Sisi Li^{1}, Diwei Shi^{2}, Li Chen^{2}, Quanshui Zheng^{2}, Hua Guo^{1}, and Junzhong Xu^{3,4,5,6}

^{1}Center for Biomedical Imaging Research, Tsinghua University, Beijing, China, ^{2}Center for Nano and Micro Mechanics, Department of Mechanics Engineering, Tsinghua University, Beijing, China, ^{3}Institute of Imaging Science, Vanderbilt University Medical Center, Nashville, TN, United States, ^{4}Department of Radiology and Radiological Sciences, Vanderbilt University Medical Center, Nashville, TN, United States, ^{5}Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, United States, ^{6}Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, United States

Quantitative microstructural imaging based on diffusion MRI provides a non-invasive means to measure microstructural parameters, e.g., cell size. However, due to the remarkable complexity of incorporating transcytolemmal water exchange into diffusion biophysical models, water exchange is usually ignored. This leads to biased estimation of microstructural parameters, particularly intracellular volume fraction. Here, we propose a new approach to incorporate water exchange naturally in diffusion biophysical models with arbitrary gradient waveforms, making it possible to fit cell size, density, and intracellular water lifetime simultaneously. This establishes a general framework to incorporate transcytolemmal water exchange in any diffusion MRI-based microstructural imaging models.

$$S=v_{i n} S_{i n}+v_{e x} S_{e x}=v_{i n} S_{i n}+\left(1-v_{i n}\right) S_{e x}\tag{1}$$

Although Eq. (1) has shown clinical relevance

Karger’s model is usually used to tackle water exchange, but it relies on approximations such as sufficiently long diffusion time and low water exchange

In this work, we propose a general framework to tackle this challenge. First, we discretize any arbitrary-shaped gradient waveforms into a series of short pulses based on multiple propagators

$$\begin{gathered}S_{i n}=\exp (-\varphi(t)), \varphi(t)=\frac{\gamma^{2}}{2} \sum_{k} B_{k} \int_{0}^{t} d t_{1} \int_{0}^{t} d t_{2} \exp \left(-a_{k} D_{i n}\left|t_{1}-t_{2}\right|\right) g\left(t_{1}\right) g\left(t_{2}\right) \\S_{e x}=\exp (-\phi(\mathrm{t})), \phi(t)=\gamma^{2} D_{e x} \int_{0}^{t}\left(\int_{0}^{t_{1}} g\left(t_{2}\right) d t_{2}\right)^{2} d t_{1}\end{gathered}\tag{2}$$

where

Because each discretized pulse is short enough, the water exchange can be included in the diffusion biophysical model as

$$\begin{aligned}\frac{d S_{i n}}{d t} &=-\frac{\varphi\left(t_{i+1}\right)-\varphi\left(t_{i}\right)}{\tau} S_{i n}-K_{i n} S_{i n}+\frac{v_{e x}}{v_{i n}} K_{e x} S_{e x} \\\frac{d S_{e x}}{d t} &=-\frac{\phi\left(t_{i+1}\right)-\phi\left(t_{i}\right)}{\tau} S_{e x}-K_{e x} S_{e x}+\frac{v_{i n}}{v_{e x}} K_{i n} S_{i n}\end{aligned}\tag{3}$$

for

Fig. 4 shows the fitting results of

Similarly, the fitting results of

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Fig. 1 Graphical illustration of
discretizing a finite-length gradient waveform.

Fig. 2 Different
finite-length gradient waveforms used in the valiation. (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 Comparison of estimated cell diameter d using
the proposed model and the conventional two-compartment model ignoring water
exchange.

Fig. 4 Comparison
of estimated volume fraction *v*_{in} using the proposed model and conventional
two-compartment model ignoring water exchange.

Fig. 5 The
fitting results of the intracellular water lifetime *τ*_{in}.

DOI: https://doi.org/10.58530/2022/4754