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Abstract: There have been suggestions that heat caused by cerebral metabolic activitymay constrain mammalian brain evolution, architecture, and function. Thisarticle investigates physical limits on brain wiring and corresponding changesin brain temperature that are imposed by thermodynamics of heat balancedetermined mainly by Na$^{+}$-K$^{+}$-ATPase, cerebral blood flow, and heatconduction. It is found that even moderate firing rates cause significantintracellular Na$^{+}$ build-up, and the ATP consumption rate associated withpumping out these ions grows nonlinearly with frequency. Surprisingly, thepower dissipated by the Na$^{+}$-K$^{+}$ pump depends biphasically onfrequency, which can lead to the biphasic dependence of brain temperature onfrequency as well. Both the total power of sodium pumps and brain temperaturediverge for very small fiber diameters, indicating that too thin fibers are notbeneficial for thermal balance. For very small brains blood flow is not asufficient cooling mechanism deep in the brain. The theoretical lower bound onfiber diameter above which brain temperature is in the operational regime isstrongly frequency dependent but finite due to synaptic depression. For normalneurophysiological conditions this bound is at least an order of magnitudesmaller than average values of empirical fiber diameters, suggesting thatneuroanatomy of the mammalian brains operates in the thermodynamically saferegime. Analytical formulas presented can be used to estimate average firingrates in mammals, and relate their changes to changes in brain temperature,which can have important practical applications. In general, activity in largerbrains is found to be slower than in smaller brains.



Autor: Jan Karbowski

Fuente: https://arxiv.org/



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