Personalized Radiotherapy Planning for Glioma Using Multimodal Bayesian Model Calibration

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1 Personalized Radiotherapy Planning for Glioma Using Mltimodal Bayesian Model Calibration Jana Lipkováa,, Panagiotis Angelikopolosb, Stephen W, Esther Albertse, Benedikt Wiestlere, Christian Diehle, Christine Preibishf, Thomas Pykag, Stephanie Combsh, Panagiotis Hadjidokasd, Koen Van Leempti, Petros Komotsakosd, John S. Lowengrbj, and Bjoern Menzea Department of Informatis, TU Mnih, Germany; b D.E. Shaw Researh, L.L.C, USA; Institte of Statistial Mathematis, Tokyo, Japan; d Comptational Siene and Engineering Laboratory, ETH Zürih, Switzerland; e Department of Neroradiology, Klinikm Rehts der Isar, TU Mnih, Germany; f Department of Diagnosti and Interventional Neroradiology & Neroimaging Center & Clini for Nerology, Klinikm Rehts der Isar,TU Mnih; g Department of Nlear Mediine, Klinikm Rehts der Isar, TU Mnih; h Department of Radiation Onology, Klinikm Rehts der Isar, TU Mnih & Institte of Innovative Radiotherapy, Helmholtz Zentrm Mnih & Detshes Konsortim für Translationale Krebsforshng, Partner Site Mnih; i Harvard Medial Shool, Boston, MA,USA & Department of Applied Mathematis and Compter Siene, TU Denmark, Denmark; j Department of Mathematis & Center for Complex Biologial Systems & Chao Family Comprehensive Caner Center, UC Irvine, USA a This mansript was ompiled on Jly, 8 Existing radiotherapy (RT) plans for brain tmors derive from poplation stdies and sarely aont for patient-speifi onditions. We propose a personalized RT design throgh the ombination of patient mltimodal medial sans and state-of-the-art omptational tmor models. Or method integrates omplementary information from high-resoltion MRI sans and highly speifi FET-PET metaboli maps to infer tmor ell density in glioma patients. The present methodology relies on data from a single time point and ths is appliable to standard linial settings. The Bayesian framework integrates information aross mltiple imaging modalities, qantifies imaging and modelling nertainties, and predits patient-speifi tmor ell density with onfidene intervals. The omptational ost of Bayesian inferene is reded by advaned sampling algorithms and parallel software. An initial linial poplation stdy shows that the RT plans generated from the inferred tmor ell infiltration maps spare more healthy tisse thereby reding radiation toxiity while yielding omparable aray with standard RT protools. Moreover, the inferred regions of high tmor ell density oinide with the tmor radio-resistant areas, providing gidane for personalized dose esalation. The proposed integration of data and models provides a robst, non-invasive tool to assist personalized RT planning. Glioblastoma Bayesian inferene Radiotherapy planning FET-PET G lioblastoma (GBM) is the most aggressive and most ommon type of primary brain tmor, with a median srvival of only 5 months nder treatment (). The standard treatment onsists of immediate tmor resetion, followed by ombined radio- and hemotherapy targeting tmor residals. All treatment proedres are gided by magneti resonane imaging (MRI), mainly T gadolinim enhaned (TGd) and flid attenation inversion reovery (FLAIR) sans. TGd enhanes vaslarized parts of the tmor, while FLAIR shows srronding tmor edema. In ontrast to most tmors, GBM infiltrates the srronding tisse, instead of forming a tmor with a well-defined bondary. The entral tmor, whih is visible in the standard morphologial images, is ommonly reseted. However, the qestion of where the nearby tisse is highly infiltrated by tmor ells, and as sh is likely to be the loation of a later progression, remains nanswered. Crrent radiotherapy (RT) planning is handling these nertainties in a rather rdimentary fashion. The irradiated volme, referred to as linial target volme (CTV), is designed by extending the visible tmor region by a niform margin to aont for the invisible tmor infiltration. However, the extent of this margin varies by a few