Volume Calibration Phantom and Calibration Method Thereof

Abstract

A volume calibration phantom is disclosed in the present invention, which comprises a container; a plurality of plates stacking up inside the container; and at least one slab of radioactive source, each of which is disposed between the adjacent plates and comprises a plurality of radionuclides. With the volume calibration phantoms, the present invention further provides a calibration method which is an improvement over conventional calibration methods of space geometric center point source and relative penetration factor ratios. The method comprises the steps of generating a calibration curve of density vs. counting efficiency corresponding to the several different volume calibration phantoms; calculating the density of a radioactive waste specimen to obtain a corresponding radioactive activity according to the calibration curve, and then revising the corresponding radioactive activity according to the energy dependency and equation of gamma gross radioactivity for multiple radionuclides so as to obtain the correct gamma gross radioactivity of the radioactive waste specimen. By means of the method disclosed in the present invention, a precise and accurate result can be obtained.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing a volume calibration phantom and a waste curie monitor.

FIG. 2A is a schematic diagram showing a standard container of the invention.

FIG. 2B shows the stacking of pates and slabs of radioactive sources according to the present invention.

FIG. 3A is a cross sectional view of a slab of radioactive sources according to the present invention.

FIG. 3B is a schematic diagram depicting the distribution of radionuclides on a slab of radioactive sources according to the present invention.

FIG. 4 shows the steps of a calibration method of the invention.

FIG. 5 shows the minimum detectable activities (MDAs) of radionuclides of different densities according to the present invention.

FIG. 6 shows the relationship between counting time and MDAs according to the present invention.

FIG. 7 shows the variations of photonic efficiency with respect to of calibration phantoms of different densities.

DESCRIPTION OF THE PREFERRED EMBODIMENT

For your esteemed members of reviewing committee to further understand and recognize the fulfilled functions and structural characteristics of the invention, several preferable embodiments cooperating with detailed description are presented as the follows.

Please refer to FIG. 1, which is a schematic diagram showing a volume calibration phantom and a waste curie monitor. The waste curie monitor 1 of FIG. 1 is substantially a shield box 10 whose six walls is made of lead with equal thickness, in which an inspection space 100 is formed while having six large-area radiation detectors 11 being arranged respectively on the inner walls of the shield box 10 encasing the inspection space 100. In this preferred embodiment of the invention, each large-area radiation detector 11 can be a plastic scintillation detector. Moreover, a weight meter is disposed in the inspection space 100 for weighting an object-to-be-tested. In addition, the waste curie monitor is connected to a computer 12, which is programmed with a software and calibration parameters for performing operations such as counting the radioactivity (Bq) or specific radioactivity (Bq/g) of a sample and its back ground, calibrating the minimum detectable activity (MDA) of the monitor, and printing and displaying the result of a detection.

As seen in FIG. 1, a volume calibration phantom 2 of uniform radioactivity is received in the inspection space 100. Please refer to FIG. 2A and FIG. 2B, which are schematic diagrams respectively showing a standard container and the stacking of pates and slabs of radioactive sources according to the present invention. The volume calibration phantom 2 is substantially a stacking of uniform plates 22 and slabs of radioactive source 23, being disposed in an inner space 21 of a standard container 20. In a preferred aspect, each plate 21 can be made of a metallic material or a non-metallic material, whereas the metallic material can be iron; and the non-metallic material can be paper, wood, gypsum, acrylic resin, rubber or glass.

In a preferred embodiment of the invention, uniform plates made of seven different materials are being cut into plates of 33 cm wide, 33 cm long and 1 cm thick, and are stacked to form a calibration phantom about the same size as the standard container 20, that is about 33 cm long, 33 cm wide and 30 cm height, while enabling the weight of the calibration phantom to be ranged between 5 kg to 100 kg. The average density of the calibration phantom can be acquired with respect to its volume, i.e. 33 cm³. In a preferred aspect, the calibration phantom is a multi-density calibration phantom, composing of paper plates at a density of 0.15 gcm⁻³, wood plates at a density of 0.55 gcm⁻³, gypsum plates at a density of 0.75 gcm⁻³, acrylic plates at a density of 1.13 gcm⁻³, rubber plates at a density of 1.80 gcm⁻³, glass plate at a density of 2.5 gcm⁻³, and iron plates at a density of 3 gcm⁻³.

