Search tips
Search criteria 


Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Magn Reson Med. Author manuscript; available in PMC 2010 June 17.
Published in final edited form as:
PMCID: PMC2887312

Noninvasive Measurement of Myocardial Tissue Volume Change during Systolic Contraction and Diastolic Relaxation in the Canine Left Ventricle


In coronary circulation the flow in epicardial arteries and veins is observed to be pulsatile and out of phase with each other. Theoretical considerations predict that this phenomenon extends to all levels of the vascular tree and leads to a cyclic fluctuation of regional tissue volume. Intramyocardial tissue volume change between end-systole and end-diastole was measured noninvasively with MRI in 10 closed-chest beagles. The displacement encoding with stimulated-echo technique was used to obtain pixel-by-pixel tissue displacement field between end-diastole and end-systole and vice versa in the midlevel left ventricle, from which the 3D strain matrix and volume changes were calculated. The volume change was between 0.8 ± 0.5% (mean ± STD) in the epicardial layer and 1.5 ± 0.6% in the subendocardial layer of the left ventricle. Tissue volume fluctuation reflects the amount of arterial inflow in a heartbeat under the assumption that regional arterial inflow and venous outflow have little time overlap. The corresponding perfusion level was estimated to be from (1.0 ± 0.6) ml/min/g in the epicardial layer to (1.7 ± 0.6) ml/min/g in the subendocardial layer, in good agreement with microsphere measurements in the same dog model. The result supports the notion of high arterial resistance at the microvascular level from intramyocardial pressure during systole.

Keywords: coronary blood flow, microcirculation, capillary permeability, magnetic resonance imaging, DENSE

In coronary circulation blood is transported into the myocardium via the arteries and out of the myocardium via the veins and the lymphatic network. The pulsatility of coronary flow has been studied for several centuries (1): the squeezing effect of myocardial contraction causes arterial blood inflow to peak during diastole and venous blood outflow to peak during systole. Such a direct interaction between contraction and flow also makes myocardial perfusion dependent on the contractility and loading conditions of the heart on the time scale of a heartbeat and is possibly one of the regulatory mechanisms of coronary flow (2). The out-of-phase arterial and venous flow suggests that blood is stored in the vasculature during diastole and is ejected from it during systole, causing the vascular volume to fluctuate in a cardiac cycle. This was indeed observed in several studies (35). We hypothesize that given the intrinsic incompressibility of muscle tissue and the rapid time scale on which the volume change occurs, the periodic change in intramyocardial intravascular blood volume causes the volume of the myocardium to expand and contract periodically.

In particular, if in a local volume of the myocardium the arterial inflow and venous outflow are completely out of phase, then by conservation of mass, the difference between the maximum and minimum tissue volume equals the amount of arterial inflow that takes place during a cardiac cycle. As a consequence of this, the coronary blood flow (per unit of mass) would be given by the product of the heart rate and the change of tissue volume. Because in canine hearts the perfusion rate is approximately 1.1 mL/min/g in the endocardium and 0.8 mL/min/g in the epicardium (6), the expected tissue volume fluctuation is on the order of 1% (7), which is below the sensitivity of previous studies using echocardiography, CT, and MRI tagged imaging (816).

Displacement encoding with stimulated echoes (DENSE) is a phase-difference MRI method capable of high-resolution displacement and strain mapping of the myocardial wall (1725). This technique precisely measures the deformation of the myocardium during any given period of time in the cardiac cycle, and the change of volume can be computed from the deformation.

In this study, DENSE data were acquired in canine hearts for the periods of systolic contraction and diastolic relaxation, from which the tissue volume change was computed. Specifically, the equatorial one third of the left ventricle was divided into three concentric layers, and the volume change of each layer was measured with sufficient precision to detect a 1% change (26).


