Functional Inertia Index of Memory-Retaining Brain Dynamics: A Measure of Large-Scale Brain Adaptability.

Adaptive cognition relies on brain activity that is both flexible and resilient to noise, a property we term functional inertia. Conventional dynamic fMRI metrics treat networks as memoryless and cannot capture the persistence that makes some states fleeting and others entrenched. We introduce the functional inertia index (FII), the first index to quantify temporal momentum by measuring the force required to deviate from a brain's long-running trajectory. Applied to resting-state fMRI from a multisite schizophrenia cohort, FII revealed distinct recurrent states, with prolonged residence in a high-inertia plateau predicting greater symptom severity. This effect was mediated by whole-brain FII, which also showed a positive relationship with cognition in patients but a negative relationship in controls, revealing a dissociation between adaptive and maladaptive rigidity. At the regional level, FII unifies two long-standing observations in schizophrenia: excessive rigidity in associative hubs and pathological volatility in sensory pathways, situating both within a single inertial framework and offering a candidate dynamic biomarker.