Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization Setup for Capsule Endoscopy

Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic... DE GRUYTER Current Directions in Biomedical Engineering 2020;6(3): 20203017 Samuel Zeising*, Daisuke Anzai, Angelika Thalmayer, Georg Fischer, and Jens Kirchner Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization Setup for Capsule Endoscopy https://doi.org/10.1515/cdbme-2020-3017 it would be desirable to know the location of interest in ad- vance. Furthermore, the conventional procedure requires anes- Abstract: In this paper, the impact of interference due to the thesia and can be perceived as unpleasant by the patient. Wire- geomagnetic field on a static magnetic localization setup for less capsule endoscopy (WCE) provides a less invasive alter- capsule endoscopy, which is suitable for a wearable applica- native and thus could tackle these problems; capsules for en- tion, was investigated. For this purpose, a study was carried doscopy are up to 32 mm long and have a diameter of about out in which the average abdomen size of 15 subjects was 12 mm. Therefore, they are suitable to be swallowed. Their evaluated. With the determined geometry values, a setup con- main components are a camera, a battery, a printed circuit sisting of three elliptical sensor rings was modeled. Simula- board, and an antenna for transmitting a video stream. For fur- tions were performed, where the magnetic flux density was ther diagnosis and treatment, each video frame must be corre- evaluated at the sensors by using different-sized magnets. The lated with the exact traveled distance of the capsule in the GIT measured values were compared with each other and the geo- to determine the location of interest. [2] magnetic flux density. The results revealed that the measured A promising method to tackle this problem is the static values were for all evaluated magnet sizes of the order of the magnetic localization [2–6]. Therefore, a permanent magnet geomagnetic flux density, which is problematic since the cal- is embedded in the capsule; the resulting static magnetic flux ibration of sensors is no longer valid if the orientation of the density is measured vectorially by magnetic sensors arranged wearable sensor array is changed. However, it is suggested that in arrays outside of the body. a differential measurement is suitable for the proposed system Considering that it takes the capsule about 8 hours to and could reduce static interference caused by the geomag- travel through the GIT, the patient cannot be expected to re- netic field. main in a fixed position during the examination. Therefore, to Keywords: capsule endoscopy, geomagnetic field, magnetic enable the patient to continue daily routine during the appli- localization, wireless capsule endoscopy. cation of WCE, the sensor system must be wearable, compact and robust towards static interference of the geomagnetic field. In [4], a bulky cuboid wearable system with 16 sensors was 1 Introduction designed with 2 additional sensors for canceling interference of the geomagnetic field, whereas in [5], a wearable system The conventional method for the diagnosis and treatment of consisting of 3 rings with 96 sensors was proposed. In the lat- diseases of the gastrointestinal tract (GIT) is endoscopy. Dur- ter, however, it was not stated which size the sensor array had. ing the examination, a flexible tube is guided through the GIT The proposed size of the permanent magnet for localization to the location of interest. Since the GIT is about 9 m long [1], varies widely in the literature, e. g. in [4], a magnet with size of 15×10 mm (diameter × length) was used, whereas in [5], a *Corresponding author: Samuel Zeising, Institute for magnet of size 6×12 mm, respectively. A smaller magnet was Electronics Engineering, Friedrich-Alexander-Universität implemented in [7] of a size 5×6 mm. In [3, 5], it was not Erlangen-Nürnberg (FAU), Cauerstr. 9, Erlangen, Germany, stated which magnet size was used. However, the used mag- E-Mail: samuel.zeising@fau.de net size as well as dimensions of the sensor array matter for Daisuke Anzai, Nagoya Institute of Technology, Graduate School of Engineering, Nagoya, Japan the localization performance, since the magnitude of the mag- Angelika Thalmayer, Institute for Electronics Engineering, netic flux density of a permanent magnet is determined by the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), magnet size and decreases rapidly with distance and the space Erlangen, Germany for a magnet in a capsule is limited due to the built-in compo- Georg Fischer, Institute for Electronics Engineering, nents. If the magnitude of the flux density of the magnet be- Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), comes comparable to that of the geomagnetic field, the latter Erlangen, Germany Jens Kirchner, Institute for Electronics Engineering, Friedrich- significantly disturbs the localization process. With the patient Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Ger- many Open Access. © 2020 Samuel Z eising et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License. 