entimeters even aross the offiial RT gidelines (). Moreover, GBM invasiveness is highly patient-speifi, and ths not all patients benefit eqally from the same margin. Finally, a niform margin might not provide an optimal dose distribtion for omplex anisotropially growing tmors. Despite treatment almost all GBMs ndergo rerrene (3). Biopsies (4) and a post-mortem stdies (5) show that an inomplete tmor overage by the CTV is a possible ase of RT ineffiieny. At the same time radio-resistane of tmor residals inside the CTV an frther rede RT effiieny. Tmor radio-resistane appears in regions with omplex miroenviroment and hypoxia (6), both ommonly enontered in areas of high tmor elllarity. To address the tmor radio-resistane, several stdies have sggested a loal dose esalation (6 8). A boosted dose is sally delivered into a single or mltiple o-entered regions defined by niform margins added to the tmor otlines visible in MRI (9). The Radiation Therapy Onology Grop (RTOG) phase-i-trial (8) showed an inrease in median srvival of 8 months with dose esalation. However, no benefit in a progression-free srvival was observed, indiating a omplex relation between the tre progression of the nderlying disease and the tmor extent visible in MRI sans. Positron emission tomography (PET) sans offer s to diretly map tmor metaboli ativities sing targeted traers. A promising traer sed in GBM imaging is 8F-floro-ethyltyrosine (FET) (), whose ptake vales are proportional Signifiane Statement We demonstrate that patient-speifi, data driven modeling extends the apabilities of personalized radiotherapy (RT) design for infiltrative brain tmors. We ombine patient-speifi strtral and metaboli sans from a single time point with a omptational tmor growth model throgh a Bayesian inferene framework and predit the tmor distribtion beyond its otlines visible in medial images. These preditions enable personalized RT designs with improved delineation of tmor regions and identified radio-resistant areas. In trn the ensing RT spares healthy tisse and redes radiation toxiity, while reahing omparable aray with standard RT protools. Athor ontribtions: J.L. researh exetion; P.A.,S.W.,P.H.,P.K.,K.V.L., Bayesian analysis spport; E.A.,B.W.,C.D.,T.P.,C.P.,S.C. data aqisition/proessing; B.M., J.S.L., P.K. researh organization The athors delare no onflit of interest. To whom orrespondene shold be addressed. jana.lipkova@tm.de PNAS Jly, 8 vol. XXX no. XX 6

2 to tmor ell density (). A prospetive phase II stdy (3) demonstrated that dose esalation based on FET-PET enhanement delineates the tmor strtre better than niform margins, ths leading to lower radiation toxiity. Still, it did not inrease the progression-free srvival. One possible explanation is that FET san shows a baseline signal also in normal tisse, whih together with the rather poor resoltion of PET limits its ability to distingish between healthy and normal tisse in regions of low infiltration in the tmor periphery. The standard RT plans an be improved by inorporating information from omptational tmor models (, 3). Most brain tmor growth models are based on the Fisher-Kolmogorov (FK) eqation (4). These models, alibrated against patient medial sans, provide estimates of tmor infiltration that extend the information available in medial images and an gide the personalized RT designs. Despite great advanes in the design of tmor growth models (4 8) ritial qestions remains for the appliability of these models, sh as how to link model featres (e.g. tmor ell density) to linial image observations. Crrent approahes for alibrating glioma models onsider varios deterministi (3, 4, 9, ) and probabilisti Bayesian (, ) methods for establishing this link. In (3, 4, 9 ), athors assme a fixed tmor ell density at the tmor borders visible in TGd and FLAIR sans and the model parameters are estimated by fitting the volme (9, ) or shape (3, ) of the visible lesion. However, the tmor ell density varies along the visible tmor otlines de to anatomial restritions and inhomogeneos growth