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The application of spherical standards for the evaluation of the accuracy of mapping shape in computed tomography

The application of spherical standards for the evaluation of the accuracy of mapping shape in... Anatomical structures are characterized by free surfaces, and most are in lobed and pseudo-spherical shapes. The aim of this article is to analyze selected procedures for accuracy assessment of the shape and dimensions of these structures using certified sphere and Ball Bar standards and to propose metrology parameters facilitating comparison of diagnostic devices. The spherical standard of various materials and Ball Bar standards with various distances between spheres centers can be a tool for evaluation of computed tomography metrology applications. Errors in geometry mapping can be identified on the basis of standardized control systems used in coordinate measuring techniques. Keywords: accuracy; computed tomography; mapping; shape; spherical standards. precision, a CT scanner is calibrated using special references and phantoms. For medical CT, this problem requires the use of special references and measurement strategies. At the current stage of imaging no unambiguous normative requirements are available, specifying measurement accuracy for medical CT scanners. Study objective The aim of this study is to analyze selected procedures for accuracy assessment for shape and dimensions reproduction in medical CT using references and to propose metrology parameters facilitating comparison of measurement applications available in various diagnostic devices. Computed tomography and metrology The accuracy of CT scanners used for industrial measurements is specified in VDI/VDE 2630 and associated standards, characterizing parameters in four groups related to length measuring error, scanning error, relationship between shape and dimension, and resolution [1­5]. These parameters characterize tomography systems with a flat or cone X-ray beam. In industrial tomography, the parameter related to the length measuring error is determined with material length standards [6]. The determined parameter value is compared with a maximum permissible error, MPE, for length measurements: MPE =±(A + L/K) µm (1) Introduction The advanced diagnostic and preoperative procedures using computed tomography (CT) require not only imaging but also spatial reproduction of tissue structures with an analysis of their dimensions and shapes. A very important problem in imaging of an object is measurement precision in scans used to select implants or plan a non-standard surgical procedure. To ensure appropriate measurement *Corresponding author: Lukasz Bojko, Faculty of Mechanical Engineering and Robotics, AGH University of Science and Technology, Krakow, Poland, E-mail: lbojko@op.pl. http://orcid.org/0000-0002-6024-458X Andrzej Ryniewicz, Ksenia Ostrowska, Jerzy Sladek and Marcin Krawczyk: Laboratory of Coordinate Metrology, Faculty of Mechanical Engineering, Cracow University of Technology, Krakow, Poland Wojciech Ryniewicz: Faculty of Medicine, Department of Prosthetic Dentistry, Jagiellonian University Medical College, Krakow, Poland. http://orcid.org/0000-0003-3564-2321 where: A ­ error in standard construction [m]; L ­ measured length [mm]; K ­ constant depending on a device type. In medical CT, the use of a length standard in the form of standard plates is limited due to specific conditions of measurement (the X-ray beam penetrates through 232Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT the whole length of the standard); therefore, the use of spherical length standards is a better solution. The VDI/ VDE 2630 standard, in two procedures, A and B, describes in detail a resultant correlation, considering material, dimension, shape, and spacing of measuring points of the standard [5, 7­10]. In medical applications, the measurement accuracy can be established by measuring special phantoms. They consist of bodies of specified geometric parameters and materials of known X-ray attenuation coefficient. The quality of the scan itself depends mainly on an operational condition of the radiation source and auxiliary equipment. Therefore, the use of coordinate metrology methods for assessment of CT reproduction accuracy appears interesting, particularly for spherical standards. Verification of industrial CT scanners With the development of digital techniques for mathematical analyses and CAD software, the geometry of real products can be recorded as 3D information. When structural light scanners were used, only external surfaces were recorded, without an option for deeper penetration. The use of tomography enables three-dimensional recording of an object together with its internal structures. With an option for full 3D description of objects, an issue of their use for dimension evaluation and a problem of measurement accuracy assessment arose. Works on that problem were conducted in numerous research centers, including the National Metrology Institute in