# Three-Dimensional Modeling of Heart Soft Tissue Motion
## 3 Results
### Effect and Explanation of the Physical Modeling of Heart Soft Tissue
#### 3.2.3 Nonlinear Effect Verification of the Parameter Dynamics  
To verify that the model with dynamic parameters had a better nonlinear fitting ability, different forces were applied to a single particle in the classical particle spring model, the displacement data of the particle were recorded, and the relationship between the force and the displacement was found.  
After that, the parameter dynamics was introduced, the elastic coefficient in the mass-spring model was mapped into Equation (12), and the mass displacement was recorded under the same force. The following Figure 12 was obtained.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Particle Data** & \begin{tabular}{c} **The Initial Position** \\ **of a Particle** \\ \end{tabular} & \
\begin{tabular}{c} **Large Bending** \\ **Spring Coefficient** \\ \end{tabular} &
\begin{tabular}{c} **The Reinforced Spring** \\ **Coefficient Is Large** \\ \end{tabular} \\ \hline First point & \(-3.000\), \(0.000\), \(45.000\) & \(-3.000\), \(0.000\), \(45.000\) & \(-3.000\), \(0.000\), \(45.000\) \\ Second point & \(-1.000\), \(0.000\), \(45.000\) & \(-0.998\), \(0.192\), \(44.994\) & \(-1.002\), \(0.184\), \(44.981\) \\ Third point & \(1.000\), \(0.000\), \(45.000\) & \(0.996\), \(0.105\), \(44.998\) & \(0.996\), \(0.104\), \(44.998\) \\ Fourth point & \(3.000\), \(0.000\), \(45.000\) & \(3.000\), \(0.000\), \(45.000\) & \(3.000\), \(0.000\), \(45.000\) \\ Fifth point & \(-3.000\), \(0.000\), \(43.000\) & \(-2.994\), \(0.192\), \(42.998\) & \(-2.981\), \(0.184\), \(43.002\) \\ Sixth point & \(-1.000\), \(0.000\), \(43.000\) & \(-0.989\), \(0.568\), \(42.989\) & \(-0.980\), \(0.649\), \(42.980\) \\ Seventh point & \(1.000\), \(0.000\), \(43.000\) & \(0.999\), \(0.150\), \(42.999\) & \(0.999\), \(0.144\), \(42.997\) \\ Eighth point & \(3.000\), \(0.000\), \(43.000\) & \(2.987\), \(0.076\), \(43.001\) & \(2.993\), \(0.034\), \(43.004\) \\ Ninth point & \(-3.000\), \(0.000\), \(41.000\) & \(-2.998\), \(0.105\), \(41.004\) & \(-2.997\), \(0.104\), \(41.004\) \\ Tenth point & \(-1.000\), \(0.000\), \(41.000\) & \(-0.999\), \(0.150\), \(41.001\) & \(-0.997\), \(0.144\), \(41.001\) \\ Eleventh point & \(1.000\), \(0.000\), \(41.000\) & \(0.999\), \(0.073\), \(41.001\) & \(0.998\), \(0.070\), \(41.002\) \\ Twelfth point & \(3.000\), \(0.000\), \(41.000\) & \(2.999\), \(0.001\), \(41.000\) & \(3.004\), \(0.001\), \(40.997\) \\ Thirteenth point & \(-3.000\), \(0.000\), \(39.000\) & \(-3.000\), \(0.000\), \(39.000\) & \(-3.000\), \(0.000\), \(39.000\) \\ Fourteenth point & \(-1.000\), \(0.000\), \(39.000\) & \(-1.001\), \(0.076\), \(39.013\) & \(-1.004\), \(0.034\), \(39.007\) \\ Fifteenth point & \(1.000\), \(0.000\), \(39.000\) & \(1.000\), \(0.001\), \(39.001\) & \(1.003\), \(0.001\), \(38.996\) \\ Sixteenth point & \(3.000\), \(0.000\), \(39.000\) & \(3.000\), \(0.000\), \(39.000\) & \(3.000\), \(0.000\), \(39.000\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Initial positions of the particles and the effect of springs.  
Figure 12: Comparison diagram of force vs. displacement.