pattern. A Bayesian approah aonting for varying tmor ell density was proposed in (). All these alibrations however se MRI sans from at least two time points, making them nsitable for real linial setting, where only sans aqired at single preoperative time point are available. In this paper we present a systemati Bayesian framework to develop robst tmor growth models informed from linial imaging featres. Or approah overomes limitations speifi to different imaging modalities and in trn integrates their information to alibrate the tmor growth models for the RT planning. We ombine omplementary information from strtral MRI and fntional FET-PET metaboli maps, aqired at a single time point, to identify the patient-speifi tmor ell density. Or Bayesian approah infers modeling and imaging parameters nder nertainties arising from measrement and modeling errors. We propagate these nertainties to model preditions to obtain robst estimates of the tmor ell density together with onfidene intervals that an be sed for personalized RT planning. The estimated patient-speifi tmor ell density offers an advantage in determining margins of the CTV as well as regions for dose esalation. A stdy ondted on a small linial poplation is sed to assess the benefits of the personalized RT plans over standard protools.. Bayesian model personalization The tmor ell density ( M ) is ompted by a model M with parameters. The parameters are patient-speifi and a probability distribtion of their plasible vales is inferred from tmor observations (data) D = {y k }S k= obtained from S medial sans. We postlate that the model preditions and eah image observation y k are related by a stohasti imaging model F k with parameters F k as!! "! y k = F k θ M, ε θf k "", [] where Á is a predition error aonting for modelling and measrement nertainties. Parameters = {, F,, F S } of the model M = {M, MF,, MF S } are assmed to be nknown. A. Parameters estimation and nertainty propagation. A prior probability distribtion fntion (PDF) P( M ) is sed to inorporate any prior information abot. Bayesian model alibration pdates this prior information based on the available data D. The pdated posterior PDF is ompted by the Bayes theorem: P(θ D, M ) P(D θ, M ) P(θ M ), [] where P(D, M ) is the likelihood of observing data D from the model M for a given vale of. In most ases an analytial expression for Eq. () is not available and sampling algorithms are sed to obtain sample (l), l œ {,, N } from the posterior P( D, M ). We sed a Transitional Markov Chain Monte Carlo (TMCMC) sampling algorithm (3), whih iteratively onstrts a series of intermediate PDFs: Pj (θd, M ) P(Dθ, M )pj P(θM ), [3] where = p < p < < pm = and j = {,, m} is a generation index. The term pj ontrols the onvergene of the sampling proedre and is ompted atomatially by the TMCMC algorithm. TMCMC onstrts a large nmber of independent hains that explore parameter spae more effiiently than traditional sampling methods (3) and allow parallel exetion. A highly parallel implementation of the TMCMC algorithm is provided by the Π4U framework (4). The inferred parametri nertainties are propagated throgh the model M to obtain robst posterior preditions abot, given by the PDF: P( D, M ) = P( θ, M ) P(θD, M ) dθ, [4] Θ or by simplified measres sh as the µ = E[( )] m and variane = E[ ( )] m m m, derived from the first two moments mk, k =, : mk = Θ! (θm ) "k P(θD, M ) dθ N N ÿ! (θ(l) M ) l= "k, [5] where Θ denotes the spae of all nertain parameters. B. Tmor growth model. Tmor models of varios omplexity an be personalized sing the Bayesian approah desribed above. Here, we model ( M ) with the FK model whih desribes anisotropi tmor growth in the brain Ω œ R3 as: ˆ ˆt Ò n = Ò (D Ò) + fl ( ), =, in ˆΩ, in Ω [6] [7] where = {i (t)}#voxels and i (t) œ [, ] is a normalized tmor ell density at time t and voxel i = (ix, iy, iz ) œ Ω. The term fl [/day] denotes tmor proliferation rate. The tmor infiltration into the srronding tisses is modeled by the tensor D = {Di I}#Voxels where I is a 3 3 identity matrix and Di = I Dg Dw if i Ωgray, if i Ωwhite, if i / Ωgray Ωwhite. [8] The terms Dw and Dg denote tmor infiltration in white and gray matter and we assme Dw = Dg [mm /day] (). The

