The effect of dipole model misspecification on the bias and variance of evoked potential amplitude and amplitude ratio estimates

In dipole modeling, the generators of evoked potentials (EPs) are modeled as dipoles inside a misspecified model of the head. Most research studies EP changes as a function of stimulus characteristics, disease states, or other differences between data sets. The Dipole Components Model (DCM) is a dipole modeling algorithm that can be applied to multiple data sets gathered under different experimental conditions, and can be used to estimate effects on the amplitude of the equivalent generators (amplitude estimates).; The DCM was applied to auditory evoked P50 EPs for comparison of the reliability (measured by the intraclass correlation coefficient) of P50 suppression estimated using dipole modeling vs. peak-picking. The DCM fit P50 using a homogeneous sphere head model, a decaying sinusoid magnitude function, and a single dipole. Conditioning and testing amplitude parameters were fit, and P50 suppression was measured by dividing the testing amplitude by the conditioning amplitude (amplitude ratio). The DCM improved amplitude ratio but not amplitude reliability over peak-picking, an apparent paradox. It was proposed that the estimation of amplitude and amplitude ratios might be differentially affected in a noisy, misspecified dipole model.; Using the theory of linear least squares fitting, it was shown that dipole model misspecification led to biased amplitudes and unbiased amplitude ratios for three generator cases: (1) single dipole, (2) equal amplitude multiple dipoles, and (3) multiple dipoles with equal amplitude ratios across data sets. The variance of amplitudes and amplitude ratios could not be shown theoretically, so P50 was simulated by generating potentials due to dipoles in a boundary element skull model and adding EEG noise. Modeling of the simulated P50 using a homogeneous sphere showed that model misspecification and noise led to more variation in amplitude estimates than derived amplitude ratios.; It was proposed that improved amplitude estimation might be achieved by discarding the model. A model-free amplitude estimation method using singular value decomposition (SVD) was developed and tested using simulated and real P50 data. The SVD method estimated reliable amplitudes and ratios when the data were generated by one of the three cases above.