Device for estimating the half-value layer or the quarter-value layer of rotating x-ray sources used in computed tomography

Abstract

Certain embodiments are directed to devices useful for determination of HVL or the QVL of an x-ray source. The device includes an elongated radio-opaque cylindrical body having an incremental or continuous decrease in circumference.

Claims

1. A device for half-value layer measurements and quarter-value layer measurements comprising: a hollow cylinder having a proximal and distal end, and constant inner diameter and a variable outer diameter along a central axis, the hollow cylinder having an initial outer diameter at the proximal end with a series of segments having decreasing outer diameters to a minimal outer diameter at the distal end.

2. The device of claim 1, wherein the constant inner diameter is 5 mm to 20 mm.

3. The device of claim 1, wherein the constant inner diameter is 13 mm.

4. The device of claim 1 wherein the outer diameter is between 13.2 mm and 50 mm.

5. The device of claim 1, wherein the minimal outer diameter is 13.2 mm.

6. The device of claim 1, wherein the initial outer diameter is 50 mm.

7. The device of claim 1, wherein the outer diameter increases from the distal end to the proximal end by 0.1 to 3 millimeter in 10 mm to 50 mm segments or steps.

8. The device of claim 1, wherein the outer diameter of a segment increases by either 1 mm or 2 mm per segment from the distal end to the proximal end.

9. The device of claim 1, wherein each segment is 10 mm in length as measured along the central axis.

10. The device of claim 1, comprising 5 to 20 segments having an incremental increase in the outer diameter from the distal end to the proximal end.

11. The device of claim 1, wherein the device is metal, a metal alloy, solid-state semiconductor, or a polymer material.

12. The device of claim 11, wherein a percentage aluminum in the aluminum or aluminum alloy is 99% aluminum or greater.

13. The device of claim 1, wherein the device is aluminum, copper, tin, brass, lead, or a metal alloy.

14. The device of claim 1, wherein the device is aluminum or an aluminum alloy.

15. The device of claim 1, wherein the device body has an alignment point, or alignment line, or both an alignment point and an alignment line.

16. The device of claim 1, further comprising a cylindrical casing.

17. The device of claim 16, wherein the cylindrical casing is hollow or the cylindrical casing is filled with a liquid or a solid.

18. The device of claim 17, wherein the liquid is water.

19. The device of claim 17, wherein the solid is a polymer, polymer gel, tissue equivalent material, or material simulating water.

20. The device of claim 1, further comprising an x-ray radio-opaque material, or radiation detector positioned in the hollow cylinder.

21. The device of claim 20 wherein the radiation detector is an ion chamber, solid-state semiconductors, thermo-luminescence dosimeters, optically-stimulated dosimeters, or radiochromic film.

22. The device of claim 21, wherein the radiochromic film substantially covers an inner surface of the hollow cylinder.

23. An apparatus for half value layer measurements of x-ray sources comprising a device of claim 1 and a radiation detector or radio-opaque material operatively positioned within the device.

Description

DESCRIPTION OF THE DRAWINGS

(1) The following drawings form part of the present specification and are included to further demonstrate certain aspects of the present invention. The invention may be better understood by reference to one or more of these drawings in combination with the detailed description of the specification embodiments presented herein.

(2) FIG. 1A shows a front view of one embodiment of a device; a HVL cylindrical “step” wedge. The hollow center is to accommodate radiation detectors, sensors, or dosimeters.

(3) FIG. 1B shows a side/top view of one embodiment of a device; a HVL cylindrical “step” wedge. Each “step” is of equal length along the long axis and the outer diameter of the cylinder increases with every “step”.

(4) FIG. 1C shows an isometric view of one embodiment of a device; a HVL cylindrical “step” wedge. The hollow center is to accommodate radiation detectors, sensors, or dosimeters.

(5) FIG. 2A shows an isometric view of one embodiment of a device insert; a piece of radiochromic film is designed to fit in the hollow center of a device. The film extends thru all “steps” along the long axis.

(6) FIG. 2B shows an isometric view of one embodiment of a device insert; an insert consisting of a piece of radiochromic film placed in between a two thin frames and designed to fit in the hollow center of a device. The insert extends thru all “steps” along the long axis.

(7) FIG. 2C shows an isometric view of one embodiment of a device insert; an insert having small samples of iodine, calcium, lead, radioactive material, or other materials/substances, placed on a thin frame and designed to fit in the hollow center of a device. The insert extends thru all “steps” along the long axis.