Animal Preparation

The animal protocol was approved by the Animal Care and Use Committee of the National Institutes of Health and conformed to all relevant institutional and federal guidelines. Ten closed-chest beagles were used in this study (body weight 8.7–12.5 kg). Animals were initially given an intramuscular (i.m.) dose of acepromazine (0.1 mg/kg). Anesthesia was induced i.v. with sodium thiopental (11 mg/kg). The animals were intubated and ventilated at 25–30 breaths/min. Then a cephalic vein, a jugular vein, and a femoral artery were catheterized for blood gas sampling, physiologic monitoring, and drug administration. Body temperature was monitored and maintained with an air heater. Other physiologic parameters that were monitored as well include CO2 level, arterial pressure, ECG, and heart rate. To ensure physiologic stability, blood gas analyses were performed at least every hour. Anesthesia was maintained by isoflurane (1–1.5%). The level of anesthesia was checked with paw and tongue pinching according to NIH Animal Care and Use guidelines to ensure sufficient anesthesia. A cardiac pacing catheter was inserted through the femoral vein into the right atrium to pace the sinoatrial node and maintain a constant heart rate. This rate was chosen to be approximately 10% above the intrinsic rate and was an integer multiple of the breathing rate. Heart rate was typically 120–140 beats/min. Cardiac pacing and ventilation were electronically phase locked to reduce breathing-related motion artifacts in the MRI data.

MRI Protocol

Magnetic resonance imaging was performed on a 1.5 T clinical scanner (Sonata, Siemens, Erlangen, Germany), with a maximum gradient strength of 40 mT/m and a maximum slew rate of 200 T/m/s. The three-dimensional displacement vector field of the myocardial tissue was measured with the DENSE technique (1719,25). It is a phase-difference method that utilizes the stimulated-echo acquisition mode to extend the phase coherence of the proton spins over hundreds of milliseconds. The technique consists of three stages. In the first stage, the spin phase is encoded with its spatial coordinate and stored as longitudinal magnetization all within a duration of 4 ms. In the second stage, the longitudinally stored spin phase does not change while the object moves. The duration of this stage (mixing time) depends on the displacement to be measured, but it is typically 150–250 ms in our case. The minimum mixing time, used in reference measurements, is 10 ms. In the third stage, the magnetization is decoded, so that a phase-shift during the mixing time is proportional to the displacement. This stage takes 3.1 ms and is repeated 16 times using a true-FISP-like readout (27,28), so 16 k-space lines are acquired in 50 ms.

DENSE encoding strength was 3.75 mm/π in the short-axis direction and 1.90 mm/π in the long-axis direction. This low value of the DENSE encoding gradients keeps signal loss due to intravoxel dephasing low. However, this also results in the stimulated echo being mixed with residual stimulated anti-echo and free induction decay (FID) components (28). To isolate the stimulated echo, a phase cycling scheme (0°, 120°, and 240°) of the first 90° pulse was implemented (30,31). Furthermore, an inversion pulse was applied during the mixing period to further suppress the FID component (19). Prior to the DENSE scans a cine data set was acquired at 15 ms temporal resolution based on which the times of end-systole and end-diastole were determined.

Motion during the acquisition would result in artifacts due to the motion sensitivity of the technique. For this reason, acquisition must take place during a period in which the heart motion is minimal, i.e., end-systole (isovolumic relaxation) or end-diastole (isovolumic contraction). Conversely, the absence of visible artifacts in the DENSE images indicates that the heart has not moved during the acquisition. This in turn implies that there is little contraction or dilation of the ventricle during this period, and therefore the strain or volume change is negligible when compared with the net volume change over the net systolic contraction or diastolic dilation.

The DENSE technique is inherently a tissue-tracking technique so regardless of whether the tissue moved within or out of the slice the 3D displacement is accurately measured. Imaging parameters were as follows: field of view (FOV) was 192 × 120 × 48 mm3. Acquisition matrix was 128 × 64 × 16, sinc interpolated to 128 × 80 × 32, giving a final spatial resolution of 1.5 × 1.5 × 1.5 mm3. Overall imaging time for a dataset (including the reference acquisition) was about 40 min.

