## Highlights

- •Intraventricular vortices support right and left ventricular (RV and LV) function.
- •Flow energy loss in pulmonary and systemic circulation has two peaks.
- •Systemic flow energy loss (EL) is controlled only by heart rate and RV stroke volume (SV).
- •Pulmonary flow EL is independent from LV hemodynamics.
- •RV-SV controls pulmonary and systemic energy dynamics as a blood volume reservoir.

## Abstract

### Background

Biventricular physiological interaction remains a challenging problem in cardiology. We developed a four-dimensional (4D) flow magnetic resonance imaging (MRI) scan and clinically available analysis protocol based on beat tracking of the cardiovascular lumen without contrast medium, which enabled measurement of the biventricular hemodynamics and energetic performance by calculating flow energy loss (EL) and kinetic energy (KE). The aim of this study was to observe the flow patterns and energy dynamics to reveal the physiology of the right and left ventricular systems.

### Methods

4D flow MRI studies were performed in 19 healthy volunteers including 11 male and 8 female. The right and left ventricular systems were segmented to visualize the flow patterns and to quantify the hemodynamics and energy dynamics.

### Results

A large vortex was observed in the left ventricle (LV), along the longitudinal axis, during end diastole and early systole. At early systole, the vortex appeared to facilitate smooth ejection with little EL. In contrast, in the right ventricle (RV), there were vortices near the free wall in both the short and long axes during the diastolic filling phase. Mean EL index during a single cardiac cycle in the right and left heart systems was 0.63 ± 0.16 (0.42–0.99) mW/m

^{2}, and 1.02 ± 0.26 (0.58–1.58) mW/m^{2}, respectively. EL is inevitable loss caused by the vortex flow to facilitate smooth right and left ventricular function and left-sided EL tended to correlate positively with heart rate and right ventricular stroke volume. Kinetic energy at the aortic valve was influenced by LV end-diastolic volume/stroke volume. No gender difference was observed.### Conclusions

The RV appears to function as a regulator of the energy dynamics of the LV system.

## Keywords

## Introduction

Assessment of biventricular hemodynamics and blood flow is an essential part of the work-up in the diagnosis and treatment of cardiovascular disease. Although the right ventricle (RV) and left ventricle (LV), being connected to the pulmonary and systemic circulation, would interact with each other, the biventricular hemodynamics have not yet been fully revealed. For the assessment of biventricular hemodynamics and its interaction, one of the comprehensive approaches is to reveal the mechanical energy dynamics of the RV and LV or pulmonary and systemic circulation, and for this purpose blood flow visualization is one of the novel candidates because it is based on the fluid mechanics of blood flow.

Blood flow visualization using several techniques has been around for decades [

1

, 2

–[3]

] and it has become a powerful technique for assessing the detail of hemodynamics and assessment of blood flow [[4]

]. Echocardiography and cardiac magnetic resonance imaging (MRI) are the most commonly used modalities for blood flow visualization [[4]

,[5]

]. Echocardiography vector flow mapping is one of the well-established methods of blood flow imaging that enables visualization of vortex flow patterns within the heart chambers, especially inside the LV. In this flow visualization tool, kinetic energy (KE) of blood flow and flow energy loss (EL), calculated from the flow velocity vector distribution, has become an important parameter in assessing cardiac workload in a wide range of cardiovascular diseases, including heart failure [[6]

], congenital heart disease [[7]

], and heart valve disease [[8]

]. However, echocardiography has several limitations in clinical application, such as 2D flow measurement and scan accessibility. More specifically, it is difficult to visualize hemodynamics in the RV and the ascending aorta by echocardiography.In the recently introduced technique of 3D cine time-resolved phase-contrast MRI (4D flow MRI), velocity can be measured non-invasively, enabling the assessment of novel hemodynamic measurements [

[9]

,[10]

]. 4D flow MRI is also useful for assessing the blood flow of complicated heart anatomy, even in congenital heart disease [[4]

], or when the pulmonary circulation and right ventricular system is abnormal [[10]

]. We developed 4D flow MRI technique and analysis protocols, based on beat tracking of the cardiovascular lumen, without the use of contrast medium. In the clinical setting, it is desirable to obtain reference values of the parameters in energy dynamics, including EL in the RV and LV systems in the young group. There are some reports about KE of the LV and RV [[11]

,[12]

], but the reference value of the EL is not established. Thus, the aim of this study was to observe the normal flow pattern and energy dynamics to reveal the physiology of the biventricular system, and to establish reference values for these parameters.## Methods

### Study population

The study was approved by the local ethics committee of Kyoto Prefectural University of Medicine, and written informed consent was obtained from all participants.

