Transmembrane Dynamics of Water Exchange in Human Brain

Abstract

Tracking arterial spin labeled (ASL) water in the human brain with magnetic resonance imaging can provide important information on the dynamics of the trans-capillary and trans-membrane water exchange. This information however, is not only important from a basic biological standpoint, but also is essential for deciphering positron emission tomography and MRI perfusion experiments based on the movement of labeled water. While substantial information exists on water exchange through cellular membranes in vitro, the in vivo information remains limited and controversial. In this MRI study, we use a combination of pulsed ASL and recently developed quantitative blood-oxygen-level-dependent technique to address this question. Our approach is based on the measurements of the intrinsic MR transverse relaxation $\left(T_2^{*}\right)$ properties of the ASL-labeled water. We discovered that $T_2^{*}$ of the ASL-labeled water in the extravascular space is 87 ms ± 10 ms while $T_2^{*}$ of the corresponding tissue water is much shorter, 50 ms ± 4 ms. This suggests that the ASL-labeled water does not reach equilibrium with the extravascular tissue and is mostly localized to the extraneuronal space. We estimated that the water transport time through the neuronal membranes is on the order of several tens of seconds; a finding consistent with older PET tracer kinetic studies using ¹⁵O-water.

The structure of brain tissue is a complex system of cellular membranes and heterogeneous aqueous regions with water occupying nearly 80% of the tissue volume. Understanding the movement of water in the tissue and among its cellular compartments is of central physiologic and clinical importance because neuronal activity and ion water homeostasis are inextricably connected (1,2). Despite a long history of research (3,4), the question of how water travels from blood to brain and then distributes within and among brain cells remains unanswered. This is primarily due to the lack of techniques capable of addressing this issue in vivo. Despite data to the contrary (3,4), the notion persists that water, upon leaving the blood, instantaneously equilibrates within and among all brain extravascular compartments (5,6). Verifying whether or not this is correct is essential to interpret a wide range of positron emission tomography (PET) or MR based experiments involving the compartment-sensitive movement of labeled water (i.e., ¹⁵O-labeled water in PET and arterial spin labeled (ASL) water in MRI).

Early PET tracer kinetic models often relied on the assumption, either explicitly or implicitly, that the tracer was distributed instantaneously between intravascular and extravascular compartments upon arrival (7,8). More recent PET studies have demonstrated that the limited dynamic exchange rate of labeled water between intra- and extra-vascular spaces (9,10) as well as between intracellular and interstitial spaces (3,4) should also be taken in to account. Similar effects have also been considered in the modeling of MR signal time course during the wash-out phase of the paramagnetic contrast agent injected in the blood stream during dynamic contrast-enhanced MRI experiments (5,6). In MR ASL-based cerebral blood flow (CBF) measurement (11,12), recently proposed multicompartment ASL signal models incorporated extravascular and intravascular compartments (13–15) accounting for the limited water permeability of capillary walls (16,17). These models assumed (explicitly or implicitly) that the extravascular labeled water, whether residing in the intracellular or extracellular (interstitial) space, would have the same longitudinal and transversal relaxation properties due to the fast exchange between intracellular and extracellular (interstitial) compartments (11,12). However, the measured apparent pre-exchange lifetime for intracellular water could be as long as one second (5), indicating that the extravascular distribution of the labeled water may not reach equilibrium within the time scale of the ASL experiment (3,4).

The recently developed MRI-based technique, quantitative blood-oxygen-level-dependent (qBOLD) (18), revealed that the transverse relaxation time constant $\left(T_2^{*}\right)$ of the water MR signal in the extracellular (interstitial) space is different from the $T_2^{*}$ of the intracellular water. This provides a means to study the distribution of water among different compartments with very high temporal resolution and address the dynamics of water exchange processes. Herein we combine the ASL and qBOLD techniques to study trans-capillary and trans-membrane water exchange. This allows for quantification of the dynamic distribution of magnetically labeled ASL water among intravascular, extracellular and intracellular (neurons and glial cells) spaces. We have demonstrated that the extravascular water movement between extracellular and intracellular spaces is not diffusion-limited with water moving freely within and among cells, but rather is differentially regulated by cellular membranes. Preliminary results from this study have been presented at several scientific conferences (19–21).

MATERIALS AND METHODS

MR Imaging

This study was approved by the Institutional Review Board at Washington University in St. Louis, and written informed consent was obtained from each recruited subject. A total of eight studies were conducted on normal healthy volunteer subjects (age of 27+/8 years old, 5 males, and 3 females). All images were acquired on a Siemens 3T Trio whole body scanner (Siemens Medical Systems, Erlangen, Germany), using a body RF coil as a transmitter and a twelve channel head coil as a receiver. To reduce motion artifacts, a vacuum mold pillow was used as a head restrainer. The volunteer subjects were instructed to rest quietly during the study.

