Download Quantification of left and right atrial kinetic energy using four

J Appl Physiol 114: 1472–1481, 2013.
First published March 14, 2013; doi:10.1152/japplphysiol.00932.2012.
Quantification of left and right atrial kinetic energy using four-dimensional
intracardiac magnetic resonance imaging flow measurements
Per M. Arvidsson,1 Johannes Töger,2 Einar Heiberg,2 Marcus Carlsson,1 and Håkan Arheden1
1
Department of Clinical Physiology, Lund University, Skane University Hospital, Lund, Sweden; and 2Department of
Numerical Analysis, Centre for Mathematical Sciences, Lund University, Lund, Sweden
Submitted 30 July 2012; accepted in final form 6 March 2013
four-dimensional phase-contrast magnetic resonance; cardiac magnetic resonance; energy; cardiac function
ON A CONCEPTUAL LEVEL, the heart aims to deliver a pressurized
amount of blood to the systemic and pulmonary circulation.
The external work performed by the heart can be divided into
kinetic energy (KE) and stroke work. Stroke work constitutes
the vast majority (about 99%) of the external work of the left
ventricle (LV) at rest (30, 31) and slightly less (94%) in the
right ventricle [RV (6, 31)]. KE is a measure of how much
potential energy is used to accelerate a volume of blood, for
example, the blood that enters the ventricles from the atria
during ventricular diastole. In other words, KE is a measure of
the amount of work that is directly involved in moving blood,
due to its inertia. KE thus relates to the momentum of blood,
which explains why blood continues to flow out of the heart in
late ventricular systole (34) and has been postulated as an
important factor for cardiac pumping efficiency (23), espe-
Address for reprint requests and other correspondence: H. Arheden, Dept. of
Clinical Physiology, Skane Univ. Hospital, Lund Univ., 22185 Lund, Sweden
(e-mail: [email protected]).
1472
cially so during exercise (22). Atrial KE constitutes a previously unaccounted part of the ventricular external work because ventricular contraction drives atrial filling (2, 36). The
importance of the conservation of KE in the looped heart has
recently been under debate (24, 39, 40). Recent studies have
demonstrated rotational flow patterns in atrial blood and suggested that this arrangement may be beneficial for energy
conservation (14, 23). However, the energy involved in rotational flow has not yet been quantified. We hypothesized that
the organization of atrial blood into rotational flow structures
may function as a hydraulic flywheel. Such a mechanism could
conserve blood KE, which may be increasingly important for
ventricular filling during exercise. Normal physiology aside,
KE and pressure are independent parts of the external work of
the heart, wherefore KE may be affected in disease with
normal blood pressure. Interestingly, while cardiac stroke work
has been thoroughly investigated and holds an important place
in the clinic, intracardiac KE remains largely unexplored. The
current debate on the potential value of energy conservation
lacks data (23, 39). Therefore, the importance of KE in cardiac
function remains unclear.
Cardiac magnetic resonance (CMR) with three-dimensional,
time-resolved phase-contrast sequences (4D PC) is the only
imaging modality that allows for direct quantification of KE in
a volume of blood (14, 25). Recent studies quantified the KE of
ventricular blood during ventricular diastole (12, 13) and over
the entire cardiac cycle (6) and provided new insights into
cardiac energetics and ventricular function. Likewise, studies
of atrial KE may provide new insight into the mechanisms of
atrioventricular interaction. Therefore, the aims of this study
were to quantify the KE of the left and right atria over the
entire cardiac cycle using four-dimensional phase-contrast
magnetic resonance imaging (4D PC-MRI), to measure the
fraction of KE involved in rotational flow, and to identify the
mechanisms contributing to atrial KE.
METHODS
Study population. Fifteen healthy volunteers (age 23–52, 7 females) were included in the study. Subject characteristics are summarized in Table 1. All subjects had blood pressure ⱕ140/90 mmHg,
normal electrocardiogram (ECG), were without medication, and had
no history of cardiovascular or systemic disease. The local institutional committee approved the study, and written informed consent
was obtained from all subjects, in accordance with the Helsinki
declaration.
Magnetic resonance imaging. The subjects underwent CMR examination at rest in the supine position in a 3 T Philips Achieva scanner.
We acquired 4D PC flow images from a box covering the entire heart
and balanced steady-state free precession cine images in the twochamber, three-chamber, four-chamber, and short-axis views. The
sequences used have been previously described in greater detail (6).
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Arvidsson PM, Töger J, Heiberg E, Carlsson M, Arheden H.
Quantification of left and right atrial kinetic energy using fourdimensional intracardiac magnetic resonance imaging flow measurements. J Appl Physiol 114: 1472–1481, 2013. First published March
14, 2013; doi:10.1152/japplphysiol.00932.2012.—Kinetic energy
(KE) of atrial blood has been postulated as a possible contributor to
ventricular filling. Therefore, we aimed to quantify the left (LA) and
right (RA) atrial blood KE using cardiac magnetic resonance (CMR).
