WO2025199226A1

WO2025199226A1 - Numerical optimization of attenuator geometry for photon radiation

Info

Publication number: WO2025199226A1
Application number: PCT/US2025/020552
Authority: WO
Inventors: Benjamin A. INSLEY; Dirk Alan BARTKOSKI; Mohammad Reza SALEHPOUR; David Jaffray
Original assignee: University of Texas System; University of Texas at Austin
Current assignee: University of Texas System; University of Texas at Austin
Priority date: 2024-03-21
Filing date: 2025-03-19
Publication date: 2025-09-25
Anticipated expiration: 2026-09-21

Abstract

A method of designing an attenuator for shaping a radiation field includes defining a radiation field of a radiation source, defining an attenuator geometry of an attenuator configured to receive the radiation field, and optimizing the attenuator geometry based on an objective function. The objective function is based on a radiation transport of the radiation field through the attenuator geometry. The radiation transport is based on a non-stochastic process. Advantageously the method can determine an optimal, arbitrary attenuator geometry for any radiation source (e.g., any complex emission profile) and/or objective functions (e.g., flux, fluence, dose, ionization, KERMA, exposure, etc.), determine an optimal configuration of a dynamic attenuator, utilize a non-stochastic (e.g., deterministic) radiation transport model, avoid iterative Monte Carlo calculations, increase computational efficiency of the optimization process, and thus reduce required parameter constraints on the attenuator geometry.

