauses of the synchrotron. This is greatly facilitated by efficient online intensity control, as for example also needed for phase-controlled rescanning [37].
Dosimetric results are shown in Table 2. For SFUD, 3D-optimized beam tracking though improving on interplay dose errors could not achieve acceptable dose parameters, with marked under- and overdoses, see also Fig. 2. Dose coverage could be restored to the level of the static plan by 4D-optimization methods. For 4D-multigating and 4D-sectors the dose homogeneity was slightly reduced in comparison to the static plan due to their inherent dose gradients. 4D-rescanning essentially exceeded the results of the static irradiation as it essentially represents the average of numerous optimizations to a uniform dose. The 4D-sector and 4D-rescanning
m X v h m OAR i2 i2 X Xh ! X ! ! i i Dik Dik E N ¼ pre N Dact þwOAR pre N Dact k¼1 i¼1
k¼1 i¼1
þ
(3)
Table 2 Dosimetric results from the patient simulation study for both single field (SFUD) and simultaneous multifield (IMPT) optimization. Results were partially previously published in Refs. [34,35]. V95 [%] SFUD Static Interplay 3D beam tracking 4D-rescanning 4D-sectors 4D-multigating IMPT Static Interplay 4D-rescanning 4D-sectors
V107 [%]
D5-D95 [%]
CN [%]
98.5 72.5 89.5 99.4 98.7 99.9
0.0 6.5 11.5 0.0 0.0 0.0
2.7 29.9 19.9 2.4 3.8 4.2
70.8 52.5 62.1 75.6 81.5 64.6
99.3 76.4 100.0 97.7
0.0 13.9 0.0 0.1
4.3 31.5 2.2 6.1
83.4 56.4 82.1 88.2
Please cite this article in press as: Graeff C, Motion mitigation in scanned ion beam therapy through 4D-optimization, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.03.011
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Figure 2. Dose cuts from the SFUD patient study illustrating the different 4D-optimization techniques. On the left (topebottom), a reference static plan on end-exhale, an interplay pattern and a 3D-optimization beam tracking irradiation, which partially restores the interplay dose errors. On the right, 4D-multigating, 4D-sectors, and 4D-rescanning show good dose coverage with slightly varying conformity to the target.
method even resulted in better conformity than the static plan, likely due to the higher number of beam spots involved and thus greater degree of freedom available to the optimizer. The dose cuts in Fig. 2 especially highlight the difference between 4D-multigating, which was restricted to the same size as the static RST to 4Drescanning and 4D-sectors which both had a considerably higher number of beam spots. In the IMPT plans (see Fig. 3 and Table 2), with again increased degrees of freedom, CN was further increased for all modalities, but now strongly inhomogeneous fields of 4D-sectors also lead to a slightly worse D5-D95. 4D-sectors with its inhomogeneous doses to each motion phase offered the highest conformity, but also might be the least robust due to the dose gradients and resulting sensitivity to motion uncertainty. The averaging effect of 4Drescanning maintained the high homogeneity of the SFUD optimization, which now clearly exceeded the static case. Discussion In summary, a set of workable strategies for 4D-optimization in scanned ion beam therapy has been investigated. They offer highly conformal dose delivered to moving targets, with range variations factored into the treatment plan so that online range adaptations are no longer necessary. Different delivery methods that require only software changes to existing scanned beam control systems were presented, though precise motion monitoring is necessary.
The 4D-optimization concept relies heavily on the validity of the planning 4D-CT. The motion contained in the 4D-CT should be representative of the breathing trajectory occurring under treatment. Depending on the degree of variability of the breathing motion, 4D-optimization might not be useful or even do harm as it creates the illusion of successful motion mitigation which can’t be transferred to clinical reality. The same is true though to some degree for all mitigation techniques derived from a 4D-CT; be it a range-considering ITV, gating windows, or the range component of beam tracking vectors. It is currently not possible to determine range changes accurately from online motion monitoring, except from the underlying 4D-CT. A suitable motion mitigation technique should thus be chosen individually for each patient, depending on various factors such as tumor location, motion amplitude, breathing reproducibility and cooperativeness. Planning and delivery should take place within a short time period to avoid anatomical shifts. This may be challenging for certain anatomical regions such as the pancreas, which is influenced by comparably rapid bowel movement [41]. Adaptive treatment planning might be necessary, where a plan that was carefully designed and validated offline is online adapted to the current treatment situation. Care should be taken therefore to assure as far as possible a reproducible breathing of the patient, e.g., through coaching with an audiovisual feedback. Minor deviations from the expected motion trajectory cannot be avoided though, and thus have to be dealt with by robustness measures discussed in the following.
Figure 3. Dose cuts from the IMPT study showing the improved conformity to the target for both static and 4D-optimized treatment plans.
