Effects of water exchange on the measurement of myocardial

Transcription

Effects of water exchange on the measurement of myocardial
Magnetic Resonance in Medicine 41:334–342 (1999)
Effects of Water Exchange on the Measurement of
Myocardial Perfusion Using Paramagnetic Contrast Agents
Robert M. Judd,1* Scott B. Reeder,2 and Karen May-Newman2
To investigate the effects of water exchange on quantification of
perfusion, data were acquired in isolated hearts (n ⴝ 11) and
used to develop a model of exchange. Myocardial T1 was
measured 3 times/sec during step changes in concentration of
intravascular (polylysine-gadolinium-diethylene-triamine-pentaacetic acid) and extracellular (gadoteridol) agents. For the
intravascular agent, the change in 1/T1 (⌬R1) was lower than
predicted by fast exchange (2.7 ⴞ 0.5 vs. 7.8 sec-1, respectively),
and suggested an intra-extravascular exchange rate of 3 Hz. For
the extracellular agent, contrast kinetics were similar to those of
similarly sized molecules (wash-in time constant 38 ⴞ 5 sec),
and the data suggested fast interstitial-cellular exchange. Modeling showed that perfusion is underestimated for both agents if
exchange is ignored, although the relationships of measured to
actual perfusion were monotonic. We conclude that myocardial
water exchange strongly affects first-pass enhancement but
that ignoring the effects of exchange may still provide reasonable estimates of regional perfusion differences. Magn Reson
Med 41:334–342, 1999. r 1999 Wiley-Liss, Inc.
Key words: myocardial perfusion; magnetic resonance imaging; contrast agents
The importance of information regarding regional myocardial perfusion is underscored by large-scale clinical studies demonstrating that prompt restoration of perfusion is
one of the primary determinants of long-term prognosis
(1–4). Current methods of non-invasively measuring myocardial perfusion are subject to significant limitations. In
several recent studies, regional first-pass time-intensity
curves were generated from magnetic resonance (MR)
images acquired once each heartbeat after bolus administration of paramagnetic MR contrast agents such as gadolinium diethylene triamine pentaacetic acid (Gd-DTPA) (5–
12). The results of these studies clearly demonstrate a
qualitative relationship between myocardial enhancement
and regional blood flow.
A potentially confounding issue in the interpretation of
myocardial first-pass contrast enhancement patterns, however, is that the presence of Gd in the myocardium is not
directly detected by MRI but rather is inferred based on
changes in proton relaxation times, usually T1, which are
shortened by the magnetic moment associated with Gd.
Most myocardial protons are located on water molecules,
and contrast agent molecules like Gd-DTPA are compartmentalized into, for example, the myocardial extracellular
space. In this setting, the rate of water exchange among the
1Feinberg Cardiovascular Research Institute, Northwestern University Medical
School, Chicago, Illinois.
2Johns Hopkins Medical Institutions, Baltimore, Maryland 21287.
*Correspondence to: Robert M. Judd, Feinberg Cardiovascular Research
Institute, Northwestern University Medical School, 303 East Chicago Ave.,
Tarry 12–703, Chicago, IL 60611–3008. E-mail: [email protected]
Grant sponsor: Biomedical Engineering Research Grant, the Whitaker Foundation; Grant sponsor: NIH-MSTP; Grant sponsor: NIH; Grant number: HL53411.
Received 6 February 1998; revised 13 July 1998; accepted 28 July 1998.
r 1999 Wiley-Liss, Inc.
intravascular, interstitial, and intracellular compartments
may limit the number of water molecules that ‘‘sense’’ the
presence of Gd in the tissue. As a consequence, the
relationship between MR image intensity and contrast
agent concentration on the voxel scale (mm) may become
non-linear, precluding quantification of myocardial perfusion in ml/min/g by direct application of the well-known
indicator-dilution theory (13–16).
The effects of intercompartmental water exchange on
contrast enhancement have been studied by a number of
groups (17–25) and have recently been reviewed (26). The
results of these studies underscore the fact that the influence of water exchange on contrast enhancement depends
on many factors including time-varying contrast concentrations, the kinetics of the contrast agent molecule movement among compartments, the rate of water exchange
among compartments, and the particular MR method used
to sample the proton signal. Due at least in part to the
complex nature of the problem, the extent to which water
exchange affects quantification of myocardial perfusion
remains unclear.
