## 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 endocardi. 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]. [PERSON] 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 [PERSON] 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 [PERSON] 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.