Between September 2016 and June 2018, 21 healthy volunteers without history of cardiac disease were enrolled: 13 males and 8 females. The mean age was 29.9 ± 5.0 (23–39) years. All subjects underwent MRI scanning including cine MRI (TrueFISP) and whole heart 4D flow MRI. There is no time interval between cine MRI and 4D flow MRI. All subjects were in sinus rhythm. The exclusion criteria were poor image quality and a frame rate of <12/beat caused by elevated heart rate (HR). Two subjects were excluded due to poor quality of the TrueFISP images in one, and to imaging failure in the systolic phase in the other, leaving a final total of 19 subjects (11 males, 8 females).

### 4D flow MRI data acquisition protocol

Non-contrast free-breathing and breath-holding multi-slice 2D cine true fast imaging with steady-state precession (TrueFISP) and free-breathing 4D flow MRI were acquired using a 3T scanner (Magnetom Skyra, Siemens Healthcare GmbH, Erlangen, Germany) with a combination of 18-channel body coil and 32-channel spine coil.

### Fast imaging with steady-state precession sequence

To quantify and facilitate segmentation of the atrial and ventricular volumes and ejection fractions of the right and left ventricles, non-contrast free-breathing and breath-holding sagittal cine views were acquired with TrueFISP. The scanning parameters were as follows: spatial resolution, 0.8 × 0.8 × 4.0 mm; flip angle, 60°; echo time (TE), 1.44 ms; repetition time (TR), 68.46 ms; section thickness, 4.0 mm; average 2; iPAT factor, 4. The typical volume for cine TrueFISP acquisition was 144 mm (right–left), 334 (340 × 98.1%) mm (anterior–posterior), 340 mm (feet–head). However, the field-of-view in each direction was adapted to the body size of the subject. The average acquisition time for TrueFISP was 7 min (range, 5–11 min) with free breathing, and 13 min (range, 12–15 min) with breath hold.

### 4D flow MRI (3D time-resolved cine phase-contrast) sequence

The scanning parameters were as follows: spatial resolution, 1.8 × 1.8 × 4.0 mm; flip angle, 8.0°; TE, 2.86 msec; TR, 67.8 msec. The typical volume for a whole-heart 4D flow MRI acquisition was 144 mm (right–left), 234 (340 × 68.0%) mm (anterior–posterior), 340 mm (feet–head). Velocity encoding of 150 cm/s was used in all three directions. Prospective electrocardiogram gating was used. The cardiac phase depends on the R-R interval of each volunteer, and 13–20 cardiac phases were reconstructed to represent one average heartbeat. Free breathing was allowed and no respiratory motion compensation was performed. Parallel imaging was used for acceleration, with a GRAPPA factor of 2. The average acquisition time for 4D flow MRI acquisition was 18 min (range, 12–25 min).

### Postprocessing of 4D flow MRI

Image analysis was performed by the consensus of three observers (a board-certified radiologist, a cardiac surgeon, and a master course student of medical engineering). Although quantitative evaluation of intra/inter observer differences were difficult in the image segmentation process, we examined the qualitative difference among these 3 observers in more than 3 case, and in each observer, sufficiently small intra observer differences were also qualitatively evaluated using more than 3 cases. The endocardial contours were traced semi-automatically on the sagittal slices for all acquired phases in cine view. Ventricular and atrial volumes were calculated at the end-diastolic and end-systolic phases using commercially available software (iTFlow ver 1.8.5; Cardio Flow Design Inc., Tokyo, Japan). The right and left end-diastolic and systolic volumes (EDV and ESV) were measured on segmented ventricular lumen from multi-slice sagittal TrueFISP images. Papillary muscles and other muscular structures were excluded from the measurement, and outflow structures such as the conus portion were included in the ventricular volume. Cardiac output (CO) was computed from the TrueFISP data as LV or RV stroke volume × HR. Flow volumes were calculated from the 4D flow MRI data. Segmentation of the LV cavity in the 4D flow MRI acquisition was required for the energy analysis, and this was obtained by transforming segmentation of multi-slice TrueFISP sagittal images. Any aliasing was corrected by phase shifting.

Cardiovascular lumen was extracted using the region-growing method on the TrueFISP images, and 3D cine phase contrast image series were superposed on the segmented cardiovascular lumen. The EL in the left heart was calculated from the left atrium to the descending thoracic aorta. EL in the right heart was calculated from the right atrium to the pulmonary artery (PA). Aortic flow was measured at the cross section of aortic valve annulus. PA flow was measured at the cross section of pulmonary valve annulus. KE of the aortic and pulmonary arterial flow was measured at the same levels. KE was defined as

where ρ is the density of blood (1060 kg/m

$\text{KE}=\frac{1}{2}\rho \int \left(\sum _{i}{{u}_{i}}^{2}\right)dA,$

where ρ is the density of blood (1060 kg/m

^{3}), i is the arbitrary direction of the Cartesian coordinates, u_{i}is the velocity vector component of direction i, and*dA*is the increment of area change in the cross-section. Kinetic energy index (KEI) is defined as KE per body surface area (BSA). Visualization techniques used for 4D flow MRI include vector maps, streamlines, and pathlines. The flow energy loss was calculated from the visualized flow velocity distributions, with the methods described in Appendix 1. Energy loss index (ELI) is defined as EL per BSA.### Statistical analysis of clinical and measured data

Clinical data including sex, age, height, body weight, and BSA were collected. The hemodynamic parameters obtained from MRI included HR, ejection fractions (EF), EDV, ESV, and stroke volume (SV). From the 4D flow MRI, the flow streamline, total flow rate, KE, EL, and energetic performance index of the right and left sides of the heart were calculated.