3 TGd FLAIR FET-PET TGd b FLAIR x A B x x C x D Fig.. Shemati illstrating the relation between the image observations D (top) and the tmor ell density (bottom). A: Atal FLAIR san and shemati of the tmor ell density along the line indiated by the blak arrow. B,C: Binary segmentations of the visible tmor and their relation to the nknown threshold vales TGd, FLAIR. D: FET-PET metaboli map and the nknown onstant of proportionality b. ventriles and skll are not infiltrated by the tmor and at as a domain bondary with an imposed no-flx bondary ondition Eq. (7), where n is the otward nit normal to ˆΩ. The tmor is initialized at voxel (ix, iy, iz ) and its growth is modeled from time t = ntil detetion time t = T [day]. The model parameters {Dw, fl, T, ix, iy, iz } are onsidered nknown and patient-speifi. The model M is implemented in a 3D extension of the mlti-resoltion adapted grid solver (5) with typial simlation time -3 mintes with ores. C. Mltimodal imaging model. We extrat the tmor information from TGd and FLAIR MRI and metaboli FET-PET maps. The MRI sans provide morphologial information abot the visible tmor in the form of binary segmentations. The FET signal is proportional to tmor ell density with an nknown onstant of proportionality (). A relation between the image observations D = {y TGd, y FLAIR, y FET } and tmor ell density is skethed in Fig.. Sine eah of the sans aptre a different physiologial proess, the observations are assmed independent and the likelihood an be express as:! TGd P(D, M ) = P y "! "! FLAIR, M P y FET, M P y k ", M. A stohasti imaging model F is sed to define the likelihood fntion for eah modality y k. The binary segmentations y s, s œ {TGd, FLAIR}, assign a label yis = to eah voxel with visible tmor and yis = otherwise. The probability of observing a segmentation y s with a simlated tmor ell density is assmed as a Bernolli distribtion (): d Ny s s P(y θ, M ) = Ÿ d Ny s P(yis θ, i ) = ys Ÿ s αi i ( αi ) yi. [9] = sign(i s ) A e (i s ) σα B, [] where s denotes an nknown ell density threshold below whih tmor inded hanges are not visible in the MRI represents nertainty in s. The san, while the term α d parameter Nys denotes the set of voxels sed for the likelihood omptation. The MRI sans were aqired at niform mm resoltion. To ope with potential orrelations between neighboring voxels, only every seond voxel is inlded in Nyds, introding a orrelation length d = mm. The binary segmentations have three nknown parameters, FLAIR, α }.A normalized FET sig{ F TGd, F FLAIR } = {TGd nal y FET has ontinos vales yifet œ [, ] whih an be related with the tmor density i by a Gassian distribtion: N dfet FET P(y, M ) = y Ÿ N dfet P(yiFET, i ) = y Ÿ N (i b yifet, ), where b is an nknown onstant of proportionality and desribes the noise in the FET san. To eliminate signal from a healthy and neroti tisse, NydFET onsists of the voxels inlded in the TGd and FLAIR tmor segmentations, exlding the tmor neroti ore. The FET san, aqired at 4.3 mm resoltion, is interpolated to mm resoltion, leading to a orrelation length d = 4.3 mm. The FET san introdes two additional nknown parameters F FET = {b, }. The nknown parameters = {, F TGd, F FLAIR, F FET } are assmed independent with niform prior distribtion P ( M ) given in Spplementary Information (SI). Here i is the probability of observing the tmor in the MRI san and it is assmed as a doble logisti sigmoid: αi (i, s ) Fig.. The reslts of the Bayesian alibration for the syntheti ase. Above the diagonal: Projetion of the TMCMC samples of the posterior distribtion P(θD, M ) in D spae of the seleted parameters. Colors indiate likelihood vales of the samples. The nmber in eah plot shows the Pearson orrelation oeffiient between the parameter pairs. Diagonal: Marginal distribtions obtained with Gassian kernel estimates. Boxplot whiskers