The probem is diagnosis. Sciatic pain is very, very rare but anytime evocated by physiscians, PT and patients. In 99% of cases the pains are muscular and not a compression of sciatic roots. 

From a very long experience of back pains as the founder in Algeria and after in France of Back School. Claude Hamonet MPR

I agree that diagnosis is challenging and also that muscles often refer to the lower limb. I disagree that 99% are muscular in origin...do you have a source for that figure? There are well-recognised criteria for the diagnosis of radicular pain (see IASP and Bogduk et al.). Radicular and somatic pain may also co-exist. 

This publication utilized time of flight magnetic resonance angiography and found an association between low back pain and sciatic pain with lumbar artery stenosis: Article Association of Lumbar Arterial Stenosis with Low Back Sympto...

This study utilized thermography to examine skin temperature in those with lumbar disc herniation:

Article Altered Lower Limb Vascular Perfusion in Patients With Sciat...

There are other similar studies on this topic:

https://europepmc.org/article/med/7316446

https://europepmc.org/article/med/8274812

https://journals.lww.com/spinejournal/fulltext/1996/07150/altered_lower_limb_vascular_perfusion_in_patients.9.aspx?casa_token=GER1sypi0ssAAAAA:VkQCBKOSCIxLf592qzSJdUwe8h1Df72nmIyc0N55YwLpgjXas7WJlFdtpAc-8XQYevIVYXNcuYDtOIn2Vmh7RGXW

https://thejns.org/view/journals/j-neurosurg/69/4/article-p556.xml

https://journals.lww.com/spinejournal/Fulltext/1997/07150/Disc_Degeneration_Back_Pain_and_Calcification_of.23.aspx?casa_token=tHeTd79iepYAAAAA:nVJgWfrd5w4LI8ppd_zz4ZHEjxY4na7Y7XTjqMrDuqh5x2GkvyFLtRHj1aeQASx_5kSrIhoZRIZcnqU3gh1iT8Mh

Hope this is helpful,

Thanks