Diffusing alpha-emitter radiation therapy for glioblastoma

JP2022189778A5Inactive Publication Date: 2025-06-09ALPHA TAU MEDICAL LTD
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Patent Information

Application Number
JP2022093362
Authority / Receiving Office
JP · JP
Patent Type
Applications
Current Assignee / Owner
Priority Date
2021-06-10
Filing Date
2022-06-08
Publication Date
2025-06-09
Estimated Expiration
Not applicable · inactive patent

AI Technical Summary

Technical Problem

Existing radiotherapy methods using alpha-emitting radium atoms struggle to deliver sufficient radiation doses to tumors while minimizing damage to healthy tissues due to the short range of alpha particles and the lack of a practical method to distribute alpha-emitters uniformly throughout the tumor volume.

Method used

A method and apparatus for precisely controlling radiation therapy by using diffuse alpha-emitter radiotherapy (DaRT) sources with adjustable radon emission rates and optimized source spacing to ensure uniform tumor coverage, minimizing healthy tissue exposure.

Benefits of technology

This approach enhances tumor destruction while reducing the risk of radiation overdose in healthy tissues by ensuring adequate radon distribution and controlled radiation delivery, improving treatment efficacy for tumors like glioblastoma.

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Abstract

To provide an apparatus and method for releasing tumor-specific radiation dosages in radiotherapy treatment.SOLUTION: A method for treating a tumor comprises identifying a tumor as a glioblastoma tumor and implanting, in the tumor identified as a glioblastoma tumor, at least one diffusing alpha-emitter radiation therapy (DaRT) source with a suitable radon release rate and for a given duration, such that the source provides during the given duration cumulated radioactivity of released radon between 6.5 mega becquerel (MBq) h and 14.3 MBq h, per centimeter length.SELECTED DRAWING: Figure 1
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Description

[Technical Field]

[0001] The present invention relates to an apparatus and method for providing tumor-specific radiation doses in radiotherapy, and more particularly in radiotherapy treatment. [Background technology]

[0002] Ionizing radiation is commonly used to treat certain types of tumors, including malignant cancerous tumors, by destroying cells. However, because ionizing radiation can also damage a patient's healthy cells, care is taken to maximize the dose to the tumor while minimizing the amount of radiation delivered to healthy tissue outside the tumor.

[0003] Ionizing radiation destroys cells by damaging their DNA. The biological effectiveness of different types of radiation in killing cells depends on the type and severity of DNA damage they produce. Alpha particles are a powerful tool in radiotherapy because they induce clustered double-strand breaks in DNA that cells cannot repair. Unlike conventional types of radiation, the destructive effect of alpha particles is less affected by low cellular oxygen levels and is equally effective against hypoxic cells, whose presence in tumors is a major cause of failure in conventional photon or electron-based radiotherapy. Furthermore, because alpha particles have a short reach within tissue (less than 100 micrometers), surrounding healthy tissue is protected if the alpha-emitting atoms are confined to the tumor volume. On the other hand, the short reach of alpha particles has limited their use in cancer treatment so far, as there has been no practical way to place a sufficient concentration of alpha-emitting atoms throughout the entire tumor volume.

[0004] For example, Diffuse alpha-emitter radiotherapy (DaRT), described in Kelson's U.S. Patent No. 8,834,837 (Patent Document 1), expands the therapeutic range of alpha-emitter radiation by using radium-223 or radium-224 atoms. Radium-224 has a half-life of 3.6 days, and radium-223 has a half-life of 11.4 days. In DaRT, the radium atom adheres firmly to a source (also called a "seed") implanted in the tumor and does not leave the source in a way that would be wasted (by being removed from the tumor via the blood), and a significant proportion of its daughter radionuclides (radon-220 in the case of radium-224, and radon-219 in the case of radium-223) leave the source and enter the tumor during radium decay. These radionuclides and their own radioactive daughter atoms spread around the source by diffusing to a radius distance of several millimeters before decaying with the alpha-emitter. Therefore, the range of tumor destruction increases compared to the radionuclides remaining in the source along with the daughter.

[0005] For tumor treatment to be effective, the DaRT seeds used in the treatment must emit a sufficient number of radon atoms to destroy the tumor with a high probability. If a sufficient amount of radiation is not used, too many cancer cells will remain in the tumor, and these cells may regenerate and reform the malignant tumor. On the other hand, the seeds should not emit too many radon atoms, because some of them may be removed from the tumor through the bloodstream, potentially damaging healthy tissues in the patient, such as bone marrow, kidneys, and ovaries.

[0006] The amount of radium atoms in a DaRT source is quantified in terms of radioactivity, i.e., the decay rate of radium. DaRT source radioactivity is measured in units of microcuries (μCi) or kilobecquerels (kBq), where 1 μCi = 37 kBq = 37,000 decays / second. When using DaRT, the amount of radiation delivered to tumor cells depends not only on the radium radioactivity of the source but also on the probability that radon atoms, daughters of radium, will detach from the source and enter the tumor during alpha decay. This probability is referred to herein as the "detachment probability." Therefore, instead of referring to the source's radioactivity, the "radon emission rate," defined herein as the product of the source's radioactivity and the detachment probability of radon from the source, can be used as a measure of the source's DaRT-related radioactivity. Like radioactivity, the radon emission rate is expressed in μCi or kBq. Unless otherwise specified, the radioactivity and radon emission rate values ​​described herein refer to the source at the time of implantation into the tumor.

[0007] Kelson's U.S. Patent No. 8,834,837 (Patent Document 1) above suggests using radioactivity of "about 10 nanocuries to about 10 microcuries, more preferably about 10 nanocuries to about 1 microcury." [Prior art documents] [Patent Documents]

[0008] [Patent Document 1] U.S. Patent No. 8,834,837 [Overview of the project]

[0009] Embodiments of the present invention relate to delivering a precisely controlled amount of radiation to a tumor in radiotherapy treatment. Embodiments include a kit comprising a radiotherapy source designed to deliver an appropriate amount of radiation, and an appropriate number of sources for a tumor of a particular size. Further embodiments relate to a method for preparing a kit of radiotherapy sources for a particular tumor and a method for treating a tumor.

[0010] Accordingly, embodiments of the present invention provide a method for treating a tumor, comprising: the step of identifying a glioblastoma tumor; and the step of implanting at least one diffusion alpha emitter radiotherapy (DaRT) source into the tumor identified as a glioblastoma tumor for a predetermined period of time at an appropriate radon emission rate, wherein the source provides a cumulative radioactivity of emitted radon between 5.6 megabecquerels (MBq) and 8 MBq hours per centimeter of length during the predetermined period.