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The steepness of dose gradients between motion phases and fields in IMPT should be restricted by introducing a corresponding penalty analog to Nohadani et al. [23]. As the restriction of MLC motion is not relevant for particle therapy, the motion of the target’s center of mass could be factored in the equation. In this way, the likely overall motion of the tumor is considered, but too strong gradients due to inhomogeneous fields as a result of IMPT are avoided. For essentially all proposed 4D-optimization strategies, lateral beam tracking could be employed to compensate target motion differences to the planning 4D-CT. Lateral tracking does not incur the cost of an online range changing system, while the previous 4Doptimization would lead to comparably small residual tracking vectors. In that way, the remaining error of the uncompensated range stays small as well as a potential error of the merely transitional beam tracking used to compensate a potentially more complex motion. The residual tracking would make sense only if the data was provided by a motion monitoring system that detected or determined (e.g., by a neural network) the 3D tumor motion rather than using information from the deformation field of the planning 4D-CT. In addition, the motion monitoring system’s measurement uncertainty has to be considerably smaller than the size of the residual tracking vectors. Also, if larger deviations from the expected breathing curve occur, the above stated limitations of beam tracking will again come to bear. Also, as 4D-optimization requires or at least highly benefits from intensity control, and in some cases also necessitates timing estimations, methods like breath-sampled [42] or phase-controlled [37] rescanning could be added with little additional effort. This would help to reduce for example residual motion within motion phases or other random and periodic errors. A good way of testing the robustness of (not only) a 4D-optimized plan is the concept of artificial 4D-CTs generated with motion maps extracted from 4D-MRI [43]. In this way, continuous breathing motion of sufficient length to simulate the entire treatment is available, most likely resulting in a closer-to-reality dose calculation than 4D-CT based calculations. Breathing curves of different irregularity can be studied in detail, and robustness measures can be developed that allow the transferal of a plan from a planning 4D-CT to a clinical treatment situation. The identified likely scenarios can be included into the optimization to make it inherently robust [44,45]. This might require an improved optimization code or procedures to handle the resulting large nonlinear problems for carbon ion treatment. To this end, studies have to be conducted that systematically violate the prescribed synchronization of delivery and patient motion, similar to those already performed for photon therapy [17,23]. As already stated, carbon ion therapy using LEM requires the knowledge of the entire particle spectrum for each dose voxel, so that it is not possible to calculate individual pencil beams independent of each other. This makes such studies more complex and requires additional modifications to the existing 4D-dose calculation, especially if extended to sequential 4D-CT data derived from MRI as opposed to a single periodic 4D-CT used for the entire irradiation. The effects of residual motion within 4D-CT phases could be investigated by interpolating the voxel positions between the phases. A good estimation of beam range in this case is challenging [46]. The method of 4D-rescanning in this context is especially promising. Due to the inherent dose averaging, dose statistics in part even exceeded those of the static reference irradiation. This effect is likely to translate into robustness against variable motion, motion monitoring and range uncertainties, but this has to be further investigated in appropriate studies as outlined above.
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Finally, more experiments with realistic phantoms are needed to investigate the complex effects of delivery timing of 4D treatment plans, uncertainties in beam shape and intensity as well as in motion monitoring, before animal or possibly patient studies should be considered. Conclusion 4D-optimization is a concept that permits highly conformal doses to moving targets. It has been studied for nearly a decade in the photon community, but may result in even greater benefits for particle therapy due to the high range dependence. The feasibility of several strategies including delivery has been investigated in treatment planning studies as well as first, simple experiments. After necessary studies concerning its robustness, 4D-optimization might offer a viable route for precise motion compensation, especially for hypofractionation and radiosurgery of intrafractionally moving targets. A likely candidate for a transition to the clinic is the inherently robust 4D-rescanning method. References [1] Ferlay J, Shin HR, Bray F, Forman D, Mathers C, Parkin DM. Estimates of worldwide burden of cancer in 2008: GLOBOCAN 2008. Int J Cancer 2010;127: 2893e917. [2] Greco C, Zelefsky MJ, Lovelock M, Fuks Z, Hunt M, Rosenzweig K, et al. Predictors of local control after single-dose stereotactic image-guided intensitymodulated radiotherapy for extracranial metastases. Int J Radiat Oncol Biol Phys 2011;79:1151e7. [3] Sharma A, Wong D, Weidlich G, Fogarty T, Jack A, Sumanaweera T, et al. Noninvasive stereotactic radiosurgery (CyberHeart) for creation of ablation lesions in the atrium. Heart Rhythm 2010;7:802e10. [4] Constantinescu A, Lehmann HI, Graeff C, Packer D, Durante M, Bert C. Planning studies for non-invasive isolation of the pulmonary veins with a scanned carbon ion beam. In: PTCOG 52. Essen, Germany; 2013. [5] Bert C, Durante M. Motion in radiotherapy: particle therapy. Phys Med Biol 2011;56:R113e44. [6] Knopf AC, Boye D, Lomax A, Mori S. Adequate margin definition for scanned particle therapy in the incidence of intrafractional motion. Phys Med Biol 2013;58:6079e94. [7] Keall PJ. 4-dimensional computed tomography imaging and treatment planning. Semin Radiat Oncol 2004;14:81e90. [8] Papiez L, Rangaraj D, Keall P. Real-time DMLC IMRT delivery for mobile and deforming targets. Med Phys 2005;32:3037e48. [9] Papiez L, McMahon R, Timmerman R. 4D DMLC leaf sequencing to minimize organ at risk dose in moving anatomy. Med Phys 2007;34:4952e6. [10] Trofimov A, Rietzel E, Lu HM, Martin B, Jiang S, Chen GTY, et al. Temporospatial IMRT optimization: concepts, implementation and initial results. Phys Med Biol 2005;50:2779e98. [11] Rietzel E, Chen GTY, Choi NC, Willet CG. Four-dimensional image-based treatment planning: target volume segmentation and dose calculation in the presence of respiratory motion. Int J Radiat Oncol Biol Phys 2005;61: 1535e50. [12] Ma Y, Lee L, Keshet O, Keall P, Xing L. Four-dimensional inverse treatment planning with inclusion of implanted fiducials in IMRT segmented fields. Med Phys 2009;36:2215e21. [13] Zhang T, Jeraj R, Keller H, Lu W, Olivera GH, McNutt TR, et al. Treatment plan optimization incorporating respiratory motion. Med Phys 2004;31:1576e86. [14] Zhang T, Lu W, Olivera GH, Keller H, Jeraj R, Manon R, et al. Breathing-synchronized delivery: a potential four-dimensional tomotherapy treatment technique. Int J Radiat Oncol Biol Phys 2007;68:1572e8. [15] Ma Y, Chang D, Keall P, Xie Y, Park JY, Suh TS, et al. Inverse planning for fourdimensional (4D) volumetric modulated arc therapy. Med Phys 2010;37: 5627e33. [16] Chin E, Otto K. Investigation of a novel algorithm for true 4D-VMAT planning with comparison to tracked, gated and static delivery. Med Phys 2011;38: 2698e707. [17] Chin E, Loewen SK, Nichol A, Otto K. 4D VMAT, gated VMAT, and 3D VMAT for stereotactic body radiation therapy in lung. Phys Med Biol 2013;58: 749e70. [18] Schlaefer A, Fisseler J, Dieterich S, Shiomi H, Cleary K, Schweikard A. Feasibility of four-dimensional conformal planning for robotic radiosurgery. Med Phys 2005;32:3786e92. [19] Tewatia D, Zhang T, Tome W, Paliwal B, Metha M. Clinical implementation of target tracking by breathing synchronized delivery. Med Phys 2006;33:4330e6. [20] Tewatia D, Chebrolu V, Tolakanahalli R, Paliwal B, Tome W. Efficacy assessment of breathing phase adaptive lung tumor motion management for
