Simulation and quantification of the interplay e ect in treatment of lung tumors with IMPT

Transcription

1 TU Delft Master s Thesis Simulation an quantifiation of the interplay e et in treatment of lung tumors with IMPT Author: Dominique Reijtenbagh Supervisors: Dr. D. Lathouwers Dr. M. Hoogeman Dr. P. Trnková Dr. Z. Perkó MS T. Jagt A thesis submitte in fulfillment of the requirements for the egree of MS Applie Physis in the RST-RPNM group Applie Sienes July 12, 2017

2 ii In the ebate of photons versus protons one shoul not take the matter lightly, but positively

3 iii TU DELFT Abstrat Applie Sienes MS Applie Physis Simulation an quantifiation of the interplay e et in treatment of lung tumors with IMPT by Dominique Reijtenbagh In spot sanning irraiation tehniques the appliation to moving tumors an ause interplay e ets that an severely eteriorate the tumor overage. In this thesis a moel is presente with whih IMPT treatment eliveries an be simulate for moving lung tumors. Two i erent respiratory motion moels are analyze for interplay e ets an three patients are planne with i erent methos to analyze their robustness against interplay. For the planning four methos are use, of whih three use robust optimization. One of the methos is robust multi CT optimization, a novel tehnique propose by Erasmus MC. This type of optimization is use for the analysis of the respiratory moels, an it was foun that the i erent respiratory moels result in i erent interplay e ets. The robust multi CT optimization was foun to be the most robust planning metho against interplay e ets in omparison with the other optimization types suh as ITV planning, espeially after frationation. It was the only metho that woul onverge towars the planne V95% an V107% value, as more frations were simulate. Other optimization tehniques an hypofrationation require interplay mitigation methos to improve the tumor overage. The moel has shown the apability to simulate the interplay e et for IMPT in lung tumors an analyze the 4D robustness of planning methos.

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5 v Aknowlegements I woul like to thank my supervisors an all the people that have helpe me to finish this thesis. I am grateful to Danny an Misha for their input an the opportunity to o this projet, as it has strengthene my interest in meial physis even more. Petra an Zoltán, who joine this projet along the way, I want to thank you for your isussions an e orts to help me to think about the other possibilities in my work. I want to thank Thyrza for introuing me to Erasmus MC an helping with all the small struggles I have enountere along the way. Lastly, I want to thank Weny an Bas for their fresh input on my work an the nie fikas we have ha.

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7 vii Contents 1 Introution 1 2 Movement of targets in proton therapy Proton therapy Impat of raiation Proton treatment failities Moving targets in proton therapy Lung tumors Desribing tumor movement Treatment plans for moving targets The interplay e et Mitigating the interplay e et Simulation of the interplay e et Builing an interplay moel Simulating the patients an their breathing Obtaining the eformable image registrations Generation of treatment plans Proessing the plan optimization output Calulating the interplay ose Proessing the output of the interplay moel Appliation of the interplay moel Results an isussion Patients use in stuy Tuning the moel Comparison of planning methos Impat of frationation Comparison results to literature Future researh an reommenations Improvement of the interplay moel Reution of omputation time Optimization of DIRs Inlusion of a realisti breathing senario Inlusion of hysteresis Inlusion of ranom an setup errors Evaluation on more phases PCE analysis Interplay robust optimization icyle optimization Implementation in icyle A Coverage plans 51 B Results 59 Bibliography 69

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9 1 Chapter 1 Introution Caner has been a problem of all times, but was still responsible for one in every four eaths in the US in Lung aner was responsible for one fourth of those aner eaths (Siegel, Miller, an Jemal, 2016). The ultimate ure for aner oes therefore not appear to be foun. Raiotherapy has however evelope signifiantly over the past years. New treatment moalities have been evelope an new types of planning have been implemente. One of these novel tehniques is isusse in this thesis. The tehnique, IMPT (Intensity Moulate Proton Therapy), elivers high energy protons to the patient while spot sanning the target. Protons possess features that make them a more interesting treatment moality over photons in some ases. IMPT is promising as it has shown the apability to spare OARs (Organs At Risk) better than IMRT, while maintaining exellent tumor overage (Zhang et al., 2010). An exemplary ose istribution of a single spot is epite in Figure 1.1a. When all spots are applie, a ose istribution looking as shown in Figure 1.1b arises. It is visible that the separate spots with protons are fully stoppe in the boy, in ontrast with photon base moalities. (a) Exemplary IMPT ose istribution of a single spot (b) Exemplary IMPT ose istribution text Figure 1.1: Visual epition of an exemplary IMPT ose istribution of a single spot an of ombine spots. In re the target is elineate. As an be seen in Figure 1.1a the spot oes not exit the boy Applying a spot sanning tehnique suh as IMPT to moving tumors (e.g. the lung) on the other han, might give rise to istortions in the ose istributions, also alle interplay e ets. The interplay e ets are mostly large inhomogeneities in the target, leaing to loal uner- an overosage. Conlusions in literature i er in final verit, mostly ue to i erent planning tehniques an evaluation methos (Li et al., 2014, Knopf, Hong, an Lomax, 2011, Grassberger et al., 2015). The aim of this stuy is to simulate the interplay e et in a moving tumor in orer to quantify the e et as a funtion of i erent treatment parameters. With the

10 2 Chapter 1. Introution opening of new proton treatment failities in The Netherlans, the wish is there to fin better unerstaning an possibly a solution for the e et, suh that high treatment quality an be establishe for moving tumors. In this thesis an interplay moel is presente for the lung, apable of preiting the magnitue of the interplay e et as a funtion of i erent (possibly influential) fators. These fators inlue planning tehniques, (ir)regularity of breathing motion, an magnitue of tumor movement. A pratial bakgroun to give more unerstaning about ertain aspets of the moel is given in Chapter 2. The aim of the stuy is to use the moel to give a preition about the magnitue of the interplay e et an the apability of the planning methos to ope with the e et. In Chapter 3 an elaborate explanation of the moel is given. The moel uses 4DCT sequenes of three atual lung aner patients with ontours on the referene phase, of whih the CT sans are use to etermine the eformable image registrations. With the help of these registrations ontours are warpe from the referene phase to the other respiratory phases. Four types of planning are use on the ontour sets, robust single CT, robust multi CT, ITV an robust ITV planning, of whih the referene CT san is use for planning for all but the seon planning metho. In Chapter 4 the results are lai out, after all planning methos of all three patients are teste for robustness against interplay. The robust multi CT results of one patient are also use to fin the i erene of the impat of breathing motion on the ose istribution ue to interplay. Finally, a omparison with literature is mae. In Chapter 5 reommenations are given for future researh, both iretly an iniretly relate to this thesis.

11 3 Chapter 2 Movement of targets in proton therapy 2.1 Proton therapy Impat of raiation In ontemporary aner treatment multiple options are available, in whih hemotherapy an irraiation play a big role. Irraiation is performe to inue DNA amage in the tumor ells, inhibiting ell ivision an ultimately ausing ell eath. Tumor ells have a lower apability of regeneration mehanisms to repair ouble stran DNA breaks in omparison with normal tissue ells, iniating a funamental appliation of irraiation. Over the years i erent tehniques have been evelope, with photon irraiation being the most wiely applie. However, there are other options, some being more or less benefiial. Base on the tumor harateristis an ombinations with other treatment forms suh as hemotherapy, it will be etermine whih irraiation metho is most promising to ontrol the tumor growth an hopefully ure the patient from aner. The question is why a partiular irraiation metho is sometimes more benefiial for the patient than another. The first an primary i erene between photon base methos an others is base on the nature of the raiation. There are multiple possibilities, suh as eletron, neutron or ion base. Ion base raiation has some subategories, given by the Z-number of the ion use for irraiation, an oes therefore also inlue proton therapy. The i erene in nature of the partile, is best shown in the energy eposition as a funtion of the travele path of the partile. This is visualize in Figure 2.1. As one an see, the shape of the ose eposition urve an i er a lot base on weight, energy an harge of the partile. Ions an photons have i erent ose eposition harateristis, that an be exploite when treating a patient. From now on only proton an photon therapy shall be isusse, sine these are most linially applie an will be the most relevant for the thesis. Other tehniques, suh as arbon ion therapy, also show promising results, but are onsiere beyon the sope of this researh. In this thesis only external beam raiotherapy is isusse. Now the i erene between the ose eposition urves of protons an photons shall be further elaborate. When looking at Figure 2.1 one an see that photons have a relatively early an broa peak, with a graual ose fall-o. This is in ontrast with protons, that have a later an sharper peak, with a very sharp ose fall-o (Bragg peak). Combining multiple of these Bragg peaks in one beam an reate a ose eposition urve having a plateau in the tumor only. An example of suh a

12 4 Chapter 2. Movement of targets in proton therapy Figure 2.1: Relative ose eposition as a funtion of epth in water for i erent partiles. It is visible that epening on the type of partile, the ose eposition is i erent. The heavier ions show a shallow an late peak, while photons an neutrons show a broa an early peak. Depening on the energy of a partile the eposition urve hanges. As is also shown, ions are more easily stoppe in the boy than gammas an neutrons. Taken from Paganetti, result is given in Figure 2.2, the so-alle sprea out Bragg peak (SOBP). This is muh more i ult, if not impossible, to ahieve with photons in a single beam. Figure 2.2: Sprea out Bragg peak (SOBP) ompose of protons with i erent energies. Their ose eposition urves ombine (with eah their istint Bragg peak) ompose a plateau, whih is ieally overing only the tumor. Taken from Paganetti, Naturally, both tehniques have their isavantages. Photons have energies that make them fully traverse the boy, an they eposit ose along their entire path. This ose eposition is unwante, as it harms healthy tissue unneessarily. The ose eposition behin the tumor oul be irumvente with protons, but they have on the other han a high sensitivity to plaement errors an movement. This is a partiular problem for tumor sites, or tumor sites lose to organs, unergoing anatomial hanges, e.g. bowel an blaer filling. The ensity hanges ause overshoot or unershoot of the proton beam, meaning that ue to a higher i erene in ensity along the path the beam is stoppe earlier (unershoot), or ue to a lower i erene along the path is stoppe later (overshoot). Mahine range unertainties

