Role of Non-Invasive Hemodynamic Forces through Four-Dimensional-Flow Magnetic Resonance Imaging (4D-Flow MRI) in Evaluating Mitral Regurgitation with Preserved Ejection Fraction: Seeking Novel Biomarkers

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Emphasizing the potential of hemodynamic force as a biomarker of MR evaluation.

Abstract

Mitral regurgitation (MR) is the systolic retrograde flow from the left ventricle (LV) to the left atrium. Despite the recognized importance of hemodynamic force (HDF) in cardiology, its exploration in MR has been limited. Therefore, we aimed to explore non-invasively assessed HDF as a novel biomarker for evaluating MR utilizing 4D-flow MRI. The study cohort comprised 15 healthy controls (19–61 years, 53% men) and 26 MR patients with preserved ejection fraction (EF) (33–75 years, trivial–severe, 54% men). The HDF analysis involved the semi-automatic calculation of systolic–diastolic root mean square (RMS), average, and transverse/longitudinal ratio across three directions (S-L: septal–lateral, I-A: inferior–anterior, and B-A: basal–apical) using Segment, v2.2 R6410 (Lund, Sweden, Medviso). A noticeable trend shift emerged in HDF as the MR severity increased (p-value < 0.05). The MR severity demonstrated a noteworthy correlation with systolic RMS B-A, average B-A, diastolic average B-A, systolic average S-L, B-A, and systolic–diastolic ratio (rho = 0.621, 0.457, 0.317, 0.318, 0.555, −0.543, −0.35, respectively; p-value < 0.05). HDF significantly correlated with LV function (end-diastolic volume, end-systolic volume, EF, and mass; p-value < 0.05). Systolic RMS B-A and diastolic RMS S-L emerged as significant predictors of MR (Beta, 95% CI [3.253, 1.204–5.301], [5.413, 0.227–10.6], p-value < 0.05). This study emphasizes HDF as a potential hemodynamic biomarker for evaluating MR.

1. Introduction

Mitral regurgitation (MR) results from the retrograde flow of blood from the left ventricle (LV) to the left atrium (LA) through a malfunctioning mitral valve, causing a holosystolic murmur best heard at the apex of the heart in which the sound radiates to the left axilla [1]. It ranks among the common types of valvular heart disease (VHD) in developed countries [2,3], affecting about 2% to 3% of the global population [4]. It is the second most common valvular disorder requiring surgical intervention and underlining the importance of early detection and assessment [5,6]. Although Doppler echocardiography is the primary imaging tool for MR assessment, its limitations in determining severity levels and post-surgical outcomes are well documented [1,7]. Time-resolved three-dimensional velocity-encoded magnetic resonance imaging, also known as four-dimensional-flow magnetic resonance imaging (4D-flow MRI), has emerged as a promising alternative, offering a more accurate depiction of intracardiac flow patterns and defeating the shortcomings of echocardiography [1,8]. Unlike conventional imaging techniques, 4D-flow MRI allows the comprehensive visualization and quantification of the temporal evolution of complex blood flow in three-dimensional space over time, providing detailed insights into the hemodynamic environment [9]. It has been increasingly used to study various cardiac conditions, including valvular diseases, where traditional biomarkers may fall short of capturing the full extent of the disease severity [10].

Recent cardiovascular research has underscored the importance of the hemodynamic force (HDF) as a biomarker for various cardiac conditions, including heart failure (HF), repaired Tetralogy of Fallot (rTOF), and cardiomyopathy [11,12,13]. These researchers emphasized that HDF is capable of detecting cardiac pathologies at an early stage [14]. HDF denotes the global force exchanged between the blood volume and the endocardium. HDF analysis represents a promising approach to blood flow study within the ventricular chambers through calculating intraventricular pressure gradients (IVPGs) [15]. The IVPGs represent pressure variations between different points within the blood pool and elucidate fundamental mechanisms of cardiac function, such as suction-initiated filling and relaxation phases [11]. J. Eriksson et al. highlighted that HDF primarily follows a trajectory from the mitral valve to the apex of the heart in a healthy LV, whereas this distribution is altered in myopathic LV [16]. HDF remains unexplored in patients with MR, presenting a gap in our understanding of its influence on this condition. Therefore, our study seeks to elucidate the impact of HDF on MR patients with preserved ejection fraction (EF) and various MR severities, aiming for comprehensive pathological knowledge.

While G. Pedrizzetti et al. pioneered HDF evaluation using echocardiography for cardiac resynchronization therapy (CRT) [17], its application in assessing diseased states has been limited by challenges such as suboptimal imaging resolution and limitations in capturing complex flow dynamics. These issues arise due to factors such as variability in acoustic window quality [18], difficulty in visualizing certain cardiac structures, the limited ability to provide detailed flow information, and the invasiveness of catheterization procedures [14,19]. A recent study by D. Laenens et al. recommended the echocardiographic assessment of HDF for clinical setup. However, their study was limited to the first part of systole, which raises a concern about the demonstrated method [20]. Recent studies have demonstrated high accuracy and reproducibility in intraventricular HDF measurements using 4D-flow MRI [21,22]. HDF metrics quantify the forces exerted by blood flow on cardiac structures and offer a unique perspective on cardiac function that complements traditional volumetric and flow-based assessments. Current cardiovascular magnetic resonance (CMR) metrics (regurgitation volume and fraction) can assess MR accurately; however, they have notable limitations, such as variability in the metrics due to patient-specific anatomical differences and inconsistencies in imaging protocols, leading to measurement discrepancies that affect clinical decision-making. It is important to note that determining the timing of mitral valve surgery is still complicated by the lack of good markers of LV deterioration in patients with mitral valve surgery. Many investigators recommend watchful waiting, particularly in asymptomatic patients with preserved LV function. Thus, it is concerning that we cannot predict when the LV function (LVEF and end-systolic dimension) will decline. Traditional metrics (regurgitant volume and fraction) often fail to account for the complex hemodynamic forces and flow patterns involved in MR, limiting their ability to provide a comprehensive assessment and prognostic information [23,24]. To the best of our knowledge, there is currently no research evaluating HDF among the MR cohort. Consequently, our study intends to utilize 4D-flow-derived HDF in MR patients with preserved EF to assess the MR severity as well as the relationship between LV function and derived HDF. The method used for HDF analysis in this study is based on the approach developed by J. Töger et al. [21]. Here, we extend this methodology by introducing advanced parameters and applying them to MR patients with preserved EF. We hypothesize that HDF could serve as a biomarker to differentiate between MR patients and healthy controls and potentially aid in stratifying MR severity levels. We tested the hypothesis with a retrospective cross-sectional study design.

2. Materials and Methods

2.1. Study Population

The study cohort included a total of 41 adult subjects. Among them, n = 15 were healthy controls (19 to 61 years) and n = 26 were MR patients with preserved EF (33 to 75 years). Out of the initial 50 MR cases, we selected n = 26 for our study. The remaining n = 24 cases were excluded due to MRI sequences and non-repairable noise issues. All subjects underwent a 4D-flow MRI scanning to evaluate their condition. Controls with no history of cardiac disease and patients with ‘Trivial-Severe’ MR were included in this study. The patients were categorized into three groups as follows: trivial–mild, mild–moderate, and moderate–severe following the current guidelines set by the American College of Cardiology and American Heart Association (ACC and AHA) [25,26].

2.2. Ethics and Registry

All study populations were retrospectively recruited from the Cardiovascular Imaging Registry of Calgary (CIROC, NCT04367220). CIROC, a clinical outcomes registry of the Libin Cardiovascular Institute, routinely engages patients referred to cardiac imaging services in Southern Alberta, Canada. Patients enrolled between March 2019 and August 2022 were considered for this study. The Conjoint Health Research Ethics Board approved the study at the University of Calgary (REB#13-0902). All participants provided written consent at the MRI scan examination. All research activities were performed following the Declaration of Helsinki.

