T2-based Arterial Spin Labeling measurements of blood to tissue water transfer in human brain

Abstract

Purpose

To investigate blood to tissue water transfer in human brain, in vivo and spatially resolved using a T2-based arterial spin labeling (ASL) method with 3D readout.

Materials and Methods

A T2-ASL method is introduced to measure the water transfer processes between arterial blood and brain tissue based on a 3D-GRASE pulsed ASL sequence with multi-echo readout. An analytical mathematical model is derived based on the General Kinetic Model, including blood- and tissue compartment, T1 and T2 relaxation and a blood-to-tissue transfer term. Data has been collected from healthy volunteers on a 3 Tesla system. The mean transfer time parameter T_bl→ex (blood- to extravascular compartment transfer time) has been derived voxel-wise by non-linear least-squares fitting.

Results

Whole-brain maps of T_bl→ex show stable results in cortical regions, yielding different values depending on brain region. The mean value across subjects and ROIs in grey matter is 440±30 ms.

Conclusion

A novel method to derive whole-brain maps of blood to tissue water transfer dynamics is demonstrated. It is promising for the investigation of underlying physiological mechanisms and development of diagnostic applications in cerebro-vascular diseases.

INTRODUCTION

Arterial Spin Labeling (ASL) is a non-invasive MR imaging technique to measure cerebral perfusion (f) by using blood water molecules as intrinsic tracers [1]. ASL is easy to apply together with conventional MRI scans, easy to repeat for serial measurements, and also offers the possibility of absolute perfusion quantification. Because of these benefits, the technique has gained considerable interest as alternative to other tracer based techniques for perfusion measurements, such as PET and SPECT, which rely on radioactive labels or contrast enhanced MRI, which requires injection of a paramagnetic contrast agent. Over the years, ASL has been used in a wide range of applications, including measurements of bolus arrival time [2, 3] and blood volume [4], brain activation in functional MRI [5], vascular territory imaging in regional ASL experiments [6–8] and for studies of coupling between cerebral blood flow and oxygen consumption [9]. Among the unique features of ASL imaging is the possibility to measure the dynamics of the blood water labels with unprecedented temporal resolution. For instance, to determine regional variations in bolus arrival times, ASL MRI is repeated with different inflow times TI, yielding a map of inflow curves sampled at discrete time steps. The shape of an inflow curve in ASL can be modeled on the basis of physiological parameters, such as perfusion, bolus arrival time and characteristic relaxation times of the spin labels [10].

Another interesting challenge is to measure the exchange dynamics between blood and tissue using ASL, which depends on capillary permeability and can be expressed as transfer time. Two-compartment models including an exchange term have been presented and the influence of water transfer to tissue on ASL quantification has been discussed [11, 12], also including T2 relaxation [13], and presenting approaches to measure capillary permeability [14, 15]. Those studies underline the importance of proper knowledge of the transfer dynamics for perfusion quantification. In practice, however, this is not a known property and the power of ASL to measure the transfer time has been questioned [16], mainly based on grounds of limited SNR. Specifically, it has been argued that an increase in SNR of at least two orders of magnitudes would be required to reliable measure permeability. The problem of SNR in ASL is amplified for because the signal, which is governed by T1 relaxation in conventional ASL, is substantially diminished due to T1 decay at later time steps. Another limiting factor is that the acquired ASL signal contains a convolution with the inflow function along TI. This results in loss of information about the instantaneous physiological processes, complicating a distinction between permeability and inflow effects.

An alternative approach to measure the transfer dynamics (and which will be described in the current work) is to harness variations in the T2 relaxation of the ASL signal as TI increases. An earlier implementation of the method has been presented in [17]. T2 relaxation is ideal for permeability quantification because this parameter differs significantly between blood and tissue. As a further advantage, the convolution of the T2-ASL signal by other physiological processes occurs only for a short period defined by the spin-echo time TE when the transverse magnetization of the ASL signal is subject to T2 decay. Since TE is typically much shorter than TI in ASL experiments, T2 is less prone to inflow effects. Changes in T2 over TI will largely reflect processes on the arterial side of the vascular tree because of a common capillary transit time of several seconds [14]. The TI-dependence of T2 has been used in recent publications to investigate the ASL signal origin in gerbils [18] and in the human brain [19]. These publications used 2D-EPI readout techniques and did not provide spatially resolved maps of blood-to-tissue transfer parameters.

In the cerebral microvascular system, capillaries are enclosed by endothelial cells, linked to each other by tight junctions, thus forming the blood-brain barrier which constrains the delivery of molecules to the parenchyma. While hydrophilic substances generally require an active process to cross the lipid walls of the endothelial cells, water molecules are believed to cross the blood-brain barrier passively due to their small size via diffusion. In conventional ASL models, an instantaneous transfer is assumed. In the two or multiple compartments mentioned above, a restricted water transfer is postulated, which depends on capillary wall permeability. Many cerebro-vascular diseases are known to disrupt the blood-brain-barrier, like in multiple sclerosis, tumors, and stroke. This is revealed by measurements with intravascular contrast agent, which do not cross the intact blood-brain barrier but accumulate in tissue surrounding the affected vessels. A technique to reliably measure the exchange dynamics non-invasively may have substantial impact on diagnosis and outcome prediction of the considered diseases.