(8) FIG. 2D shows an isometric view of one embodiment of a device insert; an insert to hold thermo-luminescence dosimeters (TLD) on a thin frame and designed to fit in the hollow center of a device. The insert extends thru all “steps” along the long axis.

(9) FIG. 2E shows an isometric view of one embodiment of a device insert; an insert to hold optically-stimulated-luminescence dosimeters (OSL) on a thin frame and designed to fit in the hollow of a device. The insert extends thru all “steps” along the long axis.

(10) FIG. 2F shows an isometric view of one embodiment of a device insert; an insert holds a radiation probe or detector within a frame and designed to fit in the hollow center of a device. The insert extends thru all “steps” along the long axis.

(11) FIG. 3A shows a front view of one embodiment to perform HVL measurements where the device is centered at the axis of rotation of a CT scanner. The device is advanced thru the plane of the central axis of rotation while the x-ray beam scans the device. During the scan the x-ray tube rotates around the central axis or remains at a fixed position. A radiation detector, insert, or probe is inside the hollow center that extends along the long axis (which is also the center of rotation).

(12) FIG. 3B shows a side view of one embodiment to perform HVL measurements where the device is centered at the axis of rotation of a CT scanner. The device is advanced thru the plane of the central axis of rotation while the x-ray beam scans the device. During the scan the x-ray tube rotates around the central axis or remains at a fixed position. A radiation detector, insert, or probe is inside the hollowed center that extends along the long axis (which is also the center of rotation). The device is held in place with a supporting structure designed to use a CT patient table to advance the device thru the plane of the central axis of rotation during the scan while avoiding radiation attenuation and scatter contributions from the table.

(13) FIG. 3C shows a side view of one embodiment to perform HVL measurements where the device is centered at the axis of rotation of a CT scanner. The device is advanced thru the plane of the central axis of rotation while the x-ray beam scans the device. During the scan the x-ray tube rotates around the central axis or remains at a fixed position. A radiation detector, insert, or probe is inside the hollow center of the device that extends along the long axis (which is also the center of rotation). The device is placed inside a cylindrical casing held in place with a supporting structure designed to use a CT patient table to advance the device thru the plane of the central axis of rotation during the scan.

(14) FIG. 4A shows a side view of one embodiment to perform HVL measurements where the device is centered at the axis of rotation of a CT scanner. The device is advanced thru the plane of the central axis of rotation while the x-ray beam scans the device. During the scan the x-ray beam is attenuated by the “steps” of different material thicknesses. Different radiation intensities are measured with a radiation detector, insert, or probe inside the hollow center of the device that extends along the long axis (which is also the center of rotation). A portion of the radiation detector, insert, or probe is outside the device's structure to measure the radiation intensity without any attenuating material, i.e., Jo.

(15) FIG. 4B shows one embodiment of an attenuation pattern after scanning the device and corresponding radiation detector, insert, or probe. An unexposed radiation sensor and a formula to calculate the pixel density ratio are also shown.

(16) FIG. 5 illustrates that symmetrical scatter contribution within the apparatus approaches ideal broad-beam geometry/attenuation conditions. As the x-ray tube rotates, the same amount of photons lost due to scatter are replaced when the tube is in the opposite location and detected within the ion chamber's sensitive volume.

(17) FIG. 6 is a flow chart illustrating the steps included in measurement of mass-energy absorption coefficient and/or the narrow-beam geometry HVL or QVL.

(18) FIG. 7 shows broad-beam geometry transmission/attenuation curves (small and large BT, ST=5 mm) obtained with using one embodiment of the device described herein.

(19) FIG. 8 shows graphical results showing (large bow-tie filter only), as theorized by Evans, the experimental setup may approach ideal broad-beam geometry and ideal broad-beam attenuation conditions.

(20) FIG. 9 shows linear regression model for the narrow-beam geometry HVL quoted by the manufacturer as a function of the broad-beam geometry HVL measured using an embodiment described herein.

(21) FIG. 10 shows narrow-beam geometry HVL quoted by the manufacturer and straight-line linear regression models (ST=1.25, 5, 10 mm, simplified fit), as a function of tube potential (small and large BT filters).

(22) FIG. 11 shows the use of a pencil-type ion chamber for expedient, real-time, measurements and eliminates the need for post-processing required for other type of detectors like radiochromic film, TLDs, or OSLs.

