Inter-Discharge Interval Distribution of Motor Unit Firing Patterns With Detection Errors

Inter-discharge interval (IDI) distribution analysis of motor unit firing patterns is a valuable tool in EMG decomposition and analysis. However, the firing pattern obtained by EMG decomposition may have detection errors: false positives (incorrectly classified firings) and false negatives (missed firings). In this paper, the mathematical derivation of an IDI distribution model that accommodates false positives and false negatives of the detection process is presented. An approximation of the general model to adapt to specific EMG decomposition conditions is also presented. To illustrate the usefulness of the model, the obtained distribution is used to derive the maximum likelihood estimates of the statistics of motor unit firing patterns, the IDI mean and standard deviation, and estimates of the false negative and false positive ratios. Results obtained from simulation experiments and tests with real motor unit firing patterns show an enhanced estimation performance when compared to previously available algorithms. Goodness-of-fit tests applied to estimations for real data corrupted with false positives showed that the model-driven estimations fitted the uncorrupted data better than EFE estimations: 82% versus 52% not rejectable, respectively, when false positives were about 10% of IDIs. With about 5% false positives, the not rejectable estimations were 85% versus 70%.