To study the $T_2^{*}$ properties of ASL water, a hybrid of the pulsed arterial spin labeling and gradient echo sampling of spin echo (GESSE) (18,22) sequences were developed to acquire images from a single 2D slice (Fig. 1). ASL method is based on flow-sensitive alternating inversion recovery (FAIR) (12) with background suppression (23) and QUIPPS II (24) techniques. Region IV (Fig. 1) is the GESSE imaging block which consists of a set of read-out gradients embedded around the spin echo (18,22). This allows for the simultaneous acquisition of images corresponding to different gradient echo times (TE) before and after spin echo (TE = 0 corresponds to a position of spin echo). The gradient echoes in the readout direction are flow compensated. On the slice selection direction, a pair of crusher gradients with a velocity encoding value of 60 mm/s is placed around the refocusing RF pulse to remove the contamination from the fast moving labeled water in arteries.

FIG. 1.

FAIR-GESSE pulse sequence with background suppression (23) and QUIPPS II (24) technique. INV – adiabatic inversion (labeling) RF pulse. The shaded gradient strength is alternatively changed for tagged and control states. In region I, SAT 1 suppresses the incoming arterial/venous blood from superior side of imaging volume; SAT 2 provides presaturation of imaging slice. In region II, BS1, and BS2 suppresses the stationary gray matter and white matter tissues (24). Region III is a train of saturation RF pulses, SAT3, applied every 300 ms at the inferior side of imaging volume starting at time TI₁ after tagging RF pulse (INV), filling the interval TD (postsaturation delay) before the GESSE imaging block in region IV (TI = TI₁+TD).

In FAIR preparation, adiabatic hyperbolic secant 180° RF pulses are used for spin inversion. To achieve a uniform inversion profile across the imaging slice, the slice thickness of the inverted region is 24 mm wider than the imaging slice thickness; the slice thickness is 200 mm for the control inversion. The slice-selective gradient (shaded in Fig. 1) strength is alternatively changed for tagged and control states. Control and tagged k-space lines are acquired in an interleaved manner to reduce the influence of the subject’s motion in the data. Background suppression (23) and QUIPPS II (24) technique are incorporated for the reduction of artifacts in the flow quantification, and for the shaping of the labeling bolus. In region I, SAT 1 suppresses the incoming arterial/venous blood from the superior side of imaging volume, while SAT 2 provides presaturation of the imaging slice. In region II, BS1 and BS2 are nonselective inversion pulses applied to suppress MR signal originated from the stationary gray matter, white matter tissues and CSF (24). Region III is a train of saturation RF pulses, SAT3, applied every 300 ms at the inferior side of imaging volume starting at time TI₁ after the tagging RF pulse (INV), filling the interval TD (post saturation delay) before the GESSE imaging block (region IV).

The MRI parameters for the FAIR-GESSE sequence were as follows: TR of 4 s, field of view of 256 × 192 mm², sampling matrix of 64 × 48. The total labeling time TI varied from 1200 to 2200 ms, while the post saturation delay TD varied from 800 to 1600 ms. An 8-mm thick axial slice was positioned about 10 mm above the corpus callosum, thus containing the frontal and parietal lobe of the brain. The slice was slightly tilted toward the occipital lobe to avoid areas with strong field inhomogeneities. Other MR parameters for GESSE acquisition were: spin echo at 30 ms after the RF imaging excitation pulse; the gradient echo train spacing was 2.4 ms (bandwidth of 550 Hz/pixel) with a length of 75 echoes and spin echo which occurred at third echo. The acquisition time of 6.5 min was needed to obtain a complete set of perfusion images with single TI/TD. In some studies only TI or TD varied. For each study, a reference image was acquired using the same FAIR-GESSE sequence without the background-suppression inversion pulses.

ASL Signal Model

In the arterial spin labeling experiment, the spins of water protons residing in arteries feeding tissue are inverted (labeled) by RF pulses. The MRI signal intensity change between images, obtained with and without labeling, provides a measure of blood perfusion. When the arterial blood enters the capillary bed, water passes between the intravascular and interstitial space. The labeled water entering the extravascular interstitial space may then engage in the exchange processes with the intracellular water of parenchymal tissue (see Discussion). Eventually, a portion of the labeled water in the extravascular space returns to the intravascular compartment via capillaries and is washed out of the brain. At the same time, a certain portion of the labeled water remains within the intravascular compartment throughout the transit. Under normal physiological conditions, the vascular water transit time [the time it takes for blood to pass through microvasculature—about 3 to 4 s (25)] is much longer than the time scale of our ASL experiment (about 2 s). The proportion of the labeled water entering venules or veins is negligible. Therefore, to describe the $T_2^{*}$ behavior of the ASL signal, three types of signal contribution should be discussed.

