Step 1: Know what neuroendocrine tumors are.
Neuroendocrine tumors (NETs) are growths that come from cells of the diffuse neuroendocrine system, seen in the gut, pancreas, lungs, and other sites. Common examples are carcinoid tumors and pancreatic NETs.
Step 2: Recall the key feature these tumors share.
Most neuroendocrine tumor cells carry a large number of somatostatin receptors on their surface. This receptor is the target used for imaging.
Step 3: Match the receptor to the test.
A radionuclide study called somatostatin receptor scintigraphy (the octreotide scan, done with indium-111 labeled octreotide) binds to these receptors and lights up the tumor and any spread on a whole-body scan. This makes it the investigation of choice for finding the primary tumor and looking for metastases in one sitting.
Step 4: Rule out the other options.
Endoscopic ultrasound is useful for small pancreatic lesions but cannot survey the whole body for spread. SPECT is only a type of image acquisition, not a receptor-specific test by itself. MRI shows anatomy well but does not pick out neuroendocrine tissue the way a receptor-based scan does.
Step 5: Note the modern update.
Today Ga-68 DOTATATE PET/CT, a newer form of the same receptor-based radionuclide imaging, has mostly replaced the older octreotide scan because it is more sensitive. This does not change the answer here, since both fall under the same principle of a radionuclide study.
Final Answer:
The investigation of choice for neuroendocrine tumors is
\[ \boxed{\text{Radionuclide study (somatostatin receptor scintigraphy)}} \]