Comparison of neuro-fuzzy systems for classification of transcranial Doppler signals with their chaotic invariant measures

Transcranial Doppler (TCD) is a non-invasive diagnosis method which is used in diagnosis of various brain diseases by measuring the blood flow velocities in brain arteries. In this study, chaos analysis of the TCD signals recorded from the middle arteries of the temporal region of the brain of 82 patients and 24 healthy people was investigated. Among 82 patients, 20 of them had cerebral aneurism, 10 patients had brain hemorrhage, 22 patients had cerebral oedema and the remaining 30 patients had brain tumour. It was found that all of the TCD signals represented nonlinear dynamics and had an underlying low-level determinism. All of the TCD signals were passed through the nonlinearity tests which involved the application of surrogate data method. The maximum Lyapunov exponent (λ1) which is the strongest quantitative indicator of chaos was found to be positive for all TCD signals. The correlation dimension (D2) was found as greater than 2 and as fractional value for all TCD signals. This result indicates that the nonlinear dynamics of the TCD signals corresponds to a strange attractor in phase space which implies a non-ergodic dissipative system having low-level chaotic behaviour. Besides, the values of λ1 and D2 were approximately the same for the TCD signals of the patients having the same brain disease. Relying on this observation, these two chaotic invariant measures were divided into training and test subsets including 52 and 54 subjects, respectively. For comparison purposes, the training set was used to build two different neuro-fuzzy models, namely ANFIS and NEFCLASS. The rule base of the NEFCLASS model was created by applying the samples in the training subset for 1000 epochs. On the other hand, the ANFIS model was trained for 250 epochs until the convergence error has decreased to 0.42 × 10−5. The ANFIS model achieved better classification accuracy than the NEFCLASS model for the samples in the test set. The classification accuracy of the ANFIS model after training was 94.40% whilst this value was found as 88.88% for the NEFCLASS model.