The first is the contribution from the labeled water within the capillaries (intravascular space). As the blood inside the capillaries is partially deoxygenated, it has different magnetic susceptibility than that of the neighboring parenchymal tissue, thus leading to a dependence of the MR signal frequency on the capillary orientation. Assuming the orientations of the capillaries in gray matter are uniformly distributed, in addition to the intrinsic blood $T_2^{*}$ decay, the orientation dependent MR frequency of blood signal will result in an extra signal decay (“powder distribution” effect). The normalized MR signal at gradient echo time TE can be expressed as (18,26):

$$s_b(TE)=\exp \left(i\cdot \mathrm{\delta }\mathrm{\omega }\cdot TE/2-R{2}_b^{*}\cdot TE\right)\cdot \left[C\left(|3\mathrm{\delta }\mathrm{\omega }\cdot TE{|}^{1/2}\right)-i\cdot sign(TE)\cdot S\left(|3\mathrm{\delta }\mathrm{\omega }\cdot TE{|}^{1/2}\right)\right]$$ (1)

Where C and S are Fresnel cosine and sine integral functions, respectively; sign is a sign function; $R{2}_{\text{b}}^{*}$ is the bulk blood signal decay rate constant, which depends on the average blood hematocrit level (Hct) and the average oxygenation level within the capillary, δω relates to the average oxygenation level of the capillary blood $\overline{\mathrm{Y}}$ as follows:

$$\mathrm{\delta }\mathrm{\omega }=\gamma \cdot \frac{4}{3}\cdot \mathrm{\pi }\cdot \mathrm{\Delta }{\chi }_0\cdot Hct\cdot (1-\overline{Y})\cdot B_0,$$ [2]

where γ is the nuclear gyromagnetic ratio, $\Delta {\chi }_{0^{-}}$ the susceptibility difference between completely deoxygenated and completely oxygenated red blood cells [0.264 ppm (27)]. The R2* of the blood depends on its hematocrit level (Hct) and oxygen saturation level (Y). Also note that Hct within microvasculature is smaller than that of large blood vessels. Under a typical Hct of 0.40, at 3 T we will use the phenomenological relationship established in (27) (extrapolated from 1.5 to 3.0 T):

$$R{2}_b^{*}\left({\sec }^{-1}\right)=4.83+540\times {(1-\overline{Y})}^2.$$ [3]

Second, is the contribution from the labeled water in the extravascular space. In the first approximation it can be described by means of a standard $T_2^{*}$ decay:

$$s_{ev}(TE)=\exp \left(-R{2}_{ev}^{*}\cdot TE\right),$$ [4]

However, (see Discussion Section), the extravascular ASL-labeled water should be separated into two separate components: intraneuronal and extraneuronal (containing extracellular and possibly dynamically-mixed extracellular/intraglia). In this case, Eq. 4 should be replaced by a sum of two signals:

$$s_e(TE)\propto \exp \left(-R{2}_e^{*}\cdot TE\right),$$ [5]

$$s_i(TE)\propto \exp \left(-R{2}_i^{*}\cdot TE\right).$$ [6]

In all of the above equations we elected to ignore small nonlinear effects from the mesoscopic magnetic field inhomogeneities created in the tissue by the deoxyhemoglobin-containing blood (18,28).

Data Processing

The raw data from the Siemens scanner was imported into Matlab (MathWorks, Natick, MA) running on a PC with Pentium 4 CPU and 2 GB memory for image reconstruction and processing. To reduce Gibbs ringing artifacts and increase SNR, all images were filtered with a 2D Hanning filter before further processing. A nonlinear least square curve fitting algorithm from the Matlab Optimization Toolbox was used for the fitting procedure. As the phase of the measured signal in both control and tagged images could be affected by unknown factors (eddy currents, magnet field drifting and/or patient movements), only the magnitude of the perfusion signal was used in the fitting procedure.

Magnitude images from the T1-weighted high resolution field mapping sequence were used to delineate gray and white matter areas. Based on the approach described in (29), voxels with high content of arterial blood contamination were excluded from analysis. Also, to reduce errors due to macroscopic magnetic field inhomogeneities, voxels where these fields would induce more than 50% of signal decay at 75 ms were also discarded. After correcting for macroscopic field inhomogeneities using the procedure described in (18), signals from the remaining voxels within the gray matter were averaged together and used for data analysis. On average, ~350 GM voxels (almost entire GM area in the imaging slice) were selected for $T_2^{*}$ quantification. Note that after background suppression, the ASL perfusion signal accounts for ~20 to 30 percent of the total perfusion weighted (control) signal with SNR of ASL perfusion signal at individual GM voxel being ~20 at the spin echo time.