In this work, a two compartment ASL model is derived by extending the General Kinetic Model (GKM) [10] for T2 decay. T1 and T2 decays are different in both compartments (Fig. 1), while the exchange dynamics are characterized by the parameter T_bl→ex (transfer time). Data has been acquired from healthy volunteers using a single-shot 3D-GRASE readout with FAIR pulsed ASL-preparation on a 3 Tesla imaging system (Trio, Siemens). Resulting whole-brain maps of transfer time are shown, demonstrating water exchange dynamics in human brain, spatially resolved by single voxel fits.

Fig. 1.

Schematic diagram of a voxel containing perfused tissue; There are two compartments, a blood (considered purely capillary), and an extravascular (tissue) compartment, distinguished by different relaxation constants.

THEORY

Two-compartment model and T1 relaxation

In two compartment models, the ASL signal can originate from a vascular (i.e. blood) and an extravascular compartment (tissue), characterized by different relaxation times of the spin labels (schematically shown in Fig. 1). Accordingly, the overall signal can be split into a vascular (blood) S_bl(t) and an extravascular S_ex(t) component:

$$S(t)=S_{bl}(t)+S_{ex}(t)$$ [1]

In the GKM, the components are calculated forming the convolution over the input function c(t) with a residue function, generally modeling signal loss.

$$\begin{gathered} S_{bl}(t)=2·M_{a,0}·f·\underset{0}{\overset{t}{\int }}c(t^{\prime })·r_{bl\to ex}(t-t^{\prime }) \\ ·m_{bl}(t-t^{\prime })·r_{bl,\mathit{out}}(t-t^{\prime }){dt}^{\prime } \end{gathered}$$ [2]

$$\begin{gathered} S_{ex}(t)=2·M_{a,0}·f·\underset{0}{\overset{t}{\int }}c(t^{\prime })·(1-r_{bl\to ex}(t-t^{\prime })) \\ ·m_{ex}(t-t^{\prime })·r_{ex,\mathit{out}}(t-t^{\prime }){dt}^{\prime } \end{gathered}$$ [3]

with perfusion f, arterial longitudinal equilibrium magnetization M_a,0, blood to tissue transfer function r_bl→ex, magnetization relaxation functions m, and outflow functions r_out. In Equ. [3], the inflow to the extravascular compartment is governed by the outflow from the blood compartment, yielding the term (1 − r_bl→ex).

The bolus arrival time τ defines the arrival of labeled blood in the voxel. Since labeled blood water can reach the voxel only via the vasculature, at t = τ the first labeled water molecules reach the vascular compartment of the voxel. For t > τ, as blood fills the capillary bed, a labeled water molecule may diffuse from vascular space across the blood-brain barrier into the extravascular space. In the case of pulsed ASL, where blood arrives in the voxel at time τ and the bolus is saturated by Q2TIPS after bolus length BL, the inflow function is given by

$$c(t)=\{\begin{array}{l}0\hfill \\ \alpha ·e^{-t·R{1}_{bl}}\hfill \\ 0\hfill \end{array}\text{for}\{\begin{array}{l}t<\tau \hfill \\ \tau <t<{\tau }_2\hfill \\ t>{\tau }_2\hfill \end{array}$$ [4]

with

• α: Labeling efficiency

• R1_bl: Longitudinal blood relaxation rate

• τ: Bolus arrival time

• τ₂ = τ + BL : Bolus cutuff

• BL: Bolus length

This corresponds to a block input function without dispersion while blood is prone to T1 decay.

Assuming a time invariant probability for the diffusion process and an instantaneous homogeneous distribution of water within each compartment, the residue function governing the water transfer can be modeled as

$$r_{bl\to ex}(t)=exp(-t/T_{bl\to ex})$$ [5]

T_bl→ex is the characteristic transfer time after which the probability for a labeled water molecule to remain in the vascular compartment has reached 1/e. The associated transfer rate is R_bl→ex=1/T_bl→ex.

The residue functions for T1 relaxation in the compartments are

$$\begin{array}{l}{m}_{bl}(t)=e^{-t·R{1}_{bl}}\\ m_{ex}(t)=e^{-t·R{1}_{ex}}\end{array}$$ [6a,b]

With R1_ex: Longitudinal extravascular relaxation rate

Neglecting outflow, the outflow functions in [A2] and [A3] are

$$r_{bl,\mathit{out}}(t)\equiv r_{ex,\mathit{out}}(t)\equiv 1$$ [7]

The chosen residue functions reflect two simplifying assumptions: First, the outflow of labeled water from the voxel is neglected (Equ. [7]). This assumption can be justified by microvascular dynamics. It takes several seconds for blood to pass the microvasculature (17). Second, backflow from extravascular to blood compartment can be neglected. This is a reasonable assumption if the extravascular compartment and blood compartment volumes (V_ex and V_bl) fulfill V_ex≫V_bl and additionally λ/f≫TI (λ: blood–brain partition coefficient). The first relation guarantees that the larger amount of the considered free water (which contributes to λ) belongs to the extravascular compartment. The second relation ensures that within the chosen inflow times, only a small percentage of the total amount of free water molecules in the voxel is replaced by labeled inflowing water molecules. Common literature values for V_bl/V_ex range between 0.02 and 0.06 (17) which fulfils the first relation. With common values f=90ml/100g/min and λ=0.9, the ratio λ/f is 60 s. This justifies neglecting outflow and backflow effects when considering inflow times of several (<5) seconds. All above considerations rely on the assumption of pure tissue/capillary voxel.

