Table 2.

Terminology and parameter values for glucose extraction model.

Symbol	Name, definition	Scale*: single capillary level/network level	Value	Unit
CA	Arterial glucose concentration in plasma	Network		μmol/100 mL_plasma
CA′	Arterial glucose tracer concentration in plasma	Network	<0.5	μmol/100 mL_plasma
CMRglc	Glucose metabolism	Network		μmol/100 mL_brain/min
Cp	Glucose concentration in plasma	Single capillary	Varies along the capillary axis	μmol/100 mL_plasma
Cp′	Glucose tracer concentration in plasma	Single capillary	Varies along the capillary axis	μmol/100 mL_plasma
Ct	Glucose concentration in extravascular tissue	Single capillary		μmol/100 mL_brain
${\overline{\text{C}}}_{\text{t}}^{\text{t}}$	Glucose concentration in extravascular tissue. Target value (input)	Network		μmol/100 mL_brain
${\overline{\text{C}}}_{\text{t}}$	Glucose concentration in extravascular tissue	Network	${\overline{\text{C}}}_{\text{t}}$ = ${\overline{\text{C}}}_{\text{t}}^{\text{t}}$	μmol/100 mL_brain
CTH	Capillary transit time heterogeneity	Network		Second
GEF	Glucose extraction fraction	Network
h	Capillary transit time distribution	Network		1/s
$\tilde{\text{h}}$	Capillary transit time distribution	Network		1/s
KM	Michaelis-Menten parameter for glucose metabolism	Network	5	μmol/100 mL_brain
KM'	Michaelis-Menten parameter for glucose tracer phosphorylation	Network	5	μmol/100 mL_brain
KT	Michaelis-Menten parameter for glucose transport across the capillary membrane	Network	Parameter set SH: 50 Parameter set SR:150	μmol/100 mL_brain
KT'	Michaelis-Menten parameter for glucose tracer transport across the capillary membrane	Network	KT' = KT	μmol/100 mL_brain
LC	Lumped constant (GEF/GEF' in steady state)	Network		No unit
M	Glucose metabolism	Single capillary		μmol/100 mL_brain/min
M'	Glucose tracer metabolism phosphorylation rate	Single capillary		μmol/100 mL_brain/min
MTT	Mean transit time	Network		Second
Q	Glucose extraction fraction	Single capillary		No unit
Q'	Glucose tracer extraction fraction	Single capillary		No unit
Vcap	Cerebral capillary volume	Network	1.4	mL/100 mL_brain
Vd	Physical distribution space of glucose in the brain	Network	0.77	mL_accessible_extra-vascular_tissue/mL_brain
Vd'	Physical distribution space of glucose tracer in the brain	Network	0.77	mL_accessible_extra-vascular_tissue/mL_brain
vmax_m	Effective maximum rate at which glucose is phosphorylated by hexokinase	Network	30 in the resting state with parameter set SH	μmol/100 mL_brain/min
vmax_m'	Effective maximum rate at which glucose tracer is phosphorylated by hexokinase	Network	0.3·vmax_m	μmol/100 mL_brain/min
vmax_t	Maximum rate at which glucose is transported across the capillary membrane	Network	Parameter set SH: 68 Parameter set SR: 136	μmol/100 mL_brain/min
vmax_t'	Maximum rate at which glucose tracer is transported across the capillary membrane	Network	1.4·vmax_t	μmol/100 mL_brain/min
τ	Transit time	Single capillary		Second

^*Network level refers to parameters with same value for each capillary of the network, or to quantities than can only be defined at this level. Single capillary level refers to parameters which can take different values between capillaries.