Patent Application
20190054316
Intensity modulated radiation therapy (IMRT) is a cornerstone of modern radiation therapy physics. By modulating the incident X-ray intensities, IMRT has provided unprecedented control over X-ray dose distributions to target tumors and spare normal tissues. IMRT was afforded by the development of inverse optimization algorithms and enabling hardware. With a few exceptions, such as the compensator based IMRT (Chang et al. (2004) J. Appl. Clin. Med. Phys. 5(3): 15-36; Tajima et al. (2015) Br. J. Radiol. 88(1052): 20150122; Waghorn et al. (2013) J. Appl. Clin. Med. Phys. 14(3): 4210; Robinson et al. (2012) Med. Phys. 39(1): 342-352; Nangia et al. (2006) Clin. Oncol. (R. Coll. Radiol.), 18(6): 485-492), the multileaf collimator (MLC) that consists of a large number of thin moving tungsten leaves has been the dedicated device to modulate the X-ray fluence.
Due to considerations including the mechanical complexity, cost, accessibility and reliability of early MLCs, attempts have been made to use only the orthogonal jaws on conventional linacs for IMRT (Mu and Xia (2009) Phys. Med. Biol. 54(18): 5613-5623; Earl et al. (2007) Med. Phys. 34(1): 307-314; Webb (2002) Phys. Med. Biol. 47(2): 257-275). Jaws-only IMRT requires the entire IMRT plan to be delivered using exclusively rectangular apertures. Different methods have been used to generate these apertures, including fluence stripping (Dai and Hu (1999) Med. Phys., 26(12): 2562-2570) and direct aperture optimization (DAO) (Earl et al. (2007) Med. Phys. 34(1): 307-314). In the former method, a fluence optimization was first performed and the resulting fluence was subsequently stripped to rectangles for jaws-only delivery. The method inevitably suffered from dosimetric quality compromise and low delivery efficiency due to sequential simplification of the fluence maps. To address these difficulties, additional collimator devices such as masks (Webb (2002) Phys. Med. Biol. 47(2): 257-275) and rotational and dynamic jaws (Webb and Poludniowski (2010) Phys. Med. Biol. 55(21): N495-506) have been theorized but not implemented.
The direct aperture optimization (DAO) approach has been incorporated into a commercial planning system (Earl et al. (2007) Med. Phys. 34(1): 307-314). This approach utilizes a simulated annealing process to search and select rectangular apertures that minimized an objective function. It was shown that for simple cases, the jaws-only IMRT can achieve superior plan quality to 3D conformal plans (Kim et al. (2007) Phys. Med. Biol., 52(8): 2147-2156). In a follow up study, Mu and Xia showed that even for more complex head and neck IMRT plans, the jaws-only approach can result in acceptable dosimetry, at a cost of longer delivery time (Mu and Xia (2009) Phys. Med. Biol. 54(18): 5613-5623).
With the maturation of MLC technology, the problems that plagued early IMRT delivery, such as reliability and cost, have been partially mitigated. To the best of our knowledge, the jaws-only IMRT has not been clinically adopted due to limitations in its dosimetric quality and delivery efficiency.
To deliver high quality intensity modulated radiotherapy (IMRT) using a novel generalized sparse orthogonal collimators (SOC), a novel direct aperture optimization (DAO) approach based on discrete Haar wavelet representation was introduced. In various embodiments the formulation of the inverse optimization problem that consists of an L2 fidelity term and an L1 regularization term (Nguyen et al. (2015) Med. Phys., 42(4): 1858-1870). The solution algorithm based on the first-order primal-dual approach gives remarkable freedom to modify and simplify the optimized fluence maps. Because the optimization was performed in the dose domain, substantial modification and simplification of the fluence maps is possible without degrading the dosimetric quality. This development paves the path to a new algorithm that optimally the use of s sparse orthogonal collimator as described herein.
A total of 7 patients-2 GBM, 3 head & neck (including 1 with 3 prescription doses) and 2 lung were included. Twenty non-coplanar beams were selected using a column generation and pricing optimization method. The SOC is a generalized conventional orthogonal collimator with N leaves in each collimator bank, where N=1, 2, or 4. SOC degenerates to conventional jaws when N=1. For SOC-based IMRT, Haar-based fluence optimization (HFO) was performed to optimize the fluence maps in the Haar wavelet domain, producing fluence maps that can be directly converted into a set of deliverable rectangular apertures. In order to optimize the dose distribution and minimize the number of apertures used, the overall objective was formulated to incorporate an L2 penalty reflecting the difference between the prescription and the projected doses, and an L1 sparsity regularization term to encourage a low number of non-zero Haar wavelet coefficients. The optimization problem was solved using the Chambolle-Pock algorithm, a first-order primal-dual algorithm. Performance of HFO was compared to conventional two-step IMRT optimization including fluence map optimization and Direct stratification for MLC Segmentation (DMS) using the same number of segments. For the HFO plans, segment travel time for SOC delivery was evaluated for the N=1, N=2, and N=4 SOC designs to characterize the improvement in delivery efficiency as a function of N.
Comparable PTV dose homogeneity and coverage were observed between the HFO and the DMS plans. The HFO plans were slightly superior to the MLC based DMS plans in sparing critical structures. On average, the maximum and mean critical organ doses were reduced by 2.27% and 1.38% of the prescription dose. The average number of delivery segments was 16.39 segments per beam for both the HFO and DMS plans. The N=2 and N=4 SOC designs were, on average, 1.78 and 2.18 times more efficient than the N=1 SOC design to deliver. The mean aperture size produced by the HFO plans was 4.4 times larger than that of the DMS plans. The DAO and dose domain optimization approach enabled high quality IMRT plans using a low-complexity collimator setup. The dosimetric quality is comparable or slightly superior to conventional MLC-based IMRT plans using the same number of delivery segments. The SOC IMRT delivery efficiency can be significantly improved by increasing the leaf numbers, but the number is still significantly lower than the number of leaves in a typical MLC.
Accordingly, in certain embodiments, sparse orthogonal collimators and methods of optimizing fluence maps for use there with are provided.