The characteristic shapes of inflow curves in a two compartment model are shown in Fig. 2. While the blood compartment signal rises fast as water labels reach the image voxel, the rise of the extravascular signal lags behind because the transfer rate of water molecules to reach the extravascular compartment is limited. With increasing time (i.e. longer TI), the extravascular curve becomes increasingly dominant, as more water reaches the extravascular space, but simultaneously the ASL signal diminishes with the characteristic T1 relaxation rate of each compartment toward thermal equilibrium.

Fig. 2.

Theoretical inflow curves showing blood component S_bl, extravascular component S_ex and total signal from voxel S. The plots are calculated with parameters f=87.5 ml/100g/min, τ=600 ms, BL=1000 ms, T2_bl=1500 ms, T1_ex=1100 ms and T_bl→ex =300 ms.

Two-compartment model and T2 relaxation

When a 90°-RF excitation pulse is applied after inflow time TI, the magnetization M_TI of the spin labels is tipped into the transverse plane and the signal intensity is governed by the transverse relaxation rate R2=1/T2. Using a refocused spin-echo sequence, the signal under the readout imaging gradient can be partially recovered at echo time TE, where the static signal is reduced to M_TI·exp(−TE/T2). In addition, labeled blood from an adjacent voxel may enter the target voxel during TI < t < TI+TE, contaminating the original signal of the voxel, thereby increasing the signal intensity. Transverse relaxation and inflow from TI until TI+TE can be included in the model using the GKM formalism as follows:

$$S{2}_{bl,TI}(te)=2·M_{a,0}·f·\underset{0}{\overset{te}{\int }}c{2}_{TI}(t^{\prime })·r_{bl\to ex}(te-t^{\prime })·m{2}_{bl}(te-t^{\prime })·r_{bl,\mathit{out}}(t-t^{\prime }){dt}^{\prime }$$ [8]

$$S{2}_{ex,TI}(te)=2·M_{a,0}·f·\underset{0}{\overset{te}{\int }}c{2}_{TI}(t^{\prime })·(1-r_{bl\to ex}(te-t^{\prime }))·m{2}_{ex}(te-t^{\prime })·r_{ex,\mathit{out}}(t-t^{\prime }){dt}^{\prime }+S_{ex,TI}·m{2}_{ex}(te)$$ [9]

A new temporal variable te (defined by t=TI+te, thus te=0 corresponds to TI) and an index “2” in the characteristic terms are chosen to clearly distinguish from Equ. [2,3]. It is possible that at TI, labeled water has already arrived in the extravascular compartment which simply decays with R2_ex. This term is added in Equ. [9] after the convolution.

The inflow function now depends on the specific TI.:

$$\begin{array}{c}c{2}_{TI}(te)=\{\begin{array}{l}0\hfill \\ \alpha ·e^{-TI·R{1}_{bl}}·e^{-te·R{2}_{bl}}+\delta (0-te)·S_{bl}(TI)/(2·M_{a,0}·f)\hfill \\ 0\hfill \end{array}\\ \text{for}\{\begin{array}{l}te<max(\tau -TI,0)\hfill \\ max(\tau -TI,0)\le te<{\tau }_2-TI\hfill \\ te\ge {\tau }_2-TI\hfill \end{array}\end{array}$$ [10]

$$\begin{array}{l}m{2}_{bl}(te)=e^{-te·R{2}_{bl}}\\ m{2}_{ex}(te)=e^{-te·R{2}_{ex}}\end{array}$$ [11a,b]

$$r_{bl,\mathit{out}}\equiv r_{ex,\mathit{out}}\equiv 1$$ [12]

In the analytical model, the discrete inflow and echo times are replaced by continuous variables ti and te. In this context, the inflow curve becomes a two-dimensional function of ti and te:

$$S(ti,te)=S_{bl}(ti,te)+S_{ex}(ti,te)$$ [13]

The analytic result of S(ti, te) is shown in the appendix. Characteristic two-dimensional inflow curves are shown in Fig. 3. Since the parameters are the same as in figure 2, the same signal curves along ti arise for te=0 but as te increases, while relaxation differences can be seen along te for the two compartments.

Fig. 3.

Two-dimensional plots showing blood component, extra-vascular component and total signal. Signal decay due to T2 along the te axis differs significantly between extravascular and blood components. Parameters are f=87.5 ml/100g/min, τ=600 ms, BL=1000 ms, T1_bl=1500 ms, T1_ex=1100 ms, T2_bl=165 ms, T2_ex=50 ms and T_bl→ex =300 ms.

In the above formulae, the phenomenological exchange term r_bl→ex(t) and the corresponding characteristic time constant T_bl→ex. have been introduced to describe in statistical terms the average time it takes labeled blood water to diffuse from the vascular to the extravascular compartment. In addition to diffusion, the transfer rate of labeled water also depends on physiological factors, such as the partial capillary volume fraction V_c and permeability surface PS. For voxel with pure capillary blood (cf. [11, 14]):

$$r_{bl\to ex}(t)=exp(-(PS/V_c)·t)$$ [14]

In addition to capillaries, small vessels are present in the voxel where no exchange occurs. As pointed out in [12], V_c only accounts for one third of the microvasculature, but in earlier studies [20, 21] using PET, the total microvascular blood volume was used to calculate PS. This leads to an “average PS” over arterioles, capillaries and venules.

