Investigation of Coronary Vessels in Microscopic Dimensions by Two- and Three-dimensional NMR Microscopic Imaging in the Isolated Rat Heart
Visualization of Vasoactive Effects of Endothelin 1
Background Nuclear magnetic resonance (NMR) imaging of macroscopic coronary vessels is rapidly advancing, whereas little attention has focused on development of NMR techniques for investigation of coronary microvessels. Such techniques would be of particular importance, since conventional methods to visualize coronary microvessels have specific limitations. The aim of our study was to develop two- and three-dimensional (2D and 3D) high-resolution imaging of coronary microvessels. Quantitative analysis of vessel size was performed in tomograms and applied to evaluate the vasoconstrictor effect of endothelin 1.
Methods and Results Angiographic imaging was performed on an 11.75-T magnet by 2D and 3D gradient-echo pulse sequences. In tomograms, the validity of this method in providing correct vessel size was tested by phantom experiments. Experiments were carried out in the isolated constant-pressure–perfused rat heart with continuous registration of coronary flow and left ventricular pressure. NMR pulse sequences were pressure-triggered in mid diastole. Four groups of hearts were studied. In group 1 (n=20), 2D imaging perpendicular and parallel to the long axis of the heart was performed. Cross sections of vessels with diameter >140 μm were clearly detectable. In group 2 (control, n=5) and group 3 (n=13), tomograms perpendicular to the long axis were obtained before and after administration of vehicle (group 2) and 200 pmol endothelin 1 bolus (group 3). Vehicle had no effect on vessel cross section. Endothelin 1, which decreased global coronary flow by 47%, reduced vessel cross section by 38±19%. A weak but, on average, significant inverse correlation between area of cross section and vessel size was found. In group 4 (n=10), 3D imaging was performed in 7 normal hearts and 3 hearts with anterior myocardial infarction. A 3D image of the entire coronary artery tree was obtained, revealing excellent agreement with anatomic studies. In infarcted rat hearts, occlusion of the left coronary artery was demonstrated.
Conclusions Visualization and quantification of coronary microvessels are feasible by NMR microscopy. NMR microscopy bears the potential of becoming a powerful tool for the investigation of the coronary microcirculation.
The field of applications of coronary imaging by means of nuclear magnetic resonance (NMR) techniques is expanding because its technical quality is improving. Initial attempts to use NMR techniques for coronary vascular imaging focused on proximal coronary arteries1 and patency of bypass grafts.2 Burstein3 demonstrated the feasibility of visualizing large coronary arteries of isolated and in vivo rat hearts by a variety of pulse sequences and even determined global flow velocity at the origin of a coronary artery by a bolus tracking pulse sequence. ECG gated pulse sequences that use k-space segmentation4 and spiral k-space trajectories5 allowed high-resolution images of the coronary system in humans with high sensitivity and specificity for coronary stenosis compared with conventional contrast coronary angiography.6
NMR angiographic techniques so far allow visualization of macroscopic coronary vessels; however, methods of investigating coronary vessels in microscopic dimensions are sparse. In vivo microscopy7 is restricted to a small area on the epimyocardial surface; morphometric methods do not provide functional information. Monochromatic synchrotron radiation has recently been applied to visualize coronary arteries with a diameter of approximately 150 μm.8 The latter required intracoronary injection of contrast media. Therefore, additional complementary methods are urgently needed. The technology of NMR microscopy at high fields (>9 T) has advanced greatly during recent years and has become a promising instrument for microscopic coronary imaging.
The detection of microvessels in tomograms requires certain prerequisites. NMR techniques using no contrast agents visualize vessels on the basis of blood flow. Since flow velocity is low in coronary microcirculation, tomographic slices must be thin and therefore gradient fields strong. A powerful external magnetic field and sophisticated switching of gradient fields are required to obtain high spatial resolution. Inside the microscope, available space is limited to maintain high magnetic field homogeneity. Therefore, only small objects can currently be studied. The isolated rat heart is a well-defined model for coronary perfusion and cardiac performance and matches spatial requirements.
The goal of our study was to obtain high-resolution images of the coronary system by flow-weighted pulse sequences in the beating heart. Two- and three-dimensional (2D and 3D) NMR imaging was performed. For 2D imaging, the quality and the limitations of this method had to be defined to resolve cross sections of coronary vessels. The effect of the vasoconstrictor endothelin 1 on cross sections of vessels was tested as an application. Endothelin 1 was used because we had previous experience in the model of the isolated rat heart9 10 and because there is evidence that its vasoconstrictor potency is high, is long lasting, and depends on vessel size.11 In addition, we applied 3D NMR imaging to the coronary artery tree, including small branches. Images were compared with the established postmortem anatomy of the rat coronary artery tree. Finally, hearts with chronic coronary artery occlusion were investigated.