[0011] As an option, the step of implanting at least one radiotherapy source includes the step of implanting an array of sources, where each source is no more than 4 millimeters away from adjacent sources in the array. In some embodiments, the step of implanting at least one radiotherapy source includes the step of implanting an array of sources in a hexagonal arrangement, where each source is no more than 4 millimeters away from adjacent sources in the array. As an option, at least one radiotherapy source has a radon emission rate between 1.4 and 3.1 microcuries per centimeter of length. As an option, at least one radiotherapy source has a radon emission rate between 1.8 and 2.6 microcuries per centimeter of length. As an option, the method includes the step of selecting a given period of time before implanting at least one DaRT source into the tumor, and removing the source from the tumor after a given period of time has elapsed since the implantation of the source.

[0012] According to embodiments of the present invention, a method is provided for preparing radiotherapy, comprising: identifying a tumor as a glioblastoma tumor; receiving an image of the tumor; and providing a layout of diffusion alpha-emitter radiotherapy (DaRT) sources for the glioblastoma tumor, wherein the sources have a radon emission rate of 1.4 to 3.1 microcuries per centimeter of length. The step of providing a layout as an option comprises providing a layout in which the spacing between sources in the tumor is 4 millimeters or less. The option is that the sources have a radon emission rate between 1.8 and 2.6 microcuries per centimeter of length.

[0013] According to embodiments of the present invention, an apparatus for preparing radiotherapy is provided, comprising: an input interface for receiving information about a tumor; a processor configured to determine that the tumor is a glioblastoma and to generate a layout of diffusion alpha-emitter radiotherapy (DaRT) sources for the tumor, wherein the sources in the layout have a radon emission rate of 1.4 to 3.1 microcuries per centimeter in length and the sources in the layout are arranged in a regular pattern with a distance of 5 millimeters or less between adjacent sources; and an output interface for displaying the layout to a human operator.

[0014] According to embodiments of the present invention, a method for preparing radiotherapy is provided, comprising: receiving a request for diffusion alpha-emitter radiotherapy (DaRT) sources for glioblastoma tumors; determining the number of radiotherapy sources required for glioblastoma tumors; and providing a kit comprising the determined number of radiotherapy sources, wherein the sources have a radon emission rate of 1.4 to 3.1 microcuries per centimeter in length.

[0015] The step of determining the number of radiotherapy sources required as an option involves determining the number of sources required so that the extent of the tumor is covered by sources with a spacing of 4 millimeters or less between sources. The options include sources having a radon emission rate between 1.8 and 2.6 microcuries per centimeter in length.

[0016] According to embodiments of the present invention, a diffusion alpha-emitter radiotherapy (DaRT) source for transplantation into glioblastoma tumors is further provided, wherein the DaRT source has a radon emission rate of 1.4 to 3.1 microcuries per centimeter in length. Optionally, the radon emission rate is between 1.8 and 2.6 microcuries per centimeter in length.

[0017] According to an embodiment of the present invention, there is further provided a kit of diffusion alpha emitter radiotherapy (DaRT) sources for implantation into glioblastoma tumors, comprising: a package; and a plurality of DaRT sources arranged in the package, the sources being DaRT sources having a radon emission rate of 1.4 to 3.1 microcuries per centimeter of length. As an option, the radon emission rate of the sources is between 1.8 and 2.6 microcuries per centimeter of length.

[0018] According to an embodiment of the present invention, there is further provided a method for treating a tumor, comprising: identifying the tumor as a glioblastoma tumor; and implanting an array of diffusion alpha emitter radiotherapy (DaRT) sources regularly arranged with a spacing of 3.5 to 4.5 millimeters between two adjacent sources into the tumor identified as a glioblastoma tumor. As an option, the step of implanting the array of sources is a step of implanting in a hexagonal arrangement, and each source is no more than 4 millimeters away from adjacent sources in the array.

Brief Description of the Drawings

[0019] [Figure 1] FIG. 13 is a schematic diagram of a system for planning radiotherapy according to an embodiment of the present invention. [Figure 2] FIG. 16 is a flowchart of actions performed when preparing for radiotherapy treatment of a tumor according to an embodiment of the present invention. [Figure 3-4] FIG. 3 is a schematic diagram of a regular arrangement of sources in a hexagonal arrangement according to an embodiment of the present invention. FIG. 4 is a schematic diagram of a kit of DaRT sources according to an embodiment of the present invention. [Figure 5] FIG. 22 is a schematic diagram of a radiotherapy source according to an embodiment of the present invention. [Figure 6A-6B]A graph showing a wide range of radon emission rate values required to ensure a nominal alpha particle dose of at least 10 Gray (Gy) for various seed spacings, the leakage probability of lead-212, and the diffusion lengths of radon-220 and lead-212. [Figure 6C-6D] A graph showing a wide range of radon emission rate values required to ensure a nominal alpha particle dose of at least 10 Gray (Gy) for various seed spacings, the leakage probability of lead-212, and the diffusion lengths of radon-220 and lead-212. [Figure 6E-6F] Figure 6E is a contour graph showing the required radon emission rate values over a target range for various possible radon-220 and lead-212 diffusion lengths for a 4 mm spacing, 50% lead-212 leakage, and a radiation dose of 10 Gy, according to an embodiment of the present invention. Figure 6F is a contour graph showing the minimum radiation dose expected to reach the cells of a tumor for various possible radon-220 and lead-212 diffusion lengths, according to an embodiment of the present invention, with seeds of 3 microcuries per centimeter length implanted at 4 mm intervals and assuming 50% lead-212 leakage. [Figure 7] A graph showing the safety rate for various intervals and the range of radon emission rates for glioblastoma, according to an embodiment of the present invention. [Figure 8A-8B] Figure 8A shows the spatial distribution of the optically stimulated luminescence (PSL) signal in a tissue section of a 4T1 tumor. The display range of the sample data is white (0 - 4 mm), and the fit range is the magenta dashed line (0.5 - 3 mm). ; Figure 8B is a graph of the radial radioactivity distribution of the sampled data of Figure 8A, fitted by a theoretical model for extracting the effective diffusion length. [Figure 8C-8D] Figure 8C shows the PSL spatial distribution in another histological section from the same tumor, where the seed positions are automatically determined by a step of calculating the intensity centroid. Figure 8D is a graph of the radial radioactivity distribution of the sampled data of Figure 8C, fitted by a theoretical model for extracting the effective diffusion length. [Figure 9-10]This figure shows the effective diffusion length as a function of tumor mass for different tumor types. [Figure 11-12] This figure shows the effective diffusion length as a function of tumor mass for different tumor types. [Figure 13-14] This figure shows the effective diffusion length as a function of tumor mass for different tumor types. [Figure 15-16B] Figure 15 shows four tissue sections of a DaRT-treated tumor, acquired using a digital autoradiography system to measure the diffusion length of radon-220. Figure 16A shows a single tissue section used for measuring the radon-220 diffusion length. Figure 16B shows the average count calculated as a function of distance from the seed location. A fitted model is used to measure the diffusion length of radon-220. [Modes for carrying out the invention]

