Distortion-Free Magnetic Tracking of Metal Instruments in Image-Guided Interventions
<p>An infinitely long cylindrical rod with inner radius <math display="inline"><semantics> <msub> <mi>r</mi> <mi>i</mi> </msub> </semantics></math> and outer radius <math display="inline"><semantics> <msub> <mi>r</mi> <mi>o</mi> </msub> </semantics></math>. The axis of the rod is oriented along the <span class="html-italic">z</span>-direction. The radial and azimuthal coordinates are denoted by <span class="html-italic">r</span> and <math display="inline"><semantics> <mi>θ</mi> </semantics></math>.</p> "> Figure 2
<p>The normalised magnitude of the magnetic flux density for two different excitation frequencies for a conductivity of <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>1.35</mn> </mrow> </semantics></math> MS/m. In subfigures (<b>a</b>) and (<b>b</b>), we have <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 2 mm and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>o</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 4 mm, while in subfigures (<b>c</b>) and (<b>d</b>), we have <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 6 mm and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>o</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 8 mm.</p> "> Figure 3
<p>The magnitude of the normalised magnetic flux density as a function of (<b>a</b>) conductivity and (<b>b</b>) frequency for a number of different rod geometries.</p> "> Figure 4
<p>The phase difference between the magnetic flux density inside and outside the rod as a function of frequency for a number of different rod geometries.</p> "> Figure 5
<p>A schematic of the circuit used to drive the Helmholtz coils.</p> "> Figure 6
<p>The experimental setup used to measure the shielding effect and phase induced by stainless steel rods.</p> "> Figure 7
<p>The experimental setup with (<b>a</b>) the robotic positioning system, (<b>b</b>) the optical tracking system and (<b>c</b>) the optical tool with IR markers and the stainless steel rod and sensor rigidly attached.</p> "> Figure 8
<p>Experimental measurements of (<b>a</b>) the shielding effect and (<b>b</b>) induced phase for the two stainless steel rods. Analytical results given by (<a href="#FD32-sensors-24-05364" class="html-disp-formula">32</a>) are denoted by solid curves.</p> "> Figure 9
<p>The cumulative distribution of the tracking errors with a sensor fixed within (<b>a</b>) rod 1 and (<b>b</b>) rod 2.</p> ">
Abstract
:1. Introduction
2. Mathematical Formalism
2.1. Conductive Rod in a Transverse Magnetic Field
2.2. Conductive Rod in a Longitudinal Magnetic Field
2.3. Magnetic Field Solutions in the Innermost Region
3. Methods
3.1. Helmholtz Coil Driver Design
3.2. Influence of Transmitter Frequency
3.3. Impact on Electromagnetic Tracking
4. Results and Discussion
4.1. The Influence of Transmitter Frequency
4.2. Impact on Electromagnetic Tracking
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
EMT | Electromagnetic tracking |
DAC | Digital-to-analog converter |
ADC | Analog-to-digital converter |
IA | Instrumentation amplifier |
FFT | Fast Fourier transform |
IR | Infrared |
RMSE | Root-mean-square error |
ME | Mean error |
STD | Standard deviation |
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Rod | Material | (mm) | (mm) | (MS/m) |
---|---|---|---|---|
1 | 316 L Stainless Steel | 4 | ||
2 | 316 L Stainless Steel | 5 | 6 |
RMSE (mm) | ME (mm) | STD (mm) | |||||||
---|---|---|---|---|---|---|---|---|---|
Frequency (kHz) | No Rod | Rod 1 | Rod 2 | No Rod | Rod 1 | Rod 2 | No Rod | Rod 1 | Rod 2 |
1 | 0.89 | 1.09 | 1.09 | 0.71 | 0.89 | 0.92 | 0.53 | 0.63 | 0.59 |
5 | 0.98 | 1.16 | 1.55 | 0.79 | 0.94 | 1.29 | 0.58 | 0.68 | 0.85 |
10 | 1.26 | 1.69 | 4.55 | 1.01 | 1.38 | 3.97 | 0.75 | 0.98 | 2.21 |
15 | 1.38 | 2.75 | 10.01 | 1.13 | 2.30 | 8.83 | 0.80 | 1.52 | 4.72 |
20 | 2.33 | 12.74 | 25.53 | 1.89 | 11.08 | 22.17 | 1.37 | 6.30 | 12.68 |
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Higgins, E.; Crowley, D.; van den Bosch, C.; Cantillon-Murphy, P. Distortion-Free Magnetic Tracking of Metal Instruments in Image-Guided Interventions. Sensors 2024, 24, 5364. https://doi.org/10.3390/s24165364
Higgins E, Crowley D, van den Bosch C, Cantillon-Murphy P. Distortion-Free Magnetic Tracking of Metal Instruments in Image-Guided Interventions. Sensors. 2024; 24(16):5364. https://doi.org/10.3390/s24165364
Chicago/Turabian StyleHiggins, Eoin, Daragh Crowley, Christian van den Bosch, and Pádraig Cantillon-Murphy. 2024. "Distortion-Free Magnetic Tracking of Metal Instruments in Image-Guided Interventions" Sensors 24, no. 16: 5364. https://doi.org/10.3390/s24165364