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Dose Calculation Algorithms for External Radiation Therapy: an Overview for Practitioners

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Dose Calculation Algorithms for External Radiation Therapy: an Overview for Practitioners applied sciences Review Dose Calculation Algorithms for External Radiation Therapy: An Overview for Practitioners Fortuna De Martino 1, Stefania Clemente 2, Christian Graeff 3, Giuseppe Palma 4,*,† and Laura Cella 4,*,† 1 Post Graduate School in Medical Physics, University of Naples Federico II, 80131 Naples, Italy; [email protected] 2 Unit of Medical Physics and Radioprotection, A.O.U Policlinico Federico II, 80131 Naples, Italy; [email protected] 3 Biophysics Department, GSI Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany; [email protected] 4 Institute of Biostructure and Bioimaging, National Research Council (CNR), 80145 Naples, Italy * Correspondence: [email protected] (G.P.); [email protected] (L.C.) † These authors share senior authorship. Featured Application: Radiation therapy treatment planning. Abstract: Radiation therapy (RT) is a constantly evolving therapeutic technique; improvements are continuously being introduced for both methodological and practical aspects. Among the features that have undergone a huge evolution in recent decades, dose calculation algorithms are still rapidly changing. This process is propelled by the awareness that the agreement between the delivered and calculated doses is of paramount relevance in RT, since it could largely affect clinical outcomes. The Citation: De Martino, F.; Clemente, aim of this work is to provide an overall picture of the main dose calculation algorithms currently S.; Graeff, C.; Palma, G.; Cella, L. used in RT, summarizing their underlying physical models and mathematical bases, and highlighting Dose Calculation Algorithms for their strengths and weaknesses, referring to the most recent studies on algorithm comparisons. External Radiation Therapy: An This handy guide is meant to provide a clear and concise overview of the topic, which will prove Overview for Practitioners. Appl. Sci. useful in helping clinical medical physicists to perform their responsibilities more effectively and 2021, 11, 6806. https://doi.org/ efficiently, increasing patient benefits and improving the overall quality of the management of 10.3390/app11156806 radiation treatment. Academic Editors: Chang Ming Keywords: radiation therapy; calculation algorithm; treatment planning system Charlie Ma, Vittoria D’Avino and Mariagabriella Pugliese Received: 18 June 2021 Accepted: 22 July 2021 1. Introduction Published: 24 July 2021 Technological advances in external beam radiation therapy (RT) allow high-precision dose delivery in terms of the target volume, and the improved control of side effects [1–3]. Publisher’s Note: MDPI stays neutral A key feature of modern RT techniques includes the calculation of an accurate dose with regard to jurisdictional claims in in order to assure treatment quality and consistency. Attaining an accurate and fast published maps and institutional affil- dose distribution calculation is indeed one of the most challenging tasks in modern RT. iations. Improvements in dose calculation accuracy could positively affect the effectiveness of treatments, mainly in highly heterogeneous tissues, such as the lungs, where detailed secondary particle tracking is required [4]. This task can be very time-consuming and may lead to unaffordable computational burdens in clinical practice. Since the first works on Copyright: © 2021 by the authors. three-dimensional (3D) dose calculation in the early 1970s [5,6], the evolution of computing Licensee MDPI, Basel, Switzerland. power allowed the deep rethinking of dose calculation algorithms: radiation transport This article is an open access article calculation allowed for more and more accurate reconstructions of energy deposition distributed under the terms and patterns within a clinically acceptable computation time. conditions of the Creative Commons Here, we provide a general overview of modern dose calculation algorithms, through Attribution (CC BY) license (https:// a brief description and discussion of their critical issues. creativecommons.org/licenses/by/ 4.0/). Appl. Sci. 2021, 11, 6806. https://doi.org/10.3390/app11156806 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 6806 2 of 20 Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 21 2. Dose Calculation Algorithm for Photon Beams 2. DoseA photon Calculation dose Algorithm calculation for algorithm Photon Beams must model the energy deposition pattern inducedA photon by a clinical dose calculation RT X-ray algorithm beam from must a radiationmodel the source,energy mostdeposition commonly pattern fromin- a linearduced accelerator by a clinical (LINAC), RT X-ray in beam patient from tissues, a radiation characterized