DETAILED DESCRIPTION OF THE INVENTION

(23) For decades the half-value-layer (HVL) has been the standard of image quality in diagnostic x-ray imaging. However, measuring the HVL in CT scanners requires “parking” the x-ray tube. If the scatter contribution of a solid object on a signal measured at the axis of rotation could be successfully predicted, then the HVL could be accurately measured in CT scanners without the need to “park” (stop) the x-ray tube. This would allow medical physicists in radiology departments/clinics, consulting businesses and academia worldwide to easily and effortlessly measure the HVL “on-demand” which in turn could provide early detection of any problems or deterioration related to the x-ray tube. In addition, a CT HVL Phantom can be used to further enhance the patient dosimetry calculations which today are mostly based in Monte Carlo simulations.

(24) Embodiments are directed to devices, inserts, and methods, examples of which are shown in FIG. 1A to FIG. 4B. Variations in the methodology for using the device and inserts/probes for measuring the HVL, variations in the design of the device and/or inserts, or other variations on the device and how to use the device are disclosed herein. The methods, devices, inserts/probes, and/or data/image analysis can vary so long the objective(s) of the invention is/are attained.

(25) Shown in FIG. 2C is an embodiment of a HVL “step-wedge” insert designed to hold radio-opaque materials such as iodine, iodine contrast, calcium, barium, lead, etc. The resulting CT scan images resulting from this insert embodiment can be analyzed to determine the attenuation thru each “step” and to then calculate the HVL. The insert can also hold small amounts of photon-emitting radioactive materials which, when inserted inside the HVL “step-wedge”, can then be used to create an attenuation pattern image. The attenuation pattern image may also be used to estimate attenuation correction factors.

(26) FIG. 1A to FIG. 1C shows an embodiment of a device to measure the HVL and can be used in CT imaging systems or other medical imaging modalities. Certain embodiments can also be referred as a HVL “step-wedge”. The embodiment of the HVL “step-wedge” shown in FIG. 1A to FIG. 1C is a cylindrical device with a hollow center along the long axis (z-axis). In certain aspects the hollow center can have a constant diameter. The “steps” can be, but not necessarily, equal length along the long axis (z-axis) and of equal increasing increments in diameter (i.e., thickness) in the x-y plane from one end of the cylinder to the other.

(27) In one embodiment the HVL “step-wedge” hollow center is designed to accommodate a radiation measuring instrument, detectors, or inserts similar, but not limited to those shown in FIG. 2A to FIG. 2F. As shown in FIG. 3A to FIG. 3C, and FIG. 4A, when the combined HVL “step-wedge” and radiation detector/insert assembly is radiated with x-ray photons that are preferentially attenuated by the different “steps” with the resulting attenuated radiation being detected/measured by the radiation detector/insert. If the x-ray tube is rotating (for example, in the x-y plane), then the long axis (z-axis) of the combined HVL “step-wedge” and radiation detector/insert assembly is centered and aligned along the x-ray tube's axis of rotation (z-axis). Notice that a portion of the radiation detector/insert can extend outside the HVL “step-wedge” to measure I.sub.0 (I.sub.0 is the photon beam intensity measured without any attenuating material in its path).

(28) In one embodiment the HVL “step-wedge” is preferably made of machined aluminum, tin, copper, or any other material as needed for the intended use. The thickness and length of the “steps” can be machined to suit the photon energy and radiation source application. The embodiment of the HVL “step-wedge” shown in FIG. 1A to FIG. 1C is made of aluminum type 1100.

(29) In one embodiment the thickness of the “steps” (i.e., outer radius minus inner radius in the x-y plane) can be machined to any thickness from approximately 0.1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 mm to approximately 25 mm (including values and ranges there between) or any other thickness as needed for the intended use. The embodiment of the HVL “step-wedge” shown in FIG. 1A to FIG. 1C has “steps” (i.e., outer radius minus inner radius in the x-y plane) machined to an initial “step” thickness of 1.0 mm, then incrementing the thickness by 1.0 mm for each “step” until reaching a thickness of 10.0 mm for the last “step”.

(30) In one embodiment the length of the “steps” along the long axis (i.e. z-axis) can be machined to any length from approximately 10, 15, 20, 25, 30, 35, 40, 45 mm to approximately 50 mm (including values and ranges there between) or any other length as needed for the intended use. In one embodiment the HVL “step-wedge” shown in FIG. 1A to FIG. 1C has “steps” along the long axis (i.e., z-axis) machined to a “step” length of 10.0 mm for each “step”.

