Volumetric and dosimetric variations during fractionated radiotherapy of anal cancer and
potential for margin reduction
Ingrid Flølo Hawkins
Thesis submitted for the degree of Master in Biophysics and Medical Physics
Department of Physics
Faculty of mathematics and natural sciences UNIVERSITY OF OSLO
June 2021
Volumetric and dosimetric variations during fractionated radiotherapy of anal cancer and
potential for margin reduction
Ingrid Flølo Hawkins
© Ingrid Flølo Hawkins June 2021
Volumetric and dosimetric variations in fractionated radiotherapy of anal cancer and potential for margin reduction
Ingrid Flølo Hawkins http://www.duo.uio.no/
Trykk: Reprosentralen, Universitetet i Oslo
Preface
This thesis was performed at the department for Biological and medical physics at the department of Physics, University of Oslo, in collaboration with the cancer clinic at Ullevål and Radium hospital.
I would like to thank my supervisor, Eirik Malinen, for all the help and guidance I have received during this process. I appreciate having been able to work with a clinically relevant and interesting thesis, which has been both educational and challenging. I would also like to thank Bernt Louni Rekstad for helping me retrieve patient data and giving me an
introduction to Eclipse as well as for the guidance he has given me with various issues that emerged during the treatment planning process. I am also grateful to my co-supervisor, Taran Paulsen Hellebust, for help with all practical issues.
I wish to thank everyone at the department of Biological and medical physics for making my time as student here educational and enjoyable.
Abstract
Curative chemoradiotherapy (CRT) is the treatment of choice for squamous cell anal carcinoma. However, as many anal cancer patients experience normal tissue toxicity as a result of this treatment, especially related to the small bowel, minimizing toxicity becomes a crucial issue. A reduction in planning target volume (PTV) margins would reduce the volume of normal tissue irradiated and as such the risk of toxicity. There is sparse data regarding the inter-fractional motion of anal tumours during fractionated radiotherapy. Therefore, the purpose of this study is to quantify the inter-fractional motion of anal tumours, as such motion may impact treatment outcomes. By quantifying tumour motion statistics, treatment margins to account for inter-fractional tumour motion can be determined to evaluate reductions in the standard margins applied in the clinic.
20 patients diagnosed with anal canal squamous cell carcinoma were included in this retrospective study. Cone beam CT(CBCT) images acquired at varying treatment fractions were rigidly aligned to the planning CT, using a pelvic bone match. Furthermore, the gross tumour volume (GTV) outline was transferred from the planning CT to each of the per fraction CBCTs and moved to align with the visible tumour. The motion of the GTV centre of mass relative to that at planning was recorded. The observed motion of the GTV was small, with population random errors in the left/right, anterior/posterior, and cranial/caudal direction of 0.8 mm, 1.8 mm, 0.6 mm , respectively, and corresponding systematic errors of 1.0 mm, 1.8 mm, 0.6, respectively. Furthermore, the clinical target volumes (CTV) were moved according to the registered motion of the GTV centre of mass. To determine an adequate population-based margin to account for the internal inter-fractional CTV motion, incremental isotropic reductions of the institution standard clinical internal target volume (ITV) margin were simulated. The margins were evaluated based on CTV coverage for 95% of all CTV positional variations. A margin of 6 mm ventrally and 3 mm in all other directions was found to be adequate, suggesting the possibility of a 2 mm reduction in the standard clinical ITV margin.
To determine the dosimetric impact of a 2 mm margin reduction on the bowel and bladder, this margin reduction of the institution standard PTV margin was implemented.
Radiotherapy treatment plans were generated for 10 patients both with standard clinical PTV margins of 11 mm ventrally and 8 mm in all other directions and with the reduced PTV margins. Treatment plans were made using volumetric arc therapy (VMAT) with 6MV photons and delivered over 27 fractions. A statistically significant reduction in bowel volumes V45 and V30 of 21 cm3 and 20 cm3, respectively, and a reduction in mean bladder dose of 0.9 Gy was found for the plans with smaller margins.
In conclusion, for the patient population small internal motion of the GTV was observed and a 2 mm reduction in the standard margins to account for internal motion was suggested.
This margin reduction was shown to result in a reduction in dose volume parameters associated with bowel toxicity. Before a margin reduction can be recommended clinically, a more complete evaluation combining data from the remaining sources of uncertainty is needed.
List of abbreviations
CBCT Cone Beam Computed Tomography COM Centre of mass
CT Computed Tomography CRT Chemoradiotherapy CTV Clinical target volume CNS Central nervous system
DIR Deformable image registration DVH Dose volume histogram
FBP Filtered Back Projection FOV Field of view
Gantry A mechanical support for mounting a device to be moved in a circular path, allows irradiation from multiple angles in radiation therapy and
CT.
GTV Gross tumour volume Linac Linear accelerator LET Linear energy transfer HPV Human papillomavirus
HIV Human immunodeficiency virus HU Hounsfield units
IMRT Intensity Modulated Radiation Therapy ITV Internal target volume
MLC Multi leaf collimators
NTCP Normal tissue complication probability PTV Planning Target Volume
ROI Region of interest RT Radiation therapy
RTOG Radiotherapy Oncology Group
SCCA Squamous cell carcinoma of the anus
SIB Simultaneous integrated boost – IMRT technique which allows for
simultaneous delivery of different dose levels to different target volumes within a single fraction
TCP Tumour control probability VMAT Volumetric Arc Therapy
Table of contents
1 Introduction 1
2 Theory 3
2.1 Ionizing radiation 3
2.1.1 Photoelectric effect 4
2.1.2 Compton effect 4
2.1.3 Pair production 5
2.1.4 Dosimetric characteristics of photon beams 6
2.2 Radiobiological effects of ionizing radiation 8
2.2.1 Linear quadratic model for cell survival 9
2.3 Anal cancer 10
2.3.1 Staging and classification 12
2.4 External beam radiotherapy 13
2.4.1 Treatment planning 13
2.4.2 Computed Tomography 13
2.4.3 Volumes in radiotherapy 16
2.4.4 Linear accelerator 17
2.4.5 Intensity modulated radiotherapy and Volumetric arc therapy 18
2.4.6 Dose volume analysis 20
2.5 Errors and margins 22
2.5.1 Random and systematic errors 23
2.5.2 Margin recipes 24
2.6 Image guided radiotherapy and image registration 25
2.6.1 kV cone beam CT 27
2.7 Tumour control probability 28
2.8 Normal tissue toxicity and dose-volume effects 29
3 Methods 31
3.1 Patient cohort 31
3.2 Treatment protocol 32
3.2.1 Delineation of target volumes and organs at risk 32
3.2.2 kV CBCT image acquisition protocol 35
3.3 Retrospective kV CBCT image registration 35
3.4 Inter-fractional internal tumour motion 37
3.4.1 Quantifying inter-fractional GTV motion 38
3.4.2 Correlation of GTV extension and GTV motion 38
3.4.3 Random and systematic errors 39