[0020] One aspect of several embodiments of the present invention relates to the step of setting the radon emission rate of a DaRT source used when treating different types of tumors according to the characteristics of the tumor. The applicant has created a model for estimating the dose reaching tumor cells as a function of the diffusion length of lead-212 in the tumor, the diffusion length of radon-220 in the tumor, and the leakage probability of lead-212. Diffusion length represents the general distance from the point where an atom is produced by the decay of a radiophile nuclide to the point where the atom decays. It determines the spatial distribution of diffusing atoms around a seed; for every 1 diffusion length increase in radial distance from the seed, the alpha particle dose decreases by approximately one-third. For the seed of the radon emission rate considered here, the diameter of the range around the seed that receives a 10 Gy alpha particle dose is approximately 10 times the diffusion length. A method for measuring the effective diffusion length and estimating the range of values ​​for the diffusion length of radon-220 and lead-212 is described in the appendix. The probability of lead-212 leakage represents the likelihood that lead-212 atoms released from the source will leave the tumor via the bloodstream before decaying.

[0021] The diffusion length of radon-220 and the leakage probability of lead-212 vary depending on the type of cancerous tumor. Generally, the shorter the diffusion length of radon-220, the more radioactivity is required to achieve the same result. The applicant estimated the diffusion length of radon-220 in various types of tumors and, therefore, determined the radon emission rate of supply sources used to treat these tumor types.

[0022] Figure 1 is a schematic diagram of a system 100 for planning radiotherapy according to an embodiment of the present invention. The treatment generally involves implanting multiple radiation sources into a tumor to be destroyed. System 100 includes an imaging camera 102 for acquiring images of the tumor requiring radiotherapy. Furthermore, system 100 includes an input interface 104, such as a keyboard and / or mouse, for receiving input from a human operator, such as a physician. Alternatively or additionally, system 100 includes a communication interface 106 for receiving commands and / or data from a remote computer or a human operator. System 100 further includes a processor 108 configured to generate a layout plan of radiotherapy sources within the tumor and thus provide details of each kit of radiotherapy sources for the treatment of the tumor via an output interface 110. The output interface 110 may be connected to a display and / or a communication network. The processor 108 optionally includes a general-purpose hardware processor configured to run software and perform the tasks described below. Alternatively or additionally, the processor 108 includes a dedicated processor such as a signal processing processor, a digital signal processor (DSP), or a vector processor, and is configured with appropriate software for performing its tasks as described herein. In other embodiments, the processor 108 includes a dedicated hardware processor, such as an FPGA or ASIC, for performing its tasks.

[0023] In some embodiments, the processor 108 is further configured to estimate the radiation dose expected to reach each point within the tumor, as described, for example, in PCT application PCT / IB2021 / 050034, filed on January 5, 2021, titled “Therapeutic Planning for Alpha Particle Radiotherapy,” the disclosure of which is incorporated herein by reference.

[0024] Figure 2 is a flowchart of the actions performed when preparing a radiotherapy treatment for a tumor according to an embodiment of the present invention. The method in Figure 2 generally begins with the step (202) in which the system 100 receives input about the tumor, such as an image of the tumor and / or the type of tumor. The spacing between the sources to be inserted into the tumor is selected for the tumor (204), and thus the number of sources to be included in the tumor treatment kit is determined (206). Furthermore, the treatment period is selected (208). The radon emission rate of the sources is also selected (210). In some embodiments, instructions regarding the layout of the sources in the tumor are also prepared (212). Subsequently, a kit containing the number of sources for the selected parameters is prepared (214) and packaged in a suitable sterile package. In some embodiments, the method further includes a treatment procedure. In those embodiments, the method includes the step (216) of implanting the supply sources from the kit into the tumor according to the prepared (212) layout. In some embodiments, the method includes the step (218) of removing the sources after the selected (208) period. In other embodiments, the radiation source is not removed and remains in the patient.

[0025] In some embodiments, the tumor type is determined based on clinical and / or histopathological observations, such as an analysis of the amount and / or density of blood vessels within the tumor, determined from a portion of the tumor taken by biopsy and / or images of the tumor. The tumor type is selected from a list that includes, for example, squamous cell carcinoma, basal cell carcinoma, glioblastoma, sarcoma, pancreatic cancer, lung cancer, prostate cancer, breast cancer, and colorectal cancer.

[0026] In some embodiments, the radiation sources are arranged in a regular geometric pattern layout that achieves a relatively short distance between each point in the tumor and at least one of the radiation sources.

[0027] Figure 3 is a schematic diagram of a regular arrangement of radiation sources in a hexagonal arrangement 160 according to an embodiment of the present invention. In the hexagonal arrangement 160, the surface into which the radiation sources enter the tumor to be treated is divided into hexagons 164, and the center 162 of each hexagon is designated for the insertion of a radiation source. The centers 162 for inserting the radiation sources are located at the vertices of the equilateral triangles between each pair of radiation sources, and hereof the distance 166 is referred to as the spacing of the layout. The hexagons 164 are formed by the bisectors of the centers 162 to lines connecting their nearest six adjacent centers 162. The minimum dose of radiation from the radiation sources is at the centroid of the triangle, which is at the vertices of the hexagon. As options, the spacing between sources is less than 5 millimeters, 4.5 millimeters or less, 4 millimeters or less, 3.5 millimeters or less, or 3 millimeters or less. As will be discussed below, the spacing between sources is very important in determining the treatment plan for a particular type of cancer.