The goal of this study was to provide a conceptual
framework for the understanding of the effects of water
exchange on measurements of myocardial perfusion. Our
approach was first to obtain experimental data concerning
both the myocardial kinetics of commonly used MR contrast agents and intercompartmental myocardial water
exchange rates. The experimental results were then used to
develop a mathematical model of water exchange. Finally,
the model was used to estimate the effects of water
exchange on perfusion measurements.
MATERIALS AND METHODS
Experimental Data
Myocardial T1 was measured in isolated, non-beating
hearts as a function of time during step changes in perfusate contrast concentrations for both intravascular and
extracellular contrast agents.
Animal Preparation
Eleven 3.0–3.5 kg rabbits were anesthetized (IV pentobarbital sodium) and heparinized. The chests were then opened,
and the hearts were rapidly excised and immersed in cold
(47C) saline, and then retrograde perfused via the aortic
root using a cardioplegic (high K⫹) solution at room
temperature, to study the viable (24,27,28) but non-beating
heart. The composition of the perfusate was (in mM): Na⫹
120, K⫹ 16, Mg2⫹ 16, Cl- 160, HCO3-10. Adenosine was
added to ensure maximal coronary vasodilatation (1 mM).
The perfusate was bubbled with 95% O2 and 5% CO2.
Perfusion pressure and flow were continuously monitored using a Statham pressure transducer and an in-line
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Effects of Water Exchange on Perfusion Measurements
electromagnetic flowmeter (Biotronics). The hearts were
placed horizontally on a tray with the left ventricular free
wall facing up. A 4 mm diameter single-turn surface
radiofrequency (RF) coil was placed over the heart between
the left anterior descending and circumflex arteries and
away from all other large arteries. The diameter of the RF
coil was chosen specifically to avoid signal from the left
ventricular cavity. The hearts were studied in a 4.7 T
Omega CSI Spectrometer (General Electric).
Contrast Agents
An intravascular MR contrast agent, polylysine-Gd-DTPA,
was generously donated to us by Schering (Berlin, Germany). According to Schering, the average molecular weight
of the polylysine was 52,300 daltons, with 15% of the
compound being larger than 75,000 and an additional 15%
being smaller than 35,000. For each polylysine molecule,
95–98% of the lysines are loaded with Gd-DTPA, resulting
in about 75–80 gadoliniums per molecule. The relaxivity at
4.7 T was 8.3 mM-1sec-1 (concentration of Gd). Due to the
limited amount of polylysine available to us, only two
perfusate contrast concentrations for polylysine were investigated (1 and 15 mM).
The extracellular agent, gadoteridol (29,30), was obtained from Squibb [Gd(HP-DO3A), Prohance). The molecular weight of gadoteridol is about 800 daltons, and the
relaxivity at 4.7 T is 4.3 mM-1sec-1 (24). The molecular
weight and relaxivity of gadoteridol are similar to that of
Gd-DTPA. Gadoteridol differs from Gd-DTPA mainly in
that gadoteridol is non-ionic. Gadoteridol perfusate contrast concentrations were 0.5, 1.0, 1.5, and 2.0 mM.
Measurement of Myocardial T1
Myocardial T1 was estimated approximately 3 times/sec
using a saturation-recovery technique. The method has
been previously described and validated (24). Briefly, a
train of adiabatic 907 RF pulses (4 msec duration) were
transmitted with a repetition time (TR) of 351.2 msec and a
free induction decay (FID) acquired after each RF pulse.
The efficacy of the adiabatic pulse was examined by
acquiring gradient echo images using the adiabatic transmit pulse. These images verified that the sensitive region of
the coil was approximately one diameter (4 mm). We chose
a TR of 351.2 msec because we determined that this value
maximizes the sensitivity of longitidinal relaxation to the
changes in T1 expected during contrast transit and because
stimulated echoes are avoided since TR is long compared
with T2. Each FID (one signal average) was fit to the
equation S(t) ⫽ A e-(1/T2* ⫹ i␻) t ⫹ ␾ using a non-linear least
squares optimization where ␻ is the off-resonance frequency and ␾ is phase. Myocardial T1 was estimated using
the equation T1 ⫽ -TR/ln(1-A/Ao) where Ao is the value of
A for a fully relaxed FID (measured experimentally). The
equation implicitly assumes monoexponential T1 relaxation (see Discussion, Study Limitations). As previously
described (24), the T1 measurements were validated in 11
test tubes were filled with a linearly increasing amount of
contrast agent.
Experimental Protocol
Step changes in contrast concentrations were achieved by
rapidly switching between two perfusate reservoirs, one
335
with and the other without the contrast agent. For each
step, FIDs were acquired for 3 min. The reservoirs were
switched in all cases 15 sec after the beginning of the 3 min
data acquisition period.