Heart Preparation and Perfusion System
Hearts of male Wistar rats (body weight, 300 to 400 g, anesthetized with pentobarbital sodium 20 mg IP) were rapidly excised and immersed in ice-cold buffer. The interval between thoracotomy and attachment to the perfusion system was <2 minutes. Retrograde perfusion via the aorta started in the Langendorff mode at 37°C with Krebs-Henseleit buffer (concentrations in mmol/L: NaCl 118, KCl 4.7, CaCl2 1.75, MgSO4 1.2, KH2PO4 1.2, EDTA 0.5, NaHCO3 25, glucose 11) equilibrated with 95% O2/5% CO2 (pH 7.4) at constant perfusion pressure (100 mm Hg). A heat-bath jacket of all reservoirs and tubes containing buffer allowed perfusion at constant temperature (37°C) inside the NMR microscope. Before entering the aorta, the perfusate passed a Windkessel, which served as a bubble trap. A small polyethylene tube pierced through the apex of the left ventricle served for drainage of thebesian vein flow. Hearts were placed in an NMR tube (inner diameter, 18 mm), where they were immersed in Krebs-Henseleit buffer. The fluid level was held constant above the heart by means of a suction pump.
We have described the induction of myocardial infarction in detail.12 13 Rats were anesthetized with ether, and left thoracotomy was performed, followed by exteriorization of the heart. The left coronary artery was ligated, and the heart was returned to its normal position. The thorax was immediately closed. After 8 weeks, infarcted hearts were isolated as described above. The model of chronic infarction was used to avoid acute functional complications, including hemodynamic and electrical instability.
Measurement of Hemodynamic Parameters
Coronary flow was measured by an ultrasonic probe (T106, Transonic System Inc). A water-filled latex balloon was inserted into the left ventricle through an incision in the left atrial appendage and through the mitral valve. The balloon was connected to a Statham P23XL pressure transducer (Gould Instruments) by a rigid polyethylene tube to measure left ventricular pressure. Left ventricular pressure was determined by the balloon volume, which was adjusted to an end-diastolic pressure of 5 mm Hg. Left ventricular pressure and coronary flow were recorded on a four-channel recorder (Polygraph, ZAK). Left ventricular pressure was also recorded by a personal computer and used to trigger NMR pulse sequences. The geometry of the NMR microscope demanded that pressure be transduced over a distance of ≈3 m by a polyethylene tube. Therefore, preliminary tests had to confirm the fidelity of pressure recording in magnitude and timing. To exclude an underestimation of systolic and an overestimation of diastolic pressures by potential elasticity of the polyethylene tube, the pressure measuring system was exposed to pressure oscillations with known magnitude. It could be demonstrated that for an oscillation frequency in the range of the heart rate (<320 beats per minute), pressure values of systolic and diastolic pressures were correct. Measurements of pressure actually present inside the left ventricle and pressure recorded at the transducer revealed a delay of <5 ms, which is negligible compared with heart cycle length (>180 ms).
NMR Imaging Techniques
1H images were obtained with a Bruker AMX 500, 11.75-T, 89-mm bore system operating at a proton frequency of 500 MHz. A gradient insert (ID, 43 mm) capable of generating 0.35 T/m with 250-μs switching times was used. The NMR tube (ID, 18 mm) containing the heart was placed in a 20-mm-diameter imaging coil. The offset of tomograms perpendicular to the long axis of the heart corresponds to the valvular plane. The heart was rotated to a standard anterior/posterior position in the NMR imaging coil.
Because of cyclic variation of coronary perfusion, flow-weighted coronary NMR imaging was triggered in diastole. Maximum cardiac motion is present in systole, but passive movement might also occur in diastole. In preliminary experiments with four hearts, the diastolic interval with the minimum extent of motion was defined for triggering. This is important to avoid motion artifacts. The extent of motion inside the NMR tube was determined by a “movie” constructed by cine-pulse sequences. For this purpose, the heart cycle was divided into 32 equidistant intervals, giving the number of pictures in one heart cycle. Flash imaging with a flip angle of 10°, repetition time (TR) of 1/32 of heart cycle length, echo time (TE) of 2.42 ms, and one phase-encoding step per heart cycle was performed for 64 phase-encoding steps in the valvular plane. Comparison of these movies with pressure recording revealed a maximum transversal displacement during systole of 1.5 to 2 mm in one heart cycle. Motion was absent after onset of diastole except for an uncertainty of ≈15 ms due to temporal resolution of the movie; ie, most of the diastole was suitable for image triggering. NMR pulse sequences were triggered by left ventricular pressure 85 to 100 ms after pressure maximum. The ratio of systole and diastole is approximately 1 for the normal heart cycle length of rat heart (≈200 ms); ie, pulse triggering started in mid diastole.
