Compressed radiation therapy planning

Abstract

Systems and methods are provided for optimizing a radiotherapy treatment for a patient. A method for optimizing radiotherapy treatment comprises discretizing a region of interest of the patient into a plurality of voxels, wherein the voxels comprise tumor voxels and non-tumor voxels; receiving a prescribed radiation dose for each tumor voxel; discretizing one or more radiation emitters of a radiotherapy machine into a plurality of two- dimensional beamlets; defining an initial intensity vector for each beamlet; determining a radiation dose delivered to each voxel by each 2D beamlet, the radiation dose based on the initial intensity vector, thereby creating a dose influence matrix; compressing the dose influence matrix; applying an automated planning algorithm to approximate the prescribed radiation dose for tumor voxels and minimize the radiation dosage for non-tumor voxels, thereby creating an optimized intensity vector; and providing an optimized radiotherapy treatment for the patient based on the optimized intensity vector.

Description

COMPRESSED RADIATION THERAPY PLANNING

[0001] This application claims the benefit of U.S. Provisional Application. No. 63 / 672890 filed July 18, 2024, which is hereby incorporated by reference in its entirety.TECHNICAL FIELD

[0002] Embodiments of the present disclosure are related to a system, method, and computer program product for creating an optimized radiotherapy treatment.BACKGROUND OF THE DISCLOSURE

[0003] Radiation therapy is used to treat over half of all cancer patients, using specialized machines to direct high-energy beams at tumors, aiming to damage cancer cells while minimizing harm to nearby healthy tissues. Customizing the shape and intensity of radiation beams for each patient involves solving computationally challenging large-scale optimization problems that need to be solved within a clinical timeframe.

[0004] A framework to compress radiotherapy treatment planning is needed to enable quick and accurate solutions to optimization problems. This framework (known as “CompressRTP” herein) comprises a set of algorithms and mathematical models designed to provide a compressed and hierarchical representation of radiotherapy data, addressing several critical issues in alternate systems including: 1) the sub-optimality of radiotherapy plans and their outcomes due to using gross approximations for computational efficiencies; 2) underutilization of recent advanced radiotherapy machines due to the gap between software and hardware stemming from the computational challenges; and 3) unnecessary plan complexity and delivery inefficiency due to the lack of global smoothness and explicit constraints in the existing mathematical models.SUMMARY

[0005] According to certain aspects of the present disclosure, methods, systems, and computer program products are disclosed for optimization of radiotherapy treatment.

[0006] In one embodiment, a method for optimizing a radiotherapy treatment comprises discretizing a region of interest of a patient into a plurality of voxels, wherein the plurality of voxels comprise tumor voxels and non-tumor voxels; receiving a prescribed radiation dose for each tumor voxel; discretizing one or more radiation emitters of a radiotherapy machineinto a plurality of two-dimensional (2D) beamlets; defining an initial intensity vector for each beamlet; determining a radiation dose delivered to each voxel by each 2D beamlet, the radiation dose based on the initial intensity vector, thereby creating a dose influence matrix; compressing the dose influence matrix; applying an automated planning algorithm to approximate the prescribed radiation dose for tumor voxels and minimize the radiation dosage for non-tumor voxels, thereby creating an optimized intensity vector; and providing an optimized radiotherapy treatment for the patient based on the optimized intensity vector.

[0007] In an alternative embodiment, a system for optimizing a radiotherapy treatment comprise a computing node comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor of the computing node to cause the processor to perform a method comprising discretizing a region of interest of a patient into a plurality of voxels, wherein the plurality of voxels comprise tumor voxels and non-tumor voxels; receiving a prescribed radiation dose for each tumor voxel; discretizing one or more radiation emitters of a radiotherapy machine into a plurality of two-dimensional (2D) beamlets; defining an initial intensity vector for each beamlet; determining a radiation dose delivered to each voxel by each 2D beamlet, the radiation dose based on the initial intensity vector, thereby creating a dose influence matrix; compressing the dose influence matrix; applying an automated planning algorithm to approximate the prescribed radiation dose for tumor voxels and minimize the radiation dosage for non-tumor voxels, thereby creating an optimized intensity vector; and providing an optimized radiotherapy treatment for the patient based on the optimized intensity vector.

[0008] In another embodiment, a computer program product for optimizing a radiotherapy treatment comprises a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to perform a method comprising discretizing a region of interest of a patient into a plurality of voxels, wherein the plurality of voxels comprise tumor voxels and non-tumor voxels; receiving a prescribed radiation dose for each tumor voxel; discretizing one or more radiation emitters of a radiotherapy machine into a plurality of two-dimensional (2D) beamlets; defining an initial intensity vector for each beamlet; determining a radiation dose delivered to each voxel by each 2D beamlet, the radiation dose based on the initial intensity vector, thereby creating a dose influence matrix; compressing the dose influence matrix; applying an automated planning algorithm to approximate the prescribed radiation dose for tumor voxels and minimize the radiation dosage for non-tumor voxels, thereby creating anoptimized intensity vector; and providing an optimized radiotherapy treatment for the patient based on the optimized intensity vector.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The accompanying drawings, which are incorporated into and constitute a part of this specification, illustrate various exemplary embodiments and together with the description, serve to explain the principles of the disclosed embodiments.

[0010] FIG. 1 is a graph illustrating the performance of treatment planning algorithms.

[0011] FIG. 2 is a block diagram of comparison between a manual and automated workflow, in accordance with one or more embodiments of the present disclosure.

[0012] FIG. 3 is a flow chart illustrating an exemplary method of optimizing a radiotherapy treatment for a patient, in accordance with one or more embodiments of the present disclosure.

[0013] FIG. 4A is a graph illustrating the distribution of singular values with exponential decay in a low rank data structure, in accordance with one or more embodiments of the present disclosure.

[0014] FIG. 4B is an illustration of a sparse plus low rank compression decomposition, in accordance with one or more embodiments of the present disclosure.

[0015] FIG. 4C is a graph illustrating a dose discrepancy without compression, in accordance with one or more embodiments of the present disclosure.

