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Filtered water diffusion pore imaging on a 14.1T spectrometer using strong gradients and capillary phantoms in the presence of extraporal fluid

Dominik Ludwig^1,2, Frederik B. Laun³, Karel D. Klika⁴, Mark E. Ladd^1,2,5, Peter Bachert^1,2, and Tristan A. Kuder¹
¹Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany, ²Faculty of Physics and Astronomy, Heidelberg University, Heidelberg, Germany, ³Institute of Radiology, University Hospital Erlangen, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Germany, ⁴Molecular Structure Analysis, German Cancer Research Center (DKFZ), Heidelberg, Germany, ⁵Faculty of Medicine, Heidelberg University, Heidelberg, Germany

Synopsis

Diffusion pore imaging (DPI) can be used to retrieve the pore space function of arbitrary closed pores. In this study, we show that DPI of glass capillaries is possible even under difficult experimental conditions. By separating the long gradient into a CPMG-like gradient echo train, matching the magnetic susceptibility and adding an additional filter diffusion weighting, it was possible to acquire diffraction patterns of glass capillaries that were placed orthogonally to the main magnetic field. Furthermore, the feasibility of doing DPI in the presence extraporal water using our filtered approach was demonstrated.

Introduction

Diffusion pore imaging enables the direct measurement of the shape of arbitrary closed pores that are filled with an NMR-detectable medium [1-3]. The first implementation of diffusion pore imaging on an NMR spectrometer [1] made use of the long–narrow approach [4] in order to retrieve the phase information necessary for reconstruction of the pore space function. To achieve correct measurements for 20 µm capillaries, a CPMG train of 180° pulses was used in [1], where the long gradient with low amplitude was split into many short pulses. Also, the short high-amplitude gradient at the end of the pulse train was spilt into two parts separated by a 180° pulse. More recently, it has been shown that it is also possible to use a spin echo approach with a readout gradient in order to counteract gradient imperfections [3]. In last year’s ISMRM abstract [5] we showed, that it is also possible to acquire pore functions in the presence of extraporal fluid. The aim of this study was to further improve this method by adding an additional diffusion weighting acting as a filter, similarly as in [6] for the faster-diffusing extraporal compartment, which in turn significantly improves the outcome.

Methods

Glass capillaries of 3.5 mm length and inner diameter of 10 µm were stacked horizontally inside a 5 mm NMR tube, i.e. with orthogonal orientation to the main magnetic field. The capillaries were filled with a saturated aqueous NaCl solution – necessary to weaken the susceptibility effects introduced by the glass capillaries – resulting in a free diffusion coefficient $$$D=1.48$$$ µm²/ms for the water inside the capillaries at $$$T=298$$$ K. A schematic representation of the pulse sequence used for the experiments is presented in Figure 1. The long gradient of the long–narrow approach was split into a CPMG-like gradient pulse train separated by inserting 180° pulses. The long gradient was split into 11 segments of $$$\delta_\text{l}=10$$$ ms each, yielding a total time of $$$\delta_\text{L}=110$$$ ms. The narrow gradient had a duration of $$$\delta_\text{S}=2.3$$$ ms with $$$G_{\text{S,max}}=6.3$$$ T/m, resulting in $$$q_{\text{max}}=\gamma \delta_\text{S} G_{\text{S,max}}=3680$$$ mm^-1. q-Values and the sampling of the gradient ramps had to be selected in order to match the available 16-bit raster of the gradient amplifier for all experiments. This resulted in small individual adjustments to for the different q-values in order to counterbalance these limitations. The necessary phase cycling for the different 180° pulses is shown in Table 1. The filter consisted of 8 gradient pulses with a duration of 10 ms each, generating $$$b_{\text{filter}}=2750$$$ s/mm². The signal decay in the intrapore space was simulated with a matrix-based approach as in [7].

