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Probing restriction and exchange in the human brain using free waveforms on a high-performance gradient system

Arthur Chakwizira¹, Ante Zhu², Thomas Foo², Carl-Fredrik Westin³, Filip Szczepankiewicz¹, and Markus Nilsson⁴
¹Medical Radiation Physics, Lund, Lund University, Lund, Sweden, ²GE Research, Niskayuna, New York, NY, United States, ³Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States, ⁴Clinical Sciences Lund, Lund University, Lund, Sweden

Synopsis

Keywords: Diffusion/other diffusion imaging techniques, Microstructure

Monitoring time dependence with diffusion MRI provides observables sensitive to restricted diffusion and exchange. Probing these phenomena by simply varying the diffusion time is a challenge because they have opposite effects on the diffusion-weighted signal and may cancel each other. A theoretical framework was recently proposed for disentangling the effects using free gradient waveforms. Here we explore the potential of the approach for neuroimaging in vivo using a high-performance gradient system. Results demonstrate unprecedented ability to disentangle the effects of restriction and exchange. Maps of the exchange rate show plausible contrast in both cortical and subcortical regions of the brain.

Introduction

Water molecules diffusing in environments with permeable membranes exhibit time-dependent diffusion, which can be probed with diffusion MRI for mapping of observables related to both the restriction length (size) and exchange rate (permeability) of the microstructure^1–3. Mapping these features in vivo is important for the characterisation of pathology and treatment response^4–6. However, estimation of size and exchange by varying the diffusion time alone is a challenge because the two phenomena have opposite effects on the diffusion-weighted signal^7,8. We recently proposed the use of free gradient waveforms to address this challenge⁹. Here, we utilise this novel approach to map restriction and exchange in vivo using a high-performance gradient system.

Theory

The framework is based on a signal representation given by⁹
$$\ln (S/S_0)\approx -b\left[ E_{\beta_0}+V_{\omega}E_{\beta_2}\right] + \frac{1}{2}b^2\left[V_{\beta_ 0}+2V_{\omega}C_{\beta_0\beta_2}+V_{\omega}^2V_{\beta_2}\right]\cdot (1-k{\Gamma}),\quad\quad (1)$$
where $$$ S_0$$$ is the non-diffusion-weighted signal and $$$b$$$ is the b-value ($$$b=\int_0^Tq(t)^2dt$$$), $$$q$$$ is the dephasing q-vector ($$$q(t)=\gamma \int _0^tg(\tau)d\tau$$$ where $$$g(\tau)$$$ is the gradient waveform), and $$$\gamma$$$ is the gyromagnetic ratio. Furthermore, $$$V_{\omega}$$$ is the restriction weighting
$$V_{\omega}=\frac{1}{2\pi b}\int_{-\infty}^{\infty}|q(\omega)|^2\omega ^2d\omega = \frac{\gamma^2}{b}\int_0^Tg^2(t)dt,\quad\quad (2)$$
where $$$q(\omega)$$$ is the Fourier transform of $$$q(t)$$$, and $$$\Gamma$$$ is the exchange weighting
$$\Gamma = 2\int_0^Tt\tilde{q_4}(t)dt,\quad\quad (3)$$
where $$$\tilde{q_4}(t)=q_4(t)/b^2$$$ and $$$q_4(t)=\int _0^Tq^2(t')q^2(t'+t)dt'$$$. The representation features three experimental parameters ($$$b,V_{\omega}$$$ and $$$\Gamma$$$) and six microstructure-related parameters: $$$E_{\beta_0}=\langle\beta_0\rangle$$$ is the mean time-independent diffusivity, $$$E_{\beta_2}=\langle\beta_2\rangle$$$ is the average restriction coefficient, $$$k$$$ is the exchange rate, $$$V_{\beta_0}$$$ and $$$V_{\beta_2}$$$ are the variances in $$$\beta_0$$$ and $$$\beta_2$$$, and $$$C_{\beta _0\beta_2}$$$ is their covariance. The principle is that independently varying $$$V_{\omega}$$$ and $$$\Gamma$$$ enables us to disentangle effects of restriction and exchange.

Methods

Two experiments were performed on a single volunteer using a 42-cm diameter head-only gradient – MAGNUS ¹⁰ at 3.0 T, capable of a maximum gradient strength of 200 mT/m and slew rate of 500 T/m/s. To span the $$$V_{\omega}$$$ vs $$$\Gamma$$$ space, the experiments featured multiple gradient waveforms, limited to a gradient strength of 200 mT/m, and a slew rate of 220 T/m/s to satisfy PNS limits. Two experiments were performed, both had the same pulse sequence parameters (TE=115 ms, TR=3 s, resolution = 2x2x5 mm³), whereas the diffusion encoding waveform sets were varied.

The first experiment was a ‘discovery protocol’ tailored to explore the change in contrast from changing the exchange and restriction weighting. To this end, 150 unique waveforms with different values of $$$V_{\omega}$$$ and $$$\Gamma$$$ were generated (Fig.1A). The waveforms were applied along a single direction (y-direction) at three b-values (0, 2 and 4 ms/µm²). The scan time was 15 minutes.