Standard sequences of macroscopic NMR angiography of arterial vessels were applied on the basis of the inflow/outflow effect for the detection of coronary vessels. Images obtained by these sequences show enhanced signal intensity of perfused vessels and reduced intensity of stationary tissue. The cross sections of vessels transsecting the imaging plane14 15 or the whole vessel16 show signal enhancement in 2D or 3D imaging, respectively.
A 256×256 matrix gradient-echo sequence was used for 2D imaging with field echo time (FET) of 2.02 ms, TR of one heart cycle length, four acquisitions, and slice thickness of 200 μm, which resulted in a pixel size of 70×70×200 μm3. Only arterial flow should be imaged, since NMR triggering takes place in diastole and venous flow disappears shortly after systole.17 To demonstrate this, a slice perpendicular to the long heart axis was imaged without and with presaturation below the imaging plane in the apex direction. Potential venous flow directed from the apex should appear on slices before presaturation and disappear afterward.
3D imaging was achieved by a 3D gradient-echo sequence with TE of 2.4 ms and TR of one heart cycle recording a 1283 3D data set with a (140-μm)3 pixel size. The signal of myocardial tissue was additionally suppressed by a magnetization-transfer experiment that preceded the pulse sequence above. Data acquisition time, tac, for angiographic imaging was determined by the equation
with phase-encoding steps p, TR =1/heart rate, and number of acquisitions, nac.
Quantification of Vessel Size in Tomograms
Vessel size was quantified by cross-sectional areas in tomograms. The boundaries of cross sections were determined by the gap between high signal intensity inside the vessel and low intensity in extravascular myocardial tissue. For this purpose, the distribution function of signal intensity of extravascular myocardial tissue with its mean, s̄, and SD, ς, was determined from a region of ≈3 mm2 ≈600 pixels. As preliminary experiments had already shown, no pixels inside this area had signal intensity >s̄+2×ς, whereas inside vessels, only values >s̄+4×ς were found. Thus, cross sections of vessels were clearly distinguished from extravascular tissue, and the area could be determined by counting pixels with intensity >s̄+4×ς. As a lower limit for vessel cross section, an area of 5 pixels was considered.
The vessel cross section visualized in tomograms depends on the angle between intersecting plane and axis of vessel. For angles ≠90°, the area is overestimated. Therefore, vessels were selected that intersected perpendicularly. Criteria of perpendicular intersection were assumed to be fulfilled when the ratio of long to short axis of the cross section was <1.5.
Variations of vessel cross sections after vehicle or drug administration were expressed as relative changes, ie, Δ=(cross section after−cross section before)/cross section before.
Phantom experiments were performed (1) to prove that measurements of vessel cross section were reproducible, (2) to exclude flow dependence of cross-sectional images, and (3) to estimate a potential systematic error of cross-sectional measurements.
Vessel phantoms consisted of polyethylene tubes 500 and 200 μm in diameter perfused by Krebs-Henseleit buffer. Flow was provided and regulated by a perfusion system and measured by the ultrasonic probe mentioned above. The imaging sequence described above for 2D imaging was used. TR was chosen to be 200 ms, corresponding to a heart rate of 300 beats per minute. The intersection angles of the tubes with the imaging plane were 90° (2 tubes), 30° (1 tube), and 45° (1 tube). Each tube was imaged at eight different height positions, including the range of offsets of vertical short-axis images. Imaging and measurement of the cross section were performed five times at each location and at a mean flow velocity of 4 and 100 mm/s, respectively. In summary, we performed, for each phantom, (five measurements per location and flow rate)×(two flow rates)×(eight locations per tube)×(four tubes). The two flow velocities through the tubes included the range found in large coronary arteries down to arterioles. The perfusion system did not allow flow velocity <4 mm/s.
Reproducibility of cross sections was expressed by the SD of the five measurements at each location and flow rate (n=2×8×4=64 for each phantom). The ratio Δcross section/Δmean flow velocity was calculated from differences of corresponding cross sections at 100 and 4 mm/s to evaluate any flow dependence (n=5×8×4=160). The validity of spatial information was expressed by the difference between measured cross section and tube cross section, where the value of tube cross section was adjusted to the intersection angle of tube and imaging plane (n=5×2×8×4=320).
All hearts were given a 10-minute stabilization period after surgical preparation. Four groups of hearts were studied with angiographic imaging.