For the intravascular agent (polylysine), the step protocol was designed to minimize the use of polylysine while
ensuring that steady-state enhancement had been achieved.
This was accomplished by holding polylysine concentration at 1 mM for 120 sec and measuring T1 as described
above. In preliminary experiments we found that myocardial T1 reached a plateau within 30 sec. Therefore, the 15
mM polylysine steps, which consume a large amount of the
contrast agent, were maintained for 30 sec in all subsequent experiments to conserve polylysine. For the extracellular agent (gadoteridol), T1 data were collected 10 min
after the step change in addition to during the initial 3 min
period to determine the steady-state value of myocardial
T1. For both agents, myocardial T1 was monitored between
steps to ensure that T1 had returned to baseline before the
next step.
Model of Water Exchange
Based on the data (see Results), water exchange was
assumed to be limited between the intravascular and
interstitial compartments whereas exchange between the
interstitial and cellular compartments was assumed to be
fast. To describe this, a model proposed by Bauer and
Schulten (31) was modified as shown in Fig. 1.
In the model, the intravascular and interstitial proton
compartments were separated by a membrane (shaded area
of Fig. 1) that restricts water exchange. Diffusion of water
across the membrane mixes the spins of the intravascular
and interstitial compartments such that after a while spins
relaxed through the presence of the contrast agent in the
intravascular compartment appear in the interstitial compartment. Spins in the interstitial compartment, whose T1s
may have been shortened by exchange with the intravascular space or, in the case of gadoteridol, by leakage of the
contrast agent into the interstitium, mix with spins in the
cellular compartment. As a result, the whole population of
nuclear spins will exhibit relaxation enhancement.
Bauer and Schulten (31) showed that for the case of two
proton compartments the equations governing exchange
can be reduced to:
3 r D ⭸r 1r ⭸r2 ⫺ T 4 T
⭸
1
⭸
1
i
1local(r)
⫽ ⫺1
[1]
i
where the index i denotes the compartment (i.e., intravascular) and the mean local relaxation time, T1local(r), is the
monoexponential rate that best approximates the true
(multiexponential) local recovery of longitudinal magnetization (31). Equation (1) is subject to the boundary conditions:
Div⭸m(Riv)⫺/⭸r ⫽ Dim⭸m(Riv)⫹/⭸r
[2a]
Dim⭸m(Riv ⫹ h)⫺/⭸r ⫽ Dis,cell⭸m(Riv ⫹ h)⫹/⭸r
[2b]
Dis,cell⭸m(Rcell, t)/⭸r ⫽ 0
[2c]
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Judd et al.
FIG. 1. Model of water exchange. Left: Intravascular and interstitial compartments are separated by a membrane (shaded area) that limits
water exchange. Middle: For polylysine-Gd-DTPA, the agent was assumed to be restricted to the intravascular compartment. Based on the
experimental results, intravascular-interstitial water exchange was modeled using the equations given in the text while interstitial-intracellular
water exchange was assumed to be fast. Right: For gadoteridol, water exchange was assumed to be the same as for polylysine-Gd-DTPA, but
the gadoteridol was allowed to diffuse into the interstitial space.
where m is magnetization, r is the distance from the origin,
R is the radius of each compartment (Fig. 1), and D is the
water diffusion coefficient of each compartment. The
subscripts above were defined as follows: iv ⫽ intravascular, im ⫽ intramembrane (shaded area of Fig. 1), is ⫽
interstitial, and cell ⫽ intracellular. The intrinsic relaxation times (T1 in the absence of water exchange) of each
compartment are taken as T1iv, T1im, T1is, and T1cell, respectively. Within each compartment, the diffusion coefficients
and intrinsic relaxation times are assumed to be constant.
The first two boundary conditions [Eqs.( 2a) and (2b)] state
that the flux of magnetization out of one compartment
must equal the flux into the next compartment so that spins
are neither created or destroyed at compartmental boundaries. The last boundary condition [Eq. (2c)] states that the
flux of magnetization is zero at the edge of each model unit
(i.e., at Rcell of Fig. 1).
Based on the literature (31–33), the following parameters
were chosen for the model: Riv, Ris, Rcell ⫽ 2.5, 5, 10 ␮m, h ⫽
0.2␮m; Div ⫽ Dis ⫽ Dcell ⫽ 1.5 ␮m2/msec; Dm based on our
experimental data; T1im ⫽ T1cell ⫽ 1150 msec (based on the
experimental pre-contrast T1); and T1iv, T1is calculated
based on the contrast concentrations of those compartments, as described below. The diffusion coefficients were
chosen from studies of the net water diffusion coefficient
through the ventricular wall (13,31). Using the above
parameters, intracapillary volume is 6.25%, the interstitial
space is approximately 18.75%, and the intracellular volume is 75%, all of which are similar to the known values in
myocardial tissue (32,33).
