AUTHOR=Ghaffari Hamed , Grant Samuel C. , Petzold Linda R. , Harrington Michael G. 

TITLE=Regulation of CSF and Brain Tissue Sodium Levels by the Blood-CSF and Blood-Brain Barriers During Migraine

JOURNAL=Frontiers in Computational Neuroscience

VOLUME=14

YEAR=2020

URL=https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2020.00004

DOI=10.3389/fncom.2020.00004

ISSN=1662-5188

ABSTRACT=<p>Cerebrospinal fluid (CSF) and brain tissue sodium levels increase during migraine. However, little is known regarding the underlying mechanisms of sodium homeostasis disturbance in the brain during the onset and propagation of migraine. Exploring the cause of sodium dysregulation in the brain is important, since correction of the altered sodium homeostasis could potentially treat migraine. Under the hypothesis that disturbances in sodium transport mechanisms at the blood-CSF barrier (BCSFB) and/or the blood-brain barrier (BBB) are the underlying cause of the elevated CSF and brain tissue sodium levels during migraines, we developed a mechanistic, differential equation model of a rat's brain to compare the significance of the BCSFB and the BBB in controlling CSF and brain tissue sodium levels. The model includes the ventricular system, subarachnoid space, brain tissue and blood. Sodium transport from blood to CSF across the BCSFB, and from blood to brain tissue across the BBB were modeled by influx permeability coefficients <italic>P</italic><sub><italic>BCSFB</italic></sub> and <italic>P</italic><sub><italic>BBB</italic></sub>, respectively, while sodium movement from CSF into blood across the BCSFB, and from brain tissue to blood across the BBB were modeled by efflux permeability coefficients <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>C</mml:mi><mml:mi>S</mml:mi><mml:mi>F</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msubsup></mml:math></inline-formula> and <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>B</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msubsup></mml:math></inline-formula>, respectively. We then performed a global sensitivity analysis to investigate the sensitivity of the ventricular CSF, subarachnoid CSF and brain tissue sodium concentrations to pathophysiological variations in <italic>P</italic><sub><italic>BCSFB</italic></sub>, <italic>P</italic><sub><italic>BBB</italic></sub>, <inline-formula><mml:math id="M3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>C</mml:mi><mml:mi>S</mml:mi><mml:mi>F</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msubsup></mml:math></inline-formula> and <inline-formula><mml:math id="M4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>B</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msubsup></mml:math></inline-formula>. Our results show that the ventricular CSF sodium concentration is highly influenced by perturbations of <italic>P</italic><sub><italic>BCSFB</italic></sub>, and to a much lesser extent by perturbations of <inline-formula><mml:math id="M5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>C</mml:mi><mml:mi>S</mml:mi><mml:mi>F</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msubsup></mml:math></inline-formula>. Brain tissue and subarachnoid CSF sodium concentrations are more sensitive to pathophysiological variations of <italic>P</italic><sub><italic>BBB</italic></sub> and <inline-formula><mml:math id="M6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>B</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msubsup></mml:math></inline-formula> than variations of <italic>P</italic><sub><italic>BCSFB</italic></sub> and <inline-formula><mml:math id="M7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>C</mml:mi><mml:mi>S</mml:mi><mml:mi>F</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msubsup></mml:math></inline-formula> within 30 min of the onset of the perturbations. However, <italic>P</italic><sub><italic>BCSFB</italic></sub> is the most sensitive model parameter, followed by <italic>P</italic><sub><italic>BBB</italic></sub> and <inline-formula><mml:math id="M8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi><mml:mi>B</mml:mi><mml:mi>B</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msubsup></mml:math></inline-formula>, in controlling brain tissue and subarachnoid CSF sodium levels within 3 h of the perturbation onset.</p>