13 2.1. Proton therapy 5 also ontribute to this problem. One an imagine that the latter oul pose signifiant problems. If proton therapy is hosen to avoi an OAR, overosage in the OAR ue to overshoot is efinitely unesire. The problem esribe above is visualize in Figure 2.3. The figure shows that in the nominal senario, in whih one assumes the treate anatomy is exatly as expete, the SOBP perfetly overs the tumor. The heart, an organ that shoul get a ose as low as possible, reeives a negligible ose when protons are use. In the ase of photons a higher ose is seen, whih is an iniation to swith to protons. However, when one turns to a more realisti senario, an unertain situation, in whih only the approximate anatomy with respet to the beams is known, it beomes lear that this potentially has a big e et on the heart ose. This is in ontrast with the photon ose, in whih it has little to no e et. There are multiple ways to aount for the e et, but it is obvious that the ifferenes in nature of ose eposition also imply a i erent approah in treatment planning. Therefore optimal proton plans will have to be foun in a i erent way than photon plans. This will be isusse in the setions below. Figure 2.3: Di erenes in e et in the ase of range unertainties for photons an protons when treating a lung tumor. A bigger impat for a proton path is seen, ausing a higher unwante ose in the heart. Taken from Knopf an Lomax, Proton treatment failities In photon therapy the treatment tehniques are numerous. The priniple is the same for all, as hanging the energy of the beam is one quite easily in ontrast with protons. Having taken this hurle, there is room for more flexibility in time an position. This ategory of treatment is IMRT (Intensity Moulate Raiation Therapy), whih basially means that the beam an be shape in form an in energy. There are i erent types in this ategory, suh as the aforementione LINAC, CyberKnife an VMAT. The most basi tehnique of the three is the LINAC (LINear ACelerator), that an shape the beam an allows a 360 egree rotation aroun the patient. VMAT (Volumetri Moulate Ar Therapy) is one step more sophistiate. VMAT, ontrary to onventional LINAC, an be applie ontinuously as the beam rotates aroun the patient, reuing treatment time. More flexibility in

14 6 Chapter 2. Movement of targets in proton therapy position an be obtaine with the CyberKnife, whih has the strength in its aurate an quik roboti arm. This allows the traking of the tumor when ouple to a movement etetor. In proton therapy two major moalities an be onsiere, passive sattering an IMPT (Intensity Moulate Proton Therapy). It is quite i ult to fin iret parallels with photon therapy, as the priniples of the tehniques are quite i erent. Passive sattering is the first tehnique isusse here, an has its priniple as esribe in the name. With the use of ollimators an sattering in ompensators the beam is shape to give a 3D ose istribution with an appropriate SOBP. The major isavantage of this type of proton therapy is the neessity for patient-speifi ollimators an ompensators, an the lak of flexibility when the anatomy of the patient hanges (Paganetti, 2012). Intensity Moulate Proton Therapy (IMPT), a form of penil beam sanning, allows a more ynami treatment of patients. In making the plan eah spot is optimize together with the other spots, to eliver a goo treatment. The beams are therefore not uniform separately, but the ombination of the beams gives a uniform ose to the tumor. This is in ontrast with Single Fiel Uniform Dose (SFUD), in whih fiels are optimize separately to be uniform. With the use of bening magnets the IMPT treatment is elivere to the patient spot by spot. The beam sans the tumor aoring to an afore-alulate treatment plan, easily allowing small or big hanges. The elivery of a single spot is in the orer of milliseons, followe by a spot-o time in whih no ose elivery is possible (also in the orer of milliseons). Swithing to i erent proton energies an take up to seons. In both IMPT an passive sattering, it beomes lear that the elivery of the proton beam is prone to less flexibility than photon base elivery. The nee for a ylotron or synhrotron with a big gantry for auray severely eteriorates the possibilities of eveloping a CyberKnife-like roboti elivery. Only IMPT shall now be isusse in the remainer of this thesis. 2.2 Moving targets in proton therapy In this setion a more in-epth explanation will be given about a speifi problem in raiotherapy, whih is on how to eal with moving targets. In ontrast with stationary targets, aitional measures have to be taken to eal with moving targets with all types of treatment moalities. However, in proton therapy the onsequenes are more severe, an therefore the solutions more ompliate. The main fous is on lung tumors, as this type of tumor was the main fous of this thesis. First an explanation is given on how tumor movement is esribe in orer to inorporate this in planning or analysis, then the key problem of this thesis, the so-alle interplay e et, is be explaine. Finally, literature is isusse in whih possible solutions for the interplay e et are given Lung tumors Lung aner has been the most ommon aner for eaes, globally speaking. The most frequent type of lung aner is non-small ell lung aner (NSCLC), aounting for 85% of the ases, after that omes small ell lung aner (SCLC) (Navaa et al., 2006). The survival rate for these types is generally low; the ratio of mortality is as high as 87%, epite in Figure 2.4. In aition to that, lung aner is responsible for one out of five aner eaths in the US (WHO, 2012). The most ommon treatment for lung aner is ombination of hemotherapy an irraiation, but surgial

15 2.2. Moving targets in proton therapy 7 resetion appears to be the most suessful option. However, most patients annot be treate this way (Nesbitt et al., 1995). One limitation of lung tumor irraiation is the iniene of raiation pneumonitis ue to irraiation of healthy lung tissue. When applying a regular frationation sheme there is a risk of pneumonitis, but this risk gets bigger when hypofrationation (elivering the treatment in only a few frations, instea of 20+ frations) is applie (Seppenwoole et al., 2003). An overview of other risk organs (tumors with intrafrational movement) is given by Langen et al. (Langen an Jones, 2001). Figure 2.4: Mortality of NSCLC an SCLC, groupe by years after iagnosis. The ashe line is for small ell lung aner (SCLC), the soli line is for non-small ell lung aner (NSCLC). Mae from ata from IKNL, When treating lung tumors, there are multiple organs at risk to take into aount when planning the treatment. In Table 2.1 a short overview is given of the organs with the possible toxiities that might arise. Table 2.1: Organs at risk with their possible toxiities when treating NSCLC or SCLC. Organ Toxiity Lungs Pulmonary fibrosis an raiation pneumonitis (Mehta, 2005) Heart Coronary artery isease (CAD), valvular isease, hroni periarial isease, arrhythmias an onution isturbanes, ariomyopathy, or aroti artery stenosis (Carver et al., 2007) Spinal Cor Raiation myelopathy (Kair et al., 2012) Plexus Brahialis Transient neuropathy, aute ishemi plexopathy (Delanian, Lefaix, an Praat, 2012) Oesophagus Raiation esophagitis (Kwint et al., 2012) Trahea Traheitis (Levy et al., 2013) Proximal bronhial trees Bronhial striture, bronhial nerosis, an fatal hemoptysis (Gukenberger et al., 2007)

16 8 Chapter 2. Movement of targets in proton therapy The toxiities an beome quite serious, an might even be a ause to stop treatment if the patient su ers too muh from them. When reating a treatment plan for the patients use in this stuy, the optimization takes into aount the OARs an tries to get a feasible treatment plan while keeping the ose to the OARs as low as ahievable. Consiering the atual OAR ose elivere in treatment is therefore important to see if these toxiities will arise. Depening on the type of planning the ose to the OARs an be a limiting fator in the treatment Desribing tumor movement Tumor movement an have omplex shapes, epening on the tumor site an speifi patient. This setion explains i erent senarios to esribe tumor movement. Ieal senario One an approximate respiratory motion by esribing tumor motion with a perfet osine base on literature stuies, as shown in Figure 2.5. Here the y-iretion oul be for example the aual-ranial iretion an the x-iretion the anterior-posterior iretion. If x an y are in phase, Figure 2.5.b takes plae. If they are not, Figure 2.5. is appliable, whih means there is hysteresis in the movement of the tumor. This means that the tumor loation is i erent in 50% exhale position from the 50% inhale position. In this thesis hysteresis is not aounte for. This means that only the motion urves of Figure 2.5.a an 2.5.b are implemente in the thesis. Figure 2.5: Approximating respiratory motion with osines in two normal iretions. In a both iretions are in phase, in they are not, ausing hysteresis. In b an the resulting motion trajetory is shown. Taken from Ehrhart, Lorenz, et al., When a patient shows breathing similar to this ieal senario, the tumor loation oes not obey a Gaussian istribution ue to its sinusoial movement. The tumor will spen more time in full exhale an full inhale position than it will mi-exhale or mi-inhale position, whih is shown in Figure 2.6. This way of evaluating motion is onsiere less aurate than atual patient s breathing motion. Dowell et al. reasons that using an ieal senario will result in a worst ase senario (Dowell et al., 2013). Sine fewer averaging e ets take plae in perfet motion, less favorable ose istributions are reate. In a real treatment the e et of breathing on the

17 2.2. Moving targets in proton therapy 9 ose eposition will be less visible. Whether this is atually the ase is isusse in Chapter 4. Figure 2.6: A few (raw ata) breathing perios are analyze to fin the probability ensity funtion of the tumor movement. As an be seen, the tumor is more likely to be foun at full exhale an full inhale. Taken from Bortfel, Jiang, an Rietzel, 2004 Binning senario Another option is to use raw signal of patients, whih oul be obtaine with a breathing monitor. An example of this kin of signal is shown in Figure 2.7. Figure 2.7: Exemplary signal from CyberKnife respiratory motion traking system, position of the traker as a funtion of time. Baseline shifts are visible an big variations in amplitue, as well as gaps without ata. By efining the relative positions of the phases, the signal an be binne. This is shown in Figure 2.8, in whih it is visible that the motion is approximate with isrete steps in time instea of ontinuous ones. Binning was onsiere too i - ult for the breathing signal use in this thesis, as the signal was eeme to be too irregular.