Various embodiments contemplated herein may include, but need not be limited to, one or more of the following:
A sparse orthogonal collimator for shaping a radiotherapy beam, said collimator comprising first bank of individually longitudinally movable elongate leaves, and a second bank of individually longitudinally movable elongate leaves the second bank being disposed in an opposed relationship to the first bank; third bank of individually longitudinally movable elongate leaves, and a fourth bank of individually longitudinally movable elongate leaves the fourth bank being disposed in an opposed relationship to said third bank; and said first bank and said second bank being oriented orthogonal to said third bank and fourth bank; and said first bank, second bank, third bank, and fourth bank each individually contain from two to four leaves.
The collimator of embodiment 1, wherein all of the leaves comprising said first bank and said second bank form a first layer in said collimator and all the leaves comprising said third bank and said fourth bank form a second layer disposed beneath said first layer.
The collimator of embodiment 1, wherein: a first subset of the leaves comprising said first bank and said second bank are disposed in a first layer in said collimator and a second subset of the leaves comprising said first bank and said second bank are disposed in a second layer in said collimator; a first subset of the leaves comprising said third bank and said fourth bank are disposed in said first layer in said collimator and a second subset of the leaves comprising said third bank and said fourth bank are disposed in said second layer in said collimator; and the first subset of the leaves comprising said first bank and said second bank are disposed in said first layer so that they do not collide with the first subset of leaves comprising said third bank and said fourth bank disposed in said first layer; and the second subset of the leaves comprising said first bank and said second bank are disposed in said second layer so that they do not collide with the second subset of leaves comprising said third bank and said fourth bank disposed in said second layer.
The collimator according to any one of embodiments 1-3, wherein the total number of leaves is a power of 2.
The collimator according to any one of embodiments 1-4, wherein said first bank said second bank said third bank and said fourth bank each contain the same number of leaves.
The collimator according to any one of embodiments 1-5, wherein said collimator contains 4, 8, 16, or 32 leaves.
The collimator according to any one of embodiments 1-6, wherein each bank contains 2, 4, or 8 leaves.
The collimator of embodiment 7, wherein each bank contains 4 leaves.
The collimator according to any one of embodiments 1-8, wherein the width of leaves comprising said collimator ranges from about 2.5 mm up to about 5 cm.
The collimator of embodiment 9, wherein leaves comprising said collimator have a width of about 0.5 cm, or about 1 cm, or about 1.5 cm, or about 2 cm, or about 2.5 cm, or about 3 cm, or about 3.5 cm, or about 4 cm, or about 4.5 cm, or about 5 cm.
The collimator of embodiment 9, wherein leaves comprising said collimator have a width of 1 cm.
The collimator of embodiment 11, wherein leaves comprising said collimator have a width of 2.5 cm.
The collimator of embodiment 11, wherein leaves comprising said collimator have a width of 2.5 mm.
The collimator according to any one of embodiments 1-13, wherein the leaves comprising said collimator are all the same width.
The collimator according to any one of embodiments 1-13, wherein said collimator produces a physical field size at the collimator ranging up to about 10 cm×10 cm.
The collimator according to any one of embodiments 1-13, and 15, wherein said collimator produces a maximum field size at treatment depth of about 20 cm×20 cm.
The collimator according to any one of embodiments 1-11, wherein said collimator produces a maximum field size up to about 2 cm×2 cm at the treatment depth.
The collimator according to any one of embodiments 1-17, wherein said collimator produces a minimum field size of about 1 mm×1 mm at the treatment depth.
The collimator according to any one of embodiments 1-18, wherein the thickness of leaves comprising said collimator ranges from about 1 cm to about 6 cm.
The collimator of embodiment 19, wherein the thickness of leaves comprising said collimator is about 1 cm, or about 1.5 cm, or about 2 cm, or about 2.5 cm, or about 3 cm, or about 3.5 cm, or about 4 cm, or about 4.5 cm, or about 5 cm, or about 5.5 cm, or about 6 cm.
The collimator according to any one of embodiments 1-20, wherein the length of leaves comprising said collimator ranges from about 2 cm up to about 15 cm.
The collimator according to any one of embodiments 1-20, wherein the length of leaves comprising said collimator is about 2 cm, or about 3 cm, or about 4 cm, or about 5 cm, or about 6 cm, or about 7 cm, or about 8 cm, or about 9 cm, or about 10 cm, or about 11 cm, or about 12 cm, or about 13 cm, or about 14 cm, or about 15 cm.
The collimator according to any one of embodiments 1-22, wherein leaves comprising said collimator includes a material selected from the group consisting of brass or brass alloy (for kV X-rays), and tungsten or tungsten alloy (for MV X-rays), 24: The collimator according to any one of embodiments 1-23, wherein each leaf in said collimator is operably coupled to a drive mechanism that provides longitudinal movement of the coupled leaf independent of the longitudinal movement of the other leaves comprising said collimator.
The collimator according to any one of embodiments 1-24, wherein said drive mechanism includes mechanism selected from the group consisting of a stepping motor, a magnetic actuator, and a pressure actuator.
The collimator of embodiment 25, wherein said drive mechanism includes a stepping motor.
The collimator of embodiment 26, wherein said stepping motor provides a step having a resolution as low as 1 μm.
The collimator according to any one of embodiments 24-27, wherein said drive mechanism provides a leaf position adjustable to an accuracy of at least at least ±0.1 mm.
The collimator according to any one of embodiments 1-28, wherein each leaf comprising said collimator is operably coupled to a position encoder.
The collimator of embodiment 29, wherein said position encoder includes a position encoder selected from the group consisting of a laser encoder, an optical encoder, and a magnetic encoder.
The collimator according to any one of embodiments 1-30, wherein said collimator is coupled to a controller that determines and adjusts the positions of the leaves comprising said collimator.
The collimator of embodiment 31, wherein said controller is configured to determine and adjust the positions of the leaves comprising said collimator during a radiotherapy treatment.
The collimator according to any one of embodiments 1-32, wherein said collimator is configured as a component of a linac and disposed to control the field size and shape of radiation emitted from said linac.
A system for collimating a therapeutic radiation beam, the system comprising: a sparse orthogonal collimator according to any one of embodiments 1-32; a radiotherapy device comprising said sparse orthogonal collimator disposed to control the field size and shape of emitted radiation; and a controller configured to adjust the position of the leaves comprising said sparse orthogonal collimator.
