Bayesian modelling of organ deformations in radiotherapy

Moderne strålebehandling mot kreft er skreddarsydd for å gje ein høg stråledose tilpassa svulsten (målvolumet), mens så lite dose som mogleg vert gitt til det friske vevet omkring. Den totale dosen vert levert over nokre veker i daglege "fraksjonar", noko som reduserer biverknader. Under og mellom desse fraksjonane rører dei indre organa på seg heile tida på grunn av pust, fylling av blæra, tarmar si rørsle og ekstern påverknad. Likevel vert posisjonen til målvolumet og relevante risikoorgan bestemt på grunnlag av eit statisk 3D-skann som er tatt før behandlinga startar. Den vanlege måten å sikre seg mot konsekvensar av denne rørsla er å legge til marginar rundt svulsten. Slik sikrar ein å treffe målvolumet, men til gjengjeld får det friske vevet meir dose. Marginane sin storleik er fastsett ved hjelp av statistikk over tidlegare behandla pasienter. Dei statistiske metodane som vert brukte er ofte enkle, og tek berre omsyn til rigid rørsle, altså at heile kroppen rører seg i eitt. Dessutan vert det ikkje teke omsyn til rørsla til risikoorgan. For å berekne dose til risikoorgana er det vanleg å anta at forma til organa i planleggingsskannet er representative for forma deira under behandling. Arbeidet i denne avhandlinga handlar om å bruka teknikkar frå Bayesiansk statistikk for å modellere korleis organ rører og deformerer seg mellom fraksjonane. Målet er å estimere nøyaktig den statistiske fordelinga av rørsle for eit eller fleire organ til ein pasient. Fordelinga gjev innsikt i korleis organa forandre seg medan behandlinga går for seg. Denne innsikta er nyttig for evaluering av stråleterapiplanar, statistisk prediksjon av biverknader, såkalla robust planlegging og å berekna størrelsen på marginar. Metodane som vert presentert er evaluerte for endetarmen (rektum) sine rørsler hjå prostatakreftpasientar. For desse pasientane er rektum eit viktig risikoorgan, som kan bli ramma både av akutte og seine biverknader, som lekkasje, bløding og smerter. Samanlikna med eksisterande metodar har den Bayesianske tilnærminga to fordelar: For det første gir kombinasjonen av populasjonsstatistikk og individuelle data meir nøyaktige anslag av den pasientspesifikke fordelinga. For det andre estimerer dei nye metodane den såkalla systematiske feilen i tillegg til variasjonar frå fraksjon til fraksjon. Den systematiske feilen er forskjellen mellom den estimerte forma på organet under planlegging, og gjennomsnittsforma til organet under bestråling. Denne typen feil var tema for artikkel I. Her fekk vi til å redusere den systematiske feilen til rektum hjå 33 av 37 prostatakreftpasientar ved å bruke ein metode som kombinerer forma på rektum under planlegginga og gjennomsnittsforma i populasjonen. Vi vurderte og om denne forbetringa hadde påverknad på estimering av summert dose til rektum. Metoden gav ikkje signifikant forbetring for to antatt relevante parametrar (ekvivalent uniform dose og D5%), men gav signifikant reduksjon av bias på det estimerte dose-volum-histogrammet i intervallet 52.5 Gy til 65 Gy. Hovudarbeidet i dette prosjektet er publisert i artikkel II. Der presenterer vi to modellar for organrørsle basert på Bayesianske metodar. Inndata til desse metodane er organformer som er henta frå 3D-skanningar. Metodane kan ta ulikt tal slike former, og produserer meir nøyaktige resultat jo fleire former dei får. Dei gjev anslag av gjennomsnittsforma og kor stor uvissa om denne forma er, i tillegg til anslag av fordelinga av variasjon av former frå fraksjon til fraksjon. Vi evaluerte metodane etter kor godt dei kunne berekne "dekningssannsyn", altså sannsynet for at organet skal dekke eit gitt punkt i pasientkoordinatsystemet til ei gitt tid. For denne berekninga måtte titusenvis av organformer gjerast om til såkalla binærmasker, som er 3D-matriser av punkter i pasient-koordinatsystemet der verdien til eit punkt er 1 dersom punktet er inne i organet, og 0 elles. Denne berekninga var mogleg på grunn av programvare som blei implementert for dette prosjektet, og som er presentert i artikkel III. Også her var det prostatakreftpasientar sitt rektum som vart brukt til evaluering. Berekningane til dei nye metodane var likare det sanne dekningssannsynet enn tilsvarande berekningar frå tidlegare metodar, i signifikant grad, i alle fall opp til tre input. Forskjellen mellom dei to nye algoritmane er i hovudsak kompleksiteten og nøyaktigheita, og valet mellom algoritmane i ein gitt bruk vil vere ei avveging mellom desse faktorane. Vi viste ein måte modellane kan verte brukte i artikkel IV, som handlar om pasientar som får re-bestråling for tilbakefall av prostatakreft. Her brukte vi modellane til å berekne forventa akkumulert dose til rektum frå dei to behandlingane, og også uvissa rundt den forventa dosen. Metoden er basert på representative former" av rektum, altså former som rektum kan ta som er sannsynlege, men lite fordelaktige. Desse formene kan brukast som visuell hjelp for onkologar og doseplanleggjarar, og metoden kan implementerast ved hjelp av eksisterande funksjonar i programvaren for behandlingsplanlegging. Overordna gir denne avhandlinga nye løysingar for den sentrale utfordringa med å redusere konsekvensar av organrørsle i stråleterapi. Dei presenterte modellane er dei første som utnyttar statistikk for populasjonen og data frå den enkelte pasienten samstundes, og som tar omsyn til både systematiske og tilfeldige feil.Modern radiotherapy tends to be highly conformal, meaning that a high and uniform dose is delivered to the target volume and as little dose as possible to the surrounding normal tissue. The total