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Artificial Intelligence in Adaptive Radiation Therapy
6.2.3.2 Dosimetrists
Dosimetrists play a large role in both online and ofine ART. In ofine ART, their role may be more straightforwardoptimizing the new adapted plan using the image from re-simulation following the same approach as the initial plan. However, they need to have an intimate understanding of the planning strategies and concerns in the adaptive approach. Their role in OnART can be much more involved. There is less time to digest the case, and even less time to re-contour and re-optimize the plan. This demands thorough training and experience from dosimetrists so that they are comfortable in the adaptive environment.
6.2.3.3 Physicians
Physicians play an instrumental role in the ART workow, primarily in deciding when to adapt, and after re-optimizing, whether to accept the new plan or choose to deliver the original plan. They may plan to adapt ahead of time or know when to trigger adaptation based on the circumstances during treatment, such as the changed positions of internal organs or changes in the tumor size and shape. In some cases, they may drive the decision to escalate dose based on what they see during treatment [47]. This demands new expertise from physicians, including new trials to investigate new approaches and the impact of ART. Physicians also play important roles in reviewing and approving imaging, contours, and plans. The fast-paced OnART environment thus demands an increased presence and engagement at the treatment machine.
6.2.3.4 Physicists
Along with sharing the roles of the dosimetrists, physicists provide the technical expertise to commission and implement the ART workow in their clinics. They must understand the details of the imaging, registration, contouring, optimization, dose calculation, and QA to safely bring each stage to operation. They should also ensure continuous safe operation of all procedures by working with therapists, dosimetrists, and physicians. Physicists are also responsible for establishing QA procedures and educating the rest of the team on executing those procedures [37].
6.2.3.5 Collaboration
Although each member of the radiotherapy team bears many unique responsibilities in the adaptive workow, it is ultimately a highly collaborative environment. Physician input on imaging and re-planning are crucial to aid the therapists and dosimetrists in their roles. Physics input for safe and effective treatment delivery help inform the physicians. The room is often full of different team members working closely together. Furthermore, a strong collaborative effort is necessary to continue pushing the eld of ART forward. Kristy Brock discussed this importance in her 2019 article, calling for collaboration between physicians, physicists, and industry partners to further improve the clinical workow, increase technical accuracy, and enable the best decision-making ability in ART [28]. AI provides a promising avenue to push the boundaries of every aspect of ART, and it will require a strong effort from all parties to develop and implement this technology safely and accurately.
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6.3 Considerations for implementing online ART

6.3.1 Time as a limiting factor
The effective administration of ART, which responds promptly to changes in tumor and surrounding tissue conditions, requires reliable and efcient clinical execution. With advancements in rapid imaging acquisition and computational resources, OnART has emerged to address inter-fraction variations based on pre-treatment in­room imaging. While ofine ART primarily targets systematic errors manifested between treatments, OnART can accommodate both random and systematic errors in daily anatomy and set-up changes, thereby maximizing dosimetric benets [4850]. However, the successful implementation of OnART imposes unique requirements on time and resource allocation.
Currently, only a limited number of OnART systems are available for clinical use, which can be categorized into CT-based OnART, represented by Varian Ethos, and MR-based OnART, exemplied by ViewRay MRIdian and Elekta Unity.
In an initial investigation into clinical OnART efciency, a single institutional study examined the treatment logs of 450 CT-based OnART fractions for various sites, including the prostate, GYN, breast, lung, HN, as well as abdomen. They reported an average duration of 37 ± 16 min for daily adaptive treatments, from patient simulation to delivery completion. Specically, the additional steps for generating online adaptive plans took an average of 20 min [51]. Similarly, another institution implementing CT-based ART reported on over 1000 fractions, indicating an average time of 34.52 ± 11.42 min from start to nish, with physicist/physician­involved steps totaling around 20 min [52].
In MR-based OnART, the current workow entails slightly prolonged t reat­ment sessions attributable to extended acquisition times and additional steps in treatment planning. An institutional inquiry into 80 adapted pelvic and abdominal SBRT fractions, conducted with the 0.35 T MR-based ViewRay MRIdian system, unveiled an average overall session duration of 54 min, with the adaptive steps pertaining to planning and evaluation consuming 31 min [42]. Similarly, another institution employing a 1.5 T MR-based Elekta platform for 65 liver and pancreas SBRT cases reported an average session duration just below 70 min (ranging from 50 to 90 min) [53].
