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© 2001 American Heart Association, Inc.
Integrative Physiology |
Fast High-Resolution Magnetic Resonance Imaging Demonstrates Fractality of Myocardial Perfusion in Microscopic Dimensions
From the Medizinische Universitätsklinik, Universität Würzburg (W.R.B., K.-H.H., P.G., C.W., G.E.), Germany; Department of Cardiovascular Medicine (S.B.), John Redcliffe Hospital, Oxford University, United Kingdom; Institut für Röntgendiagnostik (J.K.), Klinikum Mannheim, Universität Heidelberg, Germany; and Physikalisches Institut (EPV), Universität Würzburg (A.H.), Germany.
Correspondence to Wolfgang R. Bauer, Medizinische Universitätsklinik Würzburg, Josef Schneider Strasse 2, 97080 Würzburg. E-mail w.bauer{at}medizin.uni-wuerzburg.de
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Abstract |
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Abstract—The fractal nature of heterogeneity of myocardial blood flow and its implications for the healthy and diseased heart is not yet understood. The main hindrance for investigation of blood flow heterogeneity and its role in physiology and pathophysiology is that conventional methods for determination of myocardial perfusion have severe limitations concerning temporal and spatial resolution and invasiveness. In isolated rat hearts, we developed a nuclear magnetic resonance technique that does not depend on contrast agents and in which the apparent longitudinal relaxation time is made perfusion sensitive by selective preparation of the imaging slice. This perfusion-sensitive relaxation time is determined within 40 seconds as a map with a high spatial in-plane resolution of 140x140 µm2 and a thickness of 1.5 mm. Perfusion imaging was validated with the established microsphere technique. Additionally, the congruence between perfusion-sensitive T1 maps and first-pass perfusion imaging was demonstrated. As an application of high-resolution perfusion imaging, fractal analysis of the spatial distribution of perfusion was performed. We were able to demonstrate that the fractality of this distribution exists even in microscopic dimensions. Vasodilation by nitroglycerin modulated the fractal pattern of perfusion, and the decrease of the fractal dimension indicated a shift toward homogeneity. This implies that parameters of the fractal distribution depend on the microvascular tone rather than on anatomic preformations; ie, fractality is a functional characteristic of perfusion.
Key Words: magnetic resonance imaging • perfusion • microcirculation • fractality
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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The understanding of the local regulation and coordination of myocardial blood flow is an important goal in cardiac and integrative physiology. It is well established that myocardial blood flow shows considerable spatial heterogeneity.1 2 Quantitative analysis demonstrated3 that after division of the heart into N sections, the relative dispersion RD=SD/mean value of flow of these sections follows a power law,
 | (1) |
1.1 to 1.3.
A gaussian distribution of regional flow would reveal a value of 1.5
and a homogeneous flow of 1. This implies that heterogeneity of blood
flow is neither organized in a purely random way, nor is it uniform,
and that the spatial correlation of regional flow is long ranging. The
origin of this pattern of flow heterogeneity is not understood. Some
theories relate this to the branching of the vessel tree, ie, anatomic
preformations; others postulate that this pattern of heterogeneity is a
result of adaptive coordination of perfusion between myocardial
segments; ie, fractality is a functional characteristic of
perfusion.
Although the understanding of myocardial flow heterogeneity
is of paramount interest in cardiac and integrative physiology,
progress in this field of research is hampered by the limitations of
available methods. The "gold standard" method is the application of
microspheres,3 the
deposition of which in tissue is proportional to perfusion. However,
this is an invasive procedure, the microspheres itself affect
perfusion, the spatial resolution is limited to pieces of 0.2 g, the
preparation of tissue implies systematic errors, and there are only a
few states of perfusion assessable because of the restricted number of
labels of microspheres. Quantitative magnetic resonance techniques that
depend on contrast agent determine perfusion from signal-time
curves4 during the first pass
of the contrast agent; however, repetitive measurements that are
necessary to increase precision or to investigate different perfusion
states are hampered by residual contrast agent.