Fifteen healthy volunteers underwent CMR at 3 T, including a
four-dimensional phase-contrast flow sequence. Mean LA KE was
lower than RA KE (1.1 ⫾ 0.1 vs. 1.7 ⫾ 0.1 mJ, P ⬍ 0.01). Three KE
peaks were seen in both atria: one in ventricular systole, one during
early ventricular diastole, and one during atrial contraction. The
systolic LA peak was significantly smaller than the RA peak (P ⬍
0.001), and the early diastolic LA peak was larger than the RA peak
(P ⬍ 0.05). Rotational flow contained 46 ⫾ 7% of total KE and
conserved energy better than nonrotational flow did. The KE increase
in early diastole was higher in the LA (P ⬍ 0.001). Systolic KE
correlated with the combination of atrial volume and systolic velocity
of the atrioventricular plane displacement (r2 ⫽ 0.57 for LA and r2 ⫽
0.64 for RA). Early diastolic KE of the LA correlated with left
ventricle (LV) mass (r2 ⫽ 0.28), however, no such correlation was
found in the right heart. This suggests that LA KE increases during
early ventricular diastole due to LV elastic recoil, indicating that LV
filling is dependent on diastolic suction. Right ventricle (RV) relaxation does not seem to contribute to atrial KE. Instead, RA KE
generated during ventricular systole may be conserved in a hydraulic
“flywheel” and transferred to the RV through helical flow, which may
contribute to RV filling.
Atrial Kinetic Energy in Humans
Table 1. Subject characteristics
Subject No.
Gender
Age, yr
Heart Rate,
beats/min
BSA, m2
Blood Pressure,
mmHg
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
F
F
M
M
M
M
M
F
M
M
M
F
F
F
F
52
36
24
23
29
28
28
25
26
25
25
25
30
26
28
58
60
57
58
78
60
69
69
72
77
61
58
70
85
69
1.6
1.9
2.1
2.2
2.1
1.8
1.8
1.8
2.3
2.1
2.2
1.9
1.8
1.8
1.6
140/90
120/65
120/65
110/70
130/80
100/70
120/90
130/90
140/75
125/75
120/70
95/65
120/70
110/70
105/60
M, male; F, female; BSA, body surface area.
Arvidsson PM et al.
1473
We hypothesized that atrial KE during ventricular systole would be
dependent on atrioventricular (AV) plane velocity and atrial volume.
Atrial KE during ventricular diastole was hypothesized to vary with
ventricular wall mass and systolic atrial KE. To determine the contribution of AV plane velocity to atrial KE, the AV plane displacement (AVPD) was measured in all subjects. The measurements were
performed in the three long-axis images, using the same method as
previously described (8, 9). Mean AV plane velocity was computed
by dividing AVPD by the duration of ventricular systole. Atrial and
ventricular volumes, as well as LV and RV masses, were measured by
planimetry.
To enable phase-by-phase comparison of KE between individuals
with minimal smearing due to different duration of cardiac phases
between subjects, KE data were linearly interpolated in time to a
reference heartbeat. For the interpolation, the cardiac cycle was
divided into the following four phases: ventricular systole, early
ventricular diastole (corresponding to the Doppler E wave), diastasis,
and late ventricular diastole (atrial systole, Doppler A wave). The start
of ventricular systole was defined as the first timeframe in each
dataset, triggered to the ECG R wave. The end of ventricular systole
was defined by extrapolating the down slope of the aortic flow curve
to zero. Figure 1 shows how the end of the E wave was defined from
through-plane measurement of transmitral flow. The beginning of the
A wave was defined using the same method and marked the end of
diastasis. In three of the subjects, the resting heart rate was elevated
with subsequent shortening or loss of diastasis, so that the curve
extrapolation method was not applicable. In these cases, we visually
determined the end of the E wave and the beginning of the A wave.
In the two cases without diastasis, only data from the other three
cardiac phases were entered in the mean KE calculations.
After collating data points in one set with mean values, the duration
of each cardiac phase in the reference heartbeat was set equal to the
mean phase duration for all subjects. The mean energy was then
calculated for each time point. To determine the energy content by
volume, the mean energy was divided by the mean volume in each
time point. This produced a measure of KE density, which is proportional to the squared blood velocity. The difference in mean energy
between the atria was also calculated for each cardiac phase. The
increase of KE during early ventricular diastole was measured as the
difference between the early diastolic KE and a baseline, as shown in
Fig. 2. The baseline was estimated by an exponential decay whose
asymptote was zero and whose initial height was chosen to match the
KE just before the beginning of the early diastolic peak. The exponential function of the baseline was determined by performing a linear
Fig. 1. Definition of time phases from in-plane transmitral flow measurements.
The part between 25 and 75% of peak flow of the descending limb of the E
wave and the ascending limb of the A wave were extrapolated to zero to define
the end of early ventricular diastole and the beginning of late ventricular
diastole. Diastasis was defined as the time between the crosses. E, early
ventricular diastole; D, diastasis; A, atrial systole, similar to transmitral
Doppler echocardiography.
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The sequence for 4D PC flow measurements has been validated (7).
Typical imaging parameters for the four-dimensional (4D) flow acquisitions were: echo time (TE)/repetition time (TR) 3.7/6.3 ms, ␣ 8°,
SENSE factor 2, spatial resolution 3 mm isotropic, acquired temporal
resolution of 50 ms, and a reconstructed temporal resolution of 25 ms.
Typical cine imaging parameters were: TE/TR 2.8/1.4 ms, ␣ 60°,
in-plane spatial resolution 1.3 ⫻ 1.3 mm, slice thickness 8.0 mm, no
gap, and temporal resolution 30 ms. In total, the scan time for flow
measurements and cine imaging was about 50 min.