2 Zeising S et al., Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization moving during WCE, this leads to a time-varying interference, not only a static offset. In this paper, the impact of interference of the geomag- netic field on a wearable system for the localization of en- doscopy capsules was investigated in COMSOL. An approach for prevention of interference caused by the static geomagnetic field, which is suitable for the proposed setup, was suggested. Fig. 1: Scenario of the static magnetic localization method. The sensors are arranged in rings. 2 Methods and by minimizing it according to the parameters 𝑎, 𝑏, 𝑐, 𝑚, 𝑛 and 𝑝, the position and orientation of the magnet are estimated. 2.1 Static Magnetic Localization One specific drawback of this method is that it is prone to the interference from static magnet fields. For Central Eu- A well-established method for the localization of capsules for rope, the 𝑥- (north), 𝑦- (west), and 𝑧- (vertical)-components of endoscopy is the static magnetic localization [2–6]. A magnet the geomagnetic flux density 𝐵 are about (20, −1, −45) µT, geo of length 𝑙, radius 𝑘 and magnetization 𝑀 (along the longitu- which leads to an absolute value of 49 µT with a worldwide dinal axis of the magnet) in ampere per meter, is embedded in variation of 25 µT to 65 µT [8]. a capsule which is swallowed by a subject. By arranging mag- netic sensors on the abdomen of a subject, a magnetic flux den- sity 𝐵(𝑥 , 𝑦 , 𝑧 ) is measured at the 𝑖th sensor. The proposed 𝑖 𝑖 𝑖 2.2 Geometry of the Localization Setup magnetic sensor array system was established with three iden- tical, stable and elliptical rings with the diameters 𝑑 and 𝑑 1 2 For the static magnetic localization, sensors have to be ar- (Fig. 1) and four magnetic sensors were mounted on each ring. ranged around the body. Sensors arranged in rings are eligi- The rings had a distance of ℎ/2 from each other. The number ble for that purpose. Therefore, the dimensions of the human and distribution of the sensors are optimization parameters for abdomen were estimated. Thereby, the geometry of the sensor the position and orientation error [6]. However, this work was setup, which can be described with the parameters 𝑑 , 𝑑 and 1 2 focused on the evaluation of the impact of the geomagnetic ℎ (Fig. 1), can be determined. Therefore, a study population field on the proposed system, therefore, optimization was not of 15 subjects (3 females and 12 males) was considered. Care within the scope of this study. was taken to ensure that the body-mass index (BMI) of the test The magnetic flux density of a permanent magnet for the subjects varied widely. For each subject, the BMI, the distance 𝑖th sensor can be approximated as a magnetic dipole if the 𝑑 from the stomach to the back, the large diameter 𝑑 and 2 1 distance from the magnet to the 𝑖th sensor is much larger than the height of the abdomen were measured and the average val- the geometry of the magnet. The magnetic dipole model is then ues concerning the subjects were determined. Based on these described by [7] values, the localization setup was modeled in COMSOL. (︂ )︂ 𝜇 𝜇 𝑀 𝑙𝜋𝑘 3⟨𝐻 , 𝑃 ⟩𝑃 𝐻 r 𝑖 𝑖 0 0 0 0 𝐵(𝑥 , 𝑦 , 𝑧 ) = − , (1) 𝑖 𝑖 𝑖 5 3 4𝜋 𝑅 𝑅 𝑖 𝑖 where 𝑃 indicates the vector from the center of the per- 2.3 Evaluation of the Measured Magnetic manent magnet 𝑃 = (𝑎, 𝑏, 𝑐) to the position of the 𝑖th mag Flux Density sensor 𝑆 = (𝑥 , 𝑦 , 𝑧 ) , where 𝐵(𝑥 , 𝑦 , 𝑧 ) is measured. 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 Moreover, 𝐻 = (𝑚, 𝑛, 𝑝) is the normalized orientation vec- The material of the permanent magnet was set to neodymium- tor of the permanent magnet and 𝑅 = ‖𝑆 − 𝑃 ‖ is iron-boron (NdFeB) with grade N52 since that material yields mag i 𝑖 2 the Euclidean distance between the center of the magnet to the highest remanence-to-volume ratio for permanent mag- the 𝑖th sensor. The permeability in vacuum is expressed by nets [9]. The corresponding magnetization 𝑀 was approx. −7 µ = 4𝜋 × 10 Vs/Am and the relative permeability 𝜇 of the 1140 kA/m and was set along the longitudinal axis of the mag- human body and free space are approx. equal. net. Considering the maximal length and diameter of a cap- For the estimation of the position (𝑎, 𝑏, 𝑐) and orienta- sule are around 32 mm and 12 mm, respectively. Therefore, tion (𝑚, 𝑛, 𝑝) of the magnet, the respective components of the the magnet size has to be adapted. With the information on the measured magnetic flux density 𝐵(𝑥 , 𝑦 , 𝑧 ) at the 𝑖th sensor average dimensions of the human abdomen, 12 sensors were 𝑖 𝑖 𝑖 are subtracted from the corresponding analytical components arranged in three elliptical rings and as a next step, the whole of 𝐵(𝑥 , 𝑦 , 𝑧 ). In this way, an error function is determined localization setup was simulated. Different magnet sizes were 𝑖 𝑖 𝑖 Zeising S et al., Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization considered and at first, the absolute value of 𝐵 was evaluated 6 Earth‘s Magnetic Field concerning the distance from the magnet and compared with k = 5mm l = 2.5mm k = 5mm l = 5mm the absolute value of 𝐵 . Subsequently, the three individ- geo k = 5mm l = 10mm k = 4mm l = 10mm ual components of 𝐵 at the respective sensor positions were k = 5mm l = 20mm evaluated. Therefore, the different magnets were placed in the ⊺ 10 representative position of (50, 50, 50) mm (see Fig. 1 for the coordinate system), which covers realistic distances from all sensors. The orientation of the magnet was set to (1, 0, 0) , 0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 which was also the orientation of 𝑀 . The three components Distance R in cm of 𝐵 were evaluated at the known sensor positions and com- Fig. 2: |𝐵| concerning the distance from the magnet. |𝐵 | is geo pared with the three components of 𝐵 . geo compared with the |𝐵| of different magnet sizes. The 𝑥- and 𝑦-axis are in linear- and logarithmic-scale, respectively. 3 Results the sensors, for different magnet sizes, are shown. For all eval- 3.1 Study of the Abdomen Size Tab. 1: Average values of the three components of the measured 𝐵 for different magnet sizes. The average BMI of the subjects was 26.4±4.3. The result ^ ^ ^ Magnet Size 𝑘× 𝑙 ∅ 𝐵 in µT ∅ 𝐵 in µT ∅ 𝐵 in µT x y z for the average distance from the stomach to the back 𝑑 was 26±4 cm. The average value of the parameter 𝑑 was 5×2.5 mm 3.4 ±2.7 2.4 ±2.5 2.1 ±2.5 5×5 mm 6.8±5.4 4.8 ±5.0 4.2 ±4.9 35±3 cm. For the height of the abdomen ℎ, the average value 5×10 mm 13.5 ±10.9 9.6 ±10.0 8.5 ±9.9 was 17± 2cm. Therefore, three identical elliptical sensor rings 4×10 mm 8.7±7.2 6.1 ±6.4 5.5 ±6.3 with 𝑑 = 40 cm and 𝑑 = 33 cm were proposed (Fig. 1). A 1 2 5×20 mm 27.1 ±21.7 19.2 ±20.1 17.1 ±19.9 tolerance of 7 cm was added to the average value of 𝑑 . Con- sequently, the movement of the abdomen during breathing and the standard deviation of 𝑑 were considered. For 𝑑 , a tol- 2 1 uated cases, the average 𝑥-component was higher than the 𝑦- erance of 5 cm to the average value was added. The average and 𝑧-component, this was expected since the orientation of abdomen height plus its standard deviation was 19 cm. Thus, ⊺ 𝐻 was set to (1,0,0) . The standard deviation was for all three to cover most of the abdomen and, in consequence, the GIT, components of the order of the average value, which indicates the distance ℎ/2 from one ring to another, was set to 10 cm. a huge difference for the values at the individual sensors. This is due to the position of the magnet. Fig. 3 shows the three components of 𝐵, for a magnet with a length and diameter 3.2 Evaluation of the Measured Flux of 10 mm, concerning the respective sensors and the compo- Density nents of 𝐵 . As expected, the sensors 8–12 with a distance of geo The absolute value of 𝐵, produced by a cylindrical permanent magnet, concerning the distance to the magnet, was evaluated. B ^ y The |𝐵| decays approx. as 1/𝑅 with distance. The results for 40 different lengths and radii are depicted in Fig. 2. A distance x,geo y,geo of about 9 cm to 20 cm to the magnet led to a |𝐵|, which had 25 z,geo the magnitude of |𝐵 | in all the evaluated cases. This holds geo true, even if the variation of the geomagnetic field worldwide (25 µT to 65 µT) is considered. The higher the volume of the 1 2 3 4 5 6 7 8 9 10 11 12 magnet, the higher is the |𝐵|, in terms of the distance. Sensor Number Taken into account the geometry of the sensor rings and Fig. 3: 𝐵(𝑥 , 𝑦 , 𝑧 ) for a magnet with length and diameter of ⊺ 𝑖 𝑖 𝑖 the position of the magnet (50, 50, 50) mm and that 12 sen- 10 mm. The horizontal lines are the values of 𝐵 . geo sors were arranged in three elliptical rings as depicted in Fig. 1, there was a distance from the center of the magnet to the respective sensors in the interval of 13.5–29.6 cm. In Table 1, 13.5–19.6 cm from the magnet had the highest measured val- the average absolute values of the three components of 𝐵 at ues. Sensor 4 was approx. 30 cm away from the magnet and Abs. Magnetic Flux Density B in T Magnetic Flux Density |B| in µT 4 Zeising S et al., Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization its components were still in the µT-range. No measured value not stable and the orientation of the additional sensors can vary was higher than the 𝑧-component of 𝐵 . The 𝑦-component of highly, if the patient’s spine is not straight, e. g. during sitting, geo 𝐵 was exceeded for all sensors, whereas the 𝑥-component from those of the sensors used for localization. geo only for sensors 11 and 12. Overall, the individual components In the future, a differential measurement will be con- of the measured 𝐵 were for each sensor and magnet size in the ducted. For this purpose, the sensors will be divided into sen- µT-range and, therefore, had the magnitude of 𝐵 . sor pairs, each consisting of two identically oriented sensors. geo Since the geomagnetic field is equal for such sensor