Due to the limited SNR of the combined perfusion ASL signal, a good initial estimate of the decay rate constants is essential for a robust optimization procedure. The initial values for the decay rate constants of the intraneuronal and extraneuronal water components were estimated by fitting the simplified two-exponential decay model to the high SNR reference tissue MR signal (18).

RESULTS

R2* Attenuation of ASL Signal

In this study, the $T_2^{*}$ relaxation profile of the arterial spin labeling (ASL) water was measured under different labeling conditions using the introduced FAIR-GESSE pulse sequence. This allowed for the separation of the contributions based on different $T_2^{*}$ relaxation profiles from the labeled water in the intravascular, extraneuronal and intraneuronal compartments and the evaluation of trans-capillary and trans-membrane water transport processes providing insights on their time scales. Figure 2a shows a representative perfusion weighted image (acquired with slice selective inversion RF pulses), the corresponding high resolution Tl-weighted image, and a series of ASL water images acquired at different gradient echo times using FAIR-GESSE sequence with total inversion recovery time (TI) of 1800 ms and post saturation delay (TD) of 800 ms. By comparing image intensity at different gradient echo times, the $T_2^{*}$ attenuation behavior of the ASL signal in gray matter can be observed. Notice that relative to the ASL signal from most of gray matter areas, the ASL signal from large veins including sagittal sinus (the hyperintensity areas as shown in the Tl-weighted image) attenuated much more rapidly. This can be explained by the lower $T_2^{*}$ relaxation time constant of venous blood as compared to that of the tissue. A corresponding average apparent $T_2^{*}$ relaxation time constant of the venous blood in superior sagittal sinus from these studies was about 16 ms. In the same study, the $T_2^{*}$ characteristics of the arterial blood signal was also investigated from the pulsed arterial spin labeling images acquired with very short total labeling duration (TI = 600 ms, with QUIPPS II and background suppression mechanisms turned off) in regions with significantly higher ASL signal than the rest of gray matter area. The corresponding average apparent $T_2^{*}$ relaxation time constant of the labeled water in the arterial and arteriole side was about 92 ms.

FIG. 2.

Example of data demonstrating $T_2^{*}$ attenuation characteristics of arterial spin labeling (ASL) water MR signal obtained with FAIR-GESSE technique. a: High resolution T1-weighted image (T1W), perfusion weighted (PW) MR image (acquired with slice-selective inversion RF pulses) and the ASL images acquired at different gradient echo times are shown (numbers represent TE time in ms, the spin echo corresponds to TE = 0). The perfusion images were acquired with TI (total labeling duration) of 1800 ms and TD (postsaturation delay) of 800 ms (to saturate blood at the arteriole side of vasculature). b: The corresponding GESSE MR signal $T_2^{*}$ attenuation curves from gray matter at different gradient echo times; triangles represent averaged ASL signal and circles represent reference tissue signal (scaled to the same amplitude as ASL signal).

Figure 2b illustrates the corresponding GESSE $T_2^{*}$ signal attenuation curves at various gradient echo times for the reference tissue signal and the average ASL signal within the gray matter. The estimated apparent intrinsic $T_2^{*}$ relaxation time constants for gray matter tissue and ASL signal were found to be 49 and 64 ms, respectively. Therefore, the apparent $T_2^{*}$ value of the ASL signal is much longer than the $T_2^{*}$ of tissue, yet significantly shorter than the $T_2^{*}$ of the labeled water in arteries and arterioles.

Composition of ASL Signal

To investigate the composition of the ASL signal, we proposed and tested ASL models that included labeled water from intravascular and extravascular components as described by Eqs. 1–6 in the Methods section. An example of the fitting curves and the estimated contributions from individual ASL signal components is presented in Fig. 3a, using the model based on a single extravascular compartment. For this study, the estimated $T_2^{*}$ relaxation time constant for the extravascular labeled water was 85 ms; $T_2^{*}$ of the labeled water in capillaries was 80 ms with estimated blood oxygenation level of 83%. The proportions of labeled water in the extravascular and intravascular spaces were 78% and 22%, respectively. It is important to observe that while intrinsic $T_2^{*}$ relaxation time constants are similar for the intravascular and extravascular water compartments, the intravascular ASL signal decays much faster than the extravascular signal. This is because the blood vessel orientation-dependent dispersion of blood resonance frequencies (“powder distribution” effect) as described in Eq. 1. After averaging over six studies, each with different labeling time (Tl’s) and fixed TD of 800 ms, $T_2^{*}$ of the labeled water in the extravascular space was 87 ± 10 ms. For comparison, the $T_2^{*}$ of the tissue water signal (estimated from reference images) was much shorter, 50 ± 4 ms, suggesting that the extravascular ASL-labeled water does not reach equilibrium with extravascular tissue water and is mostly localized to the extracellular fluid space.

FIG. 3.