Continuous data were expressed as the mean ± standard deviation (SD). All results were corrected according to the BSA. Wilcoxon signed-rank tests were used to compare paired data between males and females. Correlations between the biventricular EL, flow, and other parameters (i.e. contralateral EL, KE, flow and KE/EL EDV, ESV, SV, and EF of both sides of the heart, HR) were evaluated. In the case of the number of subjects was 19, correlation values

*r*> 0.433 is equivalent to*p*-value <0.05. Values of*p*<0.05 were considered statistically significant. The statistical analyses were performed using JMP software version 14 (SAS Institute Inc., Cary, NC, USA).## Results

### Clinical characteristics and biventricular dynamics

Demographic data of the studied subjects and the parameters derived from TrueFISP are listed in Table 1. Chamber sizes were adjusted for BSA and identified using an index; e.g. LV-EDVI indicates left ventricular end diastolic volume index. Gender difference was detected only in body size (Table 1).

Table 1Demographic data and results of TrueFISP of 19 volunteers.

Numbers | Total 19 | Male 11 | Female 8 | P value |
---|---|---|---|---|

Age (years) | 29.9 ± 5.0 | 32.6 ± 2.8 | 26.3 ± 5.3 | 0.0135 |

Height (cm) | 166.2 ± 7.5 | 169.2 ± 7.0 | 162 ± 6.4 | 0.0344 |

Weight (kg) | 60.1 ± 10.5 | 65.5 ± 9.1 | 52.5 ± 7.3 | 0.0090 |

BSA (m²) | 1.6 ± 0.2 | 1.7 ± 0.1 | 1.5 ± 0.1 | 0.0057 |

HR (bpm) | 73.7 ± 14.4 | 67.8 ± 8.58 | 81.8 ± 17.4 | 0.1165 |

LV | ||||

LV-EDV (ml) | 125.7 ± 26.1 | 133.0 ± 31.0 | 115.7 ± 13.4 | 0.1485 |

LV-ESV (ml) | 48.4 ± 10.7 | 51.6 ± 12.5 | 44.0 ± 5.62 | 0.2312 |

LV-SV (ml) | 77.3 ± 21.1 | 81.4 ± 26.3 | 71.7 ± 9.37 | 0.4828 |

LV-EF (%) | 61.2 ± 5.6 | 60.7 ± 6.91 | 61.9 ± 3.33 | 0.2473 |

Cardiac output (L/min) | 5.71 ± 1.9 | 5.55 ± 2.05 | 5.94 ± 1.77 | 0.5915 |

Cardiac index (L/min/m^{2}) | 3.5 ± 1.2 | 3.25 ± 1.15 | 3.95 ± 1.12 | 0.2006 |

LV-EDVI (ml/m^{2}) | 77.5 ± 13.6 | 78.0 ± 17.5 | 76.8 ± 6.1 | 0.9014 |

LV-ESVI (ml/m^{2}) | 29.8 ± 5.3 | 30.2 ± 6.82 | 29.2 ± 2.4 | 0.6494 |

LV-SVI (ml/m^{2}) | 47.7 ± 11.7 | 47.8 ± 15.1 | 47.7 ± 5.2 | 0.4824 |

RV | ||||

RV-EDV (ml) | 139.8 ± 26.3 | 147.0 ± 25.9 | 129.6 ± 25.3 | 0.3020 |

RV-ESV (ml) | 67.3 ± 15.5 | 72.7 ± 13.5 | 59.6 ± 15.9 | 0.1731 |

RV-SV (ml) | 72.5 ± 13.6 | 74.3 ± 14.9 | 69.9 ± 12.0 | 0.6497 |

RV-EF (%) | 52.1 ± 5.0 | 50.4 ± 4.04 | 54.5 ± 5.61 | 0.0905 |

RV-EDVI (ml/m^{2}) | 85.7 ± 12.8 | 85.0 ± 13.9 | 86.7 ± 12.1 | 0.9014 |

RV-ESVI (ml/m^{2}) | 41.1 ± 7.4 | 42.0 ± 6.38 | 39.8 ± 9.1 | 0.5357 |

RV-SVI (ml/m^{2}) | 44.6 ± 7.7 | 43.0 ± 8.91 | 46.6 ± 4.9 | 0.2650 |

Data are shown as the mean ± standard deviation.

Wilcoxon signed-rank tests were used to compare paired data between male and female.