2.3. Severity Classification of Mitral Regurgitation

The degree of MR severity was assessed using the guidelines set by ACC and AHA following the grading criteria A–D [25,26]. The primary marker for the evaluation was regurgitation fraction (RF, %) and the corresponding cut-off ranges are as follows: trivial: <5%, mild–moderate: 5–15%, moderate: 16–25%, moderate–severe: 26–48%, severe: >48% [27,28]. Mitral regurgitant volume (MRV, mL) ranges are defined as per the AHA/ACC treatment guidelines: trivial/mild <30 mL, moderate 30–59 mL, and severe ≥60 mL [29]. The EF (%) is a powerful parameter in detecting VHD as well as MR, and the cut-off range is as follows: mild–moderate: normal–mildly reduced (50–70%), moderate: normal–mildly reduced (40–49%), moderate–severe: mild–moderately reduced (30–39%), severe: severely reduced (<30%) [25]. All patients had an EF between 50% and 70%; therefore, we identified the MR patients with preserved EF. The MRV was calculated by subtracting aortic forward flow volume from LV stroke volume (SV), where LV SV = LV end-diastolic volume (EDV) − LV end-systolic volume (ESV) [30,31,32]. The RF was calculated by using the formula: RF = [(MRV/LVSV) × 100] [33,34]. The EF was calculated from EDV and ESV estimates using the following formula: EF = (EDV − ESV)/EDV [26].

2.4. 4D-Flow Magnetic Resonance Imaging Protocol

All participants underwent a consistent standardized imaging protocol using 3T MRI scanners (Skyra, Prisma, Siemens, Erlangen, Germany). Multi-planar segmented electrocardiogram (ECG) gated, time-resolved balanced steady-state free precession (bSSFP) cine imaging was conducted in four-chamber, three-chamber, two-chamber, and short-axis views to assess the LV function. The imaging covered the entire heart at end-expiration. In addition, for volumetric assessment, a 3D magnetic resonance angiography (MRA) of the whole heart was performed with the administration of 0.2 mmol/kg gadolinium contrast (Gadovist, Bayer, Canada). A comprehensive intracardiac 3D in vivo volumetric blood flow assessment was conducted using 4D-flow MRI, 5–10 min after contrast administration. The parameters set for 4D-flow MRI examination are demonstrated in

Table 1. Scan parameters for 4D-flow MRI.

Parameters	Details
Scan Technique	Free-breathing retrospective ECG-gated technique
Flip angle (FA)	15°
Velocity encoding range in all directions (VENC)	1.5–2.0 m/s
Spatial resolution	2.0–3.6 × 2.0–3.0 × 2.5–3.5 mm3
Temporal resolution	25–35 ms
Number of phases	30
Bandwidth (BW)	455–495 Hz/Pixel
Echo time (TE)	2.01–2.35 ms
Pulse repetition time (TR)	4.53–5.07 ms

Notes: The overall scan time varied between 8 and 12 min, depending on the physiological factors, defined scan parameters, and respiratory gating efficiency. Abbreviations: 4D = four-dimensional; MRI = magnetic resonance imaging; ECG = echocardiography.

.

2.5. Semi-Automated Hemodynamic Force Analysis

The method was adapted from the work of J. Töger et al. for HDF calculation. This study used the semi-automated ‘Segment’ software v2.2 R6410 (Lund, Sweden, Medviso) for image processing. This software is freely available, and all the post-processing steps were described and validated in detail by J. Töger et al. The ‘Segment’ software is designed to analyze 4D-flow data, provided that the cine and 4D-flow MRI data can be loaded into it [21]. The overall force extraction method is illustrated in Figure 1. Intraventricular pressure gradients (g) were computed from 4D-flow velocity data using Navier–Stokes equations (Equation (1)) [35], and HDF was computed by integrating ‘g’ over the entire LV cavity (Figure 1).

$$\mathit{Intraventricular}\mathit{pressure}\mathit{gradients}\mathbf{,}\mathbf{(}\mathit{g}\mathbf{)}\mathbf{=}\mathbf{-}\mathit{𝛒}{\displaystyle \frac{\mathit{\partial }\mathit{v}}{\mathit{\partial }\mathit{t}}}\mathbf{-}\mathit{𝛒}\mathbf{(}\mathit{v}\mathbf{.}\mathit{\nabla }\mathit{v}\mathbf{)}\mathbf{+}\mathit{\mu }{\mathit{\nabla } }^{\mathbf{2}}\mathit{v}$$

(1)

where v is the velocity (m/s), ρ the density (1060 kg/m³) and µ is blood viscosity (0.004 Ns/m²) [36]. HDFs were calculated using pressure gradients along three axes (Figure 1, pressure gradients), following a spatial reference system originating at the atrioventricular (AV) plane (Figure 1, defined force direction). The heart’s orientation was defined in three perpendicular directions. Firstly, the apical-basal (B-A) direction was set perpendicular to the AV plane. Secondly, the lateral wall–septum (S-L) direction was set perpendicular to the apical–basal (B-A) direction and aligned to the LV outflow tract (LVOT). Lastly, the inferior–anterior (I-A) direction was set perpendicular to the apical–basal and lateral–septal directions. As mentioned by J. Töger et al., the automated segmentation was only available for the LV; however, the directions were placed manually following the reference mentioned above. A standardized time axis has been created to effectively compare the heart displacement function among subjects with different heart rates. This was achieved by linearly resampling the force curves for systole and diastole separately, as previously described [21,22,37].

The mean amplitude of the longitudinal force along the entire cardiac cycle is usually expressed as the root mean square (RMS). The RMS HDF was computed for each direction (Equation (2)), where f_n is the force in time frame n, and N is the number of timeframes in a cardiac phase. The RMS HDF in each direction was computed for systole and diastole separately.

$$\mathit{RMS}\mathbf{=}\sqrt{{\displaystyle \frac{\mathbf{1}}{\mathit{N}}}{\sum }_{\mathit{n}\mathbf{=}\mathit{1}}^{\mathit{N}}{\mathbf{|}\mathit{f}\mathit{n}\mathbf{|}}^{\mathbf{2}}}$$

(2)

The relative magnitude of transverse (inferior–anterior and septal–lateral) and longitudinal (basal–apical) forces were calculated using the ratio between transverse and longitudinal forces (Equation (3)), where RMS_B-A, RMS_I-A, and RM_S-L were the RMS force components in the B-A, I-A, and S-L directions, respectively. The ratio was computed for systole and diastole separately.

$$\mathit{Ratio}\mathbf{=}{\displaystyle \frac{\sqrt{{\mathit{R}\mathit{M}\mathit{S}}_{\mathit{I}\mathbf{-}\mathit{A}}^{\mathbf{2}}\mathbf{+}{\mathit{R}\mathit{M}\mathit{S}}_{\mathit{S}\mathbf{-}\mathit{L}}^{\mathbf{2}}}}{{\mathit{R}\mathit{M}\mathit{S}}_{\mathit{B}\mathbf{-}\mathit{A}}}}$$

(3)

The pressure field calculation was performed for visualization purposes where the Pressure Poisson equation (PPE) was solved following a previously published multigrid solver [36]. The problem is initially solved on a relatively coarse grid, and then the solution is transferred to progressively finer grids until it arrives at the grid of the input data, which is the original grid of the MRI velocity data. This pattern is then repeated until the finest grid is reached. The PPE is used to compute the pressure distribution in a fluid when the velocity field is known. The PPE was derived from the Navier–Stokes (Equation (1)) for incompressible flow (Equation (4)) to calculate the pressure field.

∇ ⋅ v = 0

(4)

where ∇ denotes the divergence operator and v is the velocity field. Then, the PPE was derived by taking the divergence of the momentum equation leading to simplified Equation (5). Equation (5) relates the Laplacian of the pressure (p) to the velocity field (v), allowing the calculation of pressure distribution [35,38].