METHODS

ASL preparation and readout

A pulsed ASL sequence was used with a FAIR labeling scheme [5, 22]. Post-labeling saturation of the readout slab was applied to prepare the readout region equally for non-selective and slice-selective acquisitions and to suppress magnetization transfer effects. Background suppression pulses were applied to ensure stationary signal nulling at readout. Q2TIPS [23, 24] saturation was used to define a fixed bolus length. A 3D-GRASE sequence was used for readout. Centric reordering ensured to sample the center partition with k_z=0 at echo time TE after the first refocusing pulse. The basic sequence containing ASL preparation and 3D-GRASE readout has been presented in detail in [25].

The readout was extended to acquire several echo times (Fig. 4). Using an EPI-like planar readout for each partition, the center of k-space is acquired between the first two refocusing pulses, on the first spin echo. This corresponds to the echo time TE₁ in Fig 4, where the center of partition “P1” is acquired.

Fig. 4.

Readout scheme of the modified 3D-GRASE for T2 measurements; To acquire different echo times TE, the readout blocks are shifted to later TE after the 90° preparation pulse in separate measurements.

For an acquisition with longer echo time TE₂, the first refocusing pulse of the GRASE readout is applied at a later time TE₂/2, with a fixed flip angle of 180°. The first spin echo then appears at TE₂, and the first k-space partition of the second echo time can be acquired. The subsequent partitions are encoded and acquired without change.

As in GRASE, the readout of a single TE is sampled in one shot. For each spin echo between two refocusing pulses, one partition is sampled using an EPI readout. For each TE, the ASL measurement is repeated. To ensure that stimulated echoes coincide with later spin echoes, the echo times acquired are odd integers of TE1, i.e. TE₁, 3·TE₁, 5·TE₁ etc., as shown in Fig. 4. An earlier implementation has been presented in [26].

Measurement protocol

All measurements were performed using a clinical MR scanner (Trio, Siemens, Erlangen, Germany; field strength 3 Tesla). The acquisition protocol was composed of an ASL sequence and a clinical T1 weighted anatomical gradient echo sequence for segmentation and registration. A 32 channel head coil was used for signal detection. The ASL GRASE readout allowed the single-shot acquisition of 26 partitions of 4 mm thickness (partial Fourier factor 6/8) and a matrix size of 128×56 with 3 mm resolution inplane (6 mm interpolated, FoV: 38.4 × 16.8 cm²). 20 different TI were acquired, ranging from 150 to 3000 ms with a TI increment of 150 ms, using pulse triggering to minimize physiological noise. The protocol was optimized to allow variable averaging, i.e. averages ranged from two on early time steps to five on late time steps. Three different TE of 16.5, 49.4 and 82.3 ms were acquired. The blood bolus length, as defined by Q2TIPS pulses, was 900 ms. Repetition time was 3800 ms, nominal measurement time 22 min. Pulse triggering increased the actual measurement time to about 25 min.

Five healthy volunteers between 24 and 36 years old were scanned. The volunteers were asked to lie still inside the magnet. Heads were cushioned with foam plastics to reduce head motion. The study was conducted in compliance with local ethics standards for human research, including written informed consent.

Data Processing

Standard motion correction of non-selective and slice-selective images using a 6 degrees of freedom (DOF) affine registration (translation and rotation) was not beneficial in most cases because of changing image contrast and perfusion weighting over TI. Motion correction was therefore only applied in one case of substantial head motion. The non-selective and slice-selective datasets were then subtracted to yield difference images. No smoothing was applied to maintain the initial frequency range of the ASL signal evolution and to keep partial volume effects minimal. Whole-brain masks and gray and white matter probability maps were created to mask the voxels of interest before postprocessing. Corresponding anatomical and ASL datasets of each subject were realigned using 7 DOF affine transformations available in SPM5. The two-dimensional model of Eq. [13] was then applied to fit the ASL curves in each voxel within the whole-brain mask using least-squares optimization routines from Minuit [27]. The fitting routine minimized the chi-square based on linear least-squares and the single-voxel noise and yielded error estimates for each parameter.

To allow for local deviations of T1_ex and T2_ex depending on tissue type, partial volume and susceptibility effects, T1_ex and T2_ex were included for fitting within close limits representing grey and white matter liteature values [28, 29]. To improve fit stability, the tissue values were fitted separately first, at the three largest TI to ensure that the ASL signal originates predominantly from brain tissue. In the second step, the initial values of T1_ex and T2_ex were fixed to the first step fitting results, and the physiological parameters perfusion, bolus arrival time and transfer time were estimated. The fitting errors on parameters T1_ex and T2_ex were passed to the second step fit to guarantee correct propagation of single voxel error. T2_bl and T1_bl were fixed to literature values 165 ms [30] and 1550 ms [31]. For perfusion calibration, the density of labeled blood water α·M_0,a was approximated based on the maximum signal intensity in difference images at short TI that depicted presumably a voxel completely filled with arterial blood. The mean value of α·M_0,a from all subjects was used. This allowed the estimation of absolute perfusion values in units [ml/100g/min] without affecting the other parameters. Fitting parameters, starting values and curve fitting constraints are listed in Tab. 1.