*BSA*: body surface area,

*EDV*: end-diastolic volume,

*EDVI*: end-diastolic volume index,

*EF*: ejection fraction,

*ESV*: end-systolic volume

*, ESVI*: end-systolic volume index,

*HR*: heart rate,

*LV*: left ventricle,

*RV*: right ventricle,

*SV*: stroke volume, S

*VI*: stroke volume index.

In validation of the present scan protocols, segmented lumen from TrueFISP images obtained with and without breath hold were superposed onto each other and also onto the phase-contrast images. For most of the cases, there was misalignment within five pixels between the two breathing conditions, and between TrueFISP and the phase-contrast images.

### Hemodynamics in the left ventricular system

Table 2 lists the energy dynamics in the LV circulation as derived from the 4D flow MRI data. The ELI in the LV system was 1.02 ± 0.26 (0.62–1.58) mW/m

^{2}, and the KEI in the LV system was 16.4 ± 7.5 (7.5–41.3) mW/m^{2}. Flow patterns in the LV system and its EL are illustrated in Fig. 1. In mid systole, peak flow acceleration in the ascending aorta had mildly spiral property and ELI in this phase was the highest in one cardiac cycle with the flow acceleration. During late systole, flow deceleration in the ascending aorta mildly decreased ELI, and with the closure of the aortic valve, ELI had the minimum value with the blood flow stasis. In peak diastole, transmitral flow caused vortex around the mitral valve with the flow detachment, and it caused slight elevation in the ELI in diastole. In late and end diastole, flow decelerated with gradual decrease in ELI. These flow and EL patterns were observed in all healthy cases, and we noticed that these were typical patterns in LV system flow (Fig. 1).Table 2Results of 4D flow MRI in 19 volunteers.

LV | Total 19 | Male 11 | Female 8 | P value |
---|---|---|---|---|

Flow through aortic valve (L/min) | 5.40 ± 1.36 | 5.63 ± 1.45 | 5.07 ± 1.24 | 0.3423 |

EL (mW) | 1.65 ± 0.45 | 1.63 ± 0.52 | 1.68 ± 0.38 | 0.6794 |

ELI (mW/m^{2}) | 1.02 ± 0.26 | 0.95 ± 0.28 | 1.12 ± 0.20 | 0.1600 |

KE at the aortic valve | 26.8 ± 14.0 | 28.5 ± 17.2 | 24.5 ± 8.3 | 0.9671 |

KEI at the aortic valve (mW/m^{2}) | 16.4 ± 7.5 | 16.6 ± 9.3 | 16.1 ± 4.4 | 0.4828 |

RV | ||||

Flow through the pulmonary valve (L/min) | 5.19 ± 1.29 | 5.39 ± 1.51 | 4.91 ± 0.74 | 0.7726 |

EL (mW) | 1.02 ± 0.29 | 1.02 ± 0.33 | 1.02 ± 0.25 | 0.8043 |

ELI (mW/m^{2}) | 0.63 ± 0.16 | 0.60 ± 0.17 | 0.67 ± 0.15 | 0.3016 |

KE at the pulmonary valve (mW) | 11.9 ± 7.2 | 13.3 ± 8.66 | 10.02 ± 3.69 | 0.3859 |

KEI at the pulmonary valve (mW/m^{2}) | 7.25 ± 3.89 | 7.73 ± 4.70 | 6.57 ± 2.30 | 0.7102 |

*EL*: energy loss,

*ELI*: energy loss index,

*KE*: kinetic energy,

*KEI*: kinetic energy index.

Blood ejected from the LV flows smoothly to the ascending aorta with a small spiral flow formation. There are two EL peaks: the first in peak systole, mainly in the LV outflow tract (LVOT) and at the ascending aorta; and the second in the diastolic filling phase, mainly dissipated in the LV.

To further evaluate the blood flow patterns, we observed 2D streamline reconstructions in several cross-sections. A characteristic flow pattern in the long-axis cross-section was observed in all subjects (Fig. 2). In peak systole, a small vortex was seen in the basal portion of the LV, with smooth connection to the ejected streamline. EL was slightly elevated near the aortic wall, but not inside the vortex in the LV. In the early diastolic phase, trans-mitral flow formed a small vortex beneath the anterior leaflet of the mitral valve, with slightly elevated EL. In late diastole, a large vortex with small EL that formed in the LV appeared to facilitate ejection flow in the following systolic phase. We observed these flow patterns in the LV cross section in all healthy cases, and we noticed that these vortex flow patterns were typical flow patterns inside the LV.

Correlations between the 4D flow MRI parameters and cine TrueFISP are listed in Table 3. The EL of the left side of the heart showed significant correlations with HR. KE (aortic valve) tended to have positive correlations between LV-EDV, LV-SV, RV-EDV, and RV-SV. KEI tended to have positive correlations between LV-EDV and RV-SV.

Table 3Correlations between left heart parameters of 4D flow MRI and cine TrueFISP parameters.