All methods mentioned have a rather low spatial resolution; ie, at the present it is not clear whether the fractal principle of flow heterogeneity also holds in microscopic dimensions. Therefore, our aim was to develop and validate a fast high-resolution nuclear magnetic resonance (NMR) perfusion imaging technique that does not require contrast agents. With this technique, spatial heterogeneity of perfusion should become visible on high-resolution images, and our next aim was to perform quantitative analysis of this heterogeneity in pilot studies.
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Materials and Methods |
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Experimental Preparations
All experiments with animals were conducted in accordance with the European regulation on care and use of laboratory animals.
Isolated Heart Model
Isolated hearts of male Wistar rats (body weight 300
to 350 g) were perfused (Langendorff mode) with oxygenated
Krebs-Henseleit buffer (37°C) in a perfusion system that was adapted
to a NMR-microscopy system.5
Coronary flow was measured by an ultrasonic flowmeter (T106, Transonic
Systems Inc), and left ventricular pressure was measured by a balloon
that was inserted in the left ventricle and connected to a Statham
P23XL pressure transducer (Gould Instruments). Left ventricular
end-diastolic pressure (LVEDP) was adjusted to 5 mm Hg by the balloon
volume at the beginning of the experiment.
Induction of Coronary Artery Stenosis
To obtain hearts with a stenotic coronary artery,
rats were intubated under ether anesthesia, and after thoracotomy the
heart was exposed. A suture including a probe of 300 µm was
positioned 2 to 3 mm from the origin of the left coronary artery. After
ligation the probe was removed, the heart replaced, and the thorax
closed. Hearts were excised after 2 weeks and treated as described
above.
NMR Imaging
Pulse Triggering
Because the timing and the mode of NMR pulse
triggering by the left ventricular pressure were described in detail
elsewhere,5 only essentials
are repeated. NMR imaging was triggered in early diastole. Cine NMR
imaging had revealed a maximum transversal displacement during systole
of 1.5 to 2 mm in the short-axis view. Motion was absent in diastole;
ie, NMR imaging triggered at the beginning of diastole was not affected
by artifacts.
Noncontrast Perfusion Imaging
Non–contrast-agent techniques make the apparent
T1 of
tissue perfusion sensitive by different labeling of inflowing arterial
spins and stationary spins in the imaging slice. To achieve this, we
performed, in a vertical high-field system (Bruker AMX 500, 11.75 T), a
slice-selective spin
inversion6 (thickness 3 mm,
rectangular shaped) in the short-axis view 3 mm below the valvular
plane of the heart. This was followed by a series of 16 2-dimensional
FLASH images7 8
(TE=1 ms, TR=2.5 ms, flip angle=3°, pixel size in plane=140x140
µm2) within this slice. The imaging slice
had a thickness of 1.5 mm (gaussian shaped) and was located
symmetrically within the inversion slice; ie, >95% of the
gaussian-shaped imaging profile was covered symmetrically by the
inversion slice. It was verified in static fluid phantoms that the
thickness of the inversion slice was the minimum value for which
T1
without slice-selective preparation and
T1 with
slice-selective preparation were identical. This procedure provided
high perfusion sensitivity and excluded systematic errors due to
insufficient inversion of spins in the imaging slice. Imaging was
performed in the short-axis view, because epicardial flow is directed
from base to apex; ie, myocardium in the selected slice is mainly
perfused by equilibrium spins.
A
T1 map
was obtained by a single exponential fit for each pixel from the time
course of the 16 signal
intensities.7 Four
acquisitions were performed to gain the final
T1 map.
The T1
value of a pixel was rejected when the average relative deviation of
the fitting curve and the time course of the signal intensities within
this pixel were >5%. Those pixels appeared black on the
T1 map.
The high-resolution
T1 map
was obtained in <40 seconds. In our setup, the magnetization of
inflowing spins was that of thermomagnetic equilibrium; ie, the
apparent
T1
relaxation in the imaging slice was accelerated. This acceleration
depended on perfusion and mixing of intra- and extravascular spins,
which were predominantly located in the capillary region. Estimation of
the intracapillary-extracapillary water exchange
rate6 and taking into account
the volume distribution of coronary vessel segments and the geometry of
the experimental setup implied a linear dependence between perfusion
and relaxation
rate,6
 | (2) |
is the tissue/perfusate partition
coefficient of water.