demarate the 95% perentiles. Below the diagonal: Projeted densities in D parameter spae onstrted by D Gassian kernel estimates. The blak dots mark the vales sed to generate the syntheti data.. Reslts Syntheti data are first sed to test the sensitivity of the inferene and to show the relevane of mltimodal image information for the model alibration. Clinial data are then sed to infer patient-speifi tmor ell densities and to design personalized RT plans. The personalized and standard RT plans are evalated based on the tmor rerrene pattern. A. Sensitivity stdy. Syntheti data are generated by the glioma model M sing the BrainWeb anatomy (6) and parameters reported in Table. The simlated grond-trth (GT) tmor and the orresponding image observations are shown in Fig. 3. The TGd and FLAIR tmor segmentations are onstrted by thresholding the GT tmor at TGd =.7 PNAS Jly, 8 vol. XXX no. XX 3

4 Table. The syntheti data are generated with the grond trth (GT) vales. The inferred maximm a posterior () estimate, and standard deviation () of the marginal distribtion of the parameters. The nits of time and spae are days and mm, respetively. GT Dw GT ρ T ix iy Mean Mean INPUT MRI+PET iz TGd FLAIR MRI Observations Fig. 3. The syntheti ase. Orange box: Grond trth (GT) tmor (top) and the image observations (bottom); Otlines of the TGd (yellow) and FLAIR (pink) tmor segmentations, together with the normalised PET signal with additive noise (red-ble olor sale). Reslts of the Bayesian alibration with mltimodal data (ble box) are in lose agreement with GT data, while alibration based on the binary data only (green box) annot reover the tmor ell density profile orretly. σ b TGd FLAIR σα Eq. (5), are almost indistingishable from the GT tmor (see Fig. 3). The low (shown in Fig. 3) implies that, with the present Bayesian formlation, the information ontained in the mltimodal data from a single time point is sffiient to infer the patient tmor ell density. For omparison, if the model alibration is performed only with the MRI sans, i.e. y = {y TGd, y FLAIR }, the inferred tmor ell density varies signifiantly from the GT tmor as shown in Fig. 3. The reason is that the strtral MRI data does not ontain information abot the tmor density profile. This is also refleted by higher vales inside the tmor region. Nonetheless, the inferred tmor otline is similar to the GT data, sine the FET sans do not provide additional information in the regions of lower tmor infiltration. Natrally, the inferene with more data yields better reslts. However, this omparison illstrates the importane of alibrating the tmor model against information from different imaging modalities. B. Patient stdy. A retrospetive linial stdy is ondted and FLAIR =.5. The FET signal is emlated by restrit ing the GT tmor to the region of the tmor segmentations, adding Gassian noise with zero and standard deviation (), followed by a normalization. The vale of is hosen as average of the FET signal in the healthy brain. Sine the syntheti and patient data have the same resoltion, the orrelation lengths as speified in Setion C are assmed. A sensitivity stdy for the nmber of samples per TMCMC generation was performed, indiating that 6 samples were adeqate for the glioma model. The TMCMC proedre onverged after generations, forming the posterior probability distribtion with manifold shown in Fig. and alibrated parameters reported in Table. The inferene shows that single time point data does not ontain enogh information to infer time dependent parameters (Dw, fl, T ) exatly, whih is refleted by their high relative vales and strong orrelations between them. This is expeted, sine different ombinations of Dw and fl an generate the same spatial tmor ell density, althogh at different time points T. Hene, Bayesian inferene identifies the distribtion of all plasible parameters for the given set of data. At the same time, parameters that affet the tmor spatial pattern, like the initial tmor loation (ix, iy, iz ), are identified with high aray refleted by their