[0016] FIG. 4D is a graph illustrating a dose discrepancy with compression, in accordance with one or more embodiments of the present disclosure.

[0017] FIG. 5A is a graphic illustrating a radiotherapy treatment plan without compression, in accordance with one or more embodiments of the present disclosure.

[0018] FIG. 5B is a graphic illustrating a radiotherapy treatment plan with compression, in accordance with one or more embodiments of the present disclosure.

[0019] FIG. 5C is a graph illustrating a comparison between a radiotherapy treatment plant with and without compression, in accordance with one or more embodiments of the present disclosure.

[0020] FIG. 6A is pseudocode for an exemplary recursive trust-region algorithm, in accordance with one or more embodiments of the present disclosure.

[0021] FIG. 6B is a graph of the exemplary recursive trust-region algorithm as compared to alternative treatments, in accordance with one or more embodiments of the present disclosure.

[0022] FIG. 7 A is pseudocode for an exemplary rectified R-Trust algorithm, in accordance with one or more embodiments of the present disclosure.

[0023] FIG. 7B is pseudocode for an exemplary randomized R2-Trust algorithm, in accordance with one or more embodiments of the present disclosure.

[0024] FIG. 8 is pseudocode for an exemplary Randomized Minor-value Rectification (RMR) algorithm, in accordance with one or more embodiments of the present disclosure.

[0025] FIG. 9 is a series of graphs illustrating the performance of the RMR algorithm, in accordance with one or more embodiments of the present disclosure.

[0026] FIG. 10A is a series of graphs illustrating the performance of different algorithms for lung patients, in accordance with one or more embodiments of the present disclosure.

[0027] FIG. 10B is a series of graphs illustrating the discrepancies in Dose Volume Histogram for one lung patients, in accordance with one or more embodiments of the present disclosure.

[0028] FIG. 11A is a graphic representation of dosimetric data in a 3D tensor form, in accordance with one or more embodiments of the present disclosure.

[0029] FIG. 11B is a graphic representation of dosimetric data in a 3D tensor form, in accordance with one or more embodiments of the present disclosure.

[0030] FIG. 12 is an exemplary computing node.DETAILED DESCRIPTION

[0031] Reference will now be made in detail to the exemplary embodiments of the present disclosure, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used through-out the drawings to refer to the same or like parts.

[0032] The systems, devices, and methods disclosed herein are described in detail by way of examples and with reference to the figures. The examples discussed herein are examples only and are provided to assist in the explanation of the apparatuses, devices, systems, and methods described herein. None of the features or components shown in the drawings or discussed below should be taken as mandatory for any specific implementation of any of these devices, systems, or methods unless specifically designated as mandatory.

[0033] Also, for any methods described, regardless of whether the method is described in conjunction with a flow diagram, it should be understood that unless otherwise specified or required by context, any explicit or implicit ordering of steps performed in the execution of a method does not imply that those steps must be performed in the order presented but instead may be performed in a different order or in parallel.

[0034] As used herein, the term “exemplary” is used in the sense of “example,” rather than “ideal.” Moreover, the terms “a” and “an” herein do not denote a limitation of quantity, but rather denote the presence of one or more of the referenced items.

[0035] Radiation therapy (RT) is integral to cancer treatment, utilized in approximately half of all cases, either alone or in combination with other treatments like surgery or chemotherapy. RT involves using specialized machines to emit and direct high-energy radiation beams at tumors, with the primary goal of destroying cancer cells while minimizing damage to healthy tissues. This process requires precise optimization of machine parameters, such as beam shapes and angles, tailored to each patient's unique anatomy. Optimization involves solving large-scale, constrained, non-linear optimization problems swiftly within clinical time constraints. The urgency of this task is heightened in modern online adaptive radiotherapy techniques, where a rapid solution is essential since patients remain immobilized on the treatment couch during preparation. Delays not only compromise patient comfort but can also affect treatment outcomes, as any rapid anatomical changes (e.g., bladder filling in prostate cancer) can render treatment plans based on initial anatomy sub-optimal. As such, quickly solving these optimization problems is crucial.

[0036] Radiotherapy treatment planning is a decision-making challenge focused on balancing tumor control against the risk of radiotoxic complications to nearby organs-at-risk (OARs). The patient's unique anatomy, combined with the treatment machine's capabilities, determines feasible treatment options. Treatment planning algorithms navigate this search space to select a plan with the most favorable trade-offs. FIG. 1 illustrates this concept: circles 101 represent various treatment options with differing trade-offs, while the arrows indicate the algorithm's route to identify an optimal plan. FIG. 1 depicts an enhancement to this process by introducing improved options (circles 102), generated using precise dosimetry, helping to close the optimality gap in alternative practices.

[0037] A range of automated planning algorithms are available, from classical techniques (e.g, knowledge-based prioritized optimization) to modem Al-based approaches (deep / reinforcement learning). Although the choice of automated planning algorithminfluences the pathway to the optimal plan, the actual treatment options are defined by the specifics of the patient's anatomy and the principles of radiation physics.

[0038] During treatment planning optimization, available treatment options are calculated based on pre-computed dosimetric data, typically represented in a large matrix known as the dose influence matrix. This matrix reflects the radiation dose delivered from various machine configurations or beamlets. However, due to the complexity of processing large, dense dosimetric data, they are often truncated and sparsified to enhance computational efficiency, such as by excluding scattering radiation dose components. This crude approximation can lead to the generation of sub-optimal treatment options based on incomplete data (circles 101 in FIG. 1). By employing compression techniques for highly compact and accurate data representation, treatment options may be created using detailed dosimetric data, leading to improved treatment options with reduced risks associated with OAR complications and / or local control failure, as illustrated by circles 102 in FIG. 1. This optimization can improve the efficacy of any automated treatment planning algorithm to generate optimal plans with less radiation exposure to nearby radiosensitive organs and adequate radiation to tumors.

[0039] Embodiments of the present disclosure provide a compact yet accurate data representation, circumventing the need for gross approximation. The data is presented in a hierarchical format, enabling the use of multi-scale algorithms where the more critical parts of the data are prioritized and ingested in treatment planning optimization, reducing computational time and memory consumption.