Description

NUMERICAL OPTIMIZATION OF ATTENUATOR GEOMETRY FOR PHOTON RADIATION CROSS-REFERENCE TO RELATED APPLICATION [0001] This application claims priority to U.S. Provisional Application No. 63/568,101, filed March 21, 2024, which is hereby incorporated herein in its entirety by reference. FIELD [0002] The present disclosure relates to radiation apparatuses, systems, and methods, for example, attenuator modeling and attenuator apparatuses, systems, and methods. BACKGROUND [0003] Radiation therapy utilizes ionizing radiation to control cell growth, typically as part of cancer treatment to destroy malignant cells. Ionizing radiation includes particle radiation (e.g., alpha, beta, proton, neutron, electron, etc.) or electromagnetic (EM) radiation (e.g., ultraviolet (UV), extreme UV (EUV), X-rays, gamma rays, etc.) that have sufficient energy to ionize atoms or molecules by detaching electrons from them. During treatment, ionizing radiation damages the DNA of cancerous tissue leading to cellular death. [0004] Radiation therapy may be curative in a number of types of cancer if localized to one area. Current radiation therapy is used to direct radiation to a target region (e.g., a region containing a tumor) and destroy those cells within the target region. To reduce exposure of healthy tissue (e.g., tissue which radiation must pass through to treat the tumor), radiation beams can be aimed from different angles to intersect at the target region. [0005] Radiobiology investigates the interaction of ionizing radiation with biological systems to help develop an improved delivery of radiation for radiation therapy. Similar to clinical techniques, current radiobiology aims to irradiate small target volumes with high levels of precision and accuracy. Biological systems, including but not limited to small animals, humans, tissues, cells, food, etc., can be used for irradiation applications and radiobiology investigations. For example, small animal models (e.g., mice) have been applied in radiobiology studies due to the genetic and physiologic similarities with humans. Further, complex emission profiles may be needed to maintain safety and high levels of precision and accuracy for different radiation applications (e.g., intraoperative radiotherapy, food sterilization, small animal irradiation, tissue irradiation, irradiation of animate and/or inanimate objects, for example, radiotherapy, sterilization, etc.). [0006] Geometric modulation of the emitted radiation field is a necessary feature of any irradiation platform, especially for complex emission profiles. An attenuator can be used to size, shape, and/or modulate the radiation field passing through the attenuator to the target region. The attenuator can align the radiation field in a particular direction (e.g., collimated radiation) and/or reduce a spatial cross-section of the radiation field (e.g., beam limiting). For example, a multileaf collimator (MLC) can include a number of individual and independently adjustable leaves that can be used to shape a radiation field to a desired field shape and intensity for localized radiotherapy. An attenuator can also be used to modulate the relative intensities across a beam profile. For example, a compensator is a specially-designed, low-attenuating material placed in the path of a radiation beam to influence the shape of isodose contours at depth within a patient. [0007] Determining an optimal attenuator geometry for a specified irradiation objective (e.g., high intensity, high precision, field flatness, specific size/shape/intensity goals, etc., or a combination of multiple objectives) can be complicated by intricate emission profiles of highly distributed radiation sources (as opposed to point source radiation emitters). Current optimization methods resort to iterative Monte Carlo calculations (e.g., radiation transport) that limit the computational efficiency of the attenuator design process. Current Monte Carlo-based optimization methods thus require numerous parameter and geometric constraints and therefore cannot provide a generic optimization method for an arbitrary attenuator geometry, regardless of the radiation source and/or objective function complexities. SUMMARY [0008] Accordingly, there is a need to develop an attenuator optimization process that can determine an optimal, arbitrary attenuator geometry for any radiation source (e.g., any complex emission profile) and/or objective functions (e.g., mathematical functions of radiation flux, fluence, dose, ionization, kinetic energy released in materials (KERMA), exposure, etc.), utilize a non-stochastic (e.g., deterministic) radiation transport model, avoid iterative Monte Carlo calculations, increase the computational efficiency of the optimization process, and thus reduce the required parameter constraints on the attenuator geometry. Further, there is a need to utilize an attenuator optimization model to determine an optimal design and construction of an attenuator (e.g., a static attenuator) for a particular application to produce a desired radiation field (e.g., emission profile). Additionally, there is a need to utilize an attenuator optimization model to determine an optimal configuration of a dynamic attenuator for a particular application (e.g., radiotherapy treatment planning, intensity-modulated radiation therapy (IMRT) treatment, volumetric modulated arc therapy (VMAT) treatment, spatially fractionated radiotherapy (SFRT) treatment, microbeam therapy, patient-specific therapeutic target, etc.) to produce one or more desired radiation fields, for example, over time as one or more parameters of a radiation source changes (e.g., source position, source energy, etc.). [0009] In some aspects, a method of designing an attenuator for shaping a radiation field can include defining a radiation field of a radiation source. In some aspects, the method can further include defining an attenuator geometry of an attenuator configured to receive the radiation field. In some aspects, the method can further include optimizing the attenuator geometry based on an objective function. In some aspects, the objective function can be based on a radiation transport of the radiation field through the attenuator geometry. In some aspects, the radiation transport can be based on a non-stochastic process. [0010] In some aspects, the attenuator can include a static attenuator (e.g., fixed geometry). In some aspects, the method can determine an optimal geometry of the static attenuator. In some aspects, the attenuator can include a dynamic attenuator (e.g., adjustable geometry). In some aspects, the method can determine one or more optimal geometries of the dynamic attenuator. [0011] In some aspects, the attenuator can include a collimator. In some aspects, the collimator can include a high-attenuation material (e.g., high density material, high atomic number, lead (Pb), etc.). In some aspects, the attenuator can include a modulator. In some aspects, the modulator can include a low-attenuation material (e.g., low density material, low atomic number, carbon (C), plastic, glass, water, aluminum, copper, etc.). In some aspects, the modulator can include a flattening filter. In some aspects, the attenuator can include a collimator, a modulator, or both. In some aspects, the attenuator can include an arbitrary attenuator geometry, for example, a combination of one or more collimators and one or more modulators. [0012] In some aspects, optimizing the attenuator geometry can be based on simulated annealing. In some aspects, optimizing the attenuator geometry is not based on iterative Monte Carlo calculations. [0013] In some aspects, the radiation source can include a photon radiation source. In some aspects, the photon radiation source can include an X-ray source. In some aspects, the photon radiation source can include an orthovoltage X-ray source. In some aspects, the photon radiation source can include a megavoltage X-ray source. In some aspects, the photon radiation source can include a Gamma-ray source. [0014] In some aspects, defining the radiation field can include defining a phase space model based on a differential flux probability density. In some aspects, the phase space model can be based on a four-dimensional (4D) differential flux probability density, for example, for a cylindrically symmetrical emission profile and a polyenergetic radiation field. In some aspects, the phase space model can be based on a three-dimensional (3D) differential flux probability density, for example, for a cylindrically symmetrical emission profile and a monoenergetic radiation field. [0015] In some aspects, the attenuator geometry can be symmetric. In some aspects, the attenuator geometry can be cylindrically symmetric. In some aspects, the attenuator geometry can include a plurality of annuli stacked along a longitudinal direction of the radiation field. In some aspects, the plurality of annuli can include at least six annuli. In some aspects, optimizing the attenuator geometry can include adjusting inner radii, adjusting outer radii, or both of the plurality of annuli. [0016] In some aspects, adjusting inner radii, adjusting outer radii, or both of the plurality of annuli can include optimizing the objective function based on a desired radiation field size. In some aspects, optimizing the objective function can include optimizing a first objective function configured to be intensity-weighted. In some aspects, optimizing the objective function can include optimizing a second objective function configured to be precision-weighted. In some aspects, optimizing the objective function can include optimizing a third objective function configured to be flatness-weighted. In some aspects, optimizing the objective function can include optimizing a fourth objective function configured to be intensity-precision weighted, precision-flatness weighted, intensity- flatness weighted, or intensity-precision-flatness weighted. [0017] In some aspects, the attenuator geometry can be asymmetric. In some aspects, the attenuator geometry can include a plurality of segments each defined by a set of inner radii, a set of outer radii, and a set of azimuthal ranges. [0018] In some aspects, the method can further include manufacturing the attenuator based on the optimized attenuator geometry. [0019] In some aspects, the method can further include configuring a dynamic attenuator based on the optimized attenuator geometry. In some aspects, the dynamic attenuator can include one or more adjustable elements configured to form the optimized attenuator geometry. [0020] In some aspects, a system for designing the geometry of an attenuator can include a computing device and a processor in communication with the computing device. In some aspects, the processor can be coupled to a memory storing instructions that when executed cause the processor to perform operations including defining a radiation field of a radiation source. In some aspects, the operations can further include defining an attenuator geometry of an attenuator configured to receive the radiation field. In some aspects, the operations can further include optimizing the attenuator geometry based on an objective function. In some aspects, the objective function can be based on a radiation transport of the radiation field through the attenuator geometry. In some aspects, the radiation transport can be based on a non-stochastic process. [0021] In some aspects, optimizing the attenuator geometry can include optimizing the objective function based on one or more treatment parameters. In some aspects, the one or more treatment parameters can include an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a heat distribution, a photon flux, a radiation field size, a focal spot size, a shape of the focal spot, a combination thereof, or a derivative thereof. [0022] In some aspects, the system can further include a manufacturing system configured to manufacture the attenuator based on the optimized attenuator geometry. [0023] In some aspects, the attenuator can include a dynamic attenuator having one or more adjustable elements. In some aspects, the one or more adjustable elements can each include a multileaf. In some aspects, the one or more adjustable elements can each include one or more stacks of adjustable elements. [0024] In some aspects, the attenuator can include a collimator. In some aspects, the collimator can include a multileaf collimator (MLC) having one or more adjustable elements. In some aspects, the one or more adjustable elements can each include a multileaf. In some aspects, the one or more adjustable elements can each include one or more stacks of adjustable elements. [0025] In some aspects, the attenuator can include a set of attenuators. In some aspects, optimizing the attenuator geometry can include optimizing a set of attenuator geometries of the set of attenuators based on one or more objective functions. [0026] In some aspects, the system can further include a configuration system configured to configure (e.g., adjust, arrange, shape, etc.) a dynamic attenuator based on the optimized attenuator geometry. In some aspects, the configuration system can send one or more control data signals to the dynamic attenuator to configure one or more adjustable elements (e.g., leaves) of the dynamic attenuator based on the optimized attenuator geometry. In some aspects, the configuration system can dynamically adjust the dynamic attenuator over time. In some aspects, for example, the configuration system can dynamically adjust the dynamic attenuator over time based on one or more optimized attenuator geometries. In some aspects, the system can dynamically optimize the attenuator geometry of the dynamic attenuator. In some aspects, for example, the system can dynamically optimize the attenuator geometry of the dynamic attenuator based on a change of one or more parameters of the radiation field (e.g., source position, source energy, etc.). In some aspects, the dynamic attenuator can include a dynamic collimator. For example, the dynamic collimator can include a MLC. In some aspects, the dynamic attenuator can include one or more adjustable elements configured to form the optimized attenuator geometry. [0027] In some aspects, the attenuator can include a collimator, a modulator, a flattening filter, a compensator, or a combination thereof. In some aspects, the attenuator can include a collimator. In some aspects, the attenuator can include a modulator. In some aspects, the attenuator can include a flattening filter. In some aspects, the attenuator can include a compensator. [0028] Implementations of any of the techniques described above can include a system, an apparatus, a device, a method, a process, and/or a computer program product. The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims. [0029] Further features and exemplary aspects of the present disclosure, as well as the structure and operation of various aspects, are described in detail below with reference to the accompanying drawings. It is noted that the aspects are not limited to the specific aspects described herein. Such aspects are presented herein for illustrative purposes only. Additional aspects will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES [0030] The accompanying drawings, which are incorporated herein and form part of the specification, illustrate the aspects and, together with the description, further serve to explain the principles of the aspects and to enable a person skilled in the relevant art(s) to make and use the aspects. [0031] FIG. 1 is a schematic illustration of an attenuator optimization system for optimizing an attenuator, according to an exemplary aspect. [0032] FIG.1A is a schematic illustration of the attenuator optimization system shown in FIG.1 for optimizing a collimator, according to an exemplary aspect. [0033] FIG.1B is a schematic illustration of the attenuator optimization system shown in FIG.1 for optimizing a modulator, according to an exemplary aspect. [0034] FIG.2 illustrates a modeling flow diagram for optimizing an attenuator, according to an exemplary aspect. [0035] FIG.3 is a schematic illustration of a system for designing and manufacturing an attenuator, according to an exemplary aspect. [0036] FIG.4 is a plot of flux comparisons for different collimator designs determined by attenuator optimization system shown in FIG.1, according to an exemplary aspect. [0037] FIG. 5 is a plot of optimization progress for a collimator design determined by attenuator optimization system shown in FIG.1, according to an exemplary aspect. [0038] FIG.6A is a plot of optimized collimator geometries for different radiation source positions determined by attenuator optimization system shown in FIG.1, according to an exemplary aspect. [0039] FIG.6B is a plot of resultant flux of the optimized collimator geometries shown in FIG.6A. [0040] FIG.7A is a plot of optimized collimator geometries for different radiation source positions determined by attenuator optimization system shown in FIG.1, according to an exemplary aspect. [0041] FIG.7B is a plot of resultant flux of the optimized collimator geometries shown in FIG.7A. [0042] FIG. 8A is a plot of resultant flux from optimized collimator geometries for different radiation source positions for an intensity-weighted objective function determined by attenuator optimization system shown in FIG.1, according to an exemplary aspect. [0043] FIG.8B is a plot of resultant flux from optimized collimator geometries for different radiation source positions for a precision-weighted objective function determined by attenuator optimization system shown in FIG.1, according to an exemplary aspect. [0044] FIG.8C is a plot of resultant flux from optimized collimator geometries for different radiation source positions for a flatness-weighted objective function determined by attenuator optimization system shown in FIG.1, according to an exemplary aspect. [0045] FIG.9 is a schematic illustration of a computing system, according to an exemplary aspect. [0046] The features and exemplary aspects of the present disclosure will become more apparent from the detailed description set forth below when taken in conjunction with the drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements. Additionally, generally, the left-most digit(s) of a reference number identifies the drawing in which the reference number first appears. Unless otherwise indicated, the drawings provided throughout the disclosure should not be interpreted as to-scale drawings. DETAILED DESCRIPTION [0047] Provided herein are system, apparatus, device, method, process, and/or computer program product aspects, and/or combinations and sub-combinations thereof, for optimizing an attenuator geometry. [0048] An attenuator optimization system as described below can define a radiation field of a radiation source, define an attenuator geometry of an attenuator configured to receive the radiation field, and optimize the attenuator geometry based on an objective function. [0049] An optimization method as described below can numerically optimize an attenuator geometry for a radiation source. [0050] An attenuator optimization system as described below can determine an optimal configuration of a dynamic attenuator to produce one or more desired radiation fields. [0051] An attenuator optimization system as described below can define a radiation field of a radiation source, define a collimator geometry of a collimator configured to receive the radiation field, and optimize the collimator geometry based on an objective function. [0052] An optimization method as described below can numerically optimize a collimator geometry for a radiation source. [0053] An attenuator optimization system as described below can determine an optimal configuration of a dynamic collimator to produce one or more desired radiation fields. [0054] An attenuator optimization system as described below can define a radiation field of a radiation source, define a modulator geometry of a modulator configured to receive the radiation field, and optimize the modulator geometry based on an objective function. [0055] An optimization method as described below can numerically optimize a modulator geometry for a radiation source. [0056] An attenuator optimization system as described below can determine an optimal configuration of a dynamic modulator to produce one or more desired radiation fields. [0057] This specification discloses one or more aspects that incorporate the features of this present disclosure. [0058] The aspect(s) described, and references in the specification to “one aspect,” “an aspect,” “an example aspect,” “an exemplary aspect,” etc., indicate that the aspect(s) described can include a particular feature, structure, or characteristic, but every aspect may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same aspect. Further, when a particular feature, structure, or characteristic is described in connection with an aspect, it is understood that it is within the knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other aspects whether or not explicitly described. [0059] Spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “on,” “upper” and the like, can be used herein for ease of description to describe one element or feature’s relationship to another element(s) or feature(s) as illustrated in the figures. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. The apparatus can be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein can likewise be interpreted accordingly. [0060] The term “about” or “substantially” or “approximately” as used herein means the value of a given quantity that can vary based on a particular technology. Based on the particular technology, the term “about” or “substantially” or “approximately” can indicate a value of a given quantity that varies within, for example, 0.1–10% of the value (e.g., ±0.1%, ±1%, ±2%, ±5%, or ±10% of the value). [0061] Numerical values, including endpoints of ranges, can be expressed herein as approximations preceded by the term “about,” “substantially,” “approximately,” or the like. In such cases, other aspects include the particular numerical values. Regardless of whether a numerical value is expressed as an approximation, two aspects are included in this disclosure: one expressed as an approximation, and another not expressed as an approximation. It will be further understood that an endpoint of each range is significant both in relation to another endpoint, and independently of another endpoint. [0062] Aspects of the disclosure may be implemented in hardware, firmware, software, or any combination thereof. Aspects of the disclosure may also be implemented as instructions stored on a machine-readable medium (e.g., memory), which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustic, or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.); and others. Further, firmware, software, routines, and/or instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. [0063] The term “observable field” as used herein indicates an observable, dobs, that can be measured, for example, but not limited to, a physical quantity, a field, a distribution, an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a flux, a heat distribution, a photon flux, a radiation field size, a focal spot size, a combination thereof, a derivative thereof, or any other observable quantity, field, or distribution. In some aspects, the observable field can be known. In some aspects, the observable field can be a desired observable field. [0064] The term “model” as used herein indicates an observable field, F(p), resulting from a current set of parameters, p, and a forward map, F, that maps p into F(p). In some aspects, the observable field F(p) can include a model of a radiation field of a radiation source. In some aspects, the observable field F(p) can include a model of an attenuator geometry of an attenuator (e.g., collimator, modulator, flattening filter, compensator, or a combination thereof). In some aspects, the observable field F(p) can include a model of a radiation transport of the radiation field through the attenuator geometry. In some aspects, the set of parameters p can be unknown and adjustable. [0065] In some aspects, the set of parameters p can be parameters of an attenuator, for example, but not limited to, a geometry of the attenuator (e.g., inner radii, outer radii, thickness, etc.), a volume of the attenuator, materials of the attenuator, a position of the attenuator relative to a radiation source, or any other parameter of the attenuator. [0066] The term “optimizing” as used herein indicates optimally solving an inverse problem, p = F^-1d_obs, of a forward problem, d_obs = F(p), to determine the set of parameters p that produce a known or desired observable field dobs. In some aspects, the observable field dobs can be known and the set of parameters p can be unknown, and the set of parameters p can be solved (e.g., optimized) with the constraint that the optimized model produces the known observable field d_obs. [0067] In some aspects, if the inverse F^-1 does not exist, or if the solution is untenable due to various physical, technical, and/or computational constraints, then an objective function, G, can be defined to solve the inverse problem. For example, the objective function G can define a metric, G(dobs, F(p)), that describes a difference between dobs and F(p), to be optimized (minimized or maximized). In some aspects, various optimization algorithms (e.g., simulated annealing, etc.) can be used to determine the set of parameters p that optimize G subject to physical and/or user-defined constraints (e.g., symmetric attenuator geometry, asymmetric attenuator geometry, desired intensity, desired precision, desired flatness, available materials, volume constraints, etc.). [0068] The term “desired” as used herein indicates a unique, optimized, and/or predetermined value, distribution, or design for a particular application (e.g., radiotherapy application, irradiation application, etc.), for example, a desired observable field for a radiotherapy application (e.g., treatment planning) or a desired observable field for an irradiation application (e.g., food sterilization, tissue irradiation, animate object, inanimate object, radiotherapy, sterilization). [0069] Exemplary Attenuator Optimization System [0070] As discussed above, radiation therapy utilizes ionizing radiation to control cell growth, typically as part of cancer treatment to destroy malignant cells. Ionizing radiation includes particle radiation (e.g., alpha, beta, proton, neutron, electron, etc.) or EM radiation (e.g., UV, EUV, X-rays, gamma rays, etc.) that have sufficient energy to ionize atoms or molecules by detaching electrons from them. [0071] Current radiation therapy is used to direct radiation to a target region (e.g., a region containing a tumor) and destroy those cells within the target region. To reduce exposure of healthy tissue (e.g., tissue which radiation must pass through to treat the tumor), radiation beams can be aimed from different angles to intersect at the target region. [0072] Current radiobiology aims to irradiate small target volumes with high levels of precision and accuracy. Biological systems, including but not limited to, small animals, humans, cells, food, etc., can be used for irradiation applications and radiobiology investigations. For example, small animal models (e.g., mice) have been applied in radiobiology studies due to the genetic and physiologic similarities with humans. Further, complex and unique emission profiles may be needed to maintain safety and high levels of precision and accuracy for different radiation applications (e.g., intraoperative radiotherapy, food sterilization, small animal irradiation, tissue irradiation, irradiation of animate and/or inanimate objects, for example, radiotherapy, sterilization, etc.). [0073] As the field of radiotherapy explores new realms of treatment, including ultra-high dose rate therapy, microbeam therapy, spatially fractionated radiotherapy (SFRT), and highly conformal stereotactic radiosurgery, there is a greater demand for increasingly complex radiation sources and beam shaping devices (e.g., attenuators) in the clinical and pre-clinical space. Traditional wisdom on X-ray source design has been upended by the advent of technologies such as field emission carbon nanotube sources, X-ray tube miniaturization, complex target design, and X-ray focusing lenses among others. With the implementation of complex sources into clinical practice, it has become clear that if the X- ray source deviates from conventional design principles, then the corresponding construction of other necessary accessory devices, including dosimetry tools, positioning apparatuses, and collimating structures should be reassessed. [0074] Geometric modulation of the emitted radiation field is a necessary feature of any irradiation platform, especially for complex emission profiles. An attenuator can be used to size, shape, and/or modulate the radiation field passing through the attenuator to the target region. The attenuator can align the radiation field in a particular direction (e.g., collimated radiation) and/or reduce a spatial cross-section of the radiation field (e.g., beam limiting). For example, a MLC can include a number of individual and independently adjustable leaves that can be used to shape a radiation field to a desired field shape and intensity for localized radiotherapy. An attenuator can also be used to modulate the relative intensities across a beam profile. For example, a compensator is a specially-designed, low- attenuating material placed in the path of a radiation beam to influence the shape of isodose contours at depth within a patient. [0075] However, determining an optimal attenuator geometry for a specified irradiation objective (e.g., high intensity, high precision, field flatness, specific size/shape/intensity goals, etc., or a combination of multiple objectives) can be complicated by intricate emission profiles of highly distributed radiation sources (e.g., as opposed to point source radiation emitters). Also, current optimization methods resort to iterative Monte Carlo calculations (e.g., radiation transport) that limit the computational efficiency of the attenuator design process. Further, current Monte Carlo-based optimization methods thus require numerous parameter and geometric constraints and therefore cannot provide a generic optimization method for an arbitrary attenuator geometry, regardless of the radiation source and/or objective function complexities. [0076] Aspects of attenuator modeling apparatuses, systems, and methods as discussed below can determine an optimal, arbitrary attenuator geometry for any radiation source (e.g., any complex emission profile) and/or objective functions (e.g., mathematical functions of radiation flux, fluence, dose, ionization, KERMA, exposure, etc.), utilize a non-stochastic (e.g., deterministic) radiation transport model, avoid iterative Monte Carlo calculations, increase the computational efficiency of the optimization process, and thus reduce the required parameter constraints on the attenuator geometry. Further, aspects of attenuator modeling apparatuses, systems, and methods as discussed below can utilize an attenuator optimization model to determine an optimal design and construction of an attenuator (e.g., a static attenuator) for a particular application to produce a desired radiation field (e.g., emission profile). Additionally, aspects of attenuator modeling apparatuses, systems, and methods as discussed below can utilize an attenuator optimization model to determine an optimal configuration of a dynamic attenuator for a particular application (e.g., radiotherapy treatment planning, IMRT treatment, VMAT treatment, SFRT treatment, microbeam therapy, patient-specific therapeutic target, etc.) to produce one or more desired radiation fields, for example, over time as one or more parameters of a radiation source changes (e.g., source position, source energy, etc.). [0077] FIG. 1 illustrates attenuator optimization system 100 for designing an attenuator, according to an exemplary aspect. Attenuator optimization system 100 can be configured to optimize an arbitrary attenuator geometry for any radiation source and/or objective function(s). Attenuator optimization system 100 can be further configured to utilize a non- stochastic process (e.g., a deterministic radiation transport model) and avoid iterative Monte Carlo calculations. Attenuator optimization system 100 can be further configured to increase computational efficiency of the optimization process so that required parameter constraints on the attenuator geometry can be reduced. Attenuator optimization system 100 can be further configured to determine an optimal design and construction of an attenuator for a particular application to produce a desired radiation field. Attenuator optimization system 100 can be further configured to determine an optimal configuration of a dynamic attenuator for a particular application to produce a desired radiation field. Although attenuator optimization system 100 is shown in FIG. 1 as a stand-alone apparatus and/or system, aspects of this disclosure can be used with other apparatuses, systems, and/or methods, for example, modeling flow diagram 200, system 300, and/or computing system 900. [0078] As shown in FIG. 1, attenuator optimization system 100 can include radiation source 110, attenuator 120, and radiation transport 130. In some aspects, attenuator optimization system 100 can include a radiation source model, an attenuator model, and a radiation transport model based on a radiation transport (e.g., photon flux) of a radiation field of radiation source 110 through attenuator 120. [0079] Radiation source 110 can be configured to provide a radiation field (e.g., complex emission profile). In some aspects, radiation source 110 can be characterized by a radiation source model. In some aspects, radiation source 110 can include any radiation source. In some aspects, radiation source 110 can include a photon radiation source. For example, radiation source 110 can include an X-ray source, for example, a miniature X-ray source having an ultra-thin conical target optimized for high intensity, forward-directed energy fluence (e.g., complex emission profile) as previously described in International Appl. No. PCT/US2023/084160, filed December 15, 2023, which is hereby incorporated by reference herein in its entirety. [0080] In some aspects, radiation source 110 can include an orthovoltage source (e.g., operating voltage in the kV range). For example, radiation source 110 can include an orthovoltage X-ray source producing X-ray energies from 0 to the max energy (e.g., for a 100 kV orthovoltage source, the photon energies can be in the range (0, 100] keV). In some aspects, radiation source 110 can include a megavoltage source (e.g., operating voltage in the MV range). For example, radiation source 110 can include a megavoltage X-ray source producing X-ray energies from 0 to the max energy (e.g., for a 1 MV megavoltage source, the photon energies can be in the range (0, 1] MeV). As shown in FIG.1, radiation source 110 can emit radiation field 112 characterized by phase space plane 114. Phase space plane 114 can define a photon starting position (x', y') 116 of a photon track 132 of radiation field 112. [0081] In some aspects, phase space plane 114 can be positioned from a detector plane 134 by a radiation source position (z0) 138. In some aspects, a phase space of radiation field 112 can be modeled as a histogram differential (e.g., four-dimensional (4D) histogram) in photon starting position (x', y') 116 in phase space plane 114, photon ending position (xdet, ydet) 136 at detector plane 134 with a preset radiation source position (z0) 138 (e.g., source- to-detector distance), and photon energy (E). In some aspects, radiation field 112 can be defined by a phase space model based on a differential flux probability density (e.g., 4D differential). [0082] In some aspects, radiation source 110 can be characterized by a radiation source model describing radiation field 112 emitted from radiation source 110. In some aspects, the radiation source model can reference phase space plane 114 (e.g., surface flush to aperture of radiation source 110) and detector plane 134 (e.g., downstream parallel surface that can represent an isocentric plane in a treatment context). Coordinates in phase space plane 114 can be described as (x', y') (e.g., photon starting position (x', y') 116), and coordinates in detector plane 134 can be described as (xdet, ydet) (e.g., photon ending position (x_det, y_det) 136). Phase space plane 114 and detector plane 134 can be separated by a constant, arbitrary distance z0 (e.g., radiation source position (z0) 138). [0083] In some aspects, for a cylindrically symmetric radiation source 110, the radiation source model can describe radiation field 112 using the following differential flux density e_quation: _ర _{^^^^^ᇱ, ^^ᇱ, ^^ ௗ ே} _{ௗ^௧ , ^^^ = ௗ௫ᇲௗ௬ᇲௗ௫^^^ௗா (1)} _{The differential flux density, ^^^^^ᇱ, ^^ᇱ, ^^ௗ^௧ , ^^^, is defined by the mean number of photons,} _{^^^ − ௗா , ^^ ௗா} _{ଶ + ଶ ^ from a differential area} segment in phase space plane 114 located at ^^^^ᇱ,^^^ᇱ^ with area ^^^^^ᇱ^^^^^ᇱ and passing through a_{differential area segment in detector plane 134 located at ^^^ௗ^௧ , 0^ with area ^^^^ௗ^௧^^^^ௗ^௧} for a constant radiation source position (z₀) 138. The y-component, ^^_ௗ^௧, does not appear explicitly in this formula because of the cylindrical symmetry of radiation field 112, thus allowing calculation of radiation transport 130 (e.g., photon flux) along one arbitrary axis (_{e.g., the ^^ axis). The units of ^^^^^ᇱ, ^^ᇱ, ^ ି^ ିଶ} _{ௗ^௧ ^^ௗ^௧ ,^^ are ^^^^^^^^^^^^ × ^^^^^^^^ .} [0084] In some aspects, for an asymmetric radiation source 110, the radiation source model can describe radiation field 112 in two-dimensions (2D) using the following differential f_{lux density equation:} T_{he differential flux density, ^^^^^ᇱ, ^^ᇱ, ^^ௗ^௧ , ^^ௗ^௧ ,^^^ is the mean number of photons, ^^,} _{^^^ − ௗா} _{ଶ , ^^ + ௗா} _{ଶ ^ from a differential area segment} in phase space plane 114 located at ^{^}^^^ᇱ,^^^{ᇱ^} with area ^^^^^ᇱ^^^^^ᇱ and passing through a differential area segment in detector plane 134 located at ^{^}^^_ௗ^௧ ,^^_ௗ^௧ ^{^} with area ^^^^_ௗ^௧^^^^_ௗ^௧ _{for a constant radiation source position (z0) 138. The units of ^^^^^ᇱ, ^^ᇱ, ^^ௗ^௧ , ^^ௗ^௧,^^^ are} _{^^^^^^^^^^^^ି^ × ^^^^^^^^ିଶ.} [0085] In some aspects, for an asymmetric radiation source 110, the radiation source model can describe radiation field 112 in three-dimensions (3D) using the following differential f_{lux density equation:} _{^^ ^^ ,^^ , ^^ௗ^௧ ,^^ௗ^௧, ^^ௗ^௧, ^^^ = ௗర} _{^ ᇱ ᇱ ே} _{ௗ௫ᇲௗ௬ᇲௗ௫^^^ௗ௬^^^ௗ௭^^^ௗா (1b)} _{The differential flux density, ^^^^^ᇱ, ^^ᇱ, ^^ᇱ, ^^ௗ^௧ , ^^ௗ^௧, ^^ௗ^௧,^^^ is the mean number of photons,} _{ௗா ௗா} _{^^^ − ଶ , ^^ + ଶ ^ from a differential area} _{segment in phase space plane 114 located at ^^^ᇱ,^^ᇱ, ^^^^ with area ^^^^ᇱ^^^^ᇱ and passing} _{through a differential volume segment in detector plane 134 located at ^^^ௗ^௧ , ^^ௗ^௧, ^^ௗ^௧^} with volume ^^^^_ௗ^௧^^^^_ௗ^௧^^^^_ௗ^௧ for a constant radiation source position (z₀) 138. The units o_{f ^^^^^ᇱ, ^^ᇱ, ^^ , ^^ , ^^ ,^^^ are ^^^^^^ ି^ ି^ ି^} _{ௗ^௧ ௗ^௧ ௗ^௧ ^^^^^^ × ^^^^^^^^ × ^^^^^^^^^^^^ .