## 3 Results
### Characteristics of Study Population
(**C1–C3**) demonstrate the average volume and HDF among mitral patients with trivial–mild, mild–moderate, and moderate–severe severity. The B-A HDF showed a significant reduction where the volume was elevated among severity levels compared to controls (\(p\)-value \(<\) 0.05). Notes: The cardiac 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). A–C = systolic phase and D–F = diastolic phase. Abbreviations: HDF = hemodynamic force; LV = left ventricle; BA = basal– apical; MR = mitral regurgitation. 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 presents only the significant [PERSON]'s correlation coefficients (r) elucidating the relationships among distinct groups, including controls and MR severity  
Figure 6: The physiological pattern of HDF and blood flow in one cardiac cycle. The upper panel shows the 4-chamber view, and the bottom panel demonstrates the 3-chamber view of each phase. The demonstrated 4D-flow MRI images were acquired from a 65-year-old male patient with trivial–mild MR. In phase (**A**), higher pressure was observed in the LV as all valves were closed. In phase (**B**), the blood flowed from the LV to the aorta through the aortic valve, and the LV pressure was relatively low. Phase (**C**) shows the relaxation phase with negligible pressure difference. The (**D**,**E**) phase shows the pressure right before the opening of the mitral valve in the diastolic phase (ventricular relaxation) during the mid-phase, when the pressure drops gradually, and phase (**F**) shows the atrial contraction when the LV fills with blood. Due to the relaxation phase of LV, the LV pressure was relatively low. Notes: White arrows represent the force direction, and red arrows represent the blood flow direction. The color bar represents the strength of the LV pressure exerted by the blood. Abbreviations: HDF = hemodynamic force; MR = mitral regurgitation; 4D = 4-dimensional; MRI = magnetic resonance imaging; LV = left ventricle; LA = left atrium; MV = mitral valve; AoV = aortic valve; RV = right ventricle; RA = right atrium; TV = tricuspid valve; EF = ejection fraction; SV = stroke volume; EDV = end-diastolic volume; ESV = end-systolic volume. 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)).