[0028] The spacing between sources is chosen as a compromise between the desire to ensure tumor destruction without using radioactivity levels that may be close to the safety limit, which requires a small spacing, and the simplicity of a simple procedure (204). Generally, the largest spacing that is still considered to destroy the tumor with seeds that do not have excessively high radioactivity levels is chosen. The spacing is chosen according to the type of tumor, as radon-220 and lead-212 have different diffusion lengths in different tumor types, and therefore DaRT sources have different effective ranges in different tumor types (204). Furthermore, different types of tumors require different radiation doses. In some embodiments, the spacing is chosen according to the type of tumor treatment (204). One type of treatment aims at a step to completely destroy the tumor cells. Another type of treatment aims at a step to reduce the tumor mass to a size invisible to the naked eye or a size that makes the tumor resectable. To completely destroy the tumor, it is usually necessary to increase the radioactivity level of the sources or narrow the spacing between sources.

[0029] Alternatively or additionally, when selecting the interval (204), accessibility to the location of the tumor within the patient's body is considered. For example, in the case of a visceral tumor that needs to be accessed by catheter or endoscope, a wider interval is preferred than for a similar tumor that is easily accessible. In some embodiments, the interval between sources is selected while considering the time and complexity of source implantation. Smaller intervals require more sources, and consequently, longer source implantation times. Therefore, according to some embodiments of the present invention, the largest possible interval that still allows for tumor destruction is used.

[0030] Figure 4 is a schematic diagram of a kit 700 of a DaRT source 21 according to an embodiment of the present invention. The kit 700 includes a sterile package 702 containing multiple alpha-emitter radiotherapy sources 21 for insertion into a tumor.

[0031] As an option, the radiation source 21 is provided in a vial or other casing 706 that prevents radiation from escaping from the casing. In some embodiments, the casing is filled with a viscous liquid such as glycerin, which prevents radon atoms from escaping from the casing 706, as described in PCT application PCT / IB2019 / 051834, titled “Radiotherapy Seed and Applicator,” which is incorporated herein by reference. In some embodiments, the kit 700 further includes a seed applicator 708 used to insert the radiation source 21 into the patient, as described in PCT application PCT / IB2019 / 051834. As an option, the applicator 708 is provided with one or more supply radiation sources 21 pre-loaded therein. According to this option, separate radiation sources 21 in the casing 706 are provided for cases where more than the number of pre-loaded radiation sources are required. Alternatively, the radiation source 21 in the casing 706 is not provided in the kit 700, and only the radiation source in the applicator 708 is included in the kit 700.

[0032] The number of sources included in the tumor treatment kit 700 is determined to cover the entire tumor according to the selected spacing and source layout (206). In some embodiments, an additional 10-20% supply sources are provided in the treatment kit.

[0033] The duration of treatment (e.g., the time the seed remains in the tumor) is selected as an option by the operator according to the desired treatment (e.g., complete destruction, mass reduction). In some embodiments, the duration of treatment is pre-selected based on tumor parameters such as the location of the tumor in the patient's body and the patient's availability for removal of the radiation source (208). Alternatively, the duration of treatment is selected during treatment based on the progress of treatment (208).

[0034] The radioactivity of the radiation sources and their detachment probabilities are selected as options depending on the chosen interval, treatment duration, and tumor type (210). In some embodiments, the radioactivity of the radiation sources and their detachment probabilities are further selected in response to the type of tumor treatment. For example, if the operator indicates that the goal should be the complete destruction of tumor cells, it may be necessary to remove the tumor from macroscopic observation or reduce its size to make it resectable. As options, the radioactivity of the radiation sources and their detachment probabilities are selected depending on the tumor type with the aim of achieving at least a specific radiation dose at each point throughout the tumor, which is described in more detail below.

[0035] While the risk of radiation overdose for a single small tumor is low, it should be noted that when treating large tumors and / or multiple tumors, treatment may involve implanting hundreds of radiation sources. In such cases, it is crucial to precisely adjust the radioactivity of the sources to prevent over-radiating the patient. Generally, it is considered undesirable to implant a patient with radiation levels exceeding a few millicuries (e.g., 2-5). However, as a precaution, a limit of approximately 1 millicurie is currently used. For large tumors requiring seeds of 170 cm or more, this sets a limit of approximately 6 microcuries for the radioactivity of a 1 cm long seed. Regarding radon emission rates, given a 38-45% detachment rate, this sets a limit of approximately 2.5 microcuries. This limit is not the same for all tumor types. Some tumor types, such as glioblastoma multiforme (GBM), prostate cancer, breast cancer, and squamous cell carcinoma, are generally expected to be treated with radiation when small. Therefore, the number of seeds used and their total length are expected to be less than 170 cm, and higher radon emission rates can be used. Other types of cancer, such as pancreatic cancer, are expected to require radiation therapy for large tumors. Further types of cancer, such as melanoma and colorectal cancer, are expected to require radiation therapy for several different tumors. These types of cancer may require seeds larger than 170 cm in length.

[0036] Please note that the actions in Figure 2 are not necessarily performed in the order presented. For example, if the source radioactivity is not selected according to the treatment period (210), the source radioactivity (210) can be selected before or concurrently with selecting the treatment period (208). As another example, the preparation of the layout and the preparation of the kit can be performed simultaneously or in any desired order.

[0037] Figure 5 is a schematic diagram of a radiotherapy source 21 according to an embodiment of the present invention. The radiotherapy source 21 includes a support 22 configured to be inserted into the body of a subject. The radiotherapy source 21 further includes radium-224 radionuclide atoms 26 on the outer surface 24 of the support 22, as described, for example, in U.S. Patent No. 8,894,969, which is incorporated herein by reference. Note that for ease of explanation, the atoms 26 and other components of the radiotherapy source 21 are depicted disproportionately large. Generally, the atoms 26 are bonded to the support 22 so that the radionuclide atoms 26 do not leave the support, however, in the event of radioactive decay, their daughter radionuclides, symbolically shown as 28, may leave the support 22 due to recoil resulting from the decay. The percentage of daughter radionuclides 28 that leave the support due to decay is called the detachment probability. Bonding of the atoms 26 to the support 22 is achieved by heat treatment in some embodiments. Alternatively or additionally, the coating 33 covers the support 22 and the radionuclide atoms 26 in a manner that prevents the release of the radionuclide atoms 26 and / or modulates the release rate of daughter radionuclides 28 during radioactive decay. The daughter radionuclides can escape from the radiotherapy source 21 by passing through the coating 33 due to recoil, or the recoil can bring them into the coating 33 and escape from there by diffusion. In some embodiments, as shown in Figure 5, in addition to the coating 33, an internal coating 30 of thickness T1 is placed on the support 22 and the radionuclide atoms 26 adhere to the internal coating 30. However, not all embodiments include an internal coating 30, in which case the radionuclide atoms 26 adhere directly to the support 22.