pairs, sub- tracting the measured magnetic flux density of the two sen- sors, from which the positions are known, from each other, the 4 Discussion and Outlook static disturbance will be reduced. Thus, no additional sensors, which are not part of the array, will be needed and the system By evaluating the average abdomen size of the study popu- will be more stable. Another interesting method of prevention lation, a circular sensor array system was designed. Due to of magnetic interference is the signal space separation (SSS) its elliptical shape and its lower amount of sensors compared method which will be investigated in the future [11]. More- with [4, 5], the system is more suitable for a wearable applica- over, number and distribution of the sensors will be optimized. tion. The three components of the magnetic flux density 𝐵 at Author Statement the sensors were evaluated and compared, for different magnet Research funding: The authors state no funding was involved. sizes, with the components of 𝐵 . Assuming that one-third geo Conflict of interest: The authors state no conflict of interest. of the space inside the capsule is used for the magnet, a magnet length of 2.5–10 mm appears reasonable. The radius of a cap- sule is approx. 6 mm, considering its enveloping plastic layer, a radius 𝑘 of 4–5 mm is appropriate. References The magnetic flux density, of a magnet of that size, would [1] Kent G. Human Anatomy. 5th ed. McGraw-Hill College 2000. be detectable at the proposed sensor positions, for state-of-the- [2] Mateen M, Basar R, Ahmed A and Ahmad M. Localization of art magnetic sensors. According to [10], the 𝐵 of the mag- Wireless Capsule Endoscope: A Systematic Review. IEEE net must be at least four times higher than 𝐵 at the sen- geo Sensors Journal, vol. 17, no. 5, pp. 1197-1206, 2017. sors to get an average position error below 10 mm. Since the [3] Wang M, Shi Q, Song S, Hu C, Meng, M. A Novel Relative measured 𝐵(𝑥, 𝑦, 𝑧) and 𝐵 , for all evaluated magnet sizes, geo Position Estimation Method for Capsule Robot Moving in Gastrointestinal Tract. Sensors, vol. 19, 2019. were both in the µT-range, elimination of the inference of 𝐵 geo [4] Shao G, Tang Y, Tang L, Dai Q and Guo Y. A Novel Passive is mandatory, especially if the orientation of the sensors is Magnetic Localization Wearable System for Wireless Cap- changed during the examination. sule Endoscopy. IEEE Sensors Journal, vol. 19, no. 9, pp. In 2019, Shao et al. [4] proposed a method of prevent- 3462-3472, 2019. ing interference caused by the geomagnetic field. For this pur- [5] Hu C et al. Locating Intra-Body Capsule Object by Three- pose, two additional magnetic sensors, mounted on the back Magnet Sensing System. IEEE Sensors Journal, vol. 16, no. 13, pp. 5167-5176, 2016. and chest, were used. It was assumed that a distance of ap- [6] Kanaan M and Cil M. Cramer-Rao Lower Bounds for Mag- prox. 20 cm to the sensor array, would lead to a neglectable netic Localization of a Wireless Capsule Endoscope based value for the measured magnetic flux density at the additional on the Magnetic Dipole Model. International Symposium on sensors compared with the value measured at the sensor ar- Personal, Indoor and Mobile Radio Communications, 2019. ray. Therefore, it was assumed that by subtracting the values [7] Jackson J. Classical Electrodynamics. 1st ed. New York: John Wiley & Sons 1962. of the additional sensors from the values of the sensor array, [8] National Centers for Environmental Information, 2020. the static interference would be eliminated. However, the re- Accessed on: March 04, 2020. [Online]. Available: sults of this paper show that even if the distance from the https://www.ngdc.noaa.gov/ magnet reached about 30 cm, there was still a measured flux [9] Mukhopadhyay S C and Gupta G S. Smart Sensors and density, which was in the µT-range and, therefore, had an im- Sensing Technology. 1st ed. Berlin Heidelberg: Springer- pact on the localization error. Thus, it is concluded that Shao’s Verlag 2008. [10] Shao G and Guo Y, "An Optimal Design for Passive Magnetic approach is dependent on the position of the magnet because Localization System Based on SNR Evaluation," in IEEE as the magnet travels in the lower region of the GIT and, thus, Transactions on Instrumentation and Measurement, vol. 69, further away from the additional sensors, the error by applying no. 7, pp. 4324-4333, 2020. that method should be decreasing. Furthermore, the additional [11] Taulu S, Simola J and Kajola M, "Applications of the signal sensors were not part of the sensor array; thus, the relative po- space separation method," in IEEE Transactions on Signal Processing, vol. 53, no. 9, pp. 3359-3372, 2005. sition regarding the coordinate system of the sensor array was http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Current Directions in Biomedical Engineering de Gruyter

Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization Setup for Capsule Endoscopy

Download PDF
4 pages

Loading next page...