3.4.4 Inter-fractional internal CTV motion 40
3.5 Margin simulations 41
3.5.1 CTV-ITV margin 42
3.5.2 Quantifying impact of inter-fractional CTV motion 43
3.5.3 Isotropic margin reductions 45
3.6 Inter-fractional variations in bowel and bladder volumes 46
3.7 Treatment planning 49
3.7.1 Dose-volume restrictions and recommendation 49
3.7.2 Dose calculations 49
3.8 Statistical methods 50
3.8.1 Wilcoxon signed rank test 51
3.8.2 Wilcoxon rank sum test 51
4 Results 51
4.1 Inter-fractional GTV motion 53
4.1.1 Quantifying inter-fractional GTV motion 53
4.1.2 Random and systematic errors 53
4.1.3 Correlation between GTV position and GTV motion 56
4.2 Margins 59
4.2.1 Impact of inter – fractional CTV motion 60
4.2.2 Impact of inter-fractional CTV motion on CTV coverage by ITV 61
4.2.3 Isotropic margin reductions 63
4.2.4 CTV48.6-PTV48.6 margin 65
4.3 Inter-fractional bowel and bladder volume variations 68
4.3.1 Inter-fractional bowel volume variations 70
4.3.2 Volume of bowel within PTV48.6 70
4.3.3 Inter-fractional bladder volume variations 72
4.4 Treatment planning study 74
4.4.1 Patient specific bladder dose distributions 78
4.4.2 Population based bowel dose estimates 79
4.4.3 Effect of inter-fractional bowel variations on 82
planned bowel dose 4.4.4 Patient specific bladder dose distributions 84
4.4.5 Population based bladder dose estimates 84
4.4.6 Effect of inter-fractional bladder variations on 86
planned bladder dose 4.4.7 Dose estimates to target volumes 89
4.4.8 Dose estimates to remaining organs at risk 89
5 Discussion 90
5.1 Methodical considerations 90
5.1.1 Quantifying inter-fractional tumour motion 90
5.1.2 Margin reduction simulations 92
5.1.3 Bowel delineation in CBCT images 93
5.2 Discussion and future considerations 94
5.2.1 Quantifying inter-fractional GTV motion 94
5.2.2 Correlation between GTV position and GTV motion 95
5.2.3 Tumour regression 96
5.2.4 Deformations of the lower rectum and anal canal 97
5.2.5 Margins 98
5.2.6 Van Herk margin recipe 102
5.2.7 Effects of 2 mm margin reduction on bowel toxcicity 104
5.2.8 Possibility of further margin reductions 106
5.2.9 Correlation between bladder volume and bowel V45 109
5.2.10 Effects of inter-fractional bowel and bladder variation on 112
planned bowel and bladder dose 6 Conclusion 114
References 115
Appendix 119
I. Margins 119
A. Calculations to quantifying impact of inter-fractional 119
CTV motion and margin reduction simulations II. Population based dose calculations 126
III. Patient specific dose estimates 129
A. Target volumes 129
IV. Patient specific dose estimates to organs at risk 133
A. Bowel 133
B. Bladder 140
C. Remaining organs at risk 142
1
Introduction
Squamous cell carcinoma of the anus (SCCA) is a relatively rare form of cancer, with incidence rates between 1 and 2 per 100000 people [1]. The incidence of SCCA has been increasing over the last 30 years. Two known factors related to increased risk of anal cancer are infection by the human papilloma virus (HPV) and the human immunodeficiency virus (HIV)[2, 3]. Recommended treatment for anal cancer is a combination of chemotherapy and radiation therapy (RT), concurrent chemoradiotherapy (CRT), which has shown superior outcomes compared to RT alone[4, 5]. Norwegian guidelines recommend CRT with 5- flourouacil (5-FU) and mitomycin C (MMC) as chemotherapy. The radiation therapy is fractionated, and the total dose is delivered in 27 fractions of 1.8-2.13 Gy. Treatment is given 5 days a week with a maximum treatment time of 39 days. This modern CRT treatment has shown excellent outcomes in a recent study performed at Oslo University Hospital (OUS). Here, 132 anal cancer patients were treated with CRT between 2013-2017, with 3-year disease free survival of > 80% [6]. These disease-free survival rates are higher than values reported in earlier Norwegian studies[7]. The proximity of radiosensitive organs to the tumour, particularly the small bowel, means that normal tissue is exposed to high doses of radiation. This results in the risk of toxicity [8, 9], with moderate to severe gastrointestinal toxicity seen in 20-30% of patients[10, 11]. It is therefore of interest to investigate strategies which aim to reduce the associated bowel toxicity without compromising the high level of tumour control achieved.
The goal of radiotherapy is to maximize the effect of the tumour eradication whilst ensuring that adverse normal tissue effects are minimised. Treatment delivery using Volumetric arc therapy (VMAT) allows for shaping of radiation dose distributions to conform closely to the target volume. As such, VMAT reduces the volume of normal tissue receiving high doses and has been associated with a reduced risk of normal tissue toxcicity compared to 3D
conformal radiotherapy[10]. However, the sharp dose gradients between target volume and normal tissue result in an increased need for accurate target localisation. SCCA is a
locoregional disease and for CRT the anal tumour and involved lymph nodes receive a dose of 54-58 Gy, whilst the remaining pelvic and inguinal lymph nodes receive an elective dose (typically 46 Gy) to eradicate possible microscopic disease. In anal cancer, VMAT is given using a simultaneous integrated boost technique (SIB) which allows for dose coverage of the tumour, involved lymph nodes and elective volume within the same delivery.
Modern radiotherapy depends on high accuracy for successful execution, but a number of errors in patient setup, delivery, imaging, biology and motion limit the accuracy.
Radiotherapy treatment plans are based on a single computed tomography (CT) session prior to treatment, which only provides a snapshot of patient anatomy. As such, one of the largest error sources is the internal motion of the clinical target volume (CTV) during the course of the treatment [12]. Motion of the CTV relative to the position at planning can cause detrimental effects on the planned dose. To incorporate potential errors and thereby ensure that the CTV receives the planned dose, a safety margin is added to the CTV to create the planning target volume (PTV). For radiotherapy of anal cancer separate CTV-PTV
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margins are generated around the inguinal lymph nodes, main tumour CTV and the elective CTV volume.
The implementation of in room kilo voltage image guidance systems, like cone beam computed tomography (CBCT) has become more widespread. Image guidance allows for patient repositioning prior to delivery of each treatment fraction, reducing setup related uncertainties. For anal cancer patients the prevalent image guidance technique utilises pelvic bony anatomy for alignment and there are few studies investigating the internal inter- fractional motion of the anal tumour relative to pelvic bony anatomy. As such, little is known about the inter fractional motion of the anal tumours. It is therefore of interest to gain insight into the inter-fractional motion of anal tumours relative to bone. Based on tumour motion statistics, adequate margins can be determined and possible reductions in the current standard clinical CTV-PTV margin can be assessed. Locoregional recurrences dominate and occur most often in the primary tumour site [6, 7] and as such insight into the internal motion of the tumour is vital before contemplating reduction of PTV margins.