Image analysis and KE calculation. Images were analyzed using an
in-house-developed module for the image analysis software Segment
(http://segment.heiberg.se) (17). A first-order polynomial fit to stationary tissue was used to compensate for eddy currents and other
phase background effects. Velocity aliasing was corrected using phase
unwrapping. The velocity in X, Y, and Z directions was squared for
each voxel and the three-dimensional velocity vector for each voxel
was computed as the square root of the sum of these squared
velocities. The resulting velocity magnitude datasets may be broken
up into slices to facilitate delineation of the atrial blood pool. Velocity
data were therefore sliced with the short-axis cine images as spatial
reference. This enabled us to delineate both atria in the cine images,
after which the delineations were transferred to the 4D dataset and
manually corrected when needed. To calculate the blood mass, the
volume of each voxel was multiplied by the blood density, assumed to
be 1.05 g/cm3. The KE of the blood within each voxel was then
calculated as KE ⫽ ½mv2, where m is the mass of the blood in each
voxel, and v is the blood velocity in each voxel. Total atrial KE was
then calculated by summation of all voxels within the delineations.
The amount of rotational KE in both atria was quantified in each
time frame as follows. First, the instantaneous atrial center of mass
was found using the atrial delineations. Angular momentum around
the center of mass was calculated for each point in time using the
velocity and position vectors for each voxel. Total angular momentum
was obtained through summation of all voxels. The rotational axis was
determined from the center of mass and the direction of angular
momentum around this point. The rotational KE (RKE) about this axis
was then calculated for each voxel as RKE ⫽ ½mv␣2, where v␣ is the
angular velocity component around the computed axis in each voxel.
Total rotational KE was then calculated by summation of all voxels in
each atrium. The degree of helicity in atrial flow during early ventricular diastole was quantified as follows: the average flow direction
was determined from the vector sum of the atrial blood pool. The
angle between this average flow direction and the rotational axis was
then computed. Values near 0 or 180 degrees indicate a net movement
of blood along the rotational axis (helical flow), and values near 90
degrees indicate nonhelical flow.
•
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•
Arvidsson PM et al.
Table 2. Statistical analysis
Compared KE peaks
Ventricular Systole
vs. E Wave
Ventricular Systole
vs. A Wave
E Wave vs.
A Wave
Left atrium
Right atrium
⬍0.001
⬍0.001
⬍0.01
⬍0.001
⬍0.001
⬍0.001
P values are shown. Comparison between kinetic energy (KE) peaks in the
left and right atrium during ventricular systole, early ventricular diastole (E
wave), and late ventricular diastole (A wave), using the Wilcoxon signed-rank
test.
regression analysis of the middiastolic KE down slope, when the
ventricles and atria are stationary. This model thus approximates the
exponential decay of KE in the absence of further cardiac movements
after ventricular systole. The early diastolic KE increase was then
measured as the height of the early diastolic KE peak over the
baseline.
Visualization of KE. The location of KE in the heart was visualized
using the open-source 4D flow visualization software FourFlow
(http://fourflow.heiberg.se). The 4D PC-MRI velocity data and anatomical three-chamber, four-chamber, and short-axis images were
exported to FourFlow using a plugin for Segment. In the visualization,
low KE (⬍0.01 mJ/ml) was gradually faded out, and KE ⬍0.005
mJ/ml was completely masked for clarity, but was included in the total
KE calculations.
Statistical analysis. Measurements of energies and volumes are
expressed as means ⫾ SE, unless stated otherwise. Wilcoxon’s paired
nonparametric test was used to test the significance of differences
between energy peaks. Linear regression analysis was performed to
test the significance of the correlation between AV plane velocity and
mean KE, and atrial volumes and KE. Results with a P value ⬍0.05
were considered statistically significant.
RESULTS
Atrial volumes were within the normal range (20). The mean
left atrial (LA) peak volume was 89 ⫾ 5 ml, and 45 ⫾ 2 ml/m2
normalized to body surface area (BSA). The mean right atrial
Fig. 3. Mean left (LA) and right (RA) atrial KE over the cardiac cycle for all
subjects. Error bars indicate SE. Gray vertical lines differentiate between
ventricular systole (S), early ventricular diastole, diastasis, and atrial contraction, respectively. Three energy peaks are seen: 1) ventricular systole, 2) early
ventricular diastole, and 3) late ventricular diastole. During ventricular systole,
the RA KE is significantly larger than the LA KE. The early diastolic peak was
larger in the LA, and the increase in KE from ventricular end systole to early
ventricular diastole was larger in the LA. The late diastolic peaks were caused
by atrial contraction and did not differ between the atria.
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Fig. 2. Kinetic energy (KE) of the left and right atrium in one representative
subject. Gray boxes indicate actual measurements, and black circles denote
hypothetical KE decay if the heart would cease moving at ventricular end
systole. To find the exponential function of the decay curve, a linear regression
analysis was performed on the middiastolic downward slope, when the ventricles and atria are stationary. The regression curve was then aligned to the
downward slope during ventricular end systole. The shaded area between the
curves therefore is the amount of KE that is added by cardiac movements
during early ventricular diastole. The increase in KE was quantified as the
height of the early diastolic peak over the decay curve, indicated by the
double-headed arrow. The results of these measurements are shown in Fig. 8.
(RA) peak volume was 125 ⫾ 7 ml, and 63 ⫾ 3 ml/m2
normalized to BSA. The ratio between mean RA and mean LA
volumes averaged 1.45 ⫾ 0.07.