Tab. 1.

Starting values and limits of the T2-ASL parameter fit.

Parameter	Units	Description	Starting value	Lower limit	Upper limit
f	ml/100g/min	Perfusion	125	0	500
τ	ms	Bolus arrival time	400	0	1500
Tbl→ex	ms	Transfer time	500	0	1200
T2ex	ms	Extravascular T2	80	40	100
T1ex	ms	Extravascular T1	1000	800	1200
BL	ms	Bolus length	900	fixed
T2bl	ms	Blood T2	165	fixed
T1bl	ms	Blood T1	1550	fixed
α·M0,a	a.u.	Arterial equ. magn.	0.0021	fixed

RESULTS

Fig. 5 shows one slice of a T2-ASL dataset with different TI and TE before processing (no masking applied). Inflow and T1 relaxation occurs along axis ti, T2 relaxation along axis te. The fitting curves from two typical voxel (frontal and occipital lobe) are shown in Fig. 6. Fitting results are listed along with standard errors on the single-voxel fit. The T1_ex values in the shown voxel returned were 1200 ms. This was the upper limit (corresponding to pure grey matter tissue) and is therefore given without errors. T2_ex additionally allowed compensation of local susceptibility differences and could be fitted reliably with fitting errors between 10 and 20%.

Fig. 5.

ASL difference image dataset (images skipped in ti direction); Along the ti axis, the inflow of blood can be seen first in areas around large vessels (e.g. MCA). At later ti the signal diffuses and is assumed to come predominantly from tissue. T2 relaxation occurs along te.

Fig. 6.

Data and fit from typical gray matter voxel (frontal and occipital lobe). Resulting parameters are given with standard fitting errors. Fixed parameters were chosen according to table 1. Fit parameter results are listed on the right.

In Fig. 7, the resulting maps from one representative subject are shown for the fitted parameters and for four slices. The fitting routine performed reliably in larger cortical areas, where the T_bl→ex maps show stable results with single voxel errors below 20%..

Fig. 7.

Parameter maps and corresponding anatomical images from one subject in four selected slices. The T_bl→ex map shows stable results for larger cortical regions. Perfusion and bolus arrival time maps are stable on gray and white matter and are comparable with state of the art ASL images. Selected ROIs: GM_L, GM_R (left and right lateral grey matter), OC (occipital lobe) and MSC (margo superior cerebri).

For ROI evaluation, masks have been created based on the grey matter probability masks. Only voxel with p(GM)>0.66 were included. To exclude outliers, only voxel with stable fit and therefore reliable T_bl→ex values were included, verified by a T_bl→ex error < 20%. On all dataset, ROIs were selected in the left and right lateral frontal lobes (ROI GM_R and GM_L), the occipital lobe (OC), and the areas of the paracentral lobule and superior frontal gyrus (margo superior cerebri, MSC). In Fig. 7, hand-drawn template ROIs are shown for one subject, which were automatically refined based on grey matter and error values. Fitted T_bl→ex values in white matter regions typically showed errors >100% and were therefore not considered for evaluation.

The results are listed in Tab. 2. Mean values of the ROIs are given, the errors represent calculated confidence intervals (p=95%) based on the standard deviations within each ROI (which exceeded the mean standard fitting error in all cases). The weighted average value across ROIs and subjects for grey matter is 440 ms, with a derived outer error of 30 ms.

Tab. 2.

Mean T_bl→ex values in [ms] for subject (S1..S5) and ROIs with 95% confidence intervals calculated from the statistical distribution within each ROI. Weighted average values are given with outer errors based on the confidence intervals.

ROI	Age	GM_R	GM_L	OC	MSC	GM
Subj....
S1	22 f	399 ± 27	393 ± 22	433 ± 90	576 ± 36	429± 40
S2	30 f	358± 49	514± 55	541± 44	633± 72	496± 66
S3	29 m	517± 61	790± 150	884± 119	580± 59	601± 120
S4	26 f	297± 45	325± 56	510± 96	641± 64	396± 82
S5	38 m	256± 39	267± 56	453± 153	734± 69	347± 114
AVG	29	359± 37	392± 39	545± 54	612± 26	438± 29

DISCUSSION

Summary

We introduced a novel T2-based ASL approach and demonstrated feasibility to assess the temporal dynamics of water transfer between the vasculature and the brain. A two compartment model was developed, including different transverse relaxation rates. The proposed method yielded whole-brain maps of transfer time for several healthy subjects. The transfer time could be measured on a single-voxel basis with standard deviation below 20% in cortical regions.

To the best of our knowledge, this ASL study is the first to derive parametric maps of the temporal exchange dynamics of labeled blood water via T2 relaxation on the human brain. Previous dynamic ASL studies predominantly relied on T1 relaxation. T2-ASL is not compromised by the limitations outlined in [16] that led to the conclusion ASL has limited power to derive permeability unless SNR of ASL increases dramatically. Recently published T2-based ASL studies [18, 19] also used T2 as a marker for signal origin. In the current work it was possible in addition, to derive water transfer values from blood to tissue spatially resolved on a single voxel basis, and showing whole-brain maps of transfer time.