ASL signal obtained in a typical FAIR-GESSE ASL study (triangles) and estimated contributions from different tissue compartments obtained by fitting theoretical model in Eqs. 4–6 to experimental data (lines). The horizontal axis represents the gradient echo time from the position of spin echo (in ms). a: Labeled water in the extravascular space is described by a single extravascular compartment, Eq. 4. b: Labeled water in the extravascular space is described by two distinct compartments that can be attributed to the extraneuronal and intraneuronal spaces.

To test this hypothesis, we used a model that separates extravascular ASL-labeled water into two distinct compartments. The results of the estimated contributions from individual ASL signal components are presented in Fig. 3b. The estimated $T_2^{*}$ relaxation time constants for these components were 89 ms, and 61 ms, while the $T_2^{*}$ of the labeled water in capillaries was 78 ms with an estimated blood oxygenation level of 84%. This result suggests that the extravascular short $T_2^{*}$ component should be attributed to the intraneuronal space and the long $T_2^{*}$ component should be attributed to the extraneuronal space (Discussion). The proportions of the labeled water in the extraneuronal, intravascular and intraneuronal spaces were 59%, 24%, and 17%, respectively. Averaged over all studies, the $T_2^{*}$ relaxation time constants for the labeled water in the extraneuronal and the intraneuronal spaces were 100 ms ± 18 ms and 50 ms ± 6 ms, respectively. The average capillary blood oxygenation level was estimated as 83.0% ± 2.4%. The ASL signal fractions originated from intravascular, extraneuronal and intraneuronal spaces were 25% ± 6%, 65% ± 9%, and 11% ± 8%, respectively. The estimated signal contribution from the labeled water in the intraneuronal space was very small, with the standard deviation comparable to the mean value.

Dependency of ASL Water Composition on TI

In FAIR-GESSE studies with fixed post saturation delay TD (so that the tail of the labeling bolus within vasculature is fixed), increase in TI leads to increase in the length of the labeling bolus. Figure 4a displays typical ASL signal intensity evolution profiles from the same subject at varying TI (from 1.2 to 2.2 s) but with a fixed post saturation delay of 800 ms. For comparison, the $T_2^{*}$ attenuation curve for the tissue reference signal is also displayed in Fig. 4a. Although the amplitudes of the ASL signal vary, reflecting competing effects of signal T1 decay and duration of the labeling bolus, there is very little change in the shape of the $T_2^{*}$ attenuation profiles. This indicates small changes in the composition of the ASL signal in this experiment, which has been verified by fitting the proposed theoretical models to the ASL signal. Figure 4b shows ASL signal contributions at varying TI (data averaged over five subjects). Except for the data corresponding to TI of 1200 ms, which may contain a small amount of transit artifacts, the extravascular ASL signal fraction increased from 69 to 78% when TI increased from 1.4 to 2.0 s. Simulation results, based on Eq. A1 in the Appendix, with exchange rate constant λ of 1.54 s^–1 (cyan line, corresponding to capillary transit time of 1.5 s) and 0.96 s^_1 (green line, corresponding to capillary transit time of 2.4 s), are also plotted in Fig. 4b. If the data point corresponding to the measurement at TI of 1200 ms is ignored, the estimated average exchange rate constant is 1.39 s^–1, which corresponds to a mean capillary transit time of 1.65 s.

FIG. 4.

Composition of ASL-labeled signal. a: Open circles represent examples of the FAIR-GESSE ASL signal $T_2^{*}$ attenuation time courses from the same subject corresponding to different inversion times; filled circles represent tissue signal (scaled to fit amplitude of the ASL signals). b: FAIR-GESSE ASL signal fractions of the extravascular (red) and intravascular (brown) spaces at varying labeling durations (TI) with a fixed postlabeling saturation duration (TD) of 800 ms. Each filled circle in (b) represents data averaged across five subjects; error bars represent intersubject variability standard deviation. Broken cyan and green lines are simulated extravascular ASL signal fractions based on Eq. A1 in the Appendix. They are derived under the assumption that the extravascular and intracellular labeled water have the same longitudinal relaxation rate constant. The water exchange rate constant λ between intravascular and extravascular spaces in Eq. A1 is assumed to be 1.54 s^–1 and 0.96 s^–1 for cyan line and green line, respectively. Blue open circles and error bars represent the signal fraction from intraneuronal labeled water if extravascular space is divided into extraneuronal and intraneuronal spaces.

The contribution from the labeled intraneuronal water is also plotted in Fig. 4b (blue circles and lines). This was estimated by assuming two distinct compartments for the extravascular labeled water. The result demonstrates that the signal fraction from the intraneuronal labeled water is relatively small. Based on the simulation described in the Appendix, such low signal fraction of the labeled water in the intraneuronal space implies an apparent pre-exchange life time of intraneuronal water about several tens of seconds.