∇ ²p = ∇ · (𝛒v · ∇v)

(5)

2.6. Statistical Analysis

The statistical analysis was performed using IBM SPSS Statistics for Windows v26 software (IBM Corp., Armonk, NY, USA). A histogram and Shapiro–Wilk test were conducted to ensure the normality of the data. An independent sample T-test was used to determine any significant mean differences between controls and MR patients with preserved EF for the normally distributed data and the Mann–Whitney U test was utilized to determine the differences for non-parametric data. The one-way ANOVA test was used to determine the differences among three MR severity levels for normally distributed data and the Kruskal–Wallis test was utilized for non-parametric data. For the post hoc analysis, the Bonferroni test was used for parametric data, and the Mann–Whitney U test was used for non-parametric data. Pearson’s correlation coefficient (continuous data) was utilized to investigate the direction and strength of the association between HDF and LV function in systolic and diastolic phases among the controls and mitral severities. Spearman’s rank order correlation (ordinal data) was utilized to analyze the impact of HDF on diverse mitral severity. Multivariate linear regression was conducted to analyze the factors influencing mitral severity grades. All assumptions were met before running non-parametric statistical tests. p-value < 0.05 was considered statistically significant. The percentage deviation was calculated as ΔV/V1 × 100, where ΔV is the difference between the 2nd and 1st values.

3. Results

3.1. Characteristics of Study Population

The study population comprised healthy controls (n = 15) and MR patients with preserved EF (n = 26). The ‘Controls’ group comprised eight men (53%) and seven women (47%), with a median age of 33 years (interquartile range, IQR = 20). In contrast, the ‘Patients’ group included 14 men (54%) and 12 women (46%), with a median age of 61.5 years (IQR = 15). Baseline characteristics encompass age (year), heart rate (HR, bpm), systolic blood pressure (SBP, mmHg), diastolic blood pressure (DBP, mmHg), and body surface area (BSA, m²). The cardiac function includes left ventricular end-diastolic volume indexed (LVEDVI, mL/m²), left ventricular end-systolic volume indexed (LVESVI, mL/m²), left ventricular mass indexed (LVMI, g/m²), LVEDV (mL), LVESV (mL), LVM (g), and left ventricular ejection fraction (LVEF, %). Only HR, SBP, DBP, and BSA exhibited a normal distribution among the baseline characteristics. The normally distributed continuous data are presented as mean ± standard deviation (SD), while non-normally distributed data are expressed as the median (interquartile range, IQR). Among the baseline characteristics, notable differences in age and DSP were observed between controls and MR patients with preserved EF (p-value < 0.05). MR patients demonstrated significant elevation for LVEDV, LVEDVI, LVESV, and LVESVI compared to controls. The data were missing for LV mass in controls due to the retrospective nature of the collection.

Table 2. Overview of the study population’s baseline characteristics and cardiac function.

	Controls (n = 15)	MR Patients (n = 26)	p-Value
Baseline characteristics
Sex	F = 7 (47%), M = 8 (53%)	F = 12 (46%), M = 14 (54%)
Age (years)	33 (20)	61.50 (15)	<0.001 ***
HR (beats/minute)	68.48 ± 11.53	67.85 ± 13.85	0.88
SBP (mmHg)	108.20 ± 11.90	116.54 ± 15.51	0.06
DBP (mmHg)	61.22 ± 10.45	69.04 ± 11.07	0.03 *
BSA (m2)	1.86 ± 0.32	1.92 ± 0.24	0.53
LV function
LVEDV (mL)	143 (78)	168 (94)	0.032 *
LVESV (mL)	51 (41)	68.50 (48)	0.037 *
LVM (g)	-	115 (49)	-
LVEDVI (mL/m2)	80 (21)	87.80 (43)	0.025 *
LVESVI (mL/m2)	27.84 (14)	36.65 (21)	0.045 *
LVMI (g/m2)	-	56.65 (22)	-
LVEF (%)	59.20 (7.8)	57.95 (8.5)	0.449

Notes: Parametric data is presented as mean ± SD. Non-parametric data are presented as median (IQR). p-value < 0.001 ***, p-value < 0.05 * (2-tailed). ‘-’ denotes the missing data in controls due to the retrospective collection form. Abbreviations: F = female; M = male; MR = mitral regurgitation; SD = standard deviation; IQR = interquartile range; HR = heart rate; SBP = systolic blood pressure; DBP = diastolic blood pressure; BSA = body surface area; LVEDV = left ventricle end-diastolic volume; LVEDVI = LVEDV indexed; LVESV = left ventricle end-systolic volume; LVESVI = LVESV indexed; LVM = left ventricle mass; LVMI = LVM indexed; LVEF = LV ejection fraction.

provides a comprehensive overview of the baseline characteristics and cardiac function of the study participants.

3.2. Navigating Hemodynamic Forces: Unveiling Trends in Healthy Controls vs. MR Patients with Preserved EF

Figure 2 demonstrates the visual presentation of the statistical differences between controls and patients with MR for systolic–diastolic average (AVG) HDF in the S-L, I-A, and B-A directions (Figure 2(A1,A2)); systolic–diastolic RMS HDF in the S-L, I-A, and B-A directions (Figure 2(B1,B2)); overall AVG HDF (Figure 2(C1)); and RMS ratios (Figure 2(C2)). This outcome highlights the importance of considering hemodynamic forces when evaluating patients with MR.

Table 3. Comparison of AVG HDF (mN/mL), RMS HDF (mN/mL), and RMS ratio between controls and MR patients with preserved EF.

HDF	Controls (n = 15)	MR Patients (n = 26)	p-Value
AVG Systole S-L	0.55 (0.22)	0.33 (0.33) [40%ꜜ]	0.007 **
AVG Systole B-A	0.49 (0.26)	0.26 (0.25) [46.9%ꜜ]	0.001 **
RMS Systole I-A	0.34 ± 0.12	0.46 ± 0.19 [35.3%ꜛ]	0.023 *
RMS Systole B-A	1.37 (0.30)	0.93 (0.66) [32.1%ꜜ]	0.001 ***
RMS Diastole I-A	0.07 (0.07)	0.16 (0.23) [56.3%ꜛ]	0.007 **
AVG HDF S-L	0.25 (0.15)	0.19 (0.22) [24%ꜜ]	0.04 *
AVG HDF B-A	0.50 ± 0.14	0.37 ± 0.28 [26%ꜜ]	0.039*
RMS Ratio (Systole)	0.65 (0.18)	0.86 (0.65) [32.3%ꜛ]	0.001 ***
RMS Ratio (Diastole)	0.33 (0.19)	0.57 (0.37) [72.7%ꜛ]	0.003 **

Notes: Normally distributed data are presented as mean ± SD and non-normally distributed data are presented as median (IQR). p-value < 0.05 *; p-value < 0.01 **; p-value < 0.001 *** (2-tailed). Abbreviations: MR = mitral regurgitation; EF = ejection fraction; SD = standard deviation; IQR = interquartile range; HDF = hemodynamic force; RMS = root mean square; AVG = average; S-L = septal–lateral; I-A = inferior–anterior; B-A = base-apex.

presents the distinctive numerical values indicating only significant differences in HDF between controls and patients with MR. The full analysis will be available in Supplementary Table S1.