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[35] Graeff C, Constantinescu A, Luchtenborg R, Durante M, Bert C. Multigating, a 4D optimized beam tracking in scanned ion beam therapy. Technol Cancer Res Treat; 2013 [Epub ahead of print]. [36] Graeff C, Luchtenborg R, Eley JG, Durante M, Bert C. A 4D-optimization concept for scanned ion beam therapy. Radiother Oncol 2013;109:419e24. [37] Furukawa T, Inaniwa T, Sato S, Shirai T, Mori S, Takeshita E, et al. Moving target irradiation with fast rescanning and gating in particle therapy. Med Phys 2010;37:4874e9. [38] Miyamoto T, Yamamoto N, Nishimura H, Koto M, Tsuji H, Mizoe JE, et al. Carbon ion radiotherapy for stage I non-small cell lung cancer. Radiother Oncol 2003;66:127e40. [39] Shackleford JA, Kandasamy N, Sharp GC. On developing B-spline registration algorithms for multi-core processors. Phys Med Biol 2010;55:6329e51. [40] Elsässer T, Weyrather WK, Friedrich T, Durante M, Iancu G, Krämer M, et al. Quantification of the relative biological effectiveness for ion beam radiotherapy: direct experimental comparison of proton and carbon ion beams and a novel approach for treatment planning. Int J Radiat Oncol Biol Phys 2010;78: 1177e83. [41] Kumagai M, Hara R, Mori S, Yanagi T, Asakura H, Kishimoto R, et al. Impact of intrafractional bowel gas movement on carbon ion beam dose distribution in pancreatic radiotherapy. Int J Radiat Oncol Biol Phys 2009;73:1276e81. [42] Seco J, Robertson D, Trofimov A, Paganetti H. Breathing interplay effects during proton beam scanning: simulation and statistical analysis. Phys Med Biol 2009;54:N283e94. [43] Boye D, Lomax T, Knopf A. Mapping motion from 4D-MRI to 3D-CT for use in 4D dose calculations: a technical feasibility study. Med Phys 2013;40: 061702. [44] Nohadani O, Seco J, Martin BC, Bortfeld T. Dosimetry robustness with stochastic optimization. Phys Med Biol 2009;54:3421e32. [45] Chen W, Unkelbach J, Trofimov A, Madden T, Kooy H, Bortfeld T, et al. Including robustness in multi-criteria optimization for intensity-modulated proton therapy. Phys Med Biol 2012;57:591e608. [46] Kraus KM, Heath E, Oelfke U. Dosimetric consequences of tumour motion due to respiration for a scanned proton beam. Phys Med Biol 2011;56: 6563e81.
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Motion mitigation in scanned ion beam therapy through 4D-optimization Christian Graeff Biophysics, GSI Helmholzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 January 2014 Received in revised form 28 March 2014 Accepted 31 March 2014 Available online xxx
The treatment of moving tumors remains challenging, especially with scanned ion beam therapy due to interplay effects and the strong range dependence. This is especially true in the context of radiosurgery with high dose delivered in few or single fractions. Inverse treatment planning on the entire 4D-CT may result in conformal plans inherently adapted to the moving anatomy of the patient. Existing studies on this topic for photon therapy are reviewed, but arguably the benefits for ion beam therapy can be even greater. Compared to the main conformal mitigation technique of beam tracking, 4D-optimization permits a) easier, offline handling of range changes, b) handling of complex motion patterns, and c) improved dose shaping capabilities outside of the target. Different approaches for 4D-optimization in scanned ion beam therapy are proposed and compared, together with delivery methods that provide the necessary synchronization between irradiation and detected patient motion. Potential solutions for the improvement of robustness in 4D-optimization are discussed. A method for delivery of homogenous doses to each motion phase is presented that might be a potential solution for robust conformal dose delivery for future clinical use. In an exemplary lung cancer patient case with a large motion amplitude, 4D-optimization resulted in conformal dose coverage while beam tracking did not. In conclusion, different strategies of 4D-optimization could provide increased OAR sparing and highly conformal dose delivery for targets with complex motion patterns and large amplitudes. Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: Treatment planning 4D-optimization Motion mitigation Intrafractional motion
Introduction Motion mitigation in radiotherapy is a crucial element of treating tumors or also non-malignant diseases of the lung or upper abdomen. Many of these cancers have a high incidence and are associated with high mortality [1]. Recent advances in radiotherapy have led to high local control rates at least for early stage NSCLC or small metastases in the lung [2]. Treatment of atrial fibrillation by radiotherapy is currently under investigation and might offer huge benefits to a large patient population [3,4]. The high doses applied in single or few fractions in these strategies increase the benefit of motion mitigation techniques leading to highly conformal dose distribution. Thus, the normal tissue can be spared more effectively through the use of a smaller PTV that still ensures adequate dose coverage. Also, as fractionation can no
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longer be used to average out dose errors, the necessary precision of such strategies has to be higher. Motion mitigation in scanned particle therapy has to cope with two additional effects in comparison to photon therapy, namely the finite range of the particle beam and the interference between beam scanning and target motion (interplay). The breathing motion can lead to large changes in radiological depth or range, caused for example by the solid tumor moving in and out of a given plane. A failure to consider this effect leads to massive dose errors due to under- and overshooting [5]. On the other hand, the physical dose distribution and biological effectiveness of particles permit for an even stronger sparing of normal tissue, so that this increased complexity can be justified. Several motion mitigation techniques exist, such as rescanning, gating, or beam tracking with different advantages and disadvantages. Also motion reduction techniques such as abdominal compression, breath holding, jet ventilation or irradiation under apnea can be employed just as under photon therapy. Nevertheless, a 4D-optimization strategy might lead to
http://dx.doi.org/10.1016/j.ejmp.2014.03.011 1120-1797/Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
