Dose evaluation method, irradiation planning method, dose evaluation device, control program, and recording medium

Abstract

According to the invention, the clinical dose is accurately evaluated. The dose evaluation method includes: a calculation information acquisition step (S1) for acquiring calculation object information including: information relating to radiation including a dose or a dose rate of the radiation to be irradiated to an irradiation object; and information pertaining to the type of cells constituting the irradiation target that is irradiated with the radiation, the information pertaining to the type of cells constituting the irradiation target. An absorbed dose acquisition step (S2) for acquiring, for each type of cells constituting the irradiation target, an absorbed dose indicating the energy of the radiation absorbed by the type of cells; and a calculation step (S4) for calculating, on the basis of the calculation object information and the absorbed dose information, a clinical dose to be irradiated to the irradiation object for each type of cells.

Description

Technical Field

[0001] The present invention relates to a dose evaluation method, an irradiation planning method, a dose evaluation device, a control program, and a recording medium for evaluating a clinical dose during radiation irradiation. Background Art

[0002] Conventionally, in performing radiation therapy, in order to predict the effects on irradiated objects such as tumors that appear in an organ and normal organs around the tumors, the dose distribution in the body is estimated to create a treatment plan. For example, the clinical dose is calculated by the method described in Patent Document 1 or Patent Document 2, the dose distribution in the subject body is estimated based on the clinical dose, and a treatment plan is created based on the dose distribution.

[0003] Prior Art Documents

[0004] Patent Documents

[0005] Patent Document 1: Japanese Patent No. 5454989 Gazette

[0006] Patent Document 2: Japanese Unexamined Patent Application Publication No. 2019-180908 Summary of the Invention

[0007] Problems to be Solved by the Invention

[0008] In the conventional clinical dose estimation method, there is room for improvement in the accuracy of the clinical dose estimation result.

[0009] Means for Solving the Problems

[0010] To solve the above problems, a first aspect of the present invention relates to a dose evaluation method, which includes: a calculation information acquisition step for acquiring calculation object information, the calculation object information including: information related to radiation, the information including the dose or dose rate of the radiation to be irradiated to the irradiated object; and information related to the type of cell, the type of cell being the type of cell constituting the irradiated object, the irradiated object being irradiated with the radiation; an absorbed dose acquisition step for acquiring absorbed dose information indicating an absorbed dose for each type of cell constituting the irradiated object, the absorbed dose being the energy of the radiation absorbed by the type of cell; and a calculation step for calculating a clinical dose to be irradiated to the irradiated object for each type of cell based on the calculation object information and the absorbed dose information.

[0011] In addition, a second aspect of the present invention relates to an irradiation planning method for creating an irradiation plan for the radiation of the irradiated object based on the clinical dose calculated by the dose evaluation method according to the first aspect above.

[0012] In addition, a third aspect of the present invention relates to a dose evaluation device, which includes: a calculation information acquisition unit for acquiring calculation target information, the calculation target information including: information related to radiation, the information including the dose or dose rate of the radiation to be irradiated to an irradiation target; and information related to the type of cells, the type of cells being the type of cells constituting the irradiation target, and the irradiation target being irradiated with the radiation; an absorbed dose acquisition unit for acquiring absorbed dose information representing the absorbed dose for each type of cell constituting the irradiation target, the absorbed dose being the energy of the radiation absorbed by the cells of this type; and a calculation unit for calculating the clinical dose to be irradiated to the irradiation target for each type of cell based on the calculation target information and the absorbed dose information.

[0013] The dose evaluation device according to each aspect of the present invention can be implemented by a computer. In this case, by causing the computer to operate as each part (software element) included in the dose evaluation device, a control program for the dose evaluation device of the dose evaluation device implemented by the computer, and a computer-readable recording medium storing the control program also fall within the scope of the present invention.

[0014] Effects of the Invention

[0015] According to the dose evaluation method and the like of the present invention, the clinical dose can be evaluated more accurately than conventional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is an example of a graph showing the relationship between the survival rate of adenocarcinoma cells derived from the human submandibular gland (HSG cells) and the dose of the irradiated radiation in an ultra-high dose rate heavy particle beam irradiation experiment.

[0017] Figure 2 It is an example of a graph showing the relationship between the survival rate of bronchus-derived epithelial cells (Nuli-1 cells) and the dose of the irradiated radiation in an ultra-high dose rate heavy particle beam irradiation experiment.

[0018] Figure 3 It is an example of a graph showing the relationship between the survival rate of human skin fibroblasts (HDF cells) and the dose of the irradiated radiation in an ultra-high dose rate heavy particle beam irradiation experiment.

[0019] Figure 4 It is an example of a graph showing the relationship between the survival rate of other types of cells X except HSG cells, Nuli-1 cells, and HDF cells and the dose of the irradiated radiation in an ultra-high dose rate heavy particle beam irradiation experiment.

[0020] Figure 5 It is a graph showing an example of the measurement results obtained from a heavy particle beam irradiation experiment regarding the radiation dose of heavy particle beam irradiation and the cell survival rate, and the results calculated in accordance with the present invention in a manner consistent with the measurement results.

[0021] Figure 6 It is a block diagram showing an example of the configuration of a dose evaluation device.

[0022] Figure 7 It is a flowchart showing an example of the process performed in the dose evaluation device.

[0023] Figure 8 It is a graph showing an example of the relationship between the absorbed dose and the depth measured from the surface of the irradiated object when the object is irradiated with radiation, where the absorbed dose represents the amount of energy of the radiation absorbed by the irradiated object.

[0024] Figure 9 It is a graph showing the relationship between the absorbed dose and the depth measured from the surface of the irradiated object when multiple energy beams are overlapped and irradiated in radiation therapy, where the absorbed dose represents the amount of energy of the radiation absorbed by the irradiated object.

[0025] Figure 10 It is a graph showing the relationship between the absorbed dose, the biological dose, and the clinical dose.

[0026] Figure 11 It is an example of a dose distribution map showing the results obtained by estimating the dose distribution in heavy particle beam therapy using a conventional dose distribution calculation method. Detailed implementation mode

[0027] 〔Embodiment 1〕

[0028] <Heavy particle beam therapy>

[0029] The dose evaluation method, irradiation planning method, etc. according to the present invention can be applied to heavy particle beam therapy. Heavy particle beam therapy is a radiation therapy using heavy particle beams (such as carbon ion beams) in radiation therapy, which is one of cancer treatments. Compared with the radiation (such as photon rays (X-rays, etc.), electron rays, or proton rays) used in conventional radiation therapy, heavy particle beams have a higher killing ability against cancer cells in the tumor area. Therefore, heavy particle beam therapy is a radiation therapy suitable for cancer treatment.