In this study per fraction CBCT images acquired at the linear accelerator directly prior to treatment are utilised to visualise patient anatomy. The CBCT images provide 3D volumetric information and soft tissue contrast and allow for determination of the daily position of the anal tumour and thereby quantification of the inter-fractional motion of the tumour.
Reductions of the standard clinical margins are simulated to estimate whether reduced margins are still adequate to account for the observed tumour motion. The margins are evaluated based on accounting for 95% of the positional variations of the CTV and are applicable when daily image guidance using pelvic bony antomy alignment is performed.
VMAT treatment plans are generated for the original standard clinical CTV-PTV margin as well as for the largest possible margin reduction, to assess any potential dosimetric benefit to the bowel for the reduced margin.
The aim of this study is to quantify the inter-fractional motion of anal tumours and to estimate adequate margins to account for the observed motion, thereby assessing if a reduction of the standard clinical CTV-PTV margin is possible. Comparison of the dose distribution to the bowel with standard clinical margins and the dose distribution to the bowel using the margins determined based on the observed tumour motion is performed using dose volume histogram analysis.
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2 Theory and background 2.1 Ionizing radiation
Radiotherapy is the treatment of cancer using ionizing radiation to damage and kill cancer cells. Ionizing radiation carries enough energy to cause orbital electrons to be ejected from an atom or molecule, thereby ionizing the atom. Ionizing radiation is classified as either charged particle radiation or electromagnetic radiation. All charged particles like electrons, protons, alpha particles, and heavy ions are directly ionizing. This means that the particles interact directly with the atomic electrons, directly causing chemical and biological changes in the matter they traverse. Charged particles always interact with matter and transfer some or all their energy. The energy transfer typically occurs through many small coulomb force interactions, causing the particle to lose energy gradually along its track[13].
Electromagnetic radiation is energy in the form of photons and is indirectly ionizing. Photons first transfer their energy to secondary charged particles (mostly electrons) in the matter that they traverse. It is then the secondary charged particles which deposit the transferred energy to the matter and cause the chemical and biological damage. Photons have a
probability of interacting with matter through different interaction processes and therefore also a probability of passing through matter without interacting. This means that photons can travel much further through matter than charged particles, for which the distance the particle can travel in the matter is determined by its kinetic energy[13]. The energy transferred per unit length along the particle path is defined as the linear energy transfer (LET). Particles with a higher LET, like alpha particles and heavier ions will deposit their energy over a shorter distance whilst electrons and photons which have a lower LET have a longer range with less energy deposited per unit length.
The most important interaction processes of photons with matter are the photoelectric effect, the Compton effect, and pair production. The probability of each of these processes taking place depends on the photon energy 𝐸 = ℎ𝜈 as well as the atomic number Z of the absorbing medium. For low Z matter like human tissue, with Z<20, and for the energy
spectrum utilised in therapeutic beams, which ranges from 200 KeV to 15 MeV the Compton effect is the dominating process[13]. Figure 1 shows the region of Z and E where each interaction dominates.
Figure 1: Shows region of energy hν and atomic number Z, where each interaction dominates.
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2.1.1 Photoelectric effect
The photoelectric effect occurs when a photon interacts with a tightly bound atomic electron.
Figure 2: Illustrates the kinematics of the photoelectric effect. Here, hν is the energy of the incoming photon and T is the kinetic energy of the atomic electron.
Figure 2 shows the kinematics of the photoelectric effect. The incident photon is absorbed and transfers its energy to the atomic electron, giving the electron a kinetic energy of T = hν - Eb . Here Eb is the binding energy of the electron. The electron departs at an angle Ɵ
relative to the direction of the incident photon. To conserve momentum the atom departs at an angle φ but with negligible kinetic energy. The energy of the photon must be greater than the binding energy of the electron to the atom for the effect to take place. The probability of photoelectric effect occurring is higher the lower hν is, if hν > Eb.
As seen from figure 1, photon interactions through the photoelectric effect dominate for lower energy photons. Figure 1 also shows that the energy region for which the
photoelectric effect is the dominant interaction process increases as the atomic number Z of the absorbing material increases. For the energy region below 0.1 MeV, where the
photoelectric effect is most important, the linear attenuation coefficient µτ, which describes the probability of a single photon interacting through the photoelectric effect per unit length of material traversed is proportional to:
𝜇𝜏 ∝ 𝑍3/(ℎ𝜈)3 (1)
2.1.2 Compton effect
The Compton effect occurs when a photon with energy E = ℎ𝜈 collides with an unbound stationary electron. In this case the incoming photon transfers some of its energy and momentum to the electron. The incoming photon is scattered an angle φ with respect to its original direction, with a lower energy E’𝛾 = ℎ𝜈′. The electron departs at an angle Ɵ with kinetic energy 𝑇 = ℎ𝜈 − ℎ𝜈′. These kinematics are illustrated in figure 3.
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Figure 3: Illustration of the kinematics of the Compton effect
In the collision the energy transferred to the electron can vary from zero to a large part of the photon energy. The fraction of energy absorbed by the unbound electron increases with the energy of the incident photon and approaches 1 for energies over 10MeV. [13].
The probability of Compton scattering occurring is only very weakly dependant on atomic number Z but is inversely proportional to the photon energy as well as being directly proportional to the electron density ne of the material. The linear attenuation coefficient 𝜇𝑐 is proportional to:
𝜇𝑐 ∝𝑛𝑒
ℎ𝜈 (2)
2.1.3 Pair production
Pair production can occur when a photon passes near an atomic nucleus and is subject to the strong coulomb forces. The photon disappears and an electron and a positron are created in the energy/mass conversion. Pair production can only occur if the photon energy is at least equivalent to the mass of two electrons, ℎ𝜈 = 2𝑚0𝑐2 = 1.022 MeV. Energy conversion gives
ℎ𝜈 = 2𝑚0𝑐2 + 𝑇−+ 𝑇+ (3) Here 𝑇− and 𝑇+ is the kinetic energy given to the electron and positron, respectively. The kinetic energy given to the positron and electron does not need to be equal, but the average kinetic energy, Tmean is given by
𝑇𝑚𝑒𝑎𝑛 = ℎ𝜈−1.022 𝑀𝑒𝑉
2 (4) The probability of pair production occurring increases with increasing photon energy as well as quadratically with increasing atomic number. This gives a linear attenuation coefficient µκ
proportional to:
µ𝜅 ∝ ℎ𝜐𝑍2 (5) The probability per unit length of any interaction occurring can be expressed as the total linear attenuation coefficient, µ, and is the sum of the individual attenuation coefficients 𝜇 = 𝜇𝜏+ 𝑢𝑐+ 𝜇𝜅 (6)
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The total attenuation coefficient decreases with energy, meaning that higher energy photons are attenuated at a lower rate than low energy photons.