18 10 Chapter 2. Movement of targets in proton therapy Figure 2.8: Binning a breathing signal. In this example is visualize an example of amplitue binning. Half a breathing perio an be binne in 10 regions, of whih the regions are linke to a position of the tumor. Taken from Lujan et al., Hybri senario The final senario that is onsiere in this thesis is the hybri senario. In this senario a raw breathing signal is analyze to fin the probability ensity istribution of the breathing perio of the patient. In Figure 2.9 the fitte probability ensity funtion of the signal of Figure 2.7 is epite, together with the breathing perios foun in the signal. Then, to simulate the motion of the tumor, i erent perios are sample in aorane with this probability ensity funtion an are onseutively plae behin eah other in time. Figure 2.9: The signal from Figure 2.7 is filtere an proesse to fin the breathing phases an their istribution. A Gaussian istribution is assume an fitte to the ata, whih is use for sampling later on. Perios below 2.5 s an above 5.5 s were onsiere noise an isare. The Gaussian fit is sale for visibility. The iea is that this senario is more realisti than the ieal senario, but less realisti than the binning senario. The hybri senario is also easier to apply than the binning. Aoring to a stuy performe by Quirk et al. the perioiity of a signal is more stable than the amplitue (Quirk, Beker, an Smith, 2013). This means that statistial moeling woul be easier to o with the perioiity as it is

19 2.2. Moving targets in proton therapy 11 easier to preit. In their stuy volunteers were ompare to patients, an it was foun that patients have more irregular breathing an smaller amplitues Treatment plans for moving targets The nature of the irraiation metho an the nature of the tumor etermine the approah to treat the patient. In treatment planning the lear tumor bounaries are rawn an name the GTV (Gross Tumor Volume). To aount for mirosopi sprea of the tumor a margin is ae to the GTV, to form the CTV (Clinial Target Volume). So far the methoology for proton an photon therapy is the same. The last step, however, tens to be i erent. To aount for set-up errors an inter frational tumor movement in photon therapy, an extra margin is ae aroun the CTV. This extra margin is the planning target volume (PTV) an is ue to the slow, approximately linear, ose fall-o for photons, a mostly uniform expansion of the CTV. An extra i ulty is introue when a patient has a tumor that moves intra frationally ue to, for example, breathing motion. In this ase the patient nees a 4 imensional CT san (4DCT), whih reors the patient while breathing to fin the positions of the tumor in i erent breathing phases. The most extreme positions an then be foun an are then elineate an ombine, to form the ITV (internal target volume) (Kang et al., 2007). The PTV an also be applie to ompensate for motion, by expaning the ontour non-uniformly more in the iretion of the motion (Paganetti, 2012). This oes not neessarily require a 4DCT. For protons the PTV expansion is more ompliate, as the sensitivity of the proton ose oes not allow a similar reasoning. The existene of the Bragg peak an the potential uner-/overshoot problem auses a non-linear hange in ose eposition when the anatomy is not aoring to plan. This makes the efinition of the PTV more i ult to etermine. Figure 2.10: Depition of the i erent volumes use in raiotherapy. The visible tumor is the GTV (Gross Tumor Volume). This volume oes not inorporate mirosopi expansions of the tumor, to ompensate for these the CTV (Clinial Target Volume) is reate. Depening on the unertainties in elivering the treatment the physiian might eie to expan this ontour a little more to assure a goo tumor overage, resulting in the PTV (Planning Target Volume). This is only truly appliable for photons, as they are less sensitive to ensity i erenes in the boy. Speifially for moving tumors an ITV (Internal Target Volume) is often use. Creating a ontour that enompasses all positions of the tumor an help inrease tumor overage. Solving the problem of the PTV for protons is not trivial, an the way to eal with this i ers per institution (Li et al., 2015, Grae, Durante, an Bert, 2012).

20 12 Chapter 2. Movement of targets in proton therapy Erasmus MC tries to aount for this problem (in researh) by planning robustly to aount for set-up unertainties an inter fration motion, an in the ase of intrafrational motion, on multiple CT sans simultaneously. The optimization is performe by not simply implementing a bigger margin, but instea by onsiering multiple CT sans, as shown in Figure By using multiple CT sans a hange in surrouning anatomy uring respiratory motion is inlue as well, whih is not the ase with ITV or PTV planning. The sans are loae into the optimization, while sharing information about the spatial position of the organs an tumor (in orer to etermine the respetive loations to the beam). This makes it possible to investigate the outome of eah spot on all phases simultaneously, an even inlue robustness senarios. Figure 2.11: When applying multi-ct optimization, the 0% inhale, 50% exhale an 100% inhale CT sans are use for optimization simultaneously. The spatial position of the tumor is known in all three ases, whih makes simultaneous optimization possible. The nine robustness senarios that are use in robust optimization are applie to all three phases separately, resulting in a total of 27 senarios to be optimize. If robustness is inlue, whih means that patient shifts an unertainty in spot elivery are antiipate, there is a new senario to optimize for eah patient shift or unertainty. Normally, this woul mean 9 senarios for a phase, as shown in Figure In this ase, where 3 phases are use, this as up to 27 senarios. Robust optimization is therefore more time-onsuming an intensive than ITV or PTV optimization, an requires more omputational power. On the other han, it is meant to give better robustness to set-up errors in patient positioning an unertainties in beam elivery (Stoel, 2016). The plan that is onstrute will therefore not only show goo overage in the 9 senarios, but also in all other breathing phases an their senarios. Figure 2.12: The nine robustness senarios taken into aount in the robust optimization. Five are isplaye, but the patient shift is for the 3 imensions separately (x, y an z) an therefore inlues 4 extra senarios. The plan is mae to not only over the nominal senario, but the error senarios as well. Courtesy of M. Hoogeman.

21 2.2. Moving targets in proton therapy The interplay e et Lung tumors are i erent from many other types of tumors in the sense that they are not stati. Movement of the tumor may ause uner- or overosage of the tumor or OARs, possibly reuing the tumor ontrol probability an inreasing risks of ompliations. But how oes this happen? Again, protons are very sensitive to ensity hanges they fin along the way, a proton an travel 1000 times further in air than in water (Suplee, 2009). Therefore it is intrinsially important for the suess of a treatment that the anatomy of the patient is similar to the planning anatomy. This is a problem even without movement of the tumor. Air avities in the beam path ause overshooting of protons in tumors near these organs. This is an issue for lung tumors, as the tissue thikness an omposition aroun the lungs epens highly on the position in the lung. The i erenes in anatomy an be aounte for by using multiple CTs of breathing phases in the optimization. Aounting for these i erenes in anatomy an be alle a 3D robust plan, whih means that if the tumor were stati in a breathing position, the overage woul be su ient in eah of these breathing positions. This oes however not neessarily mean that a plan is 4D robust. The 4D robustness of a plan an be investigate by evaluating the movement of the tumor uring a treatment. Not only might the tumor surpass the bounaries of the planning volume (although this an be fixe by inreasing the margin), the tumor aumulates spots uring irraiation that o not neessarily en up in the planne position. In this ase the total ose to the tumor might be aoring to plan, but the final (ynami) ose istribution is almost ertainly not. This problem is epite in Figure 2.13 an shows the arising of hot- an olspots in the tumor. Therefore the interplay e et an be esribe as the ose egraation ue to unplanne hot- an olspots beause of interfrational anatomial movement. The interplay e ets auses possible inhomogeneities in target overage an ose blurring along the eges of the targete strutures (Zhang et al., 2012). Therefore, even when the anatomy is taken into aount, whih oul be onsiere a 3D robust plan, a robust 4D plan is not guarantee. Interplay is not only an issue for IMPT, but also a ets IMRT an other forms of treatments that involve spot sanning. Figure 2.13: Consequenes of the interplay e et. A spot sequene for a tumor is applie to the moving tumor. One an see that, ue to respiratory motion as isplaye in the graph, the tumor reeives spots in plaes i erent from the spot sequene in the most left piture. One shoul take into aount that the figure has a plan that is base on a stati onition with small margins, but the interplay e et will a et plans with bigger margins too. Taken from Rietzel an Bert, 2010.

22 14 Chapter 2. Movement of targets in proton therapy In literature the opinions on the onsequenes of the interplay e et i er. Aoring to Kraus et al. the interplay e et will be reue signifiantly after frationation, but the e et will remain visible. Irregular breathing motion will also help this reution (Kraus, Heath, an Oelfke, 2011). Grassberger et al. foun that the spot size use uring treatment has an e et on the magnitue of the interplay e et, as well as the motion amplitue. On the other han they also foun that motion amplitue is not a goo preitor of the magnitue of the interplay e et (Grassberger et al., 2013). Bert et al. performe a phantom stuy an also agree on frationation to mitigate the e et, an expet a resiual i erene from the stati ase as well. They also express their onerns on hypofrationation in these ase, an preit that the use of extra mitigation tehniques (as will be isusse in the next setion) will be ruial (Bert, Grözinger, an Rietzel, 2008). To onlue, Inoue et al. foun that inreasing the robustness settings from 5 to 7 mm when applying minimax robust optimization i not mitigate the interplay e ets, yet inluing frationation an resanning i (Inoue et al., 2016). A fator that has not been taken into aount in the above mentione stuies is hanging anatomy uring treatment. Aoring to Ho man et al. 61% of the NSCLC patients they investigate woul have neee re-planning if they ha been treate with IMPT (Ho mann et al., 2017). This means that, on top of the preite resiual e et of the interplay, the ose eposition is also istorte by hange in anatomy by an unquantifie amount. Another fator influening the magnitue, as emonstrate by Knopf et al., is the hoie of the fiel geometry an the number of fiels (Knopf, Hong, an Lomax, 2011). Even if a beam angle is benefiial to mitigate interplay, however, it might not be benefiial with respet to OARs Mitigating the interplay e et The interplay e et ours with all tumors that move intra frationally, meaning it will not only influene lung, but also e.g. liver an panreas tumors. There are multiple ways to get a suppose reution of the e et, aoring to literature. The priniple of mitigation is either fouse on ontrolling the movement, ontrolling the beam-on time, or a ombination of both. A visual epition of some methos is shown in Figure Resanning The first tehnique is rather easy to implement, as no extra equipment is neee, an only has its isavantage in longer treatment times. By lowering the intensity of irraiation, but irraiating the tumor multiple times uring a fration, the overage of the tumor will be enhane. The priniple is base on the assumption amongst many researhers that the interplay e ets will average out over the ourse of many frations. Therefore, if the patient is treate aoring to the ITV priniple hot- an olspots will arise, but by simulating more frations in the form of resanning, hanes are that they are anele out. One an istinguish volumetri or layere resanning. With the first approah the target is sanne entirely, an this is repeate. With the latter an energy layer is sanne, an then resanne a fixe number times, after whih the beam ontinues to the next layer (Rietzel an Bert, 2010). Layere resanning is faster than volumetri resanning, as fewer beam energy swithes have to be exeute (Grassberger et al., 2015). Breath hol The priniple of this metho, although being rather intuitive, is to plae the patient in a position in whih he or she an hol his or her breath. This an either be one voluntarily, or with the help of extra equipment that allows longer breath hols. By holing breath, the tumor gets an approximately fixe position, whih makes it a stati target. This reues the hanes of hot- an olspots. However, multiple

23 2.2. Moving targets in proton therapy 15 breath hols are neessary to omplete the fration an the fixe position of the tumor may vary per breath hol. Therefore there is still an unertainty in ose elivery, but the benefit might be big enough (Duek et al., 2016). Gating Gating basially hols the same priniple as breath hol, but in this tehnique (ontrolle) free breathing is allowe. Although this souns ontraitory, in both tehniques the tumor is irraiate in only one phase of the breathing motion. Aitional tehniques are use to etermine the position of the tumor, an the beam is only swithe on when the patient is in the pre-etermine irraiation phase (Rietzel an Bert, 2010). This is usually en-expiration, as this appears to be the most stable phase (Song et al., 2008). Traking The tehnologially most hallenging tehnique of this list is traking. Traking allows a faster treatment than gating, as gating only allows a fration of the breathing yle to be use, thus requiring a lot of yles. By traking the tumor throughout treatment it an be mae sure that all ose ens up in the tumor homogeneously, mitigating interplay e ets. The tehnique requires a perfet etetion of tumor motion an a fast swithing time. Nevertheless, it annot ompensate for i erenes in anatomy uring sanning (Water et al., 2009). Figure 2.14: Di erent tehniques to ompensate for the movement of tumors, some of them being more robust to interplay than others. In resanning the total ose is the same, but instea of elivering it in one sanning sequene, it is elivere in multiple. Pratially this means the fration is elivere multiple times, but with smaller intensity. Gating fouses on traking the patient s breathing, an when the breathing enters a preetermine breathing phase, the ose is elivere. It is relatively slow, as only a small part of the breathing of the patient an e etively be use. Thir is traking, whih allows onstant ose eposition as the tumor is trake with breathing monitoring. It is tehnologially the most hallenging one, yet oes not guarantee perfet irraiation. Lastly is breath hol, whih is quite similar to gating. The patient is only irraiate in one breathing phase, but the elivery will be faster as the patient spens more time in the partiular phase. As the patient is irraiate uring multiple breath hols, the position of the tumor might not always be the same.