In the equatorial one-third section of the left ventricle, tissue displacement between end-diastole and end-systole (D–S) and between end-systole and end-diastole (S–D) were measured at 1.5 × 1.5 × 1.5 mm spatial resolution. In order to calculate the local strain and volume change the spatial gradient of the displacement field must be calculated. This is accomplished by using the displacement data from 27 adjacent imaging voxels to estimate the volume change at the location of the central voxel as seen in Fig. 1. The centers of all 27 voxels are shown as spheres, and bound within them is a volume equivalent to 8 voxels. The strain tensor is calculated by a linear fit of voxel displacement versus voxel position, and the volume change is the determinant of the strain tensor. The data from the entire LV section was then segmented into three concentric transmural layers of equal thickness, and the mean tissue volume change over each layer was calculated.

FIG. 1
Spatial configuration of the voxels used in the calculation of the local volume change. Each of 27 displacement measures is used in the linear estimation of the volume change at the location of the central voxel. The centers of all 27 voxels are shown ...

Data acquisition and processing were repeated two or three times for each animal in order to obtain the measurement precision. Additionally, tissue volume change over systolic contraction (D–S) and diastolic relaxation (S–D) were measured separately in each animal and checked for consistency with each other.

Reference data were acquired to correct for measurement errors. In this case, volume change was measured using a 10-ms mixing time during end-systole or end-diastole during which there should be no volume change. This reference measurement is then subtracted from the volume change measurement to obtain the corrected measurement. Only this corrected measurement is reported.

Error Analysis

The range of tissue volume change is approximately ±1%, a small value around zero. So the technique must be sufficiently sensitive around zero volume change. For this reason, it is necessary to investigate the potential sources of error.

As the magnetization is stored along the main field during the mixing time between the encoding and image acquisition, it does not accumulate any phase since longitudinal magnetization does not precess and therefore is not subject to phase errors during this time. For this reason, only phase errors during end-systole and end-diastole, corresponding to the periods in which information is carried by transversal magnetization in our experiment, are relevant.

Along with the phase shift due to tissue motion, other sources of phase shift include thermal noise, gradient errors, main field inhomogeneity, and RF field phase variation. The phase error is given by


where the εT in the sum represents phase errors due to thermal noise, εG errors due to gradient errors, εB main field inhomogeneity variations, and εRF RF field phase variation.

Phase errors due to thermal noise are random and independent among voxels and between measurements and have an average value of zero. Their effect on volume change measurements can be calculated from the signal-to-noise ratio (SNR) of the images. In this work, the apparent volume change expected from thermal noise is 0.08%, well below the measurement accuracy. This estimate is detailed in the Appendix.

Phase errors due to gradient imperfections are independent of the mixing time and should be correctable by acquiring a reference image of minimum mixing time and displacement and subtracting this reference. This procedure was tested using a phantom measurement.

Since the tissue volume change is expected to be on the order of ±1%, a small value around zero, the above correction procedure was tested in a cylindrical static phantom (13 cm length, 4 cm diameter) composed of agarose gel (0.5% concentration), which simulated the spin relaxation behavior of cardiac muscle (T1 = 890 ms, T2 = 60 ms). All imaging parameters and data processing are the same as in the dog experiments. Before reference correction, the volume change was 0.60 ± 0.05% (mean ± SD, n = 3). After reference correction it was 0.00 ± 0.05%. This demonstrates that the reference measurement can correct for gradient imperfections.

The last sources of error are main field inhomogeneity and RF phase variations. Although the stimulated-echo sequence removes phase errors due to magnetic field inhomogeneity, chemical shift, and RF field phase variation (32), it is possible to have imperfect refocusing (and therefore phase errors) if the main field or the phase distribution of the RF field vary during the mixing time with the movement of the heart. To evaluate their influence, S–D and D–S datasets were acquired in three dogs with all displacement encoding gradients set to zero. The apparent volume changes were the result of B0 and B1 phase changes during the mixing period. The measured volume change from end-systole to end-diastole (S–D) is expected to be the negative of the change from end-diastole to end-systole (D–S), so to calculate the average of the two measurements the D–S values were negated first. The overall apparent volume change due to main field inhomogeneity and RF phase variations was 0.20 ± 0.57% (mean ± SD, n = 5). Since a product 1.5 T quadrature volume head coil was used for signal reception and the body coil for RF excitation, RF phase variation over the dog heart was small and the above error was likely dominated by the B0 field.