Germany, where a standard for CT metrology applications cooperating with coordinate measuring machine (CMM) was drafted [6]. The use of industrial tomography for assessment of geometric precision of tested objects was possible with the development of algorithms for determining edges of relevant objects [11­14]. In this case, an issue of finding edges is more complicated than in medical CT that for different materials grayscale is not expressed in units, and therefore, it is not possible to assign a given grayscale level to a given material [12, 15]. Due to similarities in results obtained with CT scanners and with CMMs, works are currently conducted to adapt ISO 10360 standards to verify length and shape in industrial CT scanners (Figure 1) [6]. Studies on the possibility to use length standards for this purpose were conducted in many centers. Also, other Control tests in coordinate measuring systems Currently, a set of ISO 10360 standards specifies three types of tests for which measuring characteristics are determined. The first is used to determine error variability for length measurements. This test usually consists of measuring, in three replications, five standards of various uniformly distributed lengths, with the last length exceeding the length of the verified axis by 66%. It is repeated in different orientations. It is recommended for selected orientations to be parallel to relevant axes and diagonals of the measurement space. For coordinate measuring machines, this test is usually performed across seven different positions: three parallel to X, Y, and Z axes and four along diagonals of the measurement space. For other tests, a spherical standard is used to determine shape and dimension errors. In the test establishing the shape error, measurements are performed for a specified number of points, usually 25, evenly distributed on the standard hemisphere, and then a substitute feature, a sphere, is determined with the least squares method. Then angles between radius vectors of individual measuring points, starting in the center of the determined sphere, are established. This test aims at determining measurement variability for the points, depending on an acquisition direction. The last test is the dimension test, performed in accordance with the procedure described above, with a diameter of a sphere determined from a specified number of points compared to a correct value provided in a calibration certificate for that standard. Figure 1:Standards used to define the length error [16]. Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT233 standards were developed, in which a concept for reference measurements was based on determining a distance between spheres centers. Image quality control for medical CT systems CT quality control is conducted in accordance with international standards or national guidelines. In Poland, relevant requirements are specified in the Minister of Health Regulation of 24 December 2002 [17]. The provisions concern health care centers working with devices using ionizing radiation. In the Regulation, the Minister imposes an obligation to conduct periodic internal quality control tests verifying performance of devices used for diagnostic imaging. The Regulation provides a list and a frequency for the relevant tests. The control is performed with a phantom, being a standard containing components of materials having Hounsfield unit values corresponding to the gray level of human tissues. Materials for phantoms construction are selected to cover the whole range of values recorded by medical CT scanners. Performance of imaging systems in diagnostic devices is subject to periodic quality control. Verification is performed by scanning of the phantoms (Figures 2 and 3). The phantom consists of the head section (1) including components such as a physical layer (3), a water layer (4), a multi-needle layer (5), a copper duct (6), and a 45° wedge (7). That part of the phantom is made of PVC and filled with water. The physical layer is designated to test the resolution and thickness of a tomographic layer; the water layer is used to measure noise and uniformity, while the contrast scale is verified using the multi-needle layer. The whole assembly forms a cylinder of 200 mm in diameter. The second part of the phantom, the body section (2), consists of a two-component cylinder of 300 mm in diameter, with a Teflon needle and a water needle. There are several types of inspections, including daily or monthly quality tests, and advanced quality control. The daily quality tests are performed to ensure the best quality of the scanned image, and they cover both the head section and the body section. Additionally, monthly inspections performed on the head section of the phantom are obligatory, to verify the contrast scale and artifacts. This inspection is performed on the multi-needle layer. Furthermore, relevant procedures have also been established to solve nonconformities found during daily inspections. They involve more complex algorithms, obligatory for medical