24

25 17 Chapter 3 Simulation of the interplay e et The goal of this thesis is to emonstrate a moel, that an aurately preit the influene of the interplay e et on the ose elivery of IMPT in the lung. In this hapter the esign of the moel is explaine. 3.1 Builing an interplay moel To simulate the interplay e et a similar approah is taken that has been esribe in literature before. Examples are Karar et al. (Karar et al., 2014), an Dowell et al. (Dowell et al., 2013). There are some i erenes, as Karar et al. use a synhrotron, whih a ets treatment times, an Dowell et al. only analyze perfet an perioi breathing motion, whih woul not be the ase in a real treatment senario. The implementation of the moel is epite in a flowhart, whih is shown with its omponents in Figure 3.1. The moel is explaine step by step Simulating the patients an their breathing The basis of the simulation is forme by 4DCT sequenes of the lung aner patients esribe above, all having the referene breathing phase (50% exhale) ontoure. The phases available always inlue the extremities an the in-between phases; 0%, 25%, 75%, 100% inhale an referene phase 50% exhale. For the thesis no hysteresis in breathing motion was onsiere, whih ause the assumption that the 25% inhale is equal to the 75% exhale an so forth. The assumption is that this 4DCT sequene is representative for the patient s motion throughout the treatment. Aoring to Gukenberger et al. this is a vali assumption when the patient has tumors that are not loate in the lower lobe (Gukenberger et al., 2007). Therefore, by esribing the respiratory movement, the tumor motion is also foun. For this thesis five respiratory phases are inlue in the simulation (0% inhale, 25% inhale, 50% exhale, 75% inhale an 100% inhale). By sequening these phases in aorane with the hosen breathing senario, a CT time line is onstrute. The CT time line is epenent on the type of breathing input. As an input three senarios are implemente, a hybri (or sample) senario, in whih the breathing is approximate as sequenes of ranom perios with perfet shape, sample from a fitte Gaussian (mean of 3.8 s) to raw ata. The other two senarios are ieal, in whih the first one has a single breathing perio that is fixe throughout all frationation shemes, the seon being a ombination of two fixe breathing perios. These senarios are visualize in Figure 3.2.

26 18 Chapter 3. Simulation of the interplay e et 4DCT sequene Obtain DIRs Warp ontours to other 4DCTs Optional Ieal Realisti Hybri Create CT time line with breathing senario, ranom starting time an 4DCTs Create ITV Plan optimization Use plan outome Plan reomputation Mahine parameters For all breathing phases Dose per spot matries Create treatment time line Transform ose per spot matries Treatment time line CT time line Transforme ose per spot matries Assign spots to 4DCT phase A ose matries for all selete spots Interplay ose Evaluate ose istribution New sample? No Save results Yes Figure 3.1: Flowhart of the interplay moel use in this thesis. The blue boxes represent proesses to be performe, the white boxes inlue available or alulate ata. The otte line enloses the steps for whih Erasmus MC RTStuio is use, all other proesses are performe in separate MATLAB oes.

27 3.1. Builing an interplay moel 19 Figure 3.2: A visual representation of the i erent breathing senarios use for simulation. The first senario is the ieal senario, with one fixe T throughout treatment. In the mile is the ieal senario with two alternating breathing perios uring treatment. Lastly there is the hybri senario, with Gaussian istribute breathing perios. The starting point of treatment is hosen ranomly, an an be anywhere on these time lines. Depening on whether the ieal or hybri senario is hosen, this time line is repetitive. For this thesis the ieal motion is esribe as os 4 ( fit T +Ï). The power of the osine is base on information from George et al., an the starting ieal breathing perio is hosen to be T =4.2 s, in aorane with Lujan et al. an Karar et al. (George et al., 2005, Lujan et al., 1999, Karar et al., 2014). When a fixe ombination of two alternating perios was applie the hosen times were T =3.8 s an T =4.2s. The 4DCTs are also use to etermine the eformable image registrations (DIRs) between the referene phase an all other phases, isusse in the next setion Obtaining the eformable image registrations To fin the movement of the tumor, eformable image registration (DIR) was performe on all 4DCT phases an the referene phase (whih was set to 50% exhale, as mentione before). The metho for the DIR is the Grey-Sale Mean Squares metho, as it gave goo results on the patients an uses the funtionalities of Erasmus MC RTStuio. The image registration an then provie a more natural transition. The work flow to etermine the DIRs is epite in Figure 3.3.

28 20 Chapter 3. Simulation of the interplay e et Referene phase CT Phase CT Set region of interest Assign unique frame of referene to CT Set DIR parameters Perform DIR Visually inspet quality DIR Is the visual quality goo enough? No Inrease omputational power Reompute ose matrix on phase CT Yes Transform reompute ose to referene phase Calulate DVH of phase CT Calulate DVH of referene phase CT Compare DVH urves Are the DVH urves similar enough? No Yes Save DIR Figure 3.3: Flowhart of the valiation of the DIR. The input to etermine the DIR are the CT sans of both referene phase an phase of interest, an the realulate ose matrix on the phase of interest. The first inspetion of the DIR is one visually help of an alternating view between two CT sans, the seon is by omparing DVH urves before an after transformation. The hoie of a type of image registration, instea of ontour registration was eie base on phantom stuies. Both have their avantages an isavantages, but the main reason to go for the image registration is to keep a reliable ose istribution aroun the tumor. As shown in Figures 3.4a an 3.4b, the ontour registration only fouses on the ontours use for registration.

29 3.1. Builing an interplay moel 21 Outsie these ontours strange results may our, espeially when there is an extreme eformation. (a) A ose istribution with four beams optimize for a phantom. text text (b) A ose istribution with four beams optimize for a phantom with half the imensions as in Figure 3.4a, whih is then eforme Figure 3.4: An example of ontour registration problems. On the left a phantom is shown, with a ose istribution that is optimize for the phantom. On the right a ose plan was optimize for a phantom with half the imensions of the left image, then a ontour registration was performe from the small to the big phantom, whih was use to eform the ose istribution to the bigger phantom. This eforme ose istribution is isplaye on the right. The ose istribution insie the target is still uniform, but outsie the target a lear blurring an smearing of the ose is visible ue to the eformation. A eformable image registration woul have been more suitable in this ase. Starting with the CT sans of both the referene phase an phase of interest, the first step to unertake is to assign the phase of interest with a new frame of referene. As both CT sans originate from the same 4DCT sequene, a new frame of referene is neessary to istinguish between the two. When this is assigne, the region of interest is hosen. The key here is to hoose a region of interest that is big enough to follow the most important organs (lungs, OARs), but small enough to ensure goo resolution. After setting the region of interest, parameters onerning the DIR routine are hosen an the DIR routine is starte. These are empirially foun, after trying multiple rouns with ifferent settings. The tune parameters inlue inreases in gri size, number of pixels an number of iterations. In all ases, the moifiation of three parameters woul work. The number of pixels per resolution level was set to 200 an 1000, the vetor fiel gri size per resolution level was set to 15 an 30, an the number of optimization iterations per resolution level was set to 10. When the routine is finishe, inspetion of the DIR is possible in RTStuio. The referene phase an transforme phase of interest are overlappe, whih makes it possible to spot ifferenes an inspet quality. This type of inspetion is arbitrary in the sense that it requires a traine eye, but is goo enough as a first inspetion. This transformation is then use to propagate the ontours, after whih plan optimization or reomputation an be exeute. The DIR is teste more elaborately after the plan optimization or reomputation is finishe, an when the ose istributions on the phase of interest are available. With these ose istributions, the DVHs (Dose Volume Histograms) an be ompute. As these urves have to be

30 22 Chapter 3. Simulation of the interplay e et the same after transformation, the istribution is transforme with the DIR to the referene phase to be heke. If the DVH urve oes not eviate too signifiantly, the DIR an thus transformation is onsiere goo enough. The DIR an then be use to transform all ose per spot istributions to the referene phase. An example of the DVH urve omparison is shown in Figure 3.5. Figure 3.5: Dose volume histogram of the reompute ose istributions on other phases than the referene phase an the DVHs after transformation from the other phases to the referene phase. A goo math iniates a reliable transformation. The transformation is not perfet, but is onsiere to be reliable enough to show interplay e ets. The i erenes an be explaine by interpolation i erenes after ose transformation aroun the eges of the target strutures, or by small moifiations to the propagate ontours ue to transformation mistakes. Multiple settings were trie, but a perfet overlap was unfortunately not foun. Goo enough is hereby efine as oul not be improve with more omputational power. The quality assurane of the DIR may seem like an overkill, but is very important. To investigate the eterioration in ose elivery it is ruial to have absolute ertainty about the origin of the e et. By assuring that the quality of the transformation is goo enough, inhomogeneities in ose istribution are ertainly not ause by errors in transformation, an are therefore a iret onsequene of the interplay e et Generation of treatment plans Single robust optimization For this thesis four planning methos are use, of whih the single robust optimization is the first. In the ase of the single robust optimization the 50% exhale (mi-exhalation) position was hosen, as was assume this was the position miextremities. Then a robust optimization was performe on these ontours, whih means that multiple error senarios are taken into aount uring the planning. These error senarios are shifts of patient loation in the ±x-, ±y- an ±z-iretion, an an unertainty in proton range, whih results in a total of 9 senarios (inluing the nominal senario without errors). This hopefully leas to a better tumor overage in real life, as limite shifts or unertainty in tumor loation will not eteriorate