[0030] Figure 8It is a graph showing an example of the relationship between the absorbed dose and the depth measured from the surface of the irradiated object when irradiated with radiation, where the absorbed dose represents the amount of energy of the radiation absorbed by the irradiated object. Here, as an example, the relationship between the absorbed dose in proton radiation, which is one of the particle radiations, and the depth measured from the surface of the irradiated object is shown. As Figure 8 shown, radiation has the property of showing the maximum effect at a deeper part of the body of a person as the irradiated object when irradiating the body of the person as the irradiated object, and particle radiations such as carbon rays have this property.

[0031] Figure 9 It is a graph showing the relationship between the absorbed dose and the depth measured from the surface of the irradiated object when multiple energy beams are overlapped and irradiated in radiation therapy, where the absorbed dose represents the amount of energy of the radiation absorbed by the irradiated object. In radiation therapy, as Figure 9 shown, the method of overlapping multiple energy beams and irradiating the tumor region ( Figure 9 the region indicated by the arrow Y) is adopted.

[0032] Particle radiation has the property of showing the maximum effect at a deeper part of the body of the irradiated object such as a human body when irradiating the irradiated object. Utilizing this property, by overlapping multiple energy beams and irradiating the tumor region in particle radiation therapy, it is possible to concentrate the radiation irradiation on the tumor region and it is not easy to damage the normal cell region ( Figure 9 the region indicated by the arrow X) around the tumor region. Therefore, compared with the conventional radiation therapy, the treatment period of heavy particle beam therapy is short, and for the patients receiving the treatment, a higher QOL (Quality of Life) can be achieved. In heavy particle beam therapy, the dose distribution of heavy particle beams in the body is predicted in advance. Based on the prediction result of the dose distribution, the radiation dose to be irradiated to the tumor during treatment is determined, and a treatment plan is formulated.

[0033] <Conventional Dose Distribution Prediction Method in Heavy Particle Beam Therapy>

[0034] The absorbed dose refers to the amount of energy absorbed by a unit mass of substance through the irradiation of radiation. It is known that the degree of influence of heavy particles such as carbon particles on the irradiated cells cannot be evaluated only by the absorbed dose, and the dose distribution in heavy particle beam therapy cannot be predicted only based on the physical absorbed dose (also called physical dose) like in general photon radiation therapy and proton radiation therapy. In order to predict the dose distribution, it is necessary to consider the biological dose, which is the dose obtained by considering the biological effect, and the clinical dose, which is the dose obtained by considering the clinical effect.

[0035] Figure 10Indicates the relationship among absorbed dose, biological dose, and clinical dose. The biological dose is the value obtained by multiplying the absorbed dose by the relative biological effectiveness (RBE). RBE is an index used to represent the difference in the intensity of biological effects due to the type and depth of the radiation beam. RBE is the ratio of the absorbed dose of a reference radiation (benchmark X-ray) required to achieve a certain effect to the absorbed dose of the radiation (the radiation to be irradiated to the object) required to achieve the same effect. The value of RBE varies depending on the type of radiation beam, etc. RBE is a value obtained through experiments of irradiating cultured cell lines with heavy particle beams (cell irradiation experiments) and biological evaluations through cell irradiation experiments.

[0036] The clinical dose is the radiation dose actually irradiated to the irradiation object such as a tumor. Generally, the calculated biological dose is multiplied by an empirical coefficient (such as 1.46) to obtain the clinical dose.

[0037] Since the value of RBE to be adopted is obtained through experiments based on the type and quality of the radiation beam, etc., in the dose distribution prediction in heavy particle beam therapy, the RBE to be adopted is used for the absorbed dose to calculate the biological dose, and then the radiation dose (clinical dose) to be irradiated to the tumor during treatment is determined based on the calculated biological dose.

[0038] When making a treatment plan for heavy particle beam therapy, in addition to the absorbed dose, dose distribution calculations are also performed based on the doses considering biological effects (biological dose, clinical dose), and the dose distribution is predicted when heavy particle beams are irradiated according to the calculated clinical dose. This dose distribution represents the distribution of the energy applied to the irradiation object such as a tumor. Figure 11 Is an example of a dose distribution diagram showing the result of predicting the dose distribution in heavy particle beam therapy using the conventional dose distribution calculation method (described below). As Figure 11 shown, the dose distribution diagram is a diagram made by drawing contour lines connecting the positions that are supposed to have the same dose with lines ( Figure 11 the dotted lines in) on the medical image obtained by photographing the irradiation object ( Figure 11 the solid line part in).

[0039] <Previous Biological Dose Calculation Method in Heavy Particle Beam Therapy>

[0040] As a conventional biological dose calculation method, for example, the method described in Japanese Unexamined Patent Application Publication No. 2019-180908 can be used. Hereinafter, an example of the conventional biological dose calculation method will be described. Since the curve showing the relationship between the dose and the survival rate obtained in the experiment of irradiating a cultured cell line with radiation (cell irradiation experiment) conforms to the model obtained by the following formula (1), the method of calculating the cell survival rate S i is often used.

[0041]

Equation 1

[0042]

[0043] Here, d i is the absorbed dose in the standard cell. In the estimation of the clinical dose in heavy particle beam therapy, an adenocarcinoma cell line derived from the human submandibular gland (HSG cell) is often selected as the standard cell.

[0044] The coefficient α and the coefficient β are values obtained based on a function made from the survival rate curve with the linear energy transfer (LET) as a variable, and the survival rate curve is a curve obtained from the radiation irradiation experiment on cells.

[0045]

Equation 2

[0046] α = f(LET)

[0047] β = g(LET)

[0048] Based on the cell survival rate S calculated by formula (1) i , the biological dose d bio，i at the position of interest i is calculated by the conventional estimation formula, i.e., the following formula (2), and the clinical dose is calculated based on this biological dose.