Results

Figure 2 shows the measured signal for both an acquisition with and without the proposed filter as the function of the q-value as well as simulation data. Signal for the measurement with filter was normalized to $$$S(q=0)$$$, whereas the signal of the measurement without the filter was normalized to $$$S(q=1102$$$ mm^-1$$$)$$$(minimum of the signal curve) of the measurement with the filter, in order to make them comparable. It is seen that the experimental results, when using the method with the additional filter, agree well with the matrix-based simulation. The corresponding pore space function, calculated via Fourier transform of the signal in Figure 2, is shown in Figure 3, which also yields the expected diameter of 10 µm. For the measurement without the additional filter, it is obvious that the signal is mainly governed by extraporal signal for the two lowest q-values, while its contribution can be nearly completely suppressed with our method. For higher q-values, both measurements are in good agreement as the high q-values of the long-narrow sequence suppress the extraporal signal contributions themselves.

Discussion and Conclusion

The need for strong gradients is the main limiting factor of DPI. Nevertheless, we were able to demonstrate the feasibility of DPI with an ultra-high gradient system using 10 µm capillaries without exploiting the full gradient strength available. Furthermore, we were able to show that diffusion pore imaging is possible in the presence of water outside the pores without the need of extrapolation or fitting of the signal curve. Further, a very high extraporal signal fraction was used here; in biological samples, this problem will be significantly reduced. Compared to the initial approach of signal extrapolation [5], results are highly improved by implementing a bipolar gradient pair, which is split up into segments, in the first part of the CPMG train. By using this gradient pair as a filter for the water inside the pores that is more restricted, it is possible to suppress the surrounding water signal. This procedure enables the direct measurement of smaller q-values instead of extrapolating them. Therefore, this work enables the application to µm-sized objects, which have dimensions as living cells in a realistic environment, i.e. in their natural surroundings.

Acknowledgements

Financial support by the DFG (Grant No. KU 3362/1-1) is gratefully acknowledged.

References

[1]: Hertel, Stefan, Mark Hunter, and Petrik Galvosas. "Magnetic resonance pore imaging, a tool for porous media research." PRE 87.3 (2013): 030802.

[2]: Hertel, Stefan Andreas, et al. "Magnetic-resonance pore imaging of nonsymmetric microscopic pore shapes." PRE 92.1 (2015): 012808.

[3]: Bertleff, Marco, et al. "1D and 2D diffusion pore imaging on a preclinical MR system using adaptive rephasing: Feasibility and pulse sequence comparison." JMR 278 (2017): 39-50.

[4]: Laun, Frederik Bernd, et al. "Determination of the defining boundary in nuclear magnetic resonance diffusion experiments." PRL 107.4 (2011): 048102.

[5]: Ludwig,Dominik, et al. "Water diffusion pore imaging on a 14.1 T spectrometer using glass capillary phantoms in the presence of extraporal fluid." Proc. Intl. Soc. Mag. Reson. Med. 28: 4496, (2020)

[6]: Dhital, Bibek, et al. "PFG Filter for Oscillating Gradient Diffusion Measurements." Proc. Intl. Soc. Mag. Reson. Med. 22 (2014)

[7]: Grebenkov, D.S. "Laplacian eigenfunctions in NMR. I. A numerical tool." Concepts Magn. Reson., 32A: 277-301 (2008)

Figures

Figure 1: Schematic representation of the sequence used in this study. The long gradient of the long-narrow approach was split into a CPMG-like gradient train and an additional diffusion weighting, acting as a filter, was added.

Figure 2: Comparison between the newly proposed method and an acquisition without filter. While the newly proposed method is in good agreement with the simulation, the measurement without the filter strongly deviates at the lowest two q-values.

Figure 3: Reconstructed pore space function, which is calculated via Fourier transform of the signal plotted in Figure 2, using the newly introduced filter for suppression of the extraporal water. The capillary diameter of 10 µm can be inferred well from the measurement.

Table 1: Phase cycling used for the CPMG-like long-narrow approach.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)

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