LA KE contained three different energy peaks. A typical
subject is shown in Fig. 2. The first peak was found in
ventricular systole, the second in early ventricular diastole, and
the third in late ventricular diastole. P values for comparisons
between peaks are summarized in Table 2. The systolic peak
(1.5 ⫾ 0.1 mJ) was smaller than the early diastolic peak (3.5 ⫾
0.25 mJ, P ⬍ 0.001). Both the systolic and the early diastolic
peaks were larger than the late diastolic peak (0.8 ⫾ 0.1 mJ,
P ⬍ 0.01 for both). During early ventricular diastole, LA KE
increased on average by 3.2 ⫾ 0.27 mJ. Figure 3 shows mean
atrial KE for all subjects over the cardiac cycle. To investigate
the dependence of atrial KE on atrial volume, the mean KE was
divided by the mean atrial volume in each time point. The
results, a measure of KE density, are shown in Fig. 4. The
mean LA blood KE was 1.1 ⫾ 0.1 mJ and correlated with
the mean LA volume, as shown in Fig. 5 (r2 ⫽ 0.38, P ⬍ 0.05).
RA KE contained three energy peaks, similarly to the LA
(Figs. 2 and 3). However, the systolic peak was larger (3.9 ⫾
0.3 mJ) than the early diastolic peak (2.9 ⫾ 0.3 mJ, P ⬍ 0.001).
Both the systolic and early diastolic peaks were larger than the
late diastolic peak (0.9 ⫾ 0.1 mJ, P ⬍ 0.001). During early
ventricular diastole, RA KE increased on average by 1.5 ⫾ 0.1
mJ. The mean RA blood KE was 1.7 ⫾ 0.1 mJ and correlated
Atrial Kinetic Energy in Humans
•
1475
Arvidsson PM et al.
Systolic mean KE [mJ]
A
LA
4
R2 =0.26
y=25x-0.09
P=0.05
3
RA
2
R2 =0.41
y=40x+0.02
P<0.05
1
0
0.00
0.02
0.04
0.06
0.08
AV plane velocity [m/s]
Fig. 5. The relationship between atrial volume and KE. Mean LA (solid
squares) and RA (open circles) KE by mean LA and RA volume, respectively.
The atrial mean KE correlated with the mean atrial volume. These results
suggest that mean atrial volume is a strong predictor of atrial blood KE.
LA
4
R2 =0.55
y=0.014x-0.3
P<0.01
3
RA
2
R2 =0.49
y=0.018-0.02
P<0.01
1
0
0
50
100
150
200
Systolic peak volume [ml]
Fig. 6. The contribution of atrioventricular (AV) plane velocity and peak atrial
volume to atrial KE during ventricular systole. To investigate the contribution
of AV plane movement to atrial blood KE, AV plane velocity was measured
and plotted against the mean KE during ventricular systole. The systolic peak
volumes of the atria were also measured and plotted. A: the correlation between
AV plane velocity and mean atrial KE during ventricular systole. RA KE
correlated with the AV plane velocity, but there was no statistically significant
correlation between AV plane velocity and LA KE. B: the correlation between
peak atrial volume during ventricular systole and mean atrial KE, with a strong
correlation in both atria. Because of the constant-volume properties of the
heart, a decrease in ventricular volume must lead to a corresponding increase
in atrial volume (2, 5). AV plane movement drives atrial filling (2). It was
therefore expected that atrial KE would be determined in part by AV plane
velocity.
was higher than calculations of squared AV plane velocity
times peak atrial blood mass (Fig. 7B). During early ventricular
diastole, LA KE increased more than RA KE (P ⬍ 0.001). The
increase in LA KE during early ventricular diastole correlated
with LV mass (r2 ⫽ 0.28, P ⬍ 0.05; Fig. 8) and with BSA
(r2 ⫽ 0.26, P ⬍ 0.05), but not with atrial size. There was no
correlation between early diastolic RA KE increase and RV
mass, BSA, or atrial size.
The location and magnitude of KE in one representative
volunteer is shown in Fig. 9. During ventricular systole, LA
KE was located mainly at the pulmonary vein inlets, and RA
KE was observed in a toroidal pattern with connections to the
superior and inferior caval veins. During early ventricular
diastole, LA KE was concentrated to the pulmonary vein inlets
and surrounding the mitral valve, and the RA KE torus was
deformed apically through the tricuspid valve into the RV.
During peak filling, the angle between the rotational axis and
the average flow direction was 85 ⫾ 16 (mean ⫾ SD) degrees
for the LA and 39 ⫾ 23 degrees for the RA (P ⬍ 0.001),
indicating helical flow in the RA but not in the LA (Fig. 10).
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with the mean RA volume, as shown in Fig. 5 (r ⫽ 0.53, P ⬍
0.01).
Comparing the LA and RA energy patterns, the systolic
energy peak was larger in the RA (P ⬍ 0.001), and the early
diastolic peak was larger in the LA (P ⬍ 0.05). The late
diastolic peak did not differ significantly between the atria
(P ⫽ 0.17). Mean KE correlated with mean atrial volume over
the cardiac cycle for both atria (Fig. 5). During ventricular
systole, the downward AV plane velocity correlated with the
mean atrial KE (Fig. 6A). Furthermore, the systolic mean KE
correlated with the systolic peak volume in both atria (Fig. 6B).
The product of downward AV plane velocity and peak atrial
volume correlated with systolic mean KE in both atria (P ⬍
0.01 for LA, P ⬍ 0.001 for RA; Fig. 7A). KE during systole
2
Systolic mean KE [mJ]
B
Fig. 4. Atrial KE density over the cardiac cycle for all subjects (mean KE/mean
volume). Error bars indicate SE. Note that the general shapes of the curves are
preserved from Fig. 3, suggesting that volume differences alone do not explain
different KE in the atria. LA KE density increases sharply during early
ventricular diastole for two reasons. 1) As the left ventricle (LV) relaxes, it
generates a pressure gradient that aspirates blood into the ventricle. The
increase in LA KE during early ventricular diastole reflects the ability of the
LV to generate said pressure gradient. Right ventricular relaxation causes a
smaller increase in RA KE, which may be due to the asymmetric configuration
and thin wall of the right ventricle (RV). 2) The LV stroke volume exceeds the
reservoir volume of the LA. To fill the LV, blood is drawn through the atrium
from the pulmonary veins, during which the LA acts as a flow conduit.