[0049]

Equation 3

[0050]

[0051] <New Insights Obtained by Ultra-High Dose Rate Heavy Particle Beam Irradiation>

[0052] In radiotherapy using photon rays (such as X-rays), electron rays, or proton rays, irradiation is sometimes performed at a dose rate significantly higher than normal (for example, more than 400 times the dose rate used in normal radiotherapy). It is known that when performing radiotherapy at such an ultra-high dose rate, an effect can be seen where damage to normal tissues is suppressed while maintaining the local control rate of tumors. This effect is called the FLASH effect. In addition, the dose is the intensity of the radiation, and the "dose rate" refers to the dose irradiated to a certain area per unit time. Additionally, the "dose rate used in normal radiotherapy" (sometimes referred to as the "normal dose rate" below) is, for example, a dose rate of 0.03 Gy / second (irradiating a 1-liter (10 cm × 10 cm × 10 cm) irradiation volume with a range of 20 g / cm 2 in the case of irradiating a physical dose of 2 Gy). Additionally, the "ultra-high dose rate" refers to, for example, a dose rate of 40 Gy / second or more.

[0053] Although reports have been made on the FLASH effect when using photon rays (such as X-rays), electron rays, or proton rays for radiotherapy, no reports have been made on the FLASH effect when using heavy particle beams for irradiation. Additionally, at present, there are few facilities capable of performing heavy particle beam therapy, and it is not easy to conduct irradiation experiments using heavy particle beams. In particular, since heavy particle beam irradiation devices capable of irradiating at an ultra-high dose rate are extremely limited, no academic judgment has been made on the FLASH effect in heavy particle beams.

[0054] The inventors, through painstaking research, clearly confirmed the FLASH effect when performing ultra-high dose rate heavy particle beam irradiation. Figures 1 to 4 is an example of a graph showing the relationship between the survival rate of cells being irradiated in an ultra-high dose rate heavy particle beam irradiation experiment and the dose of the irradiated radiation. Figures 1 to 4 The cells being irradiated in

[0055] · Figure 1 : Human submandibular gland-derived adenocarcinoma cells (HSG cells).

[0056] · Figure 2 : Bronchus-derived epithelial cells (Nuli-1 cells).

[0057] · Figure 3 : Human skin fibroblasts (HDF cells).

[0058] · Figure 4 : Other types of cells X other than HSG cells, Nuli-1 cells, and HDF cells.

[0059] Figure 1It is a graph showing the results when HSG cells, which are standard cells, were irradiated with heavy particle beams under general dose rate and ultra-high dose rate conditions, respectively. Figure 1 In it, the dashed line is a survival rate curve showing the relationship between the dose of the heavy particle beam irradiated when irradiating with the heavy particle beam under the general dose rate condition and the survival rate, and the solid line is a survival rate curve showing the relationship between the dose of the heavy particle beam irradiated when irradiating with the heavy particle beam under the ultra-high dose rate condition and the survival rate. Figure 2 and Figure 3 They are graphs showing the results when Nuli-1 cells and HDF cells were irradiated with heavy particle beams under general dose rate and ultra-high dose rate conditions, respectively. Figure 2 and Figure 3 They are survival rate curves when Nuli-1 cells and HDF cells were irradiated with heavy particle beams under general dose rate condition and ultra-high dose rate condition, respectively. Figure 2 and Figure 3 In it, the dashed line is a survival rate curve showing the relationship between the dose of the heavy particle beam irradiated when irradiating with the heavy particle beam under the general dose rate condition and the survival rate, and the solid line is a survival rate curve showing the relationship between the dose of the heavy particle beam irradiated when irradiating with the heavy particle beam under the ultra-high dose rate condition and the survival rate.

[0060] As Figure 2 and Figure 3 shown, when irradiating cells with radiation under the general dose rate condition (the dashed line in the graph), the survival rate of the cells decreases as the dose increases. In contrast, when irradiating cells with radiation under the high dose rate condition (the solid line in the graph), if the dose is increased to a certain extent or more, the survival rate of the cells may sometimes be higher than when irradiating with radiation under the general dose rate condition (FLASH effect).

[0061] Regarding the FLASH effect when performing ultra-high dose rate heavy particle beam irradiation, the present inventors have clearly confirmed the following through detailed research: As Figure 2 and Figure 3 shown, when irradiating cells with heavy particle beams, in the high dose region, there is a difference in the survival rate of cells under general dose rate and ultra-high dose rate. Specifically, the results show that the survival rate when irradiating at ultra-high dose rate is higher than that when irradiating at general dose rate. Moreover, the results show that the degree by which the survival rate in ultra-high dose rate irradiation is higher than that in general dose rate irradiation increases as the dose increases.

[0062] Furthermore, after irradiating multiple types of cells under the same ultra-high dose rate condition, the results show that the response (survival rate) to heavy particle beams varies according to each type of cell. That is, the following was clarified: The survival rate curve of HSG cells ( Figure 1(survival curve graph) is inconsistent with the survival curve graphs of other types of cells different from HSG cells Figure 2 and the graph of Figure 3 and the survival curve graphs may vary according to each type of cell. Figure 4 is a survival curve graph showing the relationship between the dose of the heavy particle beam irradiated and the survival rate when other types of cells X other than HSG cells, Nuli-1 cells, and HDF cells are irradiated with heavy particle beams under general dose rate conditions and ultra-high dose rate conditions. The revelations are as follows: The same is true for other types of cells X other than HSG cells, Nuli-1 cells, and HDF cells. As Figure 4 shown in the graph, the survival curve graph under high dose rate conditions is not a curve approximated to the general dose rate condition (the thin dotted line in the graph: symbol 401), that is, the thin solid line (symbol 402) in the graph, but the thick solid line (symbol 403) in the graph which is very different from it. In addition, Figure 4 the dotted line graph and the solid line graph are obtained according to the calculation methods of conventional biological dose and cell survival rate.

[0063] In addition, the phenomenon that the reaction (survival rate) when irradiated with heavy particle beams varies according to the type of cell was observed. Therefore, the following was confirmed: The survival rate of the irradiated cells is also affected by the type of radiation (any one of heavy particle beam, photon beam, electron beam, and proton beam) and the energy applied to the irradiated object when irradiated with radiation, that is, the linear energy transfer.

[0064] As described above, by studying the FLASH effect during ultra-high dose rate heavy particle beam irradiation, it was clarified that the survival rate of the irradiated cells depends on:

[0065] · The type of cell (cell);

[0066] · The type of radiation (ion);

[0067] · The linear energy transfer (energy).