In the comparative analysis, distinct patterns emerged across various parameters, shedding light on the differences in cardiac dynamics. The systolic AVG HDF in the S-L and B-A directions was significantly diminished in MR patients (0.55 (0.22) vs. 0.33 (0.33) mN/mL and 0.49 (0.26) vs. 0.26 (0.25) mN/mL, p-value = 0.007 and 0.001, 40%ꜜ and 46.9%ꜜ, respectively). The RMS HDF during systole and diastole provided valuable insights. In the systolic phase, RMS I-A exhibited a significant increase in MR patients compared to controls (0.34 ± 0.12 vs. 0.46 ± 0.19 mN/mL, p-value = 0.023, 35.3%ꜛ). Conversely, RMS Systole B-A decreased in MR patients compared to controls (1.37 (0.30) vs. 0.94 (0.66) mN/mL, p-value = 0.001, 32.1%ꜜ). Diastolic forces, as depicted by RMS I-A, were notably elevated in MR patients compared to controls (0.07 (0.07) vs. 0.16 (0.23) mN/mL, p-value = 0.007, 56.3%ꜛ). The AVG HDF in the S-L and B-A directions revealed a noteworthy reduction in MR patients compared to controls (0.25 (0.15) vs. 0.19 (0.22) mN/mL, p-value = 0.04, 24%ꜜand 0.50 ± 0.14 vs. 0.37 ± 0.28, p-value = 0.039, 26%ꜜ). Both systolic and diastolic ratios exhibited significant variations between controls and MR patients (0.65 (0.18) vs. 0.86 (0.65) and 0.33 (0.18) vs. 0.57 (0.37), p-value = 0.001 and 0.003, 32.3%ꜛ and 72.7%ꜛ, respectively) highlighting distinct alterations in force distribution.

3.3. Unraveling Distinctive Patterns in Hemodynamic Forces and LV Function across Controls and MR Severities

Table 4. Differences in HDF and LV function between controls and Mitral severities.

		Controls (n = 15)	Trivial–Mild (n = 9)	Mild–Moderate (n = 11)	Moderate–Severe (n = 6)	p-Value
HDF	Direction
AVG (mN/mL)	Systole S-L	0.55 (0.22) ●■	0.35 (0.8)	0.30 (0.33) ●	0.25 (0.39) ■	0.048 *
	Systole B-A	0.49 (0.26) ▲●	0.25 (0.31) ▲	0.24 (0.13) ●	0.42 (0.67)	0.002 **
	HDF B-A	0.50 ± 0.14	0.27 ± 0.23 □	0.30 ±0.26 ○	0.63 ± 0.26 □○	0.003 **
RMS (mN/mL)	Systole I-A	0.34 ± 0.12 ■	0.42 ± 0.21	0.41 ± 0.13	0.59 ± 0.22 ■	0.025 *
	Systole B-A	1.41 ± 0.27 ▲●	0.80 ± 0.47 □▲	0.83 ± 0.35 ○●	1.37 ± 0.24 □○	0.000 ***
	Diastole S-L	0.08 (0.06) ●■	0.06 (0.12) □	0.14 (0.12) ●	0.21 (0.63) ■□	0.028 *
	Diastole I-A	0.07 (0.07) ●■	0.15 (0.27)	0.11 (0.09) ●○	0.29 (0.42) ■○	0.007 **
Ratio	Systole	0.65 (0.18) ▲●	1.21 (1.04) ▲	0.85 (0.61) ●	0.83 (0.40)	0.006 **
	Diastole	0.33 (0.19) ●■	0.55 (0.36)	0.64 (0.66) ●	0.58 (0.44) ■	0.029 *
LV function
LVESV (mL) LVEDV (mL) LVEDVI (mL/m2) LVM (g) LVMI (g/m2)		51 (41) ●■	67 (25)	89 (62) ●	87 (98) ■	0.048 *
		143 (78) ●■	148 (40) ▌□	222 (96) ●▌	237 (123) ■□	0.009 **
		80.34 (21)	83.4 (29) ▌□	116.9 (44) ▌	124.6 (67) □	0.020 *
		-	96 (28) □	123 (73)	133.5 (38) □	0.024 *
		-	48.2 (8) □	56.7 (33)	69.7 (15) □	0.01 **

Notes: Normally distributed data are presented as mean ± SD, and non-normally distributed data are presented as median (IQR). p-value < 0.05 *; p-value < 0.01 **; p-value < 0.001 *** (2-tailed). Controls were the reference of comparison, indicated by p-values. Controls vs. trivial–mild ▲; controls vs. mild–moderate ●; Controls vs. moderate–severe ■; trivial–mild vs. mild–moderate ▌; trivial–mild vs. moderate–severe □; mild–moderate vs. moderate–severe ○. ‘-’ denotes the missing data in controls due to the retrospective collection form. The pairwise comparison was performed within the severity grades when the control data were missing. Abbreviations: SD = standard deviation; IQR = interquartile range; HDF = hemodynamic force; AVG = average; RMS = root mean square; S-L = septal–lateral; I-A = inferior–anterior; B-A = base-apex; LV = left ventricle; LVESV = LV end-systolic volume; LVESVI = LVESV indexed; LVEDV = LV end-diastolic volume; LVEDVI = LVEDV indexed; LVM = LV mass; LVMI = LVM indexed.

solely displays the significant variations in HDF and LV function between controls (reference) and different MR severities (trivial–mild, mild–moderate, and moderate–severe) during the systolic and diastolic phases. A further inter-group comparison was made via post hoc Bonferroni’s and Mann–Whitney U tests for parametric and non-parametric data, respectively. The full analysis will be available in Supplementary Table S2.

AVG HDF (mN/mL). The systolic AVG HDF in the SL direction demonstrated a significant reduction in the patients with mild–moderate and moderate–severe MR when compared with controls (0.55 (0.22) vs. 0.30 (0.33) and 0.25 (0.39), p-value = 0.016 and 0.029, indicating a 45.5% and 54.5% reduction, respectively). Similarly, the systolic AVG HDF in the B-A direction exhibited a significant reduction in patients with trivial–mild and mild–moderate MR when compared with controls (0.49 (0.26) vs. 0.25 (0.31) and 0.24 (0.13), p-value = 0.008 and <0.001, indicating a 49% and 51% reduction). Furthermore, the overall AVG HDF in the B-A direction significantly differed between trivial–mild and moderate–severe MR (0.27 ± 0.23 vs. 0.63 ± 0.26, p-value = 0.017, indicating a 57.1% increase in moderate–severe MR) and between mild–moderate and moderate–severe MR (0.30 ± 0.26 vs. 0.63 ± 0.26, p-value = 0.023, showing a 52.3% increase in moderate–severe MR).

RMS HDF (mN/mL). The systolic RMS force in the I-A direction demonstrated a 73.5% increase in moderate–severe MR compared to controls (0.34 ± 0.12 vs. 0.59 ± 0.22, p-value = 0.016). In the B-A direction, the systolic RMS force revealed differences between controls and trivial–mild MR (1.41 ± 0.27 vs. 0.80 ± 0.47, p-value = 0.001, reflecting a 43.26% decrease), controls and mild–moderate MR (1.41 ± 0.27 vs. 0.83 ± 0.35, p-value = 0.001, indicating a 41.1% decrease), trivial–mild and moderate–severe MR (0.80 ± 0.47 vs. 1.37 ± 0.24, p-value = 0.02, showing a 71.25% increase), and mild–moderate and moderate–severe MR (0.83 ± 0.35 vs. 1.37 ± 0.24, p-value = 0.021, signifying a 65% increase). Furthermore, the diastolic RMS force in the S-L direction revealed notable differences between controls and mild–moderate MR, moderate–severe MR (0.08 (0.06) vs. 0.14 (0.12) and 0.21 (0.63), p-value = 0.027 and 0.024, representing a 75% and 61.9% increase, respectively). Additionally, significant differences were observed between trivial–mild and moderate–severe MR (0.06 (0.12) vs. 0.21 (0.63), p-value = 0.045, indicating a 71.4% increase). Notable differences were also observed in the diastolic I-A direction, between controls, mild–moderate MR, and moderate–severe MR (0.07 (0.07) vs. 0.11 (0.09), 0.29 (0.42), p-value = 0.05 and 0.001, demonstrating a 57.1% and 75.9% increase, respectively) and between mild–moderate and moderate–severe MR (0.11 (0.09) vs. 0.29 (0.42), p-value = 0.021, showing a 62.1% increase).

