Treatment planning for alpha particle radiotherapy

Abstract

To provide an apparatus (100) for planning a diffusing alpha-emitter radiation therapy (DaRT) treatment session.SOLUTION: An apparatus includes an output interface (110) and a memory (112) configured to include a plurality of tables. The tables provide an accumulated measure of radiation over a specific time period, due to one or more types of DaRT radiotherapy sources which emit daughter radionuclides from the source, for a plurality of different distances and angles relative to the DaRT radiotherapy source. In addition, a processor (108) is configured to: receive a description of a layout of a plurality of DaRT radiotherapy sources in a tumor; calculate a radiation dose distribution in the tumor according to the layout by using the tables in the memory; and output, through the output interface, feedback for the treatment according to the radiation dose distribution.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates generally to radiation therapy, and more particularly to a method for selecting radiation therapy parameters. [Background technology]

[0002] Alpha particles are a powerful tool for radiotherapy of certain types of tumors, including malignant tumors. One type of alpha radiotherapy source is the diffuse alpha-emitter radiation therapy (DaRT) source, also referred to herein as alpha DaRT source, which is loaded with radium-224 atoms, which have a half-life that is neither too long nor too short for therapeutic purposes.

[0003] Kelson, US Pat. No. 8,834,837, describes a method for DaRT treatment.

[0004] For a tumor to be effectively treated, the brachytherapy seeds used in the treatment should release a sufficient number of particles to destroy the tumor, but should not release too many particles, which could damage the patient's healthy tissue.

[0005] U.S. Patent Application Publication No. 2013 / 0165732 to Sgouros et al. describes a computerized system for determining the optimal amount of radiopharmaceutical therapy (RPT) to administer.

[0006] The TG-43 publication (Recommendations of the AAPM Radiation Therapy Committee Task Group No. 43, Med. Phys. 22: 209-234) specifies the necessary physical quantities (e.g., air kerma strength, radial dose function, anisotropy function, dose rate constant, etc.) to calculate quantitative dosimetry data for various interstitial brachytherapy sources.

[0007] US Patent Application Publication No. 2019 / 0099620 proposes adapting a radiation therapy treatment plan based on a set of impact parameters that quantify the impact of radiation per unit intensity emission on a target region according to the anatomical configuration of the target region.

[0008] US Patent Application Publication No. 2011 / 0184283 describes a brachytherapy treatment planning system (TPS) that uses Monte Carlo techniques to calculate doses to specific tissue types. Summary of the Invention

[0009] An aspect of some embodiments of the invention relates to a method for selecting parameters of diffuse alpha emitter radiation therapy, the method comprising calculating a dose distribution of a tumor radiation therapy and adjusting the parameters based on the dose distribution.

[0010] Thus, according to an embodiment of the present invention, there is provided an apparatus for planning a diffuse alpha emitter radiation therapy (DaRT) treatment session, comprising: an output interface; a memory configured to include a plurality of tables providing accumulated measures of radiation over a particular time period for a plurality of different distances and angles relative to the DaRT radiation therapy source resulting from one or more types of DaRT radiation therapy sources emitting daughter radionuclides from the source; and a processor configured to receive a description of a layout of a plurality of DaRT radiation therapy sources within a tumor, calculate a radiation dose distribution within the tumor according to the layout using the tables in the memory, and output feedback to the treatment according to the radiation dose distribution through the output interface.

[0011] Optionally, the memory is configured to include multiple tables for different time periods for a single source type, and the processor is configured to determine a treatment duration for the layout and select a table to use for calculating the radiation dose distribution depending on the treatment duration. Optionally, the memory is configured to include multiple tables for sources of a single source type in different zones of the tumor, and the processor is configured to select a table to use for calculating the radiation dose from each source in the layout depending on the zone in which the source is located. Optionally, the processor determines the zone in which the source is located depending on the distance between the source and the edge of the tumor. Optionally, the processor is configured to identify areas of the tumor where the dose is below a threshold and to suggest modifications to the layout that will raise the radiation dose in the identified areas above the threshold.

[0012] Optionally, the processor is configured to repeat the calculation of the radiation dose distribution for a number of different treatment durations and select one of the durations in response to the calculation. Optionally, the accumulated radiation measure provided by the table includes an accumulated radiation dose due to alpha radiation only.

[0013] Optionally, the accumulated radiation measures provided by the table include accumulated radiation doses from alpha radiation and one or more of electron radiation and photon radiation. Optionally, the accumulated radiation measures provided by the table include one or more number densities of radionuclides.

[0014] Further, according to an embodiment of the present invention, there is provided a method of planning a radiation therapy treatment session comprising receiving, by a processor, a description of a layout of a plurality of DaRT radiation therapy sources within a tumor; calculating, by the processor, a radiation dose distribution within the tumor in response to the layout using a plurality of tables, the plurality of tables providing an accumulated measure of radiation over a particular period of time for a plurality of different distances and angles relative to the DaRT radiation therapy sources due to one or more types of DaRT radiation therapy sources that emit daughter radionuclides from the source; and outputting, from the processor, feedback for the treatment in response to the radiation dose distribution.

[0015] Optionally, calculating the radiation dose distribution includes determining a treatment duration for the layout, and selecting a table to use for calculating the radiation dose distribution in response to the treatment duration. Optionally, calculating the radiation dose distribution includes selecting a table to use for calculating the radiation dose from each source in the layout in response to a zone of the tumor in which the source is located. Optionally, the method includes repeating the calculation of the radiation dose distribution for a number of different treatment durations, and selecting one of the durations in response to the calculation.

[0016] Further, according to an embodiment of the present invention, there is provided a method of planning a radiation therapy treatment session, the method including receiving, by a processor, a plurality of parameters of tissue of a tumor requiring radiation therapy; receiving, by the processor, an indication of a layout of diffuse alpha emitter radiation therapy (DaRT) sources to be placed in the tumor; calculating a distribution of Radon-220, Lead-212 and Bismuth-212 radionuclides in the tumor according to the layout of the sources; determining a distribution of dose resulting from emitted alpha radiation in the tumor according to the calculated distributions; determining an electron and photon radiation dose distribution in the tumor according to the source; and setting one or more parameters of the radiation therapy treatment session according to the determined distribution of alpha, electron and photon radiation.

[0017] Optionally, calculating the distribution of radon 220, lead 212 and bismuth 212 is performed as a function of the diffusion coefficients of radon 220 and lead 212 in the tumor. Optionally, calculating the distribution of radon 220, lead 212 and bismuth 212 is performed by solving a migration equation for lead 212, including a leakage factor that is the product of the concentration of lead 212 and a constant. Optionally, calculating the distribution of radionuclides includes calculating the distribution of radionuclides for a single source and summing the distributions of the sources in the layout.

[0018] Optionally, setting one or more parameters of the radiation therapy treatment session includes selecting a radioactivity of the source. Optionally, setting one or more parameters of the radiation therapy treatment session includes adjusting a layout of the source. Optionally, calculating the distribution of radon 220, lead 212 and bismuth 212 in the tumor and determining the distribution of alpha radiation includes pre-preparing a table of radiation distribution for a plurality of different tumor types and calculating the distribution of alpha radiation by summing values ​​from one of the tables that match the layout. Optionally, pre-preparing a table of radiation distribution includes preparing a plurality of tables for each tumor type for a respective treatment duration. Optionally, the treatment durations for which the tables are prepared are distributed unevenly over the duration of effectiveness of the source of the layout. Optionally, calculating the distribution of radionuclides in the tumor and determining the distribution of alpha radiation includes repeating the determination for a plurality of different durations, and setting one or more parameters of the radiation therapy treatment session includes selecting a treatment duration in response to the repeated determination.