For a monoenergetic photon beam, when assuming a narrow beam geometry where only primary (nonattenuated) photons reach the detector, photon attenuation occurs in an exponential fashion, according to equation 7.
𝑁 = 𝑁0𝑒−𝜇𝑥 (7) Here N is the number of photons passing a distance x through the material, N0 is the original number of photons and µ is the linear attenuation coefficient defined in equation 6.
2.2 Dosimetric characteristics of photon beams
The absorbed dose delivered to the tissue is defined as the total energy deposited per unit mass and is measured in Gray (Gy), where 1 Gy = 1 J/kg. The dosimetric characteristics of a photon beam depend on the energy of the beam and the medium which it passes through.
A central axis depth dose curves give a graphical representation of the absorbed dose along the central axis of the beam as a function of depth in tissue. Dose measurements of depth dose are made in water. This is as water has similar radiobiological properties to the human body and is therefore considered equivalent in radiotherapy. Figure 4 shows percentage photon depth dose curves (PDDs) for photon beams of varying energy.
Figure 4: Illustration of photon PDD curves for 4, 10 and 25 MV photons. Here the dose is displayed as a percentage of the maximum dose.
Depth dose curves provide important information about surface dose, depth of maximum dose and dose fall-off. As illustrated in figure 4, photons have an initial build-up of dose after they enter the surface before reaching maximum absorbed dose dmax. The dose then decreases in a close to exponential fashion. The initial dose build-up is due to the dose being deposited by the secondary electrons released in photon interactions. The fluence of the
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secondary electrons begins to build up at the surface and the number of secondary electrons passing through the medium gradually increases with depth. This causes the maximum absorbed dose to occur at depth, d. As the photon beam is attenuated the number of electrons produced in photon interactions decrease and with it the dose. The depth at which the maximum dose is reached increases with the energy of the photon beam due to higher energy photons producing more energetic secondary electrons which have a longer range. Attenuation of higher energy photons also occurs at a lower rate, resulting in a less steep dose fall off.
The depth dose curves only give information about dose along the central beam axis.
Therefore, to determine how the dose varies along a line perpendicular to the central axis, a beam profile can be constructed. The beam profile graphically represents the variations in dose as a function of transverse distance from the central axis, for a given depth (see figure 5).
Figure 5: Illustration of a beam profile for 6MV photons as a function of transverse distance from the central axis, at depth of 1.5 cm. The dose is normalised to the dose on the central axis and the dashed lines mark the penumbra width [14].
The region at the edge of the beam were the dose falls of rapidly is defined as the
penumbra. The penumbra width is typically defined as the distance between the 80% and 20% dose level on the beam profile (see figure 5). The penumbra is caused by the finite size of the source from which the radiation originates, scatter of radiation within the tissue and the scatter of radiation when the beam is transmitted through the collimators1.
To represent planar or volumetric variations in absorbed dose, information from depth dose profiles and beam profiles can be combined to create isodose curves. Isodose curves are created by drawing lines through points which receive equal dose. The curves are drawn at regular intervals of absorbed dose and expressed as the percentage of dose at a specific reference point. An isodose chart for a single beam consists of isodose curves drawn at regular intervals of percentage depth dose[15] (see figure 6).
1 Beam limiting device of high atomic number, used to shape the radiation beam
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Figure 6: Example of an isodose chart from a 6MV beam, with isodose curves drawn at intervals of the percentage depth dose[16].
Photon irradiation is still the most dominant form of radiation used in cancer treatment and when treating non superficial tumours it is beneficial to utilize higher energy photon beams (in MV range). This is as these provide greater skin sparing and a higher dose at the depth of the tumour compared to lower energy photons (see figure 4). One disadvantage when using photon beams is the near exponential dose fall off, as shown in figure 4. This results in much of the radiation being absorbed in normal tissue before reaching the tumour, as most
tumours are located centrally within the patient. By targeting the tumour with multiple radiation beams from several different angles, the dose to normal tissue can be reduced whilst concentrating the high dose region to the tumour. The dose distribution for multiple beams is found by linearly adding the overlapping isodose charts from the individual beams.
2.2 Radiobiological effects of ionizing radiation
The effect of ionizing radiation on living tissue is a complex process and consists of various events. Following the ionization of the atoms, chemical processes occur which cause primary biological damage with high levels of biological damage leading to rapid cellular death. The damage can be caused by energy deposited directly in the molecule as well as indirectly through the creation of free radicals. Free radicals are created when primary ionisations in other atoms or molecules in the cell produce atoms with unpaired electrons.
These free radicals are highly reactive and can diffuse to cause chemical changes to critical structures in the cell. Figure 7 illustrates the difference between indirect and direct action occurring in a DNA molecule.
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Figure 7: Illustrating the difference between direct and indirect action of radiation on a DNA molecule[17].
Damage can be caused to all components of the cell, but studies have shown that it is damage to the DNA contained in the cell nucleus that is the critical factor when it comes to inducing cell death[18]. The cells have a highly developed DNA repair system, but when damage is too extensive or complicated the cell is killed. In the case of incorrect repair of cells which survive radiation, mutations can occur which in turn may have long term
biological effects like oncogenic development and genetic abnormalities that do not present themselves until years later. The goal of radiation therapy is to damage the DNA of the cancer cells such that the cells lose their ability to proliferate and the cancer can be eradicated. However, the radiation also caused damage to healthy cells and a balance between the potential therapeutic benefits and the potential of detrimental normal tissue effects must be found.
Radiotherapy is delivered over several weeks. During this time patients are treated daily and in each treatment a fraction of the total dose is delivered. Fractionation of the dose allows normal tissue cells to repair some of the radiation induced damage. Tumour cells have shown reduced ability for repair of radiation induced damage. As such fractionation allows for higher dose to be delivered to the tumour than would be possible if the total dose were delivered in one fraction.
2.2.1 Linear quadratic model for cell survival
Survival curves are used to show the relationship between the fraction of surviving cells, S, and the absorbed dose, D. A number of radiobiological experiments have shown that the survival data, with the exception of small doses, can be described by a linear quadratic model, first described by Chadwick and Leenhouts in 1973[19].
𝑆 = 𝑒−𝛼𝐷−𝛽𝐷2 = 𝑒
−𝛼𝑛𝑑(1+𝛼 𝛽 𝑑)
(8) Here the total dose D = nd is delivered in n fractions of uniform dose d. The parameters α and β are constants which indicate the cells sensitivity to ionizing radiation and these
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constants describe the initial slope and the degree of curvature of the survival curve (see figure 8). The LQ model is used to predict the effects of changes in dose and fractionation and to calculate the biologically equivalent doses for different fractionation schemes.