For both polylysine and gadoteridol, Eq. 1 was solved
numerically, to determine T1local(r). The global relaxation
time, T1voxel, was estimated as the spatial average of T1local(r):
2
T1voxel ⫽ 1/␲Rcell
兰
Rcell
0
T1local(r)2␲r dr
[3]
Figure 1 summarizes the model assumptions for the
intravascular agent, polylysine. The contrast agent molecule is physically restricted to the intravascular compart-
ment. Intravascular-interstitial water exchange was assumed to be governed by the above equations. As previously
stated, interstitial-cellular exchange was assumed to be
fast, i.e., the interstitial and cellular water was well mixed
at all times. The intrinsic value of T1 within the capillary
was determined using the relaxivity equation:
1/T1iv ⫺ 1/T1ivbefore contrast ⫽ REL[Gd]
[4]
where REL is the relaxivity of the contrast agent, [Gd] is
perfusate contrast agent concentration, and 1/T1ivbefore contrast was assumed to equal pre-contrast myocardial T1 (taken
as 1150 msec based on our experimental results). For
polylysine, the intrinsic T1 of the interstitial compartment
was estimated from pre-contrast myocardial T1 (1150 msec).
Also shown in Fig. 1 are the model assumptions for
gadoteridol. Unlike polylysine, gadoteridol can passively
diffuse across the membrane into the interstitial space. The
rate of contrast agent diffusion was assumed to be linearly
related to the intravascular-interstitial gadoteridol concentration gradient and a constant, K, analogous to the capillary permeability-surface area coefficient. The interstitial
concentration of gadoteridol, [gadoteridol]is, was described
using the equation:
[Gadoteridol]is ⫽ K(([Gadoteridol]iv)i
⫺ ([Gadoteridol]is)i⫺1)
[5]
where ([gadoteridol]iv)i is the intravascular gadoteridol
concentration for the ith time point and ([gadoteridol]is)i-1
is the interstitial gadoteridol concentration for the previous
time point. The use of Eq. (5) is analogous to assuming
first-order extravasation of gadoteridol out of the capillary
and into the interstitium. The value of K was adjusted such
that ratio of gadoteridol remaining in the tissue at the end
of the myocardial first pass (defined as t ⫽ 3␤; see below) to
the amount of gadoteridol at the peak was equal to 15%
and, separately, 30%. Two different values (15 and 30%)
Effects of Water Exchange on Perfusion Measurements
337
were used to examine the effect of increased gadoteridol
first-pass extraction on contrast enhancement.
Once in the interstitial space, gadoteridol shortens the
intrinsic interstitial T1. The model assumes that the gadoteridol molecule does not enter the myocyte. For the case of
gadoteridol, the intrinsic T1 of the interstitial compartment
was determined using the equation:
1/T1is ⫺ 1/T1isbefore contrast ⫽ R[Cis ⴱ (Vis/(Vis ⫹ Vc))]
[6]
where the interstitial volume, Vis, equals extracellular
minus intravascular volume (25% - 6.25% ⫽ 18.75%),
intracellular volume, Vc, equals 75%, and T1isbefore contrast
was taken as pre-contrast myocardial T1 (1150 msec).
To model first-pass contrast enhancement, the above
equations were solved to determine T1voxel at 100 discrete
time points from t ⫽ 0 to 180 sec. A gamma variate function
was used to approximate the intravascular time-concentration curve. Specifically, we used the equation [Gd] ⫽ K t␤
e-t/␤, where ␣ ⫽ 3, ␤ ⫽ 4.5, and K was chosen such that peak
contrast concentration was 5, 10, 15, and 20 mM. The
values of ␣ and ␤ were chosen to achieve mean transit
times and dispersions similar to those observed in myocardial tissue (6,13,16). The peak concentrations were chosen
based on model estimates (24). The intrinsic T1 of the
intravascular compartment was determined using Eq. (4),
where [Gd] was determined from the gamma-variate function.
To evaluate the sensitivity of the findings to our choice of
geometry and diffusion coefficients, all model parameters
(Riv, Ris, Rcell, Div, Dim, Dis,cell) were perturbed individually
and collectively by ⫹10% and -10% for an intravascular
polylysine concentration of 25 mM for which the effects of
water exchange should be greatest.