specialists and other authorized Figure 2:Phantoms to assess the accuracy of the mapping of anatomical structures [16]. Figure 3:Phantom: (A) general view and (B) diagram [16]. persons. This inspection involves resolution, layer thickness, and layer thickness tolerance tests. Materials and methods The study concerned spherical standards: a certified class 0 ceramic standard sphere, a set of standard spheres of various materials (cemented carbida, steel, corundum ceramics, and zirconium ceramics), and a 1 m-long Ball 234Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT Bar standard from Unimetrik (Figures 4 and 5). The Ball Bar standards are certified, characterized by an accuracy, U=(1.00+0.001 L/1000) m, and used for CMM accuracy verification. Tomographic scans of standard spheres and the Ball Bar standard were conducted with a 64-slice medical CT scanner, Siemens Somaton Cardiac (resolution: 1024×1024×1024 pixels) (Siemens, Munich, Germany). The reconstruction accuracy was assessed by comparison of reconstructed models based on CT imaging versus geometric parameters specified in relevant certificates. The comparison was performed using the best fit method and 3D Reshaper (Technodigit, Genay, France), Poly Works (InnovMetric Software Inc, Quebec, Canada), Geomagic (3D Systems, Rock Hill, SC, USA), and Amira [Visualization Sciences Group, Bordeaux, France and the Zuse Institute Berlin (ZIB), Germany] applications. as surface reconstruction accuracy maps for the standard spheres, determined diameter values and experimental standard deviations for spheres made of various materials, and histograms for errors in the sphere surface shape reconstruction. Furthermore, for the Ball Bar standard, a measurement uncertainty was determined for a distance between spheres centers and a measurement uncertainty for sphere diameters. An example of the surface reconstruction accuracy map for the ceramic sphere surface, CT-scanned and reconstructed in the 3D Reshaper application versus an ideal CAD model, indicates an increase in errors in the sphere surface reconstruction with a decrease in phantom circles in successive scanning planes (Figure 6). The largest errors, of values ­0.25 mm, were located in two areas, described as tomography poles. This distribution of the reconstruction errors in the CT model of the standard sphere indicated a deformation in the form of a surface flattening in the pole areas. A histogram of the reconstruction errors for the ceramic standard sphere diameter in the CT scan is based on 100 measurements. The conducted studies demonstrate that for 90.7% of the results the error in the CT reconstruction of the sphere diameter is within the ±0.06 mm range, and for 98% it is within the ±0.12 mm range. The standard deviation is 0.04 mm, and the mean value for the sphere diameter is 24.97 mm. The analysis results for the reconstruction accuracy for the standard spheres made of four specified materials indicate that errors resulting from a comparison of CTscanned spheres and relevant reference spheres depend on a material of the standard sphere only to a small extent (Table 1). The mean values for errors in diameter measurements in two perpendicular directions, results spread and standard deviations for spheres made of cemented carbida or steel (class 0), corundum ceramics, and zirconium ceramics (class K), indicate the largest reconstruction errors for the sphere of cemented carbida, the largest spread of the results for the steel sphere, and the best reconstruction for the corundum ceramic sphere. CT measurements of a distance between spheres centers and diameters for the Ball Bar standard showed that the accuracy of their reconstruction depends on a position in the measurement space versus a plane determined by transmitters and receivers in the scanner gantry. A spread of results for reconstruction of a distance between sphere centers ranged from 0.02 mm to 0.10 mm, and a spread of results for reconstruction of sphere diameters ranged from 0.01 mm to 0.03 mm. The errors in these measurements cannot be analyzed separately, because the position of the standard spheres was related to the Results and discussion The results of reconstruction assessment for selected geometric parameters of the studied standards were presented Figure 4:Spherical standards of various construction materials (from the left): cemented carbida, steel, corundum ceramics, zirconium ceramics. Figure 5:Ball Bar spherical standard. Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT235 Figure 6:Surface reconstruction accuracy map for the CT-scanned ceramic sphere reconstructed in the 3D Reshaper application versus an ideal CAD model [16]. Table 1:A list of results for diameter measurements accuracy for standard spheres made of selected materials, based on 20 CT measurements for each model, using Geomagic and Quindos applications. Type of material sphere Cemented carbida Steel Corundum ceramics Zirconium ceramics Experimental standard deviation of diameter measurement in axis X, mm 0.12 0.21 0.07 0.08 Experimental standard deviation of diameter measurement in axis Y, mm 0.15 0.18 0.07 0.06 The experimental standard deviation of the mean, mm 0.03 0.04 0.01 0.02 operation of the CT sliding units. It was demonstrated that errors of the linear and angular positioning of the table and errors resulting from fluctuations in its speed and acceleration are significant. The experimental standard deviation and the experimental standard deviation of the mean were assumed to be the best estimates for CT measurement uncertainty. The conducted measurements allowed determining maximum permissible errors, MPE, as MPE =±(W + L/K)A·B·C [ µm] where: W ­ error in standard construction [m]; L ­ measured length [mm]; (2) K ­ constant depending on a device type; A ­ coefficient determining the effect of phantom shape; B ­ coefficient determining the effect of phantom material properties; C ­ coefficient determining the effect of phantom (estimated parameter) position versus the diagnostic plane determined by the gantry unit. The test method used in industrial CT scanners for assessment of metrology parameters using certified geometric standard can be used for medical CT systems. It appears to be particularly useful for assessments of dimension, shape, and reconstruction accuracy for free surfaces characteristic for anatomical structures. 236Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT Conclusions Spherical standard of various materials and Ball Bar standards with various distances between spheres centers can be a tool for evaluation of CT metrology applications. Medical CT introduces an error in the geometry reconstruction accuracy resulting from dimension, shape and material, a position of the scanned spherical surface versus the gantry system, and the object position in the measurement space. These errors can be identified with certified phantoms modeled after control systems used in industrial CT. Acknowledgments: The authors acknowledge the John Paul II Hospital in Krakow, Department of Radiology, Jagiellonian University Medical College and the Medical Centre iMed24 S.A. for the opportunity to carry out research on spherical standard and phantoms. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission. Research funding: None declared. Employment or leadership: None declared. Honorarium: None declared. Competing interests: The funding organization(s) played no role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the report for publication. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bio-Algorithms and Med-Systems de Gruyter

The application of spherical standards for the evaluation of the accuracy of mapping shape in computed tomography

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Abstract

Anatomical structures are characterized by free surfaces, and most are in lobed and pseudo-spherical shapes. The aim of this article is to analyze selected procedures for accuracy assessment of the shape and dimensions of these structures using certified sphere and Ball Bar standards and to propose metrology parameters facilitating comparison of diagnostic devices. The spherical standard of various materials and Ball Bar standards with various distances between spheres centers can be a tool for evaluation of computed tomography metrology applications. Errors in geometry mapping can be identified on the basis of standardized control systems used in coordinate measuring techniques. Keywords: accuracy; computed tomography; mapping; shape; spherical standards. precision, a CT scanner is calibrated using special references and phantoms. For medical CT, this problem requires the use of special references and measurement strategies. At the current stage of imaging no unambiguous normative requirements are available, specifying measurement accuracy for medical CT scanners. Study objective The aim of this study is to analyze selected procedures for accuracy assessment for shape and dimensions reproduction in medical CT using references and to propose metrology parameters facilitating comparison of measurement applications available in various diagnostic devices. Computed tomography and metrology The accuracy of CT scanners used for industrial measurements is specified in VDI/VDE 2630 and associated standards, characterizing parameters in four groups related to length measuring error, scanning error, relationship between shape and dimension, and resolution [1­5]. These parameters characterize tomography systems with a flat or cone X-ray beam. In industrial tomography, the parameter related to the length measuring error is determined with material length standards [6]. The determined parameter value is compared with a maximum permissible error, MPE, for length measurements: MPE =±(A + L/K) µm (1) Introduction The advanced diagnostic and preoperative procedures using computed tomography (CT) require not only imaging but also spatial reproduction of tissue structures with an analysis of their dimensions and shapes. A very important problem in imaging of an object is measurement precision in scans