Figure 8: Survival curve given by the LQ model with radiation sensitivity constants α and β, where S gives the surviving fraction
2.3 Anal cancer
Squamous cell carcinoma of the anus is a relatively rare form of cancer that forms in the epithelial cells of the anal canal. Just under 100 new cases are diagnosed annually in Norway, with 90 cases in 2018[20]. The incidence of anal cancer has gradually been increasing. The disease is more common in females and the median age for diagnosis in Norway is 66 years [21]. Figure 9 shows the incidence rate of anal carcinoma diagnosis per 100 000 people for males and females in Norway.
Figure 9: Anal cancer diagnosis incidence rate per 100000 people for males (orange) and females (blue) from 1954-2019. Based on data from the Cancer registry of Norway[22].
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Anal cancer can grow circularly in the anal canal, extend to the rectum or out to the anus and the cancer often spreads through the lymphatic system to regional lymph nodes like the inguinal (groin), perirectal (around rectum) and iliac(pelvic) nodes. Figure 10 shows the anatomy of the anal canal and lower rectum. Metastasis to regional lymph nodes is seen in about 30% of all cases, whilst distant metastases are uncommon. Hematogenic spread is seen at diagnosis in less than 10% of cases[23]. As distant metastases are uncommon most cases can be treated with curative radiotherapy[23].
Figure 10: Anatomy of the anal canal and rectum, showing anatomical landmarks and delimitations[24].
The standard form of treatment is a combination of chemotherapy and external beam radiation therapy and for patients receiving this treatment a 5-year survival rate of around 70%-75% is achieved[25]. A study conducted by Bentzen et al, looked at the recurrence and survival of a national cohort of 328 patients treated with chemoradiotherapy for anal canal carcinoma in the years between 2000-2007. They found that complete response was obtained for 87% of the patients but with recurrence occurring in 24%. This resulted in a recurrence free 5-year survival of 74%. The majority of the recurrences were locoregional occurring most commonly in the original tumour site[7]. Toxicities observed in patients receiving chemoradiotherapy for anal cancer are skin reactions, haematological effects, genitourinary and gastrointestinal problems[26, 27]. Bentzen et al conducted a long term follow up of 199 anal cancer survivors compared with a reference group from the normal population and found that gastrointestinal symptoms were more frequent in the survivors compared to the normal population[8].
It is therefore of interest to investigate strategies that allow for a reduction in normal tissue radiation. Reducing the radiation dose to healthy organs will reduce the occurrence and severity of toxicity for the patients. This will increase surviving patients quality of life as well as reducing the necessity for treatment breaks, which has been shown to have a detrimental
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effect on treatment outcome[28]. As most recurrences are local it is important not to compromise tumour coverage as this is detrimental to achieving tumour control.
2.4.1 Staging and Classification
To describe the size of the tumour and the spread of the disease at the time of diagnosis the TNM system is used, where the tumour (T), lymph nodes (N) and distant metastases (M) are evaluated. T describes the size as well as spread of the tumour to nearby organs, N
describes the spread of the cancer to nearby lymph nodes and M describes distant
metastases, including spread to lymph nodes outside the regional area. Table 1 gives T and N information specific to anal cancer.
Table 1: Classification of T and N for anal cancer patients[23].
Primary tumour Regional lymph nodes
Tx Primary tumour cannot be assessed Nx Regional lymph nodes cannot be assessed
T0 No evidence of primary tumour N0 No evidence of regional
lymph nodes
T1 Tumour ≤ 2 cm in largest diameter N1 Metastases in peri -or mesorectal lymph nodes
T2 Tumour ≥ 2 cm but ≤ 5 cm in largest diameter
N2 Metastases in unilateral
iliaca interna and/or inguinal lymph nodes T3 Tumour ≥ 5 cm in largest diameter N3 Metastases in peri or
meso rectal and inguinal lymph nodes and/or bilateral iliaca interna and/or inguinal lymph nodes.
T4 Tumour has invaded neighbouring organs (irrespective of size)
The main form of treatment of anal cancer is chemoradiotherapy and in Norway the TN stage determines the recommended treatment. For stages T1-T2 N0, 54 Gy to the primary tumour and 1 dose of Mitomycin C and 5-flourouracil is recommended whilst for stages T3-
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T4 N0 and T1-T4 N1 a dose of 57.5 Gy to the primary tumour and 2 doses of Mitomycin C and 5-flourouracil (MiFu) is recommended.
2.5 External beam radiotherapy
In external beam radiotherapy (EBRT) the radiation is delivered to the tumour from a source outside the body. The main components of EBRT are tumour localisation, treatment
planning, which includes delineation of target volumes and critical normal tissue structures, treatment verification and treatment delivery[15].
2.5.1 Treatment planning
Treatment planning consists of several steps which include, acquiring 3D images of the patient to accurately localise and delineate the tumour and adjacent normal tissue
structures, designing beam arrangements and shapes, calculating dose, evaluating resulting dose distributions and transferring information from the treatment planning system to the treatment delivery system[15].
Computed tomography (CT) plays a very important role in radiotherapy as it provides an accurate 3D model of the patient anatomy which is used for treatment plan design. A limitation of CT, however, is the limited soft tissue contrast. As such magnetic resonance imaging (MRI) is increasingly used in adjunct with CT to define the tumour. The 3D CT data set, acquired in the treatment position, is transferred to the treatment planning system.
Here segmentation and delineation of treatment volumes and normal tissue structures is performed, beam arrangements and shapes are designed, and dose is calculated. The treatment plans are designed to achieve an optimal dose distribution. The treatment planning system utilizes complex dose calculation algorithms to model the dose deposition and CT provides information about the attenuation properties of the different tissue, which is the basis for dose calculations. The body contour, internal anatomy and density
information regarding internal structures is needed to create a RT plan. The effect of the radiation therapy treatment hinges on accurate definition and delineation of the tumour and involved lymph nodes as well as accurate segmentation of organs at risk. Furthermore, the images which the volumes of interest and dose calculations are based on must be acquired in a position that can be replicated at treatment. This is to ensure that the treatment is directly transferable from the pre-treatment image basis to the actual treatment situation, thereby avoiding a geometrical miss.
2.5.2 Computed tomography
CT imaging is based on the attenuation value of different tissues. By using multiple x-rays taken at different angles around the patient it is possible to digitally reconstruct accurate 3D images of patient anatomy.
An image plane is defined, and x-rays are passed through the patient at different angles parallel to this plane. For each angle the number of photons that pass though the patient and reach the detector elements are counted, generating an intensity profile for each angle.