In group 1 (n=20), NMR tomograms were performed perpendicular (short-axis tomograms) and parallel (long-axis tomograms) to the long heart axis. The offset of short-axis tomograms was the valvular plane. The interval between two succesive images in the apex direction was 1.5 mm; ie, three to five such images were obtained per heart. Imaging parallel to the long heart axis started from the aortic root. The offset plane of long-axis tomograms divided the left ventricular cavity at the level of the valvular plane in two approximately equal parts. This was made possible by preceding imaging perpendicular to the heart axis. About four long-axis tomograms were obtained. In five hearts, short-axis tomograms were obtained before and after magnetic presaturation below the imaging plane to detect potential venous flow.
In group 2 (control group, n=5), the effect of vehicle and in group 3 (n=13), the effect of endothelin 1 (Sigma Chemie) on vessel cross section were tested. The control group provided information of unspecific effects of vehicle, random error of vessel size quantification, and spontaneous variations of vessel cross sections. Short-axis tomograms were obtained after stabilization, and the image that revealed the broadest spectrum of vessel sizes was selected. The slice was reimaged before vehicle (1 mL warmed buffer) or endothelin 1 (200 pmol in 1 mL warmed buffer) was administered. Long-lasting coronary constriction has been described9 for this dosage. In hearts of group 3, the same slice was imaged as soon as a new steady state of hemodynamic parameters was reached and compared with the control image. In group 2, the slice was reimaged 6 minutes after vehicle administration, since a new steady state of hemodynamic parameters is definitely achieved after endothelin 1 application within this time interval.9
In group 4, 3D imaging of hearts (n=10) was performed. In three hearts of this group, myocardial infarction had been induced.
Variations of time courses of hemodynamic parameters were evaluated with the Friedman test. The significance of effects of pharmacological agents on hemodynamic parameters was determined from the Wilcoxon-Mann-Whitney U test.
The areas of tube and vessel cross sections were determined by an investigator blinded to the protocol. The code was broken at the end of data evaluation. For each heart, the mean relative variation of vessel cross sections was determined after vehicle (group 2) or endothelin 1 (group 3) application. In group 3, this was also done for distinct locations: the epicardial region of left and right ventricles and the intramural region. The average variation of the group was calculated from the individual mean variations. The variations of hearts treated with endothelin 1 (group 3) were compared with those that received vehicle (group 2) by the Wilcoxon-Mann-Whitney U test.
In group 2 (control), vessel cross sections were classified in categories of 5 to 7 pixels, 8 to 10 pixels, 11 to 13 pixels, and so on. The average variation and SD after vehicle administration were determined for each category to estimate unspecific effects and the random error as a function of vessel size.
The correlation between vessel cross section A and its relative variation Δ=(Aafter−Abefore/Abefore after vehicle or endothelin 1 administration was tested for each heart with reciprocal linear regression analysis, Δ=m×A−1+b. The mean regression curve of each group was obtained from the individual curves. Slopes of hearts receiving endothelin 1 (group 3) were compared with those receiving vehicle (group 2) by Wilcoxon-Mann-Whitney U test.
The regression analysis was also performed separately for epicardial vessel cross sections of left and right ventricles. Inverse linear regression analysis was performed only if at least six vessel cross sections could be evaluated and if the range of vessel cross sections (largest to smallest cross section) before intervention exceeded 20 pixels.
Data are presented as mean±SD. Differences were considered significant when P<.05.
Heart weight ranged from 1.4 to 1.7 g. Hearts of group 1 and noninfarcted hearts of group 4 maintained a stable function within the magnet for at least 80 minutes after the stabilization period. Coronary flow was 17.6±4.0 mL/min; heart rate, 304±9 beats per minute; left ventricular developed pressure, 133±29 mm Hg; and end-diastolic pressure was adjusted to 5 mm Hg. Coronary flow, left ventricular developed pressure, and heart rate of infarcted hearts were 20 to 23 mL/min, 120 to 140 mm Hg, and 290 to 310 beats per minute, respectively, after stabilization. Within 80 minutes, coronary flow and left ventricular pressure decreased continuously to 16 to 19 mL/min and 100 to 110 mm Hg, respectively. Heart rate remained constant throughout the protocol.
Vehicle administration had no effect on hemodynamic parameters. Application of endothelin 1 had a long-lasting effect on coronary flow. A new steady state was always reached within 6 minutes, and no significant variations occurred for at least 30 minutes. Coronary flow was reduced significantly, from 18.11±2.9 to 9.56±4.6 mL/min (P=.0055). Left ventricular developed pressure decreased by 20% to 40% (P=.046) and heart rate by 5% to 10%; however, the latter change was not significant.
Stationary nuclear proton spins were saturated because of the short TR of gradient-echo sequences, and the corresponding extravascular myocardial tissue showed reduced signal intensity. Signal intensity of this tissue fraction was further suppressed in 3D imaging by the magnetization transfer experiment preceding the gradient-echo sequence. Water proton spins of the perfusate were aligned along the external magnetic field before they fell under the influence of radiofrequency fields. Thus, perfused vessels showed enhanced signal intensity.