[0019] Optionally, receiving the layout instructions includes receiving an image of a tumor having a source therein, and determining a location of the source within the tumor in response to the image. Optionally, determining the electron and photon radiation dose distribution is performed in a manner that ignores distribution of Radon 220, Lead 212, and Bismuth 212 within the tumor. Optionally, calculating the distribution of Radon 220, Lead 212, and Bismuth 212 radionuclides includes calculating based on at least one equation that depends on a diffusion coefficient of Lead 212, a value of the diffusion coefficient of Lead 212 being calculated as a function of a diffusion length of Lead 212. Optionally, the diffusion length of Lead 212 is assigned a value in the range of 0.2 to 0.4 millimeters. Optionally, the diffusion length of Lead 212 is assigned a value that depends on a tissue type of the tumor.

[0020] Optionally, calculating the distributions includes numerically solving the equations using finite elements. Optionally, calculating the distributions includes determining a finite element two-dimensional time dependent solution. Optionally, calculating the distributions includes numerically solving the equations using finite elements with boundary conditions for each of the sources both on an exterior surface of the source and on the axis of the source. Optionally, calculating the distributions includes numerically solving the equations using finite elements for a respective cylindrical domain surrounding each of the sources, the number density being set to zero outside the cylindrical domains. [Brief description of the drawings]

[0021] [Figure 1] 1 is a schematic diagram of a system for planning radiation therapy treatment, according to an embodiment of the present invention. [Diagram 2] 1 is a flow diagram of the operations of a method for calculating a dose distribution of a tumor radiation therapy according to an embodiment of the present invention. [Diagram 3] FIG. 2 is a schematic diagram of the operations performed in generating a table in memory according to one embodiment of the present invention. [Figure 4A] 13 is a graph showing a comparison between the DART1D solution and the asymptotic solution for the 212Pb number density 2 mm from the source. [Figure 4B] 13 is a graph showing the ratio between the DART1D solution and the asymptotic solution of the 220Rn number density at various distances from the source axis. [Figure 5A] 13 is a graph showing a comparison of dose values ​​between DART1D 220Rn+216Po and 220Bi / 220Po alpha doses and a 0D approximation for an infinite cylindrical source. [Figure 5B] 13 is a graph showing the approximation ratios of DART1D 220Rn+216Po and 220Bi / 220Po alpha doses versus the 0D approximation for an infinite cylindrical source. [Figure 6] 1 is a graph showing DART2D variation versus time step. [Figure 7A]1 is a graph showing the total alpha dose accumulated during 40 days of treatment with DaRT seeds with 224Ra initial activity of 3 μCi, seed radius of 0.35 mm, and seed length of 10 mm. [Figure 7B] 1 is a graph showing total alpha dose as a function of distance along r in the midplane and distance along z on the seed axis from the seed age. [Figure 8A] Graph showing the ratio between the total alpha dose at the seed mid-plane calculated by DART2D and the total alpha dose at the seed mid-plane calculated using the 0D source approximation, the 0D infinite cylindrical approximation, and a full 1D calculation for an infinite cylindrical source using DART1D in the low diffusion high leakage case. [Figure 8B] Graph showing the ratio between the total alpha dose at the seed mid-plane calculated by DART2D and the total alpha dose at the seed mid-plane calculated using a 0D source approximation, a 0D infinite cylindrical approximation, and a full 1D calculation for an infinite cylindrical source using DART1D in the high diffusion low leakage case. [Figure 9A] FIG. 13 shows grid total alpha dose map comparison for LRn=0.3mm, LPb=0.3mm, Pleak(Pb)=0.8 for source 0D approximation. [Figure 9B] FIG. 13 shows grid total alpha dose map comparison for LRn=0.3mm, LPb=0.6mm, Pleak(Pb)=0.3 for source 0D approximation. [Figure 9C] FIG. 13 shows grid total alpha dose map comparison for LRn=0.3mm, LPb=0.3mm, Pleak(Pb)=0.8 for a full 2D calculation with DART2D. [Figure 9D] FIG. 13 shows grid total alpha dose map comparison for LRn=0.3mm, LPb=0.6mm, Pleak(Pb)=0.3 for a source 0D approximation and for a full 2D calculation with DART2D. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] An aspect of some embodiments of the present invention relates to the use of pre-calculated tables of radiation distribution from a radiation therapy source in calculating an estimated radiation dose from an alpha DaRT source emitting daughter radionuclides to a tumor being treated, the tables providing for multiple positions relative to the source the accumulated radiation dose at that position.

[0023] In some embodiments, separate tables or table entries are used for different periods of a radiation therapy treatment.

[0024] In some embodiments, separate tables are provided for different areas within a tumor, for example, different areas within a tumor based on distance from the tumor margin.

[0025] The use of a table showing the accumulated dose over the treatment period solves the problem that the spatial distribution of the radionuclide is time dependent and cannot be decomposed into time-dependent and space-dependent components. Furthermore, the use of doses in a table avoids the problem that for DaRT the dose rate at t=0 is zero and the dose rate increases and then decreases with time.

[0026] 1 is a schematic diagram of a system 100 for planning a radiation therapy treatment, according to one embodiment of the present invention. The treatment generally involves implanting multiple sources into the tumor to be destroyed. The sources, also known as "seeds," generally include a base coated with radium-224, as described, for example, in U.S. Patent No. 8,894,969, which is incorporated herein by reference. The base may have any suitable shape, such as a thin cylinder.

[0027] The system 100 comprises an imaging camera 102 for acquiring images of a tumor requiring radiation therapy. Furthermore, the system 100 includes an input interface 104, such as a keyboard and / or a mouse, for receiving input from a human operator, such as a physician. Alternatively or additionally, the system 100 comprises a communication interface 106 for receiving instructions and / or data from a remote computer or a human operator. The system 100 further comprises a processor 108 configured to generate a layout plan for placing a radiation therapy source within the tumor. The processor 108 is further configured to estimate the radiation dose expected to reach each of the points within the tumor and accordingly provide an output to the human operator via an output device 110, such as a computer screen.

[0028] The processor 108 is coupled to a memory 112 which preferably stores tables of radiation dose as a function of distance from the source, and optionally also as a function of angle from the source, which tables have been pre-calculated for different types of sources and tumor tissue parameters, as discussed below.

[0029] 2 is a flow diagram of operations performed by system 100, according to one embodiment of the present invention. System 100 receives input regarding a tumor (202) and generates a layout of radiation therapy sources relative to the tumor (204). Optionally, the layout includes information about the sources (e.g., their radioactivity levels) and duration of treatment, in addition to the relative positions of the sources.

[0030] The processor 108 calculates (206) the dose distribution of radiation from the source for that layout, and / or calculates (208) any other parameters of the source radiation, such as a dose volume histogram and / or a dose rate distribution. In some embodiments, a determination is made (210) as to whether the dose distribution and / or other parameters are satisfactory, and if not, a new layout is generated (204) and the calculation of the dose distribution and / or other parameters of the radiation is repeated for the new layout. Optionally, the generation of the layout (204) and the calculation of the dose distribution (206) and / or the calculation of the other parameters (208) are repeated until a suitable layout for inserting the source into the tumor is identified and provided (212).

[0031] In some embodiments, the determination (210) as to whether the dose distribution and / or other parameters are satisfactory and the generation of the new layout are performed by a human operator. Alternatively, the processor 108 automatically determines (210) whether the dose distribution is sufficient, for example by determining areas of the tumor where the radiation is lower than a first threshold. Optionally, this first threshold is selected according to the type of tumor, for example the nucleus size of the cells of the tumor. In some embodiments, the processor 108 automatically determines the percentage of the tumor where the radiation dose is higher than the first threshold and compares this percentage to a second threshold. Optionally, the generation of the new layout (204) is performed automatically by moving sources from areas where the radiation is substantially higher than the first threshold to areas where the radiation dose is lower than the first threshold. Alternatively or additionally, the automatic generation of the new layout is performed by adding additional sources.