In addition to experimental noise, the circular geometry of the left ventricle leads to a nonlinear dependence of the tissue displacement field on the X and Y coordinates. In a single voxel this nonlinear deformation is approximated with a linear 3D strain matrix, which may also lead to an error in volume estimates. A simulation of this effect was performed for a typical geometry of the dog heart, which shows that there is likely a 0.1 to 0.2% overestimation of the S–D volume change in the epi- and endocardial layers and a 0.2% discrepancy between S–D and D–S values in the midwall layer. This is detailed in the Appendix.

Thus, the overall accuracy of the measurement of volume change around zero is 0.20%. However, the 0.57% variability in the error associated with the main field variations suggests that fluctuation in the position of the heart due to physiologic fluctuation over the 40 min of data acquisition was the main determining factor of measurement precision.


Figure 2 shows an example of a myocardial tissue displacement vector map over the systolic period. Each arrow represents the three-dimensional displacement vector of a tissue element of 1.5 × 1.5 × 1.5 mm3 (3.4 μL). The low noise of the measurement technique is evidenced by the smoothness of the raw displacement field. The resolution of the technique is evidenced by the large number of transmural displacement measures.

FIG. 2
Three-dimensional displacement vector field of three 1.5-mm-thick transverse slices of the LV. The displacement occurred from end-diastole to end-systole of a cardiac cycle. The voxel size is 1.5 × 1.5 × 1.5 mm3. The displacement generally ...

Figure 3 shows a graphical representation of strain for an S–D measurement in a 1.5-mm-thick slice of the LV, near the septum, using superquadric glyphs (33) gray-scaled by the value of the local volume change. Glyphs are derived from superquadric parametric functions, and the eigensystem of the strain tensor in each voxel defines the glyph shape and orientation. The stretch ratios, rather than the strain eigenvalues, are used as the glyph length scales. The glyphs are overlaid on the original image. The transmural gradient of tissue volume change is evident in this view. In addition, radial thinning as well as circumferential and longitudinal lengthening is evident.

FIG. 3
Superquadric glyph map representing strain overlaid on a magnitude image of a 1.5-mm-thick transverse slice of the LV, focused on the septum. The glyphs’ shape depends on the eigenvalues of the strain tensor and orientation depends upon the corresponding ...

An example of a fractional volume change (ΔV/V) map of a 1.5-mm-thick slice of the left ventricle is shown in Fig. 4, overlaid on the original image. Since the volume change was calculated for cubes of 3-voxel sides (see Fig. 1), the voxels at the surface of the ventricular wall did not have this value assigned. Papillary muscles were also excluded in this analysis.

FIG. 4
Fractional volume change map of a 1.5-mm-thick slice of the left ventricle. The analysis excluded the papillary muscles. Because the calculation was based on cubes of 3-voxel sides, the edge voxels do not have values assigned to them.

Significant regional heterogeneity can be seen in Fig. 1. The error analysis showed that the noise level of the data is not sufficient for a voxel-by-voxel measurement of the volume change. Instead, the ventricular wall is divided into three concentric layers, for which the mean volume changes were calculated. In doing so the variability of the measurement was 0.5%, consistent with the estimated precision under Methods, Error Analysis.

For the 10 dogs, the statistical results for each of the three layers are summarized in Fig. 5. All results are presented as means ± SD. Overall, there was a volume decrease of 0.8 ± 0.6% from end-diastole to end-systole and a corresponding 1.1 ± 0.7% increase from end-systole to end-diastole. This change varied from 1.5 ± 0.6% in the subendocardial layer to 0.7 ± 0.4 and 0.8 ± 0.5% in the mid and epicardial layers.

