Significance of mini network disruption parameters
The mini network disruption parameters U, K, and φ can be used to evaluate mini network imbalance integrally. According to Equations (1–3), with the mini network variation gets smaller, the K-value gets closer to 1 whereas the values of U and φ get closer to 0.
The simulation experiment result is presented in the Table 2. The results of single marker changing simulation indicate that the parameters U and φ are related to the variation of single marker. The results of multi-marker changing simulation 1 suggest that parameter K is related to the consistency multi-marker changing and U is sensitive to the great consistency variation of multi-marker. The results of multi-marker changing simulation 2 indicate that parameters U and φ are related to the multi-marker inconsistency variation. We summarize physiological significance of U, K, and φ with the simulation experiment evidence. U is responses to both consistency variation and inconsistency variation comprehensively. K responds to multi-marker consistency variation. φ is response to the multi-marker inconsistency variation.
Table 2  The mini network integral disruption parameters changes in simulation experiment.
Gradient (%)   K (%)   φ (%)   U (%)
Situation: single marker simulation  10  3.78  12.88  11.09
20  7.77  25.07  23.45
50  20.77  57.21  65.17
Situation: multi-markers simulation 1  10  10.00  0.00  0.27
20  20.00  0.00  6.82
50  50.00  0.00  57.85
Situation: multi-markers simulation 2  10  2.19  27.68  25.30
20  3.38  57.21  51.38
50  0.82  147.97  131.69 The boxplot of mini network disruption parameters (Figure 7A) shows that these three parameters in both AD and MCI groups are significantly greater than those in normal group (P < 0.01, based on One-way ANOVA, Table 3) which suggests that if mini network disruption parameters U, K, and φ are higher than the upper whisker of normal group, the patient may have high disease risk. Moreover, the trajectory figure (Figure 7B) shows that the variation of parameter U is similar to the disease progression.
Figure 7  (A) Box plot of mini network integral disruption parameters. “+” represents data points beyond the whiskers. (B) The trajectory figure of the mini network integral disruption parameter U. The different colors of the area under the curve indicate different time period. With the curves of U farther to the center, mini network imbalance gets worse. **P < 0.01 vs. normal.
Table 3  Estimation of disruption parameters U, K, and φ.
U   K   φ
AD  118.84 ± 87.12**  0.9684 ± 87  0.4484 ± 87**
MCI  103.80 ± 72.64**  0.9480 ± 72  0.3980 ± 72**
Normal  72.43 ± 30.35  0.923 ± 30  0.263 ± 30
The data are presented as mean ± SD.
**  P < 0.01 vs. Normal. The contribution of the mini network integral disruption parameters are shown in the Figure 8. The SVM based on all three parameters has the best classification performance compared with the other SVMs. The SVM without parameter U has the poorest performance which is same as the SVM based on CSF markers.
Figure 8  Mini network integral disruption parameters' contribution to the performance in classification.