Water exchange rates measure active transport and homeostasis in neural tissue

Abstract

For its size, the brain is the most metabolically active organ in the body. Most of its energy demand is used to maintain stable homeostatic physiological conditions. Altered homeostasis and active states are hallmarks of many diseases and disorders. Yet there is currently no direct and reliable method to assess homeostasis and absolute basal activity of cells in the tissue noninvasively without exogenous tracers or contrast agents. We propose a novel low-field, high-gradient diffusion exchange nuclear magnetic resonance (NMR) method capable of directly measuring cellular metabolic activity via the rate constant for water exchange across cell membranes. Exchange rates are $140\pm 16$ s ${}^{-1}$ under normal conditions in viable ex vivo neonatal mouse spinal cords. High repeatability across samples suggest that values are absolute and intrinsic to the tissue. Using temperature and drug (ouabain) perturbations, we find that the majority of water exchange is metabolically active and coupled to active transport by the sodium-potassium pump. We show that this water exchange rate is sensitive primarily to tissue homeostasis and provides distinct functional information. In contrast, the apparent diffusion coefficient (ADC) measured with submillisecond diffusion times is sensitive primarily to tissue microstructure but not activity. Water exchange appears independently regulated from microstructural and oxygenation changes reported by ADC and $T_1$ relaxation measurements in an oxygen-glucose deprivation model of stroke; exchange rates remain stable for 30-40 min before dropping to levels similar to the effect of ouabain and never completely recovering when oxygen and glucose are restored.

Keywords: biomarkers; diffusion exchange spectroscopy (DEXSY); membrane permeability; porous media; transcytolemmal water exchange.

Fig. 1.

Temperature dependence reveals active, steady-state water exchange. Exchange rates, k, for fixed A) and live B) spinal cords measured at different temperatures. Box and violin plots include all k measurements (three measurements per sample) and are discussed in the Methods. Connected dots show the mean k at each temperature and are colored differently for each sample. C) Arrhenius plot of the dependence of k on $T^{-1}$ (the inverse of the absolute temperature) for fixed and live spinal cords. Mean values (symbols) and standard deviations (whiskers) for all fixed and live samples at each temperature condition are presented. Data points for the first, second, and third ${25}^{\circ }\mathrm{C}$ conditions are shown separately. Lines show the mean of Arrhenius model fits. Slopes of the lines are proportional to $E_a$. D) Boxplots comparing activation energies ($E_a$) between fixed and live spinal cords. Dots show the values of $E_a$ for each sample and use the same colors as in (A) and (B). $E_a=21\pm 8$ kJ/mol (mean ± SD) for fixed samples, similar to $E_a=18$ found for water self-diffusion in artificial cerebrospinal fluid (aCSF, solid blue line, see also Fig. 2). $E_a=36\pm 7$ kJ/mol for live spinal cords and is significantly greater than $E_a$ for fixed spinal cords ($P=0.005$). Therefore, water exchange is linked to metabolic activity.

Fig. 2.

Temperature dependence of ${\mathrm{ADC}}_y$. ADCs of fixed A) and live B) spinal cords at the different temperatures. C) Arrhenius plot of ${\mathrm{ADC}}_y$ at each temperature condition for fixed and live spinal cords, as well as free diffusion coefficients of pure aCSF. D) Activation energies ($E_a$) of water diffusion for fixed and live spinal cords (boxplots) and aCSF (solid blue line). Dots show $E_a$ values for each sample using the same colors as in (A) and (B). A greater description of plot details is provided in the caption of Fig. 1. For aCSF, $E_a=18\mathrm{kJ}/\mathrm{mol}$, similar to values reported for pure water over the same temperature range $E_a=18-20\mathrm{kJ}/\mathrm{mol}$ (67). $E_a$ of ${\mathrm{ADC}}_y$ is not significantly different between live ($E_a=8.3\pm 1.5\mathrm{kJ}/\mathrm{mol}$), and fixed spinal cords ($E_a=7.0\pm 2.1\mathrm{kJ}/\mathrm{mol}$) ($P=0.21$).

Fig. 3.

Exchange rates drop by $71\pm 8\text{\%}$ after inhibiting the sodium–potassium pump with ouabain. A) Real-time exchange rate and B) percentage change in ADC from baseline measurements on live spinal cords under normal condition and after addition of 100 $\mu$M ouabain at 25${}^{\circ }\mathrm{C}$. Mean values (symbols) and standard deviations (whiskers) from $n=3$ samples are presented. In (A), solid lines show average exchange rate values from all measurements under normal conditions in this paper ($k=140{\mathrm{s}}^{-1}$) and from all measurements after ouabain addition ($k=36{\mathrm{s}}^{-1}$). (See Fig. S4 for associated f and $R_{1\mathrm{DW}}$ data.)

Fig. 4.

Exchange rates are highly regulated but eventually drop during OGD. Recordings of $R_1$, ${\mathrm{ADC}}_y$, and k while switching from normal media bubbled with $95\text{\%}{\mathrm{pO}}_2$ to glucose-free media bubbled with $1\text{\%}{\mathrm{pO}}_2$ and washing back to normal after 40 min (left column) or 70 min (right column), at 25${}^{\circ }\mathrm{C}$. A–F) Time series averages show means (symbols) and standard deviations (whiskers) of $n=8$ samples for 40 min OGD and of $n=9$ for 70 min OGD. G,H) Time series for representative samples, with $R_1$ (squares) and ${\mathrm{ADC}}_y$ (triangles) values associated with the right-hand y-axis and exchange rate (circles) values associated with the left-hand y-axis. I) Histogram of how long the exchange rate response lags behind ${\mathrm{ADC}}_y$, calculated from cross-correlation analysis on the 10 samples for which ${\mathrm{ADC}}_y$ and exchange rate are significantly correlated. J) Box and violin plots comparing the exchange rate values during recovery from 40 min OGD and 70 min OGD (averaged over the period 40–70 min after switching back to normal aCSF). Time series and Pearson correlations for all samples are shown in Fig. S9.

Fig. 5.

Comparisons between fixed, live (untreated), ouabain-treated, and post-70 min OGD reveal how treatments affect passive and active exchange. Bar graphs present the mean across all measurements (bar height), 95% CI of the mean (whiskers), and mean values from each sample (open circles). Exchange rates were compiled from the first ${25}^{\circ }\mathrm{C}$ condition in Fig. 1, and from Figs. 3 and 4. The exchange rate of live spinal cords (mean ± SD $k=140\pm 16{\mathrm{s}}^{-1}$, $n=27$) is significantly greater than fixed ($k=87\pm 10{\mathrm{s}}^{-1}$, $n=6$), ouabain-treated ($k=36\pm 11{\mathrm{s}}^{-1}$, $n=3$), and spinal cords after 70 min of OGD ($45\pm 7{\mathrm{s}}^{-1}$, $n=9$) ($P<0.001$). Furthermore, the exchange rate of ouabain-treated spinal cords is significantly less than fixed spinal cords ($P<0.001$). However, exchange rates are not significantly different between ouabain-treated spinal cords and spinal cords after 70 min OGD ($P=0.056$). Associated data and fits are compared in Fig. S10.

Fig. 6.

Experimental setup. A) 3-D technical drawing of the test chamber. aCSF inlet/outlets and temperature probes are omitted for simplicity. B) Image of the solenoid RF coil containing a mouse spinal cord. C) Technical drawing of the experimental setup. Vectors ${\mathrm{B}}_1$, g and ${\mathrm{B}}_0$ point in the x, y, and z directions, respectively.