[0038] In some embodiments, the support 22 may have any suitable shape, such as a rod or plate, and may contain a seed for complete implantation within the patient's tumor. Instead of being completely implanted, the support 22 may be partially implanted within the patient and may be part of a needle, wire, endoscope tip, laparoscope tip, or any other suitable probe.

[0039] In some embodiments, the support 22 is cylindrical and has a length of at least 1 mm, at least 2 mm, or at least 5 mm. Optionally, the seed length is 5 to 60 mm. The support 22 optionally has a diameter of 0.7 to 1 mm, but optionally, larger or smaller diameter supply sources are used. In particular, for treatment layouts with small spacing, the support 22 optionally has a diameter of less than 0.7 mm, less than 0.5 mm, less than 0.4 mm, or 0.3 mm or less.

[0040] The radioactivity of the support 22 is measured here in units of microcuries per centimeter of source length. Since the amount of radiation reaching most of the tumor is governed by the radionuclides leaving the source, the measure of “radon emission rate” is defined herein as the product of radioactivity at the source and the probability of departure. For example, a source with radioactivity of 2 microcuries per centimeter and a 40% departure probability has a radon emission rate of 0.8 microcuries per centimeter.

[0041] The detachment probability depends on the depth of the radionuclide atoms 26 within the surface of the support 22, and / or the type and thickness of the coating 33. The injection of radionuclide atoms 26 into the surface of the support 22 is generally achieved by heat treatment of the radiotherapy device 21, and the depth of the atoms 26 can be controlled by adjusting the temperature and / or duration of the heat treatment. In some embodiments, the detachment probability is between approximately 38 and 45%. Alternatively, a higher detachment probability is achieved using, for example, one of the methods described in PCT Publication WO2018 / 207105, entitled “Polymer Coating for Proximity Irradiation Therapy Device,” the disclosure of which is incorporated herein by reference. In other embodiments, a lower detachment probability is used, such as that described in U.S. Provisional Patent Application No. 63 / 126,070, entitled “Diffusion Alpha Emitter Radiotherapy with Enhanced Beta Therapy,” the disclosure of which is incorporated herein by reference.

[0042] It should be noted that not all alpha particles reaching the tumor are due to daughter radionuclides 28 of radon-220 that leave the support 22 upon decay. Some of the daughter radionuclides 28 of radon-220 produced from the decay of radionuclide atom 26 remain on the support 22. When daughter radionuclide 28 decays, its daughter radionuclide, for example, plutonium-216, may leave the support 22 due to recoil. Lead-212, produced during the decay of plutonium-216, may also leave the support 22 due to recoil.

[0043] Generally, the radionuclide atom 26 is bound to the support 22 in such a manner that it prevents the radionuclide atom 26 itself from leaving the support 22. In other embodiments, the radionuclide atom 26 is bound to the support 22 in such a manner that it allows the radionuclide atom 26 to leave the support without decay, for example by diffusion, using one of the methods described, for example, in PCT Publication WO2019 / 193464, titled “Controlled Release of Radionuclides,” which is incorporated herein by reference. Diffusion is an option achieved by using a bioabsorbable coating that initially prevents the premature departure of the radionuclide atom but allows it to decay and diffuse after implantation into a tumor.

[0044] The total amount of radiation emitted from a source within a tumor, referred to herein as the “cumulative radioactivity of emitted radon,” depends on the radon emission rate of the source and the time the source remains in the tumor. If the source is left in the tumor for a long period, for example, more than one month in the case of a radium-224 source, the cumulative radioactivity of emitted radon reaches the product of the source's radon emission rate multiplied by the average lifetime of radium, which is 63 days or 87.12 hours, divided by ln², approximately 0.693. For example, a radium-224 source with a radon emission rate of 1 microcurie (μCi) = 37,000 becquerels (Bq) has a cumulative radioactivity of emitted radon for approximately 4.651 megabecquerels (MBq) hours. It should be noted that the same amount of cumulative radioactivity of emitted radon can be achieved by implanting a supply source with a higher radon emission rate for a shorter period. For such a short period, the cumulative radioactivity would be as follows:

number

number

[0045] The amount of radiation from a source required to achieve tumor destruction varies greatly depending on the type of tumor and the spacing between sources. Therefore, it is important to specify the required radiation for each type of tumor. A method for calculating the radiation dose reaching each point in the tumor according to the radiation of the implanted source is described in U.S. Patent Application Publication No. 17 / 141,251, filed on January 5, 2021, entitled “Therapeutic Planning for Alpha Particle Radiotherapy,” and its disclosure is incorporated herein by reference. Using these calculation methods, the required radon emission rate can be calculated as a function of the diffusion length of lead-212 in the tumor, the diffusion length of radon-220 in the tumor, the spacing between the sources implanted in the tumor, the probability of lead-212 leakage from the tumor, and the radiation dose required to reach each location in the tumor.

[0046] Figures 6A-6D are graphs showing a wide range of radon emission rate values ​​required to ensure a nominal alpha particle dose of at least 10 gray (Gy) for different values ​​of the above parameters. The required nominal alpha particle dose varies depending on the type of tumor and can be as high as 20-30 Gy, so the 10 Gy level is selected as a reference. To obtain the seed radioactivity required for target doses other than 10 Gy, it is necessary to multiply the 10 Gy seed radioactivity by the ratio of the target dose to 10 Gy. Figure 6A shows the required radon emission rate as a function of lead-212 diffusion length for three different values ​​of radon-220 diffusion length, with a lead leakage probability of 80% and a spacing of 3.5 mm. Figure 6B is a similar graph for a lead leakage probability of 40%. Figure 6C shows the same graph with a lead leakage probability of 80% at a 4 mm spacing, and Figure 6D shows the required radon emission rate with a lead leakage probability of 40% at a 4 mm spacing. Readers should understand that the range of possible radon emission rate values ​​is very wide, and the following discussion provides guidance on the narrower ranges used for specific tumor types.