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the increased conformity and possibly also robustness required by radiosurgery. 4D treatment plan optimization considers the patient motion explicitly already in the planning stage using a 4D-CT instead of a 3D-CT for planning. In this way, the complex target but also OAR motion can be resolved through inverse treatment planning and can also already include the range changes caused by the motion. This latter part is crucially important for conformal particle therapy [6]. Finally, a prerequisite for 4D-optimization is also a 4D delivery that synchronizes the 4D plan to the actual patient motion during treatment. This synchronization is an integral part of 4D-optimization, needed to fulfill the assumptions on the patient motion made in the planning step. In this paper, existing efforts for 4D treatment planning in photon therapy are presented. For particle therapy, only a few studies has been published yet, but arguably the benefit of 4Doptimization is even greater due to the large dependency on beam range. Besides the theoretical background, also a set of practical realizations for 4D-optimization and scanned beam delivery is presented, exploring also specific delivery methods for particle therapy. Review of 4D-optimization in photon therapy A number of theoretical and practical realizations of 4D-optimized treatment planning has been presented for photon therapy. A principal concept paper by Keall [7] delineated steps for the optimization of an IMRT plan on the entire 4D-CT. This necessitates deformable image registration (DIR) to accumulate dose across all motion phases of the 4D-CT. Keall also gave an outlook on potential delivery schemes using a dynamic multi-leaf collimators (DMLC). The finite velocity and width of the DMLC posed a major obstacle for the synchronized delivery which restrains the dose gradients between motion phases and was investigated by Papiez et al. [8,9]. Several authors also published ideal 4D-optimized IMRT plans, which did not consider the finite leaf speed or size [10,11]. Ma et al. [12] not only included realistic DMLC motion, but also constrained the motion such that fiducials in the tumor remained visible on MV portal imaging, an important feature for a practical realization of tumor tracking. Zhang et al. [13] published a method for tomotherapy, where the synchronization of the delivery was achieved through the gantry rotation together with breath coaching for the patient [14]. Similarly, arc therapy was investigated where both the gantry rotation as well as the DMLC was used for dose shaping and the synchronization of the delivery. A scheme for the assignment of motion phases to the gantry angle was proposed [15e17]. Only a few papers present an experimental validation of 4Doptimization methods, which might be considered important due to the requirements on synchronized delivery. In a paper on robotic radiosurgery, Schlaefer et al. [18] used the CyberKnife (AccuRay Inc. USA) on a moving 3D target, where 4D-optimized beam tracking lead to improved OAR sparing compared to standard beam tracking in the presence of differential motion. Tewatia et al. showed the possibility of DMLC tracking through synchronized delivery, optimized on a single CT phase [19], and in a later conference proceeding [20] on multiple CT phases where they also showed the influence of plan parameters on the plan quality. In general, the studies found 4D-optimization to deliver highly conformal doses to the target, considerably better than margin strategies [21], in shorter treatment times than gated delivery [10,16,17]. The dose to OARs could be reduced also in comparison to conformal 3D-optimized strategies, though this effect was most pronounced in the case of artificial digital phantoms with a large
differential motion between target and OAR [15e17,22,23]. The reduced dose to normal tissue also in patient studies could be exploited for further dose escalation [17]. Robustness issues were addressed by Nohadani et al. [23] and Chin et al. [17], who both studied the effects of desynchronized delivery, i.e. dose delivered to other but the intended motion phases. In the study of Chin et al., a systematic shift of all beam spots by two motion phases mainly led to a degradation of the GTV dose of up to 10%. Up to 20% of beams could be randomly delivered either two phases too early or too late without compromising plan quality for both target and OARs. Li et al. developed a 4D-optimization method that represented an improvement over standard ITV concepts though dose delivery was not completely conformal to the target. They showed reduced normal tissue doses as well as the robustness of their method by calculating the dose of the original plan on repeat 4D-CTs in a limited number of patients [21]. In summary, a wide array of 4D-optimization techniques for different state-of-the-art photon treatment modalities has been investigated. They show the potential of 4D-optimization for motion compensation and improved dose shaping to spare normal tissue. Robustness and clinical applicability remain an issue for future studies. 4D-optimization in ion beam therapy Rationale for 4D-optimization in ion beam therapy Resulting from the physical characteristics of the particle beam, the dose distribution strongly depends on the correctly assessed water-equivalent range. A range mismatch leads to under- and overshoot and thus usually to target underdosage as well as hot spots in normal tissue. Especially in the lung due to its high density differences, the tumor and thorax motion is associated with large range changes over the motion cycle [24,25]. The 4DCTs do not only contain the anatomic motion but also depict the range changes and are thus even more useful for particle than for photon therapy. Range changes can be mitigated through range-considering ITVs, but this leads to large increases in target volume and thus irradiated normal tissue, even in excess of a geometric ITV as useful for photon therapy [6]. In addition, these range-ITVs are fieldspecific, which makes multifield optimization (intensity modulated particle therapy, IMPT) at least difficult [25]. An advantage of scanned particle therapy is the possibility of fast magnetic deflection of the beam, which allows for flexible motion mitigation techniques. A direct application is beam tracking, where online detected motion vectors are compensated, leading potentially to highly conformal doses [26]. This appealing technology has a number of disadvantages though, which might be overcome by 4D-optimization: The magnetic deflection works only for lateral motion, for range changes moving absorber wedges have to be employed, which is challenging and considerably slower [27]. Even with state-ofthe-art accelerator technology, changing between adjacent energies, equivalent to typically 3e5 mm in range, takes around 80 ms [28]. This is not sufficient for compensation of changes observed in the lung.A 4D-optimized plan includes the motion as well as range changes already, so that an online device for fast range changes is no longer necessary. As such, a hardware solution such as the sliding wedges can be replaced by an offline software solution. The added tracking vector only compensates transitional motion, but cannot adequately deal with more complex motion
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patterns, which leads to dose errors [29]. In 4D-optimization, any kind of motion can be included in the treatment plan, also rotations or deformations. Finally, the compensation of the tumor motion leads to dose inhomogeneities in tissues of the entry channel with differential motion (‘inverse interplay [30]), as typically seen in the chest wall. As the temporal dose distribution is known for 4D-optimized plans, also the out-of-target dose is known in advance, which could be critical for OAR dose constraints. In principle, for both beam tracking and 4D-optimization possible dose distributions for different motion patterns can be pre-computed to assess robustness. But for tracking, the number of degrees of freedom and uncertainty are considerably higher as every beam spot could be applied to any motion phase, making a realistic assessment more difficult.