In the calibration phantom, there are seven large-area slabs of radioactive source being sandwiched respectively between adjacent plates. Please refer to FIG. 3A, which is a cross sectional view of a slab of radioactive sources according to the present invention. As seen in FIG. 3A, each of the large-area slabs of radioactive source 23 is comprised of: a bottom laminating layer 233; a leakage-prevention filter layer 232, formed on the bottom laminating layer 233, a radiation source layer 231 with a plurality of radionuclides, formed on the leakage-prevention filter layer 232; and a top laminating layer 230, formed on top of the leakage-prevention filter layer 232, wherein, by the cooperation of the top and bottom laminating layers 230, 233, the plural radionuclides of the radiation source layer 231 are protected.

Preferably, any one of the plural radionuclides can be a gamma radioactive source, and can be a radionuclide selected from the group consisting of ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co ¹³⁷Cs and the combination thereof. Please refer to FIG. 3B, which is a schematic diagram depicting the distribution of radionuclides on a slab of radioactive sources according to the present invention. In FIG. 3B, a 6×6 matrix is formed on the radiation source layer 231 that a total of 36 drops of 0.2 cc liquid-state radioactive sources 2310 are dripped respectively onto each area of the 6×6 matrix while each drop of the liquid-state radioactive source 2310 is spread into a circle whose diameter is smaller than 5 cm, while the 36 circles are not overlapped with each other. It is noted that the gross radioactivity of large-area slabs of ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co, ¹³⁷Cs are respectively 58 kBg, 72 kBg, and 90 kBg. As there are four different energies and seven different densities, 28 calibration phantoms of different energy and different densities can be established.

Please refer to FIG. 4, which shows the steps of a calibration method of the invention. The steps of the calibration method are listed and classified into four categories as following:

(1) Density and Count Efficiency Calibration:

• • In this category, a plurality of multi-radionuclides phantoms of various densities are provided, which is referred as step 30. Thereafter, the plural calibration phantoms are measured by a specific monitor for obtaining a calibration curve of density against counting efficiency correspondingly, referring as step 31.

(2) Photonic Energy Dependency

• • In order to evaluate the ratio difference of various gamma energy with respect to that of ¹³⁷Cs, large-area gamma radioactive sources of ⁵⁷Co of 122 keV and 136 keV, ⁵⁴Mn of 834 keV, ⁶⁰Co of 1173 keV and 1332 keV, ¹³⁷Cs of 662 keV, are placed respectively at the geometrical center of a waste curie monitor for measuring, and thus the radionuclide counting efficiency of gamma nuclides ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co, ¹³⁷Cs, obtained from the measurement, are divided respectively by the energy branching ratios corresponding thereto, which are ⁵⁷Co: 96%, ⁵⁴Mn: 100%, ⁶⁰Co: 200%, ¹³⁷Cs: 85%, by which a diagram regarding to the photonic efficiency and energy of radionuclides ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co, ¹³⁷Cs of various densities can be charted as seen in FIG. 7 that the photonic efficiency is increasing with the increase of the energy. At high energy level, the variation of density will have more influence upon the photonic efficiency, and at low energy, the influence is less. Moreover, the photonic efficiency ratio of ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co with respect to ¹³⁷Cs is illustrated in Table 1 as following:

TABLE 1
photonic efficiency ratio of waste curie monitor
	density (g/cm3)	57Co/137Cs	54Mn/137Cs	60Co/137Cs
	0.15	0.40	1.25	1.49
	0.5	0.32	1.18	1.44
	0.75	0.26	1.13	1.41
	1.13	0.23	1.01	1.30
	1.8	0.17	0.79	1.11
	2.5	0.16	0.77	0.99
	3.0	0.08	0.63	0.85

(3) Waste Sample Measurement

• • In this category, a step 32 is first being performed, in which a waste specimen is filled into a container of the same volume as each of the plural volume calibration phantoms so as to be used as a test sample, and then the process proceeds to step 33. At step 33, the weight of the test sample is measured by the monitor for obtaining the density of the same, by which a sample gamma gross radioactivity of the test sample can be obtained by referencing to the calibration curve with respect to the density of the test sample, and then the process proceeds to step 34. At step 34, the sample gamma gross radioactivity is calibrated by an energy dependency factor and a formula of multi-radionuclides calculation for acquiring a correct gamma gross radioactivity.

(4) In order to match the limit of radionuclide radioactivity, it is required for a waste curie monitor to have a correct method for calculating gross gamma radioactivity. Moreover, when a waste sample is verified as a multi-radionuclide waste sample, primarily comprising ⁵⁴Mn , ⁶⁰Co, ¹³⁷Cs, it is required that the deviation of correctness for the radioactivity analysis of each radionuclide to be maintained within a specific tolerance.