} [0086] In some aspects, the radiation source model (e.g., equation 1, 1a, 1b) can be an analytical function or can be discretized into a multidimensional histogram by one or more _{resolutions and/or ranges for each parameter (e.g., ^^ᇱ, ^^ᇱ, ^^ௗ^௧ , ^^, ^^^, ^^^). For example, for a} cylindrically symmetric radiation source 110 (e.g., equation 1), one or more resolutions and/or ranges for each parameter can be given as shown below in Table I: Table I – Radiation Source Model Parameters [0087] In some aspects, a resolution of ^^^^′ can be about 0.01 mm to about 1 mm. In some aspects, a resolution of ^^^^′ can be about 0.01 mm to about 1 mm. In some aspects, a r^{esolution of ^^^^ௗ^௧ can be about 0.01 mm to about 1 mm. In some aspects, a resolution of} ^_{^^^ can be about 0.1 keV to about 10 keV. In some aspects, a resolution of ^^^^ can be about} 0.01 mm to about 1 mm. In some aspects, a range of ^^′ can be about -50 mm to about 50 mm. In some aspects, a range of ^^′ can be about -50 mm to about 50 mm. In some aspects, a range of ^^_ௗ^௧ can be about 0 mm to about 100 mm. In some aspects, a range of ^^ can be about 0.01 keV mm to about 1 MeV. In some aspects, a range of ^^_^ can be about 10 mm to about 1,000 mm. In some aspects, a range of ^^_^ can be about 1 mm to about 100 mm. In some aspects, a range of ^^_^ can include about 6 annuli to about 1,000 annuli. [0088] In some aspects, the radiation source model can be calculated independently for different focal spot size settings (e.g., 0.1 mm, 0.5 mm, 1.0 mm, 2.0 mm, 5.0 mm, etc.). For example, the radiation source model can be calculated independently for nine different focal spot size settings to determine an appropriate phase space model (e.g., phase space plane 114) of radiation field 112. In some aspects, the radiation source model can be calculated independently for different source-to-detector distances (e.g., 70 mm, 90 mm, 120 mm, 150 mm, 200 mm, etc.). For example, the radiation source model can be calculated independently for five different source-to-detector distances (e.g., radiation source position (z₀) 138) to determine an appropriate phase space model (e.g., phase space plane 114) of radiation field 112. [0089] Attenuator 120 can be configured to receive radiation field 112 and shape radiation field 112 to a desired emission profile. In some aspects, attenuator 120 can be characterized by an attenuator model. As shown in FIG.1, attenuator 120 can include attenuator geometry 122 with attenuator slices 124. In some aspects, for example, as shown in FIG.1, attenuator geometry 122 can include attenuator slices 124, each with an inner radius (ri) 126 and an outer radius (ro) 128 relative to symmetry axis 102. In some aspects, attenuator slices 124 can include a plurality of annuli (e.g., washers) each having an inner radius (r_i) 126, an outer radius (r_o) 128, or both. In some aspects, attenuator 120 can include a dynamic attenuator having one or more adjustable leaves. In some aspects, the one or more adjustable leaves of the dynamic attenuator can each include a multileaf. In some aspects, attenuator slices 124 can each be positioned from a detector plane 134 by an attenuator position (zi) 140. In some aspects, attenuator 120 can be modeled as a stack of thin annuli (e.g., attenuator slices 124) with varying inner radii (e.g., inner radius (ri) 126), outer radii (e.g., outer radius (r_o) 128), or both. [0090] In some aspects, attenuator 120 can include a collimator. For example, as shown in FIG.1A, attenuator 120 can include collimator 121a. Collimator 121a can be configured to collimate radiation field 112 to a desired emission profile. In some aspects, collimator 121a can include a high-attenuation material. For example, collimator 121a can include a high density material, a high atomic number material, lead (Pb), or a combination thereof, etc. In some aspects, collimator 121a can include a MLC having one or more adjustable leaves. In some aspects, the one or more adjustable leaves of the MLC can each include a multileaf. [0091] In some aspects, attenuator 120 can include a modulator. For example, as shown in FIG.1B, attenuator 120 can include modulator 121b. Modulator 121b can be configured to modulate radiation field 112 to a desired emission profile. In some aspects, modulator 121b can include a flattening filter. In some aspects, modulator 121b can include a low- attenuation material. For example, modulator 121b can include a low density material, a low atomic number material, carbon (C), plastic, glass, water, aluminum, copper, or a combination thereof, etc. [0092] In some aspects, attenuator geometry 122 can be symmetric. For example, as shown in FIG. 1, attenuator geometry 122 can be cylindrically symmetric about symmetry axis 102 (e.g., longitudinal axis of attenuator 120). In some aspects, attenuator geometry 122 can include attenuator slices 124 (e.g., plurality of annuli) stacked along a longitudinal direction of attenuator 120. In some aspects, attenuator slices 124 can include at least six annuli (e.g., washers). In some aspects, attenuator slices 124 can include at least ten annuli (e.g., washers). In some aspects, attenuator slices 124 can include at least one hundred annuli (e.g., washers). In some aspects, attenuator slices 124 can include a range of about six to about a thousand annuli (e.g., washers). [0093] In some aspects, attenuator 120 can be characterized by an attenuator model describing attenuation of radiation field 112 through attenuator geometry 122. In some aspects, for a cylindrically symmetric attenuator 120, attenuator 120 can be split longitudinally into thin slices (e.g., attenuator slices 124) each with an inner radius (r_i) 126, an outer radius (ro) 128, or both, resembling a stack of annuli. In some aspects, each annulus can extend beyond a range of radiation field 112 and, thus, can be characterized by two parameters: collimator position (z_i) 140 and inner radius (r_i) 126. In some aspects, for a stack of annuli that comprise the whole attenuator 120, attenuator position (zi) 140, inner radius (ri) 126, and outer radius (ro) 128 can be the i^th annulus’s position, inner radius, and outer radius, respectively. [0094] The path between a photon’s starting position (e.g., photon starting position (x', y') 1_{16) in the phase space plane 114, (^^ᇱ, ^^ᇱ, ^^^), and its final position (e.g., photon ending} _{position (xdet, ydet) 136) in the detector plane 134, (^^ௗ^௧ ,^^ௗ^௧, 0), can be uniquely defined.} The attenuation of that photon track 132 through the i^th annulus can be given by the Beer- L_{ambert exponential attenuation law:} ே_{బ = exp(−^^^^^), where ^^^ is the number of photons} _{leaving from the differential area segment at (^^ᇱ,^^ᇱ, ^^^), ^^ is the number of photons} _{arriving at the differential area segment at (^^ௗ^௧ , 0, 0), ^^ is the material- and energy-} dependent linear attenuation coefficient, and ^^_^ is the photon’s path length through the i^th annulus (e.g., attenuator slice 124). [0095] The photon track 132 path length ^^_^ can be formulated for a cylindrically symmetric system as the following piecewise function to model the material discontinuity between any empty space (e.g., hole) and the body of the annulus (e.g., attenuator slice 124) between inner radius (r_i) 126 and outer radius (r_o) 128: (₂₎ w_{here ^^^^ is the thickness of the attenuator slice 124. ^^(^^ᇱ, ^^ᇱ, ^^ௗ^௧) describes the angle of} incidence of the photon track 132 at the plane of the i^th annulus, which causes a lengthening _{of the path through the annulus. The cosine of this angle is given by ^^} ^ᇱ _{, ^^ௗ^௧)൯ =} _{௭బ Finally, ^^ᇱ} _{^ is the radius at which a given photon track 132 crosses} through the plane of the i^th attenuator slice 124, calculated using the photon’s initial and f_{inal positions as ^^ᇱ} _{In the} of ^^_^, ^^_^ ^ᇱ is compared to ^^_^ and ^^_^ to see if the photon track 132 passes through the given annulus’s empty space (e.g., central hole) or the body (e.g., attenuator slice 124). [0096] In some aspects, for example, for collimator 121a shown in FIG. 1A, the photon track 132 path length ^^_^ can be formulated for a cylindrically symmetric system as the following piecewise function to model the material discontinuity between the central hole (^{e.g., inner radius (ri) 126) and the body of the annulus (e.g., attenuator slice 124):} w_{here ^^^^ is the thickness of the attenuator slice 124. ^^(^^ᇱ, ^^ᇱ, ^^ௗ^௧) describes the angle of} incidence of the photon track 132 at the plane of the i^th annulus, which causes a lengthening o_{f the path through the annulus. The cosine of this angle is given by} ^ᇱ _{^^ , ^^ௗ^௧)൯ =} _{௭బ Finally, ^^ is the radius at which a given photon track 132} through the plane of the i^th attenuator slice 124, calculated using the photon’s initial and f_{inal positions as ^^} _{In the} of ^^_^, ^^_^ ^ᇱ is compared to ^^_^ to see if the photon track 132 passes through the given annulus’s central hole (e.g., inner radius (ri) 126) or body (e.g., attenuator slice 124). [0097] In some aspects, for example, for modulator 121b shown in FIG. 1B, the photon track 132 path length ^^_^ can be formulated for a cylindrically symmetric system as the following piecewise function to model the material discontinuity between the central hole (e.g., inner radius (ri) 126) and the body of the annulus (e.g., attenuator slice 124, outer r^{adius (ro) 128):} w_{here ^^^^ is the thickness of the attenuator slice 124. ^^(^^ᇱ, ^^ᇱ, ^^ௗ^௧) describes the angle of} incidence of the photon track 132 at the plane of the i^th annulus, which causes a lengthening _{of the path through the annulus. The cosine of this angle is given by ^^} ^ᇱ _{, ^^ௗ^௧)൯ =} _{௭బ Finally, ^^ᇱ} _{^ is the radius at which a given photon track 132 crosses} through the plane of the i^th attenuator slice 124, calculated using the photon’s initial and f_{inal positions as ^^ᇱ} _{^ =} _{. In the calculation} of ^^_^, ^^_^ ^ᇱ is compared to ^^_^ to see if the photon track 132 passes through the given annulus’s body (e.g., attenuator slice 124) or outside of the annulus’s body (e.g., beyond outer radius (ro) 128). [0098] In some aspects, attenuator geometry 122 can be asymmetric. For example, attenuator slices 124 can include a plurality of segments each defined by inner radius (r_i,j) 126', outer radius (ri,j) 128', and an azimuthal range [θi^j, θi^j+1] (e.g., azimuthal attenuator slice extending from inner radius (ri,j) 126' from first angle θi^j to second angle θi^j+1, azimuthal attenuator slice extending from outer radius (r_i,j) 128' from first angle θ_i ^j to second angle In some aspects, inner radius (ri,j) 126' is unconstrained and can be radius for a corresponding azimuthal range [θi^j, θi^j+1]. In some aspects, outer radius (ri,j) 128' is unconstrained and can be any radius for a corresponding azimuthal range [θ_i ^j, θ_i ^j+1]. In some aspects, attenuator geometry 122 can include a plurality of segments each defined by a set of inner radii (ri,j) 126', a set of outer radii (ri,j) 128', and a set of azimuthal ranges [θ_i ^j, θ_i ^j+1]. [0099] In some aspects, for an asymmetric attenuator 120, the two-dimensional (2D) position of each photon track 132 in the plane of each attenuator slice 124 can be calculated, and the photon track 132 path length can be formulated as the following function to model the material discontinuity between the open space (e.g., inner radius (rⁱi,j) 126' or outer radius (r^o _i,j) 128') and the body of the annulus (e.g., attenuator slice 124) an azimuthal range [θi^j, θi^j+1]: w_{here ^^^^ is the thickness of the attenuator slice 124. ^^(^^ᇱ, ^^ᇱ, ^^ௗ^௧ ,^^ௗ^௧) describes the angle} of incidence of the photon track 132 at the plane of the i^th annulus, which causes a lengthening of the path through the annulus, and where ^^^^{^ ^ା^} ^ ,^^_^ ൧ define some azimuthal range of an azimuthal attenuator slice extending from inner radius (rⁱ _i,j) 126' to outer radius _(ro _{i,j) 128' and from first angle θij to second angle θij+1. The cosine of this angle is given by} _{cos൫^^(^^ᇱ, ^^ᇱ, ^^ௗ^௧ , ^^ௗ^௧)൯ = ௭బ . Finally, ^^ᇱ is the radius at} _{^^^ ᇲ మ ^^^ బమ ^ which a} _{^(௫ ି௫ ) ା(௬ ି௬ᇲ)మା௭} given photon track 132 crosses through the plane of the i^th attenuator slice 124, calculated u^{sing the photon’s initial and final positions as ^^ᇱ} ^{^ =} ^_^^^ _{^ ,^^^ା^} _{^ ൧ to see if the photon track 132 passes through the given annulus’s open space} (e.g., inner radius (ri,j) 126' or outer radius (r^oi,j) 128') or body (e.g., attenuator slice 124). [0100] Radiation transport 130 can be configured to characterize the transport (transfer) of radiation field 112 through attenuator 120 (e.g., through attenuator geometry 122). In some aspects, radiation transport 130 can be further configured to characterize a photon flux of radiation field 112 through attenuator 120. In some aspects, radiation transport 130 can be characterized by a radiation transport model. In some aspects, radiation transport 130 can be part of one or more objective functions to optimize attenuator geometry 122. As shown in FIG. 1, radiation transport 130 can include photon track 132 and detector plane 134. Photon track 132 can characterize radiation field 112 through attenuator geometry 122 from photon starting position (x', y') 116 at phase space plane 114 to photon ending position (xdet, ydet) 136 at detector plane 134. Detector plane 134 can be configured to receive photon track 132 through attenuator geometry 122. In some aspects, detector plane 134 can represent an isocentric plane (e.g., a target area) in a treatment context (e.g., radiotherapy). [0101] In some aspects, for example, as shown in FIG. 1, photon track 132 can include photon track radii (r_i') 142, each defined as a radius at which photon track 132 (e.g., a ray) from photon starting position (x', y') 116 to photon ending position (x_det, y_det) 136 crosses attenuator slices 124 of attenuator 120 at attenuator position (zi) 140. In some aspects, for a cylindrically symmetric attenuator geometry 122, photon ending position (xdet, ydet) 136 can be reduced to photon ending position (x_det, 0), such that radiation transport 130 (e.g., photon flux) can be calculated along one arbitrary axis (e.g., the xdet axis). In some aspects, simulated annealing can be employed to optimize the set of inner radii (e.g., inner radius (r_i) 126), the set of outer radii (e.g., outer radius (r_o) 128), or both according to one or more objective functions calculated on radiation transport 130 (e.g., photon flux) at detector plane 134. [0102] In some aspects, radiation transport 130 can be modeled to optimize attenuator geometry 122. In some aspects, optimized attenuator geometries 122 and the resulting radiation transport 130 (e.g., photon flux) of each can be compared for different focal spot sizes and/or different positions of radiation source 110 to determine an optimal attenuator geometry 122 for a particular application. In some aspects, attenuator geometry 122 can be optimized based on one or more geometry specific parameters (e.g., inner radius, outer radius, focal length, focal spot size, shape of the focal spot, etc.). [0103] In some aspects, radiation transport 130 can be characterized by a radiation transport model incorporating a radiation source model (e.g., radiation source 110) and an attenuator model (e.g., attenuator 120). In some aspects, the radiation source model and the attenuator model can be combined for an arbitrary number of attenuator slices 124 to calculate radiation transport 130 (e.g., photon flux) at detector plane 134. [0104] In some aspects, for a cylindrically symmetric radiation transport 130 (e.g., photon flux), the radiation transport model can describe radiation transport 130 using the following e_quation: _{Ψ(^^ௗ^௧) = ∭ ^^(^^ᇱ,^^ᇱ, ^^ௗ^௧ ,^^) exp(−^^(^^)∑^ ^^^(^^ᇱ, ^^ᇱ, ^^ௗ^௧) )^^^^^^^^′^^^^′ (3)} The radiation transport 130, Ψ(^^_ௗ^௧), is defined by the flux of photons in units of inverse area that are passing through detector plane 134 as a function of distance from the central axis (e.g., symmetry axis 102). This flux profile is equivalent for any axis in detector plane 134 due to the cylindrical symmetry. In some aspects, the integration bounds of Ψ⁽^^_ௗ^௧ ⁾ can be (0, ∞) for E, (-∞, ∞) for x', and (-∞, ∞) for y'. In some aspects, alternatively, computationally the integration bounds of Ψ(^^_ௗ^௧) can be any bounds such that f goes to zero within a reasonable precision. For example, integration bounds of (0, 200] keV for E, [-8, 8] mm for x', and [-8, 8] for y' to determine Ψ(^^_ௗ^௧). In some aspects, Ψ(^^_ௗ^௧) can be m_{odulated to provide the photon fluence given by the equation:} In some aspects, for small radiation field sizes (e.g., radiation field 112) and small phase s^{pace planes (e.g., phase space plane 114), a small angle approximation can be used (e.g.,} c_{os(^^) ≈ 1), such that the planar fluence and fluence are approximately equal. For} example, this approximation can provide a significant reduction in computation time. [0105] In some aspects, for an asymmetric radiation transport 130 (e.g., photon flux), the r_{adiation transport model can describe radiation transport 130 using the following equation:} _{Ψ(^^ௗ^௧, ^^ௗ^௧) =} _{∭^^(^^ᇱ, ^^ᇱ, ^^ௗ^௧ , ^^ௗ^௧ ,^^) exp൫−^^(^^)∑^ ^^^൫^^ᇱ, ^^ᇱ, ^^ௗ^௧,^^ௗ^௧൯൯ ^^^^^^^^′^^^^′ (3b)} The asymmetric radiation transport 130, Ψ(^^_ௗ^௧,^^_ௗ^௧), is defined by the flux of photons in u^{nits of inverse area that are passing through detector plane 134 as a function of coordinates} (_{^^ௗ^௧ ,^^ௗ^௧). This can be similarly adjusted to calculate the photon fluence:} _{Ψ(^^ௗ^௧, ^^ௗ^௧) =} [0106] In some aspects, one or more objective functions G can incorporate radiation transport 130, Ψ(^^_ௗ^௧), and be defined for the optimization of attenuator geometry 122. In s^{ome aspects, attenuator geometry 122 can be optimized via radiation transport 130,} Ψ_{(^^ௗ^௧) (e.g., flux model). For example, the flux model can be modulated towards high} intensity and high precision. In some aspects, the flux model can be intensity weighted, precision weighted, flatness weighted, or a combination thereof (e.g., intensity-precision weighted, precision-flatness weighted, intensity-flatness weighted, intensity-precision- flatness weighted). In some aspects, attenuator geometry 122 can be optimized for one or more radiation field sizes (e.g., small, medium, large) and/or one or more positions of radiation source 110 (e.g., radiation source position (z₀) 138). For example, one or more objective functions can be precision weighted within the context of a desired radiation field size (e.g., 5 mm). [0107] In some aspects, for a cylindrically symmetric radiation transport 130 (e.g., photon flux), a primary objective function for optimization of attenuator geometry 122 can be d_{efined by the following equation:} T_{his primary objective function is composed of two main factors: Ψ} ⁽ ₀ ⁾ _and _{. Ψ} ⁽ ₀ ⁾ i_{s the flux at the center of detector plane 134, which is the maximum of the flux profile.