Variable | Flow | CI | KE at the aortic valve | KEI | EL | ELI |
---|---|---|---|---|---|---|

HR | 0.3969 | 0.5992P= 0.0067 | 0.0864 | 0.1443 | 0.4726P= 0.041 | 0.6096P= 0.0055 |

Left side | ||||||

LV-EDV | 0.5779P= 0.0095 | 0.4472 | 0.5142P= 0.024 | 0.4718P= 0.041 | 0.4216 | 0.2505 |

LV-ESV | 0.4803P= 0.037 | 0.2934 | 0.3276 | 0.2590 | 0.2648 | 0.0620 |

LV-SV | 0.4711P= 0.042 | 0.4042 | 0.4698P= 0.042 | 0.4521 | 0.3872 | 0.2784 |

LV-EF | 0.0836 | 0.1964 | 0.1750 | 0.2203 | 0.1979 | 0.2776 |

LV-EDVI | 0.3561 | 0.4058 | 0.3494 | 0.3770 | 0.3265 | 0.3360 |

LV-ESVI | 0.2693 | 0.2456 | 0.1710 | 0.1665 | 0.1682 | 0.1302 |

LV-SVI | 0.2897 | 0.3580 | 0.3266 | 0.3606 | 0.3014 | 0.3297 |

Right side | ||||||

RV-EDV | 0.5157P= 0.024 | 0.3124 | 0.4927P= 0.032 | 0.4326 | 0.3838 | 0.1556 |

RV-ESV | 0.4122 | 0.1628 | 0.4047 | 0.3263 | 0.2302 | −0.024 |

RV-SV | 0.5245P= 0.021 | 0.4175 | 0.4886P= 0.034 | 0.4623P= 0.046 | 0.4782P= 0.038 | 0.3296 |

RV-EF | 0.0138 | 0.2123 | −0.038 | 0.0266 | 0.2062 | 0.3788 |

RV-EDVI | 0.2426 | 0.2445 | 0.3146 | 0.3392 | 0.2644 | 0.2412 |

RV-ESVI | 0.1834 | 0.0804 | 0.2686 | 0.2532 | 0.1145 | 0.0084 |

RV-SVI | 0.2280 | 0.3350 | 0.2647 | 0.3220 | 0.3345 | 0.4019 |

*P*<0.05

*EDV*: end diastolic volume,

*EDVI*: end diastolic volume index,

*EF*: ejection fraction,

*EL*: energy loss,

*ESV*: end diastolic volume,

*ESVI*: end systolic volume index,

*HR*: heart rate,

*KE*: kinetic energy,

*LV*: left ventricle,

*RV*: right ventricle,

*SV*: stroke volume,

*SVI*: stroke volume index.

### Hemodynamics in the right ventricular system

The energy dynamics in the RV circulation derived from the 4D flow MRI data are listed in Table 2. The ELI in the RV system was 0.63 ± 0.16 (0.40–0.99) mW/m

^{2}, and the KEI in the RV system was 7.25 ± 3.89 (3.30–20.10) mW/m^{2}.Flow patterns in the RV system and its EL are illustrated in Fig. 3. Blood ejected from the RV flows smoothly to the PA in a small spiral flow formation. There are two EL peaks: the first in peak systole, mainly in the RVOT and at the PA; and the second in the diastolic filling phase, mainly dissipated in the RV.

To further evaluate the blood flow patterns, we observed 2D streamline reconstructions in several cross-sections. Characteristic flow patterns in the long- and short-axis planes were observed in all subjects (Fig. 4). In the RV system, vortices were observed mainly in the diastolic filling phase near the free RV walls, in both the short- and long-axis planes. In systole, EL was slightly elevated near the PA wall. In diastole, only small ELs were observed in the RV and PA.

Table 4 lists the correlations between the 4D flow MRI and cine TrueFISP parameters. In the RV system, there was significant correlation between EL (RA-PA) and RV-SV. There was no correlation of KE, KEI, and ELI with any of the parameters.

Table 4Correlations between right heart parameters of 4D flow MRI and cine TrueFISP parameters.