Error Analysis and Accuracy of
T1 Measurement
Spatial deviations of
T1 in
myocardium arise as a superposition of spatial heterogeneity of (1)
morphological and physiological parameters, (2) the random error, and
(3) systematic spatial deviations due to the NMR system. The latter 2
were estimated by measuring
T1 and
its SD for stationary buffer, which was added contrast agent
(Gd–diethylenetriamine penta-acetic acid [DTPA]), to cover a range
of T1=1
to
T1=3.5
seconds. There was no systematic spatial deviation of
T1. The
relative spatial SDs of the
T1 maps
were <2%.
It was demonstrated previously in detail5 that almost no motion of the heart was present in diastole in which 2-dimensional FLASH imaging was performed. This implies that T1 measurements were not affected by cardiac motion.
Validation of Perfusion Imaging
Experimental Protocols
The partition coefficient of Equation 2
was
determined from a group of 8 isolated, buffer-perfused hearts. After
beating 40 minutes at a perfusion pressure of 100 mm Hg, hearts were
removed and the wet weight of left and right ventricular wall was
measured. Hearts were placed in an oven (55°C) for 48 hours, and the
partition coefficient was determined according to the
following:
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Local hypoperfusion was investigated in hearts (n=5) with a stenotic coronary artery. Because the spatial resolution of the microsphere technique is lower than the hypoperfused area in the imaging slice, we compared perfusion-sensitive T1 mapping with first-pass imaging after application of contrast agent. First, 3-dimensional NMR angiography5 documented that the affected coronary artery was not occluded. After T1 mapping without contrast agent, a bolus of 0.2 mL Gd-DTPA (1.5 mmol/l) was injected into the Windkessel of the perfusion system, which was located just above the aorta of the heart. A series of T1-weighted diastolically triggered FLASH images (TE=1 ms, TR=2.5 ms, spatial resolution=140x140 µm2) followed.
Perfusion Measurement by Colored
Microspheres
The microsphere technique and its adaptation to the
NMR microscope were recently described by
us.9 10 The number
of microspheres (Dye-Trak; Triton Technology Inc; mean diameter 15
µm) of 1 color was 30 000. Microspheres were flushed into the
aorta with Krebs-Henseleit buffer containing 0.002% Tween 80 at 0.5 mL
per minute over 10 minutes. After the experiments, hearts were frozen
in liquid nitrogen. Transverse slices 4 to 6 mm in thickness were cut
from ventricular base to apex. Within the first slice, which definitely
included the imaging slice, the right and left ventricular wall were
prepared. In 6 hearts of the group in which LVEDP was elevated, the
left ventricular wall was further subdivided into endocardial and
epicardial layers (ratio of wall thickness, 1:2). After digestion of
tissue and solvating the dye from the microspheres, mathematical
decomposition of the composite absorption spectrum (200 to 820 nm)
revealed the absorbance of a single color. Perfusion in the left and
right ventricular wall of the slice was determined from absorbance of
the sample/absorbance of all heart samplesxcoronary flow (flow from
flowmeter+0.5 mL/min) per sample weight.
Data Analysis
In those hearts in which non–contrast-agent
perfusion imaging was correlated with the microsphere technique, the
right and left ventricular walls were delineated manually in
T1 maps
of each perfusion level. In the 6 hearts in which endo- and epicardial
perfusion was analyzed, the endo- and epicardial layers were defined in
the same way as described in the microsphere section. The spatial mean
T1 of
these structures was obtained automatically from averaging the
T1
values of each pixel within the demarcated area. Variations of
perfusion were determined from the mean
T1
values according to Equation 2, which relates perfusion to tissue
volume, whereas it is normally related to the mass. Because
specific weight of myocardium is 1 g/cm3,
NMR perfusion data could be directly converted. The variations of
perfusion obtained from
T1
measurements were compared with the corresponding data from microsphere
measurements by linear regression analysis and Bland-Altman plots
(Figure 2
).
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Pms and T1 data
In those hearts in which perfusion-sensitive
T1
mapping and first-pass imaging were compared, a stripe of 2x20 pixels
ranging from a normal to a hypoperfused region was analyzed.