[0032] In some embodiments, after inserting the sources into the tumor, an image of the tumor including the sources is acquired 214 and an actual layout of the sources within the tumor is determined 216. Optionally, the processor 108 then calculates 218 the dose distribution of radiation from the sources in the actual layout and provides suggestions for improving the layout if necessary 220.

[0033] Suggestions for improving the layout (220) and generating new layouts (204) may include adding sources for insertion into the tumor, removing unnecessary sources, moving one or more sources in the layout (e.g., changing the spacing between sources), changing the activity and / or desorption probability of one or more of the sources, and / or changing the type or size of the sources.

[0034] In some embodiments, the processor 108 automatically generates the layout by distributing the sources throughout the tumor at a default interval for that particular tumor type (204). Alternatively or additionally, the layout is generated using intervals indicated by a human operator. Further, alternatively or additionally, the human operator indicates the location of the sources on the displayed image of the tumor via the input interface 104. Optionally, the layout further includes an indication of one or more characteristics of the sources used in the layout, such as the length of the source and / or the radioactivity level of the source (i.e., the amount of radioactive atoms on the source). This information about the source may be provided by a human user or may be automatically selected by the processor 108, for example, based on default values ​​or on a code number provided by the human operator. In some embodiments, if the analysis is of an already implanted source, the processor 108 determines the characteristics of the source from an image of the tumor containing the source therein. In these embodiments, the source may include indicia of the source type and / or characteristics that are readily determinable from an image of the tumor.

[0035] Optionally, the information about the layout further includes the duration for which the analysis is performed, e.g., the time the source is planned to be in the tumor, or, if the analysis is performed after treatment is completed, the time the source was in the patient's body. In some embodiments of the invention, these calculations are performed for a number of different durations to select the most suitable duration for treatment. For example, these calculations may be performed during treatment to determine when to remove the source.

[0036] In some embodiments, the calculation (206) of the dose distribution is based on pre-generated tables stored in the memory 112. The calculation (206) optionally includes selecting one of the tables in the memory 112 depending on the type of tissue of the tumor and the type of source used in its layout. As will be explained later with reference to FIG. 3, these tables are pre-calculated for each tissue type. Each table optionally indicates the amount of radiation that reaches a position per unit activity of the source for a number of positions for the source type of the table. Optionally, these positions are specified by an angle (θ) and a distance (r) from the center of the source. The table includes, for example, 90 rows representing possible angles ranging from 0° to 180° with a granularity of 2°, and 100 columns representing distances from 0 to 10 mm with a granularity of 0.1 mm. These numbers of rows and columns are given as examples, and larger or smaller tables with coarser or finer granularity are also contemplated within the scope of the invention. For example, the table may include 180 rows with 1° granularity. In some embodiments, the dose values ​​in the table are provided in units of gray. In other embodiments, the values ​​in the table are dose values ​​per initial release rate of radon, e.g., in units of gray per microcurie.

[0037] The tables described herein may be stored in memory 112 in any suitable data structure. Each table may be stored, for example, as a single array or as multiple arrays. Each of the tables may be stored separately, or multiple tables may be stored together as a single table of larger dimensions.

[0038] In calculating the dose distribution (206), for each location of interest (e.g., locations within the tumor, and possibly even adjacent to the tumor), the processor 108 looks up the table to find the radiation dose received from each of the sources per unit activity of the source, and multiplies this value by the activity of the source. These values ​​are summed to provide the total radiation dose arriving at that point. As an alternative to multiplying by the activity of the source, the dose from the table is multiplied by the emission rate of radon from the source.

[0039] In some embodiments where all the sources have the same activity, the sum may be multiplied by the source activity or the source radon emanating rate.

[0040] Alternatively or additionally, so that this multiplication is not necessary, separate tables are provided for each radioactivity level (or radon exhalation rate), which provide values ​​for the radioactivity or radon exhalation rate.

[0041] In some embodiments, multiple tables are provided for different treatment durations for each tissue type. For example, tables are optionally provided for a range of equally spaced durations with granularity of one or two days. Alternatively, these tables are prepared for unevenly distributed durations where the calculated doses differ enough to justify additional tables. The duration of treatment is also considered when selecting which table to use for a particular source. In some embodiments, when the treatment duration is between the durations of two different tables, values ​​from both tables are taken and the actual value is calculated by interpolation from the table values. Alternatively, in cases where treatment is expected to always be for a relatively long duration, a single table of long durations longer than several half-lives of Radium-224 is used.

[0042] In other embodiments, the table shows other parameters from which the dose can be calculated relatively easily. For example, in some embodiments, the table provides, for each position relative to the source, the cumulative decay numbers of two or more radionuclides involved in the treatment. The radiation dose is calculated from the values ​​in the table by first determining the cumulative decay numbers of radionuclides involved in the treatment that are not included in the table, and then calculating the dose from the cumulative decay numbers. The calculation of the radiation dose from the cumulative decay numbers can be performed before or after summing the effects of all the sources in the layout. Optionally, the two or more radionuclides whose cumulative decay numbers are included in the table are radon 220 and bismuth 212. As an alternative to radon 220, the cumulative decay number of polonium 216 is provided. Furthermore, alternatively or in addition, as an alternative to the cumulative decay number of bismuth 212, the cumulative decay numbers in the table are the cumulative decay numbers of lead 212, polonium 212 and / or thallium 208. In some embodiments, the table may provide the cumulative decay numbers for three or more radionuclides, or possibly all the radionuclides involved in the treatment.

[0043] In some embodiments, the type of tumor is determined based on clinical and / or histopathological observations, such as analysis of a portion of the tumor taken in a biopsy. The type of tumor is selected from a list including, for example, squamous cell carcinoma, basal cell carcinoma, glioblastoma, sarcoma, pancreatic cancer, lung cancer, prostate cancer, breast cancer, and colon cancer. This list of tumor types is provided by way of example only, and tables may be prepared for larger or smaller lists of tumor types, including all or some of the types listed above and / or other types not listed in this list.

[0044] 3 is a schematic diagram of operations performed in generating a table in memory 112, according to one embodiment of the present invention. The method optionally includes determining (302) one or more tissue-specific parameters that describe the diffusion of a radioisotope from a source in tumors of different types of cancer to be treated. Optionally, the parameters describe the diffusion of the radon isotope 220 ( 220 Rn), lead 212( 212 Pb) and Bismuth 212( 212 Diffusion coefficient D of Bi Rn , D Pb and D. Bi Optionally, the diffusion coefficient D Rn , D Pb and D. Biis measured using methods known in the art, such as those described in Lior Arazi, "Diffusing Alpha-Emitters Radiation Therapy: Theoretical and Experimental Dosimetry", Thesis submitted to the senate of Tel Aviv University, September 2008, the disclosures of which are incorporated herein by reference, and / or Lior Arazi et al., "Treatment of solid tumors by interstitial release of recoiling short-lived alpha emitters", Physics in Medicine & Biology, 2007, the disclosures of which are incorporated herein by reference.

[0045] In some embodiments, the diffusion coefficient D Rn , D Pb and D. Bi is measured in mice or other test animals. Although such measurements are not completely accurate, due to, for example, convection effects, applicants have determined that the calculation achieves suitable results even when these inaccuracies are ignored.

[0046] Optionally, these tissue-specific parameters are further determined by the parameter α, which represents the leakage rate of Pb-212 and Bi-212, respectively, due to leakage from the tumor through the blood (assuming that it is uniform throughout the tumor). Pb and α Bi Optionally, a leak rate parameter α Pb and α Bi is the average leakage time ( 212 Pb and 212 The average time it takes for Bi to leave the tumor through the blood is 1 / α Pb and 1 / α Bi It is determined to be.

