CS229 Class Project: Fusion arc treatment planning strategy by adaptive learning cost function based beam selection Ho Jin Kim

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CS229 Class Project: Fuson arc treatment plannng strategy by adaptve learnng cost functon based beam selecton Ho Jn Km (eekhj87@stanford.

1 CS229 Class Project: Fuson arc treatment plannng strategy by adaptve learnng cost functon based beam selecton Ho Jn Km Abstract Current therapeutc modaltes n radaton therapy such as statc feld IMRT and rotatonal sngle-arc VMAT are more orented to ether the plan qualty or the delvery effcency. Recently, fuson arc treatment scheme has been proposed by combnng the advantages of two respectve modaltes. The basc structure s to delver the dose wth rotatonal arc to mantan the delvery effcency, whle the addtonal ntensty modulatons based on statc feld treatment are nserted to chosen angles to enhance the plan qualty. Ths work presents how to select the regons that need addtonal ntensty modulatons, based on adaptve learnng cost functons gven the beamlet ntensty map. 1. Introducton External beam radaton therapy s the most wdely used for treatng the tumor patents n these days. Before the actual treatment, how to delver the dose s planned and optmzed, whch s called 'treatment plannng'. The ultmate objectve of the treatment plannng s to optmze the beam shapes (fluence-map structures), such that t maxmzes the dose to the target, whle sparng the dose of radaton to the crtcal organs. Fgure 1 Types of dose delvery n external beam radaton therapy (a) step-and-shoot (statc) delvery (b) rotatonal arc (1-arc) contnuous dose delvery The dose can be delvered to the target volume n two dfferent ways as llustrated n Fgure 1, stepand-shoot and rotatonal arc delvery. Step-and-shoot (statc feld) treatment 1 delvers the dose n dscrete manner at the specfc gantry angles, whch s used for the ntensty modulated radaton therapy (IMRT). On the other hand, rotatonal arc treatment contnuously delvers the dose to the target, whch s appled to the volumetrc modulated arc therapy (VMAT) 2 wth a sngle arc n most cases. Statc feld treatment can provde suffcent ntensty modulatons at approprate drectons, so that t can effectvely preserve the crtcal organs. It, however, sacrfces the delvery effcency due to the feature of statc feld treatment, and 5-10 statc beams do not own large beam angular frequency to cover the entre angles. VMAT plannng guarantees a great deal of delvery effcency wth smple fluence-map structures and ther transtons for contnuous dose delvery wth a sngle arc. The strct constrant of havng a sngle aperture at each control pont, however, does not possess suffcent ntensty modulatons for some gantry angle drectons. Therefore, to overcome the ptfalls of two therapeutc modaltes, we can come up wth combnng IMRT wth VMAT plannng, whch was newly defned as fuson arc dose delvery 3. The new treatment scheme bascally delvers the dose n contnuous fashon, whle t can stop and nsert addtonal ntensty modulatons at selected gantry angles to mprove the plan qualty at small costs of delvery effcency. Ths work presents how to adaptvely choose the gantry angles based on the cost functon wth gven nformaton of the resultant fluence-map.