Because the velocity of a fluid moving through a vessel is inversely proportional to the squared diameter of the vessel, a smaller atrium results in greater
blood KE during early ventricular diastole.
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Atrial Kinetic Energy in Humans
A
Arvidsson PM et al.
LA
4
Systolic mean KE [mJ]
•
R2 =0.57
y=0.22x+0.12
P<0.01
3
2
RA
R2 =0.64
y=0.24x+0.59
P<0.001
1
0
0
5
10
15
AV plane velocity*peak atrial volume [m/s*ml]
4
3
LA
R2 =0.52
y=6.5x+0.39
P<0.01
2
RA
R2 =0.56
y=4.9x+1.19
P<0.01
1
0
0.0
0.1
0.2
0.3
0.4
0.5
½(peak atrial blood mass)*(AV plane velocity)2 [mJ]
Fig. 7. A: the contribution of downward AV plane velocity times peak atrial
volume to mean atrial KE, during ventricular systole. The combination of these
two factors was a better predictor of atrial KE during ventricular systole than
either factor by itself (cf. Fig. 6). B: the correlation between squared AV plane
velocity times the atrial blood mass and mean atrial KE during ventricular
systole. See text for details.
Late diastolic KE was concentrated to the regions surrounding
the mitral and tricuspid valves, the atrial appendages, and the
caval and pulmonary vein inlets.
Rotational KE constituted on average 46 ⫾ 7% (SD) of total
KE in the LA and 46 ⫾ 8% in the RA (P ⫽ 0.93). The ratio
between rotational KE and total KE was not significantly
correlated to heart rate (P ⫽ 0.08 for both atria) or to mean
total KE (P ⫽ 0.22 for both atria). As shown in Fig. 11,
Fig. 8. The correlation between ventricular mass and increase in atrial KE
during early ventricular diastole. The increase in LA KE correlated with LV
mass. RA KE increase showed no correlation with ventricular mass.
Fig. 9. Visualization of the location and magnitude of KE in the heart of one
representative volunteer at three time points during the cardiac cycle: at peak
ventricular systole (top), at peak early diastolic filling (middle), and during
atrial contraction (bottom). Three imaging planes are shown: three-chamber
view (3CH, left), four-chamber view (4CH, middle), and a midatrial short-axis
view (SAX, right). During ventricular systole, atrial KE is more prominent in
the RA than in the LA, where KE is mainly located near the pulmonary vein
inlets. LA KE increases sharply during early diastolic filling, which is seen as
a streak from the middle of the LA into the center of the LV. Meanwhile, RA
KE also increases, but not as much. This increase in KE is likely caused by
ventricular recoil. The KE during atrial contraction has a similar location as
during early diastolic filling, but the magnitude is smaller. Ao, aorta; Pu,
pulmonary trunk.
rotational KE increased later than nonrotational KE during
systole. The ratio between rotational and nonrotational KE
(Fig. 11) increased toward the end of ventricular systole and
during diastasis and decreased during early ventricular systole,
early ventricular diastole, and atrial contraction. The highest
ratios were attained during end-systole and diastasis.
DISCUSSION
In this article, we present for the first time an analysis of the
KE of the LA and RA blood over the whole cardiac cycle in
healthy volunteers. RA KE is higher than LA KE, and this is
only in part due to higher RA volume compared with the LA.
The higher AV plane velocity in the right heart explains part of
the remaining difference between the RA and LA. This suggests that ventricular longitudinal contraction is the mechanism
responsible for atrial filling and generation of atrial KE and that
ventricular diastolic recoil mainly drives LV filling but not RV
filling.
Relation to earlier studies. Our finding that RA KE is higher
than LA KE in all subjects during ventricular systole is consistent with those made by Prec and Katz (31), who used
intraventricular pressure measurements together with angiocardiography to approximate the amount of KE involved in LV
and RV stroke work and found that KE represents a greater
fraction of the total work in the right heart than in the left heart.
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Systolic mean KE [mJ]
B
Atrial Kinetic Energy in Humans
•
1477
Arvidsson PM et al.
Rotational KE
Non-rotational KE
Ratio RKE/NRKE
Left atrium
2.5
0.5
0.0
0.0
0.2
0.4
0.6
0.8
0.0
1.0
Time [fraction of R-R interval]
Right atrium
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
Ratio
Kim et al. (25) used CMR to estimate the KE of the LV vortex
ring during early ventricular diastole and found a mean KE of
0.43 mJ. In their study, the straight flow was not measured, and
as a consequence the total LV KE was not quantified, which
may explain the lower KE compared with our findings. The
diastolic KE of the ventricles was first quantified using 4D
PC-MRI in the LV by Eriksson et al. (12) and in the RV by
Fredriksson et al. (13). Our measurements of diastolic atrial KE
are similar to the findings of both Eriksson et al. and
Fredriksson et al. We found peak atrial KE during atrial
contraction to be 0.3–2.3 mJ, in good agreement with the
0.25–1.8 mJ described in an earlier echocardiographic study of
1.0
1.0
0.5
KE [mJ]
Fig. 10. Helicity of flow during early ventricular diastole. A: the instantaneous
angle between net flow and axis of rotation in both atria during peak
ventricular filling (mean ⫾ SD). An angle close to 0 or 180 degrees indicates
helical flow, and angles near 90 degrees indicate nonhelical flow. The angle
was significantly lower in the RA compared with the LA, indicating more
helical flow in the RA. B: a streamline visualization of flow across the AV
plane in one subject during peak rapid filling of the ventricles. Streamline color
indicates KE. Solid white arrows indicate flow direction closest to the viewer,
and dashed arrows indicate flow further away. A counterclockwise helix (as
viewed from the apex) was seen in RA flow.