} _{is defined using the function, ^^(^^) = ^^^^ ோ} _{ௗ^௧ ^^ Ψ(^^ௗ^௧)^^^^ௗ^௧ , which represents the} number of photons passing through an infinitesimal strip of thickness ^^^^_ௗ^௧ out to a distance ^^ along the ^^_ௗ^௧ axis. If ^^_^^^ measures the radius of a desired field size (e.g., 5 mm), then is the fraction of photons within the desired field size. Accordingly, field size can be defined at the detector plane 134. In some aspects, maximizing the product of _{can give a simultaneous optimum for both intensity} and precision of the flux. In some aspects, primary objective function G₁ can be configured to provide high intensity (e.g., intensity weighted) and high precision (e.g., precision weighted). [0108] In some aspects, one or more objective functions can be used for optimization of attenuator geometry 122. In some aspects, for example, a second objective function, G₂, can be implemented to provide an intensity weighted flux. In some aspects, the second o_{bjective function G2 can be defined by the following equation:} [0109] In some aspects, for example, a third objective function, G3, can be implemented to provide a precision weighted flux. In some aspects, the third objective function G₃ can be d_{efined by the following equation:} [0110] In some aspects, for example, a fourth objective function, G4, can be implemented to provide a flatness weighted flux (e.g., within a desired field size). In some aspects, the f_{ourth objective function G4 can be defined by the following equation:} _{^^^^^)൯ represents the standard deviation of the flux profile from ^^ௗ^௧ = 0 to} _{^^ = ^^ . In ி(^)} _{ௗ^௧ ^^^ some aspects, together with the inverted precision fraction, ி} _{, fourth} objective function G₄ can be minimized to create a flat field of width ^^_^^^. In some aspects, fourth objective function G4 can be configured to provide an intensity weighted and a flatness weighted flux. [0111] In some aspects, for example, the above objective functions can be combined together into a fifth objective function, G5, that can be implemented to provide all three priorities – intensity, precision, and flatness. In some aspects, the fifth objective function G₅ can be defined by the following equation: where in the second term, the constant b is selected by the user to control the relative magnitude of the first term (e.g., intensity-precision weighted) and the second term (e.g., flatness weighted), which in turn can control the prioritization between intensity-precision weighting and flatness weighting. [0112] In some aspects, attenuator optimization system 100 can utilize an optimization algorithm based on the radiation transport model (e.g., flux model) for one or more objective functions to determine an optimized attenuator geometry 122. In some aspects, the radiation transport model can be based on a non-stochastic process (e.g., non-random, deterministic). In some aspects, the optimization algorithm is not based on Monte Carlo calculations. In some aspects, the optimization algorithm is based on simulated annealing. [0113] In some aspects, the optimization algorithm can utilize simulated annealing and one or more hyperparameters to determine an optimized attenuator geometry 122. In some aspects, for a selected objective function (e.g., G1), the following process can be used to determine an optimal attenuator geometry 122: [0114] Step 1: Initialize the set of annulus inner radii ^^_^ (e.g., inner radius (ri) 126), the set of annulus outer radii ^^_^ (e.g., outer radius (ro) 128), or both of attenuator geometry 122 and calculate the objective function (e.g., G1). [0115] Step 2: Iterate through the complete set of annuli, for example, in a random order. [0116] Step 3: For each annulus, adjust the inner radius, the outer radius, or both by some small, constant value, ^^^^. Whether the inner radius ^^_^ is increased or decreased (e.g., ±^^^^) is determined by a 50/50 probability, unless a decrease would result in the inner radius ^^_^ being less than 0; in this case, the inner radius ^^_^ is increased. Whether the outer radius ^^_^ is increased or decreased (e.g., ±^^^^) is determined by a 50/50 probability, unless a decrease would result in the outer radius ^^_^ being less than the inner radius ^^_^ or if an increase would result in the outer radius ^^_^ being greater than some predetermined maximum; in this case, the outer radius ^^_^ is increased or decreased, respectively. ^{[0117] In some aspects, the algorithm can utilize a changing step size magnitude (Δs) for} ^_{^^^, rather than a constant step size magnitude (e.g., 0.05 mm). In some aspects, for} example, the changing step size magnitude (Δs) (e.g., non-constant) can be based on a change in objective function (e.g., ΔG₁). In some aspects, for example, if the objective function (e.g., G₁) has a small gradient, the changing step size magnitude (Δs) can be increased (e.g., Δs = 0.5 mm). In some aspects, for example, as the gradient of the objective function (e.g., G₁) increases, the changing step size magnitude (Δs) can be decreased (e.g., Δs = 0.005 mm). In some aspects, the changing step size magnitude (Δs) can increase a computational efficiency of the algorithm by using a changing step size magnitude for ^^^^, rather than a fixed (constant) step size magnitude. [0118] Step 4: Recalculate the objective function (e.g., G₁) for each change in annulus inner radius ^^_^, outer radius ^^_^, or both. If the objective function (e.g., G₁) value has improved, t_{he change is accepted; otherwise, the change is accepted according to the probability ^^ =} _{exp ^− where Δ^^ is the change in objective function (e.g., ΔG1} _{) values before and} after the inner radius ^^_^ change (e.g., ±^^^^) and ^^(^^) is the simulated “temperature” as a function of iteration ^^. In some aspects, ^^ is iterated after each full cycle through all the a_{nnuli of attenuator geometry 122. In some aspects, ^^(^^) = (^^)^^^^, where ^^ and ^^^ are} hyperparameters that can determine the rate at which the system cools. [0119] Step 5: Repeat Steps 2 – 4 with a different random annulus order each time. In some aspects, for some set number of initial iterations (e.g., 200 iterations), known as a grace p_{eriod, an average Δ^^ for unfavorable transitions,} ^ത _Δ ^തത _^ ^ത _^ ^തିത _{can be tracked. Following the grace} period, the number of consecutive full iterations (i.e., full cycles through all the annuli) w_{here the objective function changes by less than ^^} ^ത _Δ ^തത _^ ^ത _^ ^തିത _{can be counted, where the} _{hyperparameter ^^ is some small positive number (i.e., 0 < ^^ ≪ 1). When this count has} reached some maximum value, Δ_^^௫, the optimization can be terminated. [0120] In some aspects, the optimization algorithm can utilize one or more hyperparameters to optimize attenuator geometry 122. For example, one or more values for each hyperparameter can be give as shown below in Table II: Table II – Optimization Algorithm Hyperparameters [0121] In some aspects, a value of ^^^^ can be about 0.01 mm to about 1 mm. In some aspects, a value of ^^ can be about 0.5 to about 0.99. In some aspects, a value of ^^_^ can be a_{bout 100 to about 500. In some aspects, a value of} ^ത _Δ ^തത _^ ^ത _^ ^തିത _{can be about 10} ^-7 _{to about 10} ^-3 _{. In} some aspects, a value of Δ_^^௫ can be about 500 to about 2,000. [0122] In some aspects, optimization can be run using an objective function (e.g., G₁) for one or more different focal spot sizes and for one or more different radiation field sizes. In some aspects, optimization can be run using an objective function (e.g., G1) for one or more different initial solutions, for example, different initial attenuator geometries 122 (e.g., collimator, modulator, flattening filter, compensator, parallel hole, pinhole, converging, diverging, or a combination thereof). For example, optimization can be run for three d_{ifferent initial solutions, all parallel hole collimators: ^^ ^ ^} _{^ = ^^^^^, ^^^ = ଶ ^^^^^, and ^^^ = ସ ^^^^^,} and a single solution can be selected from the three runs based on the solution with the most optimal objective function value. [0123] In some aspects, attenuator geometry 122 can be optimized based on an objective function. In some aspects, attenuator geometry 122 can be optimized by adjusting inner radii (e.g., inner radius (ri) 126), outer radii (e.g., outer radius (ro) 128), or both of the plurality of annuli (e.g., attenuator slices 124). In some aspects, adjusting inner radii (e.g., inner radius (ri) 126), outer radii (e.g., outer radius (ro) 128), or both of the plurality of annuli (e.g., attenuator slices 124) can include optimizing an objective function (e.g., equation 4) based on a desired radiation field size. In some aspects, optimizing the objective function can include optimizing second objective function G₂ (e.g., equation 5) configured to be intensity weighted. In some aspects, optimizing the objective function can include optimizing third objective function G₃ (e.g., equation 6) configured to be precision weighted. In some aspects, optimizing the objective function can include optimizing fourth objective function G₄ (e.g., equation 7) configured to be flatness weighted. In some aspects, optimizing the objective function can include optimizing a fifth objective function G5 (e.g., combination of objective functions G2, G3, and G4) configured to be intensity-precision weighted, precision-flatness weighted, intensity-flatness weighted, or intensity-precision- flatness weighted. [0124] In some aspects, attenuator geometry 122 can be optimized based on one or more parameters. For example, the one or more parameters can include a position of the radiation source, a focal spot size of the radiation source, a shape of the focal spot of the radiation source, a field size (e.g., emission profile), an objective function, or a combination thereof. In some aspects, attenuator geometry 122 can be optimized based on one or more positions of the radiation source (e.g., radiation source position (z₀) 138), one or more focal spot sizes of the radiation source (e.g., 0.1 mm, 0.5 mm, 1.0 mm, 2.0 mm, 5.0 mm, etc.), one or more shapes of the focal spot of the radiation source (e.g., changing the electron beam shape), one or more field sizes (e.g., emission profile), one or more objective functions (e.g., G₁, G2, G3, G4, G5), or a combination thereof. [0125] In some aspects, attenuator geometry 122 can be optimized based on one or more treatment parameters. For example, the one or more treatment parameters can include an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a heat distribution, a radiation field size, a focal spot size, a shape of the focal spot, a combination thereof, or a derivative thereof. [0126] In some aspects, one or more attenuators 120 can be manufactured based on the optimized attenuator geometry 122. In some aspects, any setting of the focal spot size, source position, and/or desired field size can be accompanied by a corresponding optimized attenuator (e.g., a single, specific attenuator). In some aspects, if any settings changed during a treatment, the manufactured attenuator can automatically change its geometry accordingly. In some aspects, the manufactured attenuator can include a stack of high- resolution, variable iris attenuators that can automatically adjust their inner radius, outer radius, or both, analogous to the attenuator model used in the optimization process. In some aspects, the manufactured attenuator can include a dynamic collimator. For example, the dynamic collimator can include a MLC having one or more adjustable leaves that can automatically adjust their inner radius. [0127] In some aspects, attenuator 120 can include a set of attenuators. In some aspects, a set of attenuator geometries (e.g., each similar to attenuator geometry 122) of the set of attenuators (e.g., each similar to attenuator 120) can be optimized based on one or more objective functions (e.g., G1, G2, G3, G4, G5). [0128] Exemplary Designing Method [0129] FIG. 2 illustrates modeling flow diagram 200 for designing an attenuator (e.g., attenuator 120 (FIG.1)), according to an exemplary aspect. It is to be appreciated that not all steps in FIG.2 are needed to perform the disclosure provided herein. Further, some of the steps may be performed simultaneously, sequentially, and/or in a different order than shown in FIG.2. Modeling flow diagram 200 shall be described with reference to FIGS.1 and 3–9. However, modeling flow diagram 200 is not limited to those example aspects. Although modeling flow diagram 200 is shown in FIG.2 as a stand-alone method, aspects of this disclosure can be used with other apparatuses, systems, and/or methods, for example, attenuator optimization system 100, attenuator 120, system 300, and/or computing system 900. In some aspects, modeling flow diagram 200 can be implemented by modeling system 310, processing system 330, manufacturing system 350, and/or dynamic attenuator system 370 of system 300 shown in FIG.3. [0130] In step 202, as shown in the example of FIGS. 1 and 3–9, a radiation field (e.g., emission profile, etc.) of a radiation source can be defined. In some aspects, the radiation field (e.g., radiation field 112 (FIG. 1)) can be a desired (e.g., unique, optimized) or deliberately designed radiation field (e.g., emission profile, etc.), for example, for a particular application and/or treatment (e.g., intraoperative radiotherapy, food sterilization, small animal irradiation, tissue irradiation, irradiation of animate and/or inanimate objects, for example, radiotherapy, sterilization, etc.). In some aspects, the radiation field (e.g., emission profile, etc.) can be a unique anisotropic three-dimensional (3D) radiation field (e.g., emission profile, etc.). In some aspects, the radiation field (e.g., emission profile, etc.) can be defined by radiation source model 312 of modeling system 310 of system 300 shown in FIG. 3, for example, a desired (e.g., unique, optimized) radiation field (e.g., emission profile, etc.) for a particular application. In some aspects, the radiation field can be defined by an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a heat distribution, a photon flux, a radiation field size, a focal spot size, a combination thereof, or a derivative thereof. [0131] In step 204, as shown in the example of FIGS.1 and 3–9, an attenuator geometry of an attenuator configured to receive the radiation field can be defined. In some aspects, the attenuator geometry (e.g., attenuator geometry 122 (FIG. 1)) can be based on one or more parameters, for example, an inner radius, a focal length, a focal spot size, a shape of the focal spot, a source-to-detector distance, a position of the radiation source, a number of attenuator slices, a symmetry of the radiation field, a symmetry of the attenuator, or a combination thereof. In some aspects, the attenuator geometry can include a three- dimensional (3D) model of the attenuator. In some aspects, the attenuator geometry (e.g., attenuator geometry 122 (FIG. 1)) can be defined by attenuator model 314 of modeling system 310 of system 300 shown in FIG.3, for example, an optimized attenuator geometry for a particular application. In some aspects, for an asymmetric attenuator, the attenuator geometry (e.g., attenuator geometry 122 (FIG. 1)) can be defined by geometry (3D) subsystem 316 of modeling system 310 of system 300 shown in FIG.3. [0132] In step 206, as shown in the example of FIGS. 1 and 3–9, an optimization of the attenuator geometry can be performed based on one or more objective functions. In some aspects, the one or more objective functions can be based at least in part on a radiation transport (e.g., radiation transport 130 (FIG.1)) of the radiation field (e.g., radiation field 112 (FIG.1)) through the attenuator geometry (e.g., attenuator geometry 122 (FIG.1)). In some aspects, the radiation transport (e.g., radiation transport 130 (FIG.1)) can be defined by radiation transport model 318 of modeling system 310 of system 300 shown in FIG.3. In some aspects, the one or more objective functions (e.g., G1, G2, G3, G4, G5) can be defined by objective functions 320 of modeling system 310 of system 300 shown in FIG. 3. In some aspects, the optimization can be performed by optimization subsystem 322 of system 300 shown in FIG. 3, for example, an optimization algorithm (e.g., simulated annealing). [0133] In some aspects, step 206 can include using an optimization algorithm to optimize the attenuator geometry based on the one or more objective functions. For example, the optimization algorithm can include simulated annealing, metaheuristic techniques, global optimization, model-based parameter adaptation, machine learning (supervised, unsupervised), neural networks, an artificial intelligence (AI) module (e.g., trained using analytics of optimized attenuators), a combination thereof, or any other suitable algorithms or objective functions to optimize attenuator geometry 122 based on radiation transport 130. [0134] In step 208, optionally, as shown in the example of FIGS. 1 and 3–9, the optimization of the attenuator geometry, based on one or more objective functions, can be based on one or more treatment parameters. In some aspects, the one or more treatment parameters can include an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a heat distribution, a photon flux, a radiation field size, a focal spot size, a shape of the focal spot, an intensity weighted flux, a precision weighted flux, a flatness weighted flux, an intensity-precision weighted flux, a precision-flatness weighted flux, an intensity-flatness weighted flux, an intensity-precision-flatness weighted flux, a combination thereof, or a derivative thereof. [0135] In step 210, optionally, as shown in the example of FIGS.1 and 3–9, an attenuator (e.g., attenuator 120 (FIG. 1)) can be manufactured based on the optimized attenuator geometry after the optimization determined in step 206. In some aspects, the optimized attenuator geometry can be manufactured by manufacturing system 350 of system 300 shown in FIG.3, for example, attenuator 120 shown in FIG.1 can be manufactured based on the optimized attenuator geometry. In some aspects, the optimized attenuator geometry can be manufactured by manufacturing system 350 of system 300 shown in FIG. 3, for example, collimator 121a shown in FIG.1A can be manufactured based on the optimized attenuator geometry. In some aspects, the optimized attenuator geometry can be manufactured by manufacturing system 350 of system 300 shown in FIG.3, for example, modulator 121b shown in FIG.1B can be manufactured based on the optimized attenuator geometry. [0136] In some aspects, step 210 can include depositing one or more materials to manufacture the optimized attenuator geometry. For example, depositing can include epitaxy, physical vapor deposition (PVD), electron-beam PVD (EBPVD), sputter deposition, electrosputtering, chemical vapor deposition (CVD), plasma-enhanced CVD (PECVD), atomic layer deposition (ALD), powder bed deposition, or a combination thereof. In some aspects, depositing can be performed by manufacturing system 350 of system 300 shown in FIG.3. In some aspects, the materials of attenuator 120 can include lead (Pb), tungsten (W), copper (Cu), tantalum (Ta), aluminum (Al), brass, glass, plastic, or a combination thereof. [0137] In some aspects, step 210 can include manufacturing with a computer controlled manufacturing system. For example, the computer controlled manufacturing system can include a computer numerically controlled (CNC) machine, an additive manufacturing machine, a subtractive manufacturing machine, a drill, a lathe, a mill, a grinder, a router, a 3D printer, a lithographic machine, a photolithographic machine, an inkjet machine, a sintering machine, a fused deposition machine, or a combination thereof. In some aspects, the computer controlled manufacturing system can be part of manufacturing system 350 of system 300 shown in FIG.3. [0138] In step 212, optionally, as shown in the example of FIGS. 1 and 3–9, a dynamic attenuator (e.g., dynamic attenuator system 370 (FIG.3)) can be configured based on the optimized attenuator geometry after the optimization determined in step 206. In some aspects, the optimized attenuator geometry can be used to configure (e.g., adjust, arrange, shape, etc.) dynamic attenuator system 370 of system 300 shown in FIG.3. [0139] In some aspects, step 212 can include sending one or more control data signals to the dynamic attenuator to configure one or more adjustable elements (e.g., leaves) of the dynamic attenuator based on the optimized attenuator geometry. In some aspects, step 212 can include dynamically adjusting the dynamic attenuator over time based on one or more optimized attenuator geometries. In some aspects, step 212 can include dynamically optimizing the attenuator geometry of the dynamic attenuator based on a change of one or more parameters of the radiation field (e.g., source position, source energy, etc.). [0140] Exemplary Designing and Manufacturing System [0141] FIG. 3 illustrates system 300 for designing and manufacturing an attenuator, according to an exemplary aspect. System 300 can be configured to determine an optimized attenuator geometry based on one or more objective functions, process the optimized attenuator geometry into manufacturing instructions, and manufacture an attenuator (e.g., attenuator 120 (FIG.1)) based on the optimized attenuator geometry. System 300 can be further configured to determine an optimized attenuator geometry based on one or more objective functions, process the optimized attenuator geometry into configuring instructions, and configure a dynamic attenuator (e.g., dynamic attenuator system 370 (FIG. 3)) based on the optimized attenuator geometry. Although system 300 is