The system of embodiment 34, wherein said radiotherapy device produces electron or photon beams.
The system of embodiment 34, wherein said radiotherapy device produces electron, neutron, proton, x-ray, or gamma radiation.
The system of embodiment 34, wherein said radiotherapy device includes a linear accelerator (linac) configured to provide X-rays.
The system according to any one of embodiments 34-37, wherein said radiotherapy device is configured to operate in a coplanar beam orientation.
The system according to any one of embodiments 34-37, wherein said radiotherapy device is configured to operate in a non-coplanar beam orientation.
A method of generating a radiation treatment plan using a radiotherapy device comprising a sparse orthogonal collimator according to any one of embodiments 1-33 and/or a system according to any one of embodiments 34-39, said method comprising:
providing a fluence maps for said radiation plan; and generating using a computer a time sequence of sparse orthogonal collimator leaf settings from said fluence maps, wherein said generating includes:
generating and writing instruction files to implement said time sequence of sparse orthogonal collimator leaf settings to a tangible medium that can be executed by a radiotherapy device.
The method of embodiment 40, wherein said representing a desired fluence map includes representing a fluence map, fmat, using discrete Haar wavelet coefficients, αc, such that:
H
c
TαcHc=fmat, (1)
where Hc is the classical Haar transform matrix, but changing the differential Haar transform, Hc, to a scaling function, which is a modified Haar transform, Hm that uses a coefficient set, αm where for a 2n×2n fluence matrix, the coefficient matrix αm has dimensions (2n+1−1)×(2n+1−1), and Hm has dimension (2n+1−1)×2n.
The method according to any one of embodiments 40-41, wherein said optimizing comprises:
minimize ½∥W(AHvαv−d0)∥22+λ∥αv∥1
subject to αv≥0, (4)
where αv=vec(αm) is the optimization variable; Hv is the Haar transform matrix for the coefficient vector; W is a weighting factor for the structures of interest; A is the fluence to dose transformation matrix; and d0 is the desired dose.
The method of embodiment 42, wherein d0 is set to the prescription dose for the planning target volume (PTV) and zero for the organs at risk (OARs).
The according to any one of embodiments 42-43, wherein the fluence to dose transformation matrix is calculated using a convolution/superposition code using a 6 MV x-ray polyenergetic kernel.
The method according to any one of embodiments 42-44, wherein said optimization is solved utilizing the Chambolle-Pock algorithm.
The method according to any one of embodiments 40-45, wherein said method includes aperture constraints during the optimization stage rather than after the optimization.
The method according to any one of embodiments 40-46, wherein said writing instruction files includes writing one or more instruction files to a tangible medium selected from the group consisting of a magnetic medium, an optical medium, a PAL chip, and a static RAM chip.
The method of embodiment 47, wherein said writing instruction files includes writing one or more instruction files to a CD, a flash drive, a DVD, and a hard drive.
The method according to any one of embodiments 40-48, wherein said instruction files contain a treatment plan comprising sparse orthogonal collimator leaf positions and optionally one or more of the following: machine gantry and couch positions, beam intensities, imager positions at a given time or plan delivery point.
The method of embodiment 49, wherein said treatment plan includes couch positions and gantry angles for a non-coplanar beam treatment.
The method of embodiment 49, wherein said treatment plan includes couch positions and gantry angles for a coplanar beam treatment.
A radiation treatment planning system for preparing treatment planning information for carrying out radiation treatment, said radiation treatment planning system comprising: an input unit with which an operator inputs at least a prescription dose and a treatment volume; a computational unit configured to generate a radiation treatment plan using a radiotherapy device comprising a sparse orthogonal collimator according to any one of embodiments 1-33, and said computational unit determines apertures for said sparse orthogonal collimator, and optionally determines treatment beams, machine, and table paths; and a display unit that displays said radiation treatment plan.
The treatment planning system where said computational unit is configured to perform a method according to any one of embodiments 40-51.
The system according to any one of embodiments 52-53, wherein said system further includes a 3D scanning system.
The system according to any one of embodiments 52-54, wherein said computational unit is configured to receive a CAT scan from a CT scanner or a patient medical record.
The system according to any one of embodiments 52-55, wherein said system is configured to output a treatment plan into a patient medical record.
A method of performing intensity modulated radiotherapy (IMRT) on a subject, said method comprising: inputting into a radiotherapy device controller an instruction file generated using a method according to any one of embodiments 40-51, wherein said radiotherapy device includes a sparse orthogonal collimator according to any one of embodiments; and operating said radiotherapy device using the inputted instruction set to deliver a radiation at a plurality of different apertures to said subject.
The method of embodiment 58, wherein said radiotherapy device includes a linac.
The method according to any one of embodiments 58-59, wherein said subject includes a human.
The method according to any one of embodiments 58-59, wherein said subject includes non-human mammal.
The method of embodiment 61, wherein said non-human mammal includes a small mammal having a mass of less than about 10 kg, or less than about 5 kg, or less than about 2 kg.
Using radiation to treat cancer requires careful planning. Bombarding malignant tumors with high-energy X-rays can kill cancerous cells (or hinder their growth), but it is often impossible to deliver a terminal dose to the target without damaging nearby healthy organs in the process. Serious complications can occur when the surrounding healthy tissues receive too much of this collateral radiation. On the other hand, sacrificing a modest number of healthy cells may be tolerable since many organs are resilient enough to sustain a certain degree of damage while still providing their anatomical function and can eventually recover.
Therefore radiotherapy treatment plans seek methods of delivering a sufficient dose to the target (e.g., tumor), while carefully controlling the dose received by neighboring organs and other healthy tissues.
Intensity-modulated radiation therapy (IMRT) is a radiotherapy method that delivers higher doses to tumors and allows more precise conformation than the conventional 3D conformal radiotherapy. The primary delivery tool for IMRT is a linear accelerator that rotates on a gantry around the patient, emitting “modulated” beams of X-rays. This modulation has previously been accomplished by means of a device known as a multileaf collimator (MLC) which is attached to the accelerator. Its adjustable heavy-metal leaves act as a filter, blocking or allowing radiation through in a precise manner controlled by a computer, in order to tailor the beam shape to the shape of the tumor volume while minimizing exposure of the neighboring structures.