 
/lp/de-gruyter/evaluation-of-the-impact-of-static-interference-on-an-empirical-data-WMi4RTIo4o

References (9)

Publisher
de Gruyter
Copyright
© 2020 by Walter de Gruyter Berlin/Boston
eISSN
2364-5504
DOI
10.1515/cdbme-2020-3017
Publisher site
See Article on Publisher Site

Abstract

DE GRUYTER Current Directions in Biomedical Engineering 2020;6(3): 20203017 Samuel Zeising*, Daisuke Anzai, Angelika Thalmayer, Georg Fischer, and Jens Kirchner Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization Setup for Capsule Endoscopy https://doi.org/10.1515/cdbme-2020-3017 it would be desirable to know the location of interest in ad- vance. Furthermore, the conventional procedure requires anes- Abstract: In this paper, the impact of interference due to the thesia and can be perceived as unpleasant by the patient. Wire- geomagnetic field on a static magnetic localization setup for less capsule endoscopy (WCE) provides a less invasive alter- capsule endoscopy, which is suitable for a wearable applica- native and thus could tackle these problems; capsules for en- tion, was investigated. For this purpose, a study was carried doscopy are up to 32 mm long and have a diameter of about out in which the average abdomen size of 15 subjects was 12 mm. Therefore, they are suitable to be swallowed. Their evaluated. With the determined geometry values, a setup con- main components are a camera, a battery, a printed circuit sisting of three elliptical sensor rings was modeled. Simula- board, and an antenna for transmitting a video stream. For fur- tions were performed, where the magnetic flux density was ther diagnosis and treatment, each video frame must be corre- evaluated at the sensors by using different-sized magnets. The lated with the exact traveled distance of the capsule in the GIT measured values were compared with each other and the geo- to determine the location of interest. [2] magnetic flux density. The results revealed that the measured A promising method to tackle this problem is the static values were for all evaluated magnet sizes of the order of the magnetic localization [2–6]. Therefore, a permanent magnet geomagnetic flux density, which is problematic since the cal- is embedded in the capsule; the resulting static magnetic flux ibration of sensors is no longer valid if the orientation of the density is measured vectorially by magnetic sensors arranged wearable sensor array is changed. However, it is suggested that in arrays outside of the body. a differential measurement is suitable for the proposed system Considering that it takes the capsule about 8 hours to and could reduce static interference caused by the geomag- travel through the GIT, the patient cannot be expected to re- netic field. main in a fixed position during the examination. Therefore, to Keywords: capsule endoscopy, geomagnetic field, magnetic enable the patient to continue daily routine during the appli- localization, wireless capsule endoscopy. cation of WCE, the sensor system must be wearable, compact and robust towards static interference of the geomagnetic field. In [4], a bulky cuboid wearable system with 16 sensors was 1 Introduction designed with 2 additional sensors for canceling interference of the geomagnetic field, whereas in [5], a wearable system The conventional method for the diagnosis and treatment of consisting of 3 rings with 96 sensors was proposed. In the lat- diseases of the gastrointestinal tract (GIT) is endoscopy. Dur- ter, however, it was not stated which size the sensor array had. ing the examination, a flexible tube is guided through the GIT The proposed size of the permanent magnet for localization to the location of interest. Since the GIT is about 9 m long [1], varies widely in the literature, e. g. in [4], a magnet with size of 15×10 mm (diameter × length) was used, whereas in [5], a *Corresponding author: Samuel Zeising, Institute for magnet of size 6×12 mm, respectively. A smaller magnet was Electronics Engineering, Friedrich-Alexander-Universität implemented in [7] of a size 5×6 mm. In [3, 5], it was not Erlangen-Nürnberg (FAU), Cauerstr. 9, Erlangen, Germany, stated which magnet size was used. However, the used mag- E-Mail: samuel.zeising@fau.de net size as well as dimensions of the sensor array matter for Daisuke Anzai, Nagoya Institute of Technology, Graduate School of Engineering, Nagoya, Japan the localization performance, since the magnitude of the mag- Angelika Thalmayer, Institute for Electronics Engineering, netic flux density of a permanent magnet is determined by the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), magnet size and decreases rapidly with distance and the space Erlangen, Germany for a magnet in a capsule is limited due to the built-in compo- Georg Fischer, Institute for Electronics Engineering, nents. If the magnitude of the flux density of the magnet be- Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), comes comparable to that of the geomagnetic field, the latter Erlangen, Germany Jens Kirchner, Institute for Electronics Engineering, Friedrich- significantly disturbs the localization process. With the patient Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Ger- many Open Access. © 2020 Samuel Z eising et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License. 