31 3.1. Builing an interplay moel 23 the quality of the plan. As mentione before, an 8 mm set-up unertainty an a range unertainty of 3.5% an 1 mm were use. This margin is base on the work of Van er Voort et al. (Voort et al., 2016). Table 3.1: Robustness settings use in optimization. The values represent possible shifts of the patient, an an unertainty in the elivery of the spot. By antiipating the shifts an unertainty, a plan is eeme to be more robust in elivery, an possibly inreases the hanes of suessful treatment. Senario x [mm] y [mm] z [mm] fl per [%] fl abs [mm] Nominal Multi CT robust optimization The multi-phase part of the optimization is speifi for moving tumors, or lung tumors in this ase. Multiple CT images were obtaine from a 4DCT sequene an use. The most extreme positions are hosen (0% inhale an 100% inhale), together with the 50% exhale phase, an on these three a treatment plan is alulate with the robust multi-riteria ose optimization (this is then a 27-senario optimization). The multi CT optimization takes into aount the hanging anatomy in the other phases, whih oul pose a major avantage over other tehniques. ITV (robust) optimization For the ITV planning a slightly i erent approah was use. Using the funtionalities of Erasmus MC RTStuio an ITV (Internal Target Volume) was onstrute using the ontours of the 0% inhale, 50% exhale an 100% inhale phases. As the optimization is only performe on the 50% exhale CT san with the ITV ontour, the hange in surrouning anatomy when moving is not taken into aount. This gives the tehnique ab initio a isavantage over multi CT optimization. A plan was mae with an without using robustness settings. When robustness settings were use, they were the same as in the single phase optimization. For the ose planning Erasmus MC s in-house evelope system Erasmus MC icyle is use. The optimization is base on multi-riteria optimization with the help of a wish list. This wish list is in this ase preetermine, an ontains not only the beam information, but also the onstraints on OARs an ose values presribe to the tumor region. The system strives towars satisfation of these onstraints or minimizing or maximizing towars esire values. For this thesis a wish list was use that was evelope by Stoel et al. as shown in Table 3.2. All ose plans are elivere by three beams, epening on the loation of the tumor. The number of beam angles an angle hoie for the planning are mostly base on Stoel s work (Stoel, 2016). This work was performe at Erasmus MC an provies avie on how the beam angles shoul be hosen in orer to give optimal results. The resulting plans from optimization were evaluate for target overage, an the results an be foun in the appenix.

32 24 Chapter 3. Simulation of the interplay e et Table 3.2: Wish list use for this thesis. This wish list was ompose by Stoel (Stoel, 2016) an is use together with robustness settings. In the ase an ITV was use for planning, the CTV total (whih inlues the CTV an noes) was replae with the ITV. The rings aroun the CTV then beome rings aroun the ITV. The term Min./Max. stans for minimize or maximize value. Priority Organ Type Min./Max. Goal [Gy] Constraint CTV total Linear Max. 0.99*66 1 CTV total Linear Min. 1.06*66 2 CTV ring 0-10 mm Linear Min. 1.06*66 2 CTV ring mm Linear Min. 0.90*66 3 Lungs-GTV Mean Min. 1 4 Heart Mean Min. 1 5 Spinal Cor Linear Min Plexus Brahialis Linear Min Oesophagus Mean Min. 1 7 Trahea Mean Min. 1 8 Left Bronhial Tree Mean Min. 1 8 Right Bronhial Tree Mean Min. 1 9 CTV ring mm Linear Min. 1 9 CTV ring mm Linear Min MU Linear Min Proessing the plan optimization output The output of the plan optimization is use to onstrut the treatment time line, as step by step epite in Figure 3.6. In this output the spot list is efine, with the omposition of the beams (whih spots make up the beams). This inlues the spots energy, number of monitor units (MUs), whih is a measure for the amount of energy leaving the mahine, an ose eposition matrix on the phase(s) use for planning. With this information a treatment time line an be ompose, with a simulate time stamp for eah spot. For this, multiple parameters have to be taken into aount. Depening on the number of MUs, a spot has an on-time, in whih the mahine is irraiating the patient. After elivering the single spot, the mahine nees time to swith to the next position, whih is the o -time. Both are in the orer of milliseons, but the on-time is alulate with the mahine speifiations an the number of MUs given by the optimization. When the mahine has to swith to a i erent energy layer or a i erent beam angle there is an extra elay in the elivery of the next spot, whih is alle the energy swithing time an the beam swithing time. This is also mahine speifi, the energy swithing time is set to the orer of hunres of milliseons, the beam swithing time is epening on the size of the rotation (but in the orer of several seons). By analyzing the output file of the optimization this an be inlue in putting together the treatment time line. One final possible elay in elivery is if the patient has to be treate with a range shifter, in whih ase an extra omponent has to be inserte in the system. This an a an aitional time of tens of seons. Having all time parameters ombine, the time line is onstrute. This is the founation of the interplay simulation. One element that has not been taken into aount is a possible gantry swithing time, in whih ase the treatment time is epening on the number of gantries use for irraiation. As this is highly unpreitable it is not taken into aount. By analyzing the output file of the optimization this an be inlue in putting together the treatment time line. One final possible elay in elivery is if the patient has to be treate with a range shifter, in whih ase an extra omponent has to be inserte in the system. This an a an aitional time of tens of seons. Having all time parameters ombine, the time line is onstrute. This is the founation of the interplay simulation. One element that has not been taken into aount is a

33 3.1. Builing an interplay moel 25 possible gantry swithing time, in whih ase the treatment time is epening on the number of gantries use for irraiation. As this is highly unpreitable it is not taken into aount. Optimization results Spot list Assign first spot of treatment t =0s Fin time stamp previous spot For all other spots A t on previous spot to time stamp A t off to time stamp Does the urrent spot have a i erent energy from the previous? Yes A t eswith to time stamp No Is the urrent spot the first spot of a new beam? No Yes A t bswith to time stamp Is the urrent spot the first spot with a range shifter? No Yes A t range to time stamp Store time stamp an a to treatment time line Fin next spot No Do all spots have a time stamp? Yes Save treatment time line Figure 3.6: Flowhart of the treatment time line generation. The mahine speifi parameters are use in ombination with the spot list from the optimization results. The treatment time line that is generate ontains the starting time (time stamp) of eah spot of the treatment. Now the ose eposition matries of all separate spots of the treatment are available, but only of phases use in optimization. To also get the matries on the other

34 26 Chapter 3. Simulation of the interplay e et (intermeiate) phases, the plan is reompute on these phases. All ose eposition matries are transforme to the 50% exhale referene phase (with the same transformations use to warp the ontours as esribe above), for final ose aumulation. Therefore, if n is the number of phases use for evaluation, there will be n i erent senarios for eah spot of the treatment. To summarize, out of the plan a number of y spots are foun, meaning a time line with y timestamps, of whih the first spot is elivere at time t =0. These spots are reompute on the other n 1 phases, resulting in y times n ose eposition matries, as shown below. Eah i,y represents the ose eposition matrix of spot y on phase i. A ombination of y ose eposition matries forms an interplay ose. Q a 0%inhale,1. 0%inhale,y R Q b a 25%inhale,1. 25%inhale,y R Q b a 50%exhale,1. 50%exhale,y R Q b a 75%inhale,1. 75%inhale,y R Q b a 100%inhale,1. 100%inhale,y R b (3.1) Calulating the interplay ose Having all information about the movement of the tumor throughout the treatment is enough to atually start the interplay simulation. By hoosing a ranom (virtual) starting point in time for the patient to breathe (whih is a sample, i erent starting points an time lines therefore form i erent samples), the CT time line is efine. This time line an be ompare to the treatment time line, to fin whih spots are elivere in whih phases. A visual representation of the proess is shown in Figure 3.7. Figure 3.7: Dynami ose elivery in IMPT. Eah spot (ross on the treatment timeline) has a time stamp whih marks its elivery time after starting treatment. As the tumor moves with the respiratory motion, it reeives spots in i erent phases. Depening on the position of the tumor when the treatment starts, an the breathing senario, the spot istribution per phase will i er. If it is known in whih point in time the spot is elivere, it an be ompare to the CT time line as shown above. First however has to be eie whih phase this orrespons to, whih is epite in Figure 3.8.

35 3.1. Builing an interplay moel 27 Figure 3.8: Division of time line to CT phases. In this example only the 0% inhale, 100% inhale an 50% exhale are taken shown as example. The absolute position of the three phases are foun (blak line), after whih the intermeiate positions between the blak lines are rawn (re lines). The blue lines represent the isrete CT timeline. Now that the exat times per breathing phase are known, the spots an be assigne. By varying the starting point (an thus taking a sample), the breathing signal or breathing senario, this ose istribution will hange as spots en up in i erent phases than before (Table 3.3 shows a possible onfiguration of a spot ivision). Consequently, there will be a wie array of possible interplay ose istributions. Table 3.3: After assigning y spots to the respiratory phases, it beomes lear what the sprea of the spots looks like. An example of this sprea is given in this table. With this information the appropriate ose matries of the spots an be summe to ompose the interplay ose. Note that eah spot is only elivere to one phase. Spot number y 0% inhale x x x 25% inhale x x 50% exhale x 75% inhale x 100% inhale x Representing this in vetor form results in Equation 3.2. The final vetor shows in whih phase eah spot is elivere, e.g. the first spot is elivere in the 0% inhale phase, an the ose eposition matrix belonging to this spot an phase. As all ose eposition matries are alreay transforme to the referene phase, they an be summe to get the final ose istribution. This an be referre to as the interplay ose. Q a 0%,1 0%, %,y R b + Q a %, %, R b + Q a %, R b + Q a %, R b + Q a %, R b = Q a 0%,1 0%,2 25%,3 50%,4 25%,5 75%,6 25%,7... 0%,y R b (3.2)

36 28 Chapter 3. Simulation of the interplay e et The interplay simulation is sample many times to fin these ose istributions to examine the sprea in results in ose parameters. In this ase the sampling is efine as alulating the interplay ose for i erent starting treatment times (the treatment will start in a i erent phase eah fration). After the interplay ose is ompose of the i erent spots, ose parameters are alulate to quantify the interplay e et. The ose parameters to be foun inlue the V95% (volume reeiving more than 95% of the presribe ose), the V107% (volume reeiving more than 107% of the presribe ose) an the V70% (in this thesis esribe as volume reeiving less than 70% of the presribe ose). The interplay (or ynami) ose is not a linear ombination of the full ose istribution (all spots summe) on the separate phases, resulting in nontrivial results. The V95% value of the interplay ose of a selete optimization metho an thus be lower than the lowest value foun in the reomputation of the same optimization metho on all phases, whih is not intuitive. 3.2 Proessing the output of the interplay moel The MATLAB sript that failitates the alulation of the interplay moel saves its output in a struture ontaining all input an output information. The input information inlues the optimization results as given by the plan optimization, the hosen breathing senario, the number of samples, the ose istributions of all spots before an after transformation, the treatment time line an the CT time line. In the output information is store whih spots en up in whih phase, as shown in Table 3.3, the ose parameters before frationation an after frationation. The results of the moel are isusse in Chapter Appliation of the interplay moel With the interplay moel being built, we investigate two issues. First in literature, as mentione in Chapter 2, an interplay moel is often presente with an ieal breathing motion with the argumentation that this is a worst-ase senario. This means that alulating the interplay ose with the ieal senario gives an upper limit to the e et of the interplay e et, as in real life the patient s irregular breathing will average out the e et, aoring to the papers. It is worth fining out if this is atually the ase. Seon is to investigate the 4D robustness of plans mae for the patients. A plan an be onsiere 3D robust if its overage is su ient in all breathing phases an error senarios, but this oes not neessarily guarantee a su ient tumor overage after movement. By investigating the 4D robustness the atual quality of the plan an be better etermine, preiting the suess of the planne treatment more aurately. This is one by examining the four plans mae for eah patient (single CT robust, multi CT robust, ITV an ITV robust) an performing the interplay alulation on them.