Several mathematical problems arise in order to optimally administer IMRT. Treatment proceeds by rotating the accelerator around the patient and coordinating the leaf movements in the MLC so that the radiation delivered conforms to some desirable dose distribution at each gantry (beam) angle. Part of determining a radiotherapy treatment involves determining the number and values of the gantry angles to be used in a particular treatment. Methods of determining gantry angles for co-planar and non-coplanar radiotherapy treatments are known to those of skill in the art (see, e.g., Dong et al. (2013) Int. J. Radiat. Oncol. Biol. Phys. 85: 1360-1366; Dong et al. (2013) Int. J. Radiat. Oncol. Biol. Phys. 86: 407-413). Additionally, improved radiotherapy methods utilizing the entire 4π solid angle are described in copending patent U.S. Provisional Patent Application No. 62/128,906, filed on Mar. 5, 2015, entitled RADIOTHERAPY UTILIZING THE ENTIRE 4PI SOLID ANGLE, which is incorporated herein by reference for the methods described therein. It is noted that typically, increasing the number of gantry angles will increase the quality, the time, and the cost of the treatment.
In addition to determining the beam angles, one must also determine how intense the beams should be at each point (x, y) on the aperture for all gantry angles. These intensity profiles, or fluence maps, have typically been represented by two-dimensional, nonnegative functions, e.g. Ia(x, y) for a=1, 2, . . . , k, where k is the number of gantry angles in use. The process of determining the functions Ia(x, y) is often called fluence map optimization.
Once the fluence maps are determined, they are converted into collimator leaf sequences that attempt to realize them. The longer a collimator leaf is open at a certain position (x, y), the more dose the tissue along a straight path from that position (plus some surrounding tissue) absorbs. The process of converting fluence maps into the opening and closing movements of leaves is called leaf-sequencing.
The conventional MLC was intuitively designed as a finger like device by extending and retracting individual leaves, the radiation level of the areas under the leaf can be quantitatively controlled. Clearly, the thinner the leaves, the higher the resolution can be achieved. Currently, leaves as thin as 1 mm are used. However, making leaves this thin and moving them in and out with high accuracy and reproducibility has been a significant engineering challenge. It is very expensive and often forces a compromise between the field size and resolution. For example, the high resolution MLC option on Varian machines results in a specialized radiosurgery machine with small field size. Because of the challenges and cost, it has proven impossible to make a reliable MLC for applications such as small animal irradiators that are attempting to replicate human treatment so the experimental results are more meaningful.
To overcome these difficulty, a sparse orthogonal collimator (SOC) was designed and algorithm were determined to drive it. SOC consists of 2 layer 4 bank orthogonal collimators with 2-8 leaves in each of the 4 banks (see, e.g.
Instead of using the limited heuristic approach to create jaw-only IMRT, we introduce a novel fluence map optimization method based on wavelet decomposition and use it for IMRT. We have developed an innovative algorithm to simplify the fluence maps with minimal and predictable dose quality compromise. We further used Haar wavelet decomposition to convert the simplified fluence maps to patches that can be achieved using the SOC while maintaining high dosimetric quality. Compared to the conventional multi-leaf collimator (MLC) using 120 leaved, a similar level of intensity modulation can be achieved using 32 or fewer leaves in SOC.
It is believed that SOC will be less expensive to make and maintain. It will achieve both high resolution and large field coverage. It is also feasible to make SOC for applications that are highly limited in space and provide higher resolution modulation such as small animal irradiation and for use with robotically mounted linacs.
In various embodiments, the sparse orthogonal collimators comprise two layer four bank orthogonal collimator with 2-8 leaves in each of the four banks. One embodiment of such a collimator is schematically in
The collimator configuration shown in
Typically, in various embodiments, the sparse orthogonal collimator will contain one or more drive mechanisms that control the position/movement of the leaves. In certain embodiments, drive mechanisms are provided that allow each leaf comprising the collimator to be individually moved/positioned.
Drive mechanisms that are suitable for use in the sparse orthogonal collimators (SOCs) described herein are known to those of skill in the art and often used in multi-leaf collimators (MLCs). Illustrative drive mechanisms include, but are not limited to mechanically positioning mechanism such as a lead screw or rack and pinion driven, e.g., by a motor (e.g., a stepping motor), a pneumatic positioning system (see, e.g., U.S. Patent Pub. No: 2015/0170778), an electromagnetic positioning system (see, e.g. U.S. Patent Pub. No: 2014/0239204), a combined linear induction motor and encoder, and the like.
One illustrative drive mechanism (e.g., a stepper motor) 104 is shown in
In certain embodiments the sparse orthogonal collimators comprise one or more encoders to identify the location and/or movement of leaves comprising the collimators. Suitable encoders include, but are not limited to laser encoders (e.g., based on a displacement interferometer), optical encoders (e.g., utilizing a finely graduated scale and a compact optoelectronic readhead that converts motion relative to the scale into position data), magnetic encoders, capacitance/resistance encoders, and the like. Numerous high precision encoders are commercially available, e.g., from Renishaw Inc., Illinois.
In various embodiments, the collimator comprises 2 leaves per bank, or 4 leaves per bank, or 8 leaves per bank the last providing a maximum of 32 leaves per collimator. As explained herein a novel fluence map optimization method based on wavelet decomposition is described herein and used for IMRT with a sparse orthogonal collimator as described herein. In particular, an innovative algorithm was used to simplify the fluence maps with minimal and predictable dose quality compromise and Haar wavelet decomposition was utilized to convert the simplified fluence maps to patches that can be achieved using the SOC while maintaining high dosimetric quality. Compared to the conventional MLC using 120 leaved, similar level of intensity modulation can be achieved using 32 or fewer leaves in SOC. The SOC will be less expensive to make and maintain. It will achieve both high resolution and large field coverage. It is also feasible to make SOC for applications that are highly limited in space but higher resolution modulation is desired such as the small animal irradiation and robotically mounted linacs.