2D Imaging: Phantom Experiments
The range of SDs of repetitive measurements of tube cross sections at identical locations was 0 to 2 pixels, with a mean value of 0.78±0.41 pixel, for the 200-μm phantom (1 pixel=15.6% of tube cross section for perpendicular intersection) and 0 to 3 pixels, with a mean of 1.60±0.80 pixels, for the 500-μm phantom (1 pixel=2.5% of tube cross section for perpendicular intersection). The mean ratio Δcross section/Δflow velocity was −0.00425±0.032 pixel/(mm · s−1) for the 200-μm phantom and +0.0080±0.041 pixel/(mm · s−1) for the 500-μm phantom. Cross sections obtained by NMR imaging slightly overestimated the tube cross section, +0.5±1.64 pixels, ie, <7.8±25%, for the 200-μm phantom and +1.8±3.9 pixels, ie, <4.5±10%, for the 500-μm phantom.
2D Imaging: Vessel Detection
The myocardial walls of the left and right ventricles showed homogeneous low signal intensity (Figs 1⇓ and 2⇓). The balloon was visible inside the left ventricle; the right ventricle was collapsed. The buffer outside the heart and the water inside the balloon produced an inhomogeneous pattern of signal intensity. Short-axis tomograms showed cross sections of epicardial coronary vessels. Vessels with a cross-sectional diameter of 140 to 210 μm (≈2 to 3 times pixel size) were clearly detectable (Fig 1b⇓). Vessels can be followed through the slices, and branching is visible (Fig 1a⇓ and 1b⇓). Presaturation below the imaging plane to detect potential venous flow revealed no effect of this procedure on number and size of vessels. Thus, only arterial vessels were detected in tomograms perpendicular to the long heart axis. Long-axis tomograms showed the aortic root (Fig 2⇓). Cross sections of coronary vessels could also be detected in the right ventricular wall in epicardial and intramural locations (Fig 2a⇓).
2D Imaging of Hearts Receiving Vehicle or Endothelin
The vessel cross sections that fulfilled the criterion of nearly perpendicular intersection with the imaging plane were limited to 8 to 32 (median, 17) per heart. In the control group (group 2), the average variation of cross sections after vehicle administration was −2.8±2.9%. The mean slope of inverse linear regression analysis was 7.35±22% · pixel. Changes of cross sections that were classified according to their pixel number before vehicle administration did not depend on vessel size (Table 1⇓). However, the SD decreased from small to large vessels.
Endothelin 1 significantly reduced cross sections of vessels (Figs 3⇓ and 4⇓) by 38±19% (P=.0005 versus control), with 39±29% in the left and 36±23% in the right ventricle. Eight intramural vessel cross sections (range, 5 to 13 pixels) were detected in five hearts of group 3, with an average variation of −26±124% (nonsignificant) and a range of (−100%, +95%).
All slopes of regression lines of reciprocal vessel cross section and its relative constriction by endothelin 1 were negative (Table 2⇓) and differed significantly from slopes of control hearts (P=.0087), demonstrating an inverse relation of the two parameters (Fig 3a⇑). In three hearts, however, the slope of the individual regression curve was not significantly different from zero (Table 2⇓). The correlation coefficients suggest a weak dependence of coronary constriction by endothelin 1 on vessel cross section in most hearts. With decreasing vessel size, the range of scattering increased (Fig 3b⇑), and some vessels even showed vasodilation.
The regional analysis of vessel cross section and its variation after endothelin 1 revealed the same pattern for right and left coronary vessels, respectively. The slopes of regression lines were mainly negative (Table 2⇑), with mean values below zero.
Since 128×128 phase-encoding steps were required, 3D imaging was completed within 60 minutes (Equation 1). In 3D images, the signal intensities of extravascular myocardial tissue, buffer outside the heart, and water content of the intraventricular balloon were reduced, and only little contrast was seen among these structures (Figs 5⇓ and 6⇓). The aortic root and coronary arteries showed enhanced signal intensity. The origin of the right and left coronary arteries from the aorta was visible, and the course of the arteries with their bifurcations was clearly detected down to branches of 280-μm diameter (≈2× pixel size) (Figs 5⇓ and 6⇓). In infarcted hearts, the occlusion of the left coronary artery was visible. Since one 3D image contains the whole data set of the heart, the coronary artery tree can be displayed from any direction. Furthermore, any arbitrary plane can be positioned in the heart, and the cross sections of coronary arteries transsecting this plane can be visualized (Fig 7⇓). By this technique, the spatial course of vessels can be followed (Fig 7⇓).