37 29 Chapter 4 Results an isussion 4.1 Patients use in stuy In this stuy three non small ell lung aner (NSCLC) patients were inlue. The patients were taken from a previous stuy, performe by Stoel at Erasmus MC Daniel en Hoe (Stoel, 2016). All three patients ha noal infiltrations, an two of them also ha a visible tumor. The volumes an loations of the tumors are given in Table 4.1. Table 4.1: Volume an loation of the patients tumor. The CTV volume here is efine as the ombine volume of CTV an CTV noes. In the ase of Patient 2, only the noes were irraiate as there was no visible tumor. Volume tumor [m 3 ] Loation tumor GTV CTV Lung Lobe A/P Patient Right Upper Posterior Patient 2* N/A 205 Both Hili N/A Patient Right Mi Posterior *This patient ha no visible tumor, the numbers given here an later on are for both CTV noes. The movement of the tumors was also measure in the aforementione stuy by Stoel et al., whih is shown in Table 4.2. The movement is given in millimeters for both CTV an CTV noes. Table 4.2: Peak to peak amplitue of the tumor movement of the patients use in this stuy. The movement is efine in millimeter an in the x, y an z iretion separately. CTV CTV noes x y z x y z Patient Patient Patient

38 30 Chapter 4. Results an isussion All patients were planne with four planning methos, as esribe in Chapter 3. The beam angles were hosen aoring to Stoel s proposal, an are liste in Table 4.3. The results of these plans are given in Appenix A an are use for further proessing. Only the multi CT optimization showe goo results on all breathing phases. Table 4.3: Treatment angles for the three patients. In this ase the zero egree angle is efine as anterior, the 180 egree angle as posterior. Beam 1 Beam 2 Beam 3 Patient Patient Patient Tuning the moel Choosing the number of evaluation phases Throughout the progress of this thesis the approah has hange several times. At first only the multi-ct optimization was applie, but without robustness settings. This mae it easier to hek the quality of the transformations. Furthermore, the interplay evaluation was only performe on three phases. After the interplay moel prove to work, a swith was mae to evaluation on five phases an inlusion of i erent planning methos. The neessity to evaluate on five phases instea of three beomes lear in Figure 4.1. Intuitively it is natural that an evaluation on phases not taken into aount uring optimization is more likely to to expose problems than only using optimize phases. How muh more suboptimal beomes lear when looking at the figure. A shift in the mean of approximately 20% in the V95% for the non-robust ase, an 10% for the robust ase, shows that using three phases unerestimate the interplay e et. Therefore, it was eie to ontinue with fivephase evaluation. The setions below all follow this priniple. Choosing a CT registration metho As mentione in Chapter 3, an option for registering the eformation between to CT sans, is to use the ontours as mae by an MD. By using ontour eformation a relation an be foun between the CT sans. This tehnique was implemente an prove to only provie information about the ontours use in the eformation, making it not wiely appliable. Using all ontours turne out to be muh more omputationally extensive than the most extreme settings of the DIR, an ha the isavantage of reating istorte ose istributions outsie strutures. Therefore, it was eie to hoose the DIR instea. Choosing a breathing senario In this part the impat of the hoie of the breathing senario on the outome of the interplay ose is isusse. As mentione in Chapter 3 this is one with a hybri senario (name sample in the figures), an ieal senario with one fixe breathing perio (name ieal ) an two fixe breathing perios (name fixe ). The single fration treatments were sample 2500 times per senario for patient 1, an for eah sample the V95% an V107% of the CTV an CTV noes were alulate. Sampling is performe by varying the breathing pattern uring treatment, meaning that the patient will start in a ranom breathing phase in a ranom breathing perio (exept when only one perio is use). The start of treatment an simulate to be begin- an en-phase, or anywhere in between.

39 4.2. Tuning the moel 31 Figure 4.1: Sprea in V95% an V107% in CTV of patient 1 as a funtion of two i erent planning methos an number of evaluation phases. The re ashe line is the value foun in the optimization on the referene phase (stati ase). Planning was one in both ases with the multi CT metho (on 0% inhale, 50% exhale an 100% inhale), both non-robustly an robustly, an then evaluate for interplay. For the five-phase evaluation the plan was beforehan realulate on the in between phases, 25% inhale an 75% inhale. The V95% an V107% values are alulate for eah simulate single fration treatment, 100 times per planning metho an evaluation phases. Evaluation on five phases is more realisti, as phases are inlue that were not planne on, an shows major inrease in the sprea of the V95%. For the V107% there appears to be a smaller i erene. Evaluating on three phases appears to give an unerestimation of the interplay e et. The main goal of the use of three i erent breathing senarios was to etermine what kin of influene this woul have on the resulting interplay ose. Furthermore, literature has state that using an ieal breathing senario woul give the worst ase senario results of an interplay simulation. Figure 4.2 shows the V95% of using the three i erent breathing senarios. What stans out in general is the big sprea in V95% values for all breathing senarios, whih goes up to 35%. When looking at the senarios separately, it beomes lear that the sample ase has more extreme outliers, however the lower whisker of the ieal ase strethes further own than the sample ase. A possible explanation for this phenomenon is that in the ieal ase averaging out is less likely, an the reation of a very unfavorable senario (very low V95% an/or very high V107%) ue to hanges in breathing motion is not possible. Therefore, in the sample ase, averaging out takes plae ue to breathing motion, but also the reation of negative outliers, as visible in the graph. Finally, the fixe ase is expete to be somewhere between the ieal an sample ase, ue to the nature of the senario. It is unfortunately impossible to raw this onlusion from the results.

40 32 Chapter 4. Results an isussion Figure 4.2: Sprea in V95% in CTV an CTV noes of patient 1 as a funtion of three i erent breathing senarios. The re ashe line is the value foun in the optimization on the referene phase (stati ase). The V95% value is alulate for eah simulate single fration treatment, 2500 times per breathing senario. Figure 4.3 epits the V107% of the same ataset. The results verify the onlusions rawn as for Figure 4.2. The main onlusion that an be rawn from this setion is that the averaging e et of a hybri breathing pattern is visible, yet the worst ase senarios are also foun in this ataset. For further researh the sampling senario was hosen, not only for being more realisti, but also to inlue the most extreme ases.

41 4.3. Comparison of planning methos 33 Figure 4.3: Sprea in V107% in CTV an CTV noes of patient 1 as a funtion of three i erent breathing senarios. The re ashe line is the value foun in the optimization on the referene phase (stati ase). The V107% value is alulate eah simulate single fration treatment, 2500 times per senario. 4.3 Comparison of planning methos When omparing the 4D robustness of the planning methos, all three patients were use in the evaluation. The patients were planne with the four methos esribe before: single robust, multi CT robust, ITV an ITV-robust, an then evaluate for interplay with a hybri breathing senario ( sample ). Per patient per planning metho 2500 single fration treatments were simulate, an then evaluate on V95% an V107% for the target. The sampling is performe by ranomizing the CT time line for eah fration an ranomizing the starting breathing phase. Starting begin-, mi- an en-phase were also a possibility. The results are shown in Figures 4.4 an 4.5. The figures are ae in bigger size in Appenix B. The expetation was that the multi CT robust optimization an ITV robust optimization woul perform best onsiering the V95%, simply beause a larger area is irraiate. This is learly visible in the figure, as a higher V95 iniates a better tumor overage. Investigating Table 4.2, there appears to be no strong epenene on amplitue of movement for the meian an sprea of the V95%. The multi CT robust optimization appears to perform best. This an be explaine by the more elaborate planning proeure, as the multi CT optimization takes into aount hanges in anatomy in ontrast with ITV base planning.

42 34 Chapter 4. Results an isussion Figure 4.4: Comparing the 4D robustness of 4 i erent planning methos for three patients in the V95%. Eah subplot ontains 2500 samples per planning metho of a simulate single fration treatment, with a ompletely ranomize hybri breathing pattern eah sample. The ashe line is the value foun in the optimization on the stati ase of the referene phase. It is lear that the robust multi CT performs best for all patients, but is still heavily a ete by interplay. Figure 4.5: Comparing the 4D robustness of 4 i erent planning methos for three patients in the V107%. The same settings are use as isusse in Figure 4.4. The values are quite high ompare to the value foun in the optimization, but results are not onsistent enough to raw a efinitive onlusion.

43 4.4. Impat of frationation 35 The V107% values are less intuitively explaine. An overosage is unerstanable as parts an reeive more spots than planne, but this shoul be orrelate to a non-zero V70% (volume of the target reeiving less than 70% of the presribe ose) as well. This is ue to the fat that loal areas get more spots than planne (overosage), with as a result that other loal areas o not get enough spots (unerosage). The expetation is also that the V95% an V107% values will get more aeptable values after frationation, an this shall be isusse in the next setion together with the impat on the V70%. 4.4 Impat of frationation The results shown in the previous setion lea to some preliminary onlusions, but are not realisti in the sense that single fration treatments are not linially relevant. As they will not atually be applie to patients, it is worth asking the question what is really happening to a patient. In a frationate treatment the interplay e et shoul average out to a ertain extent (aoring to literature), an to whih extent shall be investigate in this setion. For this alulation treatments are simulate for three frationation shemes (1, 5 or 25 frations) an for four i erent optimization methos. After the simulation the V70%, V95% an V107% are alulate for the CTV an CTV noes. For the single fration treatment results from Figures 4.4 an 4.5 were use, the other frationation shemes an V70% values were simulate separately 250 times per optimization metho per frationation sheme. The results are epite in Figures 4.6 an 4.7. Figure 4.6: V95% after frationation for Patient 1. For these results 250 samples were taken for eah optimization metho an frationation sheme. The values onverge for all optimization methos, with i erent outomes. All methos benefit from frationation, as the sprea in values ereases signifiantly. However, only robust multi CT optimization reahes the value foun in the stati result of the optimization.