In certain embodiments the sparse orthogonal collimators (SOCs) described herein are effective to provide a treatment comparable to or better than that obtained with a multi-leaf collimator (MLC). In certain embodiments the dose to the planning target volume (PTV) obtained with the SOC is no less than 80%, or no less than 90%, or no less than about 95%, or no less than about 100% than the PTV obtained with an MLC and no greater than the OAR dosage, no more than about 2% greater than the OAR dosage, or no more than about 5% greater, or no more than about 10% greater OAR dosage than that obtained with an MLC.
In certain embodiments the sparse orthogonal collimators are incorporated into a treatment system for delivering radiation therapy to a subject. In certain embodiments the treatment system comprises a sparse orthogonal collimator as described herein and a radiotherapy device comprising the sparse orthogonal collimator disposed to control the field size and shape of emitted radiation, and a controller configured to adjust the position of the leaves comprising the sparse orthogonal collimator. In certain embodiments, the controller controls only the leaf position/movement in the collimator. In certain embodiments the controller, additionally controls one or more of the radiotherapy device gantry position, table position, beam time, beam intensity, and the like. In certain embodiments the radiotherapy device produces electron or photon beams. In certain embodiments radiotherapy device produces electron, neutron, proton, x-ray, or gamma radiation. In certain embodiments the radiotherapy device comprises a linear accelerator (linac) configured to provide X-rays. In certain embodiments the radiotherapy device is configured to operate in a coplanar beam orientation. In certain embodiments the radiotherapy device is configured to operate in a non-coplanar beam orientation.
In certain embodiments methods of performing fluence optimization to optimize dose distribution using a sparse orthogonal collimator as described herein are provided. In certain embodiments Haar-based fluence optimization (HFO) is performed to optimize the fluence maps in the Haar wavelet domain, producing fluence maps that can be directly converted into a set of deliverable rectangular apertures. In order to optimize the dose distribution and minimize the number of apertures used, the overall objective can be formulated to incorporate an L2 penalty reflecting the difference between the prescription and the projected doses, and an L1 sparsity regularization term to encourage a low number of non-zero Haar wavelet coefficients. The optimization problem was solved using the Chambolle-Pock algorithm, a first-order primal-dual algorithm. These methods are described in detail in Example 1.
More particularly, in certain embodiments a method of generating a radiation treatment plan using a radiotherapy device comprising a sparse orthogonal collimator is provided where the method comprises providing a fluence maps for said radiation plan; and generating using a computer a time sequence of sparse orthogonal collimator leaf settings from the fluence maps, where the generating comprises:
In certain embodiments as described in the Example, representing a desired fluence map can involve representing a fluence map, fmat, using discrete Haar wavelet coefficients, αc, such that:
H
c
TαcHc=fmat, (1)
where Hc is the classical Haar transform matrix, but changing the differential Haar transform, Hc, to a scaling function, which is a modified Haar transform, Hm, that uses a coefficient set, αm where for a 2n×2n fluence matrix, the coefficient matrix αm has dimensions (2n+1−1)×(2n+1−1), and Hm has dimensions (2n+1−1)×2n.
In certain embodiments the optimizing comprises:
minimize ½∥W(AHvαv−d0)∥22+λ∥αv∥1
subject to αv≥0, (4)
where αv=vec(αm) is the optimization variable; Hv is the Haar transform matrix for the coefficient vector; W is a weighting factor for the structures of interest; A is the fluence to dose transformation matrix; and d0 is the desired dose. In certain embodiments d0 is set to the prescription dose for the planning target volume (PTV) and zero for the organs at risk (OARs). In certain embodiments the fluence to dose transformation matrix is calculated using a convolution/superposition code using a 6 MV x-ray polyenergetic kernel although other kernels can be used. In certain embodiments, as illustrated in the Example herein, the optimization can be solved utilizing the Chambolle-Pock algorithm. In various embodiments the method includes aperture constraints during the optimization stage rather than after the optimization.
In certain embodiments the writing instruction files comprises writing one or more instruction files to a tangible medium selected from the group consisting of a magnetic medium, an optical medium, a PAL chip, and a static RAM chip. In certain embodiments the writing instruction files comprises writing one or more instruction files to a CD, a flash drive, a DVD, and a hard drive. In certain embodiments the instruction files contain a treatment plan comprising sparse orthogonal collimator leaf positions and optionally one or more of the following: machine gantry and couch positions, beam intensities, and/or imager positions at a given time or plan delivery point. In certain embodiments the treatment plan comprises couch positions and gantry angles for a non-coplanar beam treatment. In certain embodiments the treatment plan comprises couch positions and gantry angles for a coplanar beam treatment.
In various embodiments a radiation treatment planning system for preparing treatment planning information for carrying out radiation treatment is provided. In certain embodiments the radiation treatment planning system comprises an input unit with which an operator inputs at least a prescription dose and a treatment volume; a computational unit configured to generate a radiation treatment plan using a radiotherapy device comprising a sparse orthogonal collimator described herein, and said computational unit determines apertures for said sparse orthogonal collimator, and optionally determines treatment beams, machine, and table paths; and a display unit that displays the radiation treatment plan. In certain embodiments the computational unit of the treatment planning system is configured to perform a fluence map optimization for an SOC as described herein. In certain embodiments the system further comprises a 3D scanning system. In certain embodiments the computational unit is configured to receive a CAT scan from a CT scanner or a patient medical record. In certain embodiments the system is configured to output a treatment plan into a patient medical record.
The following examples are offered to illustrate, but not to limit the claimed invention.
To deliver high quality intensity modulated radiotherapy (IMRT) using a novel generalized sparse orthogonal collimators (SOC), we introduce a novel direct aperture optimization (DAO) approach based on discrete Haar wavelet representation.
II.1. Sparse Orthogonal Collimators
One illustrative sparse orthogonal collimator (SOC) design consists of two orthogonally oriented collimator systems with N number of leaves in each collimator bank, where N is a small number. The term “sparse” was chosen in contrast to the “dense” leaf arrangement in a conventional MLC. The nature of Haar wavelets requires the ideal number of leaves to be a power of 2. For this study, we estimated the delivery efficiency of SOC having N=1, N=2, and N=4 leaves in each bank, shown in
II.2. Modified Haar Wavelet Transform
Like jaws-only IMRT, the apertures deliverable by SOC are rectangular. We represent an arbitrary fluence map, fmat, using discrete Haar wavelet coefficients, αc, such that:
H
c
TαcHc=fmat, (1)
where Hc is the classical Haar transform matrix.