2D NMR Imaging
This study shows for the first time that microscopically small coronary vessels in the isolated beating heart with diameters of ≈140 μm may be visualized by NMR imaging. To the best of our knowledge, this spatial resolution has not been achieved before by NMR techniques in any intact animal or isolated organ model of the beating heart. So far, only large coronary vessels of rodents could be imaged.3 Since vessel contrast arises from intravascular flow, arteries as well as veins could have been imaged. Magnetic presaturation in the direction of arterial flow should extinguish cross sections of veins, since flow directions are opposite those inside adjacent arteries and veins.
This procedure had no effect on number and size of vessel cross sections in tomograms perpendicular to the long heart axis; ie, only arteries were imaged. This is in agreement with the observation that cardiac venous flow ceases shortly after the onset of diastole.17
Cardiac motion is one inherent obstacle to high-resolution imaging of coronary vessels in microscopic dimensions. Fixation at the perfusion- and pressure-recording system inhibits cardiac motion to some extent in the Langendorff model; however, transverse systolic motion of 1.5 to 2 mm was visible in NMR movies, whereas motion was absent in diastole. The ratio of systole and diastole was approximately 1 for a heart rate of 300 beats per minute. The interval for pulse triggering in diastole was therefore <100 ms. Other investigators reduced heart rate by perfusing the heart with buffer at room temperature.3 This approach, however, would have been a further step away from physiological conditions.
In tomograms, extravascular myocardial tissue revealed very low signal intensity because of saturation of stationary spins, which depends on TR=one heart cycle length≈200 to 250 ms, and spin-lattice relaxation time (T1)≈1500 ms at 11.75 T.18 The fraction of saturation is simply derived from exp(−TR/T1)≈85% to 88%; ie, signal intensity of extravascular myocardial tissue is only 12% to 15% of maximum intensity. Buffer outside the heart and water inside the balloon showed inhomogeneous patterns of signal intensity, since both saturated and nonsaturated spins were present in the imaging plane due to cardiac motion.
Primarily functional information about flow to vessels is provided by NMR angiographic techniques, since intravascular signal enhancement arises from the inflow/outflow effect. The application of this method to morphology requires equivalence of the morphological vascular lumen and the cross-sectional image obtained for a wide range of flow. This equivalence has been accepted for macroscopic NMR angiography; however, it should be reconsidered for applications to microscopic dimensions. Calculations (see “Appendix”) and our phantom experiments suggest flow independence of images as long as mean flow velocity ranges above 3 to 4 mm/s. This condition is definitely fulfilled in the vessels we investigated (diameter greater than pixel size=70 μm). Our phantom experiments revealed that cross sections of vessels (tubes) may be quantified by NMR microscopy. The results are reproducible, and the real cross section is only slightly overestimated. The latter is most probably due to partial-volume effects.
Epicardial microscopy allows a minimal pixel resolution of 5 μm.11 The resolution we reach in the isolated rat heart is a pixel size of 70 μm. However, NMR microscopy is at its very beginning. The maximum spatial resolution of our microscope is in the range of 10 μm in static objects.19 In the model of the beating heart, improvement of spatial resolution is hampered at present by certain restrictions: The diameter of the field of view, which is determined by the size of the heart and cardiac motion, is large for NMR microscopy. The imaging interval must be short for functional studies. At present, one tomogram with acceptable signal-to-noise ratio is constructed from four acquisitions within 4 minutes, which fulfills this condition. To improve spatial resolution by a factor of 2, ie, to 35 μm, the imaging interval must increase by a factor of 8, to 32 minutes. When the time for slice selection is added, we run out of stability of the model, which is 80 to 90 minutes. This problem will be addressed in the future. The signal-to-noise ratio may be increased by special radiofrequency coils and multislice techniques that allow reduction of the time required for slice selection by simultaneous acquisition of eight images. We have applied this technique to imaging of phantoms and will now transfer it to cardiac imaging. In conclusion, although NMR angiography of coronary microvessels has not yet reached the spatial resolution of epicardial microscopy, the advantages are obvious, and it may already be a complementary method for microvascular research. Epicardial microscopy displays only a small region of interest, whereas NMR microscopy visualizes vessels of a transmural slice. After the feasibility of qualitative perfusion imaging of microvessels has been demonstrated, quantitative measurements such as flow velocity are desirable. Pulse sequences already evaluated for macroscopic NMR angiography are to be implemented and tested now in NMR microscopy.
Effect of Endothelin 1
Vehicle administration had no effect on vessel cross section, and the magnitude of the relative variations is in good agreement with the phantom experiments. The increase in the range of scattering with decreasing vessel size probably arises from the increase in random scattering of relative variations of a quantized observable, eg, the vessel cross section, when its value decreases.