2 Zeising S et al., Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization moving during WCE, this leads to a time-varying interference, not only a static offset. In this paper, the impact of interference of the geomag- netic field on a wearable system for the localization of en- doscopy capsules was investigated in COMSOL. An approach for prevention of interference caused by the static geomagnetic field, which is suitable for the proposed setup, was suggested. Fig. 1: Scenario of the static magnetic localization method. The sensors are arranged in rings. 2 Methods and by minimizing it according to the parameters 𝑎, 𝑏, 𝑐, 𝑚, 𝑛 and 𝑝, the position and orientation of the magnet are estimated. 2.1 Static Magnetic Localization One specific drawback of this method is that it is prone to the interference from static magnet fields. For Central Eu- A well-established method for the localization of capsules for rope, the 𝑥- (north), 𝑦- (west), and 𝑧- (vertical)-components of endoscopy is the static magnetic localization [2–6]. A magnet the geomagnetic flux density 𝐵 are about (20, −1, −45) µT, geo of length 𝑙, radius 𝑘 and magnetization 𝑀 (along the longitu- which leads to an absolute value of 49 µT with a worldwide dinal axis of the magnet) in ampere per meter, is embedded in variation of 25 µT to 65 µT [8]. a capsule which is swallowed by a subject. By arranging mag- netic sensors on the abdomen of a subject, a magnetic flux den- sity 𝐵(𝑥 , 𝑦 , 𝑧 ) is measured at the 𝑖th sensor. The proposed 𝑖 𝑖 𝑖 2.2 Geometry of the Localization Setup magnetic sensor array system was established with three iden- tical, stable and elliptical rings with the diameters 𝑑 and 𝑑 1 2 For the static magnetic localization, sensors have to be ar- (Fig. 1) and four magnetic sensors were mounted on each ring. ranged around the body. Sensors arranged in rings are eligi- The rings had a distance of ℎ/2 from each other. The number ble for that purpose. Therefore, the dimensions of the human and distribution of the sensors are optimization parameters for abdomen were estimated. Thereby, the geometry of the sensor the position and orientation error [6]. However, this work was setup, which can be described with the parameters 𝑑 , 𝑑 and 1 2 focused on the evaluation of the impact of the geomagnetic ℎ (Fig. 1), can be determined. Therefore, a study population field on the proposed system, therefore, optimization was not of 15 subjects (3 females and 12 males) was considered. Care within the scope of this study. was taken to ensure that the body-mass index (BMI) of the test The magnetic flux density of a permanent magnet for the subjects varied widely. For each subject, the BMI, the distance 𝑖th sensor can be approximated as a magnetic dipole if the 𝑑 from the stomach to the back, the large diameter 𝑑 and 2 1 distance from the magnet to the 𝑖th sensor is much larger than the height of the abdomen were measured and the average val- the geometry of the magnet. The magnetic dipole model is then ues concerning the subjects were determined. Based on these described by [7] values, the localization setup was modeled in COMSOL. (︂ )︂ 𝜇 𝜇 𝑀 𝑙𝜋𝑘 3⟨𝐻 , 𝑃 ⟩𝑃 𝐻 r 𝑖 𝑖 0 0 0 0 𝐵(𝑥 , 𝑦 , 𝑧 ) = − , (1) 𝑖 𝑖 𝑖 5 3 4𝜋 𝑅 𝑅 𝑖 𝑖 where 𝑃 indicates the vector from the center of the per- 2.3 Evaluation of the Measured Magnetic manent magnet 𝑃 = (𝑎, 𝑏, 𝑐) to the position of the 𝑖th mag Flux Density sensor 𝑆 = (𝑥 , 𝑦 , 𝑧 ) , where 𝐵(𝑥 , 𝑦 , 𝑧 ) is measured. 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 Moreover, 𝐻 = (𝑚, 𝑛, 𝑝) is the normalized orientation vec- The material of the permanent magnet was set to neodymium- tor of the permanent magnet and 𝑅 = ‖𝑆 − 𝑃 ‖ is iron-boron (NdFeB) with grade N52 since that material yields mag i 𝑖 2 the Euclidean distance between the center of the magnet to the highest remanence-to-volume ratio for permanent mag- the 𝑖th sensor. The permeability in vacuum is expressed by nets [9]. The corresponding magnetization 𝑀 was approx. −7 µ = 4𝜋 × 10 Vs/Am and the relative permeability 𝜇 of the 1140 kA/m and was set along the longitudinal axis of the mag- human body and free space are approx. equal. net. Considering the maximal length and diameter of a cap- For the estimation of the position (𝑎, 𝑏, 𝑐) and orienta- sule are around 32 mm and 12 mm, respectively. Therefore, tion (𝑚, 𝑛, 𝑝) of the magnet, the respective components of the the magnet size has to be adapted. With the information on the measured magnetic flux density 𝐵(𝑥 , 𝑦 , 𝑧 ) at the 𝑖th sensor average dimensions of the human abdomen, 12 sensors were 𝑖 𝑖 𝑖 are subtracted from the corresponding analytical components arranged in three elliptical rings and as a next step, the whole of 𝐵(𝑥 , 𝑦 , 𝑧 ). In this way, an error function is determined localization setup was simulated. Different magnet sizes were 𝑖 𝑖 𝑖 