[0047] In some embodiments, αPb The value of is determined from a measurement of the lead-212 leakage probability. The lead-212 leakage probability is measured using any suitable method known in the art, such as the measurements in mice described in the above-mentioned article Lior Arazi et al., "Treatment of solid tumors by interstitial release of recoiling short-lived alpha emitters", Physics in Medicine & Biology, 2007. Alternatively or additionally, alpha Pb The value of is determined, for example, from Lior Arazi et al., "The Treatment Of Solid Tumors By Alpha Emitters Released From 224 The radioactivity levels are inferred from blood and / or urine radioactivity measurements in human patients using the biokinetic model described in "Ra-Loaded Sources - Internal Dosimetry Analysis", Physics in Medicine and Biology, February 2010.

[0048] Preclinical data collected from DaRT-treated tumor samples include: 212 from tumors independent of Pb leakage 212 It was shown that Bi leakage has a small effect. Bi ≪λ Bi (λ Bi is the decay rate constant of bismuth-212. 212 Bi is, 212 It was found that the ionized ionized nucleus is in local transit equilibrium with Pb. Bi ≦0.2D Pb Thus, in some embodiments, α Bi =0 and D Bi =0.1D PbAlternatively, α Bi is inferred from measurements in mouse-based experiments where the ratio of Bi212 to Pb212 activity is measured in small specimens. Bi is α Bi and a constant k, where k is a constant less than 1, less than 0.25, or less than or equal to 0.2, e.g., 0.2 or 0.1. Bi But, D Pb and a constant k2, where k2 is usually < 1.

[0049] The method further includes determining 304 parameters representative of a radiation therapy source. In some embodiments, the source is an initial 224 Ra radioactivity

number

number

number

[0050] The spatial distribution of an isotope, n, as a function of time, t, and position, r, relative to the source Rn (r,t), n Pb (r,t) and n B These tissue-specific and source parameters are used to determine the isotope fraction derived from the source to determine i(r,t). 220 Rn, 212 Pb and 212 Solve 306 the translation equations for each of Bi. Typically, the position r is a three-dimensional vector, but in some cases, for simplicity, a simpler measure of position is used, e.g., a measure based on symmetry considerations. Optionally, 216 Po, 212 Po and 208 Due to the short half-life of Tl, these isotopes are assumed to be in local transit and / or perpetual equilibrium with their parent isotopes and do not require separate equations to calculate their spatial distribution.

[0051] The resulting alpha radiation dose is calculated from the determined spatial distribution of the isotopes (308). Further, the electron (beta, auger, conversion electron) and photon (gamma, x-ray) radiation doses from the source are calculated (310) using any suitable method known in the art. Optionally, the calculated alpha, electron and photon radiation dose distributions D(r, θ, t) are incorporated into a look-up table for each set of tumor type and source type parameters (312), where, assuming axial symmetry, r specifies the radial distance from the source center to the point of interest, and θ specifies the angle between the source axis and a line connecting the point of interest to the source center.

[0052] movement equation In some embodiments, the Radon transport equation (also called the transport equation) is given by:

number

number

[0053] In the most general case, j Rn (r,t) consists of both diffusive and convective terms. j Rn (r,t)=-D Rn (r,t)∇n Rn (r,t)+n Rn (r,t)v(r,t) (2) v(r,t) is a vector field describing both the vascular and interstitial flow inside the tumor.

[0054] Optionally, the Pb transport equation is:

number

[0055] Optionally, the total 212 The transport equation for Bi number density is as follows:

number

[0056] Meaningful amounts of tumor tissue distant from the source 224 If Ra exists, we can obtain its number density n by solving a separate transport equation. Ra(r,t) can be found, and then s Rn (r,t)=λ Ra n Ra Using (r,t), the number density n Ra (r,t) 220 can be used as a volumetric source term for Rn.

[0057] Optionally, a source term s Rn (r,t) and s Pb (r,t) is determined based on the given physical geometry of the source inside the tumor with appropriate flux boundary conditions at the source surface.

[0058] The above equation is, 220 Rn, 212 Pb and 212 The equations are solved 306 using any suitable method known in the art, such as Monte Carlo simulations describing the stochastic motion of Bi, or solved numerically 306 using finite elements (for any source geometry, with appropriate boundary conditions). One method for numerically solving these equations using finite elements is described in the appendix of this application. These solutions are necessary if the tumor is considered as a heterogeneous, possibly time-dependent medium, with diffusion coefficients and velocity fields that depend on space and time. Alternatively, approximate solutions can be obtained if the tumor is modeled as a homogeneous, isotropic, time-independent medium. In this case, in addition to the above-mentioned solutions, the transport equations can also be solved approximately using closed-form expressions for simple geometries such as an ideal point source, an infinite line source or an infinite cylinder, and / or an infinite plane source. Exemplary solutions that can be used are described in Lior Arazi, "Diffusing alpha-emitters radiation therapy: approximate modeling of the macroscopic alpha particle dose of a point source", Physics in Medicine and Biology, 2020, the disclosure of which is incorporated herein by reference.

[0059] In some embodiments, these equations are solved by first preparing a solution for a point source and then summing the effects of the point sources to form the actual geometry of the source.

[0060] Optionally, 224 For a point source of Ra, 220 The Rn source term is given by the following equation:

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[0061] Optionally, 212 The source term for Pb is:

number

[0062] The first term is "away from the source". 216 Through Po 220 Decay of Rn 212 It represents the local generation of Pb. The second term is 216 from the source by direct recoil when Po collapses on the source 212 Pb release or previous recoil from source 216 Very close to the source when Po collapsed212 This represents the release of Pb.

number

number

[0063] Optionally, 212 Bi is away from the source 212 We assume that Pb enters the tumor only by decay. Therefore, in equation (3), 212 The Bi source terms are as follows: s Bi (r,t)=λ Pb n Pb (r,t) (9)

[0064] In some embodiments, appropriate boundary conditions for the source are added to cover the diffusion of bismuth 212 from the source when a source that allows such diffusion is used. Alternatively, for an ideal point source, a Dirac delta function term for bismuth 212 can be used as used above for radon 220 and lead 212.

[0065] In some embodiments, these equations are simplified to reduce the complexity of their solution based on one or more of the following assumptions: The tumor medium is homogeneous, isotropic and time-independent. The diffusion and leak rate coefficients are constant in space and time. Inside the tumor 224Ra daughter transport is primarily diffusive. Vascular convection through tortuous capillaries is characterized by a short correlation length (relative to therapeutically significant distances) and is therefore assumed to be randomly oriented. This can therefore be incorporated into the effective diffusion coefficient. · The source location is assumed to remain fixed throughout the treatment. All sources are the same, i.e. same length, same activity, same probability of desorption. · 220 Rn is completely destroyed inside the tumor. Interstitial convection is ignored. · 212 Pb migration is 212 It can be described using a single effective diffusion coefficient that represents the average of the Pb molecular species. Reached the major blood vessels 212 Pb atoms are trapped in red blood cells (RBCs) and rapidly removed from the tumor. This process is described by a uniform volumetric sink term. The finite clearance rate is 212 It reflects the time it takes to transport a Pb atom to reach such a trap. Short-lived 220 Rn atoms diffuse freely without chemical interactions with blood vessels and RBCs. 220 The equation for Rn does not include a sink term (i.e., the vessels 220 However, in some embodiments, in blood-rich regions of tumors, 220 A similar sink term can be added to the equation for Rn. · 212 The diffusion equation for Bi includes a sink term, however this is generally considered to be a second-order effect.

[0066] Under this set of assumptions, the above equations can be simplified to:

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[0067] In equations (10) to (12), n Rn (r,t), n Pb (r,t) and n Bi (r,t) covers the entire tumor 220 Rn, 212 Pb and 212 is the local time-dependent number density of Bi. D Rn , D Pb and D. Bi are the effective diffusion coefficients of the three isotopes, which are assumed to be independent of position and time. λ Rn , λ Pb and λ Bi are the respective decay rate constants. 212 Pb and 212 The Bi equation is 212 Pb and 212 The sink term α describes the leakage of Bi (i.e., its removal from the tumor). Pb n Pb and α Bi n Bi Includes.