shown in FIG.3 as a stand-alone apparatus and/or system, aspects of this disclosure can be used with other apparatuses, systems, and/or methods, for example, attenuator optimization system 100, modeling flow diagram 200, and/or computing system 900. [0142] As shown in FIG. 3, system 300 can include modeling system 310, processing system 330, manufacturing system 350, and dynamic attenuator system 370. Modeling system 310 can be configured to optimize (e.g., via an optimization algorithm) an attenuator geometry (e.g., attenuator geometry 122 (FIG.1)) based on one or more objective functions (e.g., G₁, flux model) characterizing a radiation transport (e.g., radiation transport 130 (FIG. 1)) of a radiation field (e.g., radiation field 112 (FIG.1)) through the attenuator geometry. As shown in FIG. 3, modeling system 310 can include radiation source model 312, attenuator model 314, geometry (3D) subsystem 316, radiation transport model 318, objective functions 320, and optimization subsystem 322. Further, modeling system 310 can be coupled (e.g., electronically, etc.) to processing system 330 in order to send and receive data (e.g., 2D/3D optimized model data) between modeling system 310 and processing system 330. [0143] Radiation source model 312 can be configured to define a radiation field of a radiation source. Radiation source model 312 can be further configured to define a desired observable field (e.g., 2D or 3D). In some aspects, radiation source model 312 can receive a desired observable field (e.g., emission profile, etc.) from a user via processing system 330. In some aspects, radiation source model 312 can include an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a heat distribution, a photon flux, a radiation field size, a focal spot size, a combination thereof, or a derivative thereof. In some aspects, radiation source model 312 can include a library or database of different observable fields (e.g., emission profiles, etc.) that can be selected (or modified) by a user or an optimization algorithm (e.g., optimization subsystem 322) to define a desired observable field (e.g., radiation field). [0144] Attenuator model 314 can be configured to define an attenuator geometry of an attenuator configured to receive the radiation field. In some aspects, attenuator model 314 can receive selected attenuator geometries (e.g., collimator, modulator, flattening filter, compensator, parallel hole, pinhole, converging, diverging, symmetric, asymmetric, a combination thereof, etc.) and/or attenuator materials from a user via processing system 330. In some aspects, attenuator model 314 can include a library or database of different attenuator geometries and/or attenuator materials that can be selected (or modified) by a user or an optimization algorithm (e.g., optimization subsystem 322) to determine an optimal attenuator geometry, for example, for a desired radiation field size. [0145] Geometry (3D) subsystem 316 can be configured to determine an optimized attenuator geometry (e.g., in 3D). Geometry (3D) subsystem 316 can be further configured to determine an optimized attenuator geometry for an asymmetric attenuator. In some aspects, geometry (3D) subsystem 316 can receive a selected geometry (3D) for the attenuator from a user (e.g., collimator, modulator, flattening filter, compensator, parallel hole, pinhole, converging, diverging, asymmetric, a combination thereof, etc.) via processing system 330. In some aspects, geometry (3D) subsystem 316 can include a library or database of different geometries (e.g., cylindrical, spherical, orthotope, stacked slices, etc.) that can be selected (or modified) by a user or an optimization algorithm (e.g., optimization subsystem 322) to determine an optimized attenuator geometry. [0146] Radiation transport model 318 can be configured to model the transport (e.g., photon flux) of the radiation field through the attenuator geometry. Radiation transport model 318 can be further configured to combine radiation source model 312 and attenuator model 314 to determine an optimized attenuator geometry based on the radiation transport of the radiation field through the attenuator geometry. Radiation transport model 318 can be further configured to define a desired observable field (e.g., 2D or 3D). In some aspects, radiation transport model 318 can receive a desired observable field (e.g., emission profile) from a user via processing system 330. In some aspects, radiation transport model 318 can include an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a heat distribution, a photon flux, a radiation field size, a focal spot size, a combination thereof, or a derivative thereof. In some aspects, radiation transport model 318 (e.g., flux model) can be part of one or more objective functions 320 to determine an optimized attenuator geometry, for example, by an optimization algorithm (e.g., optimization subsystem 322). [0147] Objective functions 320 can be configured to optimize an attenuator geometry based on one or more factors. Objective functions 320 can be further configured to be a function of radiation transport model 318 to determine an optimized attenuator geometry. Objective functions 320 can be further configured to modulate radiation transport model 318 (e.g., Ψ⁽^^_ௗ^௧ ⁾) towards one or more weighted profiles, for example, intensity weighted (e.g., G₂), precision weighted (e.g., G₃), flatness weighted (e.g., G₄), or a combination thereof (e.g., intensity-precision weighted, precision-flatness weighted, intensity-flatness weighted, intensity-precision-flatness weighted). In some aspects, objective functions 320 can include a library or database of different objective functions (e.g., weighted profiles, etc.) that can be selected (or modified) by a user or an optimization algorithm (e.g., optimization subsystem 322) to determine an optimized attenuator geometry based on the one or more objective functions 320. [0148] Optimization subsystem 322 can be configured to optimize the attenuator geometry based on the one or more objective functions 320. In some aspects, optimization subsystem 322 can perform an optimization of the attenuator geometry based on custom inputs or parameters (e.g., inner radii, outer radii, thickness, focal length, symmetry, materials, etc.) to model an optimal attenuator geometry (e.g., attenuator geometry 122 (FIG.1)) capable of producing a desired observable field (e.g., emission profile). [0149] In some aspects, optimization subsystem 322 can include an optimization algorithm to perform the optimization. For example, the optimization algorithm can include simulated annealing. In some aspects, the radiation transport model can be based on a non-stochastic process (e.g., non-random, deterministic). In some aspects, the optimization algorithm is not based on Monte Carlo calculations. In some aspects, the optimization algorithm can utilize simulated annealing and one or more hyperparameters to determine an optimized attenuator geometry. In some aspects, the optimized model of the attenuator geometry determined by optimization subsystem 322 can be transferred to processing system 330 for further processing (e.g., manufacturing control data). [0150] Processing system 330 can be configured to process the optimized attenuator geometry and convert the optimized model into a set of manufacturing instructions and/or steps. Processing system 330 can be further configured to process the optimized attenuator geometry and convert the optimized model into a set of configuring instructions and/or steps. As shown in FIG.3, processing system 330 can be coupled to modeling system 310, manufacturing system 350, and dynamic attenuator system 370, and include I/O (input/output) subsystem 332, UI (user interface) subsystem 334, construction subsystem 336, conversion subsystem 338, and configuration subsystem 340. Further, processing system 330 can be coupled (e.g., electronically, etc.) to modeling system 310 in order to send and receive data (e.g., 2D/3D input data) between processing system 330 and modeling system 310, and processing system 330 can be coupled (e.g., electronically, etc.) to manufacturing system 350 in order to send and receive data (e.g., converted model data instructions) between processing system 330 and manufacturing system 350. Further, processing system 330 can be coupled (e.g., electronically, etc.) to modeling system 310 in order to send and receive data (e.g., 2D/3D input data) between processing system 330 and modeling system 310, and processing system 330 can be coupled (e.g., electronically, etc.) to dynamic attenuator system 370 in order to send and receive data (e.g., configuration data instructions) between processing system 330 and dynamic attenuator system 370. [0151] I/O subsystem 332 can be configured to receive data relevant to optimize the model (e.g., desired emission profile, attenuator geometry parameters, attenuator symmetry, etc.). In some aspects, a desired (unique) observable field (e.g., emission profile, photon flux, etc.) can be received by I/O subsystem 332. In some aspects, an initial attenuator geometry (e.g., collimator, modulator, flattening filter, compensator, parallel hole, pinhole, converging, diverging, asymmetric, a combination thereof, etc.) can be received by I/O subsystem 332. In some aspects, a user may transfer a 2D or 3D data set to processing system 330, for example, via a storage medium, wirelessly, Internet, data packet, etc. [0152] UI subsystem 334 can be configured to provide one or more user interfaces that allow a user to interact with processing system 330 and/or modeling system 310. In some aspects, UI subsystem 334 can provide a user interface for displaying a 3D model (e.g., desired emission profile, optimized attenuator geometry, etc.), for example, based on different treatment plan types or applications, and prompting the user to make a selection. In some aspects, UI subsystem 334 can receive user input via one or more input devices, for example, a keyboard, mouse, touch-screen, or any other suitable input device. In some aspects, UI subsystem 334 can display and manipulate a 3D optimized model of an attenuator geometry received from modeling system 310. [0153] Construction subsystem 336 can be configured to construct 3D output data sets from the 3D optimized model of the attenuator geometry. In some aspects, the 3D output data set can include volumetric data (e.g., voxels, etc.) representing a geometry and material distribution of the optimized attenuator (e.g., attenuator geometry 122 (FIG.1)). [0154] Conversion subsystem 338 can be configured to convert the 3D output data sets into a set of manufacturing instructions and/or steps (e.g., control data) for manufacturing system 350. In some aspects, manufacturing system 350 can use control data from processing system 330 to manufacture optimized attenuator geometry in three-dimensions (3D). In some aspects, I/O subsystem 332 can transmit control data to manufacturing system 350, for example, via a wired or wireless connection, after conversion subsystem 338 has converted the 3D output data sets to control data. [0155] Configuration subsystem 340 can be configured to convert the 3D output data sets into a set of configuring instructions and/or steps (e.g., control data) for dynamic attenuator system 370. In some aspects, dynamic attenuator system 370 can use control data from processing system 330 to configure (e.g., adjust, arrange, shape, etc.) dynamic attenuator system 370 based on the optimized attenuator geometry in three-dimensions (3D). In some aspects, I/O subsystem 332 can transmit control data to dynamic attenuator system 370, for example, via a wired or wireless connection, after conversion subsystem 338 has converted the 3D output data sets to control data. [0156] In some aspects, configuration subsystem 340 can be configured to configure (e.g., adjust, arrange, shape, etc.) dynamic attenuator system 370 based on the optimized attenuator geometry. In some aspects, configuration subsystem 340 can send one or more control data signals to dynamic attenuator system 370 to configure one or more adjustable elements (e.g., leaves) of dynamic attenuator system 370 based on the optimized attenuator geometry. In some aspects, configuration subsystem 340 can dynamically adjust dynamic attenuator system 370 over time. In some aspects, for example, configuration subsystem 340 can dynamically adjust dynamic attenuator system 370 over time based on one or more optimized attenuator geometries. In some aspects, system 300 can dynamically optimize the attenuator geometry of dynamic attenuator system 370. In some aspects, for example, system 300 can dynamically optimize the attenuator geometry of dynamic attenuator system 370 based on a change of one or more parameters of the radiation field (e.g., source position, source energy, etc.). [0157] Manufacturing system 350 can be configured to manufacture an attenuator (e.g., attenuator 120 (FIG. 1)) with the optimized attenuator geometry that is capable of producing the desired observable field (e.g., emission profile, photon flux, etc.). As shown in FIG.3, manufacturing system 350 can be coupled (e.g., electronically, etc.) to processing system 330 in order to send and receive data (e.g., manufacturing instructions) between manufacturing system 350 and processing system 330. [0158] In some aspects, manufacturing system 350 can include depositing one or more materials to form the attenuator. For example, depositing can include epitaxy, PVD, EBPVD, sputter deposition, electrosputtering, CVD, PECVD, ALD, powder bed deposition, or a combination thereof. In some aspects, the materials of attenuator 120 can include lead (Pb), tungsten (W), copper (Cu), tantalum (Ta), aluminum (Al), brass, glass, plastic, or a combination thereof. In some aspects, manufacturing system 350 can include a computer controlled manufacturing system. For example, the computer controlled manufacturing system can include a CNC machine, an additive manufacturing machine, a subtractive manufacturing machine, a drill, a lathe, a mill, a grinder, a router, a 3D printer, a lithographic machine, a photolithographic machine, an inkjet machine, a sintering machine, a fused deposition machine, or a combination thereof. In some aspects, the computer controlled manufacturing system (e.g., lithographic machine, 3D printer, etc.) of manufacturing system 350 can form the optimized attenuator geometry with high accuracy and precision (e.g., 1 mm spatial resolution, 100 μm spatial resolution, 10 μm spatial resolution, 1 μm spatial resolution, 100 nm spatial resolution, 10 nm spatial resolution, 1 nm spatial resolution, sub-1 nm spatial resolution, etc.). [0159] Dynamic attenuator system 370 can be configured to configure (e.g., adjust, arrange, shape, etc.) a dynamic attenuator with the optimized attenuator geometry to produce a desired observable field (e.g., emission profile, photon flux, etc.). As shown in FIG. 3, dynamic attenuator system 370 can be coupled (e.g., electronically, etc.) to processing system 330 in order to send and receive data (e.g., configuring instructions) between dynamic attenuator system 370 and processing system 330 (e.g., via configuration subsystem 340). In some aspects, dynamic attenuator system 370 can include a dynamic collimator. For example, the dynamic collimator can include a MLC. In some aspects, dynamic attenuator system 370 can include one or more adjustable elements configured to form the optimized attenuator geometry. [0160] Exemplary Model Performance [0161] FIGS. 4 and 5 illustrate exemplary model performance of attenuator optimization system 100 shown in FIG.1, according to various exemplary aspects. [0162] FIG. 4 illustrates flux comparison 400 for different collimator designs 410, 420, 430 determined by attenuator optimization system 100 shown in FIG. 1, according to an exemplary aspect. Flux comparison 400 shows a plot of flux 402 (e.g., normalized to the maximum) as a function of distance (mm) 404 along the x-axis of the detector plane 134 (e.g., +^^_ௗ^௧ axis) for a first collimator 410 (e.g., parallel hole with 0.5 cm diameter), a second collimator 420 (e.g., parallel hole with 1.0 cm diameter), and a third collimator 430 (e.g., thin lead (Pb) attenuator with no central hole). Each set of curves represents the photon flux at the detector plane 134, normalized to the maximum flux of each respective curve, as a function of position along the +^^_ௗ^௧ axis for a large focal spot size (e.g., about 11 mm). As shown in FIG. 4, the performance of the radiation transport model (e.g., equation 3) is demonstrated for three separate collimator geometry scenarios, first collimator 410, second collimator 420, and third collimator 430 (shown as solid lines), and compared to the Monte Carlo calculated flux (shown as crosses). [0163] FIG.5 illustrates optimization progress 500 for the primary objective function G₁ (e.g., equation 3) determined by attenuator optimization system 100 shown in FIG. 1, according to an exemplary aspect. Optimization progress 500 shows a plot of primary objective function G₁502 (e.g., in units of flux (mm^-2)) as a function of iteration 504 for an optimization progression 510. Each iteration 504 describes the number of cycles through all collimator slices. As shown in FIG.5, primary objective function G1502 is maximized during optimization and optimization progression 510 trends upward and plateaus to a stable local maximum (e.g., around 1,100 iterations). Optimization progress 500 was measured for a small focal spot size (e.g., about 0.4 mm), rcol = 5 mm, z0 = 200 mm, c_{ollimator thickness of 1 cm, and an initial solution set to ^^ ^} _{^ = ସ ^^^^^. Each iteration 504} involves 100 collimator adjustments since there are 100 collimator slices in the 1 cm thick collimator. The solution at termination was the most optimal solution found. In some aspects, an optimization state can be saved and rerun with an adjustment to one or more hyperparameters (e.g., lower annealing temperature ^^_^) to investigate a potentially deeper local optimum. [0164] Exemplary Optimized Collimator Geometries [0165] FIGS. 6A–6B, 7A–7B, and 8A–8C illustrate exemplary optimized collimator geometries, according to various exemplary aspects. [0166] FIGS.6A and 6B illustrate optimized collimator geometries 600A and resultant flux 600B, respectively, for three different radiation source positions determined by attenuator optimization system 100 shown in FIG. 1, according to an exemplary aspect. Optimized collimator geometries 600A shows a plot of collimator position (zi) (mm) 602A as a function of radial distance (mm) 604A from the longitudinal axis (e.g., symmetry axis 102) of the collimator for a first optimized collimator 610 (e.g., z0 = 70 mm), a second optimized collimator 620 (e.g., z0 = 120 mm), and a third optimized collimator 630 (e.g., z0 = 200 mm). Optimized collimator geometries 600A shows longitudinal cross-sections of the optimized collimators 610, 620, 630 and were determined for a small focal spot size (e.g., about 0.4 mm), rcol = 5 mm, three different source positions: z0 = 70 mm, 120 mm, and 200 mm, and collimator thickness of 1 cm. [0167] Resultant flux 600B shows a plot of flux 602B (e.g., normalized to the maximum of the primary objective function G1) as a function of distance (mm) 604B along the x-axis of the detector plane 134 (e.g., ^^_ௗ^௧ axis) for first optimized collimator 610 (e.g., z₀ = 70 mm), second optimized collimator 620 (e.g., z₀ = 120 mm), and third optimized collimator 630 (e.g., z0 = 200 mm). Each set of curves represents the resultant photon flux at the detector plane 134, normalized to the maximum flux of all the source positions z0 for a small focal spot size (e.g., about 0.4 mm). [0168] FIGS.7A and 7B illustrate optimized collimator geometries 700A and resultant flux 700B, respectively, for three different radiation source positions determined by attenuator optimization system 100 shown in FIG. 1, according to an exemplary aspect. Optimized collimator geometries 700A shows a plot