The extended on-couch time during OnART imposes considerable pressure on patient immobilization, as any movement by the patient during re-planning can compromise the effectiveness of plan adaptation itself. This underscores the critical need for fast and reliable solutions in re-planning, encompassing contouring, registration, re-optimization, plan evaluation, and QA. On the other hand, the increased workload associated with plan regeneration for each treatment fraction stresses departmental resources. Consequently, there is a pressing need for enhanced workow efciency and the adoption of automated processes. Considerations for rapid plan generation and workow automation will be discussed in detail in the following sections.
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6.3.2 Implications for fast and reliable re-planning
6.3.2.1 OAR contouring
Based on current institutional reports, the additional time allocated for OnART re­planning varies depending on the imaging modality: approximately 20 min for CT­based systems and 30 min for MR-based systems [42, 49, 53]. The bottleneck in this process remains the contouring of OARs, which consumes over 10 min in both CT­and MR-based OnART sessions, with some complicated treatment sites requiring up to 24 min [54]. While deformable registration-based propagation has been widely adopted in clinical practice to expedite these steps, it still involves signicant manual editing and evaluation.
Recently, there has been a surge in the development of deep learning (DL) based auto-contouring algorithms. These algorithms have demonstrated comparable quality to manual delineation on both daily KVCT or MR images and have signicantly accelerated contouring procedures to within seconds. Specically, several DL-based auto-segmentation networks have exhibited high accuracy in OAR delineation and are readily available for clinical integration in prostate, cervical, and HN cancers [55, 56]. Some studies have even achieved one-shot auto­contouring on KVCT for up to 117 OARs throughout the body [5759]. These developments lay a robust foundation for minimal manual edits in current radio­therapy workows for a broader range of RT applications, including total marrow irradiation and cranial-spinal irradiation.
Moreover, attempts have been made to integrate labor-free auto-contouring into OnART workows for pelvic cancer treatments [60, 61]. While these attempts have demonstrated satisfactory quality without manual edits for most patients, there are still instances where manual intervention is required. Hence, continuous scrutiny of daily auto-segmentation is necessary for its full integration into clinical OnART. Additionally, the majority of these DL-based studies are primarily tailored for the pelvic or HN regions [59], which are anatomically more rigid and therefore exhibit fewer interfractional alterations. However, there remains a shortage of auto-contouring methods for the thoracic and abdominal regions, where more interfractional anatomical changes are anticipated. Despite the challenges of auto­contouring in the thoracic and abdominal regions, it is anticipated that OnART will offer greater dosimetric benets in these areas. Hence, there is an urgent need for further research in this domain.
6.3.2.2 Deformable imaging registration (DIR)
DIR plays a fundamental role in the OnART workow, encompassing tasks such as aligning planning CT scans with daily imaging, propagating target volumes, and accumulating doses. With the accessibility of parallel computing within modern OnART platforms, DIR operations themselves are not inherently time intensive. However, the inherent uncertainties associated with DIR methodologies pose challenges to downstream processes, necessitating meticulous manual scrutiny and consequently elongating the duration of the OnART workow.
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The primary uncertainties associated with DIR stem from the underlying assump­tion of homogeneous deformation properties within the image domain [62]. Most current DIR algorithms essentially seek mathematical or numerical solutions for the best match in the image space. Without prior knowledge of differential tissue properties and a physical basis for expansion, contraction, and pose changes, DIR algorithms struggle to effectively distinguish highly elastic structures undergoing substantial morphological transformations, such as the bladder in different llings, from rigid structures undergoing positional adjustments, such as pelvic bones in different positions. This often leads to implausible movements.
Various algorithms have been proposed to address the heterogeneous biome­chanical properties of tissues by introducing non-uniform constraints, including contour-guided registration [63], shape-based regularization [64], or local rigidity penalties [62]. To further leverage biomechanical properties, continuum mechanics have been incorporated into the design of regularizers, enforcing smoothed and diffeomorphic transformations for more physically realistic movement [65, 66]. However, the complexity of domain discretization and resolution schemes limits their clinical integration, particularly in OnART settings.
