Fast High-Resolution Magnetic Resonance Imaging Demonstrates Fractality of Myocardial Perfusion in Microscopic Dimensions
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 140×140 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.
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, where D is denoted as the fractal dimension, which takes values of ≈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.
Materials and Methods
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.
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=140×140 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 where λ 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
The partition coefficient λ 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: In 2 groups, the NMR perfusion imaging technique was validated with the established microspheres technique. Maps of the perfusion-sensitive relaxation time T1 were obtained in the short-axis view at different perfusion levels, and microspheres were injected simultaneously. In one group (n=5), perfusion was varied by reduction of perfusion pressure (to 100, 80, and 70 mm Hg in 4 hearts and to 100, 80, and 50 mm Hg in 1 heart). To induce more heterogeneous variations of perfusion, we elevated in another group (n=12) left LVEDP from 5 to 60 and thereafter to 80 mm Hg at a constant coronary perfusion pressure of 100 mm Hg.
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=140×140 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 samples×coronary flow (flow from flowmeter+0.5 mL/min) per sample weight.
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⇓).
In those hearts in which perfusion-sensitive T1 mapping and first-pass imaging were compared, a stripe of 2×20 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 (2×2-pixel) squares in which signal intensity–time curves were fitted to a Γ-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 16×16 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=16×16=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).
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.
Validation of Perfusion Imaging
The partition coefficient was determined as λ=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.
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 60→80 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).
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).
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.
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 (16×1 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 140×140×1500 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 ≈0.5×0.5 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.
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.
This work was supported by Grant SFB 355 and Graduiertenkolleg “NMR” Grant HA 1232/8-1, Deutsche Forschungsgesellschaft, Forschungsfonds des Klinikum Mannheim.
Original received July 6, 2000; revision received December 14, 2000; accepted December 15, 2000.
- © 2001 American Heart Association, Inc.
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