[0047] Figure 6E is a contour graph showing the required radon emission rate values ​​for various possible radon-220 and lead-212 diffusion lengths across the target range, with 4 mm spacing, 50% lead-212 leakage, and a radiation dose of 10 Gy, according to embodiments of the present invention.

[0048] Figure 6F is a contour graph showing the minimum radiation dose expected to reach tumor cells with seeds of 3 microcuries per centimeter embedded at 4 mm intervals, for various possible diffusion lengths of radon-220 and lead-212 according to an embodiment of the present invention, assuming a 50% lead-212 leak.

[0049] As shown in Figure 6E, the required radon emission rate varies significantly depending on the diffusion length. Since the diffusion length differs depending on the type of tumor, the required radon emission rate will vary depending on the type of tumor.

[0050] To estimate the diffusion lengths of lead-212 and radon-220 in various types of tumors, the applicant conducted two classes of experiments on various types and sizes of tumors. In the first class of experiments, the applicant embedded radiation sources in tumors generated in mice, dissected the tumors after several days, and measured the actual radioactivity that reached various points in the tumor. These measurements fit into the above formula, and thus the effective long-term diffusion length within the tumor is estimated. This effective diffusion length is the larger of the diffusion lengths of radon-220 and lead-212.

[0051] Tumors were removed from mice and frozen to allow for immediate slicing after removal. The tumors were then cut into slices approximately 10 microns thick. Formalin fixation was performed immediately after sectioning, directly onto the histological slices placed on glass slides for a short time (minutes). After fixation, the slides were placed on Fuji phosphorescent imaging plates in a sealed box for 1 hour. The slides were separated from the plates using thin Mylar foil to avoid contamination by radioactive decay. Subsequently, the plates were scanned using a fluorescence imaging autoradiography system (Fuji FLA-9000) to record the spatial distribution of lead-212 within the histological slices.

[0052] Details on measuring effective long-term diffusion length are described in Appendix A below.

[0053] The second class of experiments was similar to the first class, but instead of waiting several days, the tumors were removed approximately 30 minutes after source insertion. The radioactive distribution after such a short period is thought to be mainly due to the diffusion of radon-220. This is because the spatial distribution of radon-220 stabilizes very quickly, while the contribution from lead-212 increases from zero to its maximum value 1.5 to 2 days after source insertion, and is still sufficiently low at 30 minutes after insertion. Details of the measurement of the diffusion length of radon-220 are described in Appendix B below.

[0054] Initial measurements of radon-220 diffusion lengths detected values ​​between 0.23 and 0.31 mm. However, the number of measurements was relatively small. Recent results of the above measurements surprisingly showed no significant difference between long-term and short-term experiments. Therefore, the applicant assumes that the diffusion length of lead-212 is shorter than that of radon-220. Thus, the applicant assumes that lead-212 is approximately 0.2 millimeters. This assumption is used because, as can be seen in Figure 6E, the dependence of the radon-220 diffusion length values ​​on the diffusion length of lead-212 is weak. The measured radon-220 diffusion lengths are summarized for several cancer types in Table 1.

[0055] As is known in this art, different tumor types require different doses of radiation to destroy their cells. Table 1 shows the biological effective dose (BED) required for various types of cancerous tumors in gray equivalent (GyE). These dose values ​​are for photon-based radiation (X-rays or gamma rays). Since alpha rays are considered more lethal to cells, the alpha dose in gray is converted to a gray equivalent BED (GyE) by multiplying it by a correction factor called the relative biological effect (RBE), which is currently estimated to be 5. The BED for DaRT is the sum of the alpha dose multiplied by the RBE and the beta dose resulting from radium-224 and its daughters.

[0056] The probability of lead-212 leakage is relatively low in the center of the tumor, but reaches approximately 80% in the peripheral areas. To ensure complete cell destruction of the tumor, the applicant used an 80% leakage probability value when selecting the radon emission rate of the source.

[0057] To estimate the desired seeding interval and radon emission rate for a specific tumor type, the applicant estimates the required dose for the tumor type, the beta radiation dose provided by the radiation level span, and the remaining required dose to be provided by alpha radiation. The alpha radiation dose is estimated relative to the spacing span and radon emission rate, and a safety factor, which is the ratio of the estimated provided dose to the required dose, is calculated relative to the spacing span and radon emission rate. The safety factor is necessary to overcome any potential inaccuracies that may occur in the source arrangement, as some sources may be separated at wider intervals than specified. Furthermore, tumors are heterogeneous, and there may be some local variations in diffusion length.

[0058] The applicant selected a safety factor range of 1.5–4 to define the interval and radon emission range required for treatment. This safety factor is considered to provide sufficient safety for the delivered radiation to destroy the tumor, while not high enough to endanger the patient from whole-body radiation resulting from the leakage of lead-212 from the tumor through the bloodstream and subsequent uptake by various organs.

[0059] For a given tumor type, the same safety margin can be achieved with different spacings and radon emission rates. When sources are placed at relatively large intervals, such as 4.5 mm or 5 mm, the radon emission rate of the sources needs to be high, such as more than 1.5 microcuries per centimeter. In contrast, when the spacing between sources is less than 4 mm, the sources can be assigned relatively low radon emission rates.

[0060] Given a selected range of safety factors, an appropriate source spacing is chosen. As described above, the largest possible spacing is selected that still allows for tumor destruction with seeds that do not have excessively high levels of radioactivity. The applicant limits the spacing selection to increments of 0.5 millimeters, which is considered close to the level of seed placement inaccuracy. These inaccuracies are taken into account by the safety factor.

[0061] After selecting the interval, a range of radon emission rates corresponding to the interval and safety margin is selected. This range of radon emission rates is considered to provide the best results in treating tumors of the tumor type for which the calculation was performed. It should be noted that the selected range of radon emission rates is not limited to being used with the specific interval used to select the range, but rather can be used for a safety margin, encompassing a range of intervals that surround the selected interval. [Table 1]

[0062] As shown in Table 1, the effective long-term diffusion length for glioblastoma is estimated to be approximately 0.29 mm, and the required dose is approximately 100 GyE.

[0063] Table 2 shows the beta dose, corresponding required alpha dose, estimated alpha dose, and resulting safety margin for several intervals and radon emission rates in glioblastoma. Figure 7 is a graph showing the safety margin for various interval and radon emission rate ranges in pancreatic cancer according to an embodiment of the present invention.

