## 3 Results
### Characteristics of Study Population
The AVG diastolic HDF in the B-A direction was notably reduced in patients with trivial-mild MR (54%4) and mild-moderate MR (18%4) compared to controls. The force was notably increased in the moderate-severe MR by 42%4 (\(p\)-value = 0.013). The overall AVG HDF in the B-A direction was remarkably reduced in patients with trivial-mild MR (46%4) and mild-moderate MR (40%4) compared to controls. The HDF was notably increased in the moderate-severe MR by 26%7 (\(p\)-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%7; 47.2%7; 69.22%7; \(p\)-value = 0.016, Diastole: 0.5%7; 47.7%7; 60.2%7; \(p\)-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). Figure 5: The average HDF and LV volume distribution pattern in one cardiac cycle. (**A1,B1**) demonstrate the average volume and HDF among all controls and MR patients.