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I fractured my collar bone two weeks ago. What’s more sensitive in detecting bone healing: cat scan or xray.

Of the two tests you listed, X-rays would be the test of choice for evaluating a healing fracture. However, the most sensitive study would be an MRI because of its superior contrast between soft tissue densities and bone.
After a fracture, your body forms a callous consisting of fibrous tissue across the fractured bone. Bone is then deposited within this callous and over time, the callous is resorbed.
X-rays traditionally lag 1-2 weeks behind histological evidence of bone healing when evaluating a fracture. But because the extra information gained from an MRI would not necessarily change management, x-rays remain the imaging modality of choice for evaluating fracture healing.