In addition to the inherent plausibility challenges within current DIR algorithms, complex medical scenarios, such as surgical resections, nasal and pulmonary congestions, and tissue inammations, can lead to missing correspondences between moving and target images, further augmenting uncertainty [67, 68]. Consequently, to better align with the requirements of the radiotherapy eld, there is a need for site­specic ne-tunings that incorporate both physical and medical contexts.
With the adoption of encoder–decoder architectures and spatial transformer networks, deep learning-based DIR, such as Quicksilver [69] and Voxelmorph [70], demonstrate potential in accommodating the heightened computational needs for biomechanically realistic solutions. Coupled with various weakly supervised training strategies adapting to specic medical conditions in radiation oncology, AI-based DIR shows promise in providing solutions to increasingly complex radiotherapy needs within acceptable timeframes in clinical OnART [71].
6.3.2.3 Plan generation
Upon determination of OAR and target volumes, and registration of planning to treatment imaging, subsequent adjustments to plan parameters are necessary. Re­planning procedures can be categorized into two main types: adapt to position (ATP) and adapt to shape (ATS). ATP involves translating the original plan to the new isocenter and optimizing the weights and shapes of MLC segments, while ATS essentially regenerates a new plan. Although ATS affords higher degrees of MLC optimization to adapt to the new anatomy, it is more time-consuming [72]. The time required for plan regeneration can vary from seconds to minutes, depending on the adaptation mode and plan complexity.
ATP has been demonstrated to be cost-effective for adapting daily treatments with minor anatomy variations. For instance, a prospective analysis of HN cancer OnART in ten patients using a 1.5 T MR-linac revealed that the ATP workow resulted in only a 2% dose difference in target coverage and a high gamma passing
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rate. Although dose differences in OARs were higher, the delivered dose on the summation plan remained statistically comparable to the reference plan, even with one or more constraint violations in at least two fractions [73]. However, it should be noted that when patient offsets exceed 2 mm, the ATP workow fails to reproduce clinically acceptable dose distributions [74].
To maximize the dosimetric benets of OnART, ATS with a higher degree of optimization capability is preferred, if resources allow. Winkel et al investigated OnART for ve cases with various inter-fraction anatomical changes: single lymph node, prostate, rectum, esophagus, and multiple lymph nodes [72]. In both re­planning modes, various optimization methods with increased degrees of freedom were explored, including adapting segments only, optimizing weights from seg­ments, optimizing weights and shapes from segments, as well as two options available only to ATS: optimizing weights from uence and optimizing weights and shapes from uence. As expected, treatments with higher anatomical complexity and inter-fraction changes require optimization methods with greater degrees of freedom to achieve clinically acceptable plans. For instance, while the ATP work­ow with optimization of weights only from segments sufced for a single lymph node case, ATS workow with optimization of weights from uence was necessary for rectum and esophagus cases to meet the same outcome. In the more complex multiple lymph node case, full online ATS optimization had to be used to meet all constraints [72].
To expedite the optimization process, prevalent commercial OnART workows frequently utilize atlas and protocol-based algorithms [75]. Atlas-based algorithms draw upon a repository of approved contours and plans to establish associations between geometry and DVH, enabling the prediction of achievable DVH for new patients with similar contours and treatment objectives. Conversely, protocol-based algorithmsbeginwithuser-defined templates containing clinical goals and priorities, iteratively adjusting the DVH until an optimal plan is achieved. These algorithms can be augmented by DL models [76], which advance DVH prediction to 2D and 3D dose predictions [77]. Moreover, leveraging historical patient plans, additional re-planning steps, such as beam orientation selection, uence map generation, and delivery parameter generation, can be seamlessly integrated into a single DL task, further enhancing automation [78]. However, despite the demonstrated enhancement in plan efciency shown by DL-based algorithms in preclinical validation, comprehensive QA procedures are indispensable for their clinical integration into OnART.
Currently, there exists a trade-off between the time and resources allocated for plan regeneration and the dosimetric benets attained. Future research on sophis­ticated optimization algorithms and large-scale toxicity analysis are imperative to substantiate the appropriate balance between planning time and dosimetric gain.
6.3.2.4 Quality assurance (QA)
Following treatment plan generation, QA becomes imperative prior to treatment delivery. Since on-table patient-specic QA is unfeasible, leading commercially available OnART platforms, including Varian Ethos, Viewray MRIdian, and Elekta Unity, employ a rapid secondary dose calculation (SDC) method [42, 79, 80].