Dependence of ASL Water Composition on Postsaturation Delay (TD)

Similarly as implemented in QUIPSS II, periodic RF saturation pulses were used to control the shape and the length of the labeled blood bolus and eliminate vascular artifacts. Post saturation delay time (TD), which is the interval between the applying of the first saturation pulse and the beginning of the imaging block, controls the duration of the labeling bolus. Provided a fixed TI, the fraction of vascular (capillary) contribution is expected to decrease when the duration of TD increases. This is because the proportion of the fresh arrived labeled water into the capillaries would decrease. Figure 5a shows a representative ASL signal extravascular composition with a fixed TI of 2000 ms at varying TD from 800 to 1800 ms. The increase of extravascular ASL signal fraction is consistent with our prediction and the apparent $T_2^{*}$ of the ASL signal changes only slightly. Figure 5b illustrates the ASL signal composition variations that have been averaged for four different subjects. The simulation results, based on Eq. A1 with assumed exchange rate λ of 1.28 s^–1 (dashed line, corresponding to capillary transit time of 1.8 s) and 0.82 s^–1 (dash-dot line, corresponding to capillary transit time of 2.8 s), are overlapped on Fig. 5b. The estimated average oxygenation level for intravascular component decreased slightly from 83.4% ± 2.2% to 78.9% ± 3.2%. This is consistent with the concept that the labeled blood continuously loses oxygen as it passes through the capillary.

FIG. 5.

ASL signal composition changes for fixed labeling time TI of 2000 ms and varying post saturation duration (TD). a: Signal fraction of extravascular ASL labeled water from one study. b: Mean and standard deviation of ASL signal fraction of extravascular labeled water from four studies. Dashed line (upper) and dash-dot line (lower) are simulation results based on Eq. A1 with different capillary exchange rate (1.28 s^–1 for dashed line and 0.82 s^–1 for dash-dot line, respectively).

DISCUSSION

These results suggest that the ASL-labeled water does not reach equilibrium with the water within the tissue at the time scale of the ASL experiment (about 2 s). This effect cannot be explained as a diffusion limitation of water because the average time required for water molecule to diffuse across the Krogh cylinder (30) with the radius of 25 μm (average distance between capillaries in the brain is about 50 μm) is only about 150 ms. Hence, water movement in the brain tissue is limited by cellular membranes. Our analysis of the observed ASL signal reveals multiple water components with distinct $T_2^{*}$ values.

To assign these components to different tissue compartments, we may need to consider that brain neurons, astrocytes and glial cells uniquely influence water movement in different ways. Such differences became pronounced with the discovery of a family of water-specific, membrane-channel proteins — the aquaporins (AQP) (2,31–33). It was found that aquaporin-4 (AQP4), while distributed throughout the brain, resides predominantly in the plasma membrane of astrocytes, concentrating in perivascular and subpial astrocytic endfoot processes (2,31–33). While only a very small subset of neurons has been shown to possibly express AQP9, there is a general consensus that neuronal cells do not express aquaporins (34).

Aquaporins are known to dramatically facilitate water exchange across membranes (35,36) and can alter water diffusion in the brain. In a study of primary astrocyte cultures from AQP-4 deficient mice (37) a sevenfold decrease of osmotic water permeability has been reported, which is consistent with the observation that the passive water permeability of a neuron exposed to an osmotic gradient is exceptionally low. Based on existing knowledge and the in vivo measurements in the human brain of specific $T_2^{*}$ properties of ASL-labeled water signal, ASL-labeled water can be assigned into three distinct components: intravascular; extraneuronal (dynamically-mixed extracellular and astrocytic); and intraneuronal.

The smallest component (about 20 to 30%) can be identified as intravascular. Its $T_2^{*}$ profile in qBOLD signal displays a characteristic pattern for the MR signal originated from randomly oriented capillaries (the so called powder distribution pattern (26).

The component with long $T_2^{*}$ values, 100 ± 18 ms, may be attributed to the dynamically-mixed extracellular/intraglia water. The $T_2^{*}$ value of about 100 ms is much smaller than the value of bulk CSF (several hundred ms at 3T) (14). It is very close to the estimated $T_2^{*}$ value of 130 ms for the mixed water pool (unmyelinated axon, glia and extracellular water) within WM tissue (38). Conversely, this $T_2^{*}$ value is much longer than the equilibrium tissue water $T_2^{*}$ of 50 ms which is mainly defined by the intracellular water relaxation. In addition to the reduction of $\text{T}2/T_2^{*}$ due to possible interaction between extracellular water and cellular membrane, to assign this signal, we speculate that we also need to consider the facilitated water exchange through the aquaporins expressed mainly in the astrocytes perivascular and subpial end-feet processes. We speculate that the long $T_2^{*}$ component of ASL labeled water signal can be naturally attributed to a dynamic mixture of extracellular water with intra-astrocyte water located near AQP-4 water channels. The fast exchange between these two compartments substantially reduces the $T_2^{*}$ of the extracellular water.

