Figure 1
An overview over typical ways to present bioimpedance data, showing the level of complexity within the realm of presenting and analyzing bioimpedance data.
Figure 2
Overview of the methodology used for investigating the performance of different neural networks for predicting duration of ischemia based on bioimpedance using simulated measurements.
Figure 3
Simulated liver resistance and reactance profiles during ischemia.
Figure 4
Example of simulated resistance and reactance data at 100kHz for five livers (in colors) having random onsets of ischemia (marked with arrows). Five non-ischemic control livers are added in gray. The data are simulated with a 5% liver variation, no drift, and a noise level of 30 dBW.
Table 1
List of all variables used for comparing different varieties of the bioimpedance input data and hyperparameters in the machine learning for prediction of ischemic duration.
| Variable | Description | Tested levels | Values |
|---|---|---|---|
| Measurement noise | Setting for simulated input data | 3 | 0, 10, 30 |
| Liver variance | Setting for simulated input data | 2 | 5, 20 |
| Drift | Setting for simulated input data | 3 | 0 ±50 +100 |
| Frequencies | Selection of input variables | 3 | {102 104 106}, 101:7, 101:0.1:7 |
| Sample size | Training and testing data size | 2 | 20, 100 |
| Regularization | Neural network hyperparameter | 3 | 10-1, 10-2, 10-3 |
| Hidden layer size | Neural network hyperparameter | 3 | 2, 5, 25 |
| Minibatch size | Neural network hyperparameter | 2 | 16, 32 |
| Epochs | Neural network hyperparameter | 2 | 250, 500 |
Figure 5
The distribution of prediction accuracies according to the different levels of cases included in the simulated data. The distributions are shown as violin plots with medium smoothing, where the dashed and dotted lines show the median and quartiles respectively.
Table 2
Comparison of prediction performance for the different ANN architectures in three different cases of difficulty based on the liver-to-liver variance, noise and drift in the measurement. The selection of input frequencies and hyperparameters for the best prediction performance of the different ANN architectures is provided in the rows below the prediction performances. The last row presents the best prediction performance when all 70 frequencies are used as input to the ANN. RMSEP=root mean square error of prediction, RMSEC=root mean square error of calibration, both having units of ischemia duration in hours.
| Case | Easy | Medium | Hard | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Liver variance | 5 % | 5 % | 20 % | ||||||
| Noise | 0 | 10 | 30 | ||||||
| Drift | 0 | 100 | 100 | ||||||
| Drift direction | None | Increasing | Both | ||||||
| Training examples | 100 | 100 | 100 | ||||||
| Best performance | FNN | LSTM | 2LSTM | FNN | LSTM | 2LSTM | FNN | LSTM | 2LSTM |
| Mean RMSEP | 0.124 | 0.016 | 0.017 | 0.173 | 0.029 | 0.026 | 0.256 | 0.079 | 0.066 |
| Std RMSEP | 0.025 | 0.003 | 0.009 | 0.044 | 0.003 | 0.012 | 0.044 | 0.013 | 0.015 |
| Mean RMSEC | 0.112 | 0.014 | 0.015 | 0.175 | 0.026 | 0.021 | 0.256 | 0.037 | 0.038 |
| Std RMSEC | 0.029 | 0.005 | 0.007 | 0.029 | 0.006 | 0.009 | 0.029 | 0.006 | 0.018 |
| Frequencies | 70 | 3 | 7 | 70 | 7 | 3 | 70 | 3 | 3 |
| Hidden layer size | 25 | 25 | 5 | 5 | 5 | 25 | 2 | 25 | 25 |
| l2 regularization | 0.1 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
| Training epochs | NA | 500 | 500 | NA | 500 | 500 | NA | 500 | 500 |
| Minibatch size | NA | 32 | 32 | NA | 32 | 32 | NA | 32 | 16 |
| Mean RMSEP (freq=70) | 0.124 | 0.056 | 0.022 | 0.173 | 0.073 | 0.035 | 0.256 | 0.142 | 0.106 |
Figure 6
Predictions on 50 examples of liver ischemia and 50 controls from the test data for the different cases presented in table 2. Colors indicate different livers.