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A general quantitative diffusion MRI model of water exchange, confinement, and hindrance with arbitrary gradient waveform encoding

Sisi Li¹, Diwei Shi², Xiaoyu Jiang^3,4, Li Chen², Quanshui Zheng², Hua Guo¹, and Junzhong Xu^3,4,5,6
¹Center for Biomedical Imaging Research, Tsinghua University, Beijing, China, ²Center for Nano and Micro Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing, China, ³Institute of Imaging Science, Vanderbilt University Medical Center, Nashville, TN, United States, ⁴Department of Radiology and Radiological Sciences, Vanderbilt University Medical Center, Nashville, TN, United States, ⁵Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, United States, ⁶Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, United States

Synopsis

Keywords: Signal Modeling, Microstructure

This study proposed and validated a general diffusion MRI biophysical model enabling simultaneous estimation of cell size, intracellular volume fraction, and transcytolemmal water exchange. The model introduces two-mode intracellular diffusion, corrects for restriction-induced “edge-enhancement” effect, and handles arbitrary diffusion gradient waveforms. The results of both in silico and in vitro experiments suggest this model not only improves the accuracy of estimated microstructural parameters such as cell size but also provides reasonable estimates of water exchange rate constant that is usually ignored previously. Such a comprehensive model may have potential to probe tumor status more precisely which is feasible in clinics.

Introdcution

Numerous multi-compartment biophysical models ^1-12 have been developed for quantitative diffusion MRI (dMRI) to characterize cellular microstructures. However, these models usually ignore transcytolemmal water exchange ¹³, i.e., the water exchange across cell membranes, leading to misestimates of microstructural parameters such as cell size ($$$d$$$) and intracellular volume fraction ($$$v_{in}$$$).
Meanwhile, Kӓrger model-based methods ^14-17 have been proposed to estimate transcytolemmal water exchange with assumptions on pulse sequence, diffusion time, and exchange rate. Nevertheless, these methods usually overestimate transcytolemmal water exchange rate constant ($$$k_{in}$$$) due to restriction-induced “edge-enhancement effect” ¹⁸.
A few attempts have tried to unify the above two separate frameworks to a more comprehensive biophysical model, such as the work based on strong assumptions on short-pulse approximation ^19,20 and very recent work ²¹ based on cumulant expansion of the signal attenuation.
In this study, we proposed a general quantitative diffusion MRI model of water exchange, confinement, and hindrance with arbitrary gradient waveform encoding (EXCHANGE). This EXCHANGE model introduces two-mode intracellular diffusion to account for exchange, corrects for restriction-induced edge-enhancement effect, and handles arbitrary gradient waveforms. Both in-silico and in-vitro experiments were performed to evaluate the accuracy and precision of fitted microstructural parameters such as $$$d$$$, $$$v_{in}$$$, and $$$k_{in}$$$.

Theory

Two-mode intracellular diffusion
As shown in Fig. 1, during a short time interval, an intracellular water molecule has a probability of $$$p$$$ crossing the membrane (exchange) and hence $$$(1-p)$$$ staying inside the cell (confined). This effectively divides intracellular water diffusion into two modes: restricted (mode A) and hindered (mode B). Therefore, the two-mode intracellular diffusion coefficient can be defined as: $$$D^*_{in}=-1/b*ln((1-p)exp(-bADC_r)+pexp(-bD_{inh}))$$$, where $$$ADC_r$$$ is the apparent restricted diffusion coefficient and $$$D_{inh}$$$ represents an averaged hindered diffusivity of mode B. We empirically compute $$$D_{inh}$$$ by: $$$D_{inh}=v_{in}((1-p)ADC_r+pD_{in})+v_{ex}D_{ex}$$$, where $$$v_{in}$$$ and $$$v_{ex}$$$ are the volume fractions and $$$v_{in}+v_{ex}=1$$$, $$$D_{ex}$$$ is the hindered diffusion coefficient of the extracellular compartment. Note that we can find: $$$p=0.75R/sqrt(2D_{in}τ_{in})$$$, where $$$R$$$ is the cell radius, $$$τ_{in}$$$ is the mean intracellular pre-exchange lifetime, and $$$D_{in}$$$ is the intracellular diffusion coefficient without the influences of cell membranes.
For simplification, we only define an effective $$$D_{ex}$$$ to describe the overall extracellular hindered diffusion due to the very narrow interstitial space.
Correction for the restriction-induced edge-enhancement effect
One long-time overlooked problem is that Kӓrger model-based methods might overestimate the water exchange rate since exchange rate constants of magnetizations, $$$k^m_{in(ex)}$$$, are larger than exchange rate constants of water molecules, $$$k_{in(ex)}$$$ due to restriction-induced “edge-enhancement” effect. In this work, we correct for such a bias by defining $$$k^m_{in}=αk_{in}$$$, where $$$α$$$ is the correction factor greater than 1, and we empirically give out $$$α=1+2v_{in}R/sqrt(2D_{in}τ_{in})$$$; $$$k^m_{ex}≈k_{ex}$$$ because the extracellular space is a narrow interstitial space where the edge-enhancement effect can be ignored.
Based on the above work and the generalized method ²² to calculate $$$ADC_r$$$ under arbitrary gradient waveforms, we propose the EXCHANGE model. The corresponding analytical expression can be derived in a form similar to the solution of the classical Kӓrger model.