[0040] Accurate physics-based (e.g., Acuros) or Monte Carlo simulation-based dose calculations, facilitated by modem GPU hardware and accelerated algorithms, are used in clinics for final plan evaluations and pre-delivery checks. However, treatment planning optimization, which requires the pre-computation of dose calculations for thousands of varying machine configurations (beamlets), still relies on faster but less accurate methods like pencil beam dose calculation. Using accurate dose calculations to pre-compute the dosimetric data matrix could take hours, even with the latest GPU-based algorithms. For instance, GPUbased Acuros XB may require approximately 15 seconds per beamlet, leading to ~20 hours of dosimetric data pre-computation for a typical prostate case with 5,000 beamlets. This duration is impractical especially for online adaptive radiotherapy (OART) timeframes. Recent advances in Al and deep learning have shown promise for fast and accurate dose calculations. Various Al-based techniques have been developed for rapid (millisecond-scale) and precise (gamma accuracy index > 97%) dose calculations, utilizing patient CT scans and radiotherapy machine beam parameters. However, current research has primarily focused onusing these fast and accurate Al-based dose calculations for final plan evaluation or plan quality assurance, not for treatment planning optimization.

[0041] A primary challenge in integrating Al-based dosimetric data into treatment planning optimization is managing the large and dense matrices resulting from accurate dose calculations, including detailed radiation scattering components. For context, dosimetric data matrices used in optimization are -98% sparse (with only 2% non-zero elements), whereas accurate, detailed matrices are completely dense. This denseness demands -50 times more memory and significantly slows down optimization processes, potentially making them thousands of times slower and unsolvable due to the cubic computational complexity of optimization algorithms relative to data size. Accurate dosimetric data matrices render treatment planning optimization impractical, particularly for OART.

[0042] Using inaccurate dosimetric data during treatment planning leads to significant discrepancies between the planned radiation dose and the final accurate dose used for evaluation, resulting in sub-optimal plans. This issue is partially addressed through a “correction loop,” which intermittently integrates more accurate dose calculations into the optimization process. Although this heuristic method can correct minor discrepancies, it does not fully resolve the issue, leaving some level of plan sub-optimality. As such, embodiments of the present disclosure include a rapid and accurate Al-based dose calculation followed by data compression before optimization. Minor Al inaccuracies and other dose discrepancies, such as the tongue-and-groove effect, which cannot be preemptively modeled, can be addressed using a novel “correction loop” based on rank-one updates. Alternate correction techniques suffer from a “short memory” problem: each time the system inquires an accurate dose calculation and computes the data discrepancy, it overrides and forgets the previous accurate dose calculations, resulting in more correction steps. The approach in embodiments of the present disclosure adds a correction step in the form of a rank-one update, allowing for the preservation of all previous accurate calculations and reduction of the number of required corrections. This “long-memory” correction strategy not only improves computational efficiency but also enhances plan quality.

[0043] FIG. 2 illustrates a manual workflow 201, using a fast and inaccurate pencil beam dose calculation, and an automated workflow 202, using fast and accurate Al-based dose calculations and data compressions. Each workflow leads to treatment planning optimization 203, comprising optimization and intermediate dose calculation in a correction loop, as well as a final dose calculation. However, workflow 202 capitalizes on the data compression and accurate Al-based dose to provide a faster process.

[0044] Modern radiotherapy machines offer more flexibility and degrees of freedom, such as moving the couch while the patient receives treatment, to better modulate the radiation beams and generate more conformal radiation to the tumor. However, leveraging these extra degrees of freedom leads to larger and more computationally complex optimization problems. As a result, these degrees of freedom are often underutilized due to the gap between hardware and software development. Embodiments of the present disclosure bridge this gap to fully exploit the capabilities of modem machines. Some embodiments leverage redundancy in data and captures variations among neighboring machine parameters (e.g., neighboring couch positions, iso center locations, beam angles) in a computationally manageable low-rank matrix. This approach is analogous to using low-rank matrices in modern large language models to capture differences between contexts.

[0045] Robust optimization in radiotherapy treatment planning is crucial for ensuring effective and safe cancer treatment. Given the inherent uncertainties in patient positioning, tumor motion, and anatomical changes during the treatment course, robust optimization techniques are essential to account for these variables and deliver consistent therapeutic doses to the tumor while minimizing exposure to healthy tissues. By incorporating variability and potential deviations into the optimization process, robust treatment plans can better withstand the unpredictable nature of real-world conditions, thus improving treatment efficacy and reducing the risk of adverse side effects. However, robust optimization increases the computational burden and slows down the treatment planning process, often necessitating more gross approximations that could compromise plan quality. Currently, several uncertainty scenarios and patient movements are simulated upfront, each resulting in an individual large influence matrix, which are incorporated into treatment planning optimization. Embodiments of the present disclosure leverage the correlation in data between these scenarios and captures the differences among them in the form of a low-rank matrix, allowing for much more computationally efficient optimization. In other words, a low-rank matrix captures the variations in dosimetric data when the patient moves, significantly enhancing the optimization process.

[0046] The effectiveness of modern Intensity Modulated Radiation Therapy (IMRT) relies on highly conformal radiation dose distribution to sufficiently irradiate the tumor while sparing nearby critical organs. Achieving this high-dose conformity involves modulating the intensity and shape of radiation beams, enabled by modulating multi-leaf collimator. Although some modulation is necessary to shape the radiation dose to the tumor, excessive modulation can increase plan complexity and potentially compromise the accuracy of dosedelivery, a vital aspect of IMRT 19,20. Moreover, the increased complexity does not always lead to better dose conformity. Increased complexity in radiotherapy plans can lead to inaccuracies in dose delivery.