[0068] It was clarified that the survival rate of the irradiated cells also depends on:

[0069] · The dose of radiation (dose);

[0070] Or, the dose rate of radiation obtained by converting the dose irradiated to a certain area into per unit time.

[0071] Here, the types of cells refer to cells that differ in terms of their location and function in the irradiated subject. For example, "different types of cells" refer to cells that make up different organs of the subject (such as the liver and skin). For example, as types of cells, cancer cells of lung cancer, liver cancer, and pancreatic cancer, which are often the targets of radiotherapy, can be specifically cited. In addition, in order to evaluate the degree of influence on normal cells, as types of cells, normal cells of the skin, intestine, and lung can also be specifically cited.

[0072] <Method for calculating biological dose according to the present invention>

[0073] According to the conventional estimation method, regardless of the type of cells in the irradiated subject, the absorbed dose in the standard cell HSG cells is applied to Equation (1) to calculate the survival rate S i , and the survival rate S i is substituted into Equation (2) to estimate the biological dose d bio，i .

[0074] As already described, the following has been confirmed: When these conventional estimation formulas are applied to the calculation of the dose distribution in ultra-high dose rate heavy particle beams, the calculated value of the survival rate may deviate from the actual value of the survival rate.

[0075] Based on these newly obtained insights, the inventors found that the following Equation (3) obtained by modifying Equation (1) conforms to the actual survival rate.

[0076]

Equation 4

[0077]

[0078] Here, d i is the absorbed dose for each type of cell, and the coefficient α new , the coefficient β new and the correction term C are as follows.

[0079]

Equation 5

[0080] α new = f(cell, ion, energy)

[0081] β new = g(cell, ion, energy)

[0082] C = h(cell, ion, energy, dose, dose_rate)

[0083] As described above, the survival rate of irradiated cells depends on the type of cell, the type of radiation and its quality, and also on the radiation dose or dose rate. The above equation (3) represents this insight as a relationship.

[0084] Based on the coefficient α new , the coefficient β new and the correction term C, the survival rate S’ i is calculated by equation (3). This survival rate S’ i depends on the type of cell, the type of radiation, the quality of the radiation, and the radiation dose (or dose rate).

[0085] Regarding the coefficient α new and the coefficient β new , similar to the determination of the coefficients α and β for standard cells in equation (1) of the conventional method, they are values determined through experiments of irradiating cultured cell lines (cells of the type for which dose calculation is to be performed) with radiation (cell irradiation experiments). Through cell irradiation experiments, a survival rate curve representing the relationship between dose and survival rate in these cells is obtained, and the coefficients α new and the coefficient β new are determined in such a way that the data fits well with the calculation results based on equation (3). In addition, the correction term C is a value used to correct the survival rate obtained using the coefficient α new and the coefficient β new to match the results of irradiation experiments under ultra-high dose rate conditions. By correcting the survival rate obtained using the coefficient α new and the coefficient β new with the correction term C, a more accurate survival rate S’ i can be calculated, which reflects the survival rate differences between general dose rate conditions and ultra-high dose rate conditions as well as the survival rate differences caused by the type of cell.

[0086] Furthermore, the inventors found that according to the following equation (4), a survival rate that is more in line with reality than equation (3) can be obtained.

[0087]

Mathematical formula 6

[0088]

[0089] Here, similar to equation (3), d i is the absorbed dose per type of cell. In addition, the coefficient α new , the coefficient β new , the coefficient γ and the coefficient δ are as described below.

[0090]

Mathematical formula 7

[0091] α new = f(cell, ion, energy)

[0092] β new = g(cell, ion, energy)

[0093] γ = h(cell, ion, energy, dose, dose_rate)

[0094] δ = i(cell, ion, energy, dose, dose_rate)

[0095] The survival rate of the irradiated cells depends on the cell type (cell), the radiation type (ion), and the radiation quality (energy), and also depends on the radiation dose (dose) or the radiation dose rate (dose_rate). Based on this insight, Equation (4) is derived, which is the same as when deriving Equation (3). By including the coefficient α new , the coefficient β new , the coefficient γ, and the coefficient δ in Equation (4), the value of the survival rate S’ i is calculated. This survival rate S’ i depends on the cell type, the radiation type, the radiation quality, and the radiation dose (or dose rate).

[0096] Through cell irradiation experiments, a survival rate curve representing the relationship between the dose and the survival rate in the cells is obtained, and the coefficients α new , the coefficient β new , the coefficient γ, and the coefficient δ are determined in such a way that the data fits well with the calculation results based on Equation (4). By Equation (4), it is possible to calculate a more accurate value of the survival rate S’ i that reflects the survival rate difference between the general dose rate condition and the ultra-high dose rate condition and the survival rate difference caused by the cell type. Further, Equation (4) is excellent in that it can accurately calculate the survival rate in the high-dose region.

[0097] Applying the survival rate S’ i calculated using Equation (3) or Equation (4) to the previous Equation (2) gives the following Equation (5). Based on the following Equation (5), the biological dose d bio，i at the position of interest i can be calculated. In Equation (5), different from the previous Equation (2), the survival rate S’ i of each cell type calculated using Equation (3) or Equation (4) is used for the calculation.

[0098]

Equation 8

[0099]

[0100] Furthermore, by multiplying the biological dose d calculated using Equation (5) bio，i by the empirical coefficient for the reaction of converting from cells to tissue (as previously mentioned, typically 1.46) and recalibrating, the clinical dose can be calculated. The clinical dose calculated in this way is a value corresponding to the value of the survival rate S' of each cell type calculated using Equation (3) or Equation (4). i

[0101] When formulating a treatment plan, the coefficient α corresponding to the cell type to be treated, new the coefficient β, new and the value of the correction term C are applied to Equation (3), and the resulting survival rate S' i is applied to Equation (5), thereby calculating the biological dose d. bio，i For the calculated biological dose d, bio，i multiply by the coefficient specified above to calculate the clinical dose. Alternatively, the coefficient α corresponding to the cell type to be treated, new the coefficient β, new the coefficient γ, and the coefficient δ are applied to Equation (4), and the resulting survival rate S' i is applied to Equation (5), thereby calculating the biological dose d. bio，i For the calculated biological dose d, bio，i multiply by the coefficient specified above to calculate the clinical dose. When formulating a treatment plan, when evaluating the degree of influence on normal cells, Equation (3) or Equation (4) is applied to the normal cells to be evaluated. Then, based on the calculated clinical dose, the dose distribution when irradiating the irradiated object with radiation is estimated, and a treatment plan for the patient is made. In the production of the treatment plan, it may also include the process of making an irradiation plan for the radiation for the irradiated object according to the calculated clinical dose.