On average, cross sections of vessels were significantly reduced after application of endothelin 1. As mentioned above, cross sections of vessels are visualized because of their perfusion. Equivalence between morphological and visualized cross sections is given as long as flow velocity is >3 mm/s. Thus, reduction of visualized cross section means either that morphological cross section is reduced or that mean flow velocity inside the vessel has declined to <3 mm/s. The latter is unlikely in vessels with diameter >70 μm; therefore, variations of vessels represent morphological changes. The effects of endothelin 1 were similar in epicardial vessels of the left and right ventricles, respectively. The response of intramural vessels was very inhomogeneous. Since only eight vessels were considered, no conclusion can be drawn at present. The low number of intramural vessels is probably because our main intention was to find a broad spectrum of vessel sizes. This is most easily achieved by scanning various short-axis views. Most of the intramural vessels we detected during this procedure did not fulfill the criterion of almost perpendicular intersection.
There was a significant inverse correlation between vessel size and its relative decrement. In some hearts, however, this relation was rather weak (low correlation coefficient) or not significant. In those hearts with only a weak correlation, the range of data scattering increases with decreasing vessel size (Fig 3b⇑). One has to discuss whether this is due to inherent constraints of the technique, as suggested by observations in the vehicle group. However, the vehicle and phantom experiments demonstrate that even in small vessels (tubes), the range of scattering is far below the range observed in some hearts after treatment with endothelin 1.
Using epimyocardial microscopy in anesthetized dogs, Lamping et al11 found, after topical application of endothelin, an inverse relation between the degree of constriction and vessel size. Intracoronary application led to a dilation of arteries <130 μm in diameter but a slight constriction of larger vessels. A weak but significant correlation was found between vasoconstriction/vasodilation and vessel size. The mechanism of this relation is not yet understood. One may speculate11 that endothelium-derived relaxing factor (EDRF) is involved, since endothelin may release EDRF from vessels.20 The size of 130-μm diameter≈2×pixel, determining the boundary range between slight vasoconstriction and vasodilation,11 is close to the limit of our spatial resolution. This might explain why scattering of the vasoactive effect of endothelin 1 increases with decreasing vessel size. Some small vessels might already belong to an inhomogeneous group in which vasoconstriction and vasodilation may occur.
Another aspect to be considered is the variation of vessel cross section as a function of time. As a first approach, we assumed that the dynamics of coronary resistance vessels and conductance vessels, ie, the type of vessel we can image, runs parallel after administration of endothelin 1. On this assumption, NMR imaging was performed as soon as hemodynamic parameters and coronary flow, which reflects dynamics of resistance vessels, had reached a new steady state. However, from new data from our laboratory, there is evidence21 that the time courses of resistance and conductance vessels are different. Redilation was observed in images obtained 20 minutes after the first post–endothelin 1 image of many smaller vessels, whereas coronary flow remained at the same low level. This speaks in favor of nonuniform dynamics of vessels after application of endothelin 1. The image obtained shortly after administration of endothelin 1 is just a momentary view of vasodynamics. Perhaps some vessels have not reached their maximum constriction or are already going to redilate at this moment. This variable response might explain the large range of relative variations in some hearts.
3D NMR Imaging
The images show high-resolution 3D coronary angiograms (Figs 5⇑ and 6⇑). Comparison of those images with anatomic studies22 reveals excellent correspondence. A specificity of rat coronary anatomy is a septal artery of variable size arising in 45% from the right and in 55% from the left coronary artery.22 The latter was the case in the heart with chronic left coronary artery occlusion shown in Fig 6⇑. When arising from the left coronary artery, the septal artery courses deep and right, parallel to the right coronary artery and continuing close to the right ventricular surface of the interventricular septum.22
In contrast to NMR tomograms, in which the selected slice is saturated, in 3D NMR angiograms it is the amount of stationary spins inside a volume containing the whole heart. The signal used for vessel imaging arises from magnetized spins of buffer entering the coronary arteries within TR, ie, during one heart cycle. The section of vessel that is filled by magnetized spins is visible. It may not be generally assumed that perfusate filling coronary vasculature is completely exchanged within one heart cycle by perfusate from outside the selected volume. However, a simple consideration will demonstrate that, in fact, a considerable fraction of the arterial system is visualized. Since intravascular volume/heart weight is smaller than 0.20 mL/g,23 a value of 0.28 to 0.34 mL is derived for a heart weight in the range of 1.4 to 1.7 g, as obtained for our animals. Since venous volume is larger than arterial volume, an upper limit for arterial volume is 0.14 to 0.17 mL. Assuming an average coronary flow of 17 mL/min and heart rate of 300 beats per minute results in an arterial inflow of 0.057 mL per beat. Thus, at least 33% to 40% of the coronary arterial system is filled with unsaturated spins within one heart cycle and can be visualized. From this consideration, it follows that 3D imaging primarily provides information about the perfusion state of vessels. Thus, the coronary image may suggest an occlusion if time for perfusate to reach beyond the occlusion is larger than TR, ie, one heart cycle length. On images of infarcted hearts, this occlusion appears at a distance of 3 to 5 mm from the reservoir of unsaturated spins. Hence, if there is still a residual flow beyond the visualized occlusion, mean flow velocity is smaller than 1.5 to 2.5 cm/s. In normal flow conditions, this value would be considerably too small for flow velocity in a large vessel such as the left coronary artery. However, one could imagine that in the case of very low flow, the visualized occlusion would appear in the vessel course before the morphological one.