2 2. Methods 2.1 Fluence-map optmzaton for sngle-aperture rotatonal arc treatment The basc structure for treatment n ths work s the rotatonal arc treatment wth a sngle aperture. To acheve sngle-arc treatment, two factors should be consdered. Frst, the fluence-map should be smplfed to select one aperture at each control pont. If the resultant fluence-map s complcated, t s dffcult to take one aperture and mantan the optmzed plan qualty. Second, the fluence-map transton between two adjacent control ponts should be suffcently small such that the dose s contnuously delvered wth arc treatment. In fact, there s a specfc constrant to be met n the transton of the fluence-map structures for contnuous arc delvery. Eq.(1) shows the basc model for the fluence-map optmzaton to reflect two factors, N f 1 mnmze Dx + { c x x } 1 f u, v, f u, v,( f + 1) f = 1 u, v subject to λ ( A x d ) ε, x 0 2 n where D s 2D-dfference matrx, x R s the fluence-map to be optmzed (the sub-ndces denoted by u,v correspond to the beamlet components of x, whle the sub-ndex f represents m n the feld order ( n = u v f )), R ( m represents the number of voxels) s the dose matrx, A d s the dose dstrbuton, λ s the mportance factor of structure, and the resdue mposed on each structure s denoted by ε. The total-varaton (TV) mnmzaton n the frst term of the objectve s to smplfy the fluence-map varatons for takng a sngle segment, whle the second term n Eq.(1) ncreases the fluence-map smlarty between two neghborng nodes. The coeffcent c controls the fluence-map smlarty to the total-varaton of the fluence-map. In ths work, t s set to be 0.1 to both preserve the plan qualty and mantan the delvery effcency. We bascally used equ-spaced 60 control ponts for the plan optmzaton wth 6 degree angular dstant. The resultant fluence-map acqured by Eq.(1) can stll have a couple of dfferent ntenstes. In most control ponts, only one aperture s taken, whle t s assumed that two apertures are taken n certan drectons that need addtonal ntensty modulatons. The next subsequent secton wll specfy how to choose the drectons, where addtonal statc feld treatment s benefcal for mprovng the plan qualty. 2.2 Fluence-map optmzaton for sngle-aperture rotatonal arc treatment In order to acqure the actual fluence-map, the soluton acqured by Eq.(1) should pass through addtonal process, called 'leaf-sequencng'. The resultant fluence-map s classfed nto dfferent ntensty levels, fnally beng splt nto dfferent apertures. In most gantry angles, t takes only one aperture for sngle-arc dose delvery, whle ths work suggests havng addtonal segment n certan drectons. The drectons that need addtonal segment can be obtaned from the adaptve learnng approach wth the soluton acqured by Eq.(1). Wth that approach, t s mportant to see whch drectons are contrbutng to mprovng the plan qualty. Ths can be measured by summaton of the data fdelty N terms n Eq.(1), λ ( ) 1 A x d = 2. If the resdue decreases, the plan qualty s consdered to be enhanced. More specfcally, we measure the cost functon defned n Eq.(2) mnmze c ( x, ) N new k = λ ( A x new, k d ) 2 (2) where xnew, k s the fluence-map havng an extra segment at k-th statc feld, and c( x new, k ) s a cost functon wth the fluence-map. For nstance, xnew,1 represents that the extra segment s only added to the frst statc feld, whle the remanng statc felds have a sngle aperture. Ths s well descrbed n Fgure 2, where t has two cost functon values when addng an extra segment to the frst and the second statc feld. If the certan drectons have lower costs, then t would be nterpreted that the drectons can get profts by addng the addtonal segment. It selects the 6 statc felds that correspond to the 6 lowest cost functon values. The reason that t chooses the 6 locatons s to balance between = 1 (1) f

the plan qualty and the delvery effcency. For those 6 locatons, the extra segment s nserted, whereas the remanng felds contnues to have a sngle segment.

3 the plan qualty and the delvery effcency. For those 6 locatons, the extra segment s nserted, whereas the remanng felds contnues to have a sngle segment. Fgure 2 Cost functon values when the extra segment s only added to (a) the frst statc feld, and (b) the second statc feld 2.3 Evaluatons To valdate the proposed algorthm, the prostate data was appled wth the beamlet sze 18x16 (5mm beamlet resoluton). The CT mages obtaned for the treatment s down-sampled twce for plan optmzaton. The plannng target volume (PTV) s located at the center of body, correspondng to the locaton of prostate, whle the crtcal organs to be preserved are set to be bladder, rectum, and femoral heads close to the target volume. At the ntal step, the fluence-map s optmzed wth 60 statc felds by Eq.(1). The sngle segment s taken n most statc feld locatons, whle the 6 locatons chosen from the adaptve beam angle selecton method have two segments assgned. The remanng control ponts are flled wth lnear nterpolatons on two adjacent fluence-map structures, such that the entre control ponts are deployed wth 2 degree angular dstant. The fluence-map optmzaton based on the TV mnmzaton s performed by a large-scale L1-solver, called TFOCS 4. Ths study compares the two separate plans: proposed fuson arc treatment plan and conventonal VMAT plan. The plan qualty of two plans s assessed by varous crtera. The dose volume hstogram (DVH) curves, whch accumulate the dose volume matchng the amount of dose of radaton, and dose dstrbutons are used to see the dose sparng to the crtcal organs. To evaluate the dose conformty to the target, the conformaton number (CN) 5 s used as defned n Eq.(3). Vτ, ref Vτ, ref Conformaton Number( CN ) = (3) V V where V τ s the volume of PTV, V τ,ref represents the target volume recevng the dose greater than or equal to the reference dose, and V ref s the total volume recevng the dose greater than or equal to the reference dose. The frst term s requred to be equal to or greater than 95% (0.95), whle the second term s recommended to be large enough to assure the secure and safe dose delvery to the target. The delvery effcency s quantfed by the estmated dose delvery tme wth reference to two pulcatons 2,6. 3. Results and Dscussons τ ref Fgure 3 Cost functon values at whch extra segment s sequentally added to 60 statc felds

