# Easy PVC tutorial

PVEc is a method to extrapolate to what CBF would be in a voxel with pGM=100%. You can do this on multiple ways. Let's reverse engineer with a situation of 2 voxels (ignore CSF).

Within the ROI, the assumption is GM CBF = 60, WM CBF = 20, CSF CBF = 0.

The ROI contains of two voxels:

VOXEL 1

pGM = 70%

pWM = 30%

CBF = …(a) mL/100g/min

VOXEL 2

pGM = 100%

pWM = 0%

CBF = …(b) mL/100g/min

The GM CBF = 60, the WM CBF = 20. What are the CBF in the above voxels?

What do you get when you use the "conventional" solution, or when you use simple PVEc or full PVEc?

The "conventional" solution (PVEc=0 in xASL) is actually the simpliest way of PVEc, which is to only include ASL voxels above a threshold (e.g. pGM>=70%), and take the mean within this ROI. So in the above example, both voxels are included in the ROI What CBF would this give in this case?

.....(c)

Simple PVEc (PVEc=1 in xASL) would be to do a linear regression with pGM and CBF only, what would this give you, for the above ROI? Note that you can also view this as a PVEc while assuming the WM CBF to be 0.

.....(d)

Full PVEc (PVEc=2 in xASL) would be to do the linear regression with all compartments, what would this give you in the above ROI?

.....(e)

So in the ideal world, the conventional solution would give you a .....(f)-estimation of the actual GM CBF, PVEc=1 gives you an .....(g)-estimation of the actual GM CBF (because you underestimate the WM compartment), and PVEc=2 gives you a .....(h)-estimation of the actual GM CBF.

ANSWERS

a) 48 mL/100g/min

b) 60 mL/100g/min

c) (48 + 60 )/2 = 54 mL/100g/min

d) (48/0.7 + 60)/2 = 64.3 mL/100g/min

e)

voxel 1-> 60 = 100% * CBFgm + 0% * CBFwm

voxel 2 -> 48 = 70% * CBFgm + 30% * CBFwm

a matrix inversion would solve this. But if we solve it ourselves (considering super-SNR, that we don’t have in reality), we know from first voxel that CBFgm=60.

voxel 1-> 60 = 100% * CBFgm + 0% * CBFwm

voxel 2 -> 48 = 70% * CBFgm + 30% * CBFwm -> 48 = 70% * 60 + 30% * CBFwm -> 48-42 = 0.3*CBFwm -> CBFwm = 6/0.3 = 20 mL/100g/min

f) Severe under-

g) Small over-

h) correct