[0068] As stated above for the general equations (1), (3), and (5), equations (10)-(12) are 220 Rn, 212 Pb and 212 It is solved 306 using any suitable method known in the art, such as a Monte Carlo simulation that describes the stochastic motion of Bi, numerically using finite elements (for any source geometry, with appropriate boundary conditions) 306, or approximately using closed-form equations for simple geometries, such as an ideal point source, an infinite line source, or an infinite cylinder, and / or an infinite plane source 306.

[0069] In some embodiments, for simplicity, 220 Rn, 212 Pb and 212 Instead of solving the transport equations for all three of Bi, one or more of the radionuclides are assumed to have a fixed distribution or a distribution that depends on one or more of the remaining radionuclides. For example, in one embodiment, the dose calculation is 212 Calculation based on the Pb transport equation, 220 Consider the distribution of Rn to be negligible, 212 The distribution of Bi is 212 Assume that Pb is a fixed function of the Pb distribution. Alternatively, 220 Rn and 212 Solve the equation for Pb, 212 The number density of Bi (e.g., in transit or secular equilibrium) 212 It is assumed to be proportional to the number density of Pb.

[0070] Alpha Dose Calculation The alpha particle dose from the time of the procedure to time t has two components. The first is 220 Rn and 216 It arises from the alpha decay of Po (which is 216 (which occurs immediately afterwards in essentially the same location due to the 0.15 second half-life of Po) 212 Bi (36% branched) or 212 It arises from the alpha decay of Po (64% branching). The accumulated dose can be summarized by the following equations, which are the n Rn (r,t), n Pb (r,t) and n Bi Depends on the values ​​of (r,t).

[0071]

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[0072] Eα (RnPo)=(6.29+6.78)MeV=13.07MeV=2.09·10 -12 J is 220 Rn and 216 is the sum of the energies of the alpha particles emitted by Po (at essentially the same location). E α (BiPo)=7.80MeV=1.25·10 -12 J is 212 Bi or 212 is the average energy of the alpha particles emitted by Po, and ρ is the tissue density (for all practical purposes 1 g / cm 3 (It can be set to infinite time from the time of implanting the source in the tumor (in practice, 224 The asymptotic dose is defined as the dose delivered within approximately 5 half-lives of Ra as follows:

[0073]

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[0074] In some embodiments, these equations are solved based on the assumption of uniform time behavior of the number density throughout the region around the source, which is referred to as the "0D approximation."

[0075] Under the 0D approximation for a point source 220 Rn and 216 The asymptotic dose contributed by Po is given by the following formula:

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[0076] The spatial dependence of this dose is given by the following formula: 220 It is governed by the Rn diffusion length.

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[0077] 212 Bi and 212 Regarding the dose contributed by Po, first 212 Pb and 212 The diffusion length of Bi is defined as follows:

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[0078] In some embodiments, the effective 212 The Pb life is as follows:

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[0079] This parameter essentially 212 Mean radioactive lifetime of Pb, τ Pb =1 / λ Pb and its mean clearance time 1 / α Pb is the geometric mean of

[0080] Asymptotic 0D for a point source 212 Bi / 212 The Po alpha particle dose is given by the following formula:

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[0081] To calculate the approximate dose up to time t, use the following equation instead of equation (22):

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[0082] In some embodiments, the physical source can be approximated as a finite source. In this case, the total alpha particle dose D(r,θ,t) at any point (defined by r and θ relative to the source center and axis) can be calculated by dividing the source into many small point-like segments and dividing the dose from each segment by the 220 Rn / 216 Po and 212 Bi / 212 The contribution of Pb, equations (17) and (22) are obtained by summing using the radial distance from point (r, θ) to the respective segment.

[0083] The total radiation dose D(r,θ,t) from alpha particles at any point is given by 220 Rn / 216 Po and 212 Bi / 212 The contribution due to Pb is the sum of equations (17) and (22).

[0084] According to the experiment, α Pb is defined as the equivalent parameter, i.e. 212 It would be more convenient to replace it with Pb leakage probability.

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[0085] In some embodiments, 212 Diffusion length of Pb L Pb was measured in mouse tumors, and the diffusion coefficient D Pb is set using equation (19). According to measurements performed by the applicant, the diffusion length L Pb The values ​​of were found to be in the range of approximately 0.2-0.7 mm. This value varies depending on the tumor type and / or the distance between the source and the tumor periphery. Values ​​for several types of tumors are listed in the table below.

[0086] [Table 1]

[0087] Thus, in some embodiments, when calculating the radionuclide distribution: 212 Diffusion length of Pb L Pb is given the average value in the table for the corresponding tumor type. Alternatively, the lower value of the corresponding range in the table is used. In some embodiments, for cancer types not in the table, the diffusion length L Pb For , a value smaller than 0.4 mm, a value smaller than 0.35 mm or a value smaller than 0.3 mm is used.

[0088] Optionally, 220 The Rn diffusion length is estimated by a value in the range of 0.2 to 0.4 mm, such as at least 0.23 mm, at least 0.25 mm, or at least 0.27 mm. 220 A value of 0.3 mm is used for the Rn diffusion length. Alternatively or additionally, 220 The Rn diffusion length is less than 0.33 mm, less than 0.29 mm, or less than 0.27 mm.

[0089] Optionally, 212 The Pb leak probability is estimated with a probability of greater than 30%, or greater than 35%, for example, a probability of 40%. 212 The Pb leakage probability is assumed to be less than 70%, less than 60%, or less than 50%. In some embodiments, for different regions of the tumor, 212 Different values ​​of Pb leakage probability are used. Optionally, for regions close to the edge of the tumor, this value is higher than 70% or higher than 80%. Deep inside the tumor, in its necrotic core, 212 The Pb leakage probability can be made much lower than that, for example, lower than 10%.

[0090] It should be noted that instead of calculating the radiation dose from the radionuclide distribution using the integrals of equations (15)-(16), other calculation methods can be used, such as the Monte Carlo method.

[0091] Table Generation The table is generated from the total alpha particle dose D(r,θ,t) for each point from the beginning of the procedure (e.g., insertion of the source into the tumor) at time t=0 to time t. In some embodiments, instead of directly inserting the calculated radiation distribution values ​​D(r,θ,t) into the table, the calculated distribution values ​​D(r,θ,t) are converted into a form acceptable by a commercially available radiation treatment planning system (TPS), and the TPS generates the table.

[0092] Optionally, the table is generated by a treatment planning system (TPS), such as BrachyVision TPS, based on the function:

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[0093] According to some embodiments, f ak The value of is set arbitrarily, for example to 1, and the gL(r) and F(r,θ) functions are calculated from the DaRT radiation distribution values ​​D(r,θ,t) for a given time t as follows:

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number

[0094] For cases where TPS limits the value of F(), the normalized

number

[0095] Optionally, r0 is selected to prevent g(r) from falling outside the bounds of values ​​allowed by the TPS. Optionally, the value of Sk(0), Λ, is

number

[0096] Electron and photon radiation In some embodiments, separate tables are prepared for alpha radiation and electron and photon radiation. In calculating the radiation dose distribution, separate calculations are performed for alpha radiation by accessing the alpha radiation table and for electron and photon radiation by accessing the appropriate tables, and the results are then combined. Optionally, the electron and / or photon radiation table provides accumulated dose values, as provided by the alpha radiation table. Alternatively, the electron and / or photon radiation table provides dose rate values, as described in the above-mentioned TG-43 publication.

[0097] Alternatively, a single table is used for alpha, electron and photon radiation. Optionally, according to this alternative, when summing alpha, electron and / or photon radiation, the alpha radiation value or the electron and / or photon radiation value are multiplied by a user-provided relative biological effectiveness (RBE) factor determined using any suitable method known in the art. This RBE factor takes into account the different biological effectiveness of alpha radiation and electron and / or photon radiation. The RBE value for alpha particles depends on the tumor type and is typically in the range of 3-5. For electrons and photons, the RBE value is typically 1 at high energies (above several hundred keV) but is greater than 1 at lower energies.