The rest of the extravascular water signal has a short $T_2^{*}$, 50 ms ± 6 ms, and can be assigned to the intraneuronal space: neuron cell bodies and their processes – axons, dendrites, spines, plus oligodendrocytes and microglia. These cells have a much slower exchange rate with ASL water in the extracellular (interstitial) space due to the lack of aquaporin expressions in their membranes. This part of the water signal (occupying about 80% of tissue water volume) should have a $T_2^{*}$ about the same as a global tissue $T_2^{*}$. Our results show that the ASL signal fraction from this intraneuronal space is very small (11% ± 8%).

Although an exact estimation of the transmembrane water exchange time constant is not possible from this study due to the intrinsic T1 decay of the perfusion water signal (T1 of blood and tissue water is less than 2 s at 3T), the simulations in the Appendix demonstrate that the apparent pre-exchange life-time of the intracellular water is in the range of several tens of seconds. This finding is entirely consistent with the conclusions of PET tracer kinetic studies using ¹⁵O-water by Larson et al. and Kassissia et al. (3,4) that found an apparent intracellular water pre-exchange life time of several tens of seconds. Their estimated permeability surface product (PS) for parenchyma cell membranes was about one third to one fourth of the permeability surface product of the capillary.

While our results for the water pre-exchange life time are consistent with the PET tracer kinetic studies discussed, they are not consistent with other approaches and studies. For example, the estimates obtained from the dynamic contrast-enhanced MRI (5,6,39) approaches and equilibrium contrast-enhanced exchanged studies (40,41) were much smaller. The exact reasons for these differences are unknown. Allow us to note that in the above mentioned experiments, a paramagnetic contrast agent was present (absent in our study) which remains in the extracellular space. This can substantially and differentially modify relaxation properties of intraneuronal water and intracellular water in the astrocytes that exchange with extracellular water through aquaporins. This effect was not taken into account (5,6,39,40). The distribution of the labeled water estimated from this $T_2^{*}$ pulsed arterial spin labeling study is also different than the result from the recent T2 based continuous ASL (CASL) (42) and pseudo continuous ASL (pCASL) (43) studies. We posit that such discrepancy is mainly due to possible contamination from arteriole side (for short post labeling decay) and venule side [as total labeling time as long as 3.6 s approaches the mean cerebral vascular transit time of 2.8–3.0 s (25)].

Existing literature on in vivo brain tissue water compartmental structure and water exchange processes has not always been conclusive. While some studies suggested that the T1/T2 relaxation of GM may be sufficiently described by a single water component (44), there are also T2 based techniques observed the existence of multiple tissue water compartments with distinctive T1/T2 values (45,46). The $T_2^{*}$ profile of MR signal decay offers additional sensitivity for the separation of different tissue water compartments. The recently developed MRI-based qBOLD technique (18) demonstrated that not only $T_2^{*}$ of the water MR signal in the extracellular (interstitial) space is significantly different from the $T_2^{*}$ of the intracellular water, but the frequencies of these two compartments are also different. The results from this study further demonstrated the existence of multiple water compartments within brain gray matter.

Fitting a model which includes multiple exponential decaying processes is notoriously unstable, especially when the resulting decay rates are relatively close. Due to the limited SNR of perfusion MR signal, we did not notice a statistically significant difference in the fitting quality comparing two- and three- compartment perfusion signal models. The estimated signal fraction corresponding to the intraneuronal perfusion signal would be unstable if no restrictions on the decay rates for the corresponding water compartment were applied. However, because these decay rates are specific to the tissue water compartments, their values can be estimated independently and reliably from a separate experiment with sufficient high SNR, (i.e., the reference scan for tissue signal with GM ROI). Although an exact estimation of intraneuronal signal fraction cannot be determined accurately due to low SNR and its low fraction, a qualitative estimate of the intra- and extraneuronal water exchange time can still be reliably estimated.

CONCLUSION

In this study, ASL-labeled water in arterial blood was used to probe the dynamics of the trans-capillary and trans-membrane water exchange in normal human brain. A hybrid ASL-qBOLD approach was utilized to characterize the compartmental structure of the ASL labeled water signal based on its transverse relaxation $\left(T_2^{*}\right)$ properties. A multicompartment structure, corresponding to the labeled water in the intravascular, extraneuronal (extracellular and intra-astrocyte) and intraneuronal spaces, can be resolved. Our results demonstrated water entering brain tissue is distributed between intravascular and extravascular space where it primarily remains in the extraneuronal space. Most importantly, the fraction of labeled water entering intraneuronal space is relatively small, indicating that the dynamic transmembrane water transport process is slow. The apparent lifetime of the intraneuronal water is about several tens of seconds. Such observations are of practical importance for any method using labeled water as a tracer, as well as for better understanding of the cell biology of the human brain.