[0102] In addition, as the object irradiated with radiation, typically a human, but not limited to this, it can also be animals such as dogs and cats. As the specific target irradiated with radiation, for example, it is organs and tissues including the tumor region.

[0103] ​In the conventional formula, factors such as the type of cell, the type of radiation beam, and the radiation dose (or dose rate) are not considered, and the dose is calculated only based on the absorbed dose and LET in standard cells. Therefore, in the case of performing ultra-high dose irradiation that produces the FLASH effect, the dose distribution calculated by the conventional method may deviate from the dose distribution of the radiation actually acting on the irradiated cells. In particular, the conventional formula does not take into account the following situation: when heavy particle beams are irradiated onto cells other than standard cells, the dose actually acting on the irradiated cells varies depending on the type of cell. Therefore, according to the conventional formula, it is impossible to accurately estimate the dose distribution when a heavy particle beam is irradiated onto an irradiated object containing cells that react differently from standard cells.

[0104] In contrast, in the improved formulas (3), (4), and formula (5) reflecting these formulas this time, the situation where the reaction varies depending on the type of cell is taken into account. Specifically, the coefficient α in formula (3) new , the coefficient β new , and the correction term C, the coefficient α in formula (4) new , the coefficient β new , the coefficient γ, and the coefficient δ are all values depending on the type of cell. Further, in these formulas (3), (4), and formula (5) reflecting these formulas, the effect on the object during ultra-high dose irradiation is taken into account. Specifically, the correction term C in formula (3), and the coefficients γ and δ in formula (4) are also values depending on the dose (or dose rate).

[0105] As described above, by adopting the dose estimation method using the improved formulas (3) and (4), a treatment plan in the treatment using heavy particle beams at an ultra-high dose rate can be formulated more accurately.

[0106] The dose estimation method according to the present invention can also be used to optimize the dose distribution and dose rate distribution in heavy particle beam therapy at an ultra-high dose rate. In heavy particle beam therapy at an ultra-high dose rate, due to the synergistic effect of the physical characteristic of the high dose concentration of heavy particle beams on tumors and the biological effect of reducing damage to normal tissues through the FLASH effect, a higher tumor control rate than before and a lower side effect incidence rate than before can be expected. Thus, an increase in cancer treatment opportunities and a further improvement in QOL in an aging society can be expected.

[0107] In addition, reducing side effects / post sequelae is related to further determining the path of cancer / disease treatment with less physical burden. In the case of side effects / post sequelae occurring, there will be the burden of time and economy required for the patient to cope with them, as well as the load on medical resources. However, through the dose estimation method according to the present invention, an ultra-high dose rate heavy particle beam therapy is developed, and thus the economic effects brought about by reducing these burdens can also be expected.

[0108] As described above, taking the case of irradiating cells with heavy particle beams as an example, the clinical dose calculation method according to the present invention has been described. However, the clinical dose calculation method according to the present invention can also be applied to the case of irradiating cells with photon rays, electron rays or proton rays.

[0109] (Specific example of survival rate calculation according to the present invention)

[0110] Figure 5 It is the survival rate curve obtained for HSG cells, which are mostly used as standard cells in heavy particle beam therapy, according to formula (4).

[0111] Figure 5 The white open circles (○) and black circles (●) in are the data measured through heavy particle beam irradiation experiments. The white open circles (○) represent the results when heavy particle beams are irradiated under the condition of a general dose rate (0.1 Gy / s), and the black circles (●) represent the results when heavy particle beams are irradiated under the condition of an ultra-high dose rate (100 Gy / s).

[0112] The coefficients α new of formula (4) are determined in such a way that they best fit the measurement results of the heavy particle beam irradiation experiments under the general dose rate and ultra-high dose rate respectively. new The coefficients β, Figure 5 The coefficients γ and coefficient δ. Figure 5 The thick solid line (symbol 501) in represents the survival rate curve under the ultra-high dose rate condition obtained according to formula (4). Figure 5 The thin solid line (symbol 502) and the thin dashed line (symbol 503) in are the survival rate curves under the general dose rate condition and the ultra-high dose rate condition calculated according to the conventional formula (1) respectively for comparison.

[0113] Obviously, as Figure 5 shown, even under the ultra-high dose rate condition, in a wide range from the low dose region to the high dose region, the estimated data of the survival rate S’ i calculated by formula (4) of the present invention is in good agreement with the measured survival rate results. As described above, according to the survival rate S’ iThe biological dose can be calculated, and then the clinical dose can be calculated. Therefore, according to the present invention, it is clear that the clinical dose can be more accurately estimated compared with the conventional methods.

[0114] (Configuration of Dose Evaluation Device 1)

[0115] Next, use Figure 6 to describe the configuration of the dose evaluation device 1 that calculates the clinical dose using the dose evaluation method according to the present invention. Figure 6 is a block diagram showing an example of the configuration of the dose evaluation device 1 according to an aspect of the present invention. Next, use Figure 6 to describe the configuration of the dose evaluation device 1 according to an aspect of the present invention. The dose evaluation device 1 is a device that applies the dose calculation method using the formulas (3) and (5) or the formulas (4) and (5) made by the inventor as described above, and can calculate the dose using the input information and the improved formula, and output the information indicating the dose distribution based on the calculated value.

[0116] As Figure 6 shown, the dose evaluation device 1 includes a control unit 11, a storage unit 12, and an output unit 13. The control unit 11 is used to execute the control of the operations of each part of the dose evaluation device 1 and the arithmetic processing. The control unit 11 includes a calculation information acquisition unit 111, an absorbed dose acquisition unit 112, a calculation unit 113, and an evaluation information generation unit 114.

[0117] The calculation information acquisition unit 111 is used to acquire the calculation target information as the information required for the operation, and output the acquired information to the calculation unit 113. The calculation target information includes: information related to the radiation that is to be irradiated to the irradiation target; and information related to the type of cells that make up the irradiation target that receives the radiation. In addition, the information related to the radiation includes information on the dose or dose rate of the radiation. The dose evaluation device 1 may also include an input unit (not shown), and the calculation information acquisition unit 111 may acquire the calculation target information by the user of the dose evaluation device 1 inputting various information to the input unit.

