Interesting case Linh,
If the trickle flow was a low resistance waveform it might well be that the ICA is still patent and this is important as a surgical endarterectomy can still be considered.
If the flow is high resistance (the thump before the stump) then it is likely occluded,
Certainly look was distal as you can to try and prove flow,
Use SMI or whatever best low flow technology you have on your machine,
Use a low PRF, its of gain and try a few transducers to prove flow,
If you can not prove flow it is worth doing a CTA study as if there is a trickle it does change management considerably.
Can you upload the pulse Doppler waveform? and other images if you have them.
The CCA waveform is likely externalised as well.
I will have to record my carotid lecture for the website so you can enjoy it.
Steve