Variable | KE at the pulmonary valve | KEI | EL | ELI |
---|---|---|---|---|

HR | 0.1027 | 0.1652 | 0.3037 | 0.3999 |

Left side | ||||

LV-EDV | 0.3684 | 0.3223 | 0.4475 | 0.2971 |

LV-ESV | 0.2206 | 0.1455 | 0.3475 | 0.1730 |

LV-SV | 0.3438 | 0.3249 | 0.3772 | 0.2797 |

LV-EF | 0.1896 | 0.2443 | 0.1167 | 0.1815 |

LV-EDVI | 0.1815 | 0.1988 | 0.3730 | 0.3888 |

LV-ESVI | 0.0315 | 0.0126 | 0.2885 | 0.2677 |

LV-SVI | 0.1957 | 0.2243 | 0.3006 | 0.3238 |

Right side | ||||

RV-EDV | 0.4209 | 0.3469 | 0.4417 | 0.2485 |

RV-ESV | 0.3349 | 0.2400 | 0.3266 | 0.1149 |

RV-SV | 0.4299 | 0.3956 | 0.4795P= 0.040 | 0.3490 |

RV-EF | 0.0206 | 0.1025 | 0.0493 | 0.1794 |

RV-EDVI | 0.2028 | 0.1987 | 0.3646 | 0.3644 |

RV-ESVI | 0.1556 | 0.1094 | 0.2667 | 0.1997 |

RV-SVI | 0.1882 | 0.2278 | 0.3517 | 0.4187 |

*P*<0.05

*EDV*: end diastolic volume,

*EDVI*: end diastolic volume index,

*EF*: ejection fraction,

*EL*: energy loss,

*ESV*: end diastolic volume,

*ESVI*: end systolic volume index,

*HR*: heart rate,

*KE*: kinetic energy,

*LV*: left ventricle,

*RV*: right ventricle,

*SV*: stroke volume,

*SVI*: stroke volume index.

## Discussion

The aim of this study was to observe the normal flow pattern and energy dynamics to reveal the physiology of the biventricular system, and to establish reference values for these parameters. Flow visualization and correlation analysis of the hemodynamic parameters revealed the physiological roles of LV and RV. These circulatory systems are not independent; rather, RV contraction has a strong impact on the energy dynamics of the LV. Ventricular–ventricular interaction is known to be relevant to many fields of cardiovascular diseases, including heart failure and congenital heart disease [

[13]

], and some clinical observations have revealed the pathophysiology of these diseases in detail [[13]

]. However, the findings of the present study additionally suggest that even in normal physiology, ventricular–ventricular interaction plays certain roles in regulating the circulation. While the kinetic energy parameters (i.e. KE and KEI) were influenced by LV-EDV and RV-SV, which were supposed to be a type of parameters of LV and RV preload or circulatory volume, left-sided EL was controlled only by HR and RV-SV. These results suggested that RV-SV essentially controlled energy dynamics of the systemic circulation, which would be susceptible to the circulatory preload and HR, and RV could have a substantial role as a volume reservoir for the whole circulatory system. On the other hand, the energy dynamics of the RV system are rather independent and are not controlled by LV hemodynamics, which would be considered to be an important characteristic of a volume reservoir.The role as a volume reservoir was supported also by the blood flow patterns visualized within the RV, which showed several vortices in both the short- and long-axis planes around the free walls during the diastolic filling phase, and which facilitated smooth stretching of the walls of RV. Previous basic research related to biventricular hemodynamics, such as mathematical modeling of the circulatory system, revealed differences in the material properties of the systemic and pulmonary vessels [

14

, 15

–[16]

]: Pulmonary arterial capacitance is ~4 times higher than that in the aortic wall (0.274 vs 0.061 ml/mmHg), whereas aortic elastance is ~4 times higher than that in the pulmonary arterial wall (18 vs 4.12 mmHg sec^{2}/ml). These characteristics suggest that the systemic circulation should function as a blood flow pump (like a spring) that repels blood flow, whereas the pulmonary circulation should function as a volume reservoir for the circulatory system.Because they act as a spring for the circulatory system, the LV energy dynamics are strictly controlled by HR and preload, which was confirmed by the flow patterns visualized in the present study. Vortices with low EL were found in the LV in the long-axis plane, particularly at end diastole and early systole, which appeared to facilitate smooth ejection flow toward the aortic valve. Vortices with low EL were not observed in the short-axis plane.

Previous studies have demonstrated that flow EL in the LV is a parameter of cardiac workload [

6

, 7

–[8]

,[17]

] in a wide range of cardiovascular diseases, including heart valve disease [[8]

,[18]

], congenital heart disease [[17]

], and heart failure [[6]

,[19]

]. Flow EL in RVOT was also reported to be suppressed after surgical intervention [[17]

] and is also a predictor of RV deterioration [[20]

]. EL and KE are novel hemodynamic parameters for energy dynamics and cardiac workload, reference values are expected to be established. From the results in the present study, standard deviation of the right and left side heart ELI is sufficiently small compared with the ELI in the diseased heart reported in the previous literature; thus, clinical application as workload parameters would be expected with data accumulation in various types of heart diseases.Flow EL in vessels had originally been defined as total pressure drop times flow rate [

21

, 22

, 23

–[24]

]. In this theoretical expression, the flow EL (defined by total pressure drop) is essentially induced by viscous dissipation. Many of the previous applications of EL were based on reconstructed extraanatomical vessels such as Fontan circulation [[21]

–[24]

] and were estimated in computational fluid dynamics studies, as they required both pressure and velocity information. The assumption in Appendix 1 is suitable for static vessels; however, when we focus on ventricles that have dynamic wall motion, EL derived from 4D flow MRI is much more suitable than classic EL from total pressure drop, and has the advantage that it requires no pressure data.The reference values of EL and KE are considered to have very high clinical value but they are currently available only for 2D flow within the LV [