of collimator position (z_i) (mm) 702A as a function of radial distance (mm) 704A from the longitudinal axis (e.g., symmetry axis 102) of the collimator for a first optimized collimator 710 (e.g., z₀ = 70 mm), a second optimized collimator 720 (e.g., z₀ = 120 mm), and a third optimized collimator 730 (e.g., z₀ = 200 mm). Optimized collimator geometries 700A shows longitudinal cross-sections of the optimized collimators 710, 720, 730 and were determined for a medium focal spot size (e.g., about 6.2 mm), r_col = 0.5 mm, three different source positions: z₀ = 70 mm, 120 mm, and 200 mm, and collimator thickness of 1 cm. [0169] Resultant flux 700B shows a plot of flux 702B (e.g., normalized to the maximum of the primary objective function G₁) as a function of distance (mm) 704B along the x-axis of the detector plane 134 (e.g., ^^_ௗ^௧ axis) for first optimized collimator 710 (e.g., z₀ = 70 mm), second optimized collimator 720 (e.g., z₀ = 120 mm), and third optimized collimator 730 (e.g., z0 = 200 mm). Each set of curves represents the resultant photon flux at the detector plane 134, normalized to the maximum flux of all the source positions z0 for a medium focal spot size (e.g., about 6.2 mm). [0170] FIGS. 8A–8C illustrate resultant fluxes 800A, 800B, 800C for different objective functions G2 (intensity weighted), G3 (precision weighted), and G4 (flatness weighted), respectively, for three different radiation source positions determined by attenuator optimization system 100 shown in FIG. 1, according to various exemplary aspects. Resultant fluxes 800A, 800B, 800C show a plot of flux 802 (e.g., normalized to the maximum of the primary objective function G1) as a function of distance (mm) 804A, 804B, 804C along the x-axis of the detector plane 134 (e.g., ^^_ௗ^௧ axis) for first optimized collimator 710 (e.g., z₀ = 70 mm), second optimized collimator 720 (e.g., z₀ = 120 mm), and third optimized collimator 730 (e.g., z0 = 200 mm), respectively. Resultant fluxes 800A, 800B, 800C were determined for a medium focal spot size (e.g., about 6.2 mm), r_col = 5 mm, three different source positions: z0 = 70 mm, 120 mm, and 200 mm, and collimator thickness of 1 cm. [0171] As shown in FIG. 8A, resultant flux 800A is intensity weighted based on optimization of collimator geometry with second objective function G2 (e.g., equation 5). As shown in FIG.8B, resultant flux 800B is precision weighted based on optimization of collimator geometry with third objective function G₃ (e.g., equation 6). As shown in FIG. 8C, resultant flux 800C is flatness weighted based on optimization of collimator geometry with fourth objective function G4 (e.g., equation 7). [0172] Exemplary Computing System [0173] FIG. 9 illustrates computing system 900, according to an exemplary aspect. Computing system 900 can be configured to implement one or more of the above described aspects, or portions thereof, as computer-readable code. For example, the methods, processes, flow diagrams, and/or systems described herein can be implemented by computing system 900. Although computing system 900 is shown in FIG. 9 as a stand- alone apparatus and/or system, aspects of this disclosure can be used with other apparatuses, systems, and/or methods, for example, attenuator optimization system 100, modeling flow diagram 200, and/or system 300. [0174] Various aspects of the disclosure can be implemented using one or more computing devices, such as computing system 900 shown in FIG.9, by software, firmware, hardware, or a combination thereof. Various aspects are described herein in terms of exemplary computing system 900. One or more computing systems 900 can be used, for example, to implement any of the aspects described herein, as well as combinations and sub- combinations thereof. Cloud implementations can include one or more of exemplary computing system 900 operating locally or distributed across one or more server sites. [0175] As shown in FIG. 9, computing system 900 can include processor 902, controller 904, main memory 906, communication infrastructure 908 (e.g., a bus), user input/output (I/O) interface(s) 910, user I/O device(s) 912, secondary memory 920, communications interface 934, and remote device(s) 938. Computing system 900 can include one or more processors (also called central processing units, or CPUs), such as processor 902. Processor 902 can be a special purpose processor or a general purpose processor. Processor 902 can be connected to communication infrastructure 908 (e.g., a bus, a network). Processor 902 can include a CPU, a graphics processing unit (GPU), an accelerated processing unit (APU), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a digital signal processor (DSP), a microprocessor, other similar general purpose or specialized processing units, or a combination thereof. In some aspects, processor 902 can include a GPU that is a specialized electronic circuit designed to process mathematically intensive applications. For example, the GPU can have a parallel structure that is efficient for parallel processing of large blocks of data, such as mathematically intensive data common to computer graphics applications, images, videos, etc. [0176] Computing system 900 can also include a controller 904. Controller 904 can include functionalities to control data access to main memory 906 and secondary memory 920. In some aspects, controller 904 can be external to processor 902, for example, as shown in FIG. 9. In some aspects, controller 904 can be directly part of processor 902. Controller 904 can include a microcontroller or microcontroller unit (MCU). [0177] Computing system 900 can also include a main memory 906. Main memory 906 can include volatile memory (e.g., random-access memory (RAM)) and/or non-volatile memory (e.g., read-only memory (ROM), non-volatile RAM (NVRAM), flash). Main memory 906 can include one or more levels of cache and be divided into channels. Main memory 906 can have stored therein control logic (e.g., computer software) and/or data. [0178] Computing system 900 can also include user I/O interface(s) 910 coupled to user I/O device(s) 912. Computing system 900 can also include user I/O device(s) 912, such as monitors, keyboards, pointing devices, etc., which can communicate with communication infrastructure 908 through user I/O interface(s) 910. [0179] Computing system 900 can also include one or more secondary storage devices or memory 920. Secondary memory 920 can include, for example, a hard disk drive 922 and/or a removable storage device or drive 924. Removable storage drive 924 can include a floppy disk drive, a magnetic tape drive, a compact disk drive, an optical storage device, a tape backup device, a flash memory, and/or any other storage device/drive. [0180] Removable storage drive 924 can interact with a first removable storage unit 926. First removable storage unit 926 can include a computer usable or readable storage device having stored thereon control logic (e.g., computer software) and/or data. First removable storage unit 926 can be a floppy disk, a magnetic tape drive, a compact disk drive, a DVD, an optical storage device, a tape backup device, a flash memory, and/or any other computer data storage device. Removable storage drive 924 can read from and/or write to first removable storage unit 926. [0181] Secondary memory 920 can include other means, devices, components, instrumentalities, or other approaches for allowing computer programs, other instructions, and/or data to be accessed by computing system 900. Such means, devices, components, instrumentalities, or other approaches can include, for example, a second removable storage unit 932 and an interface 930. Examples of the second removable storage unit 932 and the interface 930 can include a program cartridge and cartridge interface (e.g., such as that found in video game devices), a removable memory chip (e.g., such as an EPROM or PROM) and associated socket, a memory stick and USB port, a memory card and associated memory card slot, and/or any other removable storage unit and associated interface that allow software and/or data to be transferred from the second removable storage unit 932 to computing system 900. [0182] Computing system 900 can further include a communications or network interface 934. Communications interface 934 can enable computing system 900 to communicate and interact with any combination of external devices, external networks, external entities, etc. (referenced individually and collectively by reference number 938). For example, communications interface 934 can allow computing system 900 to communicate with external or remote devices 938 over communications path 936, which can be wired, wireless, or a combination thereof, and which can include any combination of LANs, WANs, the Internet, etc. Control logic and/or data can be transmitted to and from computing system 900 via communications path 936. Communications interface 934 can include a modem, a communication port, a PCMCIA slot and card, or the like. Software and/or data can be transferred via communications interface 934 in the form of signals, which can be electronic, electromagnetic, optical, or other signals capable of being transmitted and received by communications interface 934. The signals can be provided to communications interface 934 via communications path 936 (e.g., wired, wireless, etc.). [0183] Computing system 900 can also include any computing device, for example, a laptop or notebook computer, a desktop workstation, a netbook, a tablet, a smart phone, a smart watch or other wearable device, a personal digital assistant (PDA), an Internet-of- Things (IoT) device, an embedded system, or any combination thereof. [0184] Computing system 900 can include a user device or server, accessing or hosting any applications and/or data through any delivery paradigm, including, but not limited to, remote or distributed cloud computing solutions; local or on-premises software (“on- premise” cloud-based solutions); “as a service” models (e.g., content as a service (CaaS), digital content as a service (DCaaS), software as a service (SaaS), managed software as a service (MSaaS), platform as a service (PaaS), desktop as a service (DaaS), framework as a service (FaaS), backend as a service (BaaS), mobile backend as a service (MBaaS), infrastructure as a service (IaaS), etc.); and/or a hybrid model including any combination of the foregoing examples or other services or delivery paradigms. [0185] Any applicable data structures, file formats, and schemas in computing system 900 can be derived from standard programming languages, including, but not limited to, C, C++ (e.g., Geant4/TOPAS subroutines), Python, Perl, JavaScript Object Notation (JSON), Extensible Markup Language (XML), Yet Another Markup Language (YAML), Extensible Hypertext Markup Language (XHTML), Wireless Markup Language (WML), MessagePack, XML Customer Interface Language (XUL), or any other functionally similar representations alone or in combination. Alternatively, proprietary data structures, formats or schemas can be used, either exclusively or in combination with known or open standards. [0186] In some aspects, a tangible, non-transitory apparatus or article of manufacture comprising a tangible, non-transitory computer useable or readable medium having control logic (software) stored thereon can also be referred to herein as a computer program product or program storage device. This can include, but is not limited to, computing system 900, main memory 906, secondary memory 920, first removable storage unit 926, and second removable storage unit 932, as well as tangible articles of manufacture embodying any combination of the foregoing. Such control logic, when executed by one or more data processing devices (e.g., such as computing system 900), can cause such data processing devices to operate as described herein. [0187] Based on the teachings contained in this disclosure, it will be apparent to persons skilled in the relevant art(s) how to make and use aspects of this disclosure using data processing devices, computing systems, and/or computing architectures other than those described herein (e.g., shown in FIG. 9). In particular, aspects can operate with software, hardware, and/or operating system implementations other than those described herein. [0188] It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by those skilled in relevant art(s) in light of the teachings herein. [0189] The above examples are illustrative, but not limiting, of the aspects of this disclosure. Other suitable modifications and adaptations of the variety of conditions and parameters normally encountered in the field, and which would be apparent to those skilled in the relevant art(s), are within the spirit and scope of the disclosure. [0190] While specific aspects have been described above, it will be appreciated that the aspects can be practiced otherwise than as described. The description is not intended to limit the scope of the claims. [0191] It is to be appreciated that the Detailed Description section, and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections may set forth one or more but not all exemplary aspects as contemplated by the inventor(s), and thus, are not intended to limit the aspects and the appended claims in any way. [0192] The aspects have been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. [0193] The foregoing description of the specific aspects will so fully reveal the general nature of the aspects that others can, by applying knowledge within the skill of the art, readily modify and/or adapt for various applications such specific aspects, without undue experimentation, without departing from the general concept of the aspects. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed aspects, based on the teaching and guidance presented herein. [0194] The breadth and scope of the aspects should not be limited by any of the above- described exemplary aspects, but should be defined only in accordance with the following claims and their equivalents. [0195] The present invention may also be described in accordance with the following clauses: [0196] Clause 1. A method of designing a collimator for shaping a radiation field, the method comprising: defining a radiation field of a radiation source; defining a collimator geometry of a collimator configured to receive the radiation field; and optimizing the collimator geometry based on an objective function, wherein the objective function is based on a radiation transport of the radiation field through the collimator geometry, and wherein the radiation transport is based on a non-stochastic process. [0197] Clause 2. The method of clause 1, wherein optimizing the collimator geometry is based on simulated annealing. [0198] Clause 3. The method of any one of clauses 1 to 2, wherein optimizing the collimator geometry is not based on iterative Monte Carlo calculations. [0199] Clause 4. The method of any one of clauses 1 to 3, wherein the radiation source comprises a photon radiation source. [0200] Clause 5. The method of clause 4, wherein the photon radiation source comprises an X-ray source or a Gamma-ray source. [0201] Clause 6. The method of any one of clauses 1 to 5, wherein defining the radiation field comprises defining a phase space model based on a differential flux probability density. [0202] Clause 7. The method of any one of clauses 1 to 6, wherein the collimator geometry is symmetric. [0203] Clause 8. The method of clause 7, wherein the collimator geometry is cylindrically symmetric and comprises a plurality of annuli stacked along a longitudinal direction of the radiation field. [0204] Clause 9. The method of clause 8, wherein the plurality of annuli comprises at least six annuli. [0205] Clause 10. The method of clause 8, wherein optimizing the collimator geometry comprises adjusting inner radii of the plurality of annuli. [0206] Clause 11. The method of clause 10, wherein adjusting inner radii of the plurality of annuli comprises optimizing the objective function based on a desired radiation field size. [0207] Clause 12. The method of clause 11, wherein optimizing the objective function comprises optimizing a first objective function configured to be intensity-weighted. [0208] Clause 13. The method of clause 11, wherein optimizing the objective function comprises optimizing a second objective function configured to be precision-weighted. [0209] Clause 14. The method of clause 11, wherein optimizing the objective function comprises optimizing a third objective function configured to be flatness-weighted. [0210] Clause 15. The method of clause 11, wherein optimizing the objective function comprises optimizing a fourth objective function configured to be intensity-precision weighted, precision-flatness weighted, intensity-flatness weighted, or intensity-precision- flatness weighted. [0211] Clause 16. The method of any one of clauses 1 to 6, wherein the collimator geometry is asymmetric. [0212] Clause 17. The method of clause 16, wherein the collimator geometry comprises a plurality of segments each defined by a set of inner radii and a set of azimuthal ranges. [0213] Clause 18. The method of any one of clauses 1 to 17, further comprising manufacturing the collimator based on the optimized collimator geometry. [0214] Clause 19. The method of any one of clauses 1 to 18, further comprising configuring a dynamic collimator based on the optimized collimator geometry. [0215] Clause 20. The method of clause 19, wherein the dynamic collimator comprises one or more adjustable elements configured to form the optimized collimator geometry. [0216] Clause 21. A system for designing the geometry of a collimator, the system comprising: a computing device; and a processor in communication with the computing device, wherein the processor is coupled to a memory storing instructions that when executed cause the processor to perform operations comprising: defining a radiation field of a radiation source, defining a collimator geometry of a collimator configured to receive the radiation field, and optimizing the collimator geometry based on an objective function, wherein the objective function is based on a radiation transport of the radiation field through the collimator geometry, and wherein the radiation transport is based on a non-stochastic process. [0217] Clause 22. The system of clause 21, wherein optimizing the collimator geometry comprises optimizing the objective function based on one or more treatment parameters. [0218] Clause 23. The system of any one of clauses 21 to 22, wherein the one or more treatment parameters comprises an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a heat distribution, a photon flux, a radiation field size, a focal spot size, a shape of the focal spot, a combination thereof, or a derivative thereof. [0219] Clause 24. The system of any one of clauses 21 to 23, further comprising a manufacturing system configured to manufacture the collimator based on the optimized collimator geometry. [0220] Clause 25. The system of any one of clauses 21 to 24, wherein the collimator comprises a multileaf collimator (MLC) having one or more adjustable elements. [0221] Clause 26. The system of clause 25, wherein the one or more adjustable elements each comprises a multileaf. [0222] Clause 27. The system of clause 25, wherein the one or more adjustable elements each comprises one or more stacks of adjustable elements. [0223] Clause 28. The system of any one of clauses 21 to 27, wherein: the collimator comprises a set of collimators, and optimizing the collimator geometry comprises optimizing a set of collimator geometries of the set of collimators based on one or more objective functions. [0224] Clause 29. The system of any one of clauses 21 to 28, further comprising a configuration system configured to configure a dynamic collimator based on the optimized collimator geometry. [0225] Clause 30. The system of clause 29, wherein the dynamic collimator comprises one or more adjustable elements configured to form the optimized collimator geometry.

