Table 2.

Steady state expressions¹,² for MRI signal (S) in iVASO and VASO³ experiments.

Signal Origin	TI < Δ	Δ ≤ TI ≤ Δ + δa	Δ + δa ≤ TI ≤ Δ + δa + δc
BLOOD
iVASO
a, nulled4	0	$\left(\frac{\mathit{TI}-\mathrm{\Delta }}{{\delta }_a}\right){\mathit{CBV}}_a{C}_b{M}_0\left(\frac{1-2e^{-\mathit{TI}∕T_{1b}}+e^{-\mathit{TR}∕T_{1b}}}{1+e^{-\mathit{TR}∕T_{1b}}}\right)$	${\mathit{CBV}}_a{C}_b{M}_0\left(\frac{1-2e^{-\mathit{TI}∕T_{1b}}+e^{-\mathit{TR}∕T_{1b}}}{1+e^{-\mathit{TR}∕T_{1b}}}\right)$
a, residual5	CBVaCbM0(1 − e−TR/T1b)	$\left(\frac{{\delta }_a-(\mathit{TI}-\mathrm{\Delta })}{{\delta }_a}\right){\mathit{CBV}}_a{C}_b{M}_0\left(1+e^{-\mathit{TR}∕T_{1b}}\right)$	0
c, nulled4	0		$\left(\frac{\mathit{TI}-\mathrm{\Delta }-{\delta }_a}{{\delta }_c}\right){\mathit{CBV}}_c{C}_b{M}_0\left(\frac{1-2e^{-\mathit{TI}∕T_{1b}}+e^{-\mathit{TR}∕T_{1b}}}{1+e^{-\mathit{TR}∕T_{1b}}}\right)$
c, residual5	CBVcCbM0(1 − e−TR/T1b)		$\left(\frac{{\delta }_c-(\mathit{TI}-\mathrm{\Delta }-{\delta }_a)}{{\delta }_c}\right){\mathit{CBV}}_c{C}_b{M}_0\left(1+e^{-\mathit{TR}∕T_{1b}}\right)$
v, residual5	CBVvCbM0(1 − e−TR/T1b)
VASO nulled4	CBV * CbM0(1 − 2e−TI/T1b + e−TR/T1b)
Tissue
iVASO5	(Ctis − CBV * Cb)M0(1 − e−TR/T1tis)
VASO6	(Ctis − CBV * Cb)M0(1 − 2e−TI/T1tis + e−TR/T1tis)
CSF
iVASO	CCSFM0(1 − e−TR/T1CSF)
VASO	CCSFM0(1 − 2e−TI/T1CSF + e−TR/T1CSF)

a: arteriolar; c: capillary; v: venular; b: blood; tis: tissue (GM or WM), which is defined as parenchyma without blood contribution. C_i is the water density in ml water/ml compartment volume, summarized in Table 3. CBV = CBV_a + CBV_c + CBV_v.

¹All terms need to be multiplied by their compartmental T₂ contribution (e^−TE/T_2i, in which i = b, tis, CSF).

²A single longitudinal relaxation time, T_1b, is used for all blood compartments.

³In VASO experiments, negligible exchange between blood and tissue is assumed.

⁴Parenchymal signal reduction due to blood nulling.

⁵Terms contributing to parenchymal MRI signal in iVASO.

⁶Parenchymal MRI signal in VASO.