RESULTS
Figure 2a shows typical changes in myocardial 1/T1 (⌬R1)
following step changes in perfusate polylysine concentration. For all concentrations and all hearts, ⌬R1 reached a
plateau within 30 sec, suggesting that the intravascular
space had filled with the agent by this time. Figure 2b
shows the results for gadoteridol. For gadoteridol, the time
required to reach a plateau was much longer, presumably
due to diffusion of the gadoteridol molecule out of the
intravascular space and into the interstitium. By fitting
monoexponential curves to the gadoteridol ⌬R1 vs. time
curves, the time constants for gadoteridol were 38 ⫾ 14 sec
(n ⫽ 7), 38 ⫾ 17 sec (n ⫽ 10), 33 ⫾ 13 sec (n ⫽ 3), and 40 ⫾ 5
sec (n ⫽ 5) for perfusate concentrations of 0.5, 1.0, 1.5, and
2.0 mM, respectively, and the overall value was 38 ⫾ 6 sec.
Figure 3 summarizes steady-state ⌬R1 as a function of
perfusate ⌬R1 for both polylysine (filled circles) and gadoteridol (open circles). The perfusate ⌬R1 values were calculated from the perfusate contrast concentrations based on
the relaxivity equation [Eq. (4)]. Shown for comparison is
the relationship expected for fast myocardial water exchange for polylysine assuming an intravascular volume of
6.25%.
For gadoteridol, the data of Fig. 3 were acquired following equilibration of the agent throughout the extracellular
(intravascular plus interstitial) space. In this case, the
FIG. 2. Wash-in of intravascular (a) and extracellular (b) contrast
agents. For the intravascular agent, the change in myocardial 1/T1
(⌬R1) reached a plateau in ca. 15 sec, which would be expected for
an intravascular agent. For the extracellular agent, the plateau
required additional time, presumably caused by the finite rate of
diffusion of the agent out of the intravascular and into the interstitial
spaces.
intrinsic T1s of the intravascular and interstitial compartments would be equal, but the intrinsic T1 of the intracellular space would be longer assuming gadoteridol does not
enter the cell. In this setting, if interstitial-cellular water
exchange limited contrast enhancement, the data of Fig. 3
would be expected to be non-linear. Conversely, if interstitial-cellular water exchange were fast compared with the
difference between intrinsic 1/T1s of the interstitial and
intracellular comparments, the relationship would be expected to be linear. The data were consistent with a linear
relationship, suggesting fast interstitial-intracellular water
exchange for the experimental conditions investigated.
For polylysine, ⌬R1 in Fig. 3 for the 15 mM perfusate
concentration was far lower than that predicted by fast
exchange (data: 2.7 ⫾ 0.5 sec-1, fast exchange: 15 mM ⫻
6.25% ⫻ 8.3 mM-1sec-1 ⫽ 7.8 sec-1), suggesting that ⌬R1 is
limited by water exchange between the intravascular and
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Judd et al.
that, due to the effects of myocardial water exchange, the
shapes of the ⌬R1 curves are complex.
To understand the effects of water exchange, each of the
five curves for polylysine shown in Fig. 5b and each of the
FIG. 3. Steady-state tissue ⌬R1 for polylysine-Gd-DTPA (filled
circles) and gadoteridol (open circles) vs. perfusate ⌬R1. Although
the data for the extracellular agent were consistent with fast interstitialcellular exchange, the data for the intravascular agent suggested a
limitation of water exchange between the intravascular and interstitial
spaces. See text for details.
interstitial spaces. Assuming that the intravascular T1 for a
15 mM perfusate polylysine concentration was so short
(see Discussion) that water exchange dominated myocardial ⌬R1, and assuming the intravascular space is a small
fraction of the total, the value of myocardial ⌬R1 provides
an estimate of the rate of water exchange between the
intravascular and extravascular compartments, namely,
2.7 ⫾ 0.5 Hz.
Figure 4 shows the model predictions for first-pass
myocardial ⌬R1 for perfusate contrast concentrations of 5,
10, 15, 20, and 25 mM assuming an intravascularextravascular water exchange rate of 3 Hz and assuming
intracellular-extracellular water exchange is fast. The perfusate contrast concentrations are shown in Fig. 4a (inputs); Fig. 4b and c shows the results for polylysine and
gadoteridol, respectively. For gadoteridol, the curves assume that 15% of the agent leaked into the interstitial
space at the end of the first pass. The results for 30% leakge
were similar. From Fig. 4b (polylysine), myocardial ⌬R1
did not scale linearly with contrast concentration, consistent with the effects of limited water exchange.