low relative. The inferred image related parameters (TGd, FLAIR, b) are slightly overestimated de to the assmed orrelation lengths and the effet of the omplex brain anatomy. More details abot the effet of the anatomy on the tmor ell density are shown in Fig. S. The inferred vales are expeted to be larger than the GT vale, sine aonts for all sores of disrepany between the model predition and image observations, not jst the additive noise. Despite the moderate overestimation of image related parameters, the most probable tmor distribtion, given as maximm a posteriori (), and the tmor distribtion, given by 4 on 8 patients diagnosed with GBM. Patients P- are shown Fig. 4 and the details abot the data aqisition are reported in the SI. All patients reeived the standard treatment, srgery followed by ombined radio- and hemotherapy (7). There was no visible tmor after the treatment and patients were reglarly monitored for progression. The model M is alibrated against the preoperative sans shown in Fig. 4 (A-D), with the inferene reslts presented in (E-G) and Table S. The tmor estimates are onsistent with the image observations and the low vales imply the high onfidene of the inferene. These model preditions do not aptre the omplex tmor internal dynamis, whih are ertainly more elaborated than desribed by the simple model M. Instead, the alibrated model provides an estimate abot possible tmor ell migration pathways in the periphery and srronding of the tmor, onstrained by the patient-speifi anatomy and the available tmor observations. As seen in Fig. 4, the model orretly predits that for patients P- tmor infiltration is restrited only to one brain hemisphere. Whereas, for patients,, the model arately predits tmor infiltration also inside the healthy-appearing ollateral hemisphere. The orretness of these estimates is onfirmed by the sans with the first deteted tmor rerrene shown in Fig. 4 (H-I). The presene of rerrene in all ases indiates that the poplation-based treatment is insffiient and the treatment otome old be improved by personalized dose distribtion and esalation plans. The inferred patient-speifi tmor ell density an be sed to design a stomized RT plan. The tmor rerrene pattern is sed to assess the benefits of the personalized RT plan over the standard methods. For evalation prposes, eah rerrene san is registered to preoperative san sing rigid registration whih provides a sffiient mapping for most ases. However, it annot orretly aptre tisse displaement arond ventriles in patients -, making the mapping less arate in these regions.

5 P TGd P COLOR: A) FLAIR TGd tmor Segm. C) FLAIR tmor FET-PET Preoperative B) D) F) CTV Inferene CTVRTOG E) 3D G) dose esalation TGd+RT TGd I) J) FET dose esalation Rerrene FLAIR H) Fig. 4. Reslts of the Bayesian alibration for patients P-. Orange box: Preoperative sans showing (A) TGd; (B) FLAIR; (C) Tmor segmentations: TGd (yellow) and FLAIR (pink); (D) FET-PET. Ble box: (E) and (F) of the inferred tmor ell densities shown in the preoperative FLAIR sans. The CT V RTOG margin is shown as the green rves. (G). The 3D reonstrtions show otlines of the tmor (ble) together with tmor extent visible on the sans (orange) in the preoperative anatomy (white). Green box: Sans of the first deteted tmor rerrene. (H) FLAIR tmor rerrene (pink), CT V RTOG (green), and CT V (ble) margins. (I) TGd tmor rerrene (yellow) and the dose esalation otlines proposed by FET enhanement (magenta) and estimates (orange). (J) Mltilevel dose esalation designed by estimates. PNAS Jly, 8 vol. XXX no. XX 5