[0118] The absorbed dose acquisition unit 112 acquires the absorbed dose information as the information required for the operation for each type of cell that makes up the irradiation target, and outputs the acquired information to the calculation unit 113. The absorbed dose information is information indicating the absorbed dose for each type of cell that makes up the irradiation target, and the absorbed dose is the energy of the radiation absorbed by the cells of this type. The dose evaluation device 1 may also include an input unit (not shown), and the absorbed dose acquisition unit 112 may acquire the absorbed dose information by the user of the dose evaluation device 1 inputting various information to the input unit.

[0119] The calculation unit 113 calculates the clinical dose for each cell type based on the calculation object information and absorbed dose information obtained by the calculation information acquisition unit 111 and the absorbed dose acquisition unit 112. Alternatively, the calculation unit 113 calculates the clinical dose corresponding to the radiation to be irradiated to the object based on the calculation object information and absorbed dose information obtained by the calculation information acquisition unit 111 and the absorbed dose acquisition unit 112.

[0120] Specifically, when the calculation object information and absorbed dose information required for the calculation are obtained from the calculation information acquisition unit 111 and the absorbed dose acquisition unit 112, the calculation unit 113 refers to the storage unit 12 and obtains the mathematical formula data 121 used for the calculation. When the mathematical formula data 121 is data for the above formulas (3) and (5) or formulas (4) and (5), the calculation unit 113 calculates the survival rate S' for each cell type according to the obtained information and formula (3) or formula (4). i For example, the calculation unit 113 calculates the survival rate S' according to formula (3) or formula (4). i This survival rate S' i depends on the cell type, the type of radiation, the quality of the radiation, and the radiation dose (or dose rate). In addition, the calculation unit 113 calculates the biological dose d according to the calculated survival rate S' for each cell type i and formula (5). bio，i Furthermore, the calculation unit 113 calculates the clinical dose according to the biological dose d. Since the survival rate S' bio，i and the biological dose d i depend on the cell type, the calculation unit 113 can calculate the clinical dose for each cell type. In addition, the calculation unit 113 can also be configured to calculate the absorbed dose, clinical dose, etc. according to the survival rate S' for each cell type bio，i using the method described in Japanese Patent Publication No. 5454989. i

[0121] The evaluation information generation unit 114 generates evaluation information that displays the dose distribution for each cell type based on the calculated clinical dose. In addition, the evaluation information generation unit 114 controls the output unit 13 to output the evaluation information. The evaluation information is information representing an evaluation related to the irradiated radiation. For example, it can be the survival rate S' for each cell type calculated by the calculation unit 113 i or the biological dose d. bio，i In addition, the evaluation information generation unit 114 can also further process the calculated value and output the information representing the processing result as evaluation information from the output unit 13. For example, the evaluation information generation unit 114 can also calculate according to the biological dose d calculated by the calculation unit 113 bio，i ​Calculate the clinical dose and output it as evaluation information from the output unit 13. In addition, the evaluation information generation unit 114 may also process the survival rate S’ of each type of cell calculated by the calculation unit 113 i or the biological dose d bio，i , and further output it from the output unit 13 in the form of a DVH (dose volume histogram) or a DRVH (dose rate volume histogram), etc.

[0122] In addition, the evaluation information generation unit 114 may also create a dose distribution map showing the dose distribution in the subject's body based on the clinical dose of each type of cell, for example, and output the evaluation information including the dose distribution map from the output unit 13. For example, when the calculation unit 113 is to calculate the biological dose d in cells (such as organs) at multiple sites in the subject's body bio，i , the evaluation information generation unit 114 may also create a dose distribution map formed by drawing contour lines in the image data obtained by photographing the subject's body, and the contour lines correspond to the level of the biological dose or the clinical dose calculated based on the biological dose. As the image data, it may be an X-ray CT (computed tomography) image, an MRI (magnetic resonance imaging) image, etc. In addition, the image data may also be a virtual CT image constructed by a speculation model using Dual Energy CT or AI.

[0123] The storage unit 12 is a storage device for storing various computer programs read by the control unit 11 and data used in various processes executed by the control unit 11. For example, the storage unit 12 stores the mathematical formula data 121 of formulas (3) and (5) or formulas (4) and (5) used by the calculation unit 113 in the operation. In addition, the storage unit 12 may also store a table for converting various data obtained by the calculation information acquisition unit 111 and the absorbed dose acquisition unit 112 into parameters applicable to the operation executed by the calculation unit 113. In addition, when the evaluation information generation unit 114 processes data for further operations, etc., the storage unit 12 stores the mathematical formulas or table data used in the operation, etc. When performing other operations, it also stores the formula data used for the operation.

[0124] The output unit 13 is, for example, a display device capable of displaying data, and outputs the value calculated by the calculation unit 113 or the evaluation information such as the data processed by the evaluation information generation unit 114 in a form that can be confirmed by the user of the dose evaluation device 1 under the control of the evaluation information generation unit 114.

[0125] As described above, for the dose evaluation device 1 according to the present invention, as an operation for estimating the biological dose in heavy particle beam therapy, a new formula can be used for the operation to visualize the dose distribution in the body and provide it to users such as medical staff.

[0126] (Flow of the process executed by the dose evaluation device 1)

[0127] Next, use Figure 7 to explain the flow of the process executed by the dose evaluation device 1. Figure 7 It is a flowchart showing an example of the flow (estimation method) of the process performed in the dose evaluation device 1.

[0128] First, the calculation information acquisition unit 111 acquires calculation object information (S1: calculation information acquisition step) and outputs it to the calculation unit 113. The calculation object information is each piece of information required for the operations performed in the calculation unit 113. For example, the calculation information acquisition unit 111 acquires the calculation object information through user input to the input device or communication with an external device storing each piece of information.

[0129] Next, the absorbed dose acquisition unit 112 acquires absorbed dose information representing the absorbed dose (S2: absorbed dose acquisition step) for each type of cell constituting the irradiation object and outputs it to the calculation unit 113. The absorbed dose is the energy of the radiation absorbed by this type of cell. For example, the absorbed dose acquisition unit 112 acquires the absorbed dose information through user input to the input device or communication with an external device storing each piece of information.