Interestingly, for gadoteridol ⌬R1 scaled nearly linearly
with concentration (Fig. 4c), as would be expected for the
case of fast myocardial water exchange. On closer examination, however, it was found that ⌬R1 for gadoteridol was far
lower than that predicted by fast exchange. For example,
for a peak intravascular gadoteridol concentration of 25
mM and a model-predicted interstitial gadoteridol concentration of 2.0 mM at the time of peak intravascular concentration (not shown), one can estimate that myocardial ⌬R1
would be 8.3 sec-1 [⫽ (25 mM ⫻ 6.25% (capillary volume) ⫹
2.0 mM ⫻ 18.75% (interstitial volume)] ⫻ 4.3 mM-1sec-1
(relaxivity)], whereas a value of less than 5 sec-1 was
predicted by the model (Fig. 4c). This point is further
explored in the Discussion.
Figure 5 explores the effects of varying myocardial
perfusion on the shape of the myocardial ⌬R1 curves as
predicted by the model. By comparison of the intravascular
input curves (Fig. 5a) with the model-predicted ⌬R1 for
polylysine (Fig. 5b) and gadoteridol (Fig. 5c), it can be seen
FIG. 4. Modeled effects of water exchange on myocardial ⌬R1 for
various perfusate contrast concentrations. a: Intravascular contrast
concentrations used as inputs for the model. b: Modeling results for
polylysine-Gd-DTPA. Note the non-linear scaling of myocardial ⌬R1
for the intravascular agent. c: Modeling results for gadoteridol.
Although ⌬R1 scales linearly with contrast concentration for gadoteridol, peak myocardial ⌬R1s are significantly less than those predicted
by fast exchange. See text for details.
Effects of Water Exchange on Perfusion Measurements
339
gamma variate function, the measured mean transit time
(MTT) was calculated. Fig. 5a compares the measured
MTT, i.e., that based on the gamma variate fits to the model
curves (Fig. 5b,c), to the actual MTT, i.e., that used as input
to the model (Fig. 5a). The results were plotted as 1/MTT
because for a constant vascular volume actual 1/MTT is
linearly proportional to perfusion in ml/min/g (13–15).
From Fig. 6a it can be seen that, due to myocardial water
exchange, the measured 1/MTT underestimates the actual
1/MTT for all conditions investigated. From Fig. 6a, the
magnitude of the underestimation was approximately 32%
for polylysine and was even greater for gadoteridol. Interestingly, however, the relationships of measured to actual
1/MTT were nearly linear, suggesting that relative measurements of perfusion would be accurate.
Next, the effects of water exchange on the maximum
upslope and the time-to-peak of the myocardial ⌬R1 curves
were examined (Fig. 5b,c). The results are shown in Fig. 6b
and c. In both cases, the values increased monotonically
with 1/MTT. The sensitivity (slope) of both indices were
greater for polylysine compared with gadoteridol for the
conditions investigated.
As described in Materials and Methods, the sensitivity of
the model to the choice of parameters was evaluated. We
found that the average effect of changing the parameters by
⫾10% was to change voxel T1 by 8.7%. The strongest
effects were caused by perturbations in capillary diameter,
Riv, for which a 10% increase caused a 20% decrease in
voxel T1 while a 10% decrease caused a 27% increase in
voxel T1. These changes, however, were far smaller than
the results expected for fast and slow exchange (⫹364%
and ⫺97.7%, respectively). We conclude that, although the
exact relationship between tissue T1 and contrast concentration depends on the choice of model parameters, the
model is adequate to serve as a conceptual framework in
which the effects of water exchange can be understood.
DISCUSSION
The results demonstrate that myocardial water exchange
can strongly affect myocardial enhancement for paramagnetic contrast agents, and that absolute measurements of
myocardial perfusion that ignore these effects introduce
significant error.
Study Limitations
FIG. 5. a–c: Modeled effects of blood flow on myocardial ⌬R1. These
curves were used to calculate the results of Fig. 6.
five curves for gadoteridol shown in Fig. 5c were analyzed
in several ways.