The Haar representation was motivated by the fact that SOCs would generate only rectangular apertures, since the most common classic dyadic Haar wavelets, which follow a geometric sequence of ratio 2, have the advantage to compactly represent piecewise smooth images. However, the differential forms in the Haar wavelet does not enable for the direct translation of the Haar coefficient to a corresponding non-negative fluence rectangle. Based on this, we modified the basis, essentially changing the differential Haar transform, Hc, to a scaling function, which we term the modified Haar transform, Hm. This uses a different coefficient set, notated as αm. For a 2n×2n fluence matrix, the coefficient matrix αm has dimensions (2n+1−1)×(2n+1−1), and Hm has dimensions (2n+1−1)×2n. For example, if the fluence matrix is a 4×4 matrix then the classical Haar matrix
is replaced with
And αm is a 7×7 matrix.
In order to prepare for optimization, the coefficient matrix αm and fluence map fmat were vectorized, denoted as αv and fv respectively. To handle the vectorized notation, a special transform matrix, Hv that incorporates both the vertical and horizontal operations produced by HmT and Hm, was created. An expression to relate these variables together
H
vαv=fv=vec(fmat)=vec(HmTαmHm), (3)
where vec(X) is the vectorization operator.
II.3. Optimization Formulation and Chambolle-Pock Algorithm
The optimization based on Haar wavelets is as follows:
minimize ½∥W(AHvαv−d0)∥22+λ∥αv∥1
subject to αv≥0, (4)
Where αv=vec(αm) is the optimization variable, H is the Haar transform matrix for the coefficient vector αv, W is a weighting factor for the structures of interest, A is the fluence to dose transformation matrix, and d0 is the desired dose, which is set to the prescription dose for the PTV and zero for the OARs. The fluence to dose transformation matrix is calculated using a convolution/superposition code using a 6 MV x-ray polyenergetic kernel.
The L2-norm data fidelity term penalizes any deviations in the dose from d0, and the L1-norm sparsity term encourages a low number of non-zero coefficients. The definition of norm, for some vector x of length n, is
The number of non-zero coefficients is exactly equal to the number of fluence segments for delivery. The weighting parameter A is used to regulate the number of non-zero coefficients.
Constraining αv to stay positive is possible since the Haar transform was modified such that the value of the coefficients equals the value of the fluence.
The optimization problem was solved utilizing the Chambolle-Pock algorithm, a first-order primal-dual algorithm (Chambolle and Pock (2011) J. Math. Imag. Vision, 40(1): 120-145), where equation 4 is rewritten into the form
minimize F(Kαv)+G(αv), (5)
where
F and G are convex, lower semi-continuous functions and, for our particular problem, are defined as
This formulation can be solved using the over-relaxed Chambolle-Pock algorithm presented by Condat (Condat (2013) J. Optimization Theory and App. 158(2): 460-479), which uses the iteration
As a primal-dual algorithm, the Chambolle-Pock algorithm solves both the primal problem, shown as equation 5, and its corresponding dual problem simultaneously by the iteration shown in equation set 8. Here, z is a variable in the dual formulation and is optimized alongside the primal variable αv. The proximal mapping function or “prox operator” is defined as
and proxσF*({circumflex over (z)}) are proxτG() simplified into simple low cost calculations shown in equation set 9. The over-relaxation parameter is 0<p<2, and the algorithm is equivalent to the original Chambolle-Pock algorithm when p=1. The step sizes τ and σ must satisfy the constraint τσ∥K∥2≤1 for guaranteed convergence, and, in our experiments, are chosen as to satisfy τσ∥K∥2=1. The norm of K is computed using the power iteration method (Golub and Van Loan, Matrix computations, Fourth edition. ed. The Johns Hopkins University Press, Baltimore, 2013). Further details on this algorithm are described previously (Nguyen et al. (2015) Med. Phys., 42(4): 1858-1870).
Due the convex nature of the optimization problem, the starting values αv0 and z0 can be set as anything within the boundary constraints. For this study, αv0=0 and z0=0.
II.4.A. Patient Studies
Seven previously treated patients consisting of 2 glioblastoma multiforme patients (GBM), 3 head & neck patients (H&N), including 2 SBRT patients and 1 conventional fractionated patient with 3 PTVs (H&N3PTV), and 2 lung patients (LNG) were included in the study. The prescription doses and PTV volumes are shown in Table 1. The patients were first planned on the 4π radiotherapy platform to optimize both beam orientation and fluence maps using previously described column generation and pricing approach (Romeijn et al. (2003) Phys. Med. Biol. 48(21): 3521-3542; Romeijn et al. (2005) SIAM Optimiz. 15(3): 838-862). During optimization, a 5 cm ring structure was added around the PTV to penalize the dose spillage to normal tissue. The platform has been shown to achieve superior dosimetry to coplanar volumetric modulated arc therapy (VMAT) (Dong et al. (2013) Int, J, Radiat, Oncol, Biol, Phys, 86(3): 407-413; Dong et al. (2013) Int. J. Radiat. Oncol. Biol. Phys. 85(5): 1360-1366; Dong et al. (2014) Pract. Radiat. Oncol. 4(4): 254-260). As a result of the optimization, 20 non-coplanar beams were selected from a candidate pool of 1162 equally spaced non-coplanar beams for each patient.
The dose distributions were compared after generating deliverable segments on the two different platforms: 1) the Haar fluence optimization (HFO) method and 2) the direct MLC segmentation (DMS) method.
For the HFO plans, the optimized fluences from the 4π radiotherapy plan were not used while adopting the optimized beam angles. Rectangular apertures as the Haar wavelet basis were calculated using Eq. (1) and the Chambolle-Pock algorithm. A was varied until the average number of segments per beam for each case was roughly 15.
