The measurement of transcytolemmal water exchange rate $k_{in}$ may provide insights for more specific diagnosis of pathophysiological status of biological tissues. Two diffusion-based methods, the CG¹ (constant gradient) and FEXI² (filtered exchange imaging) methods, have been developed to provide a flexible and safer means to measure $k_{in}$ non-invasively in vivo. However, neither methods have been fully validated up to date. In the present work, computer simulations and in vitro experiments with well-controlled cultured cells with different sizes and permeabilities were performed to evaluate the accuracy of the CG and FEXI methods.

Theory: $k_{in}$ can be directly fitted from the CG method by $k_{in}=-\frac{\partial S(\tilde{q}^2,t_D)}{\partial t_D}$ where $\tilde{q}$ is constant, $t_{D}$ is diffusion time, and $b$ value is sufficiently large. The FEXI method uses a diffusion filter block before ADC detection, and then provides apparent exchange rate AXR, which is $k_{in}$ modulated with extracellular water fraction $f_{ex}$, i.e. $\text{AXR}=k_{in}\times f_{ex}$.

In vitro study: Human myelogenous leukemia K562 cells were cultured, fixed and then divided into three groups (six samples in each) treated with vehicle (control), low (0.025% w/v) and high (0.05%) concentrations of saponin. Saponin is a natural detergent that selectively removes membrane cholesterols and increases cell membrane permeability without altering other cell properties³. All MR experiments were performed on an Agilent/Varian 4.7T MRI system. The CG experiments employed 30 gradients separation $\Delta$ up to 832 ms. The FEXI experiments used diffusion weighting $b_{f}$ = 3000 s/mm² in the filter block and $b$ = 0 and 1500 s/mm² in the detection block, and 19 mixing times ranging from 7 to 3000 ms.

Computer Simulation: Water molecules were allowed to diffuse in intra- and extracellular spaces with a cell membrane permeability separating the compartments. $D_{in}$ = 1 μm²/ms, $D_{ex}$ = 2 μm²/ms, and three different cell diameters 5, 10, and 20 μm were simulated while the intracellular volume fraction was fixed as 61.8%. 18 ground truth $k_{in}$ values (0.02 – 30 Hz) were simulated. All other parameters were the same as those used in the in vitro experiments.

Figure 1 shows the simulated CG method provides accurate estimations of $k_{in}$ especially when it is smaller than 15 Hz, which is in the typical physiological range of many biological tissues. Figure 2 shows the FEXI method constantly overestimates $k_{in}$ even with corrections of extracellular water fraction. However, AXR and fitted $k_{in}$ showed approximately linear dependence on the ground truth $k_{in}$. The cell diameter had minor influences on both methods when $k_{in}$ < 10 Hz, in which the CG and FEXI methods agree well with each other. Note that this $k_{in}$ range corresponds to intracellular water lifetime $\tau_{in}$ > 100 ms, which is typical for biological tissues⁴. Figure 3 and 4 show the experimental results, and the correlation between of the two methods are provided in Figure 5. Both methods have the sensitivity to probe the variations of cell membrane permeability. The linear dependence of AXR from FEXI and $k_{in}$ from CG methods is consistent with simulations, suggesting AXR is also a reliable indicator of $k_{in}$. The CG method has been long used to characterize transcytolemmal water exchange rate $k_{in}$. However, due to demands of high b values, its application in practice is limited. Although the FEXI method provides less accurate estimations of $k_{in}$, the approximately linear dependence of AXR on $k_{in}$ suggests AXR is a promising means to measure $k_{in}$. Considering the feasibility of spatially mapping $k_{in}$ in humans in vivo, the FEXI method may have a greater clinical potential compared with the non-imaging CG method, although its accuracy is compromised.