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6CCVD Research

Optimal bi-planar gradient coil configurations for diamond nitrogen-vacancy based diffusion-weighted NMR experiments

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2023-08-14
JournalMagnetic Resonance Materials in Physics Biology and Medicine
AuthorsPhilipp Amrein, Fleming Bruckmaier, Feng Jia, Dominik B. Bucher, Maxim Zaitsev
InstitutionsTechnical University of Munich, University of Freiburg
Citations2
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research details the design, optimization, and experimental validation of a compact, three-channel bi-planar gradient coil system specifically engineered for Nitrogen-Vacancy (NV) based Nuclear Magnetic Resonance (NV-NMR) diffusion weighting experiments.

  • Core Achievement: Successfully integrated a high-performance gradient system into a spatially constrained NV-NMR setup, enabling diffusion-weighted studies in microfluidic systems.
  • Design Choice: Bi-planar geometry using double-layered Printed Circuit Boards (PCBs) was selected to accommodate spatial constraints and provide necessary optical access for the NV-NMR components.
  • Key Optimization Finding: Inclined bi-planar orientations (specifically a 35° polar tilt) demonstrated superior efficiency for the transverse gradient channels (Gx and Gy) compared to traditional horizontal or vertical alignments.
  • Performance Metrics: The final PCB system achieved high, balanced sensitivities across all channels: Gx (28.7 mT/m/A), Gy (26.8 mT/m/A), and Gz (26.0 mT/m/A).
  • High Gradient Capability: The design allows for achieving gradient strengths up to 100 mT/m with only 3.8 A of pulsed current, necessary for high b-value diffusion experiments.
  • Field Accuracy: Maximum relative field errors within the 3 mm spherical region of interest (ROI) were maintained below 8% for Gx/Gy and below 6% for Gz.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Main Static Field (B0)0.175TNV-NMR experimental magnet
Target ROI Diameter3mmSpherical region of interest
Coil Orientation (Polar Tilt $\theta$)35°Chosen tilt for horizontal integration
Square Side Length ($l$)5cmFixed geometric parameter
Gz Surface Separation ($d$)3.0cmInnermost coil pair
Gx Measured Sensitivity28.7mT/m/AExperimental validation
Gy Measured Sensitivity26.8mT/m/AExperimental validation
Gz Measured Sensitivity26.0mT/m/AExperimental validation
Gx Inductance3.76”HCalculated value (FastHenry2)
Gz Max Field Error6%Deviation from linear target field
PCB Copper Thickness35”mDouble-layered PCB fabrication
Track Width / Min Gap0.5 / 0.01mmCoil winding specifications
Maximum Achievable Gradient (Pulsed)100mT/mAchieved with 3.8 A current
DC Current Limit (Continuous)1ALimit to avoid heating (< 10°C rise)

Key Methodologies

Section titled “Key Methodologies”

The optimal bi-planar geometry was determined through an extensive automated search and validated experimentally:

  1. Automated Design Generation: Over 500 bi-planar surface configurations were generated and analyzed using the MATLAB-based open-source tool CoilGen.
  2. Geometric Parameter Search: The optimization space spanned square side length ($l$, 10 mm to 200 mm), surface separation ($d$, 10 mm to 200 mm), and surface normal orientation ($\vec{n}$).
  3. Optimization Technique: The stream function approach was used to define and optimize the surface current density ($j$), solved via Tikhonov regularization (set high at $\lambda = 100,000$) to prioritize sensitivity over absolute field accuracy.
  4. Orientation Requirement: The gradient system was designed to align the static B0 field with the NV quantization axis (55° tilt relative to the diamond surface). This was achieved by physically rotating the bi-planar surface by 35° relative to the laboratory z-axis.
  5. Fabrication: The optimized stream function results were discretized into wire turns (isocontour lines) and implemented using two double-layered PCBs per channel (Gx, Gy, Gz) with 35 ”m copper thickness.
  6. Experimental Validation: The fabricated coils were mounted in a custom 3D-printed tilted holder and tested within a clinical 3T MRI scanner (MAGNETOM Prisma). Field maps were acquired using a double gradient echo sequence, and phase differences were converted to field strengths for sensitivity measurement.

Commercial Applications

Section titled “Commercial Applications”

This technology is critical for advancing high-resolution magnetic resonance techniques in constrained environments, particularly those involving quantum sensors.

  • Quantum Sensing and Metrology: Provides the necessary spatial encoding infrastructure for NV-NMR, enabling high-sensitivity detection of magnetic fields and spin states at the micro- to nanoscale.
  • Microstructural Imaging: Supports advanced diffusion-weighted imaging (DWI) studies, offering insights into particle motion and microstructural properties within biological samples (e.g., single cells, tissues).
  • Microfluidic and Lab-on-a-Chip Systems: The compact, bi-planar design is ideal for integration into small-scale experimental setups where optical access and limited space are primary constraints.
  • Miniature MRI Development: The optimization methodology for inclined bi-planar coils can be applied to design highly efficient, compact gradient systems for specialized, high-resolution MRI scanners.
  • High-Density PCB Coil Manufacturing: Demonstrates the feasibility of using double-layered PCBs for complex, high-performance magnetic field generation, minimizing ohmic losses and inductance in small gradient systems.
View Original Abstract

Abstract Introduction Diffusion weighting in optically detected magnetic resonance experiments involving diamond nitrogen-vacancy (NV) centers can provide valuable microstructural information. Bi-planar gradient coils employed for diffusion weighting afford excellent spatial access, essential for integrating the NV-NMR components. Nevertheless, owing to the polar tilt of roughly $$55^{\circ }$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msup> <mml:mn>55</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> of the diamond NV center, the primary magnetic field direction must be taken into account accordingly. Methods To determine the most effective bi-planar gradient coil configurations, we conducted an investigation into the impact of various factors, including the square side length, surface separation, and surface orientation. This was accomplished by generating over 500 bi-planar surface configurations using automated methods. Results We successfully generated and evaluated coil layouts in terms of sensitivity and field accuracy. Interestingly, inclined bi-planar orientations close to the NV-NMR setup’s requirement, showed higher sensitivity for the transverse gradient channels than horizontal or vertical orientations. We fabricated a suitable solution as a three-channel bi-planar double-layered PCB system and experimentally validated the sensitivities at $$28.7 \mathrm mT/m/A$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mn>28.7</mml:mn> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> <mml:mo>/</mml:mo> <mml:mi>m</mml:mi> <mml:mo>/</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> and $$26.8 \mathrm mT/m/A$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mn>26.8</mml:mn> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> <mml:mo>/</mml:mo> <mml:mi>m</mml:mi> <mml:mo>/</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> for the transverse $$G_{x}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:math> and $$G_{y}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> gradients, and $$26 \mathrm mT/m/A$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:mrow> <mml:mn>26</mml:mn> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> <mml:mo>/</mml:mo> <mml:mi>m</mml:mi> <mml:mo>/</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> for the $$G_{z}$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>z</mml:mi> </mml:msub> </mml:math> gradient. Discussion We found that the chosen relative bi-planar tilt of $$35^{\circ }$$ <mml:math xmlns:mml=“http://www.w3.org/1998/Math/MathML”> <mml:msup> <mml:mn>35</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> represents a reasonable compromise in terms of overall performance and allows for easier coil implementation with a straight, horizontal alignment within the overall experimental setup.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2000 - IEEE Press series in biomedical engineering

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