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From the intensity profiles an attenuation map of the attenuation properties along the path of the x -ray may be found. Passing x rays through the patient at different angles allows for information about the depth of the structures to be obtained. In the CT image each
attenuation value is given a CT value which is measured in Hounsfield units (HU) and is defined relative to the attenuation value of water
𝐻𝑈 = 1000 ∗ (µ𝑡𝑖𝑠𝑠𝑢𝑒− µ𝑤𝑎𝑡𝑒𝑟)/µ𝑤𝑎𝑡𝑒𝑟 (9) Where µtissue is the attenuation coefficient of the respective tissue and µwater is the
attenuation coefficient of water. Each voxel in the image is assigned a specific HU value and every HU value is related to a grey scale value. Depending on which structures are of
interest, the window width can be changed. The window width controls the range of CT values displayed in the image and allows for manipulation of contrast.
Figure 11: Illustration demonstrating a helical CT scan[29].
The most common type of CT scanner is referred to as the 3rd generation scanner. In these scanners the x-ray tube and detector rotate about the patient. The detector consists of a matrix of individual detectors and a fan beam is used to irradiate the detector matrix, see figure 11. The projections are acquired simultaneously as opposed to sequentially, resulting in shorter scanning times. Most CT scans are performed using a helical technique where the gantry is continuously rotating, and the patient table is constantly moving. In this case the projections are not acquired in the same z position (slice), and in order to reconstruct the image from each plane a full set of projections for the given slice is needed. To achieve this, data from projections must be interpolated. How close the projection data used to
interpolate is to the anatomical slice to be reconstructed depends on the pitch value.
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𝑃𝑖𝑡𝑐ℎ =𝑡𝑎𝑏𝑙𝑒 𝑚𝑜𝑣𝑚𝑒𝑛𝑡 𝑝𝑒𝑟 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛
𝑠𝑙𝑖𝑐𝑒 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 (10) Using a higher pitch shortens the scan time and reduces the dose, but as less data is sampled the reconstruction will be less accurate. Typically, a pitch between 1 and 2 is used[30].
When it comes to image reconstruction methods the most common are filtered back projection or iterative reconstruction. Prior to reconstruction the data is stored in a sinogram. A sinogram is a 2D matrix that displays the projection data as a function of the projection angle, see figure 12.
Figure 12: Illustration of a projection and the sinogram. Each projection fills a line in the sinogram, given by the angle θ of the x ray source.
Until now filtered back projection (FBP) has by far been the most common method of the two as it is less computationally intensive. Back projection involves smearing the
attenuation profile back at the angle the projection was obtained. By doing this for all projection angles and summing up the values from each direction the image is obtained.
Due to the smearing the resulting image is blurry and the objects in the image do not have well-defined boundaries. To reduce the blurriness mathematical filters can be applied to the projection data prior to back projection. Applying a high pass or sharpening filter results in better spatial resolution and thus more well-defined edges, but it will accentuate the image noise giving grainy images with worse low contrast detectability. Using a low pass or
smoothing filter much of the noise is filtered away and therefore the low contrast resolution remains good, but at the expense of the spatial resolution. There is always a trade-off
between spatial resolution and image noise when choosing the reconstruction filter and the choice of filter should be based on the specific clinical application.
With the advances in computing technology iterative methods have become increasingly popular. Both purely iterative methods and a hybrid of FBP and iterative methods are available. In the hybrid methods an initial image estimate is generated using FBP and used
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as the starting point before iterative methods are used to improve upon the initial image.
This is done via forward projection on the initial image to simulate artificial raw data which can then be compared to the original data. This cycle can be repeated until a set criterion is met.
Iterative image reconstruction can be divided into analytical and statistical methods. Using an analytical method, a series of linear equations with the same number of unknowns are solved and characteristics of the image acquisition process can be incorporated. With FBP the x-ray focal point is assumed to be infinitely small, the detector and scanner geometry is ignored, and each projection is assumed to be noise free. In statistical methods, models based on the noise characteristics of the system are implemented allowing for much more complex assumptions. Iterative methods typically result in longer reconstruction times but reduce image noise compared to FBP for the same imaging dose.
2.5.3 Volumes in radiotherapy
Radiotherapy volumes must be defined and delineated for dose to be prescribed, recorded and reported. A general definition of volumes is needed for the treatment planning to be reproducible and for comparison of data from different treatment methods to be
meaningful. The International committee on Radiation Units and Measurements (ICRU) defines the following volumes which need to be defined for construction of an external radiotherapy treatment plan [31] :
Gross target volume (GTV): The gross demonstrable location and extent of the tumour which can be seen or imaged. The primary tumour as well as any gross tumour visualised in lymph nodes should be included in the GTV. The GTV is considered to consist of the areas with the highest tumour cell density. The GTV is based on diagnostic imaging such as CT, magnetic resonance imaging (MRI) and position emission tomography (F18-FDG PET).
Clinical target volume (CTV): Encompasses the true location and extent of the tumour.
Consists of the GTV and an additional margin to account for sub clinical disease spread. The additional margin is based on previous clinical experience about the risk and extent of spread, stage of the disease, as well being limited by certain anatomical barriers. It is
assumed that there are no tumour cells outside the CTV and adequate dose coverage of the CTV is paramount to achieving the therapeutic goal.
Internal target volume (ITV): An additional margin is added to the CTV to account for internal physiological variations in the CTV relative to the patient coordinate system, which occur throughout the treatment. The internal margin, which can be asymmetric around the CTV, compensates for changes in size, shape and position of the CTV, caused by variations in the organs containing and surrounding the CTV as a result of e.g. variable bladder filling, variable rectum filling, bowel movements and respiration.
Planning target volume (PTV): The PTV is a geometric concept designed to ensure that the CTV receives the prescribed dose. The PTV margin includes the internal margin which is added to the CTV to account for internal organ motion as well as a margin to account for patient motion and uncertainties in patient set up and treatment delivery. In order to avoid
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an unnecessary high dose to healthy tissue the PTV- CTV margin should be as small as is possible without compromising the CTV coverage.
Treated volume: To account for limitations in the treatment technique additional margins are added to the PTV thus the minimum target dose is represented by an isodose line, which is defined as the treated volume. The treated volume is generally larger than the PTV and depends on the particular treatment technique.
Irradiated volume: The volume of tissue which receives a significant dose, defined as more than 50% of the target prescription dose, is defined as the irradiated volume
Organs at risk (OAR): Normal structures which if irradiated can suffer toxicity and therefore influence the treatment planning and dose prescriptions. Organs which are defined as organs at risk are typically in close proximity to the CTV.
Figure 13 illustrates the volumes defined above
Figure 13: Illustration of volumes recommend for radiotherapy planning and dose evaluation.
Further information regarding the sources of uncertainty affecting the accuracy of dose delivery to the CTV as well as details on how PTV margins to account for these are determined, will be presented in a later section.