For the DMS method, the raw fluence from the 4π radiotherapy plan was stratified and an MLC segmentation algorithm was applied to calculate the deliverable MLC segments. The MLC segmentation algorithm was based on a reduction level method by Xia and Verhey (Xia and Verhey (1998) Med. Phys. 25(8): 1424-1434), described previously in detail (Nguyen et al. (2015)Med. Phys., 42(4): 1858-1870). The stratification step size was adjusted through a bisection algorithm so that the number of calculated MLC segments in DMS equaled to that of HFO, and the MLC segments were calculated to be deliverable along the direction of leaf motion without any collimator rotations.
For all of the cases except the H&N3PTV HFO plan, the beamlet resolution was 0.5 cm2 and the dose matrix resolution was 0.25 cm3. Due to computational complexities of the optimization, the H&N3PTV HFO plan was evaluated with a beamlet resolution of 1 cm2 and dose matrix resolution of 0.5 cm3.
All treatment plans were normalized such that the prescription dose was delivered to 95% of the PTV. As dosimetric endpoints for comparison, R50 and PTV homogeneity, D98, D99, and Dmax, as well as OAR mean and max doses, were evaluated. R50 is a measure of high dose spillage, and is defined as the 50% isodose volume divided by the PTV volume. Homogeneity is defined as
and maximum close is gained from ICRU Report 83 (Prescribing, Recording, and Reporting Intensity-Modulated Photon-Beam Therapy (IMRT)) (Grégoire and Mackie (2011) Cancer/Radiothérapie, 15(6-7): 555-559), where Dmax is defined as D2, the dose to 2% of the structure's volume.
Aperture size, reported as number of bixels, is evaluated and compared between the HFO and DMS methods for all seven cases. A bixel is a basic square unit on an IMRT fluence map, and aperture continuity is defined as the four directly neighboring bixels. The HFO method, by design, is limited to 1 aperture per delivery segment, while the DMS method can have multiple apertures per segment.
II.4.B. Sparse Orthogonal Collimator Travel Time Estimation
In order to evaluate the potential delivery time for using SOCs with N=1, N=2 and N=4 leaves per bank, the delivery order of the segments must first be optimized. The problem was formulated as a modified form of the open traveling salesman problem (TSP), and then solved using a basic genetic algorithm, an open source MATLAB code provided by Kirk (J. Kirk, in MATLAB (2008)).
The general TSP attempts to find the shortest path through a set of points in space, traveling to each point only once. The open variation of the problem allows for the end point to be different than the start point, rather than forming a closed loop. As a genetic algorithm, the open source code solves the TSP by first generating random populations, which are different potential routes that visit all points exactly once. The genetic algorithm then groups the paths into random groups of 4. For each group, it takes the population with the shortest route, randomly selects 2 of the points along the route, and performs 3 types of mutations on the sub-route between the 2 points: 1) Swap: take the 2 points and swap their order along the sub-route 2) Flip: The sub-route existing between the 2 selected points is reversed 3) Slide: All points between and including the 2 selected points is shifted by 1, with the first point becoming the last point on the sub-route. These 3 mutations replace the 3 worst solutions of the group of 4. This is performed for every grouping and repeated for a set number of iterations, selecting a different random grouping of 4 each time. After a set number of iterations, an optimal or near-optimal solution is found.
For our problem, each rectangular segment can be defined as 4 numbers describing the location of the collimator edge. In a sense, each rectangular segment can be mathematically described as a 4-dimensional point. Subtracting two of these points tells us how far each collimator has to travel from one segment to another. The open source code by Kirk can solve the TSP in any number of dimensions by finding the Euclidean norm distance between two points. Since the limiting factor in travel time between two segments is defined by the one collimator leaf that has to travel the furthest, the code was modified such that instead of using the Euclidean distance between two points, it used the single largest distance a collimator leaf had to travel for calculation.
In this study, 100 populations and 10000 iterations were used in the genetic algorithm to solve the TSP.
Once the order of the segments was solved, the collimator travel time was calculated with an estimated jaw acceleration of 5 cm/s2 and maximal speed of 2 cm/s, which is typical for a C-arm linac.
The N=2 and N=4 SOC designs have color coded regions shown in
The same aperture ordering scheme and time calculation, using the same jaw acceleration and maximal speed, was performed for DMS as well, with each aperture described as the location of every MLC location.
The total travel time for delivery and efficiency is evaluated for the 7 patients and compared between DMS and HFO with the N=1, N=2 and N=4 leaf collimator designs.
III.1. Fluence Map Evaluation
III.2. Patient Results
Table 2 shows a comparison of PTV homogeneity, D98, D99, and Dmax as well as R50 and average number of delivery segments. Total average includes the PTVs from the 6 single target cases and the 59.4 Gy PTV from the H&N3PTV case. R50 from the H&N3PTV case is calculated based on the 59.4 Gy prescription dose and the total PTV volume contributed by all 3.
Table 3 shows the largest and smallest values found for (HFO−DMS) dose differences for the Dmax and Dmean. The average value of the dose differences between OARs for each case is included. OARs that received 0 Gy in both the HFO and DMS cases are excluded in the evaluation.
The H&N3PTV case had severe dose degradation in the DMS case after MLC segmentation. Before this post processing step, the plan was able to achieve a D95 of 55.3 Gy, 59.4 Gy, and 68.8 Gy for the 54 Gy PTV, 59.4 Gy PTV, and 69.96 Gy PTV, respectively. However, segmenting the large fluence maps into a relatively small number of deliverable segments caused the dose to degrade, and after normalization to the 59.4 Gy PTV, the D95 changed to 59.5 Gy, 59.4 Gy, and 62.9 Gy, respectively. The higher prescription level PTVs had large dose degradation, and the dose normalization caused overdosing to the 54 Gy PTV by an extra 5 Gy.