Cost function for 4D-optimization The 4D-optimization problem can be solved by minimizing the cost function given in equation (1), given as the squared difference between prescribed dose Dpre and actual dose Dact. Only overdose is counted for OARs, which are assigned a specific weighting factor w. The actual dose depends on the particle numbers N assigned to each beam spot j in each motion phase k. The voxels i are transformed to each motion phase k of the 4D-CT phases by deformable image registration (DIR). Then, the factor cijk is calculated, which describes the contribution of each beam spot j in motion phase k to the given voxel. The resulting dose matrix containing all cijk therefore already includes the target motion and the correct ranges.
3
This cost function is a 4D adaptation of the existing 3D implementation of TRiP [31]. m X v h i2 X ! ! i Dik E N ¼ pre N k Dact k¼1 i¼1
þ wOAR
m OAR i2 X Xh ! i Dik ; pre N k Dact þ
k¼1 i¼1
r ! ! X cijk Njk ; Dik act N k ¼ RBE cijk ; N k
½Aþ ¼
(1)
j¼1
AcA > 0 0 otherwise
The non-linear RBE is calculated using the local effect model (LEM) [32]. It depends on the mixed field irradiation of all beam spots from all fields in all motion phases contributing to a voxel. Therefore, it is not possible to warp the dose from one phase to another; rather all beam spot contributions have to be collected in one reference phase. Workflow The general workflow for creating and delivering plans either for 3D or 4D-optimization as well as 4D-dose recalculation is shown in Fig. 1. Both flowcharts are independent of the specific motion mitigation method used, but illustrate some fundamental differences. The workflow for 4D-dose calculation is adapted from Richter et al. [33]. Both start from treatment planning, respectively on a 3D-CT and a 4D-CT. The 4D-dose calculation in both cases
Figure 1. Workflow for both 3D (top) and 4D (bottom) treatment planning as well as delivery and dose recalculation for a moving target. A major difference is the inclusion of the 4D-CT for 4D-optimization and the resulting change of ‘temporal correlation’ from an output of to an input for dose delivery.
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requires a 4D raster treatment plan (RST), which describes which beam spots were delivered to which 4D-CT motion phase. In case of the 3D-optimized plans, the 4DRST is a result of correlating the dose delivery timing to a motion surrogate. This means that the 4D-dose distribution is essentially unknown during treatment planning, though it can be simulated before delivery using calculated delivery times. In contrast, the 4D-optimization directly results in a 4DRST; the 4D-dose distribution is thus known. Consequently, the vector fields from DIR are an integral part of the optimization, though not in case of uniform doses to each motion phase, see the next section. Treatment planning also has to provide a prescription for the synchronization of the 4DRST delivery relative to patient motion. The additional task of the 4D treatment control system (TCS) is to realize this synchronization. Again in both cases, the 4D dose can be recalculated using measured delivery data including particle numbers, exact positions, and timing of each beam spot, as well as patient motion monitoring. Realizations of 4D-optimization Different approaches resulting in a deliverable treatment plan are feasible; an overview is given in Table 1. The straightforward approach is to create a set of identical 3DRST geometries, one for each motion phase k, in the following RSTk. The particle numbers can then be optimized following equation (1). This full 4D-optimization approach leads to very large problem sizes, especially if also multiple fields are optimized simultaneously. Due to the high number of beam spots, the dose can be shaped effectively, delivering different dose distributions to each motion phase. This can be exploited for OAR sparing in case of differential motion between target and OARs [34]. Alternatively, the treatment time especially for systems with a long energy change (3.2 s at GSI) could be reduced by exploiting range changes over the motion cycle. The overall needed number of iso-energy slices (IES) could be reduced by irradiating distal target regions in motion phases where the entry channel has a low radiological path length and vice versa. Heuristic solutions Adequate dose coverage is also possible with a lower number of beam spots, provided they are selected such that a suitable 4D dose can be realized. This is not trivial: if beam spots are distributed randomly from a 3DRST to each motion phase, dose coverage is in general not possible. A kind of interplay pattern will result from different beam spots covering identical locations of the moving target. Feasible distributions can be achieved by using a beam tracking plan as basis, and re-optimizing particle numbers after application
of a chosen set of tracking vectors. This approach uses the same number of beam spots as a 3D plan, but each spot is assigned to a specific motion phase. The treatment control system has to ensure the synchronized delivery to a measured motion surrogate during delivery using fast gating for each motion phase; it was therefore named ‘multigating’ [35]. Another option is to let each RSTk cover only a subsection of the target (4D-sectors). Through simultaneous optimization, the sum of the RSTk leads to a homogenous dose. The number of beam spots as well as the steepness of the dose gradients can be controlled through an overlap factor of the individual RSTk. Computation time and number of beam spots can be reduced to about 30% of full 4Doptimization without compromising target coverage [36]. Using the arrangement of the target sections relative to the main motion direction, an efficient means of dose shaping is possible. Also the sections could be arranged to exploit range differences between motion phases to reduce the overall number of IES, similar as for the full 4D-optimization. The layout of the sectors is currently done manually, but could also be automated with respect to the different stated criteria.