One disadvantage of 3D imaging with the present technique is the long data acquisition time (≈60 minutes). This long interval might lead to inaccuracies of vessel size determination due to instability of diastolic position and variation of heart size. Furthermore, functional tests such as pharmacological applications are problematic at the moment, since at least two images are required. Thus, the time interval of three-dimensional imaging has to be considerably shortened to become useful for quantitative measurements. One way to achieve this may be Fourier interpolation techniques such as zero filling,24 which should reduce the acquisition interval at least by a factor of four.
We will derive an estimation of perfusion range, quantified by flow velocity, for which the equivalence of morphological cross section and its flow-weighted NMR image holds. The vessel cross section is determined by the number of pixels with high signal intensity. Intensity depends on the amount of magnetized spins entering the selected saturated slice during the TR.25 Maximum contrast is achieved when all spins in vessel cross section are exchanged.25 As a lower limit for maximum contrast, a mean flow velocity, v̄limit, can be derived from slice thickness, d, and TR as
which in our experiments, with d=200 μm and TR=200 to 250 ms, takes the value v̄limit=0.8 to 1 mm/s, ie, velocities just above those in capillaries. In the vessel dimensions we investigated (pixel size=70 μm), mean velocity is definitely higher than 1 mm/s.26 One might argue that the consideration above is based on the assumption of plug flow; ie, flow velocity profile is constant. However, in coronary vessels, laminar flow is present and low flow velocity near the vessel wall might not bring sufficient magnetized spins into the saturated slice; ie, vessel size is underestimated. To weaken this argument, we consider a vessel that is intersected perpendicular to its axis. We will demonstrate that the area of cross section with no maximum contrast in normal flow conditions is negligibly small. According to basic hydrodynamics, the parabolic velocity profile, v(r), in laminar flow is determined by
where v̄ is the mean velocity, r the distance from the vessel axis, and R the radius of the vessel. The distance, rlimit, defining the boundary between complete exchange [v(r)>v̄limit] and only partial exchange [v(r)<v̄limit] of spins during TR must fullfil the relation v(rlimit)=v̄limit and can be derived according to Equation 3,
Since in vessels with diameters >70 μm the relation v̄≫v̄limit=0.8 to 1 mm/s holds, one obtains f≪1; ie, the fraction is negligibly small. The question arises as to what happens when values of v̄ enter the range of magnitude of v̄limit and the difference R−rlimit turns out to be relevant; ie, it has the magnitude of pixel size. To answer this, the ratio of spins, q, exchanged within TR will be calculated for the vessel volume with partial exchange, ie, f×πR2×d. From Equations 3 and 4, one obtains
This means that even when v̄≈vlimit and f turns out to be relevant, ie, the volume of partial spin exchange reaches magnitudes of pixel size, there is still a 50% spin exchange inside this volume, which is enough for detection.
The consideration made above is simplified concerning geometry of slice profile and vessel. Under real conditions, not a rectangular but rather a gaussian slice profile with width d is present; ie, saturation of magnetization is not strictly restricted within a slice of height d. However, because of properties of the gaussian curve, it is negligibly small outside a slice with height 2d. In vessels intersecting at an arbitrary angle, α, only the perpendicular component, cos α×v, contributes to spin exchange. From our inclusion criterion for vessel cross sections (ratio of long to short axis <1.5), it follows that cos α>0.67. Taking the realistic slice profile and the range of “nonperpendicular” vessels into account, the previous paragraph suggests that, as long as v̄>3×v̄limit=2.4 to 3 mm/s, an equivalence of morphological cross section and the image holds. This theoretical consideration is supported by our phantom experiments, with v̄≥4 mm/s giving the true cross section of the tubes and revealing no dependence of pixel number on flow velocity.
This study was supported by grant SFB 355, Graduiertenkolleg “NMR” HA 1232/8-1, Deutsche Forschungsgemeinschaft.
- Received January 9, 1995.
- Accepted February 8, 1995.
- Copyright © 1995 by American Heart Association
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