Due to the unacceptable dosimetry to the target volumes of the H&N3PTV caused by the DMS method, another plan, termed the dose domain regularized (DDR) plan (Nguyen et al. (2015)Med. Phys., 42(4): 1858-1870), was included for comparison. DDR piecewise smooths the fluence using an anisotropic total variation regularization term while penalizing deviations from the optimal dose calculated from the 4π radiotherapy plan but before any post processing from the DMS plan. The DDR plan then underwent the same stratification and segmentation steps as the DMS plan. Even though the DDR plans and the DMS plans originated from the same exact 4π optimized plan, the DDR plan suffers much less from the stratification and segmentation steps, allowing for better dose coverage and homogeneity to the 69.96 Gy PTV than the HFO plan. A DVH comparison between HFO and DDR is shown in
This average difference for maximum and mean dose for all OARs between all plans, excluding structures that received zero dose from both plans, are −2.27% and −1.38%, respectively, as a percent of the prescription dose, meaning that for typical radiotherapy plans that have a prescription dose ranging from 30 to 60 Gy, we can expect to spare from 0.681 Gy to 1.362 Gy of max dose and from 0.414 Gy to 0.828 Gy of mean dose to OARs.
Limited to one aperture per delivery segment, the HFO plan produced far fewer apertures than the DMS method, which had, on average, about 3 apertures per segment. The number of bixels that make up an aperture in the HFO method are limited as a power of 2, as shown on the histogram in
In the study, we presented a novel method to generate rectangular apertures for SOC IMRT delivery. This method is based on regularization of the Haar wavelet coefficient in the dose domain to minimize the number of apertures while maintaining the dosimetric quality.
Compared to the MLC-based plans, despite the remarkable simplification of fluence maps into deliverable rectangles, the direct aperture optimization nature allows HFO to stay competitive. Our study was based on a non-coplanar beam orientation optimization platform that we previously showed to be superior to coplanar arc plans. However, the same HFO method should apply to coplanar IMRT without modification.
Although the Chambolle-Pock algorithm is remarkably efficient in solving the dose domain optimization problem, the computational cost of HFO plans remains substantial, particularly for larger PTVs. The length and width of the fluence grid are discretized to be a power of 2 to work properly. For instance, using our beamlet size of 0.5 cm2, any plan with a PTV larger than 4 cm but smaller than 8 cm in diameter must use a 16×16 fluence grid, even if it is just slightly larger than 4 cm. The H&N3PTV plan had the largest PTV dimension measuring approximately 20 cm. If HFO was performed using the regular beamlet size, this plan would have required a 64×64 fluence grid for each beam. Our modified Haar wavelet space then has a resolution of 127×127 pixels, making the optimizer solve 322580 variables simultaneously for all 20 beams. The inclusion of a dose domain transformation matrix, which contains tens of millions of non-zero entries, in the optimization further increases the computational complexity. The amount of data that must be handled simultaneously in the memory would exceed the available 512 GB RAM on our present workstation for larger PTVs and high dose calculation resolution. Therefore, the HFO method for the H&N3PTV plan was recalculated at half the dose matrix resolution and half of the beamlet resolution to achieve a reasonable cost optimization although superior dosimetric quality is expected had the higher dose resolution been used.
Jaws-only IMRT was initially developed as an alternative method to MLC based IMRT, which was costly and unreliable in its early stage. However, with the maturation of MLC technology, the need has considerably declined for general purpose IMRT on state of the art C-arm machines. The SOC IMRT, however, may be appealing in several aspects. First, even for N=4, the SOC system still has far fewer and thicker moving leaves than the conventional MLC allowing it to be further miniaturized to enable compact linac heads (Dong et al. (2014) Med. Phys. 41(4): 041709) and small animal irradiators. An effective way to reduce the linac head size is by moving the beam intensity modulator closer to the X-ray source. Moving the MLC closer to the X-ray source while maintaining the same intensity modulation resolution is increasingly difficult since a shorter source-to-collimator distance would require reduction of the already thin MLC leaf width, making fabrication more challenging, reducing mechanical reliability and increasing the interleaf leakage from the loss of the tongue and groove. In comparison, the resolution of SOC IMRT is not dependent on the leaf width, but rather on the motor accuracy capable of being in the micron range. For the same reason, the undesirable tradeoff between large field size and high resolution MLCs can be avoided with SOC. Third, as shown in the aperture size comparison, the SOC plan apertures are on average 4.4 times larger than those of the MLC plans. This would allow a significantly shorter beam-on time, reduced leakage dose and potentially improved IMRT QA results.
The dosimetric improvement was driven by the novel HFO algorithm. To overcome the other major deficiency of jaw-only IMRT, the SOC utilizing increasing number of leaves per bank can significantly improve delivery efficiency. The number of leaves in the SOC described herein is still far fewer than the typical number of leaves in a MLC, thus maintaining the ability to miniaturize and achieve a higher modulation resolution. Based on our estimation, increasing N beyond 4 may still increase the delivery efficiency but the returns start to diminish because although the same colored areas can be delivered in parallel, these areas are smaller and more fragmented with increasing N. Multiple leaves need to move in synchrony to deliver X-rays in the rest of the area, resulting in the diminished return for more leaves per bank. Considering the increasing mechanical complexity, an N=2-N=4 leaf/bank design may be an optimal balance between complexity and delivery efficiency.
In this study, the potential dosimetric advantages of using higher achievable resolution were not explored.
The IMRT problem was formulated into a direct aperture optimization problem minimizing the dose error while solving for the fluences in the Haar wavelet domain. This resulted in rectangular apertures that can be directly delivered with jaws only. The delivery efficiency may further be enhanced using modified sparse orthogonal collimators (SOC) utilizing 2-4 leaves per collimator bank. The potential gains from the greater resolution capabilities of jaws and SOCs have yet to be fully explored because of current computational limits in handling the number of discretized beamlets for Haar wavelet decomposition.
It is understood that the examples and embodiments described herein are for illustrative purposes only and that various modifications or changes in light thereof will be suggested to persons skilled in the art and are to be included within the spirit and purview of this application and scope of the appended claims. All publications, patents, and patent applications cited herein are hereby incorporated by reference in their entirety for all purposes.
This application claims benefit of and priority to U.S. Ser. No. 62/245,840, filed on Oct. 23, 2015, which is incorporated herein by reference in its entirety for all purposes.
This invention was made with government support under Grant No. NIH R43CA183390 awarded by the National Institutes of Health. The Government has certain rights in this invention.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US2016/058053 | 10/21/2016 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 62245840 | Oct 2015 | US |