(4-1) Minimum Detectable Activity (MDA)

The formula for calculating minimum detectable activity (MDA), defined by US Nuclear Regulatory Commission (USNRC), NUREG-1507 (1998), is as following:

$\mathrm{MDA}=3+4.65\frac{\sqrt{C_{\mathrm{BG}}}}{\varepsilon \times t}$

wherein 3+4.65 is defined as the limit of detector with 95% reliability

• • C_BG is defined as counts per second (cps)
  • ε is defined as radionuclide counting efficiency
  • t is defined as counting time (sec)

when the average background counting is 1500, the MDAs of ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co, ¹³⁷Cs of various average densities, detected and measured by a Eberline WCM-10PC within two-minute interval, are illustrated in Table 2 and FIG. 5. It is noted that the MDAs of ⁶⁰Co and ¹³⁷Cs at every average density are coincidence, that is, when the average density is within the range between 1 gcm⁻³ and 2 gcm⁻³, the MDAs of ⁶⁰Co and ¹³⁷Cs are at their minimum; and when the average density is smaller than 1 gcm⁻³ or larger than 2 gcm⁻³, the MDAs of ⁶⁰Co and ¹³⁷Cs are respectively 0.003 Bq/g and 0.010 Bq/g, which are about twice the MDAs of ⁶⁰Co and ¹³⁷Cs when their average density is between 1 gcm⁻³ and 2 gcm⁻³. As the variation of weight is linear and the variation of geometrical center efficiency of radionuclide is an index trend, when the weight is too light or too heavy, the variation of efficiency will be larger than that of weight. Therefore, the MDAs of ⁶⁰Co are smaller than those of ¹³⁷Cs when the two are at the same average density.

The largest MDAs of ⁵⁴Mn , ⁶⁰Co, ¹³⁷Cs are respectively 0.006 Bq/g, 0.001 Bq/g and 0.010 Bq/g. As the energy of ⁵⁴Mn is similar to that of ¹³⁷Cs, the MDAs of the two are similar no matter they are contained in cloth, water, iron tube or steel bar. In addition, the aforesaid MDAs of ⁵⁴Mn, ⁶⁰Co, ¹³⁷Cs all match the release limit defined by authority, that is, they should be 10 times lower than the radionuclide release limit defined by IAEA, e.q. ⁵⁴Mn, ⁶⁰Co, ¹³⁷Cs are all defined to be 0.1 Bq/g. In addition, according to the operation manual of the waste curie monitor 3300-200 by Antech company, the MDAs of ⁶⁰Co and ¹³⁷Cs at two-minute interval are respectively 0.006 Bq/g and 0.015 Bq/g, which are similar to those detected by the monitor used in the present invention. Moreover, by observing the relationship of MDAs , detected by plastic scintillation detectors, and time, the result of the MDA variations of ⁶⁰Co and ¹³⁷Cs are shown in FIG. 6 as the counting times are set to be 1 min, 2 min, 5 min, 8 min and 10 min. As the counting time is extended from 1 min to 5 min, the MDAs of ⁶⁰Co and ¹³⁷Cs are lowered respectively by 1.9 times and 2 times. As the counting time is extended from 1 min to 10 min, the MDAs of ⁶⁰Co and ¹³⁷Cs are lowered respectively by 205 times and 2.7 times. As the counting time is extended from 8 min to 10 min, the MDAs of ⁶⁰Co and ¹³⁷Cs are lowered respectively by 9% and 15%, which is not significant.

TABLE 2
MDA of waste curie minotor (Bq/g)
density
(g/cm3)	57Co	54Mn	137Cs	60Co
0.15	0.059	0.018	0.019	0.0095
0.5	0.021	0.0058	0.0061	0.0029
0.75	0.018	0.004	0.0042	0.002
1.13	0.013	0.003	0.0032	0.0014
1.8	0.0084	0.0017	0.0018	0.00075
2.5	0.0088	0.0018	0.0018	0.00083
3.0	0.015	0.0019	0.002	0.0008

(4-2) Calculation Formula

Total count: M=A_iε_ip_iΣ(1+R_xE_x)

wherein A_i is the radioactivity of ¹³⁷Cs (Bq/g)

• • ε_i is the photonic efficiency of ¹³⁷Cs at 662 keV
  • p_i is the energy branching ratios of ¹³⁷Cs at 662 keV
  • R_x is the specific activity of each radionuclides against ¹³⁷Cs
  • E_x is the detection efficiency of each radionuclides against ¹³⁷Cs

radioactivity ratio: R_x=A_x/A_i   (a)

wherein A_x is the radioactivity of a radionuclide (HPGe analysis)

ratio of detection efficiency: E_x=Σε_xp_x/ε_ip_i   (b)

wherein ε_x is a detection efficiency of a radionuclides (%)