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Although vendor-supplied QA tools have demonstrated good agreement with post­treatment QA measurements in small-scale studies [81], failure mode and effects analysis (FMEA) has revealed a 38% increase in the risk priority number for ART, with signicant risks associated with segmentation and treatment planning proc­esses [82]. Complementary to vendor-provided SDC, Rippke and colleagues have developed a QA analysis that re-examines additional factors, including absolute volume changes and gaps in structures, electron density maps, and uence modulation complexity [83]. Their study revealed that errors, particularly those related to contours, which may occur during OnART, can be identied through supplementary QA measures, underscoring the importance of adopting additional QA steps to ensure the safe delivery of OnART.
Moreover, beyond the errors inherent in conventional treatment planning and delivery, OnART introduces distinctive procedures that may contribute to addi­tional uncertainties. Kluter et al conrmed the additional risks posed by OnART, with approximately one-third of the risks being specic to MR-linac systems [84]. Additionally, the daily imaging utilized in OnART typically exhibits lower quality compared to planning imaging. This not only affects the delineation of OARs and targets but also inuences downstream procedures, such as daily imaging-based dose calculation and accumulation [49]. Consequently, frequent end-to-end verication of the adaptive workow is recommended [52, 83].
6.3.3 Implications for automated workow
ART programs are more demanding on clinical stafng levels than SRS/SBRT programs [51, 85]. Despite the widely accepted benets of reduced toxicity and improved target coverage, the increased logistical and resource burden of OnART limits its widespread implementation. Current clinical decisions within OnART are primarily based on physiciansor physicistsexperiences. In the absence of a standardized framework, the implementation of OnART varies with limited con­sensus on patient selection, time to adapt, and algorithms to choose. Therefore, paramount to the urgent need for fast and accurate re-planning tools, the establish­ment of a roadmap for automated workows necessitates a standardized and quantitative framework to support clinical decisions. This framework should not only dene action thresholds to initiate an OnART but also guide clinical decisions to progress through each step of the OnART process.
6.3.3.1 Action levels to initiate OnART
To establish a standardized decision-making framework, the rst step involves quantifying anatomical deviations, which greatly inuence the decision to proceed with OnART. Anatomical deviation primarily arises from inter-fraction motion, which varies in magnitude across treatment sites. For instance, it can be on the scale of millimeters in the prostate, whereas in the liver and pancreas, it can extend to centimeters [86]. However, inter-subject variations exist, as deviations exceeding 1 cm in the prostate are detected occasionally [86]. Adopting the concept of 4D planning, which integrates pre-treatment 4D imaging that is predictive of potential
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movement and incorporates adjusted intra-fraction margins into re-planning, has the potential to greatly improve automated workows and guide session scheduling.
Heterogeneous treatment responses also contribute to anatomical changes, notably through within-course tumor shrinkage, which are commonly reported in lung [ 8789] and HN radiotherapy [90]. This shrinkage can vary signicantly, ranging from 1.2% per day in lung treatments to as high as 70% in HN treatments [90, 91]. Such changes are often accompanied by secondary shifts in the surrounding OARs. For instance, a reduction in volume of up to 30% in the parotid glands has been observed during HN radiotherapy, along with a tendency to shift towards higher dose regions [92]. Therefore, a quantitative metric comprehensively evaluat­ing the overall anatomical deviation is in demand.
Furthermore, relying solely on univariate distance and volume as the primary descriptors for quantifying anatomical changes may not adequately capture critical changes with the most signicant dosimetric impact. In the case of hollow structures such as the bladder, rectum, esophagus, and ventricles, morphological alterations often stem from variations in internal llings, which may not substantially affect dosimetry. Consequently, parameters developed over tissue wall thickness or surfaces become more relevant for assessing dosimetric changes [93, 94]. Specically, surface modeling of bladder inter-fraction motion changes has revealed that while signicant motion may occur, it predominantly affects the superior– anterior bladder surface, with no discernible dosimetric impact on high-dose regions proximal to the planning target volume (PTV) [95]. Further research is needed to establish a quantitative relationship between anatomical changes and resultant dosimetric consequences to facilitate OnART decision making.
