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Oxygen delivery from the cerebral microvasculature to tissue is governed by a single time constant of approximately 6 seconds
Author(s) -
Payne Stephen John,
Lucas Claire
Publication year - 2018
Publication title -
microcirculation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.793
H-Index - 83
eISSN - 1549-8719
pISSN - 1073-9688
DOI - 10.1111/micc.12428
Subject(s) - cerebral blood flow , time constant , oxygenation , blood flow , constant (computer programming) , biological system , exponential decay , flow (mathematics) , oxygen , chemistry , exponential function , biomedical engineering , mechanics , mathematics , physics , computer science , mathematical analysis , cardiology , anesthesia , biology , medicine , electrical engineering , organic chemistry , nuclear physics , engineering , programming language
Objective The cerebral microvasculature plays a key role in the coupling between cerebral blood flow and metabolism. Although experimental imaging techniques now allow for finely detailed measurements of flow and oxygenation, within humans measurements remain confined to a voxel‐level scale, of order 1 mm. Mathematical models are thus key in interpreting such data. However, these can be highly complicated, due to the large number of vessels and the nonlinearities in the governing equations. Methods We thus propose here a new model of the cerebral microvasculature and show how its behavior can be simplified based on the order of magnitude arguments. Results The resulting model shows a dependence upon just two time constants, termed “slow” and “metabolic” time constants; the tissue oxygenation response can be characterized by convolution of the difference between the fractional flow and metabolic responses with a single exponential, with time constant equal to half the ratio of tissue volume to blood flow multiplied by the ratio of effective oxygen solubility in tissue and blood. Conclusions The overall response time for the whole network is approximately 6 seconds; this value indicates that the flow response to increases in metabolic activity cannot be driven solely by changes in tissue oxygenation.