Methods

Numerical simulations
A finite difference method was used to simulate dMRI signals based on a tightly packed, spherical cells on a face-centered-cubic lattice with $$$v_{in}=$$$51%, $$$D_{in}=1.58 μm^2/ms$$$ and $$$D^{free}_{ex}=2 μm^2/ms$$$. The cell diameter $$$d$$$ was 8~18 μm. $$$τ_{in}$$$ was set as 50, 70, 100, 200, 400 and $$$\infty$$$ ms. Diffusion sequences and parameters are shown in Fig. 2. Fitting was repeated 100 times each with Rician noise corresponding to SNR=45. The value of $$$D_{in}$$$ was fixed as $$$1.58 μm^2/ms$$$ so unknown parameters are $$$v_{in}$$$, $$$d$$$, $$$k$$$ (note: $$$k=1/τ_{in}$$$) and $$$D_{ex}$$$. The IMPULSED ²³ and JOINT ¹⁹ models were also performed to compare with the EXCHANGE model.
Restrospective cell experiments
The details of the in-vitro experiment have been reported previously ²⁴. Briefly, fixed MEL cells were treated with different concentrations of saponin to form four groups. The cell pellet samples were scanned using an Agilent 4.7 Tesla MRI scanner with a maintained temperature. IMPULSED, JOINT, and EXCHANGE models were used and then compared with the light microscopy-derived $$$d$$$ and the constant gradient (CG) method-derived cell membrane permeability $$$P_m$$$ (note: $$$1/P_m=6τ_{in}/d-d/10D_{in}$$$) ²⁵.

Results and Discussion

Fig. 3 shows the fitting results of $$$v_{in}$$$ and $$$d$$$. The IMPULSED and JOINT models underestimate $$$v_{in}$$$ and the bias increases with faster water exchange, i.e., larger $$$k$$$. By contrast, the EXCHANGE model provides the most accurate results, and the fitted $$$v_{in}$$$ matches the ground-truth well for $$$10 μm≤d≤18 μm$$$. In Fig. 3B , the IMPULSED model usually overestimates $$$d$$$. The results of the JOINT and EXCHANGE models match the ground-truth well for $$$d≤14 μm$$$ although both models underestimate $$$d$$$ for larger diameters.
Fig. 4 shows the fitting results of $$$k$$$. The JOINT model overestimates $$$k$$$ for $$$d≥10 μm$$$. The results fitted by the EXCHANGE model are closer to the ground-truth except for $$$d=8 μm$$$.
Fig. 5 shows that the EXCHANGE model can extract more accurate and more comprehensive microstructure information of cell tissues in the cell experiments.

Conclusion

The proposed EXCHANGE model not only enables simultaneous estimation of cell size, intracellular volume fraction, and membrane permeability but also improves the accuracy of estimated microstructural parameters compared with other methods. This is promising to probe tumor status more precisely and assist personalized medicine in cancer clinics.

Acknowledgements

No acknowledgments are found.

References

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Figures

Fig. 1 Graphic illustrations of three different cases for water molecule diffusion movement in intra- and extracellular spaces.

Fig. 2 Different gradient waveforms used in the numerical simulations. (a). cosine-modulated trapezoidal OGSE acquisitions with N=2 (tcos N=2) (b). cosine-modulated trapezoidal OGSE acquisitions with N=1 (tcos N=1) (c). trapezoid-shaped PGSE acquisitions.

Fig. 3 (A) Intracellular volume fraction $$$v_{in}$$$ and (B) voxel-wise mean cell size $$$d$$$, fitted by the IMPLUSED, JOINT, and the proposed EXCHANGE model, respectively, as a function of $$$k$$$ in the numerical simulations.

Fig.4 Transcytolemmal Water exchange rate constant $$$k$$$ fitted by the IMPLUSED, JOINT, and EXCHANGE model, respectively, as a function of $$$k$$$ (ground-truth) in the numerical simulations.

Fig.5 Results from the IMPLUSED, JOINT and EXCHANGE model in the four groups of in-vitro cell experiments. The shaded area indicates STD of light-microscopy obtained cell sizes.

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

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DOI: https://doi.org/10.58530/2023/4307