First, the curves were fit to a gamma variate function (see
Materials and Methods) using a least squares routine. For
the case of gadoteridol for which the ‘‘tails’’ of the curves
may cause significant errors, the data were truncated when
⌬R1 fell below 70% of the peak value, as is often done with
gamma variate fits to in vivo curves (34). From the best fit
To allow the study of water exchange, simplifications were
necessary that may affect the results. One simplification
was that the equation used to experimentally determine
myocardial T1 implicitly assumes monoexponential relaxation, even though one consequence of limited water
exchange is that T1 relaxation will become multiexponential. For several reasons, we assumed monoexponential
relaxation despite the likelihood of multiexponential relaxation. First, we were interested in studying myocardial T1
during transients in contrast agent concentrations and
there is insufficient time to measure the T1 relaxation curve
during contrast transients. Second, the model suggested by
Bauer and Schulten (31) numerically determines the ‘‘best’’
monoexponential that describes the (multiexponential)
relaxation. Third, the process of water exchange itself
tends to mix the two proton populations with different T1s,
340
Judd et al.
FIG. 6. a: Measured vs. actual reciprocal of the mean transit
time (MTT) based on the tissue curves of Fig. 5. For a constant
vascular volume, 1/MTT is linearly proportional to blood flow.
‘‘E’’ represents the percent first-pass extraction (leakage) of
gadoteridol into the interstitial space. b: Maximum upslope vs.
actual 1/MTT. c: Reciprocal time-to-peak enhancement vs.
1/MTT. Although water exchange generally results in an underestimation of absolute blood flow, the relationships are monotonic and in some cases nearly linear.
and in fact it is often difficult to distinguish multiexponential T1 relaxation even when it is known to be present
without elaborate curve-stripping techniques (35). Although the extent to which the assumption of monoexponential relaxation affected the results is unclear, it is
difficult to envision how one can study contrast transients
without such assumptions. An additional potential limitation of our study was that isolated, non-beating hearts were
examined. In vivo water exchange rates may be somewhat
different, although it appears likely that the concepts
derived from the experiments would remain valid. Finally,
it should be noted that the effects of myocardial injury on
water exchange were not investigated. In a clinical setting,
the structure of the tissue may be injured by previous
ischemic events that may alter the effects of water exchange.
Intravascular-Interstitial Water Exchange
The model predictions depend on the value used to
describe the rate of intravascular-interstitial water exchange. Donahue et al (20) reported this value to be less
than 7 Hz. As pointed out by Sobol et al (21) and by
Donahue et al. (25) the rate of intravascular-interstitial
water exchange can be directly estimated from the measured value of tissue (myocardial) T1 provided an intravascular contrast agent is employed for which the intravascular T1 becomes negligibly short. Under these ‘‘bottleneck’’
conditions, spins originally located in the extravascular
space relax instantaneously when they diffuse into the
vascular space via the efficient relaxation mechanism
provided by the high concentration of the intravascular
contrast agent. Accordingly, the global (tissue) T1 will be
Effects of Water Exchange on Perfusion Measurements
limited by the rate of diffusion of spins into the intravascular space, i.e., by intravascular-interstitial water exchange.
In the current study, we used a concentration of 15 mM of
polylysine-Gd-DTPA and measured a myocardial T1 of
2.7 ⫾ 0.5 Hz. One can calculate that this concentration
would yield an intrinsic intravascular T1 of about 8 msec
[⫽ 1/(1/1.15 ⫹ 15 ⫻ 8.3)]. Assuming 8 msec is ‘‘negligibly
short,’’ therefore, the myocardial T1 measured in our
experiments provides an estimate of intravascular-interstitial water exchange. The value we obtained, 2.7 ⫾ 0.5 Hz, is
comparable to that reported by others (20).
Interstitial-Cellular Water Exchange
The data are roughly consistent with the assumption that
interstitial-cellular water exchange can be considered ‘‘fast’’
under the conditions expected in vivo. Other groups have
come to a similar conclusion (20,25). It may be important to
note, however, that this does not necessarily suggest that
interstitial-cellular exchange is faster than intravascularinterstitial exchange. Rather, this situation may be a consequence of the physiologic reality that intravascular contrast concentrations can reach much higher levels,
especially under first-pass conditions, than interstitial
contrast concentrations. One can imagine that if interstitial
contrast concentrations reached very high levels, enhancement may become dependent on limited interstitialcellular water exchange as well, as pointed out by Donahue
et al (20). Nevertheless, it appears unlikely that this would
occur under conditions of clinical interest.
