Dear Sir,
As correctly mentioned, the cause of muscle atrophy in isolation, could be neurological. However there is a cyst called spinoglenoid notch cyst, which if present can compress a nerve called the suprascapular nerve and cause muscle atrophy. This might need surgery. Rotator cuff tears if present are best treated surgically followed by good physiotherapy.
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Health Tips
Do not rely on MRI reports. A call on your treatment should be taken only after a detailed clinical examination by a shoulder specialist. After all, the doctor treats you and not the MRI report.
Kindly visit this website. There are some short videos which will help you understand your shoulder better.
Best regards