6.3.3.2 Automated plan evaluation
As previously discussed in section 6.3.2, current auto-contouring methods often require manual review. Given the absence of ground-truth contours on daily imaging, expediting the review process necessitates ofine selection and tuning of auto-contouring algorithms. Quantitative measurements of contour accuracy com­monly fall into two categories: overlapping-based metrics, such as the Dice similarity coefcient (DSC) and Jaccard index [96], and distance-based metrics, such as the Hausdorff distance (HD) [97]. Recently, a surface-based renement of overlapping metrics, known as surface DSC, has shown higher clinical acceptability compared to traditional metrics [98, 99]. While there is no gold standard available during OnART, evaluating the dosimetric consequences is more relevant for assessing the clinical acceptability of auto-contours in scenarios with limited time and resources.
Several studies have investigated the dosimetric impact of auto-segmented contours on downstream processes and have revealed minimal differences compared to manual contours. For instance, in a study involving 20 lung SBRT patients, Vaassen et al compared DVH parameters among plans optimized using ve contour sets: fully manual, atlas-based, atlas-based with manual adjustment, deep learning­based, and deep learning-based with manual adjustment [100]. They found that the dose variations resulting from automatic contour variations were comparable to or
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lower than the intra-observer contour variability. However, manual editing was necessary for OARs with maximum dose constraints, such as the heart [100]. Similarly, in a study with 15 prostate cancer patients, Zabel et al found no signicant differences in clinically relevant dose–volume metrics between auto-segmented bladder and rectum contours [101]. In a larger study involving 247 cervical cancer patients, Rigaud et al reported differences in DVH metrics between auto-segmented and manual contours to be within 1% and 1 Gy [102]. Nonetheless, not all investigated auto-contouring workows present negligible OAR dosimetric impacts [100, 103]. Additional comparative analyses focused on site-specic dosimetric goals are crucial for determining which OARs require increased scrutiny during online review. This rened approach empowers clinicians to make nuanced decisions aligned with individual patient needs and treatment objectives.
Treatment planning evaluation relies on dosimetric endpoints for both target volumes and OARs. These endpoints are commonly expressed through DVHs, including parameters such as maximum and minimum dose (D dose received by at least n% of the structures volume (D structure receiving at least n Gy (V
). Additionally, metrics such as conformity
nGy
), and the volume of
n%
max
and D
min
), the
index, homogeneity index, and gradient index provide further insights into dose distribution beyond 1D DVHs. To expedite online plan evaluation, structured checklists of these metrics are generated to assess plan adherence to constraints [104]. The use of auto generated checklists was found to increase the error detection by 20% [105]. However, given that not all constraints can always be met, there is often a trade-off between target coverage and OAR sparing, particularly in cases with close proximity to OARs and limited planning time. In such scenarios, physician input is necessary to prioritize objectives. To integrate both objective and subjective preferences and enable ranked acceptability, Ventura et al proposed weighted scoring of dose constraints according to physician preferences, presented in a graphical radar plot [106]. To yield more insights on plan quality other than the commonly used DVH metrics, Ceballos et al further extracted 60 non-conventional parameters that specically probe for hot and cold spots, and 320 radiomic features from the 3D dose distribution to train a random forest regressor for prostate cancer RT plan quality evaluation. The resulting machine learning model using a combination of DVH and dose radiomic features achieved high grading accuracy compared to the physicians evaluation [107].
In addition to determining whether a plan meets certain constraints, an alternative approach to dening plan acceptability involves assessing whether the current plan achieves the best possible dosimetric endpoints. This entails comparing the current DVH or dose distribution with predicted values [108, 109]. By integrating this evaluation criterion with the plan generation process using the predicted DVH or dose to guide plan generation, the resulting plan is deemed optimalwithout the need for further evaluation. Indeed, several assessments of non-manually intervened auto-planning have demonstrated that such plans are non­inferior to human-generated plans in multiple sites, including prostate, endometrial, lung, and head and neck [110, 111]. Auto-planning even exhibits greater OAR sparing [110], increased dose conformity, and reduction of integral dose [111].
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Coupled with the auto-segmentation process, a fully automated contouring and planning workow tested in nine prostate cancer IMRT patients achieved acceptable target coverage and reduced mean dose to the bladder and rectum [112]. Although still in its nascent stage, with advancements in auto-contouring and auto-planning algorithms, the plan generation process itself shows promise for self­approval in the future.
