Multifractal Cascade Modeling Reveals Fundamental Limits of Current Neuroimaging Strategies

Neuroimaging assumes spatial and temporal uniformity, yet brain activity exhibits a multifractal cascade structure with intermittent bursts and long-range dependencies. We use controlled simulations to test how well standard sampling strategies (random, grid-based, hierarchical; N = 10-2000 sensors) recover statistical properties-mean, variability, burstiness, and fractal dimension-from synthetic multifractal brain fields. Estimation errors deviate substantially from the classical N-1/2 scaling expected under independent sampling. For higher-order statistics like burstiness, error reduction is remarkably flat in log-log space: orders-of-magnitude increases in sensor density yield virtually no improvement. Grid sampling performs best for fractal dimension at high densities; hierarchical sampling is more stable for burstiness. These results indicate that current neuroimaging fundamentally underestimates brain complexity and variability, with major implications for interpreting both healthy and pathological brain function.