[0047] Plan complexity may be reduced by smoothing the intensity map of each beam during fluence map optimization (FMO). This may be achieved by adding an additional “regularization” term to the objective function that measures local variations in adjacent beamlets to discourage fluctuating beamlet intensities. A significant limitation of this method is its focus on local complexity within each beam, assessing variations in adjacent beamlets but overlooking the global complexity of the plan. Another challenge is that achieving an optimal balance between plan complexity and dosimetric quality necessitates careful fine- tuning of the importance weight associated with the smoothness term in the objective function. CompressRTP addresses this issue by providing a compressed representation of the fluence map where irrelevant fluctuated fluences are explicitly excluded from the decision space. In this case, CompressRTP is intended not for computational efficiency, but to provide a more realistic representation of data and decision variables and to induce local and global smoothness and generate a high-quality plan that can be efficiently delivered.

[0048] FIG. 3 is a flow chart illustrating an exemplary method 300 of optimizing a radiotherapy treatment for a patient. For example, exemplary method 300 (e g., steps 301- 308) may be performed by a processor automatically, or in response to a request from a user.

[0049] According to one embodiment, the exemplary method 300 for optimizing a radiotherapy treatment may include one or more of the following steps. In step 301, the method may include discretizing a region of interest of the patient into a plurality of voxels, wherein the plurality of voxels comprises tumor and non-tumor voxels. The region of interest, which may include the patient's entire body or a subsection thereof, is discretized into small three-dimensional voxels indexed by i = 1, ... , m.

[0050] In step 302, the method may include receiving a prescribed radiation dose for each tumor voxel.

[0051] In step 303, the method may include discretizing one or more radiation emitters of a radiotherapy machine into a plurality of two-dimensional (2D) beamlets. Each 2D beamlet is indexed

[0052] In step 304, the method may include defining an initial intensity vector for each beamlet.

[0053] In step 305, the method may include determining a radiation dose delivered to each voxel by each 2D beamlet, the radiation dose based on the initial intensity vector, therebycreating a dose influence matrix. The radiation dose delivered to each voxel i from each beamlet j with unit intensity is precalculated and represented by atj, forming the matrix A - the dose influence matrix. This matrix is typically large, containing about 100,000 to 1,000,000 rows corresponding to the patient's voxels, and 1,000 to 100,000 columns representing the beamlets / spots of the radiotherapy machine.

[0054] In step 306, the method may include compressing the dose influence matrix.

[0055] In step 307, the method may include applying an automated planning algorithm to approximate the prescribed radiation dose for tumor voxels and minimize the radiation dosage for non-tumor voxels, thereby creating an optimized intensity vector.

[0056] In step 308, the method may include providing an optimized radiotherapy treatment for the patient based on the optimized intensity vector.

[0057] The objective is to optimize the intensities of the beamlets, denoted by x, in order to achieve a desired radiation dose, Ax, that is delivered to the patient’s body. For the tumor voxels, the aim is to achieve radiation dose that approximates the dose prescribed by a physician in step 302, while for healthy voxels the aim is to minimize the radiation dose as much as possible. The optimization problem can be described in the following general form:Minimize f0(Ax) + Afx(x) Problem (1) subject to. g(Ax) < 0 h(xj < 0 x > 0 where, f0(Ax) measures the quality and 'goodness' of the radiation dose Ax,assesses the quality of plan delivery efficiency and the parameter A balances the tradeoffs between dosimetric plan quality and delivery efficiency. The functions g and h represent constraints on the dose received by the voxels and the plan delivery efficiency, respectively. A commonly used two-sided quadratic function is used for0(Ax) and the maximum / mean constraints for g(Ax) as follows; however, any other function can be used for these two functions. f_0 (Ax) = X_(s G S) £_(ig Ax) = max(Asx) — dUsaxAnd meanQ4sx) - dMsean

[0058] In Problem (1), the framework of embodiments of the present disclosure proposes the following algorithms and mathematical models:

[0059] Matrix Compression

[0060] Embodiments of the present disclosure include algorithms to compress the large matrix A, resulting in a hierarchical and compact yet accurate representation of the dosimetric data. This approach enhances computational efficiency without compromising data integrity, contrasting with existing gross approximations. It also enables the incorporation of modern Al-based accurate dose calculations, which produce dense dose influence matrices. The hierarchical data structure facilitates the use of multi-scale (also known as multi-resolution or progressive sampling) optimization algorithms, where more critical data parts are prioritized in the optimization process.

[0061] Fluence Compression

[0062] Embodiments of the present disclosure also include algorithms to compress the fluence map x, resulting in new formulations for / j(x) and h(x) to improve delivery efficiency without compromising dosimetric plan quality. The function / j(x) ensures both local and global smoothness, unlike current techniques that only provide local smoothness. The function / i(x) will exclude overly complex plans from the decision space, addressing the issue of manual fine-tuning of the parameter present in alternate methods.

[0063] Patient Discretization

[0064] Embodiments of the present disclosure include algorithms for patient discretization into small cubical voxels. An Al-based dose prediction may identify critical areas (e.g., high dose regions, high dose-gradient regions, tumor low dose regions) requiring more voxels. The Sparse Voxel Octree may be employed for importance sampling with a hierarchical voxel data structure. This approach reduces the number of required voxels and, similar to matrix compression, enables the use of multi-scale optimization algorithms by prioritizing more critical data parts.

[0065] Low-Rank Update

[0066] Embodiments of the present disclosure include a low-rank update adding a new term to the objective function of Problem (1) every time an on-demand forward dose calculation is performed. This idea is analogous to using low-rank matrices in modern large language models to capture contextual differences and can be applied to various aspects:• Reducing Correction Steps: Discrepancies between final and intermediate dose calculations during optimization are addressed through a “correction loop,” andexisting correction techniques suffer from a “short memory” problem. The approach in embodiments of the present disclosure adds a correction step in the form of a rank- one update, preserving all previous accurate calculations and reducing the number of required corrections. This “long-memory” correction strategy improves computational efficiency and plan quality.• Robust Optimization: Alternate techniques make plans robust against changes in patient geometry and movement by simulating several uncertainty scenarios upfront and incorporating them into treatment planning optimization. Embodiments of the present disclosure capture the differences among these scenarios in a low-rank matrix and perform on-demand forward dose calculations for each scenario, enabling more computationally efficient optimization. In essence, a low-rank matrix captures the variations in dosimetric data when the patient moves, significantly enhancing the optimization process.• Exploiting Modern Radiotherapy Machines: Modern radiotherapy machines offer more flexibility and degrees of freedom, which are currently underutilized due to computational challenges. Embodiments of the present disclosure allow simultaneous optimization of many machine parameters, including beam angles, couch positions, iso centers, and collimator rotations, by performing on-demand forward dose calculations for each parameter variation. Alternatively, pre-computing the dose for all potential variations and then applying matrix compression can also be employed. While this approach has a higher upfront calculation cost, it reduces computational costs during downstream optimization.