FIG. 5
Graph with the values of the fractional volume change for each of the three layers. The vertical extent of the rectangles mark the 95% confidence range; the error bars mark the SD among the samples. D–S: from end-diastole to end-systole. S–D: ...

Table 1 gives the volume change of the three layers in the D–S and S–D experiments. The probability that the two measurements have the same mean (P value) was tested with two-way ANOVA using the measurement and the layer as two independent factors. There was no statistically significant difference between the two.

Table 1
Volume Change of the Three Layers

Among different layers, the difference between the endocardial layer and the other two layers was statistically significant (see Table 2). The difference between the two outer layers was not statistically different (see Table 2).

Table 2
Statistical Difference between Layers

Figure 6 shows a graph of the regional perfusion level estimated from the tissue volume change for the three layers, should the arterial blood inflow and venous blood outflow be completely out of phase. The overall mean flow was 1.2 ± 0.4 mL/min/g, in good agreement with the microsphere measurement of 1.2 ± 0.5 mL/min/g in the dog heart under our experimental conditions (34).

FIG. 6
Coronary blood flow estimates of the three layers of the myocardium. The vertical extent of the rectangles mark the 95% confidence range, the error bars mark the SD among the samples.


The relationship between tissue volume change and blood inflow–outflow is governed by conservation of mass. Earlier studies of LV myocardial volume variation in the cardiac cycle (816) generally concluded that the volume is approximately constant, although the possibility of a small variation was not rejected, due to insufficient precision. The out-of-phase flow between the large epicardial arteries and veins is well observed experimentally (1), and theoretical models predict a similar flow pattern in smaller vessels within the myocardium (2,3537). Our measured tissue volume fluctuation of approximately 1% provides a reference point for these microcirculation models.

The relationship between tissue volume and vascular volume fluctuations is more complex, since the capillary walls are highly permeable to water. Experimentally, Toyota et al. (4) observed in vascular casts of rat hearts a vascular volume change equivalent to 7–8% tissue volume between systole and diastole, a much higher level than our tissue volume measurements in beagles (1%). Given the rat myocardial perfusion rate of about 5 mL/min/g and the heart rate of about 400 beats/min (38), the amount of arterial inflow in a heartbeat was similar between the two experiments (1.25 mL/100 g in rats versus 1.0 mL/100 g in beagles). Therefore, the two results can only be reconciled if 6–7% of the tissue water cycles between the vascular and extravascular compartments in a heartbeat. Since this is an unlikely scenario it is possible that the measurements in the vascular casts were influenced by changes in intracoronary pressure during the rapid infusion of the cast fluid, resulting in an overestimation of the vascular volume fluctuation.

The relative large discrepancy between S–D and D–S values in the midwall layer, although not reaching statistical significance, likely came from two sources. One is the interaction between the resolution of the scan and the nonlinear dependence of the displacement field on position, which lead to a 0.2% theoretical difference between the two measurements. The other source is the variability of the position of the midwall layer, since a bias toward the endocardial surface increases the value while the opposite bias decreases the value.

Under the basic assumption that: at the regional level of several microliters of tissue, arterial inflow and venous outflow have little overlap in time, the tissue volume change in our experiments indicates a mean coronary blood flow of 1.1 mL/min/g. Although there is a lack of direct proof of this assumption beyond theoretical models (7,37), the estimate is in agreement with microsphere measurements performed under the same experimental conditions (34). Our result therefore supports the notion that arterial and venous flows in the microvasculature are largely out of phase, and the intramyocardial pressure rise during systole gives significant resistance to arterial inflow a the capillary level. To ultimately validate this assumption it will be necessary to make simultaneous measurements of volume change and perfusion rates under different coronary flow levels.

It is also interesting to note that where the tissue boundary pressure is highest (endocardium) the volume change and therefore according to our assumption the perfusion level is also highest. This transmural gradient could imply a relationship between perfusion level and boundary pressure. However, this should be taken with caution because more factors could be playing a role. More data will be needed to establish this relationship.