used to select implants or plan a non-standard surgical procedure. To ensure appropriate measurement *Corresponding author: Lukasz Bojko, Faculty of Mechanical Engineering and Robotics, AGH University of Science and Technology, Krakow, Poland, E-mail: lbojko@op.pl. http://orcid.org/0000-0002-6024-458X Andrzej Ryniewicz, Ksenia Ostrowska, Jerzy Sladek and Marcin Krawczyk: Laboratory of Coordinate Metrology, Faculty of Mechanical Engineering, Cracow University of Technology, Krakow, Poland Wojciech Ryniewicz: Faculty of Medicine, Department of Prosthetic Dentistry, Jagiellonian University Medical College, Krakow, Poland. http://orcid.org/0000-0003-3564-2321 where: A ­ error in standard construction [m]; L ­ measured length [mm]; K ­ constant depending on a device type. In medical CT, the use of a length standard in the form of standard plates is limited due to specific conditions of measurement (the X-ray beam penetrates through 232Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT the whole length of the standard); therefore, the use of spherical length standards is a better solution. The VDI/ VDE 2630 standard, in two procedures, A and B, describes in detail a resultant correlation, considering material, dimension, shape, and spacing of measuring points of the standard [5, 7­10]. In medical applications, the measurement accuracy can be established by measuring special phantoms. They consist of bodies of specified geometric parameters and materials of known X-ray attenuation coefficient. The quality of the scan itself depends mainly on an operational condition of the radiation source and auxiliary equipment. Therefore, the use of coordinate metrology methods for assessment of CT reproduction accuracy appears interesting, particularly for spherical standards. Verification of industrial CT scanners With the development of digital techniques for mathematical analyses and CAD software, the geometry of real products can be recorded as 3D information. When structural light scanners were used, only external surfaces were recorded, without an option for deeper penetration. The use of tomography enables three-dimensional recording of an object together with its internal structures. With an option for full 3D description of objects, an issue of their use for dimension evaluation and a problem of measurement accuracy assessment arose. Works on that problem were conducted in numerous research centers, including the National Metrology Institute in Germany, where a standard for CT metrology applications cooperating with coordinate measuring machine (CMM) was drafted [6]. The use of industrial tomography for assessment of geometric precision of tested objects was possible with the development of algorithms for determining edges of relevant objects [11­14]. In this case, an issue of finding edges is more complicated than in medical CT that for different materials grayscale is not expressed in units, and therefore, it is not possible to assign a given grayscale level to a given material [12, 15]. Due to similarities in results obtained with CT scanners and with CMMs, works are currently conducted to adapt ISO 10360 standards to verify length and shape in industrial CT scanners (Figure 1) [6]. Studies on the possibility to use length standards for this purpose were conducted in many centers. Also, other Control tests in coordinate measuring systems Currently, a set of ISO 10360 standards specifies three types of tests for which measuring characteristics are determined. The first is used to determine error variability for length measurements. This test usually consists of measuring, in three replications, five standards of various uniformly distributed lengths, with the last length exceeding the length of the verified axis by 66%. It is repeated in different orientations. It is recommended for selected orientations to be parallel to relevant axes and diagonals of the measurement space. For coordinate measuring machines, this test is usually performed across seven different positions: three parallel to X, Y, and Z axes and four along diagonals of the measurement space. For other tests, a spherical standard is used to determine shape and dimension errors. In the test establishing the shape error, measurements are performed for a specified number of points, usually 25, evenly distributed on the standard hemisphere, and then a substitute feature, a sphere, is determined with the least squares method. Then angles between radius vectors of individual measuring points, starting in the center of the determined sphere, are established. This test aims at determining measurement variability for the points, depending on an acquisition direction. The last test is the dimension test, performed in accordance with the procedure described above, with a diameter of a sphere determined from a specified number of points compared to a correct value provided in a calibration certificate for that standard. Figure 1:Standards used to define the length error [16]. Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT233 standards were developed, in which a concept for reference measurements was based on determining a distance between spheres centers. Image quality control for medical CT systems CT quality control is conducted in accordance with international standards or national guidelines. In Poland, relevant requirements are specified in the Minister of Health Regulation of 24 December 2002 [17]. The provisions concern health care centers working with devices using ionizing radiation. In the Regulation, the Minister imposes an obligation to conduct periodic internal quality control tests verifying performance of devices used for diagnostic imaging. The Regulation provides a list and a frequency for the relevant tests. The control is performed with a phantom, being a standard containing components of materials having Hounsfield unit values corresponding to the gray level of human tissues. Materials for phantoms construction are selected to cover the whole range of values recorded by medical CT scanners. Performance of imaging systems in diagnostic devices is subject to periodic quality control. Verification is performed by scanning of the phantoms (Figures 2 and 3). The phantom consists of the head section (1) including components such as a physical layer (3), a water layer (4), a multi-needle layer (5), a copper duct (6), and a 45° wedge (7). That part of the phantom is made of PVC and filled with water. The physical layer is designated to test the resolution and thickness of a tomographic layer; the water layer is used to measure noise and uniformity, while the contrast scale is verified using the multi-needle layer. The whole assembly forms a cylinder of 200 mm in diameter. The second part of the phantom, the body section (2), consists of a two-component cylinder of 300 mm in diameter, with a Teflon needle and a water needle. There are several types of inspections, including daily or monthly quality tests, and advanced quality control. The daily quality tests are performed to ensure the best quality of the scanned image, and they cover both the head section and the body section. Additionally, monthly inspections performed on the head section of the phantom are obligatory, to verify the contrast scale and artifacts. This inspection is performed on the multi-needle layer. Furthermore, relevant procedures have also been established to solve nonconformities found during daily inspections. They involve more complex algorithms, obligatory for medical specialists and other authorized Figure 2:Phantoms to assess the accuracy of the mapping of anatomical structures [16]. Figure 3:Phantom: (A) general view and (B) diagram [16]. persons. This inspection involves resolution, layer thickness, and layer thickness tolerance tests. Materials and methods The study concerned spherical standards: a certified class 0 ceramic standard sphere, a set of standard spheres of various materials (cemented carbida, steel, corundum ceramics, and zirconium ceramics), and a 1 m-long Ball 234Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT Bar standard from Unimetrik (Figures 4 and 5). The Ball Bar standards are certified, characterized by an accuracy, U=(1.00+0.001 L/1000) m, and used for CMM accuracy verification. Tomographic scans of standard spheres and the Ball Bar standard were conducted with a 64-slice medical CT scanner, Siemens Somaton Cardiac (resolution: 1024×1024×1024 pixels) (Siemens, Munich, Germany). The reconstruction accuracy was assessed by comparison of reconstructed models based on CT imaging versus geometric parameters specified in relevant certificates. The comparison was performed using the best fit method and 3D Reshaper (Technodigit, Genay, France), Poly Works (InnovMetric Software Inc, Quebec, Canada), Geomagic (3D Systems, Rock Hill, SC, USA), and Amira [Visualization Sciences Group, Bordeaux, France and the Zuse Institute Berlin (ZIB), Germany] applications. as surface reconstruction accuracy maps for the standard spheres, determined diameter values and experimental standard deviations for spheres made of various materials, and histograms for errors in the sphere surface shape reconstruction. Furthermore, for the Ball Bar standard, a measurement uncertainty was determined for a distance between spheres centers and a measurement uncertainty for sphere diameters. An example of the surface reconstruction accuracy map for the ceramic sphere surface, CT-scanned and reconstructed in the 3D Reshaper application versus an ideal CAD model, indicates an increase in errors in the sphere surface reconstruction with a decrease in phantom circles in successive scanning planes (Figure 6). The largest errors, of values ­0.25 mm, were located in two areas, described as tomography poles. This distribution of the reconstruction errors in the CT model of the standard sphere indicated a deformation in the form of a surface flattening in the pole areas. A histogram of the reconstruction errors for the ceramic standard sphere diameter in the CT scan is based on 100 measurements. The conducted studies demonstrate