radiation dose is delivered across several smaller daily fractions, typically spanning several weeks. During and between these fractions, internal organs are constantly in motion due to factors such as breathing, changes to bladder filling state, intestinal movement and external influences. Nevertheless, the position of the target and relevant organs at risk (OARs) are determined based on a static 3D scan acquired before start of treatment. A common safeguard which is used to take such motion into account is the addition of margins around the target. These margins reduce the chance of missing parts of the target, yet increases dose to the healthy tissue surrounding the target. The margin size is based on statistics from previous patients. However, for the most part, the statistical methods used are very simple, and typically based on an assumption of rigid patient motion. Similarly, motion of the OARs is commonly neglected. For estimation of dose to the OARs, it is common to assume that the organ shape at the static scan is representative for its shape during treatment. The work in this thesis concerns the use of techniques from Bayesian statistics for modelling inter-fraction organ motion and deformation. The goal is to estimate accurately the statistical distribution of shapes for one or more organs for a given patient. The distribution provides knowledge of how the patient's organs might move and deform during the radiotherapy course. This information is useful for the evaluation of radiotherapy plans, prediction of adverse effects, so-called motion-robust radiotherapy planning, the generation of margins and more. The methods presented in this thesis have been evaluated for predicting deformations of the rectum of prostate cancer patients. For these patients, the rectum is a crucial OAR that is affected by both early and late side effects including leakage, bleeding and pain. Compared to existing methods, the Bayesian approach developed and implemented in this thesis offers two advantages: first, combining population statistics and individual data leads to more accurate estimates of the patient-specific distribution. Secondly, the new methods estimate the distribution of the so-called systematic error in addition to variations from fraction to fraction. The systematic error is the difference between the estimated shape/position of an organ at the planning stage and its average shape/position during therapy, and was the subject of paper I. Here, we were able to reduce the systematic error of the rectum in 33 out of 37 prostate cancer patients using a straightforward method to combine the shape of the rectum at the planning CT with the population mean shape. We also evaluated the impact of this improvement on the estimation of dose to the rectum. We found no significant improvement on the estimation of two presumably relevant dose parameters (equivalent uniform dose and D5%). However, we did find significant reduction in the bias of the estimated dose-volume histogram in the range from 52.5 Gy to 65 Gy. Paper II contains the central work of this project. It presents two organ deformation models based on Bayesian methods. The input data to these algorithms are organ shapes derived from 3D scans. The methods can take a varying number of such inputs from a given patient, and will produce more accurate results the more inputs they are given. They provide an estimate of the mean shape of the organ, as well as the uncertainty of this mean, in addition to the distribution of the variation of shapes from fraction to fraction. The methods were evaluated in the task of estimating coverage probabilities, i.e. the probability that the organ will cover a certain point in the patient coordinate system, for the rectum of prostate cancer patients. For this evaluation, tens of thousands of organ shapes needed to be converted to so-called binary masks, which are 3D arrays of points in the patient coordinate system where the value of each point is 1 if the point is inside the organ and 0 if it is outside. This was enabled by the highly efficient point-in-polyhedron software presented in paper III, which was developed for this project. The models were given varying number of scans, from 1 to 10, as input, and compared to two existing (non-Bayesian) models. The estimates of the coverage probability produced by the new models were significantly more similar to the ground truth than those produced by the existing models, at least up to three input scans. The main differences between the two new algorithms are their of conceptual complexity and accuracy, and the choice of method in a given application will therefore come down to a trade-off between these qualities. An application for the models derived in paper II, concerning patients receiving re-irradiation for recurrent prostate cancer, is presented in paper IV. We introduce a way of estimating the expectation and uncertainty of the accumulated dose to the rectum from the two treatment courses. The method is based on "representative shapes" of the rectum, that is, shapes that are probable and also particularly favourable or unfavourable in terms of dose. The advantage is that these shapes can be used as a visual aid for the oncologist or dose planner, and that the method can be implemented using existing features of treatment planning systems. Overall, this thesis provides novel solutions to the central challenge of organ motion mitigation in RT. The presented models are the first to simultaneously exploit population and patient specific organ motion and addressing both systematic and random errors.Doktorgradsavhandlin