44 36 Chapter 4. Results an isussion Figure 4.7: V107% after frationation for Patient 1. The same sampling onitions were use as for Figure 4.6. The values for the V107% erease towars the value foun in the stati result of the optimization as more frations were applie, exept for ITV planning. Remarkably enough, in the ase of robust multi CT planning, the V107% value an rop below the optimize stati value. The e et of frationation is learly visible, as all planning moalities erease their sprea in the V95% an V107%, an their meians en up with better values in terms of tumor overage. One important observation is nevertheless that even with 25 frations the single robust optimization an ITV optimization fin unaeptable values for tumor overage. Robust multi CT optimization is the only planning moality that an be onsiere 4D robust after frationation, an is therefore the most interesting for treatment planning. The explanation for the 4D robustness is most likely that the metho shows the best 3D robustness to begin with (as an be seen in Appenix A), as it is the only planning metho that has full overage on all breathing phases without onsiering interplay. This guarantees a better starting point than the other planning methos. When one assumes that in the robust multi CT ase the only onern is then loal over- an unerosage, frationation proves to give great benefit by averaging out the hot an ol spots. In Figure 4.8 the V70% is isplaye, as it gives a goo view on unerosage of the tumor. It seems that only single fration treatments show high values in V70%, an frationation gets ri of the unerosage. This observation in ombination with the relatively high values of the V107% in the single fration treatments, reates the presumption of some kin of ripple e et. By epositing a large amount of ose in one part of the tumor, another part of the tumor is unerose. By applying multiple frations these ripples start averaging out.

45 4.4. Impat of frationation 37 Figure 4.8: V70% after frationation for Patient 1, again from the same ataset of Figures 4.6 an 4.7. It is foun that the values of the V70% are small, even in single fration simulations. After this, they erease even more rapily, being pratially zero for all optimization methos an both CTV an CTV noes after 25 frations. The non-zero values of the single fration treatment nevertheless strengthen the hypothesis of the interplay e et as a ripple e et in the ose elivery. This ripple e et an be visualize with the ose istributions as foun on the CT san, whih is epite in Figures 4.9a an 4.9b. (a) Optimize ose istribution (b) Interplay ose istribution Figure 4.9: Optimize ose istribution from the robust multi CT optimization for patient 1, an the interplay ose istribution as foun in the samples with the highest V107% value for a single fration treatment. In both pitures the same patient with the same ontour is isplaye. The outer shape of the ose istribution oes not hange a lot ue to interplay, but the inhomogeneity of the istribution ue to interplay is learly visible.

46 38 Chapter 4. Results an isussion The figure isplays the result of the robust multi CT optimization on patient 1. It is lear that goo overage is reahe for the entire tumor in the stati ase, as shown in Figure 4.9a. A non-uniform margin is visible, resulting from the multi CT optimization, to ompensate for goo overage in the other respiratory phases. In Figure 4.9b the interplay ose istribution belonging to the most extreme ase of the V107% foun in single fration samples is isplaye. The outer shape of the ose istribution is not preisely as the optimize ose istribution, but the shape an still be reognize easily. The strong inhomogeneity is more striking though, as lear hot an ol spots have arisen. The ripples in the ose istribution are visible. The ose has been elivere to the tumor, but istribute in a way that there is serious unerosage in some parts an onsierable overosage in others. When onsiering the e et of frationation, it seems that even with ramati inhomogeneities in ose elivery to the tumor in single fration, robust multi CT optimization performs su iently well if enough frations are applie. The goo performane is not only foun for this patient. In Figures 4.10, 4.11 an 4.12 the results are shown of frationation being applie to all patients of this stuy, after being planne with the robust multi CT optimization. The figures an again be foun full size in Appenix B. The sample size was again 250, with a hybri breathing senario. All show goo overage after 25 frations, with a reue V107% an approximate zero of the V70%. Figure 4.10: Impat of frationation on the sprea of the V95% for all patients. The planning metho is robust multi CT optimization. All V95% values onverge towars the optimization value as more frations are applie.

47 4.4. Impat of frationation 39 Figure 4.11: Impat of frationation on the sprea of the V107% for all patients uner the same onitions as Figure The same onlusions an be rawn as for that figure. Remarkably enough, after 25 frations values an be ahieve lower than the optimize value. Figure 4.12: Impat of frationation on the sprea of the V70% for all patients uner the same onitions as Figures 4.10 an The values are only non-zero in ase of single fration treatments, showing lear eviene that frationation auses averaging out of these ol spots.

48 40 Chapter 4. Results an isussion To onlue, interplay an severely eteriorate ose elivery, resulting in erease V95% of up to 40% for a single fration treatment of a robust multi CT plan. The magnitue of the e et annot be iretly orrelate to size of the movement, as the largest movements o not math the biggest sprea of V95% or the lowest meian of the V95%. It might however be interesting to vary beam angle hoie, to see to what extent this influenes the ose elivery. Furthermore, it seems that for all optimization methos require aitional interplay mitigation tehniques as esribe in Chapter 2 when hypofrationation is esire. As only robust multi CT optimization appears to be apable to reah the optimization value after 25 frations, it is avisable to investigate whether the use of the interplay mitigation tehniques an benefit the other tehniques to ompete with the robust multi CT optimization. 4.5 Comparison results to literature When omparing the results to literature, some interesting onlusions an be rawn. Kraus et al. performe a realisti simulation of the respiratory motion of lung tumors in IMPT. The planning strategy use was ITV planning. Multiple breathing variabilities were introue, suh as baseline shift, starting phase an breathing perio. The evaluation was one on ten CT sans of the 4DCT sequenes of three patients. Although it is i ult to ompare the sprea in results with the sampling an evaluation methos use by the group, they fin that frationation (30 frations) greatly enhanes tumor overage (Kraus, Heath, an Oelfke, 2011). The planne value however was not foun, but this is also the ase with the ITV planning as use in this thesis. In the ase of single fration elivery the ose inhomogeneities showe omparable patterns to the ones foun in this thesis. Bert et al. performe an interplay evaluation on five ITV-planne patients, with 108 samples eah (varying treatment perio an starting time). The treatment was not IMPT, but arbon-ion sanning, an is therefore not entirely representative. For the five patients the foun an average V95% of 71.0% ± 14.2% for a single fration treatment, although the number of evaluation phases is not given (Bert, Grözinger, an Rietzel, 2008). The result is highly omparable to the patients an evaluation use in this stuy, but the omparison shoul be one autiously as ifferent irraiation tehniques were use. Grassberger et al. varie spot size, an investigate the epeneny of interplay e ets on motion amplitue (Grassberger et al., 2013). The spot size oul not be varie in this thesis, but the motion amplitue orrelation oul not be foun. The number of patients use in this stuy is not big enough to motivate the orrelation either. More investigation on this part will have to be one, inluing more patients in the stuy. Finally, Inoue et al. planne 10 patients on an ITV with a minimax robust multifiel optimization tehnique, an evaluate for interplay on 8 phases with ieal breathing motion. The robustness settings were 5 an 7 mm.the breathing perio was equal to T = 4.5 s. The interplay i not eteriorate the patients V95% to linially unaeptable values. The reason for these i erent results is not lear. The movement of patients use in the stuy is equal or larger than the patients use for this thesis, suh that at least omparable interplay e ets are expete. The esription of their interplay moel is however quite short, suh that i erenes with the moel of this thesis are not easily foun. Inoue et al. i fin a big benefit for resanning an frationation, whih is also one of the onlusions of this thesis.

49 4.5. Comparison results to literature 41 The interplay moel built in this stuy has shown the apability to preit 4D robustness of treatment plans. As the magnitue of the interplay e et annot be iretly orrelate to tumor movement in this stuy, the moel is a useful tool to preit the magnitue of the interplay e et. There are naturally more reommenations on how the moel an be improve an fully exploite, whih are isusse in the next hapter.

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51 43 Chapter 5 Future researh an reommenations 5.1 Improvement of the interplay moel In this setion improvements for this thesis are isusse. These are mostly interesting when more use of this moel is esire, but were not implemente before ue to time onstraints or lak of ata Reution of omputation time The major point of attention for the interplay moel is the time it takes to gather samples. These samples, epening on the number of spots in one treatment, an take up to a few minutes. Sine most of this time is spent in aing full ose matries (one for eah spot), it makes sense to invest in improving this part of the omputation. One of the methos to spee up this aition is to introue a ose mask. A ose eposition matrix has the resolution of the CT san it is mathe to, an an therefore ontain millions of voxels. Having a matrix this size for eah spot, for eah breathing phase, is therefore a memory intensive proess. However, a big part of all these matries will equal zero, as only the tumor an the trajetory before the tumor will be irraiate. By beforehan seleting the extremities of the CT san where ose will be eposite (with the help of the available ose plans an realulations on other phases), only a small part of the ose eposition matrix has to be selete an save, whih will form the ose mask. If this matrix is one thir the size of the original matrix, the omputation time goes own with a fator of three as well. A final, yet more trivial, suggestion to spee up omputation time is to exeute the samples in a omputationally parallel way. However, the exat implementation is not lear yet Optimization of DIRs A relatively weak point in builing the interplay moel is the nee for qualitatively goo eformable image registrations (DIRs). Some CT sans from the 4DCT sequenes ha artifats ue to problems in proution of the 4DCT (merging issues), reating suboptimal registrations. Sine this problem is unfortunately in the nature of the proution of 4DCTs, it might be worth to look into ombine methos. By using a ombination of the ontours in the breathing phases an the CT sans themselves, a more reliable registration an be foun. One of the avantages for this type of registration is that registrations are more aurate speifially for the