Signal-to-noise ratio was too low to analyze signal intensity–time
curves in each single pixel. Therefore, the 40-pixel stripe was divided
into 10 (2x2-pixel) squares in which signal intensity–time curves
were fitted to a 
-variate function. From this function the perfusion
index of each square was determined as the slope, as follows: peak
intensity/time of peak intensity (arbitrary units/number of
heartbeats). This perfusion index was correlated with the mean
1/T1 of
each square.
Fractal Analysis of Perfusion
Heterogeneity
Equation 2 shows that the analysis of heterogeneity
of perfusion according to relation 1 is equivalent with that of the
relaxation rate
1/T1.
For fractal analysis, we therefore considered 4 nonoverlapping squares
containing 16x16 pixels that were inserted into
T1 maps
of left ventricular myocardium. In each square, the relative dispersion
RD of
1/T1 was
obtained for N=16x16=256
pixels and thereafter for
N=128, 64, 32, 16, 8, and 4
blocks of neighboring pixels (aggregates). Linear regression analysis
of
logRD(N)
versus logN followed (Figure 4). This procedure was performed for each square under various flow
conditions. We investigated 5 hearts, in each of which coronary flow
was passively altered by adjustment of perfusion pressure at 100, 80,
and 50 mm Hg. To investigate the effect of active vasodynamics on the
heterogeneity of perfusion, we investigated another group of 5 hearts
before, during, and after continuous infusion of nitroglycerin (0.5
mg/min) at constant perfusion pressure (100
mm Hg).
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Statistics
Group data are expressed as mean±SD and were
analyzed according to the Wilcoxon-Mann-Whitney
U test or Scheffe
F test when >2 groups were
compared. Differences were considered as significant when
P<0.05.
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Results |
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Validation of Perfusion Imaging
The partition coefficient was determined as
=0.83±0.003, and there was no difference between left and right
ventricular wall.
Variations of myocardial perfusion were directly reflected
by myocardial
T1
(Figure 1). When coronary flow was varied by reduction of
perfusion pressure, microspheres measured initial perfusion of the
imaged myocardium as 13±1.3 mL/g per minute, and almost equal
decrements were obtained in the right and left ventricular wall. When
variations of perfusion of the imaged region were obtained from
T1
mapping according to Equation 2, a very close correlation was found
with microsphere data
(Figure 2), which was also present when left and right
ventricular wall were analyzed separately as linear regression analysis
demonstrated, as follows:
r=0.96, slope=1.1, and
offset=0.15 mL/g per minute for the left, and
r=0.91, slope=0.92, and
offset=-0.2 mL/g per minute for the right ventricular
wall.
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In hearts in which LVEDP was elevated, microspheres
demonstrated significant different decrements of perfusion in the right
and left ventricular wall at each pressure step, 2.2±1.8 versus
3.3±1.3 mL/g per minute and 1.0±0.36 versus 1.6±0.7 mL/g per minute.
Again, a close correlation was found between perfusion obtained from
T1
mapping according to Equation 2 and microsphere data
(Figure 2). At LVEDP=5 mm Hg, perfusion was higher in the
endocardial layer than in the epicardial one (endocardial-epicardial
difference=2.3±0.3 mL/g per minute [NMR] and 2.5±0.2 mL/g per
minute [microspheres]). The increments of LVEDP induced significant
different decrements
(Figure 1) of endo- and epicardial perfusion
(endocardium/epicardium), as follows: 5
60 mm Hg, 3.8±0.8/2.5±0.4
mL/g per minute (NMR) and 4.0±0.9/2.7±0.5 mL/g per minute
(microspheres), and 6080 mm Hg, 3.5±0.6/1.8±0.3 mL/g per minute
(NMR) and 3.4±0.5/1.9±0.6 mL/g per minute (microspheres). A close
correlation was found between variations of perfusion determined by
T1
mapping and microspheres, as follows:
r=0.90, slope=0.94, and
offset=0.2 mL/g per minute for the epicardium, and
r=0.88, slope=0.90, and
offset=0.13 mL/g per minute for the endocardium.
Evident congruence was found between the hypoperfused
regions obtained from
T1
mapping and first-pass imaging in the hearts with coronary artery
stenosis
(Figure 3). This was also confirmed by the similarity
of the spatial dependence of
1/T1 and
the perfusion index in the stripes
(Figure 3), which is reflected in the close correlation of
both parameters (mean correlation coefficient 0.92, range 0.89 to
0.95).