Tissue values

In predominant grey matter areas the ROI analysis yielded stable results for T_bl→ex of 440±30 ms on average. The confidence intervals are about 10% of the resulting T_bl→ex value in most cases. Larger errors on T_bl→ex are found in ROIs of Subject 3 and 5. Using weighted averages based on the confidence intervals, those values contributed less to the cross-subject mean.

A noteworthy result is the difference of T_bl→ex between brain regions. In most subjects, T_bl→ex is lowest in the frontal lobes and highest in the MCA. Following equation [14], this could be explained by local variations in tissue composition and thereby V_c, or by differing permeability values. The variability between gray matter ROIs could also be explained by several effects not included in the model. One effect is arterial through flow. Voxel containing larger arteries will show faster apparent relaxation of the inflowing signal. This complication is compensated in the proposed model by a faster transfer to the extravascular compartment. Therefore, T_bl→ex will be underestimated in such voxel, leading to a higher apparent PS value. The effect could explain systematically faster transfer values especially in the frontal lobes (GM_L,GM_R) where such effects can be expected from the left and right middle cerebral arteries.

In white matter, the fitting routine yield values of T_bl→ex about zero together with high fitting errors, indicating that the exchange cannot be resolved. The main reason for the large error in white matter is low SNR, which is in general problematic in ASL imaging. Smaller V_c would indeed result in short exchange times, while smaller PS values as reported for white matter would have the opposite effect.

A comparison to values reported in literature is difficult. Gold standard to measure PS values are H₂O-15 PET studies, which do not provide spatial information and also relies on assumptions on the microvasculature. Using equ. 14 with V_c = 0.015 [12], reported PS values in human brain yield T_bl→ex = 625 [20] and 865 [32] ms. [33] presented a different approach to extract the transfer dynamics, by combination of ASL with diffusion imaging. They found values of 310±80 ms. Regarding all ROIs and subjects, our results are in the same range.

Limitations

While in general reliable whole-brain maps of the exchange dynamics were successfully derived, several technical limitations, related to simplifications in the model, confound the results. First, backflow to the vascular compartment is neglected as well as venous outflow. While backflow to the vascular compartment would further increase T2 by virtue of more contributions to the signal, venous outflow would lead to a shorter T2 and therefore signal loss in the voxel. However, both effects are minimal for a pure tissue and capillary voxel. Second, in voxel with large arterial vessel compartment, two other effects are expected to occur: through flow of delivering arteries through the voxel, and flow effects. In both cases, the result is shorter apparent relaxation times. Throughflow, again, is another outflow mechanism, resulting in signal loss. Flow effects would lead to exaggerated relaxation because part of the magnetization cannot be recovered in the spin echoes. Flow effects from larger vessels could in general be suppressed by crusher gradients[34] or even compensated in ASL by statistical methods [35].

More important, the empirical parameter T_bl→ex is difficult to interpret because it represents a mixture of several underlying physiological parameters. Looking at equation [14], it highly depends on the partition of feeding arteries and capillaries present in the voxel, which is not constant throughout brain tissue. This might explain the reproducible occurrence of patterns with large T_bl→ex (in the order of 200–600 ms) in some cortical regions, compared to other brain regions showing small values (0–50 ms) in the vicinity of watershed areas. Both findings together do not favour either “fast” or “restricted” water exchange but hint to different processes involved regarding the temporal evolvement of the ASL signal.

Outlook

A question that cannot conclusively be answered at this stage, relates to the physiological mechanism that underpin the T2 changes in ASL. While the presented model relies on the effect of water transfer from blood to tissue, other possibilities cannot be excluded. An alternative mechanism explaining the variations of T2 during blood delivery to the microvasculature is changing susceptibilities in the vicinity of the labeled spins due to tissue in homogeneity, changing oxygenation or hematocrit, as the labeled water passes towards the capillaries or even to the venous side. The question is intriguing since there is no gold-standard for measuring the capillary permeability to water.

How much T_bl→ex depends on permeability, could be investigated with several advanced experimental setups. Animal experiments with opening the blood-brain barrier using drugs or ultrasound can be devised to have a direct comparison between different permeability values on the same measurement protocol, throughout the brain or locally. Because of the non-invasive nature of the ASL technique, an easy transfer to patient examinations is possible. In diseases like tumors, multiple sclerosis or stroke, where a disruption of the blood-brain barrier is known, side difference comparisons between affected and healthy tissue could be examined. A direct comparison with contrast agent uptake is possible, which can be used to identify areas with disrupted blood-brain barrier. Because the blood-brain barrier permeability of water differs to that of macro-molecule contrast agent, another compelling idea is to use PET-MR, measuring T2-ASL and H₂O-15 PET on the same protocol, using the “labeled” water molecules for both modalities.

Potential applications of the proposed technique range from diagnosis to monitoring disease progression. The quantification of T_bl→ex allows investigation of the exchange dynamics and is sensitive to changes of capillary water permeability and arterial blood volume, which both can be affected in neurovascular diseases. Small changes in the permeability of the blood-brain barrier are more likely to be resolved by measuring water permeability, compared to tracer based techniques using much larger molecules. Specifically, maps of T_bl→ex could be useful to identify changes in microvascular blood delivery or capillary wall permeability in conditions like tumors, inflammation, stroke and more generally all diseases affecting the blood-brain-barrier.

