Hi Syed

The following links may help you

Low Back Pain -Part 2- Getting Down To The “CORE”

http://orthowellpt.com/low-back-pain-part-2-getting-down-to-the-core/

They stated that ' there is not a research-proven, valid testing regimen for core stability.  However, Shirley Sahrmann has proposed a test called the Sahrmann Core Stability Test which is the most common test of function.  It involves the use of a pressure cuff placed under the lumbar spine to measure one’s ability to maintain pelvic neutral while performing five exercises of progressive difficulty. '

Lumbar Examination

http://www.physio-pedia.com/Lumbar_Examination

However, there are many problematic issues regarding the concept of core muscle!

Please check the following link which is an interview with Prof  Peter O'Sullivan talking about core stability

https://www.youtube.com/watch?v=YezBG_NdLgs

Also, please check the following links which are critical reports about core stability 

The Core Stability Myth

http://www.huffingtonpost.co.uk/adrian-farrell/the-core-stability-myth_b_8696220.html

Brace yourself

http://www.bodyinmind.org/evidence-for-bracing-in-lbp/

Good Luck!

I would look at the textbook by Dr. Stuart McGill "Low back disorders: Evidenced-based prevention and rehabilitation" (3rd ed).  Dr. McGill, in my opinion, is likely one of the most prolific scholars in the study of low back disorders from a biomechanical perspective.  I agree that core is a term that has an unclear definition but certainly has some traction in the popular press.

Hi Syed

Are you looking for a clinical measure or diagnostic measure.

I hope this link can help you

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4739044/

The use of the ultrasound imaging (USI) is very interesting and not invasive. The use of ultrasound to assess muscle morphology.

(For example I sent you  article about use of US

https://www.researchgate.net/publication/317012748_The_Use_of_Ultrasound_Images_in_Manual_Therapy_and_Additionally_in_Assessment_of_Shoulder_Impingement_Syndrome

http://file.scirp.org/pdf/OJTR_2017051914544533.pdf

Article The Use of Ultrasound Images in Manual Therapy and Additiona...

 An another my article:   " The use of RUSI in the clinical practice is recommended for understand the relationships between

motor control and muscular functionality, to enhance the performance by increasing

the feedback and to document the benefits of a specific therapeutic approach

[17]. It includes a program of core strengthening/stabilization [18]. It is

expected that core exercises will attempt to allow the patient to control pelvic

position and motion to minimize symptoms while standing and walking"

https://www.researchgate.net/publication/313741191_Lumbar_Stenosis_of_the_Aging_Spine_Evaluation_and_Treatment_According_to_the_Evidence_Based_Medicine_for_the_Improvement_of_the_Quality_of_Life

Article Lumbar Stenosis of the Aging Spine: Evaluation and Treatment...

Thank you very much for such comprehensive and detailed answer.

Dear Dr. Rehman,

You might be interested with the following article as well:

Article Developing a Reliable Core Stability Assessment Battery for ...

Best regards and success in your study.

Dear dr.syed .I am also with giovana about RUSI technique. To make it precise and simple you follow the isolated muscle contraction by this technique. i had my own research done on this which is about transverse abdominus muscle contraction after giving a specialized physiotherapy exercise for abdomen.the paper is under peer review. the other techniques also mentioned above has good reliabilty and validity. hope it helps

The best way in my opinion is

Stuart mcgill core endurance test battery

It's evidence based, and invented by the pioneer if our age in core stability

Dear Samuel Georgr .

Thank you for your answer.