Relative Contributions of Intravascular and Interstitial
Gd to Enhancement
An interesting prediction of the model is that, under
first-pass conditions, the contribution of a single Gd ion to
changes in image intensity will be greater if the Gd ion is
physically located in the extravascular space than if that
same Gd ion was located in the intravascular space. This is
because a Gd ion in the extravascular space has an opportunity to interact with all extravascular protons, interstitial
and intracellular, due to ‘‘fast’’ interstitial-cellular water
exchange. Because the interstitial plus intracellular volume typically comprises 90% of the voxel, extravascular
Gd ion strongly affect image intensity. If that same Gd ion
were located in the intravascular space, on the other hand,
it would interact only with the intravascular protons,
which only comprise about 10% of the voxel, until extravascular protons diffuse into the intravascular space. This
situation underscores the facts that MRI detects the presence of Gd in the tissue only indirectly and that the
interpretation of MRI contrast enhancement under firstpass conditions is fundamentally different from that of
tracers used, for example, in positron emission tomography (PET) and single-photon emission tomography
(SPECT).
Interpretation of First-Pass vs. ‘‘Steady-State’’ Enhancement
Unlike the situation during first-pass conditions, the model
predicts that after the initial transients following bolus
administration of contrast have subsided, say for images
acquired more than 2 min post-contrast, myocardial water
341
exchange probably has little or no effect on the interpretation of image intensity. The reason for this is that after the
first few passes of the agent through the cardiovascular
system, the concentration of the contrast agent in the blood
is far lower than under first-pass conditions. Specifically,
the model predicts that water exchange will limit enhancement whenever the difference in 1/T1s in the intravascular
and extravascular spaces significantly surpasses the water
exchange rate, 2.7 Hz for our data. For a standard clinical
dose of Gd-DTPA, 0.1 mmol/kg, and assuming the agent
distributes throughout the extracellular space of the body
and that the extracellular space is 30%, the blood T1 would
be approximately 434 msec [ ⫽ 1/(1/1.15 ⫹ 0.1 ⫻ 4.3/0.3)],
whereas a value of much less than 370 msec (1/2.7 Hz) is
required to achieve the ‘‘bottleneck’’ condition. Furthermore, for the case of extracellular agents such as Gd-DTPA
and gadoteridol, the intrinsic intravascular and interstitial
T1s would be comparable due to contrast agent extravasation into the interstitium, further reducing complexities
introduced by water exchange.
We conclude, therefore, that myocardial water exchange
may play an important role under first-pass conditions but
that at later times it has little or no effect on the interpretation of image intensity. This is potentially a very important
conclusion because it suggests that in images acquired
using imaging pulse sequences for which image intensity is
linearly related to 1/T1, such as that previously described
by our group (36), the change in myocardial image intensity will be linearly related to contrast concentration for
images acquired well after the first pass. The interpretation
of imaging results under ‘‘steady-state’’ conditions, therefore, should be directly analogous to those of more established techniques such as PET and SPECT.
Implications for Clinical Studies of Perfusion
The results suggest that although myocardial water exchange introduces significant complexity for potential
quantification of regional myocardial blood flow in ml/
min/g, relative measures of perfusion may be reasonably
accurate. This is potentially an important conclusion because, in a clinical setting, relative information regarding
regional myocardial perfusion is often sufficient. Indeed,
201Tl SPECT images acquired soon after thallium injection,
either at rest or during dypridamole infusion, are routinely
used to test the hypothesis that perfusion is reduced in a
suspect region. Although 201Tl image intensity is only
qualitatively related to perfusion, the results are often the
only information available regarding perfusion in cardiac
patients, and the test has achieved widespread clinical
acceptance.
In summary, we conclude that the myocardial kinetics of
polylysine-Gd-DTPA and gadoteridol are similar to those
of molecules of comparable size, that the rate of water
exchange between the myocardial intravascular and interstitial spaces is about 3 Hz, and that the rate of water
exchange between the interstitial and intracellular spaces
can probably be considered fast under conditions of clinical interest. We also conclude that under first-pass conditions water exchange strongly affects myocardial image
intensity and significantly complicates estimation of myocardial perfusion in ml/min/g, but that regional differences
may still be useful. Finally, we conclude that for images
342
acquired well after the myocardial first pass of extracellular contrast agents such as Gd-DTPA and gadoteridol, the
effects of myocardial water exchange can probably be
ignored.
ACKNOWLEDGMENTS
The authors thank Schering Pharmaceuticals for generously donating the polylysine-Gd-DTPA, and Peter Barker,
PhD, and Dikoma Shungu, PhD, for the software used for
the least squares fits to the FID data. This work was
supported by a Biomedical Engineering Research grant
from the Whitaker Foundation (R.M.J.), an NIH-MSTP
Graduate Fellowship (S.B.R.), and NIH HL53411 (R.M.J.).
Judd et al.
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