[0064] From Figure 7, the applicant determined that a 4 mm spacing requires a seed with a radon emission rate substantially exceeding 2.5 microcuries. To avoid such high levels of radioactivity, a 3.5 mm spacing is assumed when selecting the radon emission rate of the source. In practice, the spacing used may be shorter than 3.9 mm, shorter than 3.8 mm, shorter than 3.7 mm, or even shorter than 3.6 mm. On the other hand, the spacing used may also be longer than 3.1 mm, longer than 3.2 mm, longer than 3.3 mm, or longer than 3.4 mm. [Table 2]

[0065] At a 3.5 mm interval, a safety factor between 1.5 and 4 corresponds to a radon emission rate of 1.4 to 3.1 microcuries per centimeter. While the upper end of this range is relatively high, this range of radon emission rates is reasonable given the importance of successful treatment of tumors in the patient's head, the difficulty of access, and the expectation that the tumors are relatively small. For long-term treatment, this corresponds to a cumulative radioactivity of emitted radon between approximately 6.5 MBq hours and 14.3 MBq hours per centimeter.

[0066] In some embodiments, to increase the likelihood of treatment success, radon emission rates of at least 1.5 microcuries per centimeter, at least 1.7 microcuries per centimeter, at least 1.8 microcuries per centimeter, and even at least 2.0 microcuries per centimeter are used for glioblastoma. In some embodiments, to reduce the amount of radiation the patient is exposed to, the radon emission rate is 3.0 or less, 2.8 or less, 2.5 or less, or even 2.2 microcuries or less per centimeter. In other embodiments, a safety factor of 1.5 to 2.5 is used, and therefore the radon emission rate is 1.4 to 2.3 microcuries per centimeter. In yet another embodiment, a safety factor between 3 and 4 is used, and therefore the radon emission rate of seed 21 is 2.65 to 3.1 microcuries per centimeter.

[0067] Alternatively or additionally, the sources may include, as options, at least 7 MBq hours per centimeter, at least 8 MBq hours per centimeter, at least 9 MBq hours per centimeter, and even at least 10 MBq hours per centimeter. Alternatively, the sources may include, as options, less than 12 MBq hours per centimeter, or less than 11 MBq hours per centimeter.

[0068] (Conclusion) It will be understood that the above methods and apparatus should be interpreted as including methods of using the apparatus and apparatus for performing the methods. Features and / or things described in relation to one embodiment may be used in conjunction with other embodiments, and it should be understood that not all embodiments of the present invention have all of the features and / or things described in relation to one particular embodiment shown in a particular figure. Tasks may not necessarily be performed in the exact order described.

[0069] It should be noted that some of the embodiments described above may not be essential to the present invention and may include structures, actions, or details of structures and actions described as examples. The structures and actions described herein are interchangeable with equivalents that perform the same function, even if the structures or actions differ, as is known in the art. The embodiments described above are cited as examples and the present invention is not limited to those specifically shown and described herein. Rather, the scope of the present invention includes therapies of combinations and subcombinations of the various features described above, as well as their variations and modifications.

[0070] (Appendix A) (Measurement of effective diffusion length) 7-20 days after tumor inoculation, when the lateral diameter of the tumor is approximately 6-15 mm, 2-3 uCi 224 A single DaRT seed (6.5 mm long, 0.7 mm outer diameter) carrying Ra is inserted into the center of a mouse-borne tumor. After 4-5 days, the tumor is excised (as a whole) and split in two perpendicular to the seed axis at the estimated location of the seed center. The seed is then removed using surgical forceps and placed in a water-filled tube for measurement with a gamma counter. The tumor is held at approximately 80°C for 1 hour. It is then placed in dry ice and measured with the same gamma counter, and the amount contained is... 212 Measure the radioactivity of Pb. The radioactivity measurements of the seed and tumor are taken from the tumor. 212 It is used to determine the probability of Pb leakage.

[0071] Immediately after gamma measurement, half of the tumors undergo histological sectioning using a cryostat microtome. The sections are cut to a thickness of 10 μm at 250–300 μm intervals, placed on a positively charged glass slide, and fixed with 4% paraformaldehyde. Typically, there are 5–15 sections per tumor, each 1.5–5 mm in length. Immediately after preparation, the glass slides are placed face down for 1 hour on a phosphorescent imaging plate (Fujifilm TR2040S) protected with 12 μm Mylar foil, and then placed in a light-shielding case. 212 Pb descendant atoms, 212 Bi and 212Alpha particles emitted from the section of the Po decay penetrate the foil and accumulate energy in the radioactive layer of the phosphorescent imaging plate. Next, the plate is read with a fluorescence imaging scanner (Fujifilm FLA-9000).

[0072] For each tumor section, the results are two-dimensional intensity maps proportional to the local 212 Pb radioactivity. Using appropriate calibration samples measured simultaneously with the slides, the intensity (in units of optically stimulated luminescence) is 212 converted to the radioactivity of Pb. The point where the seed crosses the section is identified either by a "hole" appearing in the radioactivity map or by obtaining the centroid of the radioactivity distribution. Examples are shown in 8A - 8D. A region of interest (ROI) centered on the estimated seed position is defined and divided into concentric rings with a width of 0.1 mm in the range of radii from 0.5 to 3 mm. For each ring, the average value of the radioactivity is calculated. If the ROI extends beyond the range of the tumor section or includes ranges with degraded tissue or image quality, the ring average is obtained in limited azimuthal sectors. Next, the curve of the radioactivity obtained as a function of the radial distance from the origin (estimated seed position) is numerically fitted by a function representing the radial radioactivity distribution from the seed based on the diffusion leakage model. In the calculation, the seed is described as a line source perpendicular to the image. The line source is divided into segments like a number of points, each providing radioactivity

Number

[0073] Figure 8A shows the spatial distribution of photostimulated emission (PSL) signals in tissue sections of a 4T1 tumor. The sampled data area is shown in white (0–4 mm), and the fitted area is shown as a magenta dashed line (0.5–3 mm). Seed positions are determined manually. Figure 8B is a graph of the radial radioactivity distribution of the sampled data from Figure 8A, fitted by the diffusion leakage model. Figure 8C shows the PSL spatial distribution in another tissue section of the same tumor. Here, the seed position is automatically determined by calculating the centroid of the intensity. Figure 8D is a graph of the radial radioactivity distribution of the sampled data from Figure 8C, fitted by the diffusion leakage model. Figure 9 shows the measured effective diffusion length as a function of tumor mass in pancreatic tumors. Figure 10 shows the measured effective diffusion length as a function of tumor mass for prostate tumors. Figure 11 shows the measured effective diffusion length as a function of tumor mass for melanoma tumors. Figure 12 shows the measured effective diffusion length as a function of tumor volume in squamous cell carcinoma tumors. Figure 13 shows the measured effective diffusion length as a function of tumor volume in triple-negative breast cancer. Figure 14 shows the measured effective diffusion length as a function of tumor volume in GBM tumors.