Uniform dose to each motion phase In case that either no differential motion is present or OAR sparing through optimization over all motion phases is not necessary, it is also possible to optimize treatment plans for each motion phase separately to a uniform dose. For each phase, the full dose constraints can be used, leading to a set of beam weights Nk. Similar to rescanning, the particle numbers for each motion phase are then weighted by their duration tk relative to the complete motion period T, resulting in the final beam weights Nk0 . The single RSTk thus deliver a uniform dose to each phase. This 4D-rescanning (or also single phase uniform dose, SPUD) approach has an improved robustness due to the lacking dose gradients between motion phases. Random, periodic errors are reduced similar as in rescanning, for example interplay due to residual motion within motion phases. The optimization problem also becomes much more tractable when m plans can be computed separately according to equation (2). For individual field optimization (SFUD), each field is optimized to the full target dose, and particles numbers are weighted also by the number of fields f. For IMPT, all fields in a single phase can be optimized to the target dose, and f is set to 1 in equation (2). v h i2 X ! ! i Dik Ek N k ¼ pre N k Dact i¼1
þ wOAR Table 1 Overview of the presented 4D-optimization techniques. Problem size shows the approximate increase of the size of the dose matrix in the cost function. With the exception of the 4D-ITV, this is proportional to the number of delivered beam spots. Modality
RST Motion Problem Characteristics monitoring size
4D-ITV
3D No
2.m
4D-multigating 3D Yes
1
4D-sectors
m/4
4D Yes
4D-rescanning 4D Yes
m1
Full 4D4D Yes optimization
m
Range-sensitive ITV for multifield optimization, enlarged VOI Based on beam tracking, difficult timing, only small changes to TCS Irradiate subset of CTV in each phase, limited dose shaping & problem size Uniform dose to phases: robust due to lack of gradients, no DIR for optimization Huge problem size, dose shaping & OAR sparing possible
! t ! Nk0 ¼ k Nk fT
OAR Xh i¼1
i2 ! i Dik ; pre N k Dact
(2)
þ
The drawback of this method is that no additional dose shaping is possible, and the motion can also not be exploited to reduce the number of iso-energy slices. Sparing of OARs can be achieved similar to standard IMPT by weighting the fields. In this case, the resulting gradients between the fields do not necessarily match for each motion phase, partially negating the stated benefit for robustness. The weighting factor for the particle numbers especially for SFUD can be high. A lower limit (typically 5000) for the final particle number in each beam spot is necessary to permit dose monitoring. During the optimization, this limit thus has to be set higher accordingly, which might be difficult for low fraction doses. This method is therefore especially suited to hypofractionation and radiosurgery.
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C. Graeff / Physica Medica xxx (2014) 1e8
A big advantage of this method is that DIR is not needed during treatment plan optimization, but only to propagate contours from a reference phase, which can be verified comparably easy. The DIR is a major potential source of errors, so that removing it at least from the planning stage also increases the robustness. It is still needed to judge total doses to normal tissue through 4D-dose calculation, though total dose constraints are guaranteed as they were observed in every optimization for each motion phase. IMPT for ITV irradiation The irradiation of an ITV can be considered a special case of a possible application for 4D-IMPT-optimization. Due to the necessary consideration of range changes, a valid ITV for ion beam therapy is field-specific [6,24]. This makes multifield optimization challenging. A solution to this problem is to include the range variations in the treatment planning itself, by optimizing a single 3DRST on each motion phase. The RST has to be large enough to cover the target propagated to each motion phase. In contrast to equation (1), equation (3) thus does not show a motion phase specific beam spot ! weight vector N k.
5
The second delivery concept addresses this inherent drawback by introducing a flexible sequence of beam spots taken from any of the RSTk to be irradiated. The TCS selects unirradiated beam spots from one RSTk depending on the current detected motion phase. In contrast to beam tracking, it is now known in which motion phase a beam spot will be irradiated, but no longer when this will be. The increased flexibility basically eliminates the timing uncertainty of the first approach, making a smooth, efficient irradiation more likely. The beam only needs to be gated when the RSTk for the current beam energy was already completely irradiated. Even this drawback could be reduced in systems with a short time for energy changes such as at PSI or NIRS, by also including adjacent IES in the sequence. This second approach can be used for any of the proposed strategies resulting in a 4DRST. An exemplary treatment planning study Methods
The result of this optimization is thus a treatment plan that fulfills the dose requirements independently of the motion phase. It can therefore be irradiated as any standard treatment plan, but has to be combined with rescanning to compensate interplay effects. This equation can be directly used for multifield optimization, with the known benefits for OAR sparing. A heuristic solution leading to a smaller problem size was proposed by Graeff et al. [25].
To show the feasibility of the presented methods, a four field treatment plan modeled on clinical plans from NIRS [38] was computed on single lung cancer patient with a 4D-CT provided by MDACC, Houston, TX. All motion phases were registered (DIR) to the end-exhale phase using Plastimatch [39]. Fields were optimized individually to a uniform dose (SFUD) or for selected methods also simultaneously (IMPT) to a single fraction total dose of 17.7 Gy (RBE) according to LEM IV [40]. For the computation of the 4D-optimized plans, ideal motion monitoring as well as the reproducibility of the 4D-CT were assumed resulting in a perfectly synchronized delivery. For comparison, a static reference irradiation on the end-exhale reference phase, an interplay case of the same static plan applied to the 4D-CT and a beam tracking plan were also simulated. DVH parameters were evaluated: V95 for dose coverage, V107 for overdose, D5-D95 for homogeneity and the conformity number CN.
Delivery
Results
To fulfill the assumed distribution of beam spots to motion phases, the delivery has to be synchronized to the patient motion. Motion monitoring is therefore an essential part of the delivery. The irradiation should also be efficient with a high duty cycle for short treatment times. Two methods were investigated as add-ons to the existing TCS implemented at GSI Cave M. Details and results of feasibility experiments can be found in Refs. [35,36]. The first one was designed for the 4D-optimized tracking (multigating) strategy and is comparably close to the original TCS for beam tracking. As the RST retains the number as well as the sequence of beam spots, the TCS keeps the synchronization to the measured patient motion through fast gating. Beam spots are only irradiated to their designated motion phase; it is a part of the treatment planning to provide a sequence of beam spots that permit a high duty cycle irradiation. This in essence means that during planning, the required time for irradiating the spots and the breathing period have to be roughly known. In practice, each motion phase is assigned a lower irradiation time as expected, so that the spot sequence is more likely to be synchronized to the breathing motion. A failure to complete the assigned spots with one motion phase leads to a gate over a whole breathing cycle, elongating the treatment time. The distribution of beam spots in a sequence likely to be smoothly irradiated is non-trivial due to the uncertainties involved, even without considering the spill pauses of the synchrotron. This is greatly facilitated by efficient online intensity control, as for example also needed for phase-controlled rescanning [37].