(31) In one embodiment, as shown in FIG. 3A to FIG. 3C, and FIG. 4A, the combined HVL “step-wedge” and radiation detector/insert assembly is secured to or placed on top of a patient table, centered in the axis of the x-ray tube's rotation, and then traverses, during the scan, thru the plane of the x-ray tube's rotation.

(32) In another embodiment, as shown in FIG. 3A to FIG. 3C, and FIG. 4A, the combined HVL “step-wedge” and radiation detector/insert assembly is secured to or placed on top of a patient table, centered in the axis of the x-ray tube's rotation, and then traverses, during the scan, thru the plane while the x-ray tube remains stationary (i.e., not rotating, “parked”).

(33) In another embodiment, the combined HVL “step-wedge” and radiation detector/insert assembly could be encased in a cylinder (also part of the invention) as shown in FIG. 3C which can then be filled with water, water-simulating resins, or other tissue equivalent materials. The cylinder includes reflective grooves and small metallic markers to help during the process of centering and aligning. In certain aspects the HVL is measured with the added attenuation contributions of the patient, filters, collimation, and the patient table. This in turn could result in improved input data for radiation dosimetry calculations.

(34) It is intended that those skilled in the art understand that FIG. 3A to FIG. 3C, and FIG. 4A show either applications of this invention during scans where the x-ray tube remains stationary (i.e., not rotating, “parked”) or where it rotates 360-degrees around the z-axis.

(35) During either type of scan (rotating or stationary source) the combined HVL “step-wedge” and radiation detector/insert assembly is radiated with x-ray photons that are preferentially attenuated by the different “steps” with the resulting attenuated radiation, and I.sub.0, being detected/measured by the radiation detector/insert.

(36) The embodiment shown in FIG. 4A is an example of the HVL “step-wedge” and radiation detector/insert assembly being exposed to x-ray photons as the table moves it thru the beam. An example of the resulting attenuation pattern is shown in FIG. 4B. The attenuation pattern could be measured with passive radiation dosimeters (such as film, TLDs, OSLs), a radiation detector/probe capable of real-time rapid data acquisition, or via analysis of the resulting CT scan images. The measured attenuation data, or an attenuation ratio, can be fitted to an equation similar to Equation 1.0 and then proceed to estimate the HVL using Equation 2.0.

(37) In certain aspects the HVL “step-wedge” shown in FIG. 1A to FIG. 1C the radiation dosimeters, inserts, or radiation detector/probe will be in close proximity (in the order of millimeters) to the inner circumference that defines the hollowed cavity along the long axis. The close proximity of the radiation dosimeters, inserts, or radiation detector/probe to the attenuating material will introduce an increased measured attenuation due to scatter “contamination” from the attenuating material. The traditional methodology to measure the HVL uses an “air-gap” of several centimeters to avoid the increased attenuation measured due to scatter “contamination” originating from the attenuating material. It is contemplated that the HVL “step-wedge” can also be used to estimate/characterize the magnitude of the scatter “contamination” to the measured attenuation. The attenuation measured can then be corrected, predicted, or modeled to account for the scatter “contamination”.

(38) The embodiment of the HVL “step-wedge” shown in FIG. 1A to FIG. 1C results in an easy to handle and easy to use device which allows for many repeated HVL measurements and consequently more precise results. The most common application of this device, system, and/or related methods will use axial CT scans with narrow beams centered over the length of each “step” and with long rotation times over each “step”. The HVL “step-wedge” and radiation detector/insert assembly remains static, centered with the axis of the x-ray tube's rotation (z-axis).

(39) It is intended that those skilled in the art understand that the maximum attenuating material thickness of the “steps” in the embodiment shown in FIG. 1A to FIG. 1C should be, based on knowledge of the photon energy and the attenuating material, greater than the expected HVL. For example, in diagnostic radiology this maximum thickness could be at least 15-20 mm of aluminum.

(40) The embodiment of the HVL “step-wedge” and radiation detector/insert assembly described herein should not require cupping (parallax) effect or, when properly centered and aligned along the x-ray tube axis of rotation, any inverse square corrections. However, a scatter correction/prediction/model may be required and/or recommended. The HVL can also be defined in terms of a factor applied to the HVL as measured using the traditional HVL measurement technique.