1.5
1.5
Ratio
KE [mJ]
2.0
2.0
0.2
0.4
0.6
0.8
0.0
1.0
Time [fraction of R-R interval]
Fig. 11. Rotational KE (open circles), nonrotational KE (filled squares), and
the ratio between the two (gray diamonds). Means ⫾ SE. When total KE
decreased, the ratio was found to increase, indicating that rotational flow
conserves KE to a greater extent than straight flow does. Systolic peaks in
rotational KE occurred after peaks in straight KE, suggesting that straight flow
drives rotation.
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LA KE by Stefanadis et al. (37). Compared with an earlier
study where we used 4D PC-MRI to quantify the KE of both
ventricles in systole and diastole (6), the present study found
atrial KE to be in the same order of magnitude as ventricular
KE, although lower during both systole and diastole.
At rest, the energy required for LV external stroke work is
typically around 1 J (30, 31). At ventricular end systole, the LA
blood holds a mean KE of 1.2 mJ, roughly one-thousandth of
the energy used for LV stroke work. Mossahebi et al. (28)
calculated the pressure work performed by the recoiling chamber during early ventricular diastole and found values in the
range of 0.05– 0.2 J, at least one order of magnitude greater
than the atrial KE. Therefore, the vast majority of the heart’s
energy expenditures are used to generate the pressure necessary to overcome the arterial pressure, and only little is used to
create flow. KE, however, is independent of pressure conditions and provides a measure of how much energy that goes
into actually moving blood, due to its inertia. Apart from the
late diastolic atrial KE, which is caused by atrial contraction,
KE in the atria is a consequence of ventricular action. Previous
studies have shown that longitudinal pumping provides the
major part of LV and RV systolic function (8), that ventricular
contraction drives atrial filling (3, 8, 36), and that the LV fills
during ventricular diastole by active suction (4, 21). Atrial KE
reflects these physiological mechanisms and gives new insights
into the relationship between the ventricles and atria.
Systolic KE. The increase in atrial KE during ventricular
systole may be explained by the mechanism driving atrial
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Atrial Kinetic Energy in Humans
Arvidsson PM et al.
tance at rest. However, given the narrow range of heart rates
in this study, it is not possible to rule out an increasing
importance during exercise.
Diastolic KE. During early ventricular diastole, the LA KE
quickly rises to the same approximate level as that of the RA
(Fig. 3) and attains a higher KE density (Fig. 4). The increase
in LA energy during early ventricular diastole is larger than
that of the RA despite the smaller AVPD of the LV. The atria
function both as volume reservoirs and flow conduits and
contribute to ventricular filling by delivery of three distinct
volume fractions: the reservoir volume, the conduit volume,
and the atrial stroke volume. The relationship between these
volumes has been thoroughly investigated (19, 20, 38). Under
normal conditions, the conduit volume flows from the pulmonary and caval veins and through the atria during early ventricular diastole. Such acceleration of atrial blood requires a
pressure gradient with lower pressure in the ventricle than in
the atrium. The cause of this gradient can be 1) preatrial,
2) atrial, or 3) postatrial/ventricular. Preatrial generation of a
pressure gradient presupposes an increase in pulmonary and
caval venous blood pressure. Atrial generation of a pressure
gradient involves either atrial contraction due to atrial depolarization or release of atrial intramural elastic energy. Postatrial generation of a pressure gradient involves a decrease in
ventricular pressure, in other words diastolic suction.
A preatrial pressure increase requires buildup of venous
pressure. In the supine position, venous return from the legs is
increased, and RA filling may therefore be somewhat augmented by caval vein pressure. To the best of our knowledge,
there are no physiological explanations as to why pulmonary
venous pressure would suddenly increase at the onset of
ventricular diastole. Furthermore, such an increase in venous
pressure would distend the atrium during early ventricular
diastole. The atria, however, decrease in volume during early
ventricular diastole. A constant pressure head in the veins
would also lead to a progressive increase in total heart volume
during diastasis, which is not observed (2, 5). Therefore, a
preatrial pressure increase seems an improbable explanation
for ventricular filling during early ventricular diastole.
An increase in pressure on the atrial level would involve
either active or passive contraction. Active atrial contraction is
known to occur from the ECG P wave, with atrial repolarization typically occurring simultaneously with the QRS complex.
Therefore, the atria are at their electrical resting state during
early ventricular diastole, and no active contraction may occur.
Passive atrial contraction entails the release of elastic energy,
stored in the atrial wall during ventricular systole. Subsequent
release of this energy was suggested as the main mechanism
for ventricular filling in a previous study (15). However, if
atrial elasticity was indeed the mechanism responsible, we
would expect to see a correlation between atrial size and KE
increase during early ventricular diastole, since a larger atrium
can be expected to store more elastic energy. Atrial size could
not predict early diastolic KE gain, and RA KE gain was
uncorrelated to both RV mass and BSA. Further to this point,
atrial elasticity would be expected to cause backflow in the
pulmonary and caval veins during early ventricular diastole,
which is not observed in healthy individuals. Atrial elasticity is
thus incompatible with the atrial conduit volume, which by
definition requires influx of venous blood during early ventricular diastole. Indeed, the only time in the cardiac cycle with
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filling. The total heart volume has been shown to remain nearly
constant over the cardiac cycle (2, 5). Within this volume, the
movement of the AV plane toward the apex draws blood into
the atria (3, 36, 41). Our results show a greater KE increase in
the RA than in the LA during ventricular systole (Fig. 3). This
finding is consistent with earlier studies that have quantified the
contribution of AVPD in left and right ventricular pumping (9).