25

, 26

, 27

]. Because of the rapid prevalence of 4D flow MRI, in addition to the reference values of the energy dynamics, the basic physiology of the biventricular system is increasing in importance and can be explored in healthy volunteers. As more attention is paid to complicated heart diseases, blood flow imaging with MRI will play an expanding role in assessing anatomical regions that have been difficult to visualize with echocardiography.## Limitations and future studies

There are several limitations to this study. First, the number of subjects was small, with potential bias of the samples. We have judged the tendency of positive correlation when

*r*> 0.433, which is compatible to*p*< 0.05, but accumulation of the subjects would increase the statistical power. Nevertheless, we performed sub-analysis between the genders for a future study with big data. Second, the volunteers were young. It is much more challenging to find healthy subjects in the elderly population and we are currently working on this issue. It is reported that EL decreases with age [[26]

]; thus, the reference values or vortex pattern in the elderly would differ from those in the present study. Third, no dependency test between the MRI machine or postprocessing software was performed. As far as we know, EL of this definition is only dealt by iTFlow series from Cardio Flow Design Inc., and we have only one MRI equipment for 4D flow MRI in our single institute. Also, no dependency was known of spatial and/or temporal resolutions on the hemodynamic parameters from the 4D flow MRI analysis results. Future studies should also include systematic image quality control and a much shorter scan time, which will enable the use of this method as a diagnostic tool for assessing cardiovascular disease in the elderly.## Conclusions

4D flow MRI with lumen tracking without contrast medium is a feasible tool for assessing biventricular hemodynamics. We have established reference values for energy dynamics in the RV and LV systems. The RV appears to function as a volume reservoir for the circulatory system, which is facilitated by vortices located near the RV free walls. LV muscle repels blood flow to the aorta, and the vortex in the long axis facilitates smooth ejection. Energy dynamics in the LV system are controlled with HR and RV-SV alone, whereas those in the RV system are independent from LV hemodynamics.

### Acknowledgments

Not applicable.

### Funding

No direct funding was received for this study.

### Disclosures

Kei Yamada has received research funding from Doctor Net, Fukushima SIC Applied Engineering INC., Nihon Mediphysics, Fuji Pharma Co, Ltd, and Daiichi-Sankyo. These fundings were not distributed to the study. The other authors declare that they have no competing interests.

## Appendix 1. Theoretical basis of flow EL

To clarify the mathematical and fluid dynamical basis of the flow energy loss (EL) calculation in the present study, here we describe the full theorem to derive the definition of EL. These theoretical backgrounds are described fully in our previous publications [

[4]

,[7]

,[8]

,17

, 18

, 19

–[20]

,[26]

,[27]

].We first define the flow velocity vector field as:

where x, y, and z indicate directions in the Cartesian coordinate system.

$\overrightarrow{u}=\left({u}_{x},{u}_{y},{u}_{z}\right),$

(1)

where x, y, and z indicate directions in the Cartesian coordinate system.

Changes in energy can be described as follows,

where ρ,

$\mathrm{d}\left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}+e\right)=d\left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}\right)+\frac{TdS-PdV}{V},$

(2)

where ρ,

*P, T, S, e,*and*V*indicate density, pressure, temperature, entropy, internal energy, and volume, respectively. The right-hand side of Eq. (2) is derived from*the first and second laws of thermodynamics*. In an incompressible and adiabatic system, this should be simply:$d\left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}\right).$

(3)

The time derivative of the energy expresses energetic change,

where the integral is the volume integral of the region of interest.

$\frac{\partial}{\partial t}\left(\int \frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}\right),$

(4)

where the integral is the volume integral of the region of interest.

For blood flow, if we assume Newtonian incompressible fluid, the mass and momentum preservation equation (termed the continuity equation) and the

where μ is viscosity.

*Navier–Stokes*equations are described as follows:$\nabla \xb7\overrightarrow{u}=0$

(5)

$\rho \frac{\partial \overrightarrow{u}}{\partial t}=-\rho \left(\overrightarrow{u}\xb7\nabla \right)\overrightarrow{u}-\nabla P+\mu \Delta \overrightarrow{u},$

(6)

where μ is viscosity.

If we substitute the time derivative of the energy to

where the tensor σ

*Navier–Stoke*s Eqs. (5) and (6),$\begin{array}{c}\frac{\partial}{\partial t}\left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}\right)=-\rho \overrightarrow{u}\xb7\left(\overrightarrow{u}\xb7\nabla \right)\overrightarrow{u}-\overrightarrow{u}\xb7\nabla P+{u}_{i}\frac{\partial 2{\sigma}_{i,j}}{\partial {x}_{j}}\hfill \\ =-\left(\overrightarrow{u}\xb7\nabla \right)\left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}+P\right)+\nabla \xb7\left({u}_{i}\xb72{\sigma}_{i,j}\right)-2{\sigma}_{i,j}\frac{\partial {u}_{i}}{\partial {x}_{j}},\hfill \end{array}$

