## 3 Results
### Characteristics of Study Population
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%\({}^{\ddagger}\)). 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%\({}^{\ddagger}\) and 0.50 \(\pm\) 0.14 vs. 0.37 \(\pm\) 0.28, \(p\)-value = 0.039, 26%\({}^{\ddagger}\)). 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%\({}^{\ddagger}\) and 72.7%\({}^{\ddagger}\), respectively) highlighting distinct alterations in force distribution. Unraveling Distinctive Patterns in Hemodynamic Forces and LV Function across Controls and MR Severities  
Table 4 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 \(\pm\) 0.23 vs. 0.63 \(\pm\) 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 \(\pm\) 0.26 vs. 0.63 \(\pm\) 0.26, \(p\)-value = 0.023, showing a 52.3% increase in moderate-severe MR). \begin{table}
\begin{tabular}{l l l l} \hline
**HDF** & **Controls (n = 15)** & **MR Patients (n = 26)** & \(p\)**-Value** \\ \hline AVG Systole S-L & 0.55 (0.22) & 0.33 (0.33) [40\%\({}^{\ddagger}\)] & 0.007 ** \\ AVG Systole B-A & 0.49 (0.26) & 0.26 (0.25) [46.9\%\({}^{\ddagger}\)] & 0.001 ** \\ RMS Systole I-A & 0.34 \(\pm\) 0.12 & 0.46 \(\pm\) 0.19 [35.3\%\({}^{\ddagger}\)] & 0.023 * \\ RMS Systole B-A & 1.37 (0.30) & 0.93 (0.66) [32.1\%\({}^{\ddagger}\)] & 0.001 ** \\ RMS Diastole I-A & 0.07 (0.07) & 0.16 (0.23) [56.3\%\({}^{\ddagger}\)] & 0.007 ** \\ AVG HDF S-L & 0.25 (0.15) & 0.19 (0.22) [24\%\({}^{\ddagger}\)] & 0.04 * \\ AVG HDF B-A & 0.50 \(\pm\) 0.14 & 0.37 \(\pm\) 0.28 [26\%\({}^{\ddagger}\)] & 0.039* \\ RMS Ratio (Systole) & 0.65 (0.18) & 0.86 (0.65) [32.3\%\({}^{\ddagger}\)] & 0.001 ** \\ RMS Ratio (Diastole) & 0.33 (0.19) & 0.57 (0.37) [72.7\%\({}^{\ddagger}\)] & 0.003 ** \\ \hline \end{tabular} Notes: Normally distributed data are presented as mean \(\pm\) 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.  
\end{table} 
Table 3: Comparison of AVG HDF (mN/mL), RMS HDF (mN/mL), and RMS ratio between controls and MR patients with preserved EF. 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 \(\pm\) 0.12 vs. 0.59 \(\pm\) 0.22, \(p\)-value = 0.016).