4 Fgure 3 shows the cost functon values of 60 statc felds when the extra segment s sequentally added to a statc feld. As stated, 6 statc feld locatons correspondng to the 6 lowest cost functon values have two segments, whch are 13, 41, 48, 53, 54, and 55th statc felds. The remanng statc felds have a sngle segment assgned, and sngle-arc based plannng s executed by lnear nterpolaton. Fgure 4 (a) and (b) reveals the dose volume hstogram and dose dstrbutons, whch mples the dose sparng to the crtcal structures n two plans acqured by our proposed fuson arc and conventonal VMAT schemes. The proposed treatment scheme has slghtly better dose sparng n femoral heads and rectum structures than that of conventonal VMAT plan. The mprovement s explctly llustrated n the dose dstrbutons, where the dose sparng to the femoral heads enhances through the addton of apertures to approprate drectons accordng to the adaptve learnng cost functon values. Fgure 4 Comparng fuson arc and VMAT (1-arc) plans n (a) DVHs and (b) dose dstrbutons of the proposed plan (b-1), and conventonal VMAT (b-2) (so-dose lnes are correspondng to 30,65, and 100% of the prescrbed dose The addtonal segments newly assgned to 6 statc felds also affect the dose conformty to the target. The proposed plan yelds greater conformaton number (CN) than the conventonal VMAT plan, as specfed n Table 1. CN acqured by sngle-arc VMAT plannng s about 0.82, whle our proposed plan produces about It demonstrates that our proposed fuson arc plannng strategy can contrbute to mprovng the plan qualty n terms of the dose sparng to the crtcal organs and dose conformty to the target. The enhancement n dose the plan qualty, however, should accompany the sacrfce n the delvery effcency, relatve to sngle-arc VMAT plan, whch s lsted n Table 1. The expense n the delvery effcency s not sgnfcant compared wth the plan done by the step-andshoot dose delvery only, whch s about 3-5 mn. Fuson arc VMAT (1 arc) CN T (s) s s Table 1 Dose conformty to the target by CN and estmated dose delvery tme of two dfferent plans 4. Concluson Ths work presents fuson arc treatment plannng strategy. It nserts addtonal segments to a certan statc felds, where sngle-arc based treatment plannng s bascally appled. The angles that need the addtonal segments assgned are determned by the adaptve learnng cost functon values, based on the resultant fluence-map. The proposed plannng scheme overcomes the drawbacks of the conventonal sngle-arc VMAT plannng, and mproves the plan qualty n terms of the dose sparng to the crtcal organs and dose conformty to the target.

5 References [1] G. A. Ezzel, J. M. Galvn, D. Low, J. R. Palta, I. Rosen, M. B. Sharpe, P. Xa, Y. Xao, L. Xng, and C. X. Yu (subcommttee IMRT and commttee AAPMRT) Gudance document on delvery, treatment plannng, and clncal mplementaton of IMRT: report of the IMRT Subcommttee," Med. Phys. 30, (2003). [2] K. Otto, Volumetrc modulated arc therapy: IMRT n a sngle gantry arc, Med. Phys. 35, (2008) [3] M. M. Matuszak, J. M. Steers, T. Long, D. L. McShan, B. A. Fraass, H. E. Romejn, and R. K. T. Haken, "FusonArc optmzaton: A hybrd volumetrc modulated arc therapy (VMAT) and ntensty modulated radaton therapy (IMRT) plannng strategy,"med. Phys. 40, [4] S. Becker, E. J. Candès, and M. Grant, Templates for Convex Cone Problems wth Applcatons to Sparse Sgnal Recovery, Math. Prog. Comp. 3(3): (2011) [5] A. van t Ret, A. C. Mak, M. A. Moerland, L. H. Elders, and W. van der Zee, A conformaton number to quantfy the degree of conformalty n brachytherapy and external beam rradaton: applcaton to the prostate, Int. J. Radaton Oncology Bo. Phys. 37(3), (1997) [6] R. L, and L. Xng, Brdgng the gap between IMRT and VMAT: dense angularly sampled and sparse ntensty modulated radaton therapy (DASSIM-RT), Med. Phys. 38: (2011)

Analysis of Continuous Beams in General

Analysis of Continuous Beams in General Analyss of Contnuous Beams n General Contnuous beams consdered here are prsmatc, rgdly connected to each beam segment and supported at varous ponts along the beam. onts are selected at ponts of support,