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Analysis of Heterogeneity of Perfusion
The perfusion-sensitive
T1 maps
appeared very heterogeneous
(Figure 1), and the relative dispersion of the maps was in
the range of 10% to 34%, which was far above the relative error of
T1
determination of 2%. Hence, the heterogeneity of
T1
reflected that of perfusion.
The correlation analysis of relative dispersion of perfusion
versus sample size (logRD
versus logN) demonstrated a
linear logarithmic dependence of both parameters
(Figures 4 and 5) with correlation coefficients ranging
between 0.90 and 0.98 (mean 0.96). In the hearts subjected to varying
perfusion pressure, the mean of the fractal dimension
D was 1.118±0.007 (100
mm Hg), 1.119±0.017 (80 mm Hg), and 1.120±0.016 (50
mm Hg).
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Nitroglycerin infusion increased coronary flow from
16.2±4.3 mL/min to19.0±4.1 mL/min, and after cessation of the drug,
coronary flow declined to 15.3±3.9 mL/min. The corresponding time
course of the mean fractal dimension revealed a decrease from
1.124±0.02 to 1.117±0.013 and thereafter a significant increase to
1.154±0.01
(Figure 5). The
1/T1
maps in
Figure 5 reveal that onset and cessation of nitroglycerin do
not simply shift local perfusion to higher or lower values, but
rearrange spatial heterogeneity of perfusion.
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Discussion |
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Development of Perfusion Imaging
There exist qualitative11 12 and quantitative13 14 15 16 17 non–contrast-agent perfusion imaging techniques. Most of the latter techniques work with active labeling of the inflowing spins. This requires spatial separation of tissue and its associated supplying artery; ie, this approach is suitable for the brain, the kidney, or the isolated perfused heart. However, in the intact heart the complex topography of coronary arteries, left ventricle, and myocardium hampers the active spin labeling. Another obstacle is that many sensitive parameters of spin labeling have to be considered.
In contrast to active spin labeling,
we6 and
others18 exploited the
inflow of equilibrium spins to accelerate longitudinal relaxation by
perfusion after selective inversion. This acceleration is due to inflow
and subsequent transcapillary mixing of equilibrium spins with
stationary spins. The dynamics of the latter are much faster than
T1,6
which implies the linear dependence of relaxation rate on perfusion
(Equation 2). In contrast to us, Reeders et
al18 performed
T1-weighted
spin-echo imaging after selective inversion. A repetition time of 12
seconds and 64 phase-encoding steps imply an acquisition time of 13
minutes, whereas we performed direct
T1
mapping from 16 complete FLASH images during one relaxation course
(snapshot FLASH); ie, 4 acquisitions provided a
T1 map
in <40 seconds. This technique combines high accuracy concerning
determination of
T1 with
a high speed of the imaging procedure.
Potential delay of the inflow effect and, hence, underestimation of perfusion due to arterial spins in the inversion slice was minimized by short-axis imaging, because epicardial flow is directed from base to apex. The contribution of intramyocardial arteries in the inversion slice such as vessels directing blood from epi- to endocardium is negligible as well, given that their volume fraction is <1% of tissue volume. This implies that perfusate inside these arteries is exchanged in <200 ms for perfusion values >3 mL/g per minute. Because we determine relaxation time from an observation period of (16x1 image per heart cycle) >3 seconds, the initial delay is negligible.
The validation of perfusion imaging with the microsphere technique is hampered in part by the fact that the imaging slice is not quite identical with the slice prepared for microsphere measurements. This is due to obvious technical restrictions of the preparation and to the fact that the microsphere technique demands more myocardial mass9 than that of the imaging slice to provide reliable data. On the other hand, the close correlation of microsphere and NMR perfusion data suggests that the difference of the slices is of minor importance. Furthermore, the elevated endocardial perfusion obtained from NMR experiments under baseline conditions (LVEDP=5 mm Hg, perfusion pressure=100 mm Hg) is in agreement with our microsphere data and data from literature.19
It is obvious that the maximum spatial resolution on which the perfusion imaging technique could be validated was that of the microsphere technique, which we already reached in our preparations. The fact that our mathematical model of determining perfusion from T1 is independent from the sample size,6 and the accuracy of the T1 measurements on the scale of 140x140x1500 µm3 makes it evident that perfusion imaging is also valid in these dimensions. The congruence between the perfusion-sensitive T1 map and signal enhancement in the first-pass experiments in hearts with coronary artery stenosis confirm the validity of the non–contrast-agent technique.