6.3.4 Clinical considerations
As AI technology continues to advance, it holds the promise of overcoming current technical limitations. With ongoing progress in AI, the generation of treatment plans can become increasingly efcient, with DL algorithms capable of producing plans in as little as 20 s, while knowledge-based planning may take up to 15 min [113, 114]. This reduction in planning time has the potential to signicantly decrease the cost of ART, thereby increasing its accessibility and benets for a larger patient population. Simultaneously, alongside the broader adoption of OnART facilitated by these technical advancements, the concept of adaptivetherapy undergoes an expansion. At its fundamental level, adaptive therapy involves modifying existing plans to accommodate known anatomical changes, while at its more sophisticated stage, it encompasses dynamically adjusting clinical objectives in response to tumor behavior and prognosis. However, uncertainties on treatment response, lack of knowledge of toxicity, and inter-patient heterogeneity challenge the clinical decision making.
The integration of functional imaging into ART represents a dynamic area of ongoing research, as functional responses often precede anatomical changes. Advanced imaging modalities, particularly MRI and PET, offer insights into tumor function, enabling early assessment of tumor response and resistance and thereby supporting prescription adjustments [115]. Recent studies have highlighted the predictive and prognostic value of diffusion-weighted imaging (DWI) across various cancers, including rectum, cervix, prostate, HN and brain [116, 117]. Perfusion­weighted MRI, notably dynamic susceptibility contrast (DSC)-MRI, provides additional physiological information and demonstrates correlations with brain glioma progression and treatment response in normal brain tissue [118, 119]. While DWI or DSC imaging modalities have an implicit correlation with the underlying biology and physiology of tumor response [116], PET imaging is more closely related to cellularity and proliferative activity, which are two major indicators of tumor aggressiveness. Furthermore, PET has demonstrated the capability to differentiate necrosis, brosis, or radiation therapy-induced inamma­tion, as well as hypoxic tumor cells, which are a hallmark of radioresistance [120].
With the increasing utilization of MR-linac and the emergence of PET-linac, biologically adaptive OnART becomes feasible. However, the reproducibility of quantitative functional biomarkers depends heavily on imaging devices and proto­cols, as signicant inter-system and inter-sequence variability have been observed [121, 122]. Consequently, quantitative functional measurements developed on diagnostic imaging systems or sequences may not translate reproducibly to hybrid MRI- or PET-linac scanners. Moreover, imaging processing methods introduce
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additional uncertainties to the development of quantitative biomarkers. For example, the selection of diffusion resultant decay models and the t quality inuence the accuracy of DWI-derived parameters [116]. RT-induced perfusion changes in normal tissue may bias the DSC metrics if selected as a reference region, potentially overestimating tumor physiological response [118]. Additionally, various correction factors can be applied to calculate the standardized uptake value (SUV) in PET, albeit contradictory results have been reported regarding which SUV calculation method best correlates with the glucose metabolic rate [122].
To develop optimal strategies for integrating functional imaging into RT, larger clinical trials with standardized imaging protocols across multiple institutions are imperative. The rising application of DL-based imaging reconstruction and post­processing allows for fast in-room scans with quality comparable to or exceeding state-of-the-art diagnostic standards [123125]. Complementing the technical advancements in imaging acquisition is the increasing integration of quantitative imaging and machine learning applications into the radiation oncology workow, notably through radiomics analyses. These developments offer an unprecedented opportunity to rene the assessment of early treatment response, OAR toxicity, and long-term clinical outcomes at an individual level [126, 127]. Such endeavors would enable more robust and reliable outcome prediction, ultimately enhancing clinical decision making.

6.4 Summary

In this chapter, we discussed the evolution of radiotherapy, which has seen signicant improvements to conformality and precision over the past few decades. Each technological leap has highlighted the remaining assumptions in our processes and pushed our eld further forward. The rise in prevalence of image guidance emphasized how we still plan on a static snapshot of the patients anatomy. Adaptive radiotherapy evolved to address the day-to-day variations and systematic changes in anatomy. In the early stages, technological limitations relegated adaptation to ofine re-simulation and re-planning. Recent years have seen a widespread push toward OnART, but the current solutions remain bottlenecks to clinical throughput. Several tasks in the adaptive workow have high potential for acceleration through AI automation, and these applications will be discussed in detail in subsequent chapters.
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