Dosimetric results are shown in Table 2. For SFUD, 3D-optimized beam tracking though improving on interplay dose errors could not achieve acceptable dose parameters, with marked under- and overdoses, see also Fig. 2. Dose coverage could be restored to the level of the static plan by 4D-optimization methods. For 4D-multigating and 4D-sectors the dose homogeneity was slightly reduced in comparison to the static plan due to their inherent dose gradients. 4D-rescanning essentially exceeded the results of the static irradiation as it essentially represents the average of numerous optimizations to a uniform dose. The 4D-sector and 4D-rescanning
m X v h m OAR i2 i2 X Xh ! X ! ! i i Dik Dik E N ¼ pre N Dact þwOAR pre N Dact k¼1 i¼1
k¼1 i¼1
þ
(3)
Table 2 Dosimetric results from the patient simulation study for both single field (SFUD) and simultaneous multifield (IMPT) optimization. Results were partially previously published in Refs. [34,35]. V95 [%] SFUD Static Interplay 3D beam tracking 4D-rescanning 4D-sectors 4D-multigating IMPT Static Interplay 4D-rescanning 4D-sectors
V107 [%]
D5-D95 [%]
CN [%]
98.5 72.5 89.5 99.4 98.7 99.9
0.0 6.5 11.5 0.0 0.0 0.0
2.7 29.9 19.9 2.4 3.8 4.2
70.8 52.5 62.1 75.6 81.5 64.6
99.3 76.4 100.0 97.7
0.0 13.9 0.0 0.1
4.3 31.5 2.2 6.1
83.4 56.4 82.1 88.2
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Figure 2. Dose cuts from the SFUD patient study illustrating the different 4D-optimization techniques. On the left (topebottom), a reference static plan on end-exhale, an interplay pattern and a 3D-optimization beam tracking irradiation, which partially restores the interplay dose errors. On the right, 4D-multigating, 4D-sectors, and 4D-rescanning show good dose coverage with slightly varying conformity to the target.
method even resulted in better conformity than the static plan, likely due to the higher number of beam spots involved and thus greater degree of freedom available to the optimizer. The dose cuts in Fig. 2 especially highlight the difference between 4D-multigating, which was restricted to the same size as the static RST to 4Drescanning and 4D-sectors which both had a considerably higher number of beam spots. In the IMPT plans (see Fig. 3 and Table 2), with again increased degrees of freedom, CN was further increased for all modalities, but now strongly inhomogeneous fields of 4D-sectors also lead to a slightly worse D5-D95. 4D-sectors with its inhomogeneous doses to each motion phase offered the highest conformity, but also might be the least robust due to the dose gradients and resulting sensitivity to motion uncertainty. The averaging effect of 4Drescanning maintained the high homogeneity of the SFUD optimization, which now clearly exceeded the static case. Discussion In summary, a set of workable strategies for 4D-optimization in scanned ion beam therapy has been investigated. They offer highly conformal dose delivered to moving targets, with range variations factored into the treatment plan so that online range adaptations are no longer necessary. Different delivery methods that require only software changes to existing scanned beam control systems were presented, though precise motion monitoring is necessary.
The 4D-optimization concept relies heavily on the validity of the planning 4D-CT. The motion contained in the 4D-CT should be representative of the breathing trajectory occurring under treatment. Depending on the degree of variability of the breathing motion, 4D-optimization might not be useful or even do harm as it creates the illusion of successful motion mitigation which can’t be transferred to clinical reality. The same is true though to some degree for all mitigation techniques derived from a 4D-CT; be it a range-considering ITV, gating windows, or the range component of beam tracking vectors. It is currently not possible to determine range changes accurately from online motion monitoring, except from the underlying 4D-CT. A suitable motion mitigation technique should thus be chosen individually for each patient, depending on various factors such as tumor location, motion amplitude, breathing reproducibility and cooperativeness. Planning and delivery should take place within a short time period to avoid anatomical shifts. This may be challenging for certain anatomical regions such as the pancreas, which is influenced by comparably rapid bowel movement [41]. Adaptive treatment planning might be necessary, where a plan that was carefully designed and validated offline is online adapted to the current treatment situation. Care should be taken therefore to assure as far as possible a reproducible breathing of the patient, e.g., through coaching with an audiovisual feedback. Minor deviations from the expected motion trajectory cannot be avoided though, and thus have to be dealt with by robustness measures discussed in the following.
Figure 3. Dose cuts from the IMPT study showing the improved conformity to the target for both static and 4D-optimized treatment plans.
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The steepness of dose gradients between motion phases and fields in IMPT should be restricted by introducing a corresponding penalty analog to Nohadani et al. [23]. As the restriction of MLC motion is not relevant for particle therapy, the motion of the target’s center of mass could be factored in the equation. In this way, the likely overall motion of the tumor is considered, but too strong gradients due to inhomogeneous fields as a result of IMPT are avoided. For essentially all proposed 4D-optimization strategies, lateral beam tracking could be employed to compensate target motion differences to the planning 4D-CT. Lateral tracking does not incur the cost of an online range changing system, while the previous 4Doptimization would lead to comparably small residual tracking vectors. In that way, the remaining error of the uncompensated range stays small as well as a potential error of the merely transitional beam tracking used to compensate a potentially more complex motion. The residual tracking would make sense only if the data was provided by a motion monitoring system that detected or determined (e.g., by a neural network) the 3D tumor motion rather than using information from the deformation field of the planning 4D-CT. In addition, the motion monitoring system’s measurement uncertainty has to be considerably smaller than the size of the residual tracking vectors. Also, if larger deviations from the expected breathing curve occur, the above stated limitations of beam tracking will again come to bear. Also, as 4D-optimization requires or at least highly benefits from intensity control, and in some cases also necessitates timing estimations, methods like breath-sampled [42] or phase-controlled [37] rescanning could be added with little additional effort. This would help to reduce for example residual motion within motion phases or other random and periodic errors. A good way of testing the robustness of (not only) a 4D-optimized plan is the concept of artificial 4D-CTs generated with motion maps extracted from 4D-MRI [43]. In this way, continuous breathing motion of sufficient length to simulate the entire treatment is available, most likely resulting in a closer-to-reality dose calculation than 4D-CT based calculations. Breathing curves of different irregularity can be studied in detail, and robustness measures can be developed that allow the transferal of a plan from a planning 4D-CT to a clinical treatment situation. The identified likely scenarios can be included into the optimization to make it inherently robust [44,45]. This might require an improved optimization code or procedures to handle the resulting large nonlinear problems for carbon ion treatment. To this end, studies have to be conducted that systematically violate the prescribed synchronization of delivery and patient motion, similar to those already performed for photon therapy [17,23]. As already stated, carbon ion therapy using LEM requires the knowledge of the entire particle spectrum for each dose voxel, so that it is not possible to calculate individual pencil beams independent of each other. This makes such studies more complex and requires additional modifications to the existing 4D-dose calculation, especially if extended to sequential 4D-CT data derived from MRI as opposed to a single periodic 4D-CT used for the entire irradiation. The effects of residual motion within 4D-CT phases could be investigated by interpolating the voxel positions between the phases. A good estimation of beam range in this case is challenging [46]. The method of 4D-rescanning in this context is especially promising. Due to the inherent dose averaging, dose statistics in part even exceeded those of the static reference irradiation. This effect is likely to translate into robustness against variable motion, motion monitoring and range uncertainties, but this has to be further investigated in appropriate studies as outlined above.