6 VCTV [m3] RT 5 ηctv [%] B) RT m RT 5 CTV [m ] A) P P P P pid protool (green) pid Fig. 5. (A) Overall irradiated volme V CTV designed by the RTOG and inferene (ble). (B) Effiieny of the dose distribtion η CTV. The CT V se smaller irradiation volme while gaining omparable effiieny as the CT V RTOG. B.. Personalized dose distribtion. An ideal CTV overs tmor residals, inlding invisible tmor infiltration, while sparing healthy tisse. The CTV effiieny, CT V, defined here as the relative volme of the rerrene tmor (V REC ) in the CTV η CTV = V REC CT V %, V REC [] is sed to assess RT plans. Figre 4 H) shows otlines of the first deteted rerrene visible in FLAIR sans (pink lines). The rim of the administrated CT V RTOG, designed by the standard RTOG plan with m margin arond the visible tmor, is marked by the green lines in (E,F,H). A personalized CT V, onstrted by thresholding the tmor ell density at =.% in all patients, is marked by the ble lines in (H-I). A omparison of the treatments displayed in Fig. 5 shows that the personalized CT V spares more healthy tisse, hene reding radiation toxiity, while maintaining the effiieny of the standard CT V RTOG. In patient, the personalized RT plan proposes to irradiate a slightly larger volme, leading to a higher effiieny than the RTOG plan. For patients -, both the CT V RTOG and CT V show a derease effiieny, whih may be ased by tmor misalignment between preoperative and rerrene anatomy. Nonetheless, the CT V again exhibits a similar effiieny as CT V RTOG, while sing a smaller irradiated volme. posed in (3) and ) estimates. We evalate the effiieny of an esalation plan by its apability of targeting the TGdenhaned rerrene tmor, marked by the yellow lines in Fig. 4 I). These are the regions where the rerrent tmor has high elllarity, despite having reeived the fll radiation dose, sggesting radio-resistane. Otlines of the esalation regions designed by FET-enhanement are marked by the magenta lines in Fig. 4 I). The FET-enhanement does not flly over the TGd rerrent tmor in patients -, providing a possible explanation for why there is no improvement in progression-free srvival observed in (3). Two possible dose esalation plans based on the inferred tmor ell density are shown in Fig. 4: I) a single level dose esalation based on the thresholded soltion with threshold = 3% marked by the orange lines and J) asaded for-level esalation onstrted by thresholding the tmor ell density at = [., 5, 5, 75]%. An optimal design of a based esalation plan wold reqire more extensive stdy, however these preliminary reslts show that the inferred high elllarity regions oinide with areas of tmor rerrene better than FET-PET enhanement alone, providing a promising tool for a rational dose esalation design. 3. Conlsion B.. Personalized dose esalation. Sine no dose esalation plan for GBM patient has been approved for se in phase III linial trials, a hypothetial omparison of two esalation plans targeting high tmor elllarity regions is performed. Namely, the dose esalation based on: ) FET enhanement as pro- The presented mltimodal Bayesian model alibration framework enables the identifiation of tmor ell distribtion beyond the limitation of the rrent medial sans. The framework is appliable to more omplex tmor growth models and other imaging modalities. Here, we showed that integration of omplementary information from morphologial and metaboli sans allows to identify tmor ell density from a single time point sans. Patient-speifi tmor estimates an be sed to design personalized RT plans, targeting shortomings of standard RT methods. In the ftre work, the framework will be tested on a larger patient ohort. Nonetheless, the presented reslts provide a proof of onept that mltimodal Bayesian model alibration holds a great promise to assist personalized RT interventions.. Stpp R, et al. (4) High-grade glioma: Esmo linial pratie gidelines for diagnosis, treatment and follow-p. Annals of Onology.. Palsson AK, et al. (4) Limited margins sing modern radiotherapy tehniqes does not inrease marginal failre rate of glioblastoma. Amerian jornal of linial onology 37(): Piroth M, et al. () Integrated boost imrt with fet-pet-adapted loal dose esalation in glioblastomas. Strahlentherapie nd Onkologie 88(4): Sohami L, et al. (4) Randomized omparison of stereotati radiosrgery followed by onventional radiotherapy with armstine to onventional radiotherapy with armstine for patients with glioblastoma mltiforme: report of radiation therapy onology grop 93-5 protool. 