Using symmetrized temporal gradient profiles for water diffusion pore imaging on a 14.1 T spectrometer
Dominik Ludwig1,2, Frederik Bernd Laun3, Karel D. Klika4, Peter Bachert1, and Tristan Anselm Kuder1

1Department of Medical 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 (FAU), Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany, 4Molecular Structure Analysis, German Cancer Research Center (DKFZ), Heidelberg, Germany


Diffusion pore imaging can be used to retrieve the pore-space function of an arbitrary closed pore. While a few publications involving pore imaging using the long–narrow gradient approach exist [1–3], all of them involve the use of sophisticated acquisition schemes like CPMG or involve an additional readout gradient. In this study, we were able to show that it is indeed possible to acquire the pore space function of capillaries with a diameter of 15 µm using a simple modification of the long–narrow gradient scheme on a 14.1 T NMR spectrometer.


Diffusion pore imaging enables the direct measurement of the shape of arbitrary closed pores which 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. In order 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 pules. 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 was shown that it is also possible to use a spin-echo approach with a readout gradient in order to counteract gradient imperfections. The aim of this work was to show the possibility of acquiring diffusion pore images of glass capillaries with a diameter of 15 µm by a simple modification of the long–narrow spin-echo approach using only one 180° pulse without any further adaptations.


Figure 1 shows the acquisition sequence used for the experiments. A 180° refocusing pulse was inserted to realize a spin echo sequence to counteract $$$T_2^*$$$ relaxation. The gradient pulses were arranged antisymmetrically around the refocusing pulse; both the long and the short gradient pulse were split into two parts. The q-value is thus given by (see Fig. 1)$$q=\gamma\delta_LG_L=-\gamma\delta_SG_S.$$ All measurements were carried out on a Bruker 14.1 T Avance 600 NMR spectrometer using a 5-mm TBI-probe with xyz-axis gradients with nominal gradient amplitudes of 0.5 T/m in both the x and y directions. The gradient amplitudes and durations used for the measurements presented here are shown in Table 1. The gradient amplitude of the narrow gradient was always set to $$$G_S=500\,$$$mT/m and the amplitude of the long gradient was adjusted accordingly. The signal was acquired for 11 q-values with 12 averages and a repetition time of 10 s. To demonstrate the effect on the measured pore space function, the duration of the short gradient pulses was varied. The gradient strength was validated using a free diffusion experiment on a doped water sample employing the known diffusion coefficient for a given temperature. Trapezoidal gradients were used and all ramp times $$$\epsilon$$$ were set to 0.3 ms. Capillaries with an inner diameter of 15 µm and an outer diameter of 360 µm were cut into 5 cm long pieces and submerged in distilled water for several days. For faster degassing, the submerged capillaries were boiled and placed in a vacuum chamber. Capillaries were then dried on the outside and vertically stacked in a 5-mm NMR tube (Figure 2). The water signal of the phantom was manually shimmed to a FWHM of 6 Hz. All measurements were carried out at 298 K; therefore a free water diffusion coefficient of D = 2.3 µm2/ms was assumed for the simulations. Simulations were conducted using a matrix approach to solve the Bloch-Torrey equations [5,6].


The measured signals, as functions of the q-values, and simulations are shown in Figure 3 A–C for three durations of the short gradient pulse. In all cases, the measurements are in good agreement with the simulations, with only slight deviations for some of the low q-values. The reconstructed pore-space functions in Figure 4 A–C represent the projection of the cylindrical shape onto the gradient direction. The pore-space functions match well to the expected function of a cylinder with a diameter of 15 µm for these gradient settings. However, due to the relatively long duration ($$$\delta_S$$$) of narrow gradients pulses, a shrinkage of the reconstructed pore space function is induced due to the edge enhancement effect, being most severe for the longest duration measurement #3 (Figure 4C).

Discussion and Conclusion

The results prove the feasibility of diffusion pore imaging using a spin-echo version of the long–narrow approach with antisymmetric arrangement of the gradient pulses without further modifications. This approach may reduce the influence of confounding effects such as concomitant fields. The measurements were limited by the available gradient strength of 0.5 T/m, which is insufficient to fully resolve pores with a diameter of 15 µm resulting in considerable edge enhancement.


Financial support by the DFG (Grant No. KU 3362/1-1 and LA 2804/6-1) is gratefully acknowledged.


[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]: Laun, Frederik Bernd, et al. "NMR-based diffusion pore imaging." PRE 86.2 (2012): 021906.

[6]: Grebenkov, Denis S. "Laplacian eigenfunctions in NMR. I. A numerical tool." Concepts in Magnetic Resonance Part A: An Educational Journal 32.4 (2008): 277-301.


Figure 1: Schematic representation of the pulse sequence. It is a simple modification of the long–short gradient approach with the short gradient split in the middle by a 180° pulse. Due to the 180° pulse, the gradients following the pulse have to be inverted. This implementation was chosen since it is completely anti-symmetrical and may thus be more reliable.

Figure 2: Sketch of the capillary phantom used in this study (not in scale). The 5-cm long capillaries filled with distilled water with an inner diameter of 15 µm and outer diameter of 360 µm were placed vertically in an NMR tube of 5 mm outer diameter.

Figure 3: Signal as a function of the q-value for measurement #1-3. Simulation and experimental results are in good agreement with slight deviations for the first non-zero q-value. This effect is most dominant for measurement #3.

Figure 4: Reconstructed pore-space functions for measurements #1-3. Measurement results correspond well to simulations but severe edge enhancement is present due to the long duration of the narrow gradient, especially for measurement #3 shown in C. Nevertheless, the results demonstrate the feasibility of the long–narrow approach for diffusion pore imaging.

Table 1: Gradient settings used in this study.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)