• • p_x is anenergy branching ratio of a radionuclide (%)

gross gamma radioactivity: A_t=M/E_i   (c)

wherein the detection efficiency of ¹³⁷Cs is E_i=ε_ip_i

index radionuclide radioactivity: A_i=A_t/Σ(1+R_xE_x   (d)

any radionuclide radioactivity: A_x=A_i×R_x

(e) release limit:

$\sum _xA_x/A_{x,0}\le 1$

wherein A_x,0 is the radioactivity limit of a radionuclide

(4-3) Multi-Nuclide Analysis

The standard total radioactivity of the seven uniform radionuclides placed inside the calibration phantom, i.e. ¹³⁷Cs (72105 Bq), ⁵⁴Mn (45309 Bq), ⁶⁰Co (86045 Bq) and ⁵⁷Co (42777 Bq), is 246239 Bq. The radioactivity ratio ⁵⁷Co: ⁵⁴Mn:⁶⁰Co: ¹³⁷Cs is 0.593: 0.628: 1.19: 1. Thus, the total gross radioactivity, using a sample of ¹³⁷Cs at 1.1 gcm⁻³, 1.8 gcm⁻³, and 2.5 gcm⁻³, is shown in Table 3. After the radioactivity of the aforesaid four radionuclides are calibrated by the foregoing formulas, the deviations of correctness form the standard total radioactivity are respectively 1.82%, 2.59% and 1.74%.

(4-3-1) ¹³⁷Cs efficiency of 1.1 gcm⁻³ phantom

as the index nuclide radioactivity A_i is ¹³⁷Cs, the gross radioactivity A_t=321197 Bq, and the E_x of ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co with respect to ¹³⁷Cs are 0.23, 1.01, and 1.30.

Thus,

$\begin{array}{c}{A}_i=A_t/\sum \left(1+R_xE_x\right)\\ =321197/\left[1+\left(0.593\times 0.23\right)+\left(0.628\times 1.01\right)+\left(1.19\times 1.30\right)\right]\\ =73500\mathrm{Bq}\end{array}$

A _x =A _i ×R _x, therefore, ⁵⁷Co=A_i×0.593=43586 Bq

⁵⁴Mn=A_i×0.628×46158 Bq

⁶⁰Co=A_i×1.19=87465

Bq

Hence, the calibrated gross gamma radioactivity A_t=250709 Bq

the standard gross gamma radioactivity is 246239 Bq

the deviation of correctness is 3.36%

(4-3-2) ¹³⁷Cs efficiency of 1.8 gcm⁻³ phantom

as the index nuclide radioactivity A_i is ¹³⁷Cs, the gross radioactivity A_t=327780 Bq, and the E_x of ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co with respect to ¹³⁷Cs are 0.17, 1.79, and 1.11.

Thus

$\begin{array}{c}{A}_i=A_t/\sum \left(1+R_xE_x\right)\\ =327780/\left[1+\left(0.593\times 0.17\right)+\left(0.628\times 0.79\right)+\left(1.19\times 1.11\right)\right]\\ =74058\mathrm{Bq}\end{array}$

A _x =A _i ×R _x, therefore, ⁵⁷Co=A_i×0.593=43916 Bq

⁵⁴Mn=A_i×0.628=46508 Bq

⁶⁰Co=A_i×1.19=88129 Bq

Hence, the calibrated gross gamma radioactivity A_t=252611 Bq

the standard gross gamma radioactivity is 246239 Bq

the deviation of correctness is 2.59%

(4-3-3) ¹³⁷Cs efficiency of 2.5 gcm⁻³ phantom

as the index nuclide radioactivity A_i is ¹³⁷Cs, the gross radioactivity A_t=325651 Bq, and the E_x of ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co with respect to ¹³⁷Cs are 0.16, 0.77, and 0.99.