2.5.4 The linear accelerator
In external beam radiation therapy (EBRT), the radiation is delivered using a linear
accelerator (linac). The linac produces high energy photons, typically in the range 4-15 MV, through radiative interactions of electrons accelerated to high kinetic energies. The
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electrons are generated by an electron gun and accelerated by a wave guide. In the linac treatment head the electrons hit a target of high atomic number. This generates the
treatment beam, which is a Bremsstrahlung spectrum with a maximum energy characterised by the accelerating potential. Thereafter the treatment beam is filtered and collimated. The beam is collimated by adjustable jaws in the treatment head of the linear accelerator[15].
During treatment the patient is placed on the treatment couch, which is adjustable, to facilitate precise patient positioning. The treatment head is mounted on a gantry which can be rotated 360° around the treatment couch to allow for irradiation of the patient at different angles. The axis of rotation of the gantry, collimators and couch is at a fixed point and the intersection of these three axes is defined as the isocentre (see figure 14B). In an isocentric treatment technique the patient is positioned such that the isocentre is located within the treatment target, which means that patient repositioning is not required for different beam orientations. The linac is calibrated to deliver a specific radiation dose at the isocentre and the linac output is measured in monitor units (MU). Each linac is calibrated to deliver a specific dose of radiation per MU. Figure 14A shows a linear accelerator from Varian.
Figure 14: A) Linear accelerator from Varian, illustrating the rotating gantry. B) Schematics of the individual components of a medical linear accelerator.
In conformal 3D radiotherapy imaging is used to create a 3D structure of the tumour and other organs. Multiple fields at different angles are applied, and for each angle the field is shaped based on the projection of the target volume, with the goal of covering the target volume and shielding the normal tissue. Multiple fields at different angles maintain the prescription dose to the target whilst reducing the dose to the organs at risk.
2.5.5 Intensity modulated radiotherapy and Volumetric arc therapy
The dose to the tumour is limited by the dose tolerance of nearby organs. Intensity modulated radiotherapy (IMRT) is a delivery technique(s) that was developed to improve
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treatment outcomes and reduce normal tissue toxicity by delivering a 3D dose distribution which is highly conformed to the target structure. This is achieved by modulating the intensity across the radiation field according to the placement and shape of the target and surrounding organs.
The radiation fields are shaped to the target by multi leaf collimators (MLCs), see figure 15.
MLCs are collimators made up of individual leaves which move independently in and out of the radiation field. The leaves are made of a high atomic number material, usually tungsten.
The MLCs shape the radiation field to the target by absorbing the radiation that is emitted from the linear accelerator head after it has been shaped to a square field by the block collimators. The use of several beams at differing angles creates a conformal dose distribution and precise shaping to the target, enabling sparing of surrounding organs at risk[32]. The width of the MLC leaves as well how they move respective to each other will result in some limitations on the possible field shapes and configurations. By varying the field configurations created by the MLC and the time of irradiation IMRT allows for different dose values to be delivered simultaneously per fraction to different areas of the target volume.
Figure 15: Illustrating showing how the multi leaf collimators shape the radiation field to the desired shape[33].
In IMRT treatment planning the desired dose distribution is known but the beam intensities needed to achieve this dose distribution are not. Starting with the desired dose distribution and working backwards to find the beam intensities is called inverse planning. The dose distribution is defined by specifying a number of objectives and constraints, like minimum and maximum dose limits as well as dose volume constraints for both target volumes and normal tissue. A computer algorithm calculates the intensity map and delivery apertures that results in a dose distribution which achieves the specified objectives and constraints.
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This is done by modulating the intensity over the fields and ensuring that their sum produces a homogenic field in the targets and a lower dose outside.
This optimisation process consists of the minimizing of a cost function. A commonly used optimisation strategy is a weighted least squares fitting, where the dose in each voxel di is calculated and compared to a desired dose dip, as shown for one structure in equation 11.
𝐶 = ∑ 𝑤𝑁𝑖 𝑖(𝐷𝑖− 𝐷𝑖𝑝) (11) Here N is the number of voxels, Di is the actual dose, Dip is the prescription dose and wi is the weight factor. In the optimisation process, target structures and normal tissue
structures with different constraints and objectives are included. However, it is the sum of the cost functions of all the structures that is to be minimised when finding the optimal delivery. During optimisation there may be conflicting objectives, for example reduced dose to normal tissue structures could come at the cost of reduced dose homogeneity or dose to the tumour. For this reason, weight factors can be used. The weight factor allows the planner to decide the relative importance of achieving a certain objective
Volumetric arc therapy (VMAT) differs from fixed field IMRT in that the gantry is continuously rotated in arcs around the patient during radiation delivery. Cone beam shaped radiation fields are utilised enabling dose coverage to the entire target volume. This results in significantly reduced treatment times compared to IMRT. In VMAT the dose distribution is shaped throughout the treatment by varying the gantry rotation speed, treatment aperture shape and dose rate. This facilitates the delivery of a highly conformal dose distribution and thereby sparing of normal tissue.
2.5.6 Dose volume analysis
To graphically summarize the simulated radiation distribution within target volumes and organs at risk, dose volume histograms (DVH) are calculated. A DVH is a 2D graph which relates the radiation dose to structure volume. The DVHs can be used to compare rival treatment plans for one patient and to compare the dose distribution to specific organs between differing treatment regimens[34]. Dose volume histograms can be visualised either as differential or cumulative. In differential dose volume histograms, the volume of a
structure receiving a certain dose is given by the dose value of the corresponding bin. A cumulative dose volume histogram represents the volume of the structure receiving a dose greater or equal to the dose value in the corresponding dose bin. Dose volume histograms can be expressed in relative and absolute values. A limitation of DVHs is that all positional information in the volumes is lost. Figure 16 shows an example of a cumulative and a differential DVH with several relevant DVH parameters.
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Figure 16: Representation of cumulative and differential DVH[35].
Definitions of some of the DVH parameters represented in figure 16 are given below[35]:
D
98% - D98% represents the near minimum dose to a specified volume of interest. D98 is the dose level which 98% of the volume receives, conversely 2% of the volume will receive a lower dose. D98% is chosen to represent the minimum dose, Dmin, instead of choosing the true point dose Dmin. This is as point doses are sensitive to dose calculation parameters like voxel size and placement. Point dose calculations are also affected by the steep dose gradients achieved in IMRT/VMAT. As such D98% is considered more reliable than dose values at a point. D98% is used to estimate dose coverage for target volumes. For PTV volumes D98% should be at least 95% of the prescribed dose[35].D
2%- D2% represents the near maximum dose and specifies the dose level received by maximum 2% of the target volume. For the same reasons explained for D98%,D2% isconsidered more clinically relevant as a measure of the maximum dose than the point dose Dmax .