Zeising S et al., Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization considered and at first, the absolute value of 𝐵 was evaluated 6 Earth‘s Magnetic Field concerning the distance from the magnet and compared with k = 5mm l = 2.5mm k = 5mm l = 5mm the absolute value of 𝐵 . Subsequently, the three individ- geo k = 5mm l = 10mm k = 4mm l = 10mm ual components of 𝐵 at the respective sensor positions were k = 5mm l = 20mm evaluated. Therefore, the different magnets were placed in the ⊺ 10 representative position of (50, 50, 50) mm (see Fig. 1 for the coordinate system), which covers realistic distances from all sensors. The orientation of the magnet was set to (1, 0, 0) , 0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 which was also the orientation of 𝑀 . The three components Distance R in cm of 𝐵 were evaluated at the known sensor positions and com- Fig. 2: |𝐵| concerning the distance from the magnet. |𝐵 | is geo pared with the three components of 𝐵 . geo compared with the |𝐵| of different magnet sizes. The 𝑥- and 𝑦-axis are in linear- and logarithmic-scale, respectively. 3 Results the sensors, for different magnet sizes, are shown. For all eval- 3.1 Study of the Abdomen Size Tab. 1: Average values of the three components of the measured 𝐵 for different magnet sizes. The average BMI of the subjects was 26.4±4.3. The result ^ ^ ^ Magnet Size 𝑘× 𝑙 ∅ 𝐵 in µT ∅ 𝐵 in µT ∅ 𝐵 in µT x y z for the average distance from the stomach to the back 𝑑 was 26±4 cm. The average value of the parameter 𝑑 was 5×2.5 mm 3.4 ±2.7 2.4 ±2.5 2.1 ±2.5 5×5 mm 6.8±5.4 4.8 ±5.0 4.2 ±4.9 35±3 cm. For the height of the abdomen ℎ, the average value 5×10 mm 13.5 ±10.9 9.6 ±10.0 8.5 ±9.9 was 17± 2cm. Therefore, three identical elliptical sensor rings 4×10 mm 8.7±7.2 6.1 ±6.4 5.5 ±6.3 with 𝑑 = 40 cm and 𝑑 = 33 cm were proposed (Fig. 1). A 1 2 5×20 mm 27.1 ±21.7 19.2 ±20.1 17.1 ±19.9 tolerance of 7 cm was added to the average value of 𝑑 . Con- sequently, the movement of the abdomen during breathing and the standard deviation of 𝑑 were considered. For 𝑑 , a tol- 2 1 uated cases, the average 𝑥-component was higher than the 𝑦- erance of 5 cm to the average value was added. The average and 𝑧-component, this was expected since the orientation of abdomen height plus its standard deviation was 19 cm. Thus, ⊺ 𝐻 was set to (1,0,0) . The standard deviation was for all three to cover most of the abdomen and, in consequence, the GIT, components of the order of the average value, which indicates the distance ℎ/2 from one ring to another, was set to 10 cm. a huge difference for the values at the individual sensors. This is due to the position of the magnet. Fig. 3 shows the three components of 𝐵, for a magnet with a length and diameter 3.2 Evaluation of the Measured Flux of 10 mm, concerning the respective sensors and the compo- Density nents of 𝐵 . As expected, the sensors 8–12 with a distance of geo The absolute value of 𝐵, produced by a cylindrical permanent magnet, concerning the distance to the magnet, was evaluated. B ^ y The |𝐵| decays approx. as 1/𝑅 with distance. The results for 40 different lengths and radii are depicted in Fig. 2. A distance x,geo y,geo of about 9 cm to 20 cm to the magnet led to a |𝐵|, which had 25 z,geo the magnitude of |𝐵 | in all the evaluated cases. This holds geo true, even if the variation of the geomagnetic field worldwide (25 µT to 65 µT) is considered. The higher the volume of the 1 2 3 4 5 6 7 8 9 10 11 12 magnet, the higher is the |𝐵|, in terms of the distance. Sensor Number Taken into account the geometry of the sensor rings and Fig. 3: 𝐵(𝑥 , 𝑦 , 𝑧 ) for a magnet with length and diameter of ⊺ 𝑖 𝑖 𝑖 the position of the magnet (50, 50, 50) mm and that 12 sen- 10 mm. The horizontal lines are the values of 𝐵 . geo sors were arranged in three elliptical rings as depicted in Fig. 1, there was a distance from the center of the magnet to the respective sensors in the interval of 13.5–29.6 cm. In Table 1, 13.5–19.6 cm from the magnet had the highest measured val- the average absolute values of the three components of 𝐵 at ues. Sensor 4 was approx. 30 cm away from the magnet and Abs. Magnetic Flux Density B in T Magnetic Flux Density |B| in µT 4 Zeising S et al., Evaluation of the Impact of Static Interference on an Empirical Data Based Static Magnetic Localization its components were still in the µT-range. No measured value not stable and the orientation of the additional sensors can vary was higher than the 𝑧-component of 𝐵 . The 𝑦-component of highly, if the patient’s spine is not straight, e. g. during sitting, geo 𝐵 was exceeded for all sensors, whereas the 𝑥-component from those of the sensors used for localization. geo only for sensors 11 and 12. Overall, the individual components In the future, a differential measurement will be con- of the measured 𝐵 were for each sensor and magnet size in the ducted. For this purpose, the sensors will be divided into sen- µT-range and, therefore, had the magnitude of 𝐵 . sor pairs, each consisting of two identically oriented sensors. geo