Table 1.

Different variables used in the model

Symbol	Name, definition	Value	Unit
${\mathrm{\alpha }}_{\mathrm{v}}$	Parameter used to describe venous compartment compliance	0.44 (CTH model) 0.60 (Buxton model)	no unit
αH	Henry constant	$3.1·{10}^{-3}$	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}/\text{mmHg}$
B	Maximum amount of oxygen that can be bound to hemoglobin	19.43	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}$
C A	Arterial oxygen concentration in blood	18.59 (up to 20.60 in Figure 7)	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}$
C B	Concentration of oxygen bound to hemoglobin	Given by Equation (1)	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}$
$C_{\text{end}}$	Oxygen concentration at the capillary end (single capillary)	$C_{\text{end}}=C_{\mathrm{A}}·\left(1-Q\right)$	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}$
C V	Venous oxygen concentration in blood	$C_{\mathrm{V}}={\overline{C}}_{\text{end}}$	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}$
C	Oxygen concentration in the blood		$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}$
$\overline{C}$	Mean oxygen concentration in the blood over the capillary length		$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}$
C p	Oxygen concentration in plasma	${\mathrm{\alpha }}_{\mathrm{H}}·P_{\mathrm{p}}$	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{blood}}$
$\text{CBV}$	Capillary blood volume	1.4	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{brain}}$
k	Rate constant for oxygen	88	1/s
$K_{\mathrm{M}}$	Michaelis–Menten parameter for oxygen metabolism	5	$\text{mmHg}$
n	Hill constant	2.8	no unit
P p	Oxygen partial pressure in plasma	$\text{Hillsinv}\left(C\right)$	$\text{mmHg}$
P t	Oxygen partial pressure in the extravascular compartment (single capillary)		$\text{mmHg}$
$\overline{P_{\mathrm{t}}}$	Mean oxygen concentration (pressure) in the extravascular compartment over the capillary network		$\text{mmHg}$
P V	Oxygen partial pressure in plasma in the venous compartment	$P_{\mathrm{V}}=\text{Hillsinv}\left(C_{\mathrm{V}}\right)$	$\text{mmHg}$
P 50	Oxygen partial pressure at which oxygen saturation is equal to 0.5	26	$\text{mmHg}$
Q	Single capillary extraction fraction		No unit
q	deoxyhemoglobin content in a voxel normalized to its baseline value		No unit
$\Delta s/s_0\hspace{0.17em}$	BOLD signal amplitude		No unit
S	Oxygen saturation		No unit
${\mathrm{\tau }}_{\text{lag}}$	Parameter used to describe venous compartment compliance	13 (CTH model) 14.5 (Buxton model)	s
${\mathrm{\tau }}_0$	Mean transit time in the venous compartment assumed at baseline	3	s
v	Volume of the venous compartment, normalized to baseline value.		No unit
$v_{\max }$	Maximum rate at which oxygen is metabolized	4.18	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{brain}}/\text{min}$
$V_{\mathrm{v}}$	Relative volume of the venous compartment		No unit
$V_{\mathrm{v},0}$	Volume of the venous compartment during baseline	3	$\text{mL}/100\hspace{0.17em}\hspace{0.17em}{\text{mL}}_{\text{brain}}$