LIST OF SYMBOLS

f	ml/g/min	Perfusion
M0,a (M_zero, a)	-	Equilibrium magnetization
α	-	Inversion efficiency
τ (tau)	ms	Bolus arrival time
BL	ms	Blood bolus length
τ2 = τ + BL (tau_2)	ms	End of labeled blood bolus inflow
T1bl = 1/R1bl	ms	Longitudinal blood relaxation time (/rate)
T2bl = 1/R2bl	ms	Transversal blood relaxation time (/rate)
T1ex = 1/R1ex	ms	Longitudinal extravascular relaxation time (/rate)
T2ex = 1/R2ex	ms	Transversal extravascular relaxation time (/rate)
Tbl→ex = 1/R1bl→ex	ms	Blood water transfer time (/rate)
R1app = R1ex − R1bl+ R1bl→ex	ms	Apparent longitudinal relaxation rate
R2app = R2ex − R2bl+ R1bl→ex	ms	Apparent transverse relaxation rate
TI	ms	Inflow time
TE	ms	Echo time

APPENDIX

Analytic solution, two compartment model with T1 relaxation

The terms in Equ. [1] are, for the blood compartment:

$$S_{bl}(t)=\{\begin{array}{l}0\hfill \\ \frac{2·f·\alpha ·M_{a,0}}{R_{bl\to ex}}·e^{-(R{1}_{bl}+R_{bl\to ex})·t}·\left(e^{R_{bl\to ex}t}-e^{R_{bl\to ex}\tau }\right)\hfill \\ \frac{2·f·\alpha ·M_{a,0}}{R_{bl\to ex}}·e^{-(R{1}_{bl}+R_{bl\to ex})·t}·\left(e^{R_{bl\to ex}{\tau }_2}-e^{R_{bl\to ex}\tau }\right)\hfill \end{array}\text{for}\{\begin{array}{l}t<\tau \hfill \\ \tau \le t<{\tau }_2\hfill \\ t\ge {\tau }_2\hfill \end{array}$$ [A1]

Extravascular compartment:

$$S_{ex}(t)=\{\begin{array}{l}0\hfill \\ \begin{array}{l}\frac{2·f·\alpha ·M_{a,0}}{R{1}_{ex}-R{1}_{bl}}·e^{-R{1}_{ex}·t}·\left(e^{(R{1}_{ex}-R{1}_{bl})t}-e^{(R{1}_{ex}-R{1}_{bl})\tau }\right)\\ -\frac{2·f·\alpha ·M_{a,0}}{R{1}_{\mathit{app}}}·e^{-(R{1}_{ex}+R_{bl\to ex})·t}·\left(e^{R{1}_{\mathit{app}}t}-e^{R{1}_{\mathit{app}}\tau }\right)\end{array}\hfill \\ \begin{array}{l}\frac{2·f·\alpha ·M_{a,0}}{R{1}_{ex}-R{1}_{bl}}·e^{-R{1}_{ex}·t}·\left(e^{(R{1}_{ex}-R{1}_{bl}){\tau }_2}-e^{(R{1}_{ex}-R{1}_{bl})\tau }\right)\\ -\frac{2·f·\alpha ·M_{a,0}}{R{1}_{\mathit{app}}}·e^{-(R{1}_{ex}+R_{bl\to ex})·t}·\left(e^{R{1}_{\mathit{app}}{\tau }_2}-e^{R{1}_{\mathit{app}}\tau }\right)\end{array}\hfill \end{array}\text{for}\{\begin{array}{l}t<\tau \hfill \\ \tau \le t<{\tau }_2\hfill \\ t\ge {\tau }_2\hfill \end{array}$$ [A2]

With R1_app ≡ R1_ex − R1_bl + R_bl→ex.

Analytic solution, two compartment model with T2 relaxation

The terms from Equ. [13] are split up in a component of signal which has not yet arrived in the voxel (indexed “A”) and a component where signal has already arrived and is still is subject to relaxation (and transfer) processes (indexed “B”):

$$\begin{array}{l}{S}_{bl}(ti,te)=S2A_{bl,ti}(te)+S2B_{bl,ti}(te)\\ S_{ex}(ti,te)=S2A_{ex,ti}(te)+S2B_{ex,ti}(te)\end{array}$$ [A3a,b]

Generally, signal depends on the results from Equ. [A1] and [A2]. A short notation for arbitrary t=TI will be used: S_bl (TI) ≡ S_bl,TI and S_ex (TI) ≡ S_ex,TI

For S2A, three cases have to be distinguished based on TI:

• 1
  TI<τ :

  $$\begin{array}{l}S2A_{bl,TI}(te)=\{\begin{array}{l}0\hfill \\ \frac{2·f·\alpha ·M_0}{R_{bl\to ex}}·e^{-TI·R{1}_{bl}}{e}^{-(R{2}_{bl}+R_{bl\to ex})·te}·\left(e^{R_{bl\to ex}te}-e^{R_{bl\to ex}(\tau -TI)}\right)\hfill \\ \frac{2·f·\alpha ·M_0}{R_{bl\to ex}}·e^{-TI·R{1}_{bl}}{e}^{-(R{1}_{bl}+R_{bl\to ex})·te}·\left(e^{R_{bl\to ex}({\tau }_2-TI)}-e^{R_{bl\to ex}(\tau -TI)}\right)\hfill \end{array}\\ \text{for}\{\begin{array}{l}te<\tau -TI\hfill \\ \tau -TI\le te<{\tau }_2-TI\hfill \\ te\ge {\tau }_2-TI\hfill \end{array}\end{array}$$ [A4]