Reducing systematic errors due to deformation of organs at risk in radiotherapy

Purpose In radiotherapy (RT), the planning CT (pCT) is commonly used to plan the full RT-course. Due to organ deformation and motion, the organ shapes seen at the pCT will not be identical to their shapes during RT. Any difference between the pCT organ shape and the organ's mean shape during RT will cause systematic errors. We propose to use statistical shrinkage estimation to reduce this error using only the pCT and the population mean shape computed from training data. Methods The method was evaluated for the rectum in a cohort of 37 prostate cancer patients that had a pCT and 7–10 treatment CTs with rectum delineations. Deformable registration was performed both within-patient and between patients, resulting in point-to-point correspondence between all rectum shapes, which enabled us to compute a population mean rectum. Shrinkage estimates were found by combining the pCTs linearly with the population mean. The method was trained and evaluated using leave-one-out cross validation. The shrinkage estimates and the patient mean shapes were compared geometrically using the Dice similarity index (DSI), Hausdorff distance (HD), and bidirectional local distance. Clinical dose/volume histograms, equivalent uniform dose (EUD) and minimum dose to the hottest 5% volume (D5%) were compared for the shrinkage estimate and the pCT. Results The method resulted in moderate but statistically significant increase in similarity to the patient mean shape over the pCT. On average, the HD was reduced from 15.6 to 13.4 mm, while the DSI was increased from 0.74 to 0.78. Significant reduction in the bias of volume estimates was found in the DVH-range of 52.5–65 Gy, where the bias was reduced from −1.3 to −0.2 percentage points, but no significant improvement was found in EUD or D5%, Conclusions The results suggest that shrinkage estimation can reduce systematic errors due to organ deformations in RT. The method has potential to increase the accuracy in RT of deformable organs and can improve motion modeling

Reducing systematic errors due to deformation of organs at risk in radiotherapy

Purpose In radiotherapy (RT), the planning CT (pCT) is commonly used to plan the full RT-course. Due to organ deformation and motion, the organ shapes seen at the pCT will not be identical to their shapes during RT. Any difference between the pCT organ shape and the organ's mean shape during RT will cause systematic errors. We propose to use statistical shrinkage estimation to reduce this error using only the pCT and the population mean shape computed from training data. Methods The method was evaluated for the rectum in a cohort of 37 prostate cancer patients that had a pCT and 7–10 treatment CTs with rectum delineations. Deformable registration was performed both within-patient and between patients, resulting in point-to-point correspondence between all rectum shapes, which enabled us to compute a population mean rectum. Shrinkage estimates were found by combining the pCTs linearly with the population mean. The method was trained and evaluated using leave-one-out cross validation. The shrinkage estimates and the patient mean shapes were compared geometrically using the Dice similarity index (DSI), Hausdorff distance (HD), and bidirectional local distance. Clinical dose/volume histograms, equivalent uniform dose (EUD) and minimum dose to the hottest 5% volume (D5%) were compared for the shrinkage estimate and the pCT. Results The method resulted in moderate but statistically significant increase in similarity to the patient mean shape over the pCT. On average, the HD was reduced from 15.6 to 13.4 mm, while the DSI was increased from 0.74 to 0.78. Significant reduction in the bias of volume estimates was found in the DVH-range of 52.5–65 Gy, where the bias was reduced from −1.3 to −0.2 percentage points, but no significant improvement was found in EUD or D5%, Conclusions The results suggest that shrinkage estimation can reduce systematic errors due to organ deformations in RT. The method has potential to increase the accuracy in RT of deformable organs and can improve motion modeling

Reducing systematic errors due to deformation of organs at risk in radiotherapy

Purpose In radiotherapy (RT), the planning CT (pCT) is commonly used to plan the full RT-course. Due to organ deformation and motion, the organ shapes seen at the pCT will not be identical to their shapes during RT. Any difference between the pCT organ shape and the organ's mean shape during RT will cause systematic errors. We propose to use statistical shrinkage estimation to reduce this error using only the pCT and the population mean shape computed from training data. Methods The method was evaluated for the rectum in a cohort of 37 prostate cancer patients that had a pCT and 7–10 treatment CTs with rectum delineations. Deformable registration was performed both within-patient and between patients, resulting in point-to-point correspondence between all rectum shapes, which enabled us to compute a population mean rectum. Shrinkage estimates were found by combining the pCTs linearly with the population mean. The method was trained and evaluated using leave-one-out cross validation. The shrinkage estimates and the patient mean shapes were compared geometrically using the Dice similarity index (DSI), Hausdorff distance (HD), and bidirectional local distance. Clinical dose/volume histograms, equivalent uniform dose (EUD) and minimum dose to the hottest 5% volume (D5%) were compared for the shrinkage estimate and the pCT. Results The method resulted in moderate but statistically significant increase in similarity to the patient mean shape over the pCT. On average, the HD was reduced from 15.6 to 13.4 mm, while the DSI was increased from 0.74 to 0.78. Significant reduction in the bias of volume estimates was found in the DVH-range of 52.5–65 Gy, where the bias was reduced from −1.3 to −0.2 percentage points, but no significant improvement was found in EUD or D5%, Conclusions The results suggest that shrinkage estimation can reduce systematic errors due to organ deformations in RT. The method has potential to increase the accuracy in RT of deformable organs and can improve motion modeling.publishedVersio