It should be noted that the pulsatile coronary blood flow also involves volume changes of epicardial vessels that are not included in the measurement here. The compliance and reserve capacity of epicardial vessels is likely to interact with intramyocardial volume changes in the dynamics of myocardial blood flow.

If validated, myocardial tissue volume fluctuation can potentially be used as a surrogate of perfusion rate. Although this study is limited to measuring the mean value over large concentric layers by its sensitivity, the effect of asynchronous arterial and venous flow can be magnified with intravascular contrast agents, which greatly influence water relaxation in the whole tissue through exchange or remote field effects. Consequently, a small vascular volume fluctuation is reflected by a greater change in the MRI signal and can be quantitatively measured for different phases of the cardiac cycle (5). This technique has potential for a myocardial perfusion measure in steady-state contrast loading conditions, without the scan time limit of bolus-passage based methods.

In this report we made volume change measurements between two phases of the cardiac cycle; given the two-point nature of most existing measurements (echocardiography, micro-CT, and MRI) (4,5,816) in the literature, our first attempt was to make such measurements as comparable to the existing values. Technically current 3D MRI measurements are still long in time, and, as a result, we were limited in getting more time points while maintaining the physiologic condition of the animal. For these reasons, this paper is a first report on noninvasive two-point volume change measurements and comparisons with published values.


Grant sponsor: NHLBI/NIH intramural research funding.

The authors thank Dr. Robert Balaban for his helpful critics of the study and Ms. Joni Taylor for her help with animal care.


The random noise level of the complex, uninterpolated 3D images was approximately 1/25th of the signal level in the heart. Using this SNR level we estimated the variability of the volume measurement from random noise. The corresponding phase noise in each displacement-encoded image is 0.04 radians. This phase noise was converted to displacement measurement noise in the three directions. The resulting noise amplitudes were 0.050, 0.035, and 0.018 mm for X, Y, and Z directions. We then generated random displacement fields for all the pixels of the left-ventricular wall of a dog. The three projections of the fields had normal distributions around zero and standard deviations equal to the displacement noise amplitudes. For each random field the volume changes of the three circumferential layers were computed, and 300 simulation runs were performed. The SD of the volume change from these runs was 0.08% and gave the estimated variability of volume change from random noise in the data.

In addition to experimental noise, the circular geometry of the left ventricle leads to a nonlinear dependence of the tissue displacement field on the X and Y coordinates. In a single pixel of 3.0 × 3.0 mm size for which we calculated the Jacobian determinant, this nonlinear deformation is approximated with a linear 3D strain matrix. This step may also lead to an error in volume estimates. We simulated this effect on a cylinder of 48 mm OD, 28 mm ID, and 24 mm length, which are typical dimensions of the midlevel left ventricle of a dog heart at end-systole, with 10% uniform longitudinal shortening, 8% circumferential shortening on the outer surface, and no volume change, which resulted in a wall thickening of 27% during systole.

The simulated “measured” displacement vector of each pixel was taken to be the mean of the tissue volume in the pixel, and the data processing procedure described under Methods, MRI Protocol, was used to compute the apparent volume changes of the three concentric layers across the cylinder wall. The calculated apparent D–S volume changes were 0.19, 0.09, and 0.10% for the endo-, mid-, and epicardial layers, respectively, and the S–D values were −0.14, 0.11, and −0.06%. This indicates that there may be a systematic overestimation of the endo- and epicardial layer volume changes of between 0.1 and 0.2% and in the midwall layer a systematic discrepancy between S–D and D–S measurements of about 0.20%.


