Phase resetting with temporal template explains complexity matching in finger tapping to fractal rhythms

Auditory-motor synchronization refers to the coupling of motor responses to rhythmic auditory stimuli. This study examined finger-tapping dynamics under three conditions: self-paced tapping, tapping to metronomic stimuli, and tapping to fractal auditory stimuli. Using Detrended Fluctuation Analysis (DFA) to estimate Hurst exponents, H, and Diffusion Entropy Analysis (DEA) to estimate scaling exponents, d, in each condition, we found that self-paced tapping exhibited persistent or super-diffusive inter-tap intervals (H=0.63±0.145, d=0.64±0.097), while tapping to metronomic stimuli showed a trend toward random noise (H=0.55±0.101, d=0.58±0.126). Complexity matching, that is, systematic adjustment of intertap intervals to match persistence levels of fractal stimuli, was observed between the Hurst exponents of auditory stimuli (H=0.25 to H=1.5) and complexity measures of tapping (H=0.54 to H=0.81; d=0.51 to d=0.72). A Gaussian linear mixed model confirmed significant associations between the Hurst exponents of auditory stimuli and H of the corresponding intertap interval time series. In contrast, the associations between the Hurst exponents of auditory stimuli and d of the corresponding intertap interval time series were mixed. To understand these empirical observations, we utilized the neural hopping model to represent the intrinsic mechanism underlying self-paced tapping and incorporated the Van der Pol oscillator to account for auditory stimuli as a driving force. Metronomic stimuli were modeled as harmonic forcing, resulting in simulated tapping with H=0.50±0.175 or d=0.53±0.115. Complexity matching to fractal stimuli was achieved through phase resetting. We evaluated four coupling variants of phase-resetting, i.e., with or without continuous harmonic drive and including or excluding reset jitter. We performed precision-weighted root-mean-square error (WRMSE) model selection across six fractal conditions with a two-stage bootstrap. The Drive+Jitter variant best reproduced the empirical scaling for both H (pointwise WRMSE = 0.05; win probability = 0.79) and d (pointwise WRMSE = 0.09; win probability = 0.70). The Drive+Jitter phase resetting model simulated tapping persistence values ranging from H=0.57 to H=0.78 or d=0.44 to d=0.85, closely aligning with the experimental data. These results indicate that fractal auditory stimuli can elicit fractal motor outputs comparable to those in healthy states, suggesting potential therapeutic benefits for motor recovery and rehabilitation. The modeling approach provides a framework for understanding the mechanisms underlying auditory-motor synchronization across different tapping conditions.