Time-resolved quantification of the dynamic extracellular space in the brain during short-lived event: methodology and simulations

Two macroscopic parameters describe the interstitial diffusion of substances in the extracellular space (ECS) of the brain, the ECS volume fraction alpha and the diffusion tortuosity lambda. Past methods based on sampling the extracellular concentration of a membrane-impermeable ion tracer, such as tetramethylammonium (TMA(+)), can characterize either the dynamic alpha(t) alone or the constant alpha and lambda in resting state but never the dynamic alpha(t) and lambda(t) simultaneously in short- lived brain events. In this work, we propose to use a sinusoidal method of TMA(+) to provide time-resolved quantification of alpha(t) and lambda(t) in acute brain events. This method iontophoretically injects TMA(+) in the brain ECS by a sinusoidal time pattern, samples the resulting TMA(+) diffusion waveform at a distance, and analyzes the transient modulations of the amplitude and phase lag of the sampled TMA(+) waveform to infer alpha(t) and lambda(t). Applicability of the sinusoidal method was verified through computer simulations of the sinusoidal TMA(+) diffusion waveform in cortical spreading depression. Parameter sensitivity analysis identified the sinusoidal frequency and the interelectrode distance as two key operating parameters. Compared with other TMA(+)-based methods, the sinusoidal method can more accurately capture the dynamic alpha(t) and lambda(t) in acute brain events and is equally applicable to other pathological episodes such as epilepsy, transient ischemic attack, and brain injury. Future improvement of the method should focus on high-fidelity extraction of the waveform amplitude and phase angle. NEW & NOTEWORTHY An iontophoretic sinusoidal method of tetramethylammonium is described to capture the dynamic brain extracellular space volume fraction alpha and diffusion tortuosity lambda. The sinusoidal frequency and interelectrode distance are two key operating parameters affecting the method's accuracy in capturing alpha(t) and lambda(t). High-fidelity extraction of the waveform amplitude and phase lag is critical to successful sinusoidal analyses.