The second experiment was the ‘application protocol’ and aimed at estimating restriction and exchange-related parameters. For this purpose, twelve waveforms were selected such that six had a constant $$$V_{\omega}$$$ but varying $$$\Gamma$$$ and six had fixed $$$\Gamma$$$ but varying $$$V_{\omega}$$$ (Fig.1B). Each waveform was applied in 10 directions per b-value using the b-values $$$0,1,2,3$$$ and $$$4$$$ ms/µm². The scan time was 25 minutes.

Data were analysed by signal inspection in various regions of interest, by computing difference images between, for example, strong and weak exchange weighting at a fixed restriction weighting, and by fitting Eq.1 to powder-averaged signals using lsqnonlin in MATLAB (MathWorks, Natick, MA, USA; R2019a).

Results

Fig.2 shows the signal at a fixed b-value for waveforms in the discovery protocol. The signal varies smoothly with $$$V_{\omega}$$$ and $$$\Gamma$$$, indicating that these parameters capture the salient features of the diffusion encoding waveforms. Effects of exchange dominate in the cerebellar cortex whereas restriction dominates in the internal capsule (white matter).

Fig.3 shows the restriction and exchange contrasts from the application protocol. The contrasts were obtained by subtracting images acquired with maximum and minimum $$$V_{\omega}$$$ and $$$\Gamma$$$ at b = 4 ms/µm². Results again indicate that time dependence in grey matter is dominated by exchange, while restricted diffusion is dominant in white matter.

Fig.4 shows powder-averaged signal-vs-b curves from the application protocol in three brain regions. Time-dependence is driven by exchange in grey matter while restriction dominates in white matter. In the thalamus, both effects appear relevant.

Parameter estimates obtained from fitting Eq.1 to the data from the application protocol are shown in Fig.5. There are high values of the restriction-related parameter $$$E_{\beta_2}$$$ in the cerebellar white matter and high exchange rates in the cerebellar cortex. Both results are in harmony with the contrasts in Fig.3.

Discussion

This work demonstrated that time dependence in vivo is well-captured by two experimental parameters: one for restriction weighting and another for exchange weighting. To the best of our knowledge, this is the first time that exchange in living tissue has been probed using this broad a set of waveforms with unique timing parameters. This was enabled by the availability of ultra-strong gradients.

Parameter maps indicate slow exchange in white matter—suggesting that axons are effectively impermeable at these time scales¹¹. Furthermore, exchange estimates in grey matter align with the upper end of the literature range (4 ms to over 100 ms^8,12). Recent work suggests faster exchange in grey matter⁸, but we note that the framework used herein underestimates fast exchange rates⁹.

A limitation of this work is that ignores other effects such as structural disorder¹³ and intra-compartmental kurtosis¹⁴which may be potential confounders¹⁵.

Acknowledgements

The authors acknowledge the funding support from Massachusetts Life Science Foundation, Swedish Cancer Society (22 0592 JIA), Swedish Research Council (2021-04844), NIH grants R01NS125781, P41EB015902

References

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Figures

Figure 1: Protocols used for in vivo experiments. (A) shows a map of the restriction- and exchange weightings of 150 unique free waveforms with some examples highlighted around the boundary. (B) shows a 12-waveform protocol chosen to selectively probe exchange (waveforms along the x-axis) and restriction (waveforms along the y-axis). All waveforms had a maximum duration of 100 ms, maximum gradient strength of 200 mT/m at a slew rate of 220 T/m/s that are within peripheral nerve stimulation limits.

Figure 2: Effect of restriction and exchange in the human brain. (A) ROI in the cerebellar cortex, (B) Average signals in the ROI at b=4 ms/µm² for all 150 waveforms from Fig.1A. Bright dots show high signal and dark show low signal. (C) and (D) show signal variation with V_ω (at Γ=20 ms) and Γ (at Vω=12000 s^-2). (E)-(F) show similar results for the internal capsule. Time dependence in cortical grey matter is dominated by exchange (dots in B have bright-to-dark trend along the x-axis) while restriction is more important in white matter (the dots in F have a bright-to-dark trend along the y-axis).

Figure 3: Restriction and exchange contrast. Images were computed by subtracting images acquired with maximum exchange/restriction weighting from images acquired with minimum exchange/restriction weighting at a b=4 ms/µm² in the cerebellum and cerebrum. Each difference image is normalized by the mean of the two images. Restricted diffusion appears to produce a stronger time-dependence in white matter while exchange is dominant in cortical grey matter (also seen in Fig. 2). Note that the contrast in the images is generally positive, which agrees with expectations based on Eq. 1.

Figure 4: Signal vs b-value showing the effect of increasing restriction and exchange-weighting in the cerebellar cortex, corpus callosum and thalamus. The figure suggests that time dependence is predominantly driven by exchange in cortical grey matter and by restriction in white matter. Both exchange and restriction appear to have significant impact on the signal in the thalamus.

Figure 5: Parameter maps obtained from fitting Eq.1 to data from the application protocol. Results are shown for the cerebellum and the cerebrum. The outline of the cerebellum is shown for clarity. Note how the exchange estimates in the cerebellum highlight the contrast between white and grey matter, in agreement with the results of Fig. 3.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)

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DOI: https://doi.org/10.58530/2023/4320