[0130] When the calculation object information and the absorbed dose information are acquired from the calculation information acquisition unit 111 and the absorbed dose acquisition unit 112, the calculation unit 113 refers to the storage unit 12 and acquires the mathematical formula data 131 for the operation. The calculation unit uses formula (3) or formula (4) in the mathematical formula, and calculates the survival rate S' of each type of cell according to the acquired evaluation object information and absorbed dose information i (S3).

[0131] When the survival rate S' is calculated i the calculation unit 113 uses formula (5) to calculate the biological dose d of each type of cell according to this survival rate S' i . The calculation unit 113 outputs the information representing the calculated biological dose d bio，i . In addition, the calculation unit 113 uses the biological dose d calculated according to the calculation object information bio，i bio，i ​, the clinical dose for each cell type is calculated according to each cell type. In other words, the calculation unit 113 calculates the clinical dose to be irradiated to the irradiation object according to each cell type based on the calculation object information and the absorbed dose information (S4: calculation step). Specifically, the calculation unit 113 multiplies the calculated biological dose d bio，i by the empirical coefficient (such as 1.46) of the reaction converted from cells to tissue and recalibrates it to calculate the clinical dose.

[0132] The evaluation information generation unit 114 performs further operations and data processing on the calculated biological dose d bi o, i or the clinical dose to produce a dose distribution map, etc. Then, the evaluation information generation unit 114 controls the output unit 13 to output the dose calculated by the calculation unit 113 or the evaluation information produced based on the dose, such as the clinical dose (S5).

[0133] (Effect)

[0134] According to the dose evaluation device 1 according to the present invention, the dose calculation method according to the above formula (3) and formula (5) or formula (4) and formula (5) is adopted. Thus, a treatment plan in the treatment using heavy particle beams at an ultra-high dose rate can be formulated more accurately. In addition, according to the dose evaluation device according to the present invention, the dose distribution can be visualized based on the calculated dose and provided to medical workers.

[0135] 〔Embodiment 2〕

[0136] Regarding the functions of the dose evaluation device 1, it is implemented by a program for causing a computer to function as the device and causing each control block (especially each part included in the control unit 11) of the dose evaluation device to function.

[0137] In this case, the above dose evaluation device includes a computer having at least one control device (such as a processor) and at least one storage device (such as a memory) as the hardware for executing the above program. By executing the above program by the control device and the storage device, the respective functions described in the above embodiments are realized.

[0138] The above program can be recorded in one or more non-temporary, computer-readable recording media. The above dose evaluation device may or may not have the recording medium. In the latter case, the above program can be provided to the above dose evaluation device via any wired or wireless transmission medium.

[0139] In addition, part or all of the functions of each of the above control blocks can also be implemented by a logic circuit. For example, an integrated circuit formed with a logic circuit that functions as each of the above control blocks is also included in the scope of the present invention. Further, for example, the functions of each of the above control blocks can also be implemented by a quantum computer.

[0140] In addition, each process described in each of the above embodiments can also be executed by AI (Artificial Intelligence). In this case, the AI can operate through the above control device or can operate through other devices (such as an edge computer or a cloud server, etc.).

[0141] 〔Summary〕

[0142] As described above, a first aspect of the present invention relates to a dose evaluation method, which includes: a calculation information acquisition step for acquiring calculation object information, the calculation object information including: information related to radiation, the information including the dose or dose rate of the radiation to be irradiated to an irradiation object; and information related to the type of cells, the type of cells being the type of cells constituting the irradiation object, and the irradiation object being irradiated with the radiation; an absorbed dose acquisition step for acquiring absorbed dose information representing the absorbed dose for each type of cell constituting the irradiation object, the absorbed dose being the energy of the radiation absorbed by the cells of this type; and a calculation step for calculating, according to the calculation object information and the absorbed dose information, the clinical dose to be irradiated to the irradiation object for each type of cell.

[0143] When irradiating an object with radiation, the absorbed dose may vary depending on each type of cell, and the absorbed dose is the energy of the radiation absorbed by the object. In addition, the absorbed dose may vary depending on the dose rate of the radiation irradiated to the object. According to the above configuration, it is possible to calculate the clinical dose for each type of cell according to the calculation object information and the absorbed dose information of each type of cell constituting the irradiation object, and the calculation object information includes information related to radiation and information related to the type of cells.

[0144] In the above first aspect, the dose evaluation method according to the second aspect of the present invention can be configured such that: the information related to radiation includes information on the type and quality of the radiation, and in the calculation step, the survival rate S' is calculated for each type of cell by the following formula (I) i , according to the calculated survival rate S' i , the clinical dose is calculated for each type of cell constituting the irradiation object:

[0145]

Equation 9

[0146]

[0147] Among them, it can be: d i is the absorbed dose of each type of the cells,

[0148] Coefficient α new and coefficient β new are values obtained according to the survival curve for each type of the cells, and the survival curve represents the relationship between the dose of the radiation to be irradiated to the irradiation object under the radiation type and the radiation quality of the radiation and the survival rate,

[0149] The correction term C is a value used to correct the survival rate obtained using coefficient α new and coefficient β new according to the dose or dose rate of the radiation.

[0150] According to the above configuration, based on the formula used in the past, the improved formula (I) can more accurately evaluate the clinical dose.

[0151] In the above first aspect, the dose evaluation method according to the third aspect of the present invention can be configured such that the information related to the radiation includes the information on the radiation type and the radiation quality of the radiation, and in the calculation step, the survival rate S' is calculated by the following formula (II) for each type of the cells i , and according to the calculated survival rate S' i , for each type of the cells constituting the irradiation object, the clinical dose is calculated:

[0152]

Equation 10

[0153]

[0154] Among them, it can be: d i is the absorbed dose of each type of the cells,

[0155] Coefficient α new , coefficient β new , coefficient γ and coefficient δ are values obtained according to the survival curve for each type of the cells, and the survival curve represents the relationship between the dose of the radiation to be irradiated to the irradiation object under the radiation type and the radiation quality of the radiation and the survival rate, and coefficient γ and coefficient δ are values depending on the dose or dose rate of the radiation.

[0156] According to the above configuration, based on the formula used in the past, the improved formula (II) can more accurately evaluate the clinical dose.

[0157] In any one of the above first to third aspects, the dose evaluation method according to the fourth aspect of the present invention may be configured such that the radiation is any one of heavy particle rays, photon rays, electron rays, or proton rays.

[0158] According to the above configuration, since a more accurate clinical dose can be calculated, the clinical dose in radiation therapy using heavy particle rays, electron rays, proton rays, etc. can be calculated more accurately. Therefore, using this dose evaluation method, a treatment plan for appropriate and safe radiation irradiation treatment can be created.

