Simulations of Electroenzymatic Glutamate Sensors in the Brain Reveal the Value of Finite Element Methods for Understanding Neurochemical Transmission

Modeling neurochemical signaling in the brain with transport and reaction equations is a much-needed application of chemical engineering fundamentals to the field of neuroscience that can clarify how neuronal activity affects local chemical concentrations in the brain extracellular space. With COMSOL Multiphysics or other numerical solvers, neurochemical systems can be modeled in great detail, allowing simulations to be tailored to address specific questions that arise in studying the chemical processes of the brain and in analyzing the data collected by chemical sensors. Great efforts have been made to develop electroenzymatic sensors, which have been used for many years to monitor the release of neurotransmitters that accompanies neuronal transmission, although the analysis of collected data has been troubled by the difference between sensor response times (>0.08 s) and the timescales of neurochemical signaling (on the order of milliseconds). This difference in characteristic times leads to unquantified distortions and reductions in the temporal integrity and magnitude of sensor response. Additionally, differences in the transport properties of the brain relative to the in vitro environment in which sensors are calibrated further complicates the analysis of sensor response, particularly since released neurotransmitters must diffuse various distances to the sensor before they are detected. Detailed mathematical modeling provides a unique perspective for analyzing collected data by showing how sensors respond to known sets of conditions in ways that cannot be done physically with existing experimental techniques.

Simulations show that electroenzymatic glutamate sensor performance in vivo is complicated by both mass transfer resistances and clearance rates of glutamate (Glut) and H₂O₂ in the brain extracellular space, which is significantly different from the in vitro conditions where sensors are tested and calibrated. Through the use of 1-D model simulations, it is shown that sensor response in vivo has a much greater dependence on H₂O₂ mass transfer and clearance in the surrounding tissue than previously thought, potentially leading to sensor measurements more than double the expected value (based on prior sensor calibration in vitro) for glutamate release events close to the sensor surface. Sensor response in general is greatly affected by the distance between the sensor and location of glutamate release, with simulations showing that detection of glutamate released through neuronal signaling is limited to events within 30 µm of the sensor surface. Further simulations of more realistic neurotransmitter releases in 3 dimensions showed that excitation of thousands of synapses over the course of ~0.5 s is likely required for Glut detection; the magnitude of release required for detection suggests that even miniaturized sensors monitor the chemical activity of many neurons. Further modeling of chemical signaling processes in the brain with transport equations will be instrumental in the analysis of data collected by neurochemical sensors and in identifying the rates of fundamental neurochemical processes in various states of health, activity, and disease.