[0074] (Appendix B) (Rn measurement method) DaRT seeds are inserted into the tumor for a relatively short time (30 minutes), after which the seeds are removed (to prevent Pb accumulation in the tumor). The tumor is then frozen and cut into 10 μm thick sections perpendicular to the seed axis. These are placed on glass slides and fixed using formaldehyde. The tumor sections are sent to a digital autoradiography system (iQID alpha camera by QScint Imaging Solutions, LLC). This system records each alpha particle hit, providing xy coordinates (with an accuracy of approximately 20 μm), a timestamp, and a signal proportional to the accumulated energy.

[0075] Figure 15 shows an example of images acquired using the iQID system, consisting of four tissue sections of a DaRT-treated tumor. This shows four tissue sections of a DaRT-treated tumor acquired using the iQID autoradiography system. For analysis, the images are cropped so that each section is analyzed independently, as seen in Figure 16A, which shows a single histological section used for analysis. For each section, the center is selected (by centroid or by identifying a “hole” in the radioactive map), and the average number of alpha particle counts is calculated by increasing the radial distance from the center. The resulting plot is then numerically fitted, assuming that the recorded radioactive map is a superposition of microsegments along the DaRT seed. Each segment is calculated using Equation 1 below:

number

[0076] To avoid the center (where the DaRT seed was located) and artificial "holes" at the far end of the distribution where statistical variability is too large, the fit is performed within a limited range of the radioactive distribution. An example of a fitted curve is shown in Figure 16B. This shows the average count calculated as a function of distance from the seed location, including the fitting function.

Claims

1. A diffusion alpha emitter radiotherapy (DaRT) source for use in the treatment of a patient's glioblastoma tumor, wherein the DaRT source comprises: a support having a length of at least 1 millimeter; and radium-224 atoms coupled to the support, wherein when the DaRT source is implanted in the tumor, no more than 20% of the radium-224 atoms leave the support and enter the tumor without decaying within 24 hours, but when decaying, at least 5% of the daughter radionuclides of the radium-224 atoms leave the support; and the administration pattern of the DaRT source has a step of implanting the DaRT source into the glioblastoma tumor for a predetermined period, wherein the source provides a cumulative radioactivity of radon released at 6.5 megabecquerels (MBq) per centimeter length per hour to 14.3 MBq per centimeter length per hour during the predetermined period. A DaRT source characterized by the above.

2. The administration pattern of the DaRT source has a step of implanting the DaRT source into the glioblastoma tumor together with other DaRT sources with a spacing of 3 to 4.5 millimeters between the DaRT sources across the entire tumor. The DaRT source according to claim 1, characterized by the above.

3. The administration pattern of the DaRT source has a step of implanting the DaRT source into the pancreatic cancer tumor together with other DaRT sources with a spacing of 3.1 to 3.9 millimeters between the DaRT sources across the entire tumor. The DaRT source according to claim 2, characterized by the above.

4. The administration pattern of the DaRT source has a step of implanting the DaRT source into the glioblastoma tumor together with other DaRT sources in a hexagonal arrangement across the entire tumor, and each DaRT source is no more than 4 millimeters away from an adjacent DaRT source within the hexagonal arrangement. The DaRT source according to claim 1 or 2, characterized by the above.

5. The administration pattern of the DaRT source has a step of selecting the predetermined period before implanting the DaRT source and removing the DaRT source from the glioblastoma tumor after the predetermined period has elapsed since the implantation of the DaRT source. The DaRT source according to any one of claims 1 to 4, characterized by the above. **Claim 6**: The DART source according to any one of claims 1 to 5, characterized in that the DART source has a radon emission rate between 1.4 and 3.1 microcuries per centimeter of length. **Claim 7** The DART source according to claim 6, characterized in that the DART source has a radon emission rate between 1.4 and 2.3 microcuries per centimeter of length. **Claim 8** The DART source according to claim 7, characterized in that the DART source has a radon emission rate between 1.4 and 1.9 microcuries per centimeter of length. **Claim 9** The DART source according to claim 6, characterized in that the DART source has a radon emission rate between 1.9 and 2.6 microcuries per centimeter of length. **Claim 10** A method of preparing for radiation therapy, comprising: identifying the tumor as a glioblastoma tumor; receiving an input regarding the glioblastoma tumor; and laying out a diffusion alpha emitter radiation therapy (DART) source for the glioblastoma tumor; and providing a kit having a determined number of the DART sources required for the glioblastoma tumor; providing one or more of: wherein the DART source has a radon emission rate of 1.4 to 3.1 microcuries per centimeter of length. A method characterized by the above. **Claim 11**: The method according to claim 10, characterized in that the step of receiving an input regarding the glioblastoma tumor includes receiving an image of the tumor. **Claim 12** The step of providing the layout includes providing a layout in which the distance between the DART sources in the tumor is 4 millimeters or less, characterized in that the method according to claim 10 or 11. **Claim 13** The method according to claim 10 or 11, characterized in that the DART source has a radon emission rate between 1.8 and 2.6 microcuries per centimeter of length. **Claim 14**: The method according to claim 10 or 11, further comprising determining the number of the DART sources required such that the range of the tumor is covered by the DART sources with a distance of 4 millimeters or less between the DART sources. **Claim 15**: A diffusion alpha emitter radiation therapy (DART) source for use in treating a patient's glioblastoma tumor, comprising: ​ a support having a length of at least 1 millimeter; and radium-224 atoms coupled to the support, wherein at least 5% of the daughter radionuclides of the radium-224 atoms leave the support upon decay; comprising the administration pattern of the DaRT source has a regular arrangement in which the distance between each two adjacent DaRT sources is 3.1 to 3.9 millimeters apart, and comprises the step of implanting the DaRT source into the glioblastoma tumor characterized by the DaRT source.

16. The DaRT source according to claim 15, wherein the DaRT source is implanted into the glioblastoma tumor in an arrangement of a hexagonal configuration, and each DaRT source is no more than 3.5 millimeters apart from an adjacent DaRT source within the arrangement.