[0098] For simplicity, optionally, the radionuclides are assumed to be all located on the source and the migration of the radionuclides within the tumor is ignored when calculating the electron and / or radiation dose. Due to the long range of electrons and the large mean free path of gamma and x-ray photons with the migration scale being dominated by the diffusion length, this assumption has been found to have only a small effect on the results. However, in some embodiments, e.g. 212 The Pb leakage probability in the tumor 212 By reducing the number of Pb radionuclides, the electron and / or photon radiation dose calculations take into account early clearance of the radionuclides by the bloodstream.

[0099] Optionally, the electron and photon radiation doses are 224 It is calculated by Monte Carlo methods (e.g. using EGS, FLUKA, GEANT4, MCNP or orbital construction codes) for the entire spectrum of emitted radiation by Ra and its daughters. Optionally, for simplicity, the medium is assumed to be water. Alternatively, other calculation methods are used, such as model based dose calculation algorithms (MBDCA).

[0100] Alternative In the above description, the tumor is considered to have the same parameters throughout its volume. In other embodiments, the tumor is considered to have different parameter values ​​in different areas. Optionally, separate tables are generated for different distances of the source from the tumor edge. For example, separate calculations are performed for sources in the range of up to 2 mm from the tumor edge, between 2-4 mm from the tumor edge, between 4-6 mm from the tumor edge, and more than 6 mm from the tumor edge. In other embodiments, more than four ranges of distances of the source from the tumor edge are used, and / or ranges of granularity coarser than 2 mm or finer than 2 mm are used.

[0101] For each of these ranges, a separate value for the tumor parameter is provided. For example, areas closer to the tumor margin are assigned a higher lead-212 leakage probability (and / or a shorter diffusion length) since leakage is higher at the tumor margin. When using these tables, for each source, a corresponding one of the tables is selected according to the location of the source within the tumor.

[0102] Optionally, the distance between the source and the edge of the tumor is measured from the closest point on the source to the closest point on the edge of the tumor. Alternatively, this distance is measured from the center of the source. Also alternatively, this distance is measured as an average distance along the length of the source or as an average between the two ends of the source. In other embodiments, in addition to this distance, a measure of the orientation of the source is used in dividing the tumor into separate zones, such as the angle between the source axis and the shortest line connecting the center of the source to the edge of the tumor.

[0103] As mentioned above, the same tumor parameters, e.g., the same diffusion length, are used for the entire duration of the treatment. However, in other embodiments, in calculating the radiation dose, one or more of the tumor parameters, such as the diffusion length, are changed over time since the beginning of the treatment due to cell death from the treatment that changes the characteristics of the tumor. It is noted that these embodiments have a greater impact on the dose calculation during longer periods than during short durations where the tumor parameters change little or not at all.

[0104] As an alternative to using tables, the above calculation method is used directly for calculating the radiation dose distribution.

[0105] Conclusion It is understood that the methods and apparatus described above should be construed to include apparatus for performing those methods and methods of using the apparatus. It should be understood that features and / or steps described with respect to one embodiment can sometimes be used with other embodiments, and that not all embodiments of the invention have all of the features and / or steps shown in a particular figure or described with respect to one of the particular embodiments. Tasks are not necessarily performed in the exact order described.

[0106] It should be noted that some of the embodiments described above may include structures, operations, or details of structures and operations that are not necessarily essential to the invention and are described as examples. The structures and operations described herein may be replaced by equivalents that perform the same functions known in the art, even if the structures or operations are different. The embodiments described above are provided as examples, and the invention is not limited to those specifically shown and described above. Rather, the scope of the invention includes both combinations and subcombinations of the various features described above, and variations and modifications of those features that are not disclosed in the prior art, that would occur to one of ordinary skill in the art upon reading the above description. Thus, the scope of the invention is limited only by the elements and limitations used in the claims, and the terms "comprises," "includes," "having," and their conjugations, when used in the claims, mean "including, but not necessarily limited to."

[0107] appendix The assumptions underlying the DL model are: · The movement of atoms inside a tumor is governed by diffusion. · Tissues are homogeneous, isotropic and time independent, therefore the diffusion coefficient is constant. · 220 Rn, 212 Pb and 212 It is sufficient to model the movement of Bi. 216 Po, 212 Po and 208 Tl is in local perpetual equilibrium with their respective parent isotopes (with appropriate branching ratios for the latter two). · 212 The transport of Pb can be described using a single effective diffusion coefficient. Reached the major blood vessels 212 Pb atoms are trapped in red blood cells and then rapidly removed from the tumor, which is represented by a single constant sink term. · 220Rn atoms do not form chemical bonds and are very short-lived, therefore the equation for Rn does not contain a sink term. · 212 Although the equation for Bi includes a sink term, it is considered a second-order effect and is typically set to zero.

[0108] Consider the case of a cylindrical source of radius R0 and length l along the z axis and assume axisymmetric. Under the above assumptions, in cylindrical coordinates (r,z), the decay sequence 220 Rn, 212 Pb and 212 The equation describing the dynamics of the main daughter atoms in Bi is:

[0109]

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[0110]

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[0111] The solution to equations (1-3) is n Rn (r,z,t), n Pb (r,z,t) and n Bi (r,z,t). The alpha dose is calculated under the assumption that the range of the alpha particles is much smaller than the dominant diffusion length of the problem (see below). The dose from source insertion to time t consists of two contributions. One is the 220 Rn+216 Po resulting from the summed alpha particle energy, and the other 212 Bi or 212 It results from the alpha decay of Po.

[0112]

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[0113] 220 Rn, 212 Pb and 212 The spread of Bi is governed by their respective diffusion lengths, which are defined as:

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[0114] The diffusion length is a gross measure of the average displacement of one atom from its site of formation to its decay or clearance by blood. For a point source, the radial dependence of the number density and alpha dose components is given by

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[0115] Another important parameter is 212 Pb leakage probability P leak (Pb), which is released from the source. 212 It is defined as the probability that a Pb atom will be removed by the blood from the tumor before it decays. Thus, the leakage probability is given by: 212 This reflects the competition between radioactive decay of Pb and its clearance through the blood.

[0116]

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[0117] Value P leak The typical range for (Pb) is about 0.2-0.8.

[0118] After a long time after the source is inserted into the tumor, the number density follows the asymptotic form

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[0119] The closed-form asymptotic solution of the DL model equations for an infinitely long cylindrical source is given by 220 For Rn, the following formula is obtained:

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[0120] In these equations, K0(ξ) and K1(ξ) are modified Bessel functions of the second kind.

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[0121] K0(r / L) is a rapidly decreasing function and is the cylindrical analogue of exp(-r / L) / (r / L) that appears in the equations for number density and dose of a point source. 212 For Pb, the following equation is obtained:

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[0122] lastly, 212 For Bi, the following equation is obtained:

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[0123] The above formula is further divided into limit R0 / l x The limit of an infinite source at →0 can be described.

[0124] To approximately account for the build-up phase of the solution, it can be assumed that the solution is uniform throughout the tumor, i.e., independent of the distance from the source. Under this "0D" time approximation, for a point source, and adapted here for the cylindrical case, the following can be written:

[0125]

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[0126] Under this approximation, the asymptotic alpha dose component is:

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[0127] The complete time-dependent solution for the DL model can be solved numerically using the finite element method. For the one-dimensional case, i.e. for an infinite cylindrical or line source along the z-axis, ∂ 2 n x / ∂z 2Solve equations (1-3) setting = 0. The solution therefore depends only on the radial coordinate r. Let us divide the domain into i=1...N regions of equal radial width Δr. r The radius of the source is R0, and Δr is an integer, R0 / Δr, and Δr is L Rn and L Pb (L Bi has a negligible effect on the solution and should therefore not constrain Δr). The central radius of the i-th shell is

[0128]

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[0129] We use a fully implicit scheme, which ensures that the solution is stable: as we explain later, the time step changes adaptively according to the relative change in the solution between the current step and the previous step.

