# 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