The AVPD is smaller in the left heart than in the right, which
partially explains why the LA KE is lower than RA KE during
ventricular systole (Fig. 3). Another cause for the lower systolic LA KE compared with the RA is the smaller total volume
of the LA. A smaller atrium gives a lower systolic KE, and, as
the LA volume is markedly smaller than the RA volume (20),
LA KE is lower during ventricular systole. Indexing atrial KE
to atrial volume reveals that RA blood has a higher KE density
during ventricular systole (Fig. 4). KE density is proportional
to the squared blood velocity, and this difference between the
atria shows that atrial volume is not the only determinant of
atrial KE. As shown in Fig. 6, AV plane velocity and the peak
atrial volume are correlated with atrial KE during ventricular
systole. The composite of these two factors showed a good
correlation with systolic KE, as shown in Fig. 7A. Therefore,
we predict that disease affecting ventricular contractility or
atrial volumes may influence atrial KE. Figure 7B shows that
systolic atrial KE far exceeds the product of squared AV plane
velocity and atrial blood mass. Values on the x-axis can be
interpreted as the theoretical KE resulting from interaction
between the AV plane and the atrial blood pool. Actual
measured KE is higher, suggesting that KE is gained not only
from cardiac movements and volumes but is also significantly
affected by the acceleration of extracardiac blood into the atria.
The size and geometric configuration of the pulmonary and
caval vein inlets may therefore affect the total atrial KE. All
other factors being equal, smaller vessels are more likely to
cause high KE in the inflowing blood.
RA flow is highly organized during ventricular systole, with
inflow from the caval veins contributing to a clockwise (as
viewed from the subject’s right side) rotational movement of
blood (23). While the net velocity of such rotational flow may
be near zero, the total energy content may be high. Indeed,
systolic RA KE was found in a toroidal pattern with connections to the superior and inferior caval veins, matching the flow
characteristics earlier described. Interestingly, we found the
ratio between mean rotational KE and mean total KE to be
almost identical between the atria. This may indicate that the
anatomically offset configuration of pulmonary and caval veins
provides energetically similar conditions in both atria. During
periods of energy loss (end-systole and diastasis), rotational
KE in both atria decreased slower than nonrotational KE and
came to constitute a larger fraction of total KE (the ratio
between rotational and nonrotational KE is shown in Fig. 11).
This finding shows that rotational flow in the heart conserves
energy better compared with nonrotational flow and casts new
light upon earlier studies that have discussed atrial flow energetics (14, 23). Increases in systolic rotational KE came with a
delay compared with nonrotational KE, suggesting that rotational flow is driven by straight flow during systole. The
relationship between total and rotational KE was independent
of heart rate and total KE. Considering the total energy expenditure of the ventricles during systole, this finding implies that
the “flywheel” mechanism is unlikely to be of major impor-
•
Atrial Kinetic Energy in Humans
Arvidsson PM et al.
1479
circulation and is structurally asymmetric compared with the
more cylindrical LV. The myocytes of the RV are also aligned
longitudinally to a greater extent than those of the LV, lacking
the circumferential “constrictor fibers” necessary for radial
stability and generation of high pressures (33). If the RV were
to function as a suction pump, the negative pressure gradient
would likely cause the RV wall to bulge inward during early
diastole. This does not occur in the healthy heart. In contrast to
the LV, the RV may instead depend on the greater reservoir
volume of the RA for filling during early ventricular diastole.
During ventricular systole, this greater volume is subject to a
larger acceleration due to the longer AVPD of the right heart.
At the beginning of ventricular diastole, the RA therefore
contains a larger volume of blood with a higher KE than the
LA. Under such conditions, it is possible that opening of the
tricuspid valve is sufficient to achieve RV filling. The KE of
the inflowing blood could thus contribute to the distension of
the RV and the basal movement of the AV plane, rather than
being a consequence of RV recoil. Meanwhile, the open
tricuspid valve allows the RV to slide past the atrial blood as
the AV plane moves basally, thereby encompassing the atrial
blood and moving it into the ventricle essentially without
imparting velocity onto it. Because this means that the blood
remains relatively stationary in relation to the body and the
CMR scanner, it does not lead to an increase in KE.
In short, the marked increase in LA KE is compatible with
the model of active LV suction during early ventricular diastole. Thus, LA KE may be understood as a consequence of, and
not a cause for, LV filling. Conversely, RA KE does not show
evidence for ventricular suction. It seems reasonable that RV
filling is optimized for the low-pressure conditions of the
pulmonary circulation, where a lack of RV wall thickness and
structural rigidity is compensated for by a higher systolic RA
KE. This RA KE spills over into ventricular diastole and may
be used to fill the relaxing RV.