[0067] Table 1 summarizes different components of the framework of embodiments of the present disclosure.Table 1: Summary of different components of the present Framework

[0068] Compression tools are integral to modem life, enabling the streaming of high- quality movies to mobile devices. However, most compression techniques require decompression of data, which is both time- and resource-intensive. Embodiments of the present disclosure include matrix compression tools that do not require decompression in the downstream optimization process.

[0069] Matrix A can be decomposed into A = S + L, where S is a sparse matrix containing large-magnitude elements (e.g., > l%max(A)), and L includes smaller elements, mainly representing scattering dose. Currently, L is often omitted in treatment planning forcomputational efficiency, leading to approximations (A«S) in treatment planning. However, as shown in FIG. 4A, matrix A demonstrates a low-rank, compressible structure, evidenced by the exponential decay in singular values (solid line in Fig. 4A). Similarly, the scattering matrix L is even more compressible, evidenced by sharper exponential decay in its singular values (dotted lines in FIG. 4A). FIG. 4A illustrates the distribution of singular values with exponential decay, revealing the data compressibility for the original data matrix A (solid line), and even more prominently for the scattering matrix L (dotted line) — this suggests the use of “sparse plus low-rank” compression (also known as low-rank plus sparse), as shown in FIG. 4B

[0070] FIG. 4B illustrates a sparse plus low-rank decomposition of matrix A. The low- rank nature of L allows its compression into two simpler matrices, L = HW, where H is a “long skinny” matrix with just a few columns and W is a “wide short” matrix with few rows. H and W can be conceptualized as the principal scattering components of the matrix L and they can be obtained by applying the Singular Value Decomposition (SVD) or one of its fast randomized versions on the matrix L = A-S (i.e., [U,S,V]= SVD(L,rank)=> H = U,W = S*V). If the non-negativity of H and W are desirable, then the Nonnegative Matrix Factorization (NMF) or one of its fast randomized versions can be applied on the matrix L (i.e., [H,W]= NMF(L,rank)). Using SVD and NMF provides a simple implementation; however, they require the pre-selection of the rank and do not optimally decompose the matrix A. In some embodiments, a new algorithm (FIGs. 6A-7B) that reads the matrix A and the desired level of accuracy as inputs and outputs the sparse matrix S and low-rank matrices H and W.

[0071] Using compressed data S+HW in treatment planning achieves around 98% compression with only ~2% error. As demonstrated in FIG. 4C, approximating A~S leads to significant discrepancies between optimized (Sx, dashed lines) and accurate doses (Ax, solid lines). FIG. 4C illustrates large dose discrepancies between the accurate dose (Ax: solid lines) and the optimized dose without compression (Sx: dashed lines)

[0072] Using the compressed version (Sx+HWx) effectively eliminates these discrepancies, aligning optimized and accurate doses, as shown in FIG. 4D. FIG. 4D illustrates small dose discrepancies between the accurate dose (Ax: solid lines) and the optimized dose with compression (Sx+HWx: dashed lines). It should be noted that in this experiment, the original matrix A is first calculated using accurate Analytical Anisotropic Algorithm (AAA) dose calculation and then truncates that for planning optimization. In most commercial systems, an inaccurate pencil beam dose calculation is often used that could result in even larger discrepancies.

[0073] The dose distribution of a plan generated using inaccurate sparse dosimetry is shown in FIG. 5A, with its corresponding dose-volume histogram (DVH) represented by lines with triangle marks in FIG. 5C. In contrast, an improved plan created using accurate compressed dosimetry is shown in FIG. 5B, with its DVH depicted by lines with square marks in FIG. 5C.

[0074] FIG. 5A-C highlight the impact of using compressed data on the quality of the final treatment plan. As shown in FIG. 5B and represented by lines with square marks in FIG. 5C, treatment planning with accurate compressed dosimetry significantly reduces radiation exposure to critical organs like the bladder and rectum. This is in contrast to plans based on a gross sparse approximation, depicted in FIG. 5A and indicated by lines with triangle marks in FIG. 5C. Both types of plans are imported into the FDA-approved Eclipse system for final dose calculations and leaf sequencing. Additionally, a correction step can be applied to both plans for enhanced accuracy.

[0075] Although “sparse plus low-rank” data representation is widely used in various fields, such as computer vision, medical imaging, and statistics, its application in data compression is unprecedented. Additionally, existing algorithms in these fields, often used fortasks, such as background-foreground separation in computer vision, are not optimized for the unique requirements of radiotherapy planning.

[0076] FIG. 6A illustrates a proposed “sparse plus low-rank” matrix decomposition algorithm tailored for radiotherapy data, called Recursive Trust-Region (R-Trust). Two improved versions of the R-Trust algorithm, Rectified R-Trust (R2-Trust) and Randomized R2-Trust (R3-Trust), are presented in FIG. 7. FIG. 6B compares the performance of R3- Trust against well-known algorithms in the literature. On this graph shown in FIG. 6B, the x- axis shows the relative number of non-zero (NNZ) elements, with lower values being preferable, and the y-axis indicates the relative Frobenius norm error. The lines marked with circles labeled R3-Trust denote a proposed algorithm, with computational times for each point marked on the plot. The proposed algorithm significantly outperforms alternate ones illustrated by lines marked with triangles (labeled VB, GoDec, ADMM) by providing greater compression, lower error, and achieving these results in a much shorter timeframe (on the scale of seconds), thereby optimizing the treatment planning process in radiotherapy. FIGs. 7A-B provides the two more efficient versions of the R-Trust algorithm, called R2-Trust and R3-Trust.