(7)

where the tensor σ

*i,j*is a shear stress tensor, defined as${\sigma}_{i,j}=\frac{1}{2}\mu \left(\frac{\partial {u}_{j}}{\partial {x}_{i}}+\frac{\partial {u}_{i}}{\partial {x}_{j}}\right).$

(8)

As the blood is incompressible, continuity Eq. (5) can be applied to (7), and we can write the first term on the right as a divergence:

$\frac{\partial}{\partial t}\left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}\right)=-\nabla \xb7\left(\left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}+P\right)\overrightarrow{u}-2{u}_{i}\xb7{\sigma}_{i,j}\right)-2{\sigma}_{i,j}\frac{\partial {u}_{i}}{\partial {x}_{j}}.$

(9)

If we integrate (9) over the whole volume of concern, such as the site of vessel anastomosis, and if we exchange the space integral and the time derivative with the Gauss theorem and the equation of continuity (5),

where $\overrightarrow{n}$ is the vector normal to the surface (outward from the domain) and

$\begin{array}{ccc}\hfill \frac{\partial}{\partial t}\left(\int \frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}dv\right)& =& -\int \left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}+P\right)\overrightarrow{u}\xb7\overrightarrow{n}dA+\int \left({\sigma}_{i,j}\xb7\overrightarrow{u}\right)\xb7\overrightarrow{n}dA\hfill \\ & & -\phantom{\rule{0.16em}{0ex}}\sum _{i,j}\int \frac{1}{2}\mu {\left(\frac{\partial {u}_{i}}{\partial {x}_{j}}+\frac{\partial {u}_{j}}{\partial {x}_{i}}\right)}^{2}dv,\hfill \end{array}$

(10)

where $\overrightarrow{n}$ is the vector normal to the surface (outward from the domain) and

*A*is the section of the surface area and its integral is the surface integral.If we apply a physiological boundary condition assuming blood vessels,

then,

$\overrightarrow{u}=0\left(@vessel\phantom{\rule{0.16em}{0ex}}wall\right)$

(11)

$\overrightarrow{u}\xb7\overrightarrow{n}\left(@inlets\phantom{\rule{0.16em}{0ex}}and\phantom{\rule{0.16em}{0ex}}outlets\right)$

(12)

$\frac{\partial {u}_{i}}{\partial {n}_{i}}=0\left(@inlets\phantom{\rule{0.16em}{0ex}}and\phantom{\rule{0.16em}{0ex}}outlets\right),$

(13)

then,

$\int \left({\sigma}_{i,j}\xb7\overrightarrow{u}\right)\xb7\overrightarrow{n}dA\cong 0.$

(14)

Thus, the integrated energetic changes become as follows:

$\begin{array}{ccc}\hfill \frac{\partial}{\partial t}\int \left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}\right)dv& =& -\int \left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}+P\right)\phantom{\rule{0.28em}{0ex}}\overrightarrow{u}\xb7\overrightarrow{n}dS\hfill \\ & & -\phantom{\rule{0.16em}{0ex}}\sum _{i,j}\int \frac{1}{2}\mu {\left(\frac{\partial {u}_{i}}{\partial {x}_{j}}+\frac{\partial {u}_{j}}{\partial {x}_{i}}\right)}^{2}dv.\hfill \end{array}$

(15)

If we assume the existence and uniqueness of the solution of the

*Navier–Stokes*equation and if we assume that the pulsatile fluid flow repeats the same fluid field in every cardiac cycle, we can derive the following equation by integrating (15) for one cardiac cycle:${\int}_{0}^{T}dt\int \frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}dv={\left[\int \frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}dv\right]}_{t=T}-{\left[\int \frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}dv\right]}_{t=0}=0.$

(16)

From Eqs. (15) and (16),

$-\int dt\int \left(\frac{1}{2}\rho {\left|\overrightarrow{u}\right|}^{2}+P\right)\phantom{\rule{0.28em}{0ex}}\overrightarrow{u}\xb7\overrightarrow{n}=\int dt\int \frac{1}{2}\mu {\left(\frac{\partial {u}_{i}}{\partial {x}_{j}}+\frac{\partial {u}_{j}}{\partial {x}_{i}}\right)}^{2}dv.$

(17)

The left-hand side of Eq. (17) is the EL calculated by the concept of total pressure, and the right-hand side of Eq. (17) is the energy dissipation caused by the confliction by the viscous fluid.

Originally, flow EL in vessel flow was defined as the total pressure drop times flow rate [

[1]

]. This theoretical explanation means that flow EL defined using total pressure drop is essentially caused by viscous dissipation. This form of EL is already described in the literature and is widely used.As this formula can be applied to the simple measured data without any requirement of calculation assumption such as boundary condition and initial flow condition, the formula can be considered to be practical and handy.

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## Article info

### Publication history

Published online: January 31, 2021

Accepted:
January 12,
2021

Received in revised form:
October 25,
2020

Received:
April 12,
2020

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