[0159] In any one of the above first to third aspects, the dose evaluation method according to the fifth aspect of the present invention may be configured such that the radiation is heavy particle rays and the dose rate of the radiation is in the ultra-high dose rate range.

[0160] According to the above configuration, since a more accurate clinical dose than before can be calculated, a treatment plan in treatment using heavy particle rays at an ultra-high dose rate can be formulated more accurately.

[0161] In the above fifth aspect, the dose evaluation method according to the sixth aspect of the present invention may be configured such that the dose rate of the radiation is 40 Gy / second or more.

[0162] The seventh aspect of the present invention relates to an irradiation plan method that creates an irradiation plan for the radiation to the irradiation target based on the clinical dose calculated by the dose evaluation method according to any one of the above first to third aspects.

[0163] According to the above configuration, since an irradiation plan is created based on a more accurate clinical dose that takes into account the cell type and dose rate, a more appropriate and safe irradiation plan can be created in radiation irradiation treatment.

[0164] The eighth aspect of the present invention relates to a dose evaluation device including: a calculation information acquisition unit that acquires calculation target information including information related to radiation, which includes the dose or dose rate of the radiation to be irradiated to the irradiation target, and information related to the cell type, which is the cell type constituting the irradiation target that receives the irradiation of the radiation; an absorbed dose acquisition unit that acquires absorbed dose information indicating the absorbed dose for each cell type constituting the irradiation target, where the absorbed dose is the energy of the radiation absorbed by the cell type; and a calculation unit that calculates the clinical dose to be irradiated to the irradiation target for each cell type based on the calculation target information and the absorbed dose information.

[0165] According to the above configuration, the same effects as those of the first aspect described above are achieved.

[0166] A ninth aspect of the present invention relates to a control program for causing a computer to function as the dose evaluation device described in the eighth aspect above, and causing the computer to function as the above calculation unit.

[0167] A tenth aspect of the present invention relates to a recording medium which is a computer-readable recording medium recording the control program described in the ninth aspect above.

[0168] The present invention is not limited to the above-described embodiments, and various modifications can be made within the scope shown in the claims. Embodiments obtained by appropriately combining technical means disclosed in different embodiments are also included in the technical scope of the present invention.

[0169] Description of reference symbols

[0170] 1: Dose evaluation device

[0171] 111: Calculation information acquisition unit

[0172] 112: Absorbed dose acquisition unit

[0173] 113: Calculation unit

[0174] 114: Evaluation information generation unit

[0175] S1: Calculation information acquisition step

[0176] S2: Absorbed dose acquisition step

[0177] S4: Calculation step

Claims

1. A dose evaluation method, comprising: A calculation information acquisition step for acquiring calculation object information, the calculation object information including: information related to radiation, the information including the dose or dose rate of the radiation to be irradiated to the irradiation object; and information related to the type of cells, the type of cells being the type of cells constituting the irradiation object, and the irradiation object receiving the irradiation of the radiation; An absorbed dose acquisition step for acquiring absorbed dose information representing the absorbed dose for each type of cell constituting the irradiation object, the absorbed dose being the energy of the radiation absorbed by the cells of this type; and A calculation step for calculating the clinical dose to be irradiated to the irradiation object for each type of cell according to the calculation object information and the absorbed dose information.

2. The dose evaluation method according to claim 1, wherein The information related to radiation includes information on the type and quality of the radiation, In the described calculation steps, the survival rate S' is calculated by the following formula (I) for each type of the cells i , based on the calculated survival rate S' i , for each type of the cells constituting the irradiated object, calculate the clinical dose: 【Equation 1】 where d i is the absorbed dose for each species of said cells, Coefficient α new and coefficient β new are values obtained according to the survival rate curve for each type of the cells, and the survival rate curve represents the relationship between the dose of the radiation to be irradiated to the irradiation object under the radiation type and the radiation quality of the radiation and the survival rate. The correction term C is a value used to correct the survival rate obtained according to the dose or dose rate of the radiation for the utilization factor α new and the coefficient β new ​ 3. The dose evaluation method according to claim 1, wherein The information related to radiation includes information on the type and quality of the radiation, In the described calculation steps, the survival rate S' is calculated according to each type of the cells by the following formula (II). i Based on the calculated survival rate S'. i According to each type of the cells constituting the irradiation object, the clinical dose is calculated as follows: 【Equation 2】 where d i is the absorbed dose for each species of said cells, Coefficient α new , coefficient β new , coefficient γ and coefficient δ are values obtained according to the survival rate curve for each type of the cells, the survival rate curve representing the relationship between the dose of the radiation to be irradiated to the irradiation object under the radiation type and the radiation quality of the radiation and the survival rate, and coefficient γ and coefficient δ are values depending on the dose or dose rate of the radiation.

4. The dose assessment method according to any one of claims 1 to 3, wherein The radiation is any one of heavy particle rays, photon rays, electron rays or proton rays.

5. The dose assessment method according to any one of claims 1 to 3, wherein, The radiation is heavy particle rays, and the dose rate of the radiation is in the ultra-high dose rate range.

6. The dosage evaluation method according to claim 5, wherein, The dose rate of the radiation is 40 Gy / second or more.

7. An irradiation plan method for making an irradiation plan for the radiation of the irradiation object based on the clinical dose calculated by the dose evaluation method according to any one of claims 1 to 3.

8. A dose evaluation device, comprising: A calculation information acquisition unit for acquiring calculation object information, the calculation object information including: Information related to radiation, the information including the dose or dose rate of the radiation to be irradiated to the irradiation object; and information related to the type of cells, the type of cells being the type of cells constituting the irradiation object, and the irradiation object receiving the irradiation of the radiation; An absorbed dose acquisition unit for acquiring absorbed dose information representing the absorbed dose for each type of cell constituting the irradiation object, the absorbed dose being the energy of the radiation absorbed by the cells of this type; And A calculation unit for calculating the clinical dose to be irradiated to the irradiation object for each type of cell according to the calculation object information and the absorbed dose information.

9. A control program for causing a computer to function as the dose evaluation device according to claim 8, and for causing the computer to function as the calculation information acquisition unit, the absorbed dose acquisition unit and the calculation unit.

10. A recording medium which is a computer-readable recording medium recording the control program according to claim 9.

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