[0130] The average number density of the i-th shell is n Rn,i , n Pb,i and n Bi,i Let p be the number of time steps. 1 <i≦N r For a shell away from the source surface where , the DL model equations take the discrete implicit form:

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[0131] For the i = 1 shell, using the boundary conditions just outside the source, equations (4)-(6), gives

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[0132] The source terms appearing in equations (29) and (30)

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[0133]

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[0134] The matrix coefficients introduced in equation (34) depend on the value of i, i=1 and i=N r Reflects the boundary condition for Δr / r i Retaining terms up to first order, the different cases can be summarized as follows:

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[0135]

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[0136] The alpha dose component is also updated at each step.

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[0137] At the end of the p+1 step, Δt is updated based on the relative change in the solution. This can be done in several ways. The particular choice made here is to update the i0 The aim of the study was to consider the relative change in total dose (the sum of RnPo and BiPo contributions) at 1 mm (e.g., at 2 mm).

[0138]

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[0139] The above finite element scheme was implemented in MATLAB in a code named "DART1D". The crucial part of the calculation, the solution of equation (39), was carried out using a tridiagonal matrix solver using the Thomas algorithm. Using this solver was found to be about four times faster than the mldivide("\") tool in MATLAB, which is about three times faster than inverting a matrix using inv(A). The code was found to converge to a level of less than one percent for a moderate choice of discretization parameter values; for example, (domain radius R max = 7 mm and 30 d treatment duration) ε tol =10 -2 Setting Δr = 0.02 mm and Δt0 = 0.1 s yields ε with a run time of about 0.5 s and ε with a run time of about 3 minutes (both on a modern laptop computer with an Intel i7 processor and 16 GB of RAM memory). tol =10 -4 , resulting in a dose that is about 0.5% off the dose obtained using Δr = 0.01 mm and Δt = 0.1 s. The latter, more accurate implementation is 220 Rn+ 216 7·10 of 0D approximation for Po dose -4 It was within.

[0140] Figures 4 and 5 explore some aspects of the numerical solution. Figure 4 shows the DART1D solution in comparison with the asymptotic equations (13) and (17). On the left, the DART1D time dependence at a distance of 2 mm from the source. 212The Pb number density is shown with the corresponding asymptotic solution. On the right, it is plotted for different distances from the source. 220 Ratio between numerical and asymptotic solutions for Rn

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[0141] FIG. 5A shows the L Rn =0.3mm, L Pb =0.6mm, L Bi =0.1L Pb , α Pb = λ Pb (i.e. P leak (Pb)=0.5), and α Bi DART1D calculated for the case of =0 220 Rn+ 216 Po and 212 Bi / 212 The Po alpha dose component is shown. The source radius is R0 = 0.35 mm. 224 The Ra activity is 3 μCi / cm and the desorption probability is P des (Rn)=0.45 and

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[0142] We now move to two dimensions to deal with a cylindrical source (the "seed") of radius R0 and finite length l. The source extends along the z-axis with z=0 at its mid-plane. From r=0 to r=R max up to, and z=-Z max From z=+Z max Solve the DL equations over a cylindrical domain extending to R max and Z max Both -l / 2 must be much larger than the maximum diffusion length of the problem. The domain has ring elements of equal radial width Δr and equal z-width Δz. R0 / Δr and l / (2Δz) are integers, and Δr and Δz are L Rn and LPb Choose Δr and Δz so that they are much smaller than . Count the rings by i,j, i=1...N r , and j=1...N z The element with i=1 is on the axis, the element with j=1 is at the bottom of the cylindrical domain, and the element with j=N z The elements of are at the top of the domain. Unlike the 1D case where the source is infinitely long and we only consider points with r>R0, for a 2D finite seed, r <R0および

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[0143] The discretization of equations (1-3) in 2D is for an interior ring element of a cylindrical domain (outside the seed, not touching the seed wall or base, i>1),

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[0144] i=N r +1, j=0 or j=N z Since the number densities for the +1 ring are all zero, equation (43) becomes i=N r , j=1 or j=N zalso applies to the ring elements on the outer surface of the domain. For the ring elements on the axis (i = 1) above or below the seed, (∂n x / ∂r) r=0 = 0 is required. 224 Since the Ra radioactivity is confined to the seed wall, the z-component of the flux density is set to zero on the seed base. That is, (∂n x ∂z) z=±l / 2 = 0. Defining i s as the radial index of the ring element in contact with the seed wall (i.e.,

Number

[0145]

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[0146] The source terms of Equations (43) and (44) are the same as in the 1D case, with the additional requirement of |z j | < l / 2.

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[0147] To solve Equation (43) in matrix form, linear indexing is used. The 2D elements

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[0148] For the 1D case, the matrix elements appearing in equation (51) depend on the values ​​of i, j (and therefore k) in such a way that the boundary conditions are satisfied. For compactness, we define the following intermediate quantities:

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[0149] Table 1 shows the i and z j Matrix elements for all possible cases for

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[0150]

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[0151] For the 1D case, the time step can be varied in a number of ways. Here we choose to update the time step according to the relative change in total activity (the sum of all isotopes in all ring elements).

[0152] The 2D numerical scheme described above was implemented in MATLAB with a code named "DART2D" that runs on a modern laptop (Intel i7 processor with 16 GB RAM) with Δr = 0.005 mm, Δz = 0.05 mm, ε tol =0.01, Δt0=0.1 seconds, R max = 7 mm, Z max = 10 mm, and takes roughly 0.5 hours to perform for a treatment time of 40 d. The most demanding process is M -1 Since M is a sparse diagonal matrix, we used MATLAB's spdiags() function, which reduces memory requirements by storing only the nonzero diagonal elements of M, allowing the code to run more efficiently.

[0153] Figure 6 shows the dependence of the adaptation time step on time up to about 11 days. The initial time step is 0.1 seconds, 220 Capture the Rn build-up with high accuracy (this is also the minimum allowed value for Δt). Then, 212 Following the build-up of Pb, the time step gradually increases until 224 It reaches its maximum allowable value in the asymptotic phase driven by the Ra decay rate (here about 1 h).

[0154] Total alpha dose accumulated during 40 days of DaRT treatment with finite size seeds ( 220 Rn+ 216 Po contribution and 212 Bi / 212 The sum of the Po contributions is shown in the rz plane in Figure 7A. The seed dimensions are R 0 = 0.35 mm and l = 10 mm. 224 The Ra activity was 3 μCi, and P des (Rn)=0.45 and

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[0155] The results of the full 2D calculation are then compared with those obtained using either the 0D analytical approximation or the full 1D calculation. Figure 8 shows these comparisons for dose profiles calculated at the seed midplane. On the left, L Rn =0.3mm, L Pb = 0.3 mm and P leak A comparison is shown for the low diffusion high leakage case with (Pb)=0.8, with L Rn =0.3mm, L Pb = 0.6 mm and P leak A comparison is shown for the high diffusion low leakage case with (Pb)=0.3. Bi =0.1L Pb and α Bi=0. The curves show the ratios between a full 2D calculation with DART2D and (1) a calculation obtained by approximating the seed to a finite line consisting of point-like segments and using the 0D approximation, (2) a calculation obtained by using the 0D approximation for an infinite cylindrical source, equations (26) and (27), and (3) a calculation obtained by using a full DART1D calculation. Approximating the seed to a finite source leads to an underestimation of the dose by up to about 80% for both low and high diffusion scenarios. Using a closed-form 0D approximation for a cylindrical source of radius R0 overestimates the dose at 2-3 mm by about 1-2% for the low diffusion / high leakage case and by about 5-10% for the high diffusion / low leakage scenario. In contrast, the full numerical solution for the cylindrical source (DART1D) provides accurate results (on a scale of 0.3%) when compared to the 2D calculation.