Thus,

$\begin{array}{c}{A}_i=A_t/\sum \left(1+R_xE_x\right)\\ =325651/\left[1+\left(0.593\times 0.16\right)+\left(0.628\times 0.77\right)+\left(1.19\times 0.99\right)\right]\\ =185345\mathrm{Bq}\end{array}$

A _x =A _i ×R _x, therefore, ⁵⁷Co=A_i×0.593=43552 Bq

⁵⁴Mn=A_i×0.628=46123 Bq

⁶⁰Co=A_i×1.19=87398 Bq

Hence, the calibrated gross gamma radioactivity A_t=250517 Bq

the standard gross gamma radioactivity is 246239 Bq

the deviation of correctness is 1.74%

TABLE 3
nuclide parameters for calibration phantoms of various
densities
parameter	gcm−3	57Co	54Mn	60Co	137Cs
Rx		0.593	0.628	1.19	1
px		96%	100%	200%	85%
εx	1.1	35%	14.5%	16.6%	17.7%
εx	1.8	2.5%	11.4%	14.1%	14.5%
εx	2.5	2.4%	11.1%	12.7%	13.2%

To sum up, the volume calibration phantom and calibration method thereof disclosed in the present invention have the following advantages:

• • (1) The MDAs of ⁵⁷Co, ⁵⁴Mn, ⁶⁰Co are 5 times lower than the release standard specified by authority, that the volume calibration phantom is suitable for measuring a box of uniform nuclear waste.
  • (2) As the waste is a multi-nuclide waste, the gross gamma radioactivity is calibrated with respect to parameters, such as A_i, ε_i, p_i, R_x, E_x, so that it is deviated from the standard radioactivity no more than 5%.
  • (3) The radioactivity uniformity of a multi-density volume calibration phantom composed of four uniform radionuclides is smaller tha 7.9%.
  • (4) The range of the density and energy level of an so-established volume calibration phantom is comparatively wide, so that the accuracy of measurement is enhanced.

While the preferred embodiment of the invention has been set forth for the purpose of disclosure, modifications of the disclosed embodiment of the invention as well as other embodiments thereof may occur to those skilled in the art. Accordingly, the appended claims are intended to cover all embodiments which do not depart from the spirit and scope of the invention.

Claims

1. A volume calibration phantom, being disposed inside a monitor having a plurality of radiation detectors received inside a accommodation space formed inside the monitor, the volume calibration phantom comprising: a container;a plurality of plates, stacking up inside the container; andat least one slab of radioactive source, each of which is disposed between the adjacent plates and comprises a plurality of radionuclides.

2. The volume calibration phantom of claim 1, wherein each plate is made of a metal.

3. The volume calibration phantom of claim 2, wherein the metal is iron.

4. The volume calibration phantom of claim 1, wherein each plate is made of a non-metal material.

5. The volume calibration phantom of claim 4, wherein the non-metal material is a material selected from the group consisting of paper, wood, gypsum, acrylic resin, rubber and glass.

6. The volume calibration phantom of claim 1, wherein any one of the plural radionuclides is a gamma radioactive source.

7. The volume calibration phantom of claim 6, wherein the gamma radioactive source is a radionuclide selected from the group consisting of 57Co, 54Mn, 60Co, 137Cs and the combination thereof.

8. The volume calibration phantom of claim 1, wherein any one of the plural radionuclides is a radioactive source of circular shape.

9. The volume calibration phantom of claim 8, wherein the diameter of the circular-shaped radioactive source is smaller than 5 cm.

10. The volume calibration phantom of claim 1, wherein each slab of radioactive source is further comprised of: a bottom laminating layer;a leakage-prevention filter layer, formed on the bottom laminating layer while having the plural radionuclides to be formed thereon; anda top laminating layer, formed on top of the leakage-prevention filter layer as the protection of the plural radionuclides.

11. A calibration method, comprising steps of: providing a plurality of volume calibration phantoms of various densities;measuring the plural volume calibration phantoms by a specific monitor for obtaining a calibration curve of density against counting efficiency corresponding to the measurement;filling a waste specimen into a container of the same volume as each of the plural volume calibration phantoms so as to be used as a test sample;obtaining a sample gamma gross radioactivity of the test sample by referencing to the calibration curve with respect to the density of the test sample measured and detected by the specific monitor;calibrating the sample gamma gross radioactivity by a calibration formula for acquiring a correct gamma gross radioactivity.

12. The calibration method of claim 11, wherein each of the plural volume calibration phantoms is capable of receiving an substance selecting from a group consisting of a metallic material and a non-metallic material.

13. The calibration method of claim 12, wherein the metallic material is an iron plate.

14. The calibration method of claim 12, wherein the non-metal material is a material selected from the group consisting of paper, wood, gypsum, acrylic resin, rubber and glass.

15. The calibration method of claim 12, wherein the radioactive source of each volume calibration phantom is a gamma radioactive source

16. The calibration method of claim 15, wherein the gamma radioactive source is a radionuclide selected from the group consisting of 57Co, 54Mn, 60Co, 137Cs and the combination thereof.

17. The calibration method of claim 11, wherein the sample gamma gross radioactivity is calibrated with respect to an energy dependency factor and a formula of multi-radionuclides calculation.