RMS Ratio. The systolic RMS ratio demonstrated significant differences between controls and trivial–mild, and mild–moderate MR (0.65 (0.18) vs.1.21 (1.04) and 0.85 (0.61), p-value = 0.008 and 0.002, indicating an 86.2% and 30.8% increase compared to controls, respectively). Similarly, the diastolic RMS ratio demonstrated significant increases in mild–moderate and moderate–severe MR when compared to controls (0.33 (0.19) vs. 0.64 (0.66) and 0.58 (0.44), p-value = 0.016 and 0.016, indicating a 48.4% and 43.1% increase, respectively).

Visual representation of the data, as illustrated in Figure 3, further accentuates the discernible differences between controls and various MR severities for HDF.

LV Function. LVESV, LVEDV, LVEDVI, LVM, and LVMI exhibited significant differences among the study groups. All the parameters demonstrated a gradual increase as the MR severity increased. The LVESV (mL) demonstrated significant differences within the study group in an increasing trend from control to mild–moderate and moderate–severe MR (51 (41) vs. 67 (25) and 87 (98), p-value = 0.019 and 0.043, a 31.4% and 70.6% increase). LVEDV (mL) exhibited significant differences across groups: controls vs. mild–moderate MR (143 (78) vs. 222 (96), p-value = 0.024, a 55.2% increase); controls vs. moderate–severe MR (143 (78) vs. 237 (123), p-value = 0.013, a 65.7% increase); trivial–mild vs. mild–moderate MR (148 (40) vs. 222 (96), p-value = 0.03, a 50% increase); and trivial–mild vs. moderate–severe MR (148 (40) vs. 237 (123), p-value = 0.009, a 60.1% increase). Notably, the LVEDVI (mL/m²) exhibited a gradual increase in volume corresponding to the escalating severity of MR (trivial–mild vs. mild–moderate and moderate–severe: 83.4 (29) vs. 116.9 (44) and 124.6 (67), p-value = 0.017 and 0.025, 40.1% and 49.4%, increase, respectively). Similarly, a significant difference was observed between trivial–mild and moderate–severe MR for LVM (g) and LVMI (g/m²) (96 (28) vs. 133.5 (38) and 48.2 (8) vs. 69.7 (15), p-value = 0.001 and 0.002 reflecting a 39% and 44.6% increase). LVEF (%) did not show any significant difference among the study groups (p-value > 0.05). The visual representation of the data, as illustrated in Figure 4, further accentuates the discernible differences between controls and various MR severities for LV function.

3.4. Understanding the Physiological Pattern of Hemodynamic Forces with LV Volume among Controls and MR Severities

Expanding upon the differential analysis, Figure 5 visually portrays the distribution of systolic and diastolic AVG HDF and LV volume across cardiac phases (systole–diastole) denoted as A-F at the top of Figure 5. The visual presentation shows the result among all controls and all patients and is further extended with MR severities. The distribution is demonstrated for one cardiac cycle. The systolic and diastolic phases were determined by the studies shown by JD. Robinson et al. [39]. The mean values for each time point were calculated and are plotted for the visual presentation. The statistical mean difference between controls and MR patients is previously shown in Table 3 and Figure 2. The statistical mean differences among mitral severities were demonstrated in Table 4 and Figure 3 and Figure 4. The mean differences for average HDF were explained in the result Section 3.2 Navigating Hemodynamic Forces: Unveiling Trends in Healthy Controls vs. MR Patients with Preserved EF. The current section describes the dynamics of blood flow and hemodynamic forces only in the B-A direction due to its significance. The AVG systolic HDF in the B-A direction was notably reduced in patients with trivial–mild MR (55.8%ꜜ) and mild–moderate MR (59.6%ꜜ) compared to controls. Interestingly, the force was slightly increased in the moderate–severe MR by 3.8%ꜛ (p-value = 0.013). The AVG diastolic HDF in the B-A direction followed a similar pattern while comparing controls and severity grades. The AVG diastolic HDF in the B-A direction was notably reduced in patients with trivial–mild MR (54%ꜜ) and mild–moderate MR (18%ꜜ) compared to controls. The force was notably increased in the moderate–severe MR by 42%ꜛ (p-value = 0.013). The overall AVG HDF in the B-A direction was remarkably reduced in patients with trivial–mild MR (46%ꜜ) and mild–moderate MR (40%ꜜ) compared to controls. The HDF was notably increased in the moderate–severe MR by 26%ꜛ (p-value = 0.003). While comparing controls and MR patients, the AVG HDF in the B-A direction demonstrated significant differences among all the combinations of study groups (p-value < 0.05). Figure 5 also visually shows the trend of systolic and diastolic volume distribution. The trend showed a gradual increase in trivial–mild, mild–moderate, and moderate-sever MR compared to the controls (Systole: 1.1%ꜛ; 47.2%ꜛ; 69.22%ꜛ; p-value = 0.016, Diastole: 0.5%ꜛ; 47.7%ꜛ; 60.2%ꜛ; p-value = 0.002, respectively). This comprehensive illustration offers insights into the intricate hemodynamic interactions during different phases of the cardiac cycle, elucidating the relationship between controls and mitral severities.

Figure 6 provides a comprehensive depiction of blood flow dynamics within the cardiac cycle, which is the period from the beginning of one heartbeat to the beginning of the next one. It consists of two parts: ventricular contraction (systole) and ventricular relaxation (diastole). Each part of the cardiac cycle consists of several phases, characterized by either significant pressure changes with constant volume or volume changes accompanied by relatively small pressure changes. The phases are delineated as A to F: A = isovolumic contraction, B = systolic ejection, C = isovolumic relaxation, D = early diastolic relaxation, E = diastasis, and F = late diastolic filling (atrial contraction). The systolic phases are denoted as A-C and the diastolic phases are denoted as D-F [15]. HDF was computed based on the pressure exerted by blood, aligning with the direction of blood flow. Therefore, this section will show the changes in the pressure gradients in every phase according to the blood flow dynamics. Since the distribution of volume and blood flow follows the same trend with a variation in magnitude. Thus, we have demonstrated a case of a 65-year-old male patient with trivial–mild MR for understanding purposes. In the isovolumic contraction, the ventricles contract so all valves are closed, and no blood is ejected. Therefore, the ventricular pressure rose considerably without any change in the ventricular volume. The blood volume in the ventricles was considerably equal to the end-diastolic volume (Figure 6A). During the first part of the systolic ejection, the ventricular pressure rose, and blood was intensively ejected to the arteries (rapid ejection). As the blood volume in the ventricles decreased, the ventricular pressure started to decline in the second part of this phase (Figure 6B). The ventricular relaxation led to a significant pressure decrease. The ventricular pressure at the end of an isovolumic relaxation was close to zero in both ventricles (Figure 6C). In the early diastolic filling and diastasis phase, the ventricles were rapidly filled with the blood cumulated in the atria before the opening of the AV mitral valve. This phase accounts for most of the ventricular filling. Although the ventricular volume increased, the ventricular pressure did not change significantly due to the ventricular relaxation. Figure 6D,E demonstrates the pressure right before the opening of the atrioventricular mitral valve. As the ventricular myocardium was relaxed, the ventricular pressure did not change significantly. The blood pressure in both ventricles was almost zero (Figure 6F).

3.5. Revealing Dynamic Correlations between LV Function and Hemodynamic Forces in the Systole and Diastole

As for LV function, we considered LVESV, LVEDV, LVM, and LVEF. The systolic volume was correlated with systolic forces and diastolic volume was correlated with diastolic forces. The LVM and LVEF were correlated with all the forces in both the systolic and diastolic phases.

Table 5. Correlation between LV function and HDF.