Physiological implications. With increasing exercise comes
a shortening of ventricular diastole, which in turn requires
more efficient ventricular filling. KE constitutes a greater share
of the total work in the right heart during rest and may become
increasingly important during work (6). In light of this relative
abundance of RA KE and lack of RV diastolic suction, RA KE
may provide a mechanistic explanation to right ventricular
filling, especially so at a higher cardiac output. The higher
end-systolic RA KE compared with the LA means that there is
already a greater movement of blood in the RA that does not
need to be accelerated in early ventricular diastole. Instead,
when the tricuspid valve opens because of declining RV
pressure, RA blood can fill the ventricle by merit of its
relatively high KE. In comparison, the LA blood is more
stationary at the end of ventricular systole. It is likely that both
LA and RA KE will be conserved to a greater extent during
exercise, since there is no diastasis during which KE can
dissipate.
During early ventricular diastole, flow in the RA was more
helical than in the LA (Fig. 10), which may be a consequence
of redirection of rotational flow from systole. This may be a
possible mechanism to facilitate RV filling through conservation of atrial KE. Helical flow is rotational flow with a net
direction along the rotational axis, and this finding appears
consistent with energy conservational redirection of flow (23).
Conserving LA rotation through conversion into helical flow
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slight backflow in the pulmonary veins is during active atrial
contraction. Thus, while atrial elasticity may contribute somewhat to ventricular filling, it is probably not a major factor in
LV filling.
The third possible explanation for a pressure gradient involves a decrease in ventricular pressure, or ventricular suction. Such a mechanism is compatible with the declining atrial
volume during early ventricular diastole and with inflow from
the pulmonary and caval veins. Ventricular suction gives a
mechanistic explanation to the conduit volume. It is also
compatible with a true diastasis, with both the ventricles and
the atria at a “resting state” with no change in volume after the
rapid filling phase. The rapid increase in LA KE during early
ventricular diastole therefore appears more consistent with
ventricular suction than with an increase in venous or atrial
pressure. Earlier studies have also provided evidence for diastolic suction in the LV (1, 4, 21, 28). The cellular mechanism
behind diastolic suction lies in elastic proteins that generate a
restoring force after myocyte shortening below slack length
(18, 32), possibly contributing to the untwisting of the ventricle
during early ventricular diastole (1). Ventricular myocytes are
macroscopically organized into bands with significant differences in direction between the LV and RV (10, 29, 33). This
organizational structure may be important for the ability of the
ventricles to generate suction and may also be important for
differences between LV and RV suction.
We found that RA KE does not increase as much as LA KE
during early ventricular diastole. It has been shown that the
myocardium contains elastic proteins that give rise to ventricular elastic recoil during early diastole (1, 16, 18, 32). Because
these proteins are evenly distributed and integral parts of the
cardiac muscle of both ventricles, ventricular mass may
be considered a measure of the total amount of proteins with
capacity to generate elastic recoil. We therefore hypothesized a
correlation between ventricular mass and the increase in atrial
KE during early ventricular diastole, which would imply that
diastolic atrial KE is generated by ventricular recoil. As shown
in Fig. 8, there was a correlation between LV mass and LA KE
increase. This suggests that suction arising from the LV accounts for about one-quarter of the variability in LA KE
increase in early ventricular diastole. Factors other than LV
suction may account for the other three-fourths of the variability in LA KE increase. A correlation between LV mass and LA
KE increase could also be explained if both factors were
dependent on an external factor, such as body size. If this was
the explanation, we would expect to find a similar correlation
between RV mass and RA KE increase, since the healthy heart
maintains a balance between LV and RV (35). There was no
correlation between RV mass and RA KE increase, implying
that RV filling depends on other mechanisms.
The lack of correlation between RV wall mass and KE
generation during early diastole leads us to believe that structural stability, and not simply the amount of myocardium
available, affects the amount of ventricular recoil. We suggest
that proper structural scaffolding (sufficiently thick and symmetrical myocardial wall) is important for elastic recoil to
occur. In a previous study where myocytes were axially compressed in the absence of sideways support, the thick filaments
tended to bulge sideways, hampering the ability of the myocyte
to generate a restoring force (18). The RV has a thin wall
because of the lower working pressures of the pulmonary
•
1480
Atrial Kinetic Energy in Humans
Arvidsson PM et al.
filling but may instead depend more on the combination of
atrial reservoir function and atrial KE for sufficient filling.
Rotational blood flow contained about one-half of the total
atrial KE and was found to conserve KE to a greater extent than
nonrotational flow did. Rotational flow in the right atrium was
redirected into helical flow during early ventricular diastole,
which may be a mechanism that facilitates RV filling through
conservation of atrial KE.
ACKNOWLEDGMENTS
We thank Christoffer Green for help with FourFlow, Ann-Helen Arvidsson
for help with data collection, and Katarina Steding-Ehrenborg for help with
data analysis.
GRANTS
This study was supported by grants from the Swedish Research Council,
Sweden (2008-2461, 2008-2949, 2011-3916), National Visualization Program
and Knowledge Foundation, Sweden (2009-0080), the Swedish Heart and
Lung Foundation, Sweden, the Medical Faculty at Lund University, Sweden,
and the Region of Scania, Sweden.
DISCLOSURES
No conflicts of interest are declared by the authors.
AUTHOR CONTRIBUTIONS
Author contributions: P.M.A., E.H., M.C., and H.A. conception and design
of research; P.M.A., J.T., and M.C. performed experiments; P.M.A., J.T., and
M.C. analyzed data; P.M.A., M.C., and H.A. interpreted results of experiments; P.M.A. prepared figures; P.M.A. drafted manuscript; P.M.A., J.T.,
E.H., M.C., and H.A. edited and revised manuscript; P.M.A., J.T., E.H., M.C.,
and H.A. approved final version of manuscript.
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