that for 90.7% of the results the error in the CT reconstruction of the sphere diameter is within the ±0.06 mm range, and for 98% it is within the ±0.12 mm range. The standard deviation is 0.04 mm, and the mean value for the sphere diameter is 24.97 mm. The analysis results for the reconstruction accuracy for the standard spheres made of four specified materials indicate that errors resulting from a comparison of CTscanned spheres and relevant reference spheres depend on a material of the standard sphere only to a small extent (Table 1). The mean values for errors in diameter measurements in two perpendicular directions, results spread and standard deviations for spheres made of cemented carbida or steel (class 0), corundum ceramics, and zirconium ceramics (class K), indicate the largest reconstruction errors for the sphere of cemented carbida, the largest spread of the results for the steel sphere, and the best reconstruction for the corundum ceramic sphere. CT measurements of a distance between spheres centers and diameters for the Ball Bar standard showed that the accuracy of their reconstruction depends on a position in the measurement space versus a plane determined by transmitters and receivers in the scanner gantry. A spread of results for reconstruction of a distance between sphere centers ranged from 0.02 mm to 0.10 mm, and a spread of results for reconstruction of sphere diameters ranged from 0.01 mm to 0.03 mm. The errors in these measurements cannot be analyzed separately, because the position of the standard spheres was related to the Results and discussion The results of reconstruction assessment for selected geometric parameters of the studied standards were presented Figure 4:Spherical standards of various construction materials (from the left): cemented carbida, steel, corundum ceramics, zirconium ceramics. Figure 5:Ball Bar spherical standard. Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT235 Figure 6:Surface reconstruction accuracy map for the CT-scanned ceramic sphere reconstructed in the 3D Reshaper application versus an ideal CAD model [16]. Table 1:A list of results for diameter measurements accuracy for standard spheres made of selected materials, based on 20 CT measurements for each model, using Geomagic and Quindos applications. Type of material sphere Cemented carbida Steel Corundum ceramics Zirconium ceramics Experimental standard deviation of diameter measurement in axis X, mm 0.12 0.21 0.07 0.08 Experimental standard deviation of diameter measurement in axis Y, mm 0.15 0.18 0.07 0.06 The experimental standard deviation of the mean, mm 0.03 0.04 0.01 0.02 operation of the CT sliding units. It was demonstrated that errors of the linear and angular positioning of the table and errors resulting from fluctuations in its speed and acceleration are significant. The experimental standard deviation and the experimental standard deviation of the mean were assumed to be the best estimates for CT measurement uncertainty. The conducted measurements allowed determining maximum permissible errors, MPE, as MPE =±(W + L/K)A·B·C [ µm] where: W ­ error in standard construction [m]; L ­ measured length [mm]; (2) K ­ constant depending on a device type; A ­ coefficient determining the effect of phantom shape; B ­ coefficient determining the effect of phantom material properties; C ­ coefficient determining the effect of phantom (estimated parameter) position versus the diagnostic plane determined by the gantry unit. The test method used in industrial CT scanners for assessment of metrology parameters using certified geometric standard can be used for medical CT systems. It appears to be particularly useful for assessments of dimension, shape, and reconstruction accuracy for free surfaces characteristic for anatomical structures. 236Ryniewicz et al.: Spherical standards for the accuracy of mapping shape in CT Conclusions Spherical standard of various materials and Ball Bar standards with various distances between spheres centers can be a tool for evaluation of CT metrology applications. Medical CT introduces an error in the geometry reconstruction accuracy resulting from dimension, shape and material, a position of the scanned spherical surface versus the gantry system, and the object position in the measurement space. These errors can be identified with certified phantoms modeled after control systems used in industrial CT. Acknowledgments: The authors acknowledge the John Paul II Hospital in Krakow, Department of Radiology, Jagiellonian University Medical College and the Medical Centre iMed24 S.A. for the opportunity to carry out research on spherical standard and phantoms. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission. Research funding: None declared. Employment or leadership: None declared. Honorarium: None declared. Competing interests: The funding organization(s) played no role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the report for publication.

Journal

Bio-Algorithms and Med-Systemsde Gruyter

Published: Dec 1, 2015

References