[0077] The sparse plus low-rank compression in some embodiments of the present disclosure is a powerful tool; however, in some applications of radiotherapy, it might bepreferred to use the sparse-only compression technique due to it easier implementation. The key of sparse-only compression is to carefully sample and scale the elements of the original dense matrix A using randomization techniques to create a sparse sketch matrix B that minimizes in the creation of the space sketch matrix B. Matrix sparsification hasbeen studied in the machine learning community for applications such as low-rank approximation and principal component analysis (PCA). The utility of matrix sparsification in radiotherapy optimization is demonstrated and shows that applying a randomized sketch to the influence matrix A significantly outperforms the current naive sparsification approach that simply zeros out matrix entities smaller than a pre-defined threshold. Furthermore, the Randomized Minor-value Rectification (RMR) algorithm exhibits superior performance compared to alternate sparsification techniques. The algorithm is presented in FIG. 8.

[0078] FIG. 9 provides detailed comparisons of the new RMR algorithm and the existing algorithms (AHK06, AKL13, DZ11) with respect to the different levels of sparsity in the output sparse matrix for one patient. The standard deviation band is plotted for all metrics (over 5 runs), however, due to the robust performance of the algorithms, the bands are not visible except in the feasibility gap plot. As demonstrated in FIG. 9 (top-left plot), all randomized algorithms surpass the current naive approach in balancing accuracy and sparsity. Among these, AHK06 and RMR stand out, exhibiting superior performance. While AHK06 marginally surpasses RMR in terms of L2-norm, RMR significantly exceeds AHK06 in terms of feasibility (top-right plot) and optimality gaps (top-middle plot) as well as the dose discrepancy error (bottom-left plot). This is further supported by reduced discrepancies among DVH plots reported in FIG. 10B.

[0079] In terms of computational efficiency, the naive approach unsurprisingly leads in speed due to its simple implementation, with AHK06 following closely behind (bottommiddle plot). However, the relatively longer runtime of the RMR algorithm should not be seen as a significant limitation. The primary computational challenge lies in solving the optimization problems which often needs to be solved multiple times for hyper-parameter tuning. The bottom-right plot illustrates the strong correlation between the number of nonzero elements in the matrix and the computational time of the constrained optimization problem, indicating that relative sparsification serves as an excellent proxy for the computational time of the optimization problems.

[0080] FIG. 10A offers a high-level comparison across 10 patients at a fixed relative sparsity level of 98%, which can also be interpreted as a fixed computational time for theconstrained optimization problem. Confirming the results of FIG. 8 for more patients, this figure demonstrates the superior performance of AHK06 in terms of the L2-norm error and algorithm runtime, while highlighting the significant advantage of the RMR algorithm in reducing optimality and feasibility gaps.

[0081] FIG. 10B showcases three DVH plots: the naive approach (left), representing current practice; the AHK06 algorithm (middle), representing the most competitive existing approach; and the proposed RMR algorithm (right). In each plot, dashed lines illustrate the approximated radiation dose, BXB, used in the optimization problem, while solid lines depict the actual radiation dose, AxB. The gap between the solid and dashed lines indicates the discrepancies resulting from using the approximated matrix B in the optimization problem, with a smaller gap being preferred. It is readily apparent that the gap is much smaller, especially for the tumor, when using the RMR algorithm, where the solid and dashed lines are closely aligned and often overlap, making the dashed lines nearly invisible.

[0082] Traditionally, dosimetric data is represented as a 2-dimensional (2D) matrix, but inherently, it is a 6D entity combining 3D spatial voxel coordinates, 2D beamlet locations, and ID gantry angle. Additional dimensions can be added corresponding to other machine parameters, including couch position, iso center location, and collimator angle. By representing this data in its natural tensor form, a more compact representation can be achieved because the inherent redundancies and correlations between data components become more apparent than in a collapsed 2D matrix format. For example, by segregating data matrices for different gantry angles and stacking them into a 3D tensor (as shown in FIG. 11 A), and then applying tensor-train decomposition, the shared and distinct information among beams can be effectively captured and compressed.

[0083] Tensor Compression

[0084] This technique can also facilitate robust optimization by segregating data matrices for different uncertainty scenarios (as shown in FIG. 11B). Results show that transitioning from 2D to 3D leads to a significant increase in data compression, from approximately 98% to 99%. Enhancing the compression rate from 98% to 99% effectively reduces the dosimetric data and memory requirements by half. More importantly, an enhanced compression rate could result in an approximately 8-fold reduction in treatment planning optimization time, due to the cubic complexity inherent in optimization algorithms. This method marks a substantial improvement in making treatment planning more efficient and feasible, especially when adopting higher-dimensional tensor representation of data to enable optimization of many machine parameters for modern linear accelerators.

[0085] Fluence Compression

[0086] Fluence compression is intended not for computational efficiency, but to provide a more realistic representation of data and decision variables to generate a high-quality plan that can be efficiently delivered. Currently, a smoothing term / )(%) = | |Px| | is added in Problem (1), where the matrix P is the total variation matrix, measuring the local intensity variations in the neighboring beamlets. To enforce explicit smoothness, SVD decomposition is performed on matrix P and then enforcing x to be in the linear subspace characterized by the trailing right singular vectors of P (i.e., P = USV, x = V2x y). Furthermore, a new matrix P incorporates global smoothness, constructed from the following components:

[0087] Hi h-frequency Wavelets

[0088] To encourage more smoothness in the direction of leaf movements, different weights can be assigned to the wavelet basis components, for example P=[H;2V;4D], where H, V, and D represent horizontal, vertical, and diagonal components in the wavelet basis. Alternatively, one can use 1-dimensional wavelets, sort them according to their frequencies, remove low-frequency components (removing fewer components in the direction of leaf movement), and then perform a tensor product.

[0089] Differential Matrices

[0090] The total variation matrix used in current practice is effectively the discrete differential matrix corresponding to the first derivative. To allow more global smoothness, differential matrices of higher derivative orders can be applied.

[0091] Influence Matrix

[0092] SVD can be performed on the influence matrix, inverting the singular values, then adding the resulting matrix into the P matrix.