Example

(41) A device prototype was fabricated as per the embodiment of the HVL “step-wedge” and radiation detector/insert assembly shown in FIG. 1A to FIG. 1C and FIG. 3B. The prototype was exposed to rotating x-ray beams in a setup similar to FIG. 3B and FIG. 4A and, using a pencil-type ion chamber, an attenuation curves similar to those shown in FIG. 7 were obtained.

(42) The measured attenuation data, or an attenuation ratio, was fitted to an equation similar to Equation 1.0 to estimate the HVL using Equation 2.0.

(43) The HVL “step-wedge” and radiation detector/insert assembly together with knowledge of the scatter contribution of a solid object on the attenuation measured at the axis of rotation, can be used to accurately measure the HVL in CT scanners without the need to “park” (stop) the x-ray tube.

(44) In certain embodiments, an apparatus was designed to measure the HVL of an incident x-ray beam from a rotating CT x-ray tube. The design allows for using a pencil-type ion chamber, centered within the apparatus to perform the necessary measurements. Measurements were performed using an axial scan protocol with the x-ray tube set to complete one rotation per second while acquiring one image per slice. The scan was repeated for multiple tube potentials, bow-tie filters and slice thicknesses. The results were compared to HVL values quoted for the manufacturer and HVL values obtained using the localizer or scout scan.

(45) The HVL measurements performed with the apparatus were fitted using a straight-line linear model to the HVL values quoted by the manufacturer and to the HVL values obtained using the scout scan resulting in regression coefficients of determination r.sup.2≥0.9985, regression p-values ≤0.0007, and percent differences ≤4.22%. The Pearson product-moment correlation coefficients were; r≥0.99 (p-values ≤0.0007, 95% CI 0.96 to 0.99).

(46) Attenuation curves, and corresponding HVL measurements, can be successfully obtained using the apparatus designed. A simplified straight-line equation can be used to correlate the HVL measured using the apparatus in broad-beam geometry to the expected narrow-beam geometry HVL.

(47) Materials: GE LightSpeed® RT 16 Slice CT scanner, RaySafe X2 (X2 Base Unit and X2 CT Sensor), and Aluminum plates (1100 alloy).

(48) HVL Scan protocol: Axial scan; ST=1.25, 5.0, 10 mm; 1 sec tube rotation; 1 image/slice; 80, 100, 120, 140 kVp; 350 mA; and Large, Small BT filters.

(49) Certain embodiments provide a new paradigm for estimating radiation dose and quality control. Devices and methods described herein provide for (i) a CT HVL and dosimetry protocol for after CT installation and acceptance testing, (ii) data for Monte Carlo simulations, other dosimetry models, (iii) optimization of scan protocols to further reduce dose to the patient while still maintaining good clinical image quality. In certain aspects devices described herein can be portable and easy to use. Such devices can obtain beam attenuation measurements for estimating the HVL and can be used with instrumentation already available. Certain aspects allows for measurements with the x-ray tube rotating. The HVL correlates to the manufacturer's HVL values by <5% difference.

(50) TABLE-US-00001 TABLE 1 Broad-beam geometry HVL (small and large BT filters, ST = 5 mm) estimated from the broad-beam geometry transmission curves obtained with the MuCT ™ device, a cylindrical step-wedge (CSW), and using Log-linear (LL) and Lambert W (LW) interpolation. SBT-BBG LBT-BBG SBT-BBG LBT-BBG (LL) (LL) (LW) (LW) kVp [mm Al] [mm Al] [mm Al] [mm Al] 80 6.93 8.71 6.82 8.80 100 9.76 12.21 9.67 12.21 120 12.65 15.37 12.65 15.42 140 15.47 17.91 15.53 18.66

(51) TABLE-US-00002 TABLE 2 Effective energy-absorption coefficient estimated from Table 1 values (MUen = Ln 2/HVL). SBT-MUen LBT-MUen SBT-MUen LBT-MUen (LL) (LL) (LW) (LW) kVp [1/mm] [1/mm] [1/mm] [1/mm] 80 0.1000 0.0796 0.1016 0.0788 100 0.0710 0.0568 0.0717 0.0568 120 0.0548 0.0451 0.0548 0.0450 140 0.0448 0.0387 0.0446 0.0371

(52) TABLE-US-00003 TABLE 3 Effective energy estimated interpolating Table 2 values using the NIST X-Ray Mass Attenuation Coefficient and Mass Energy-Absorption Coefficient tables for aluminum. SBT-Eeff LBT-Eeff SBT-Eeff LBT-Eeff (LL) (LL) (LW) (LW) kVp [keV] [keV] [keV] [keV] 80 39.28 42.24 39.00 42.35 100 44.00 47.47 43.92 47.47 120 48.12 51.44 48.11 51.53 140 51.87 54.49 52.01 55.18