Claims

WHAT IS CLAIMED IS: 1. A method of designing an attenuator for shaping a radiation field, the method comprising: defining a radiation field of a radiation source; defining an attenuator geometry of an attenuator configured to receive the radiation field; and optimizing the attenuator geometry based on an objective function, wherein the objective function is based on a radiation transport of the radiation field through the attenuator geometry, and wherein the radiation transport is based on a non-stochastic process.

2. The method of claim 1, wherein optimizing the attenuator geometry is based on simulated annealing.

3. The method of claim 1, wherein optimizing the attenuator geometry is not based on iterative Monte Carlo calculations.

4. The method of claim 1, wherein the radiation source comprises a photon radiation source.

5. The method of claim 4, wherein the photon radiation source comprises an X-ray source or a Gamma-ray source.

6. The method of claim 1, wherein defining the radiation field comprises defining a phase space model based on a differential flux probability density.

7. The method of claim 1, wherein the attenuator geometry is symmetric.

8. The method of claim 7, wherein the attenuator geometry is cylindrically symmetric and comprises a plurality of annuli stacked along a longitudinal direction of the radiation field.

9. The method of claim 8, wherein the plurality of annuli comprises at least six annuli.

10. The method of claim 8, wherein optimizing the attenuator geometry comprises adjusting inner radii, adjusting outer radii, or both of the plurality of annuli.

11. The method of claim 10, wherein adjusting inner radii, adjusting outer radii, or both of the plurality of annuli comprises optimizing the objective function based on a desired radiation field size.

12. The method of claim 11, wherein optimizing the objective function comprises optimizing a first objective function configured to be intensity-weighted.

13. The method of claim 11, wherein optimizing the objective function comprises optimizing a second objective function configured to be precision-weighted.

14. The method of claim 11, wherein optimizing the objective function comprises optimizing a third objective function configured to be flatness-weighted.

15. The method of claim 11, wherein optimizing the objective function comprises optimizing a fourth objective function configured to be intensity-precision weighted, precision-flatness weighted, intensity-flatness weighted, or intensity-precision-flatness weighted.

16. The method of claim 1, wherein the attenuator geometry is asymmetric.

17. The method of claim 16, wherein the attenuator geometry comprises a plurality of segments each defined by a set of inner radii, a set of outer radii, and a set of azimuthal ranges.

18. The method of claim 1, further comprising manufacturing the attenuator based on the optimized attenuator geometry.

19. The method of claim 1, further comprising configuring a dynamic attenuator based on the optimized attenuator geometry.

20. The method of claim 19, wherein the dynamic attenuator comprises one or more adjustable elements configured to form the optimized attenuator geometry.

21. A system for designing the geometry of an attenuator, the system comprising: a computing device; and a processor in communication with the computing device, wherein the processor is coupled to a memory storing instructions that when executed cause the processor to perform operations comprising: defining a radiation field of a radiation source, defining an attenuator geometry of an attenuator configured to receive the radiation field, and optimizing the attenuator geometry based on an objective function, wherein the objective function is based on a radiation transport of the radiation field through the attenuator geometry, and wherein the radiation transport is based on a non-stochastic process.

22. The system of claim 21, wherein optimizing the attenuator geometry comprises optimizing the objective function based on one or more treatment parameters.

23. The system of claim 22, wherein the one or more treatment parameters comprises an emission profile, a fluence profile, an energy deposition distribution, a dose distribution, a heat distribution, a photon flux, a radiation field size, a focal spot size, a shape of the focal spot, a combination thereof, or a derivative thereof.

24. The system of claim 21, further comprising a manufacturing system configured to manufacture the attenuator based on the optimized attenuator geometry.

25. The system of claim 21, wherein the attenuator comprises a dynamic attenuator having one or more adjustable elements.

26. The system of claim 25, wherein the one or more adjustable elements each comprises a multileaf.

27. The system of claim 25, wherein the one or more adjustable elements each comprises one or more stacks of adjustable elements.

28. The system of claim 21, wherein: the attenuator comprises a set of attenuators, and optimizing the attenuator geometry comprises optimizing a set of attenuator geometries of the set of attenuators based on one or more objective functions.

29. The system of claim 21, further comprising a configuration system configured to configure a dynamic attenuator based on the optimized attenuator geometry.

30. The system of claim 29, wherein the dynamic attenuator comprises one or more adjustable elements configured to form the optimized attenuator geometry.

31. The method of claim 1, wherein the attenuator comprises a collimator.

32. The method of claim 31, wherein the collimator comprises a multileaf collimator (MLC) having one or more adjustable elements.

33. The method of claim 1, wherein the attenuator comprises a modulator.

34. The method of claim 1, wherein the attenuator comprises a collimator, a modulator, a flattening filter, a compensator, or a combination thereof.

35. The system of claim 21, wherein the attenuator comprises a collimator.

36. The system of claim 35, wherein the collimator comprises a multileaf collimator (MLC) having one or more adjustable elements.

37. The system of claim 21, wherein the attenuator comprises a modulator.

38. The system of claim 21, wherein the attenuator comprises a collimator, a modulator, a flattening filter, a compensator, or a combination thereof.