[0156] Figure 9 shows the calculated dose for a hexagonal seed lattice of parallel seeds with a grid spacing of 4 mm. As already mentioned, the seed radius is 0.35 mm; 224 Ra radioactivity is 3μCi (length >1cm), P des (Rn)=0.45,

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Claims

1. 1. An apparatus for planning a diffuse alpha emitter radiation therapy (DaRT) treatment session, comprising: An output interface; a memory configured to include a plurality of tables providing cumulative measurements of radiation over a particular time period resulting from one or more types of DaRT radiation therapy sources emitting daughter radionuclides for a plurality of different distances and angles relative to the DaRT radiation therapy source; a processor configured to receive a description of a layout of a plurality of DaRT radiation therapy sources within a tumor, to calculate a radiation dose distribution within the tumor in response to the layout using the table in the memory, and to output feedback to the treatment through the output interface in response to the radiation dose distribution; An apparatus comprising:

2. 2. The apparatus of claim 1, wherein the memory is configured to include multiple tables for different durations for a single source type, and the processor is configured to determine a treatment duration for the layout and select a table to use for calculating the radiation dose distribution depending on the treatment duration.

3. 2. The apparatus of claim 1, wherein the memory is configured to include multiple tables for sources of a single source type in different zones of the tumor, and the processor is configured to select the table to use for calculating the radiation dose from each source in the layout depending on the zone in which the source is located.

4. The apparatus of claim 3 , wherein the processor determines the zone in which a source is located as a function of the distance between the source and the edge of the tumor.

5. 2. The apparatus of claim 1, wherein the processor is configured to identify areas of the tumor where the dose is below a threshold and to suggest modifications to the layout that would raise the radiation dose in the identified areas above the threshold.

6. The apparatus of claim 1 , wherein the processor is configured to repeat the calculation of radiation dose distribution for a number of different treatment durations and to select one of the durations in response to the calculation.

7. Apparatus according to any one of claims 1 to 6, wherein the accumulated measure of radiation provided by the table comprises an accumulated radiation dose due to alpha radiation only.

8. An apparatus according to any preceding claim, wherein the accumulated measures of radiation provided by the table include accumulated radiation doses from alpha radiation and one or more of electron radiation and photon radiation.

9. An apparatus according to any preceding claim, wherein the accumulated measure of radiation provided by the table comprises one or more number densities of radionuclides.

10. 1. A method for planning a radiation therapy treatment session, comprising: receiving, by a processor, a description of a layout of a plurality of DaRT radiation therapy sources within a tumor; calculating, by the processor, a radiation dose distribution within the tumor according to the layout using a plurality of tables, the plurality of tables providing cumulative measures of radiation over a particular time period for a plurality of different distances and angles relative to the DaRT radiotherapy source resulting from one or more types of DaRT radiotherapy sources emitting daughter radionuclides; outputting feedback from the processor to the treatment in response to the radiation dose distribution; A method comprising:

11. 11. The method of claim 10, wherein calculating the radiation dose distribution comprises: determining a treatment duration of the layout; and selecting a table to use for calculating the radiation dose distribution according to the treatment duration.

12. The method of claim 10 , wherein calculating the radiation dose distribution comprises selecting a table used to calculate the radiation dose from each source in the layout depending on a zone of the tumor in which the source is located.

13. The method according to any one of claims 10 to 12, comprising repeating the calculation of radiation dose distribution for a number of different treatment durations and selecting one of the durations in response to the calculation.

14. 1. A method for planning a radiation therapy treatment session, comprising: receiving, by a processor, a plurality of parameters of tissue of a tumor requiring radiation therapy; receiving, by the processor, instructions for a layout of diffuse alpha emitter radiotherapy (DaRT) sources to be placed within the tumor; calculating the distribution of radon-220, lead-212 and bismuth-212 radionuclides in the tumor as a function of said layout of sources; determining a distribution of dose resulting from alpha radiation emitted within the tumor in response to the calculated distribution; determining an electron and photon radiation dose distribution within the tumor as a function of the source; setting one or more parameters of the radiation therapy treatment session in response to the determined distribution of alpha, electron and photon radiation. A method comprising:

15. 15. The method of claim 14, wherein calculating the distribution of radon 220, lead 212 and bismuth 212 is performed as a function of diffusion coefficients of radon 220 and lead 212 in the tumor.

16. 15. The method of claim 14, wherein calculating the distribution of radon 220, lead 212 and bismuth 212 is performed by solving a transport equation for lead 212 that includes a leakage coefficient that is a product of the concentration of lead 212 and a constant.

17. 15. The method of claim 14, wherein calculating the distribution of the radionuclide comprises calculating the distribution of the radionuclide for a single source and summing the distributions of the sources in the layout.

18. The method of claim 14 , wherein the setting one or more parameters of the radiation therapy treatment session comprises selecting a radioactivity of the source.

19. The method of claim 14 , wherein setting one or more parameters of the radiation therapy treatment session comprises adjusting the layout of the sources.

20. 15. The method of claim 14, wherein calculating the distribution of radon 220, lead 212 and bismuth 212 in the tumor and determining the distribution of alpha radiation comprises: preparing a table of radiation distributions for a number of different tumor types; and calculating the distribution of alpha radiation by summing values ​​from one of the tables that match the layout.

21. 21. The method of claim 20, wherein pre-preparing tables of radiation distribution comprises preparing a plurality of tables for each of the tumor types for respective treatment durations.

22. 22. The method of claim 21, wherein the treatment durations for which the table is prepared are unevenly distributed over the duration of validity of the source of the layout.

23. 15. The method of claim 14, wherein calculating the distribution of radionuclides and determining the distribution of alpha radiation in the tumor comprises repeating the determination for a plurality of different durations, and setting one or more parameters of the radiation therapy treatment session comprises selecting a duration of the treatment in response to the repeated determination.

24. 15. The method of claim 14, wherein receiving the indication of the layout comprises receiving an image of the tumor having the source therein, and determining a location of the source within the tumor responsive to the image.

25. 15. The method of claim 14, wherein determining the electron radiation dose distribution and the photon radiation dose distribution is performed in a manner that ignores the distribution of radon 220, lead 212 and bismuth 212 in the tumor.

26. 26. The method according to any one of claims 14 to 25, wherein calculating the distribution of Radon-220, Lead-212 and Bismuth-212 radionuclides comprises calculating based on at least one equation depending on a diffusion coefficient of Lead-212, the value of the diffusion coefficient of Lead-212 being calculated as a function of a diffusion length of Lead-212.

27. 27. The method of claim 26, wherein the diffusion length of lead 212 is assigned a value in the range of 0.2 to 0.4 millimeters.

28. 27. The method of claim 26, wherein the diffusion length of lead 212 is assigned a value according to a tissue type of the tumor.

29. 26. The method of any one of claims 14 to 25, wherein calculating the distribution of radon 220, lead 212 and bismuth 212 in the tumor and determining the distribution of alpha radiation comprises numerically solving equations using finite elements.

30. 30. The method of claim 29, wherein calculating the distribution of radon 220, lead 212 and bismuth 212 within the tumor and determining the distribution of alpha radiation comprises determining a finite element two-dimensional time-dependent solution.

31. 30. The method of claim 29, wherein calculating the distribution of radon 220, lead 212 and bismuth 212 within the tumor and determining the distribution of alpha radiation comprises numerically solving equations using finite elements with boundary conditions for each of the sources both on the exterior surface of the source and on the axis of the source.

32. 30. The method of claim 29, wherein calculating the distribution of radon 220, lead 212 and bismuth 212 within the tumor and determining the distribution of alpha radiation comprises numerically solving equations using finite elements for respective cylindrical domains surrounding each of the sources, with number densities set to zero outside the cylindrical domains.

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