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7 Personalized Radiotherapy Planning for Glioma Using Mltimodal Bayesian Model Calibration Jana.73/pnas.XXXXXXXXXX A. Prior PDF. The parameters θ = {θ, θf TGd, θf FLAIR, θf FET } are assmed independent with niform prior distribtion: P (θm ) = r j= P(θj M ), where P(θj M ) = log(θjmax ) log(θjmin ) for θjmin θj θjmax, [] and zero otherwise. The logarithm ensres a similar order of magnitde for prior ranges of all onsidered parameters, whih failitates the sampling proedre. The prior ranges are hosen as follows: Dw [.3, 3.8] mm /day, ρ [7,.9] /day max as reported + 365] day, where T max is the maximm time that a propagation wave with veloity in (), T [3, T min v = min(dw ρ) needs to travel a distane eqal to the maximm radis of the visible tmor rmax. A prior for the initial loation is taken as a be with a side rmax, entered at the tmor enter of mass. Imaging model parameters are assmed to LAIR be T Gd [.5,.85], F [.5,.5], σα [.5,.], σ [.5,.] and b [.5,.]. The lower bond for the saling fator b omes from the fat the TGd and FET-PET sans sally do not enhane low grade gliomas, sggesting the same lower bond for the both modalities. B. Bayesian alibration. Table S reports the reslts of the Bayesian alibration for the linial data shown in Fig. 4 in the main text. Table S. Reslts of the Bayesian alibration for the patient data. Max a posterior () estimate, and standard deviation () of the marginal distribtion are shown for all the parameters. Time nits are reported in days, while spatial nits are in mm. Cases P: P: P: P: P: P: : : : : : : : : : : : : : : : : : : Dw ρ T ix iy iz σ b TGd FLAIR σα C. Effet of the brain anatomy on the tmor ell density. Patient-speifi anatomi restritions and anisotropi tmor growth reslt in tmor ell densities that are not onstant aross the borders of the TGd and FLAIR tmor segmentations. Figre S (A) shows the distribtion of the inferred tmor ell densities aross the tmor borders visible in TGd and FLAIR sans. The distribtions vary signifiantly along the border and among the patients. This is not srprising, sine in the regions of anatomial restritions, the otlines of the TGd and FLAIR tmor segmentations oinide. The effet of the anatomial Jana.73/pnas.XXXXXXXXXX of

8 restritions an be alleviated by onsidering the tmor ell density only at the tmor segmentation otlines far from the ventriles and skll. In this ase the inferred tmor ell density varies less and is also more onsistent among the patients as shown in Fig. S (B). This implies the importane of onsidering the imaging parameters patient-speifi, espeially when dealing with omplex anatomies sh as the brain. B) D: Box plot, P=[ ] (ΤGd*) (FLAIR*) plot, P=[ ] A) D: Box (FLAIR) (ΤGd).5.5 P P Patients P P Patients Fig. S. A) Distribtion of the inferred tmor ell densities at the border of the TGd (green) and FLAIR (prple) tmor segmentations represented by box plots. B) Distribtion of the tmor ell densities at segmentation borders far from anatomial restritions. Boxplot whiskers demarate the 95% perentiles. D. Aqisition protool. The MRI sans were ondted with 3T mmr Biograph sanner (Siemens Medial Soltions, Germany). FET-PET sans were aqired on a SIEMENS Biograph 64 PET/CT sanner. For standardized metaboli onditions, patients were asked to fast for a minimm of 6h before the PET san. Intravenos administration of 9 MBq of FET was performed, and low-dose CT (4 6 mas, kv) for attenation orretion was aqired. Ten-minte PET aqisitions were performed 3 to 4 min post-injetion. PET data were reonstrted by filtered bak-projetion sing a Hann filter with orretions for attenation, satter, and radioative deay. All patients provided informed written onsent. The stdy was approved by the ethis ommittee of the TU Mnih and arried ot in aordane with the approved gidelines.. Hana L.P. Harpold, Ellsworth C. Alvord KRS (7) The evoltion of mathematial modeling of glioma proliferation and invasion. J Neropathol Exp Nerol 66(): 9. of Jana.73/pnas.XXXXXXXXXX