In contrast to techniques with active spin labeling, the
method of perfusion mapping by selective preparation of the imaging
slice is not restricted to the isolated rat heart but can be adopted to
the intact
rat20 21 and with
some modifications also to humans, as pilot studies
demonstrate.22 Another
advantage compared with active spin labeling is that our technique is
independent from the
T1 of
perfusate; ie, the strong field dependence of this parameter is
excluded. The
T1 of
myocardium in low field systems is in the range of 1 second, ie, only a
factor of 2 to 2.5 smaller than at 11.7 T. These facts imply that
the field dependence of
T1
should not hamper the transfer to low field systems. A real challenge
for the transfer to the intact animal is that baseline perfusion
(perfusion pressure 100 mm Hg) is much lower than in the isolated
saline perfused heart (in rats, 3.5 to 4 versus 12 to 15 mL/g per
minute), which implies that variations of regional blood flow are much
smaller as well. However, preliminary data in intact rats at 7 T with
coronary artery stenosis demonstrate that under resting conditions
hypoperfused regions can be detected with a spatial in-plane resolution
of 0.5x0.5
mm2.23
In humans, perfusion is even lower, and an increase of perfusion from
baseline to maximum (0.75 versus 3.5 to 4 mL/g per minute) results in a
5% decrease of
T1. This
implies that the accuracy of
T1
determination should be 2% in the segments under consideration to
detect perfusion abnormalities.
Analysis of Heterogeneity of Perfusion
Our correlation analysis of relative dispersion versus
sample size demonstrates that heterogeneity of perfusion can be
described by the power law of Equation 1
(Figures 4 and 5). This implies that heterogeneity of
perfusion reveals a fractal behavior in microscopic dimensions that has
not been demonstrated yet. The origin of this fractality still remains
a matter of discussion. The branching of the vessel tree, which itself
follows a self-similar
pattern,24 may be
responsible as was mentioned by Van Beek et
al.25 Our experiments
demonstrate that this fractality is not a static characteristic of
perfusion. Instead, the data obtained from hearts subjected to
nitroglycerin infusion
(Figure 5) demonstrate that vasodilation modulates the
pattern of flow heterogeneity. After cessation of infusion, this
pattern differs from the initial state. The fractal dimensions in these
experiments demonstrate a shift toward a more uniform distribution of
flow during nitroglycerin infusion. In contrast, when perfusion was
varied by adjustment of perfusion pressure, almost no variations of the
fractal dimension were observed. These observations speak in favor of
the dependence of flow heterogeneity on the microvascular tone rather
than on anatomic preformations.
The fractal analysis as indicated above and the physiological experiments we performed have to be considered as the first steps for our future goals. The way data are obtained from our method allows the investigation of more sophisticated problems and the application of complex mathematical methods, eg, multifractal analysis. Because the perfusion-sensitive T1 map is obtained in <40 seconds, we achieve a high temporal resolution that allows us to study the dynamics of heterogeneity in future projects. The perfusion imaging technique can be combined with metabolic26 and oxygenation22 sensitive imaging, which will provide further insight into the origin of heterogeneity of myocardial blood flow.
Conclusion
We have demonstrated that fast high-resolution NMR
imaging of cardiac perfusion is feasible without contrast agent. The
basis for this technique is the selective labeling of spins in the
imaging slice, which made
T1
perfusion sensitive. We have demonstrated that the fractal behavior of
perfusion is maintained in microscopic dimensions and that this
fractality is most likely a result of the microvascular
tone.
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Acknowledgments |
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This work was supported by Grant SFB 355 and Graduiertenkolleg "NMR" Grant HA 1232/8-1, Deutsche Forschungsgesellschaft, Forschungsfonds des Klinikum Mannheim.
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Footnotes |
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Original received July 6, 2000; revision received December 14, 2000; accepted December 15, 2000.
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