. Author manuscript; available in PMC: 2014 Nov 1.

Published in final edited form as: Semin Pediatr Surg. 2013 Oct 14;22(4):10.1053/j.sempedsurg.2013.10.003. doi: 10.1053/j.sempedsurg.2013.10.003

Table 1.

Equations describing the pathway for blood and oxygen in the brain

Equations

[1] CMRO₂ = (CBF • CaO₂) – (CBF • CvO₂) – CiO₂

[2] Q = ΔP ÷ R

[3] Q = (π • r⁴ • ΔP) ÷ (8 η • L)

[4] Q = CBV ÷ t`

[5] CBV = 1.09 • CBF^0.29

[6] OEF = (SaO₂ – SjvO₂) ÷ SaO₂

[7] OEF = CMRO₂ ÷ (CBF × 1.34 × [Hb] × SaO₂)

Key:

CaO₂ is the oxygen content of arterial blood

CBF is the cerebral blood flow

CBV is the cerebral blood volume

CiO₂ is the oxygen content of brain tissue

CMRO₂ is the cerebral metabolic rate for oxygen

CvO₂ is the oxygen content of venous blood

[Hb] is the hemoglobin concentration

η is blood viscosity

L is vessel length

OEF is oxygen extraction fraction of brain

ΔP is the pressure gradient between inflow and outflow

Q is flow

R is resistance to flow

r is vessel radius

SaO₂ is oxyhemoglobin saturation of arterial blood

SjvO₂ is oxyhemoglobin saturation of jugular venous blood

t` is mean transit time of blood