52 44 Chapter 5. Future researh an reommenations tumor an OARs. Dose that was aumulate in a CTV or an OAR voxel before transformation will also be ontaine in the same organ after transformation. This is partiularly interesting as eges of the tumor, with the help of ontour base registration, will no longer reeive uner osage ue to a rough transformation gri, yet outsie the tumors an OARs transformations will remain aurate ue the image base registration. By improving the quality of the registration it results beome more reliable to be a ete by interplay or transformation quality, an future alulations require less fine-tuning Inlusion of a realisti breathing senario Another point of improvement is the lak of use of a iret breathing signal. While this is the most reliable soure of movement of the patient, it oul unfortunately not be use for this thesis, making it lose some of its value. By using the signal iretly, the moel beomes more realisti, espeially when ata is available with whih the patient s breathing signal is atually iretly onnete to the patient s 4DCT sequene. Hopefully it then beomes lear if this senario is really patient epenent, an if the hybri or ieal senario prove to be worthy replaements. When using this methoology in ombination with the better registrations, senarios an be simulate in whih the patient surpasses the most extreme positions foun in the 4DCTs. Breathing motion is not onstant uring treatment, an assuming a patient always breathes a full an perfet yle is therefore not always realisti. Deeper inhalation or exhalation an be loate with the use of the breathing signal, an an be proesse by reating a virtual CT to investigate the osimetri impat Inlusion of hysteresis As shown by Seppenwoole, hysteresis in tumor motion an be signifiant (Seppenwoole et al., 2003). In this thesis hysteresis is not inlue, but signifiant hysteresis in patients will most efinitely worsen tumor overage. It is assume that the 50% exhale of the patient is the intermeiate position of the motion, but with hysteresis this might atually not be the ase. Moifiation of the oe an evaluation on this extra phase will give more larity for patients that show problemati hysteresis. Optimizing on this extra 50% inhale phase might be then more 3D an 4D robust, as an be evaluate with the interplay moel Inlusion of ranom an setup errors While planning the patients, some of the planning methos inlue robust planning. The purpose of this planning metho is to ensure goo tumor overage even when the patient or tumor is slightly shifte. In the interplay moel mae for this thesis it is assume that the patient is always positione in the nominal, error-free senario. Naturally, this is not the ause. It might be interesting to see if there is a i erene in sprea in V95, V107 et. if ranom errors are introue. Perhaps the onvergene that is seen for multi CT robust planning will no longer hol, or will be benefiial for the other planning tehniques, making them feasible alternatives Evaluation on more phases In Chapter 4 it beame lear that evaluation on five respiratory phases shows learly i erent results from evaluation on three phases. One might woner if swithing

53 5.2. Interplay robust optimization 45 from five phases to even more phases shows i erent results for the magnitue of the interplay e et. Due to limite resoures of the 4DCTs an time onstraints this has not been one, but might also be worth investigating. The approahes in literature i er: Kraus et al. an Li et al. use ten respiratory phases for evaluation (Kraus, Heath, an Oelfke, 2011, Li et al., 2014), but Grassberger et al use four (Grassberger et al., 2015). As more phases intuitively shoul isplay a more reliable result (the isrete steps in time beome smaller), the impat on the ultimate results will get smaller. More respiratory phases result in more ose reomputations an are therefore more memory intensive. For the interplay moel reate in this thesis a limite number of phases shoul therefore be use, but how many has yet to be investigate PCE analysis The robust optimization metho as applie in this thesis uses a set-up error of 8 mm for optimization, base on the work by Stoel (Stoel, 2016), but set-up an ranom errors have not been introue in the simulation of the treatments. Base on the results of the appliation of frationation shemes, it appeare that 25 frations are su ient to mitigate the interplay e et su iently without these errors. Smarter robustness settings might however be esirable, either inhomogeneous (not a fixe istane aroun the tumor) or simply homogeneously bigger or smaller, when the atual treatment of the patient is onsiere with errors. Therefore, if the interplay moel is moifie to take into aount treatment unertainties, a PCE (polynomial haos expansion) moel an be built, as one by Van er Voort (Voort et al., 2016). Hopefully, with this work, better margins an be reate for moving tumors in general to ahieve better tumor ontrol while sparing healthy tissue. 5.2 Interplay robust optimization This setion is more fouse on researh that is not iretly linke to the interplay moel, but ontains reommenations for researh iniretly linke to 4D robustness. To start, a proposal is esribe for a 4D optimization tehnique to ompensate for interplay e ets. Contemporary tehniques are apable of ompensating for movement, but lak tools to prevent hot an or ol spots an high ose elivery in surrouning tissue an OARs. The tehnique esribe below has a better apability to prevent both situations an is therefore an interesting tool when one is intereste in applying hypo frationation an/or making treatment plans for tumors with serious intra-frational movement icyle optimization Erasmus MC icyle uses a multi-riteria plan optimization, an for a full explanation it is avisable to rea the work by Breevel et al. (Breevel et al., 2012). On of the elements playing a role in the optimization is Equation 5.1, whihwill be fouse on now. In this equation three elements an be istinguishe. A, whih is the ose eposition matrix, basially holing all information about the voxels of the CT sans an their onnetion to the spots. Then w, whih is the spot weight vetor an the element to be optimize. Then finally, there is the eposite ose vetor, whih esribes the total ose that ens up in the voxels alle in A (thus the voxels taken into aount in the optimization). Aw = (5.1)

54 46 Chapter 5. Future researh an reommenations In a matrix form this looks like Equation 5.2. Q R Q v voxel,1 v voxel,1. a.... b a w opt,1. R Q b = a voxel,1. R b (5.2) v voxel,m v voxel,m w opt,n voxel,m When one wants to optimize robustly, thus inlue setup an range errors in the form of ± x, ± y, ± z an ± fl, nine equations in the shape of Equation 5.2 are optimize simultaneously. In the multi CT optimization, as use in this thesis, a slightly i erent senario is use. When n CT sans are use as input with m n voxels use for optimization, ose eposition matrix is expane for the other CT sans as well. This gives the following result: Q R v voxel,ct1,1 v voxel,ct1, v voxel,ct1,m1 v voxel,ct1,m1 Q. a. v voxel,ctn,1 v voxel,ctn,1. a.... b v voxel,ctn,mn v voxel,ctn,mn w opt,1. w opt,p R Q b = a voxel,1. voxel,m1+...+m n R b (5.3) Again, in the ase of robust optimization, nine of these equations are optimize simultaneously. One an expet that the omputational time will inrease when more CT sans are use for optimization. Plans mae with icyle are Pareto-optimal, whih means that the solution foun (provie the optimization was exeute suessfully) is on the Pareto surfae. A Pareto-optimal plan is esribe by Paganetti as: Given a set of objetives an onstraints, a plan is onsiere Pareto-optimal if it is feasible an if there oes not exist another feasible plan that is stritly better with respet to one or more objetives an that is at least as goo for the rest (Paganetti, 2012). A Paretooptimal plan is not a single solution, but part of a series of solutions: the Pareto surfae. An example is given in Figure 5.1.

55 5.2. Interplay robust optimization 47 Figure 5.1: Visual example of a Pareto surfae for three organs at risk (OARs). The Pareto surfae is a olletion of treatment plans that an be onsiere optimal solutions of an optimization. Improving the ose elivery in one OAR, while navigating on the Pareto surfae an maintaining an optimal solution, results in a higher ose in a i erent OAR. Moving towars ose values lower than the Pareto surfae is a possibility, but this has the onsequene that onstraints are not met an thus the plan is not linially appliable Implementation in icyle As isusse before, movement of tumors an be aounte for by using margins for the movement or multiple CT sans for the hange in anatomy, but not yet for the appearane of hot- an olspots. Starting with Equation 5.3, a ose istribution for two phases resulting from this multi CT optimization woul then look like Figure 5.2. A plan is mae that satisfies both anatomies. Figure 5.2: Multi CT optimization on two phases. Two phases are use in the optimization, guaranteeing goo overage when the tumor is the upper an lower position. This is however a binary senario, the tumor has to be in either one for the entire treatment. A ombination of the two is not taken into aount. The plan is 3D robust an overs therefore both positions, but not neessarily possible inbetween positions an ombinations of those.

56 48 Chapter 5. Future researh an reommenations When alulating the interplay ose, as esribe in Chapter 3, the spots of the treatment are assigne to a ertain breathing phase. Then, for ose aumulation, the spots are also transforme to their referene phase, meaning that the voxels between phases are linke. Both priniples are applie in the 4D optimization. Assigning spots to a breathing phase means they will not ontribute to other breathing phases, resulting in a sparse ose eposition matrix. The key point of this new iea of optimization is that a swith is mae from a binary senario (tumor is either in one phase or the other) to a non-binary senario, in whih the tumor spens time in both phases. Spots are no longer projete on both phases, but will be projete only on one of the phases use for optimization. In Equation 5.4 an example is shown in the ase that 2 CT sans with 3 voxels are use for optimization. After the interplay simulation the spots are assigne, an in this ase the spots alternately en up in the first an seon CT san. When looking at the sans seperately, none of the ose objetives are met, as only approximately half of the ose is present on both sans. Q R v CT1,1 0 v CT1,1 0 v CT1,1 v CT1,2 0 v CT1,2 0 v CT1,2 Q v CT1,3 0 v CT1,3 0 v CT1,3 0 v CT2,1 0 v CT2,1 0 a a 0 v CT2,2 0 v CT2,2 0 b 0 v CT2,3 0 v CT2,3 0 w opt,1. w opt,5 R Q b = a 1. 6 R b (5.4) Now the relation between the voxels an be use, sine the CT sans epit the same tumor. This information is obtaine with the help of eformable image registration (DIR) an reates a link between separate voxels. Using this information there an be a reution of the ose eposition matrix of Equation 5.4, resultingina simpler an more familiar matrix as shown in Equation 5.5. This transforme an merge matrix shows the ultimate ose on the tumor, the one that an fulfill the ose objetives. Q a v CTnew,1 v CTnew, R Q b a w opt,1. R Q b = a 1. R b (5.5) v CTnew,mnew v CTnew,mnew w opt,p mnew Without this reution optimization is not possible. In the traitional multi CT optimization both CT sans are treate as binary senarios. The patient is assume to be in either of the phases uring a fration of the treatment, an not in both. In normal pratie, however, the patient swithes between phases, an therefore has a ombine ose epening on whih spots are elivere in whih phases. All phases ontribute to the total aumulate ose, whih is epite in Figure 5.3. The sparse matrix in Equation 5.4 epits this ombination mathematially: the tumor no longer has goo overage in all phases separately. This makes sense, beause treatment will be a ombination an aumulation of all those phases, in ontrast with the previous metho. Therefore the phases have to be linke, in orer to have the apability to optimize. Repetition of this simulation results in i erent istributions of spots, an therefore i erent senarios that an be interprete as robustness senarios an optimize.

57 5.2. Interplay robust optimization 49 Figure 5.3: Visual explanation why DIR information is neessary for optimization. Delivering the plan of Figure 5.2 oul result in two very extreme ases. In the top of the image, the lower part of the plan is eposite while the tumor is in the lower position, giving full overage. The upper half is eposite while the tumor is in the upper position. The tumor reeives goo overage, but is at risk of reeiving a high V107%. The bottom of the piture shows the other possibility; the tumor is in the opposite position of where the ose is elivere. The tumor oes not get full overage an an unsuessful treatment is given. The same plan, whih was onsiere 3D robust, is not 4D robust. The expete result of this tehnique is that stati ose istributions per phase no longer give su ient overage an/or an inhomogeneous ose elivery. However, most of the 4D ose istributions (or interplay ose istributions) shoul give su ient overage an aeptable inhomogeneity levels in omparison with regular planning.