[0093] Frequent low-rank Updates

[0094] A key idea of frequent low-rank updates is to perform on-demand accurate dose calculations during optimization for certain desirable parameters and incorporate them efficiently into the optimization process. This contrasts with the approach of calculating the dose upfront for all possible parameters. It is assumed that xkis the optimal solution of Problem (1) and dk= A X xk+ H X W X xkis the corresponding optimization dose at iteration k.

[0095] Rank-one Update for “Long Memory” Correction

[0096] It is assumed that the accurate forward dose calculation is performed for xk, resulting in an accurate dose of Dk. Alternate practices calculate the dose for the nextiterations as d = A x x + H x W x x +k, where Afc= Dk— dk. Embodiments of the present disclosure calculate the dose as d — A x x + H x W x x + (h x w x x, where h G Rnxl, w G Rlxmare determined such that:H x W x X = D, where H = [H, h], W = [W;w],X = [x1, x2, ..., xk], D = [D^ D2, ... , Dk.This ensures a “long-memory” correction where the optimized dose is equal to the accurately calculated forward dose not only for the last iteration but also all previous iterations. The augmented low rank matrices H, W can be obtained as / T = D, W" — pinv(X), where pinv(X) represents the pseudo-inverse of the matrix X.

[0097] Low-rank Update for Robust Optimization and Many Machine Parameters Optimization

[0098] The previous idea can be generalized to robust optimization when approximate influence matrices are available for all r scenarios, or even if the influence matrix is only available for the nominal scenario and the dose is calculated for other scenarios during optimization. In this case, every time the dose is calculated for all r scenarios, a low-rank update of rank r is added to the optimized dose, ensuring that the optimized dose equals the accurately calculated dose for all previous forward dose calculations.

[0099] A similar approach can be used when the simultaneous optimization of many machine parameters (e.g., iso center, beam angle, couch position) is desirable. In such cases, either a very approximate upfront calculation is performed with some occasional forward dose calculations or only occasional forward dose calculations are afforded. This method allows for efficient and accurate optimization even with limited computational resources.

[0100] Hierarchical Data Representation using Sparse Voxel Octree

[0101] A Sparse Voxel Octree (SVO) is a data structure used in computer graphics and 3D rendering to efficiently represent and manage volumetric data. It leverages an octree, a tree structure where each node has up to eight children, to recursively divide a three-dimensional space into smaller regions or voxels. The SVO has a hierarchical data structure that enhances its efficiency and functionality in managing volumetric data. Embodiments of the present disclosure use deep learning to predict the 3D dose distribution and then applying SVO to discretize the patient’s body. This contrasts with the practice of using regular grids or point clouds. The hierarchical nature of the data structure allows for progressive refinement of thedetailed dose; larger, less detailed voxels are subdivided only when necessary, including later iterations of the optimization, a critical voxel receiving a high dose, and a tumor voxel receiving a low dose. This results in significant memory savings and computational speed-up.

[0102] Multi-scale / progressive optimization

[0103] Multi-scale optimization, also known as multi-resolution or progressive optimization, is an approach in computational optimization that tackles problems by solving them at various levels of detail or resolution. This technique leverages the idea that solving a coarse-grained, simplified version of a problem can provide valuable insights and a good starting point for addressing finer, more detailed versions. Optimization algorithms utilizing this approach often start with a rough approximation of the problem, where computational costs are lower, and progressively refine the solution by increasing the resolution or adding complexity in stages. The hierarchical data structure provided in the proposed matrix compression and sparse voxel octree enable the use of these techniques.

[0104] Referring now to FIG. 12, a schematic of an example of a computing node is shown. Computing node 10 is only one example of a suitable computing node and is not intended to suggest any limitation as to the scope of use or functionality of embodiments described herein. Regardless, computing node 10 is capable of being implemented and / or performing any of the functionality set forth hereinabove.

[0105] In computing node 10 there is a computer system / server 12, which is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well-known computing systems, environments, and / or configurations that may be suitable for use with computer system / server 12 include, but are not limited to, personal computer systems, server computer systems, thin clients, thick clients, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments that include any of the above systems or devices, and the like.

[0106] Computer system / server 12 may be described in the general context of computer system-executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computer system / server 12 may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, programmodules may be located in both local and remote computer system storage media including memory storage devices.

[0107] As shown in FIG. 12, computer system / server 12 in computing node 10 is shown in the form of a general-purpose computing device. The components of computer system / server 12 may include, but are not limited to, one or more processors or processing units 16, a system memory 28, and a bus 18 that couples various system components including system memory 28 to processor 16.

[0108] Bus 18 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, Peripheral Component Interconnect (PCI) bus, Peripheral Component Interconnect Express (PCIe), and Advanced Microcontroller Bus Architecture (AMBA).

[0109] Computer system / server 12 typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer system / server 12, and it includes both volatile and non-volatile media, removable and nonremovable media.

[0110] System memory 28 can include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Computer system / server 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 can be provided for reading from and writing to a non-removable, non-volatile magnetic media (not shown and typically called a "hard drive"). Although not shown, a magnetic disk drive for reading from and writing to a removable, non-volatile magnetic disk (e.g., a "floppy disk"), and an optical disk drive for reading from or writing to a removable, non-volatile optical disk such as a CD-ROM, DVD-ROM or other optical media can be provided. In such instances, each can be connected to bus 18 by one or more data media interfaces. As will be further depicted and described below, memory 28 may include at least one program product having a set (e.g.. at least one) of program modules that are configured to carry out the functions of embodiments of the disclosure.

[0111] Program / utility 40, having a set (at least one) of program modules 42, may be stored in memory 28 by way of example, and not limitation, as well as an operating system,one or more application programs, other program modules, and program data. Each of the operating system, one or more application programs, other program modules, and program data or some combination thereof, may include an implementation of a networking environment. Program modules 42 generally carry out the functions and / or methodologies of embodiments as described herein.