source, most by the commonly electron from density a linear derived fromaccelerator computed (LINAC), tomography in patient (CT) tissues, imaging charac ofterized patients. by the The electron accelerator density head derived represents from the radiationcomputed source tomography and patient (CT) imaging tissues and of patients. organs stands The accelerator for the interaction head represents targets. the Photons ra- interactdiation source with matter and patient according tissues to and a stochastic organs stands process for the that interaction depends targets. on photon Photons energy andinteract on the with atomic matter number according and to densitya stochastic of theprocess medium that depends through on which photon they energy travel. and The principalon the atomic types number of photon and interaction density of inthe the me megavoltagedium through energy which range they travel. are the The photoelectric princi- effect,pal types Compton of photon scattering interaction and pairin the production, megavoltage which energy attenuate range are the the beam photoelectric according ef- to the Lambert–Beerfect, Compton lawscattering [7] with and an pair overall production linear attenuation, which attenuate coefficient the beamm(E according) given by to the the sum ofLambert–Beer single-process law attenuation [7] with an overall coefficients. linear attenuation coefficient () given by the sum of single-processModern dose attenuation calculation coefficients. algorithms (Figure1)—the so called model-based algorithms, in contrapositionModern dose to calculation correction-based algorithms algorithms—for (Figure 1)—the photon so beamscalled model-based are based on algo- the total energyrithms, released in contraposition in matter to (TERMA) correction-base value,d which algorithms—for is the total energyphoton perbeams unit are of based target on mass releasedthe total atenergy the primary released photon in matter interaction (TERMA) point value, [8 ].which is the total energy per unit of target mass released at the primary photon interaction point [8]. FigureFigure 1.1. HistoricalHistorical evolution evolution of ofdose dose calculation calculation engines engines and their and relative their relative accuracy. accuracy. Abbreviations: Abbrevia- tions:PBC: pencil PBC: pencilbeam convolution, beam convolution, AAA: analytical AAA: analytical anisotropic anisotropic algorithm, algorithm, CCC: collapsed CCC: cone collapsed convo- cone convolution,lution, MC: Monte MC: Monte Carlo, Carlo,LBTE: LBTE:linear Boltzmann linear Boltzmann transport transport equations. equations. () TheThe differentialdifferential TERMATERMA energy distribution distribution TE(r) isis related related to to the the energy energy differen- differential tial fluence () of the primary photon beam by the following relation: fluence yE(r) of the primary photon beam by the following relation: () = m(, )() (1) TE(r) = (r, E)yE(r) (1) r where () is the local density, estimated from the CT number value, and (, ) is the m wheremass attenuationr(r) is the coefficient local density, at estimated. from the CT number value, and r (r, E) is the massIntegrating attenuation over coefficient the beam at spectrum,r. we obtain the TERMA [8]: Integrating over the beam spectrum, we obtain the TERMA [8]: () =Z (, )() (2) m T (r) = (r, E)yE(r)dE (2) If released energy is absorbed locally,E r TERMA coincides with the absorbed dose. Conversely, if a secondary energy transport is considered, the dose in a homogenous me- dium can be derived as the following convolution: Appl. Sci. 2021, 11, 6806 3 of 20 If released energy is absorbed locally, TERMA coincides with the absorbed dose. Conversely, if a secondary energy transport is considered, the dose in a homogenous medium can be derived as the following convolution: Z Z D(r) = TE(s)h(r − s, E)dsdE (3) E V where h(s, E) is the normalized point spread function, or “dose spread kernel” (DSK), at energy E and position s relative to the point of scattering of the primary photon [8]. The DSK describes the energy transport by the secondary particles, including single and multiple scattered photons, photoelectric electrons, Compton electrons, electron–positron pairs, bremsstrahlung photons, photonuclear particles and so on. For inhomogeneous media, the translation invariance is broken and a single DSK can no longer account for the secondary transport throughout the target. In this case, a full superposition integral need to be carried out: 1 Z Z D(r) = TE(s)r(s)k(r, s, E)dsdE (4) r(r) E V where k(r, s, E) is the normalized energy delivered at point r by secondary particles, associ- ated to a primary photon of energy E interacting in s: Z k(r, s, E)dr = 1 (5) V 2.1. Dose Spread Kernel Monte Carlo (MC) simulation is the most practical technique for the calculation of energy deposition kernels. Kernels for monoenergetic
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