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Finally, more experiments with realistic phantoms are needed to investigate the complex effects of delivery timing of 4D treatment plans, uncertainties in beam shape and intensity as well as in motion monitoring, before animal or possibly patient studies should be considered. Conclusion 4D-optimization is a concept that permits highly conformal doses to moving targets. It has been studied for nearly a decade in the photon community, but may result in even greater benefits for particle therapy due to the high range dependence. The feasibility of several strategies including delivery has been investigated in treatment planning studies as well as first, simple experiments. After necessary studies concerning its robustness, 4D-optimization might offer a viable route for precise motion compensation, especially for hypofractionation and radiosurgery of intrafractionally moving targets. A likely candidate for a transition to the clinic is the inherently robust 4D-rescanning method. References [1] Ferlay J, Shin HR, Bray F, Forman D, Mathers C, Parkin DM. Estimates of worldwide burden of cancer in 2008: GLOBOCAN 2008. Int J Cancer 2010;127: 2893e917. [2] Greco C, Zelefsky MJ, Lovelock M, Fuks Z, Hunt M, Rosenzweig K, et al. Predictors of local control after single-dose stereotactic image-guided intensitymodulated radiotherapy for extracranial metastases. Int J Radiat Oncol Biol Phys 2011;79:1151e7. [3] Sharma A, Wong D, Weidlich G, Fogarty T, Jack A, Sumanaweera T, et al. Noninvasive stereotactic radiosurgery (CyberHeart) for creation of ablation lesions in the atrium. Heart Rhythm 2010;7:802e10. [4] Constantinescu A, Lehmann HI, Graeff C, Packer D, Durante M, Bert C. Planning studies for non-invasive isolation of the pulmonary veins with a scanned carbon ion beam. In: PTCOG 52. Essen, Germany; 2013. [5] Bert C, Durante M. Motion in radiotherapy: particle therapy. Phys Med Biol 2011;56:R113e44. [6] Knopf AC, Boye D, Lomax A, Mori S. Adequate margin definition for scanned particle therapy in the incidence of intrafractional motion. Phys Med Biol 2013;58:6079e94. [7] Keall PJ. 4-dimensional computed tomography imaging and treatment planning. Semin Radiat Oncol 2004;14:81e90. [8] Papiez L, Rangaraj D, Keall P. Real-time DMLC IMRT delivery for mobile and deforming targets. Med Phys 2005;32:3037e48. [9] Papiez L, McMahon R, Timmerman R. 4D DMLC leaf sequencing to minimize organ at risk dose in moving anatomy. Med Phys 2007;34:4952e6. [10] Trofimov A, Rietzel E, Lu HM, Martin B, Jiang S, Chen GTY, et al. Temporospatial IMRT optimization: concepts, implementation and initial results. Phys Med Biol 2005;50:2779e98. [11] Rietzel E, Chen GTY, Choi NC, Willet CG. Four-dimensional image-based treatment planning: target volume segmentation and dose calculation in the presence of respiratory motion. Int J Radiat Oncol Biol Phys 2005;61: 1535e50. [12] Ma Y, Lee L, Keshet O, Keall P, Xing L. Four-dimensional inverse treatment planning with inclusion of implanted fiducials in IMRT segmented fields. Med Phys 2009;36:2215e21. [13] Zhang T, Jeraj R, Keller H, Lu W, Olivera GH, McNutt TR, et al. Treatment plan optimization incorporating respiratory motion. Med Phys 2004;31:1576e86. [14] Zhang T, Lu W, Olivera GH, Keller H, Jeraj R, Manon R, et al. Breathing-synchronized delivery: a potential four-dimensional tomotherapy treatment technique. Int J Radiat Oncol Biol Phys 2007;68:1572e8. [15] Ma Y, Chang D, Keall P, Xie Y, Park JY, Suh TS, et al. Inverse planning for fourdimensional (4D) volumetric modulated arc therapy. Med Phys 2010;37: 5627e33. [16] Chin E, Otto K. Investigation of a novel algorithm for true 4D-VMAT planning with comparison to tracked, gated and static delivery. Med Phys 2011;38: 2698e707. [17] Chin E, Loewen SK, Nichol A, Otto K. 4D VMAT, gated VMAT, and 3D VMAT for stereotactic body radiation therapy in lung. Phys Med Biol 2013;58: 749e70. [18] Schlaefer A, Fisseler J, Dieterich S, Shiomi H, Cleary K, Schweikard A. Feasibility of four-dimensional conformal planning for robotic radiosurgery. Med Phys 2005;32:3786e92. [19] Tewatia D, Zhang T, Tome W, Paliwal B, Metha M. Clinical implementation of target tracking by breathing synchronized delivery. Med Phys 2006;33:4330e6. [20] Tewatia D, Chebrolu V, Tolakanahalli R, Paliwal B, Tome W. Efficacy assessment of breathing phase adaptive lung tumor motion management for
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Please cite this article in press as: Graeff C, Motion mitigation in scanned ion beam therapy through 4D-optimization, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.03.011