[0112] Computer system / server 12 may also communicate with one or more external devices 14 such as a keyboard, a pointing device, a display 24, etc.; one or more devices that enable a user to interact with computer system / server 12; and / or any devices (e.g., network card, modem, etc.) that enable computer system / server 12 to communicate with one or more other computing devices. Such communication can occur via Input / Output (VO) interfaces 22. Still yet, computer system / server 12 can communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and / or a public network (e.g., the Internet) via network adapter 20. As depicted, network adapter 20 communicates with the other components of computer system / server 12 via bus 18. It should be understood that although not shown, other hardware and / or software components could be used in conjunction with computer system / server 12. Examples, include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data archival storage systems, etc.

[0113] The present disclosure may be embodied as a system, a method, and / or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure.

[0114] The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD- ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storagemedium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiberoptic cable), or electrical signals transmitted through a wire.

[0115] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0116] Computer readable program instructions for carrying out operations of the present disclosure may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user’s computer, partly on the user’s computer, as a stand-alone software package, partly on the user’s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user’s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0117] Aspects of the present disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer programproducts according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer readable program instructions.

[0118] These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the fimctions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks.

[0119] The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0120] The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

[0121] The descriptions of the various embodiments of the present disclosure have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

What is claimed:

1. A method for optimizing a radiotherapy treatment, the method comprising: discretizing a region of interest of a patient into a plurality of voxels, wherein the plurality of voxels comprise tumor voxels and non-tumor voxels; receiving a prescribed radiation dose for each tumor voxel; discretizing one or more radiation emitters of a radiotherapy machine into a plurality of two-dimensional (2D) beamlets; defining an initial intensity vector for each beamlet; determining a radiation dose delivered to each voxel by each 2D beamlet, the radiation dose based on the initial intensity vector, thereby creating a dose influence matrix; compressing the dose influence matrix; applying an automated planning algorithm to approximate the prescribed radiation dose for tumor voxels and minimize radiation dosage for non-tumor voxels, thereby creating an optimized intensity vector; and providing an optimized radiotherapy treatment for the patient based on the optimized intensity vector.

2. The method of claim 1, wherein the initial intensity for each 3D voxel comprises a precalculated intensity value.

3. The method of any of claims 1-2, wherein compressing the matrix creates a hierarchical and compact representation of dosimetric data.

4. The method of any of claims 1-3, wherein compressing the matrix comprises decomposing the matrix into a sparse plus low-rank matrix.

5. The method of claim 4, further comprising outputting data from the sparse plus low- rank matrix in a hierarchical format.

6. The method of any of claims 1-5, wherein compressing the matrix comprises converting the matrix into a sparse-only matrix.

7. The method of any of claims 1-6, wherein compressing the matrix comprises: representing the matrix as a multi-dimensional tensor, the multi-dimensional tensor comprising low-rank structures; and compressing the multi-dimensional tensor.

8. The method of any of claims 1-7, further comprising performing a long memory correction of an optimized dose of the optimized intensity vector.

9. The method of any of claims 1-8, furthering comprising: creating a fluence map from the discretized region of interest, wherein creating the fluence map comprises applying a smoothing function and / or smoothing constraints to the optimized intensity vector.

10. The method of any of claims 1-9, wherein discretizing the region of interest comprises using a sparse voxel octree.

11. A system for optimizing a radiotherapy treatment, the system comprising: a computing node comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor of the computing node to cause the processor to perform a method comprising: discretizing a region of interest of a patient into a plurality of voxels, wherein the plurality of voxels comprise tumor voxels and non-tumor voxels; receiving a prescribed radiation dose for each tumor voxel; discretizing one or more radiation emitters of a radiotherapy machine into a plurality of two-dimensional (2D) beamlets; defining an initial intensity vector for each beamlet; determining a radiation dose delivered to each voxel by each 2D beamlet, the radiation dose based on the initial intensity vector, thereby creating a dose influence matrix; compressing the dose influence matrix; applying an automated planning algorithm to approximate the prescribed radiation dose for tumor voxels and minimize radiation dosage for non-tumor voxels, thereby creating an optimized intensity vector; and providing an optimized radiotherapy treatment for the patient based on the optimized intensity vector.

12. The system of claim 11, wherein the initial intensity for each voxel comprises a precalculated intensity value.

13. The system of any of claims 11-12, wherein compressing the matrix creates a hierarchical and compact representation of dosimetric data.

14. The system of any of claims 11-13, wherein compressing the matrix comprises decomposing the matrix into a sparse plus low-rank matrix.

15. The system of claim 14, further comprising outputting data from the sparse plus low- rank matrix in a hierarchical format.

16. The system of any of claims 11-15, wherein compressing the matrix comprises converting the matrix into a sparse-only matrix.

17. The system of any of claims 11-16, wherein compressing the matrix comprises: representing the matrix as a multi-dimensional tensor, the multi-dimensional tensor comprising low-rank structures; and compressing the multi-dimensional tensor.

18. The system of any of claims 11-17, further comprising performing a long memory correction of an optimized dose of the optimized intensity vector.

19. The system of any of claims 11-18, furthering comprising: creating a fluence map from the discretized region of interest, wherein creating the fluence map comprises applying a smoothing function and / or smoothing constraints to the optimized intensity vector.

20. A computer program product for optimizing a radiotherapy treatment, the computer program product comprising a computer readable storage medium having programinstructions embodied therewith, the program instructions executable by a processor to cause the processor to perform a method comprising: discretizing a region of interest of a patient into a plurality of voxels, wherein the plurality of voxels comprise tumor voxels and non-tumor voxels; receiving a prescribed radiation dose for each tumor voxel; discretizing one or more radiation emitters of a radiotherapy machine into a plurality of two-dimensional (2D) beamlets; defining an initial intensity vector for each beamlet; determining a radiation dose delivered to each voxel by each 2D beamlet, the radiation dose based on the initial intensity vector, thereby creating a dose influence matrix; compressing the dose influence matrix; applying an automated planning algorithm to approximate the prescribed radiation dose for tumor voxels and minimize radiation dosage for non-tumor voxels, thereby creating an optimized intensity vector; and providing an optimized radiotherapy treatment for the patient based on the optimized intensity vector.

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