1. Hoffman JI, Spaan JA. Pressure–flow relations in coronary circulation. Physiol Rev. 1990;70:331–390. [PubMed]
2. Zinemanas D, Beyar R, Sideman S. An integrated model of LV muscle mechanics, coronary flow, and fluid and mass transport. Am J Physiol. 1995;268:H633–H645. [PubMed]
3. Liu YH, Bahn RC, Ritman EL. Dynamic intramyocardial blood volume: evaluation with a radiological opaque marker method. Am J Physiol. 1992;263:H963–H967. [PubMed]
4. Toyota E, Fujimoto K, Ogasawara Y, Kajita T, Shigeto F, Matsumoto T, Goto M, Kajiya F. Dynamic changes in three-dimensional architecture and vascular volume of transmural coronary microvasculature between diastolic- and systolic-arrested rat hearts. Circulation. 2002;105:621–626. [PubMed]
5. Wu EX, Tang H, Wong KK, Wang J. Mapping cyclic change of regional myocardial blood volume using steady-state susceptibility effect of iron oxide nanoparticles. J Magn Reson Imaging. 2004;19:50–58. [PubMed]
6. Kim YD, Heim K, Wang YN, Lees D, Myers AK. Effects of isoflurane on regional coronary blood flow and myocardial tissue pressure in chronically instrumented dogs. Anesthesiology. 1994;81:875–887. [PubMed]
7. Spaan JA. Coronary diastolic pressure-flow relation and zero flow pressure explained on the basis of intramyocardial compliance. Circ Res. 1985;56:293–309. [PubMed]
8. Bloomgarden DC, Fayad ZA, Ferrari VA, Chin B, Sutton MG, Axel L. Global cardiac function using fast breath-hold MRI: validation of new acquisition and analysis techniques. Magn Reson Med. 1997;37:683–692. [PubMed]
9. Costa KD, Takayama Y, McCulloch AD, Covell JW. Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium. Am J Physiol Heart Circ Physiol. 1999;276:H595–H607. [PubMed]
10. Iwasaki T, Sinak LJ, Hoffman EA, Robb RA, Harris LD, Bahn RC, Ritman EL. Mass of left ventricular myocardium estimated with dynamic spatial reconstructor. Am J Physiol. 1984;246:H138–H142. [PubMed]
11. King DL, Coffin L, Maurer MS. Noncompressibility of myocardium during systole with freehand three-dimensional echocardiography. J Am Soc Echocardiogr. 2002;15:1503–1506. [PubMed]
12. Maddahi J, Crues J, Berman DS, Mericle J, Becerra A, Garcia EV, Henderson R, Bradley W. Noninvasive quantification of left ventricular myocardial mass by gated proton nuclear magnetic resonance imaging. J Am Coll Cardiol. 1987;10:682–692. [PubMed]
13. Roig E, Georgiou D, Chomka EV, Wolfkiel C, LoGalbo-Zak C, Rich S, Brundage BH. Reproducibility of left ventricular myocardial volume and mass measurements by ultrafast computed tomography. J Am Coll Cardiol. 1991;18:990–996. [PubMed]
14. Shapiro EP, Rogers WJ, Beyar R, Soulen RL, Zerhouni EA, Lima JA, Weiss JL. Determination of left ventricular mass by magnetic resonance imaging in hearts deformed by acute infarction. Circulation. 1989;79:706–711. [PubMed]
15. Swingen C, Wang X, Jerosh-Herold M. Evaluation of myocardial volume heterogeneity during end-diastole and end-systole using cine MRI. J Cardiovasc Magn Reson. 2004;6:829–835. [PubMed]
16. Moore CC, McVeigh ER, Zerhouni EA. Noninvasive measurement of three-dimensional myocardial deformation with tagged magnetic resonance imaging during graded local ischemia. J Cardiovasc Magn Reson. 1999;1:207–222. [PMC free article] [PubMed]
17. Aletras AH, Ding SJ, Balaban RS, Wen H. DENSE: Displacement encoding with stimulated echoes in cardiac functional MRI. J Magn Reson. 1999;137:247–252. [PMC free article] [PubMed]
18. Aletras AH, Balaban RS, Wen H. High-resolution strain analysis of the human heart with fast- DENSE. J Magn Reson. 1999;140:41–57. [PubMed]