		Controls (n = 15)	Trivial–Mild (n = 9)	Mild–Moderate (n = 11)	Moderate–Severe (n = 6)
HDF	Direction	r (p-Value)	r (p-Value)	r (p-Value)	r (p-Value)
5.1 Systole: Volume (mL) and HDF (mN/mL)
AVG	S-L	0.571 (0.021) *	−0.533 (0.140)	−0.101 (0.767)	−0.526 (0.044) *
	B-A	−0.491 (0.044) *	−0.298 (0.437)	0.121 (0.724)	−0.404 (0.136)
Ratio	Systole	0.502 (0.04) *	−0.824 (0.006) **	−0.053 (0.877)	−0.467 (0.079)
5.2 Diastole: Volume (mL) and HDF (mN/mL)
RMS	S-L	−0.173 (0.287)	−0.469 (0.202)	−0.201 (0.554)	0.801 (0.05) *
	B-A	0.119 (0.349)	0.029 (0.942)	−0.465 (0.150)	0.848 (0.033) *
5.3 LVEF (%) and HDF (mN/mL)
AVG	S-L	−0.039 (0.890)	0.823 (0.006) **	−0.229 (0.498)	−0.002 (0.998)
	Systole S-L	−0.02 (0.943)	0.716 (0.03) *	−0.054 (0.874)	0.369 (0.471)
RMS	Systole S-L	−0.079 (0.779)	0.701 (0.035) *	0.303 (0.365)	−0.226 (0.667)
5.4 LVM (g) and HDF (mN/mL)
AVG	I-A	-	0.782 (0.013) *	−0.225 (0.507)	−0.142 (0.788)
RMS	Systole S-L	-	0.605 (0.084)	−0.132 (0.698)	0.808 (0.052) *
	Systole I-A	-	0.753 (0.019) *	0.221 (0.514)	0.551 (0.257)
	Systole B-A	-	0.722 (0.028) *	−0.152 (0.655)	−0.189 (0.720)
Ratio	Systole	-	−0.331 (0.384)	0.053 (0.877)	0.924 (0.008) **

Notes: Correlation is presented as Pearson’s correlation coefficient, r (p-value). The correlation was significant at the 0.05 and 0.01 levels p-value < 0.05 *; p-value < 0.01 ** (2-tailed). ‘-’ denotes the missing data in controls due to the retrospective collection form. A pairwise comparison was performed within the severity grades when the control data were missing. Section 5.1 shows the correlation between systolic LV volume and systolic HDF. Section 5.2 demonstrates the correlation between diastolic LV volume and diastolic HDF. Section 5.3 shows the correlation between LVEF and both systolic–diastolic HDF. Section 5.4 shows the correlation between LVM and both systolic–diastolic HDF. Abbreviations: HDF = hemodynamic force; LV = left ventricle; AVG = average; RMS = root mean square; S-L = septal–lateral; I-A = inferior–anterior; B-A = base-apex; LVM = left ventricle mass; EF = ejection fraction.

presents only the significant Pearson’s correlation coefficients (r) elucidating the relationships among distinct groups, including controls and MR severity levels stratified by trivial–mild, mild–moderate, and moderate–severe. The full analysis will be available in Supplementary Table S3.

Figure 7 provides a visual representation of the correlations demonstrated in Table 5, depicting both positive and negative trends for enhanced clarity. In Figure 7(A1,A2) demonstrate the correlation for controls, Figure 7(B1–B6) show the correlation for trivial–mild MR, and Figure 7(C1–C4) illustrate the correlation for moderate–severe MR. Among controls, the systolic AVG B-A negatively correlated with end-systolic volume (ESV) (Figure 7(A1)) (r = −0.491, p-value = 0.044). The correlation exhibited a positive trend for systolic AVG S-L (Figure 7(A1)) (r = 0.571, p-value = 0.021) and systolic RMS ratio (Figure 7(A2)) (r = 0.502, p-value = 0.04). Figure 7(B1) demonstrates an altered negative correlation between ESV and systolic RMS ratio in patients with trivial–mild MR (r = −0.824, p-value = 0.006), compared to controls (Figure 7(A2)). Patients with moderate–severe MR showed a markedly negative correlation between ESV and systolic AVG S-L (r = −0.526, p-value = 0.044) (Figure 7(C1)) which signifies an altered correlation compared to controls (Figure 7(A1)). In the realm of the diastolic phase, the diastolic RMS S-L and B-A demonstrated a notable positive correlation with EDV (r = 0.801, 0.848; p-value = 0.05, 0.033, respectively) (Figure 7(C2)).

Within the scope of LVM, Figure 7(B2,B3) show a significant positive correlation between LVM and the following HDF among the patients with trivial–mild MR: AVG I-A (Figure 7(B2)), systolic RMS I-A, and systolic RMS B-A (r = 0.782, 0.753, 0.722; p-value = 0.013, 0.019, 0.028, respectively). Transitioning to the correlation between LVEF and the HDF (Figure 7(B4–B6)), we found significant positive correlations among the patients with trivial–mild MR. LVEF showed a strong positive correlation with the following HDF: systolic AVG S-L, AVG S-L, and systolic RMS S-L (r = 0.716, 0.823, 0.701; p-value = 0.03, 0.006, 0.035, respectively). Figure 7(C3,C4), show the positive correlation between LVM and the following HDF among the patients with moderate–severe MR: systolic RMS S-L (r = 0.808, p-value = 0.052), and systolic RMS ratio (r = 0.924, p-value = 0.008).

3.6. Examining Correlation with MR Severity

Spearman’s rank order correlation coefficient (rho) demonstrated a strong correlation between several HDF and MR severities. The correlation was positive for systolic RMS B-A, AVG B-A, systolic AVG S-L, systolic AVG B-A, and diastolic AVG B-A (rho = 0.621, 0.457, 0.318, 0.555, 0.317, p-value < 0.001, 0.003, 0.043, <0.001, 0.043, respectively). In contrast, a negative correlation was observed with the systolic and diastolic RMS ratio (rho = −0.543, −0.350; p-value < 0.001, 0.025, respectively). Transitioning toward LV function, LVEDV, LVEDVI, LVM, and LVMI demonstrated a significant positive correlation with mitral severity (rho = 0.554, 0.538, 0.547, 0.602; p-value = 0.003, 0.005, 0.004, 0.001, respectively).

Table 6. Spearman’s rank order correlation between mitral severity and HDF.

	Spearman’s Rho	p-Value
HDF (mN/mL)
RMS Systole B-A	0.621	<0.001 **
RMS Systole Ratio	−0.543	<0.001 ***
RMS Diastole Ratio	−0.350	0.025 *
AVG HDF B-A	0.457	0.003 **
AVG SystoleS-L	0.318	0.043 *
AVG Systole B-A	0.555	<0.001 ***
AVG Diastole B-A	0.317	0.043 *
LV function
LVEDV (mL)	0.554	0.003 **
LVEDVI (mL/m2)	0.538	0.005 **
LVM (g)	0.547	0.004 **
LVMI (g/m2)	0.602	0.001 **

Notes: Correlation is presented as Spearman’s rank order coefficient, rho (p-value). The correlation was significant at 0.05, 0.01 and 0.001 level: p-value < 0.05 *, p-value < 0.01 **, p-value < 0.001 ***, respectively (2-tailed). Abbreviations: HDF = hemodynamic force; LV = left ventricle; AVG = average; RMS = root mean square; S-L = septal–lateral; I-A = inferior–anterior; B-A = base-apex; LVEDV = left ventricle end-diastolic volume; LVEDVI = LVEDV indexed; LVM = left ventricle mass; LVMI = LVM indexed.

illustrates only the result of significant correlations, and the full analysis will be available in Supplementary Table S4.

3.7. Multivariate Linear Regression Analysis of Factors Influencing MR Severity Grades

The multivariate linear regression model was statistically significant in predicting MR [F (17,23) = 3.414, p-value = 0.003]. The overall model explained a substantial proportion of the variance in MR (R² = 0.716, Adjusted R² = 0.506). A positive coefficient [Beta, B = 3.253, 95% CI (1.204–5.301), p-value = 0.003] in systolic RMS B-A indicated a potential predictor of increased MR severity. Similarly, a positive coefficient [B = 5.413, 95% CI (0.227–10.6), p-value = 0.029] in the diastolic RMS S-L direction suggested its potential as an indicator for increased MR severity. The visual representation of the predictive result is presented in Figure 8.