Since the geomagnetic field is equal for such sensor pairs, sub- tracting the measured magnetic flux density of the two sen- sors, from which the positions are known, from each other, the 4 Discussion and Outlook static disturbance will be reduced. Thus, no additional sensors, which are not part of the array, will be needed and the system By evaluating the average abdomen size of the study popu- will be more stable. Another interesting method of prevention lation, a circular sensor array system was designed. Due to of magnetic interference is the signal space separation (SSS) its elliptical shape and its lower amount of sensors compared method which will be investigated in the future [11]. More- with [4, 5], the system is more suitable for a wearable applica- over, number and distribution of the sensors will be optimized. tion. The three components of the magnetic flux density 𝐵 at Author Statement the sensors were evaluated and compared, for different magnet Research funding: The authors state no funding was involved. sizes, with the components of 𝐵 . Assuming that one-third geo Conflict of interest: The authors state no conflict of interest. of the space inside the capsule is used for the magnet, a magnet length of 2.5–10 mm appears reasonable. The radius of a cap- sule is approx. 6 mm, considering its enveloping plastic layer, a radius 𝑘 of 4–5 mm is appropriate. References The magnetic flux density, of a magnet of that size, would [1] Kent G. Human Anatomy. 5th ed. McGraw-Hill College 2000. be detectable at the proposed sensor positions, for state-of-the- [2] Mateen M, Basar R, Ahmed A and Ahmad M. Localization of art magnetic sensors. According to [10], the 𝐵 of the mag- Wireless Capsule Endoscope: A Systematic Review. IEEE net must be at least four times higher than 𝐵 at the sen- geo Sensors Journal, vol. 17, no. 5, pp. 1197-1206, 2017. sors to get an average position error below 10 mm. Since the [3] Wang M, Shi Q, Song S, Hu C, Meng, M. A Novel Relative measured 𝐵(𝑥, 𝑦, 𝑧) and 𝐵 , for all evaluated magnet sizes, geo Position Estimation Method for Capsule Robot Moving in Gastrointestinal Tract. Sensors, vol. 19, 2019. were both in the µT-range, elimination of the inference of 𝐵 geo [4] Shao G, Tang Y, Tang L, Dai Q and Guo Y. A Novel Passive is mandatory, especially if the orientation of the sensors is Magnetic Localization Wearable System for Wireless Cap- changed during the examination. sule Endoscopy. IEEE Sensors Journal, vol. 19, no. 9, pp. In 2019, Shao et al. [4] proposed a method of prevent- 3462-3472, 2019. ing interference caused by the geomagnetic field. For this pur- [5] Hu C et al. Locating Intra-Body Capsule Object by Three- pose, two additional magnetic sensors, mounted on the back Magnet Sensing System. IEEE Sensors Journal, vol. 16, no. 13, pp. 5167-5176, 2016. and chest, were used. It was assumed that a distance of ap- [6] Kanaan M and Cil M. Cramer-Rao Lower Bounds for Mag- prox. 20 cm to the sensor array, would lead to a neglectable netic Localization of a Wireless Capsule Endoscope based value for the measured magnetic flux density at the additional on the Magnetic Dipole Model. International Symposium on sensors compared with the value measured at the sensor ar- Personal, Indoor and Mobile Radio Communications, 2019. ray. Therefore, it was assumed that by subtracting the values [7] Jackson J. Classical Electrodynamics. 1st ed. New York: John Wiley & Sons 1962. of the additional sensors from the values of the sensor array, [8] National Centers for Environmental Information, 2020. the static interference would be eliminated. However, the re- Accessed on: March 04, 2020. [Online]. Available: sults of this paper show that even if the distance from the https://www.ngdc.noaa.gov/ magnet reached about 30 cm, there was still a measured flux [9] Mukhopadhyay S C and Gupta G S. Smart Sensors and density, which was in the µT-range and, therefore, had an im- Sensing Technology. 1st ed. Berlin Heidelberg: Springer- pact on the localization error. Thus, it is concluded that Shao’s Verlag 2008. [10] Shao G and Guo Y, "An Optimal Design for Passive Magnetic approach is dependent on the position of the magnet because Localization System Based on SNR Evaluation," in IEEE as the magnet travels in the lower region of the GIT and, thus, Transactions on Instrumentation and Measurement, vol. 69, further away from the additional sensors, the error by applying no. 7, pp. 4324-4333, 2020. that method should be decreasing. Furthermore, the additional [11] Taulu S, Simola J and Kajola M, "Applications of the signal sensors were not part of the sensor array; thus, the relative po- space separation method," in IEEE Transactions on Signal Processing, vol. 53, no. 9, pp. 3359-3372, 2005. sition regarding the coordinate system of the sensor array was

Journal

Current Directions in Biomedical Engineering – de Gruyter

Published: Sep 1, 2020

Keywords: capsule endoscopy; geomagnetic field; magnetic localization; wireless capsule endoscopy

There are no references for this article.