D
median - The median dose is defined as the dose at which 50% of the volume receives a higher and 50% receives a lower dose.D
mean - is the arithmetic mean dose for a given volumeV
D – Designates the volume of a structure receiving a dose greater than D. For example, V45 is the volume receiving more than 45Gy. These parameters are used for organs at risk, where the volume of tissue receiving over or under a certain dose is often correlated with the risk of toxicity. Further details regarding normal tissue toxcicity will be given in section 2.822
2.6 Errors and margins
Several error sources present during radiotherapy treatment preparation and execution which limit the accuracy. Here, the term error is used to describe deviations between the planned and executed treatment. Therefore, to ensure that the CTV receives the prescribed dose a safety margin is added to the CTV to create the PTV (see section 2.5.3) The aim is to keep this margin as small as possible as the margins are applied in 3 dimensions and as such a small increase in margins can result in significant increase in normal tissue irradiated.
Transferring of image data from localisation through the treatment planning system to the linear accelerator (linac) for treatment delivery can be subject to error. Error sources include difference in laser alignment between the CT and linac, couch position indication, image resolution, isocentre position, MLC leaf accuracy as well as gantry and collimator accuracy.
These uncertainties are reduced by performing regular calibration to ensure that the differences are within a set tolerance level[36].
Another source of uncertainty is the patient set up. Set up errors incorporate uncertainties in patient-beam position relative to the treatment machine coordinate system. These
include changes in patient positioning on the treatment couch, as well as incorrect isocentre positioning and uncertainties in field size and shape.
As the tumour is imaged in an arbitrary position, changes in CTV shape, size and position relative to the patient coordinate system, caused by physiological variations in internal organs must also be accounted for. A distinction is made between internal changes that occur between fractions and those that occur during fractions. Changes in CTV position, shape and size that occurs during treatment is classified as intra-fractional whilst changes that occur from fraction to fraction are classified as inter-fractional.
Furthermore, delineation of the GTV and the CTV is a source of uncertainty. Imaging modalities are currently unable to visualize subclinical disease directly and as such the delineation of the CTV is largely based on clinical and pathological experience from a population of patients. Thus, the introduced error will be the difference between the delineated CTV and the ‘ideal’ CTV.
In the clinic CTV-PTV margins are often based on clinical experience or population-based data regarding the magnitude and direction of all the different errors for a treatment site.
This data is based on measurements performed on a group of patients drawn from a larger population which follows a probability distribution. Based on these statistics it is common to choose a margin which accounts for a specified percentage of errors, typically 95%[37]. This is as demanding a margin which accounts for 100% of the errors would mean including errors which lie in the tails of the distribution and would result in unacceptably large margins.
ICRU recommends the use of two margins to make up the total CTV-PTV margin, the internal margin (IM) and the setup margin (SM)[12]. The IM is added to the CTV to give the ITV and is designed to account for internal motion and deformation of the CTV relative to the patient coordinate system. The IM can be found in literature or by performing studies
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on a group of patients. The set-up margin (SM) should account for uncertainties in aligning the internal reference point in the patient with the isocentre of the treatment machine and alignment of treatment beams. The SM can be found by statistical analysis from onboard cone beam CT scans. The ICRU recommends that the IM and SM be added quadratically to give the total margin (TM), as adding the IM and SM linearly could result in unnecessarily large margins.
𝑇𝑀 = √𝐼𝑀2 + 𝑆𝑀2 (12)
2.6.1 Systematic and random errors
Error sources can consist of both systematic and random components. Systematic errors are defined as deviations that occur in the same direction and are of similar magnitude for each fraction. Systematic errors are stochastic among patients but systematic for a single RT treatment regime. Systematic errors may be introduced at the target localisation, planning or delivery stage and they influence all fractions. Examples of systematic errors are CTV delineation errors, set up errors relative to planning, as well as changes in CTV shape, size or position relative to that at planning. The individual patient systematic error ∑i is found by computing the mean of the measured errors over the course of the treatment. The population systematic error ∑ is defined as the standard deviation of the individual mean systematic errors about the overall population mean error
Σ = √∑ (Σ𝑖−Σ𝑚𝑒𝑎𝑛)2
𝑛−1
𝑛𝑖=1 (13)
Here the term population is used to mean all patients treated with a specific technique for a specific treatment site. The estimate for the population systematic errors are calculated based on a group of patients drawn from the population that are thought to accurately represent the population. Although small patient studies, in the region of 10 patients, may result in large uncertainties in population systematic errors[36]. The standard deviation of all systematic errors is combined quadratically to give the total systematic error ∑.
Σ = √Σ𝑜𝑟𝑔𝑎𝑛𝑚𝑜𝑡𝑖𝑜𝑛2 + Σ𝑠𝑒𝑡𝑢𝑝2 (14) Random errors vary in direction and magnitude for each fraction and are only introduced at
the treatment delivery stage. Random errors are stochastic among patients and individual treatment fractions. Examples of random errors are intra-fractional organ motion, inter fractional organ motion as well as changes in patient positioning and treatment delivery from fraction to fraction.
The random individual patient random error σi is estimated by the standard deviation of the measured errors around the patient mean over the course of the treatment. The population random error σ is estimated by the mean of the individual random errors. The SD of all random errors are combined to give the total random error.
𝜎 = √𝜎𝑚𝑜𝑡𝑖𝑜𝑛2 + 𝜎𝑠𝑒𝑡𝑢𝑝2 (15)
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It has been shown that the effect of random and systematic errors on dose differs. As systematic errors affect all fractions the systematic errors lead to a displacement of the cumulative dose distribution relative to the CTV whilst random errors cause a blurring of the dose distribution. Systematic errors therefore have a greater effect on the dose distribution than random errors[38].
2.6.2 Margin recipes
Current technology has resulted in the improved ability to quantify random and systematic errors in the target position. As such a number of margin recipes utilizing this information to determine PTV margins have been suggested. A margin recipe aims to calculate the PTV margin required to provide adequate CTV dose coverage for the errors present for a given patient population.
One of the most widely used margin recipes was developed by Van Herk et al. The Van Herk margin recipe is based on the minimum dose delivered to the CTV[39]. This margin formula was based on an idealized dose model by finding the geometrical margin required to ensure that the CTV was fully covered by 95 % of the prescribed dose. The effect of the random errors on the planned dose profile is blurring of the dose distribution. The blurred dose profile was modelled by convolving the planned dose profile with a gaussian with a standard deviation = σ . Here, σ is the population random error. The blurred dose distribution was then shifted to model the systematic error. The margin to account for systematic
uncertainties was calculated based on the probability that the systematic error caused movement of the CTV outside the region covered by the 95% dose level of the blurred distribution (see figure 17). Van Herk et al found that the margin needed to ensure that for 90% of the patients the minimum cumulative dose to the CTV should be 95% of the
prescribed dose was:
𝑃𝑇𝑉 𝑚𝑎𝑟𝑔𝑖𝑛 = 2.5𝛴 + 0.7𝜎 (16) Here Σ is the population systematic error and σ is the population random error. This margin recipe does not account for deformations in the CTV.