APPENDIX.

Intra- and Extra-Vascular ASL Water Distribution and Capillary Water Permeability

To relate the total extravascular ASL-labeled signal fraction obtained from our experiments to the water permeability of capillary walls, we used the following equation that can be obtained based on the similar approach as adopted in (47):

$$\frac{S_{ev}}{S_{ev}+S_c}=\frac{\frac{\lambda }{\Delta R_1}\left(e^{-\Delta R_1\cdot TD}-e^{-\Delta R_1\cdot (TI-ta)}\right)-\left(e^{-\lambda \cdot TD}-e^{-\lambda \cdot (TI-ta)}\right)}{\frac{\lambda }{\Delta R_1}\left(e^{-\Delta R_1\cdot TD}-e^{-\Delta R_1\cdot (TI-ta)}\right)-\frac{\Delta R_1}{\lambda }\left(e^{-\lambda \cdot TD}-e^{-\lambda \cdot (TI-ta)}\right)}.$$ (A1)

Here t_a is the arterial transit time (time required for the labeled blood in labeling region to pass through arteries/arterioles and reach capillary bed at the imaging volume); TI is the total labeling time (duration between the inversion and the excitation RF pulse within the imaging block); TD is the time interval between the applying of saturation RF pulses and the beginning of the imaging block (post saturation delay – see details in the Methods section). The Eq. A1 is derived under the assumption that the relative difference between the R₁ decay rate constants of the extra- and intravascular compartments (ΔR₁) is much smaller than the transcapillary exchange rate constant λ. Also note that λ, the capillary transit time (CTT, the average time for blood passing through the capillary), and the water extraction fraction during a single capillary passage (E) are correlated by a relationship $E=1-e^{-\lambda }{}^{CTT}$.

Tracer Kinetic Model

For a three component model of ASL-labeled water in capillaries, extraneuronal and intraneuronal spaces, the rate of water exchange can be described by the following set of equations:

$$\begin{array}{l}{\dot{M}}_1=-K_{12}{M}_1+K_{21}{M}_2+f(t)\\ {\dot{M}}_2=K_{12}{M}_1-K_{21}{M}_2-K_{23}{M}_2+K_{32}{M}_3\\ {\dot{M}}_3=K_{23}{M}_2-K_{32}{M}_3,\end{array}$$ [A2]

where M₁, M₂, M₃ represents the magnetization of labeled water in capillaries, extraneuronal and intraneuronal compartments with volumes of V₁, V₂, V₃ (in units of mL/100 g of brain tissue), respectively; f is the perfusion rate of the labeled blood in units of mL/s/100 g. Parameter K’s are introduced to characterize the exchange of water between compartments as follows:

$$K_{12}=P{S}^{cap}/V_1,K_{21}=P{S}^{cap}/V_2,K_{23}=P{S}^{cell}/V_2,K_{32}=P{S}^{cell}/V_3.$$ (A3)

where PS^cap and PS^cell are the permeability surface product of the capillary and neuronal cell membranes (in units of mL/s/100 g of brain tissue), respectively. Here we assume that the inflow of labeled blood is fully inverted; we also neglect the outflow of labeled water during a 2-s ASL experiment (14). The influence of T1 relaxation on our results is also ignored.

Solutions to Eq. A2 are presented in Fig. A1 for different sets of model parameters. With intracellular water pre-exchange lifetime of 1 s (5), using PS^cap of 2.12 mL/s/100 g (48), Fig. A1a predicts that at 1.5 to 2 s after labeling, the amount of labeled water in the intraneuronal space would be about two to three times than that of in the extraneuronal space, which is not consistent with our experimental findings. Simulation results based on the intraneuroanl water pre-exchange life time of 29 s (4) are illustrated in Fig. A1b. PS^cap is 7.89 mL/s/100 g andPS^cell is 2.83 mL/s/100 g. This result indicates that about 10% of the labeled water resides within the intraneuronal space. Similarly, the simulation results based on the intraneuronal water pre-exchange life time of 85 s (3) are presented in Fig. A1c. PS^cap is 2.93 mL/s/100 g and PS^ceIl is 0.87 mL/s/100 g. This result suggests that less than 5% of the labeled water resides within the intraneuronal space.

FIG. A1.

Simulation results of the relative distribution of labeled water from different water components under different tracer kinetic parameters. a: Intraneuronal water pre-exchange lifetime of 1 s (5); (b) Intraneuronal water pre-exchange life time of 29 s (4); (c) Intraneuronal water pre-exchange life time of 85 s (3). In all simulations we assume V₁ = 1.0 mL/100 g, V₂ = 18 mL/100 g, V₃ = 81 mL/100 g (40), and normal flow rate of 1 mL/s/100 g.