Diffusion MRI (DWI) has been previously used to quantitatively characterize tissue microstructure e.g. to estimate average volume-weighted cell diameter $$$d$$$, intracellular diffusion coefficient $$$D_{in}$$$ and intracellular volume fraction $$$f_{in}$$$. These studies used various time-varying gradient waveforms and usually assumed slow transcytolemmal water exchange between intra- and extracellular spaces. However, this assumption is usually not valid especially in pathological tissues such as tumors. The present work used both computer simulations and well-controlled cell cultures in vitro to investigate the influence of transcytolemmal water exchange on quantitative characterization of microstructure using different diffusion-encoding methods.

Models: Despite the various $$$\tau_{in}$$$ values in simulations and in vitro experiments, all diffusion data were fit to models assuming signals arose from intra- and extracellular spaces without exchange, like what have been typically done previously^1,2. Three methods were investigated. The PGSE_I and PGSE_II methods used conventional pulse gradient spin echo (PGSE) acquisitions with multiple diffusion times ($$$t_{D}$$$) and b values. Four parameters ($$$d$$$, $$$f_{in}$$$, $$$D_{in}$$$, $$$D_{ex}$$$) were fit using PGSE_I, while three ($$$d$$$, $$$f_{in}$$$, $$$D_{ex}$$$) were fit using PGSE_II which is identical to PGSE_I except $$$D_{in}$$$ was pre-defined empirically in fittings. The third method was temporal diffusion spectroscopy² (TDS) which incorporates PGSE acquisitions with a single long $$$Δ$$$ = 52 ms and two oscillating gradient spin echo (OGSE) acquisitions with two frequencies $$$f$$$ = 40 and 80 Hz and with nine different b values. Five parameters ($$$d$$$, $$$f_{in}$$$, $$$D_{in}$$$, $$$\beta_{ex}$$$, $$$D_{ex0}$$$) were fit using TDS, in which extracellular diffusion coefficient is assumed linearly dependent on $$$f$$$ as $$$D_{ex}(f)= D_{ex0} + β_{ex}×f$$$. The analytic expressions for intracellular DWI signals using PGSE and OGSE acquisitions have been reported previously³. To ensure the translatability, maximum gradient strengths were limited < 30 G/cm which is achievable on current human gradient coil⁴.

Computer Simulation: A finite difference method was used, which covered a broad range of microstructural parameters: intracellular water lifetime $$$\tau_{in}$$$ 50 – 500 ms, $$$d$$$ 5 – 15 μm, $$$D_{in}$$$ and $$$D_{ex}$$$ were 1 and 2 μm²/ms.

In vitro study: Murine erythroleukemia (MEL) cells were cultured, fixed and treated with saponin to selectively change cell membrane permeability without changing other cellular microstructure⁵. Four different concentrations of saponin, 0, 0.01%, 0.025%, and 0.05%, were used. Constant gradient experiments⁶ were used to estimate $$$\tau_{in}$$$. The mean cell diameters were measured using light microscopy.

Figure 1 shows the simulated fitting errors compared with ground truth values dependent on $$$d$$$ and $$$\tau_{in}$$$. Both TDS and PGSE_II provide accurate $$$d$$$ (error < 5%) for most $$$\tau_{in}$$$ and $$$d$$$, while PGSE_I can provide < 5% errors only when $$$\tau_{in}$$$ > 400 ms and 10 ≤ $$$d$$$ ≤ 15 μm. All three methods significantly underestimated $$$f_{in}$$$, and $$$f_{in}$$$ decreases rapidly with smaller $$$\tau_{in}$$$. Reasonable $$$D_{in}$$$ (errors < 10%) can be fit using TDS for most $$$\tau_{in}$$$ and $$$d$$$, although the fits with errors < 5% occurred only when 7≤ $$$d$$$ ≤ 15 μm. PGSE_I could provide reasonable fits of $$$D_{in}$$$ only with large $$$d$$$ and longer $$$\tau_{in}$$$, while PGSE_II could not fit $$$D_{in}$$$. Figure 2 shows that, except for fast exchange ($$$\tau_{in}$$$ < 100 ms), the choices of $$$D_{in}$$$ had minor effects on the fittings of PGSE_II, indicating the accuracy of fitted $$$d$$$ is not influenced by the empirically pre-defined $$$D_{in}$$$ used in the fittings. Figure 3 summarizes results of cultured MEL cell experiments with four different membrane permeabilities. Consistent with simulations, TDS and PGSE_II provide accurate fittings of $$$d$$$ independent of $$$\tau_{in}$$$, while fitted $$$f_{in}$$$ decreased rapidly with short $$$\tau_{in}$$$. $$$D_{in}$$$ was 0.84 μm²/ms when $$$\tau_{in}$$$ > 100 ms using TDS, while $$$D_{in}$$$ was fit as 0.55 μm²/ms using PGSE_I. All other fitted parameters showed dependence on $$$\tau_{in}$$$. Both computer simulations and in vitro cell studies suggest that: for PGSE_II, empirically pre-defining $$$D_{in}$$$ as a constant in fittings not only decreases the number of free parameters but also, more importantly, significantly increases the accuracy of other fit parameters. Both TDS and PGSE_II methods provided accurate fits of mean cell diameter $$$d$$$ independent of transcytolemmal water exchange, while intracellular volume fraction $$$f_{in}$$$ was significantly underestimated in both methods and decreased with short $$$\tau_{in}$$$. The TDS method is capable of estimating intracellular diffusion coefficient $$$D_{in}$$$ when appropriate ranges of $$$d$$$ (7 – 15 μm) and $$$\tau_{in}$$$ > 100 ms were satisfied, while $$$D_{in}$$$ cannot be reliably estimated using the PGSE methods. These results can assist better interpreting diffusion data of quantitative characterization of e.g. tumors, where transcytolemmal water exchange cannot be ignored.