  $$\begin{array}{l}S2A_{ex,TI}(te)=\{\begin{array}{l}0\hfill \\ \begin{array}{l}{e}^{-TI·R{1}_{bl}}\{\frac{2·f·\alpha ·M_{0,a}}{R{2}_{ex}-R{2}_{bl}}·e^{-R{2}_{ex}·te}·\left(e^{(R{2}_{ex}-R{2}_{bl})te}-e^{(R{2}_{ex}-R{2}_{bl})(\tau -TI)}\right)\\ -\frac{2·f·\alpha ·M_{0,a}}{R{2}_{\mathit{app}}}·e^{-(R{2}_{ex}+R_{bl\to ex})·te}·\left(e^{R{2}_{\mathit{app}}te}-e^{R{2}_{\mathit{app}}(\tau -TI)}\right)\}\end{array}\hfill \\ \begin{array}{l}{e}^{-TI·R{1}_{bl}}\{\frac{2·f·\alpha ·M_{0,a}}{R{2}_{ex}-R{2}_{bl}}·e^{-R{2}_{ex}·te}·\left(e^{(R{2}_{ex}-R{2}_{bl})({\tau }_2-TI)}-e^{(R{2}_{ex}-R{2}_{bl})(\tau -TI)}\right)\\ -\frac{2·f·\alpha ·M_{0,a}}{R{2}_{\mathit{app}}}·e^{-(R{2}_{ex}+R_{bl\to ex})·te}·\left(e^{R{2}_{\mathit{app}}({\tau }_2-TI)}-e^{R{2}_{\mathit{app}}(\tau -TI)}\right)\end{array}\hfill \end{array}\\ \text{for}\{\begin{array}{l}te<\tau -TI\hfill \\ \tau -TI\le te<{\tau }_2-TI\hfill \\ te\ge {\tau }_2-TI\hfill \end{array}\end{array}$$ [A5]

With R2_app ≡ R2_ex − R2_bl + R_bl→ex.

• 2
  τ < TI < τ2 :

  $$\begin{array}{l}S2A_{bl,TI}(te)=\{\begin{array}{l}\frac{2·f·\alpha ·M_0}{R_{bl\to ex}}·e^{-TI·R{1}_{bl}}{e}^{-(R{2}_{bl}+R_{bl\to ex})·te}·\left(e^{R_{bl\to ex}te}-1\right)\hfill \\ \frac{2·f·\alpha ·M_0}{R_{bl\to ex}}·e^{-TI·R{1}_{bl}}{e}^{-(R{1}_{bl}+R_{bl\to ex})·te}·\left(e^{R_{bl\to ex}({\tau }_2-TI)}-1\right)\hfill \end{array}\\ \text{for}\{\begin{array}{l}0<te<{\tau }_2-TI\hfill \\ t\ge {\tau }_2-TI\hfill \end{array}\end{array}$$ [A6]

  $$\begin{array}{l}S2A_{ex,TI}(te)=\{\begin{array}{l}\begin{array}{l}{e}^{-TI·R{1}_{bl}}\{\frac{2·f·\alpha ·M_{0,a}}{R{2}_{ex}-R{2}_{bl}}·e^{-R{2}_{ex}·te}·\left(e^{(R{2}_{ex}-R{2}_{bl})te}-1\right)\\ -\frac{2·f·\alpha ·M_{0,a}}{R{2}_{\mathit{app}}}·e^{-(R{2}_{ex}+R_{bl\to ex})·te}·\left(e^{R{2}_{\mathit{app}}te}-1\right)\}\end{array}\hfill \\ \begin{array}{l}{e}^{-TI·R{1}_{bl}}\{\frac{2·f·\alpha ·M_{0,a}}{R{2}_{ex}-R{2}_{bl}}·e^{-R{2}_{ex}·te}·\left(e^{(R{2}_{ex}-R{2}_{bl})({\tau }_2-TI)}-1\right)\\ -\frac{2·f·\alpha ·M_{0,a}}{R{2}_{\mathit{app}}}·e^{-(R{2}_{ex}+R_{bl\to ex})·te}·\left(e^{R{2}_{\mathit{app}}({\tau }_2-TI)}-1\right)\}\end{array}\hfill \end{array}\\ \text{for}\{\begin{array}{l}0\le te<{\tau }_2-TI\hfill \\ te\ge {\tau }_2-TI\hfill \end{array}\end{array}$$ [A7]
• 3
  TI>τ₂; :

  $$S2A_{bl,TI}(te)=0$$ [A8]

  $$S2A_{ex,TI}(te)=0$$ [A9]

For S2B, there’s no case distinction:

$$S2B_{bl,TI}(te)=S_{bl,TI}·e^{-R_{bl\to ex}·te}·e^{-te·R{2}_{bl}}$$ [A10]

$$S2B_{ex,TI}(te)=S_{bl,TI}·(1-e^{-R_{bl\to ex}·te})·e^{-te·R{2}_{ex}}+S_{ex,TI}·e^{-te·R{2}_{ex}}$$ [A11]