Our analysis revealed significant correlations between advanced HDF parameters and LV function and MR severity, which had not been previously reported to the best of our knowledge. These findings suggest that this enhanced approach provides a more nuanced understanding of the hemodynamic alterations, which may help in planning surgical time specifically in asymptomatic MR patients. To conclude, HDF may play a vital role in a comprehensive assessment of MR and clinical decision-making.

4. Discussion

Our main findings demonstrated (1) substantial disparities in HDF between controls and MR patients with preserved EF, indicating altered force distribution; (2) noteworthy variations between controls and patients across different MR severities; (3) strong correlation between HDF parameters and LV function, showing an altered relationship while comparing controls and patients with MR; (4) significant linear correlation between MR severity and HDF, especially in the B-A direction; (5) systolic RMS B-A and diastolic RMS S-L as significant predictors of increased MR severity.

Hemodynamic forces are recognized as an important factor in heart development and exert influences on the pathophysiology of the mature heart. G. Pedrizzetti et al. investigated in vivo model of patients who presented a stable normal heart function when the pacemaker was on and who were expected to develop LV remodeling when the pacemaker was switched off. They found that HDF developed misalignment hammering onto lateral walls when the pacing was temporarily switched off. They concluded that HDF was the first event that evoked a physiological activity anticipating cardiac changes and suggested that HDF could help in predicting longer-term heart adaptations [17]. A study performed by SJ. Backhaus et al. on HF with preserved EF (HFpEF) demonstrated HDF alteration between controls and patients. They indicated the association of HDF with cardiac events [19]. Another study by J. Eriksson et al. showed a similar result for dilated cardiomyopathy and concluded that HDF altered significantly between controls and patients [16]. A similar study by PM. Arvidsson et al. showed the ability of HDF to discriminate between controls and HFpEF [37]. D. Laenens et al. showed that HDF assessment is a novel approach to identifying LV pressure gradients. They also reported that the HDF pattern might be altered in myocardial infarction and non-ischemic cardiomyopathy [14]. None of the previous studies addressed the impact of HDF on patients with MR or the relationship between HDF and standard MR severity metrics. To the best of our knowledge, the present study is the first and only study that focuses on MR patients with preserved EF and reports on the association between the degree of MR, HDF, and LV function. YH. Loke et al. analyzed controls and patients with rTOF and found significant differences in diastolic HDF [12]. Similarly, our study found that the diastolic RMS in the I-A direction was significantly increased in MR patients than in healthy controls. We further extended our study to examine if there were considerable differences among MR severities. We found the diastolic RMS in the S-L and I-A directions demonstrated notable diversity among MR severities. Our study showed that all the systolic AVG, systolic RMS, and overall AVG in the B-A direction differ significantly between controls and MR patients with preserved EF. Systolic AVG and overall AVG in the S-L direction showed considerable differences. Again, the systolic AVG and systolic RMS in the B-A direction stood out as a common variable that differentiated between controls and MR severities. Besides these, the systolic AVG in the S-L direction, and systolic RMS in the I-A direction demonstrated significant differences among MR severities. A very recent study by K. Pola et al. demonstrated the transverse/longitudinal ratio of RMS as a potential biomarker for identifying patients with HF [22]. Another recent study by J. Eriksson et al. showed an association between the degree of dyssynchrony and the HDF ratio measured using 4D-flow MRI in patients with HF [40]. Our study also found a significant divergence in the transverse/longitudinal ratio of RMS between controls and MR patients with preserved EF and MR severities. Our findings indicate that HDF can effectively differentiate between healthy individuals and those with MR.

A clinical study by JB. Patel et al. identified the correlation between severe congestive HF and MR. The congestive heart failure was defined as EF less than or equal to 35%. MR was severe in 4.3%, moderate–severe in 12.5%, moderate in 21.9%, mild–moderate in 11.8%, mild in 39.1%, and absent or present in 10.4% of the patients [41]. A comprehensive study by F. Vallelonga et al. described HDF for various cardiac conditions such as HF, idiopathic dilated cardiomyopathy, and CRT and for competitive athletes (healthy). They concluded that HDF analysis could offer invaluable insights into myocardial dysfunction [15]. Previous studies on HDF demonstrated functional correlation with various cardiac disease states but lacked data on MR severities. Our study filled this knowledge gap and focused on the impact of HDF on different MR severities. MR is associated with increased cardiovascular mortality among patients with prior myocardial infarction or systolic dysfunction [41]. We know that LV function plays a vital role in assessing LV remodeling and MR classification [42]. Therefore, our study focused on the association between HDF and LV function (specifically LVESV, LVEDV, LVM, and LVEF) among different MR severities. This study was designed separately for systolic and diastolic HDF and volume. However, the correlation analysis was performed for both systolic and diastolic phases between HDF and EF, LVM.

MR leads to an LV volume overload due to increased SV, caused by increased blood volume within the LA and an increased preload delivered to the LV during diastole. Volume overload from MR causes the ventricle to expand, widens the mitral annulus, and reduces leaflet coaptation, leading to the progressive worsening of MR. Eventually, the volume overload becomes so severe that the membrane’s excitation–contraction coupling becomes impaired, and the afterload on the LV due to wall stress leads to dilation with decreased contractility, resulting in a reduction in EF [2,6,43]. We hypothesized that LV volume in both the systolic and diastolic phases is related to HDF among MR patients with preserved EF. We found a positive correlation between LVESV and systolic HDF (AVG S-L and systolic ratio) among healthy controls. On the contrary, an altered correlation was observed among moderate–severe MR and trivial–mild MR, respectively. AVG S-L HDF was significantly reduced (54.5%), while the systolic ratio was significantly increased in patients (86.2%) compared to controls. This altered correlation revealed that AVG S-L decreases with increased systolic volume indicating systolic dysfunction. Increased LVESV is reportedly associated with severe MR and with the combination with reduced EF is suggested for surgical intervention. The systolic AVG B-A demonstrated a negative correlation with LVESV among controls; however, we did not find any significant association among patients. Therefore, further investigation is warranted. In the diastolic phase, we found a positive correlation between RMS HDF in the S-L and B-A direction and volume among patients with moderate–severe MR. This reveals that, as the HDF increases, the volume also increases potentially. It is important to note that we found an altered relation among controls with a weak–negative correlation for RMS B-A; however, this result was insignificant. EF is typically significantly reduced in patients with severe MR [44]. EF is sensitive to changes in LV hemodynamic loading conditions. A decrease in the myocardial contractile state or an increase in LV afterload may cause a reduction in the EF. Regardless of the mechanism, a depressed EF can be an indication of surgical correction of MR [45]. SJ. Backhaus et al. showed no correlation between EF and HDF in patients with HFpEF [19]. On the other hand, F. Vallelonga et al. showed that HDF is directly proportional to EF in patients with HF [15]. We shed light on the contradicting prior research. Our study demonstrated a positive correlation between EF and HDF (systolic average HDF, systolic RMS HDF, and average HDF in the S-L direction) among MR patients with trivial–mild severity grading. This result indicates the impairment of LV systolic ejection force in MR. Our study suggests a significant reduction in systolic average HDF in the S-L direction as the severity increases, and it is associated with systolic impairment. Studies have shown that elevated LVM and lower LV systolic function are associated with various cardiovascular diseases, including HF, VHD, and stroke [46,47,48,49]. It is established that LVM is a key marker of severe MR. S. Uretsky et al. concluded a positive linear correlation between LVM and MRV. Therefore, as the severity of MR increases, the LVM also increases linearly [29]. Another study by p. Gjini et al. demonstrated that LVM significantly increases with MR severity [48]. A study by M. Srabanti et al. demonstrated that elevated LVM and LV volume are associated with severe MR and eccentric LV hypertrophy (LVH) [3]. This gives strong evidence to conclude that LVM is a vital biomarker for evaluating MR severity and LVH. Our study revealed a significant positive association between LVM and systolic RMS HDF in all three directions. AVG HDF in the I-A direction demonstrated a linear increment of both parameters among MR patients with a severity of trivial–mild and moderate–severe. This contributes to existing knowledge, and we propose that systolic RMS HDF in all directions and AVG HDF in the I-A direction are linked to severe MR and LV remodeling. The HDF significantly increases with LVM and increased severity. After conducting the differential and correlation analysis, we extended our study to test the predictive ability of HDF. Since HDF demonstrated significant association with LV function, it revealed the platform for us to hypothesize HDF as a novel biomarker to detect MR. Finally, the multilinear regression model showed that systolic RMS B-A and diastolic RMS S-L were independently predictive parameters for detecting MR with preserved EF.