(53) TABLE-US-00004 TABLE 4 Effective total attenuation coefficient estimated interpolating Table 3 values using the NIST X-Ray Mass Attenuation Coefficient and Mass Energy-Absorption Coefficient tables for aluminum. SBT-MUtot LBT-MUtot SBT-MUtot LBT-MUtot (LL) (LL) (LW) (LW) kVp [1/mm] [1/mm] [1/mm] [1/mm] 80 0.1568 0.1341 0.1586 0.1330 100 0.1242 0.1078 0.1249 0.1078 120 0.1055 0.0942 0.1057 0.0939 140 0.0938 0.0864 0.0935 0.0845

(54) TABLE-US-00005 TABLE 5 Narrow-beam geometry HVL (small and large BT filters, ST = 5 mm) estimated using Table 4 values (HVL = Ln 2/MUtot). The percent relative differences comparing the results with the HVL values quoted by the manufacturer are shown in parenthesis. SBT LBT SBT SBT LBT LBT SBT SBT LBT LBT Mfr. Mfr. (LL) (LL) (LL) (LL) (LW) (LW) (LW) (LW) kVp [mm Al] [mm Al] [mm Al] % [mm Al] % [mm Al] % [mm Al] % 80 4.3 5.2 4.42 (2.85) 5.17 (0.48) 4.37 (1.65) 5.21 (0.22) 100 5.4 6.3 5.58 (3.33) 6.43 (2.02) 5.55 (2.69) 6.43 (2.01) 120 6.3 7.4 6.57 (4.23) 7.36 (0.49) 6.56 (4.20) 7.38 (0.27) 140 7.3 8.3 7.39 (1.28) 8.02 (3.35) 7.41 (1.50) 8.20 (1.16)

(55) TABLE-US-00006 TABLE 6 Narrow-beam geometry HVL as quoted by the manufacturer and broad-beam geometry HVL measured using the CSW with the small and large BT filters. The small relative difference of the average of all slice thicknesses to that of ST = 5 mm suggests that one can just use ST = 5 mm for expedient measurements. Small BT-GE Small BT-CSW Small BT-CSW Small BT-CSW Average of Relative Difference ST = ? ST = 1.25 mm ST = 5 mm ST = 10 mm All ST (%) of Average to kVp [mm Al] [mm Al] [mm Al] [mm Al] [mm Al] ST = 5 mm 80 4.3 6.50 6.64 6.96 6.70 0.90 100 5.4 9.69 9.76 10.03 9.83 0.71 120 6.3 12.52 12.65 12.84 12.67 0.16 140 7.3 15.35 15.47 15.66 15.50 0.19 Large BT-GE Large BT-CSW Large BT-CSW Large BT-CSW Average of Relative Difference ST = ? ST = 1.25 mm ST = 5 mm ST = 10 mm All ST (%) of Average to kVp [mm Al] [mm Al] [mm Al] [mm Al] [mm Al] ST = 5 mm 80 5.2 8.64 8.71 9.06 8.81 1.14 100 6.3 12.10 12.21 12.51 12.27 0.49 120 7.4 15.27 15.37 15.52 15.39 0.13 140 8.3 17.70 17.91 18.02 17.88 0.17

(56) TABLE-US-00007 TABLE 7 Summary of the results for the straight-line linear regression models with the corresponding minimum and maximum relative difference. The small BT and large BT filters are indicated by “S” and “L”, respectively. Relative Relative Difference Difference X Y Slope Intercept Min (%) Max (%) S-CSW S-GE 0.337067 2.111699 0.08 0.51 ST = 1.25 mm S-CSW S-GE 0.337097 2.072163 0.17 0.68 ST = 5 mm S-CSW S-GE 0.342340 1.931753 0.09 0.62 ST = 10 mm L-CSW L-GE 0.341893 2.209314 0.40 0.72 ST = 1.25 mm L-CSW L-GE 0.337673 2.225142 0.18 0.77 ST = 5 mm L-CSW L-GE 0.347425 2.012409 0.08 0.96 ST = 10 mm S CSW S GE ⅓ 2.1 0.27 2.76 (simplified fit) L CSW LGE ⅓ 2.1 0.45 4.22 (simplified fit)