19. Aletras AH, Wen H. Mixed echo train acquisition displacement encoding with stimulated echoes: an optimized DENSE method for in vivo functional imaging of the human heart. Magn Reson Med. 2001;46:523–534. [PMC free article] [PubMed]
20. Buonocore MH. Latest pulse sequence for displacement-encoded MR imaging incorporates essential technical improvements for multiphase measurement of intramyocardial strain. Radiology. 2004;230:615–617. [PubMed]
21. Callaghan PT, Eccles CD, Xia Y. NMR microscopy of dynamic displacements–k-space and q-space imaging. J Phys E Sci Instrum. 1988;21:820–822.
22. Gilson WD, Yang Z, French BA, Epstein FH. Complementary displacement-encoded MRI for contrast-enhanced infarct detection and quantification of myocardial function in mice. Magn Reson Med. 2004;51:744–752. [PubMed]
23. Kim D, Gilson WD, Kramer CM, Epstein FH. Myocardial tissue tracking with two-dimensional cine displacement-encoded MR imaging: development and initial evaluation. Radiology. 2004;230:862–871. [PubMed]
24. Reese TG, Wedeen VJ, Weisskoff RM. Measuring diffusion in the presence of material strain. J Magn Reson B. 1996;112:253–258. [PubMed]
25. Aletras AH, Wen H, inventors. US Government, assignee. Methods and apparatus for mapping internal and bulk motion of an object with phase labeling in magnetic resonance imaging. Patent No. 773421. Issued: 24 May 2004.
26. Rodriguez I, Wen H. Quantification of myocardial volume change during systole and diastole using 3D-DENSE. Proceedings of the 12th Annual Meeting of ISMRM; Kyoto, Japan. 2004. p. 654.
27. Wen H, Bennett E, Pai V. Single breath-hold volumetric mapping of the 3D wall motion in the human heart. Proceedings of the 5th Annual Meeting of SCMR; Orlando, FL, USA. 2002. pp. 7–8.
28. Zur Y, Wood ML, Neuringer LJ. Motion-insensitive, steady-state free precession imaging. Magn Reson Med. 1990;16:444–459. [PubMed]
29. Zhu JM, Smith IC. Stimulated anti-echo selection in spatially localized NMR spectroscopy. J Magn Reson. 1999;136:1–5. [PubMed]
30. Callot V, Bennett E, Decking UKM, Balaban RS, Wen H. In vivo study of microcirculation in canine myocardium using the IVIM method. Magn Reson Med. 2003;50:531–540. [PMC free article] [PubMed]
31. Epstein FH, Gilson WD. Displacement-encoded cardiac MRI using cosine and sine modulation to eliminate (CANSEL) artifact-generating echoes. Magn Reson Med. 2004;52:774–781. [PubMed]
32. Frahm J, Merboldt KD, Hanicke W, Haase A. Stimulated echo imaging. J Magn Reson. 1985;64:81–93.
33. Ennis DB, Kindlman G, Rodriguez I, Helm PA, McVeigh ER. Visualization of tensor fields using superquadric glyphs. Magn Reson Med. 2005;53:169–176. [PMC free article] [PubMed]
34. Decking UKM, Wen H, Pai V, Bennett E, Taylor J, Balaban Quantitative assesment of myocardial perfusion by MR imaging of D2O-uptake and by high-resolution, voxel-by-voxel analysis of Gd inflow. Proceedings of the 7th Annual Conference of SCMR; Barcelona, Spain. 2004. p. 320.
35. Chadwick RS, Tedgui A, Michel JB, Ohayon J, Levy BI. Phasic regional myocardial inflow and outflow - comparison of theory and experiments. Am J Physiol. 1990;258:H1687–H1698. [PubMed]
36. Beyar R, Sideman S. Dynamic interaction between myocardial contraction and coronary flow. Anal Quant Cardiol. 1997;430:123–137. [PubMed]
37. Huyghe JM, Arts T, van Campen DH, Reneman RS. Porous medium finite element model of the beating left ventricle. Am J Physiol. 1992;262:H1256–H1267. [PubMed]
38. Hachamovitch R, Wicker P, Capasso JM, Anversa P. Alterations of coronary blood flow and reserve with aging in Fischer 344 rats. Am J Physiol. 1989;256:H66–H73. [PubMed]