Considerations and challenges in integrating 4D-flow derived HDF into clinical practice. Several challenges remain to achieve the widespread adoption and application of 4D-flow MRI. This includes limited velocity dynamic range, long and unpredictable scan times, data storage of large datasets, and time-consuming data processing. It is important to note that 4D-flow MRI is an established research technique typically conducted following clinical diagnostic sequences. But things are progressing rapidly, and some centers are now adding 4D-flow MRI to the routine clinical cardiac MRI protocols with clinically validated applications and postprocessing software [50]. Accuracy in 4D-flow MRI can be influenced by the choice of vendor sequences [51], acquisition parameters [52], and postprocessing software [53]. Therefore, local validation and quality assurance are essential. Currently, the workflow for 4D-flow derived-HDF assessment is non-standardized and time-consuming, which limits reproducibility and clinical translation. Addressing these limitations will require the development of efficient image analysis strategies with minimal user interaction. Furthermore, creating user-friendly software tools that simplify the visualization and interpretation of these metrics could facilitate their integration into clinical practice. Furthermore, developing targeted educational programs and workshops could be instrumental in equipping clinicians with the necessary skills to interpret HDF-based biomarkers effectively. Integrating these advanced metrics into existing clinical workflows can be challenging, as it requires not only technical proficiency but also adjustments to established diagnostic and treatment paradigms.

Consideration for the contrast agent. Recently, non-contrast MRA examinations have attracted increased attention after the emergence of nephrogenic systemic fibrosis (NSF) and the discovery of a connection to gadolinium-based MRA [54]. Thus, the cardiac magnetic resonance (CMR) community is moving towards non-contrasted acquisitions [50]. Though this technique is increasingly being explored, gadolinium-enhanced 4D-flow MRI remains the gold standard for better visualization of flow patterns and more precise quantification of hemodynamic parameters. For non-contrasted 4D-flow MRI, the standard FA should be set around 7° for adults and 12° for neonates [55], and TR and TE should be as short as possible [50]. By increasing the temporal and spatial resolution of 4D-flow MRI, there has been a better visualization of hemodynamic properties, as demonstrated in previous studies [56]. This may offer a valuable alternative to contrast-enhanced MRA. However, it is important to note that the HDF assessment is not impacted by the choice of 4D-flow MRI acquisition as the calculation relies on the velocity and fundamental fluid components.

Potential uncertainty. Time-resolved 3D phase-contrast (PC) MRI, also known as 4D-flow MRI, is widely utilized for hemodynamic assessment due to its capacity to offer patient-specific vessel geometries and flow data. This information is valuable for establishing fully personalized conditions at boundaries. A recent study conducted by U. Morbiducci et al. has brought attention to the potential for inaccuracies in aortic hemodynamics when using PC-MRI for flow data measurements [57]. In a recent study, S. Bozzi et al. delved into the uncertainty’s origins and outlined its quantification methodologies. Through the implementation of Monte Carlo simulations with a steady-state Navier–Stokes solver, they measured the uncertainty of blood velocity, pressure, vorticity, and wall shear stress distribution along the aorta. The analysis revealed that the uncertainty in peak systolic pressure exhibited the highest magnitude, followed by velocity and vorticity, prompting a notable concern within the scope of our study. They also emphasized that the uncertainty does not depend either on the anatomical location or on the flow regime, which again imposes the limitation on our LV-based study. The work, however, is limited by its assumption of steady flow. Nonetheless, it remains applicable in evaluating hemodynamic uncertainty [58]. They also indicated that the VENC strategy may impact uncertainty propagation in computational hemodynamics, especially during the late diastole, when blood velocity is minimal. It has been suggested that achieving higher signal-to-noise ratio levels may be possible by utilizing different VENC values for the three-phase velocity components. This principle remains applicable to the examination of uncertainty propagation. Consequently, it is advisable to conduct further research involving varying VENC values and the measurement of uncertainty in HDF calculation using the same cohort. On the contrary, a very recent study by A. Mariotti et al. demonstrated a similar finding on the anatomical location (Aorta). They demonstrated stroke volume and cardiac cycle have a significant influence on wall shear stresses (WSSs) and the velocity distribution in vessel regions. They also emphasized the spatial distribution of the inlet velocity as another source of uncertainty [59]. Therefore, patient-specific inlet conditions are recommended to obtain reliable hemodynamic predictions. A previous study by I. Campbell et al. revealed that simplified inlet velocity profiles impact mean WSS and oscillatory shear index (OSI), albeit to a lesser extent than using a non-patient-specific flow waveform and also to a lesser extent than differences in patient anatomy [60]. As geometry and flow waveform selection are greater modulators of these hemodynamic metrics (WSS, OSI), they firstly recommended a careful reconstruction of the vessel anatomy and, secondly, acquisition of the subject’s flow waveform before becoming concerned with the velocity waveform selection. The PC-MRI or 4D-flow MRI is currently considered the gold standard for HDF calculation, and the hemodynamic uncertainty related to PC-MRI shall be taken into account.

Limitations. This study is subject to several limitations that merit discussion. Firstly, the cohort size was relatively small, comprising only 41 cases. Additionally, while LV segmentation was automated, the manual placement of force axis directions (septal–lateral, inferior–anterior, and base-apex) may introduce potential errors in precision. To address this, conducting reliability tests for HDF quantification is recommended for future studies. Furthermore, cases were scarce, particularly in the severe MR category, necessitating validation in larger-scale studies before clinical implementation. We acknowledge that the MR patients were selected based on only existing MR with preserved EF of varying severities, ranging from trivial to severe. The study did not specifically focus on different types of MR (primary, secondary, or Carpentier types). Further research is recommended to draw precise conclusions about specific MR types. Although pressure calculation was performed for visualization purposes, utilizing the Pressure Poisson equation to derive numerical quantification is advisable for future investigations.

Added Value. The present study reports LV functional alterations associated with HDF in MR patients with preserved EF. The ability of HDF to amplify mechanical abnormalities enables the detection of even small kinetic dysfunctions that cannot be recognized by direct observation. HDF can identify conditions that may lead to adverse LV remodeling or predict reverse remodeling even after a therapeutic intervention takes place.

5. Conclusions

Our findings collectively contribute to a better understanding of hemodynamic forces in MR patients. This study led us to the conclusion that HDF can be used as a powerful metric to evaluate MR. Evaluating the MR severities requires a multi-parametric approach, and HDF can serve as an additional potential marker that reveals the association with the LV function. This study strongly suggests HDF as a confounder of severity stratification on MR. Systolic RMS B-A [B = 3.253, 95% CI (1.204–5.301), p-value = 0.003] and diastolic RMS S-L [B = 5.413, 95% CI (0.227–10.6), p-value = 0.029] have emerged as promising indicators. These findings enhance our understanding of LV flow dynamics in MR, advocating for the adoption of HDF as a key tool in MR evaluation.