To solve this problem, we need to determine the underlying cause of the perioral numbness experienced by the patient after a thyroidectomy. This is a classic presentation of hypocalcemia, which is a potential complication following thyroidectomy due to inadvertent damage or removal of the parathyroid glands. The main hormone involved in calcium regulation is Parathyroid Hormone (PTH). A drop in calcium levels post-surgery can lead to symptoms such as perioral numbness.
- Understanding the Symptoms: The perioral numbness suggests a decrease in calcium levels causing neuromuscular irritability, a condition known as tetany. It is commonly associated with hypoparathyroidism, where PTH levels are low.
- Identifying the Correct Investigation:
- Free T3, T4: These are thyroid hormones, checking them won't help in diagnosing hypocalcemia.
- RAI Scan (Radioactive iodine scan): This is used for thyroid tissue imaging, not relevant here.
- Calcium, Phosphate, and PTH levels: Since the symptoms indicate hypocalcemia, measuring these levels is essential. They would confirm the decrease in calcium and any associated changes in PTH and phosphate levels.
- T3, T4, TSH: These are tests to evaluate thyroid status but not helpful for post-thyroidectomy hypocalcemia investigation.
- Conclusion: The correct and most relevant investigation to perform in this situation is to measure Calcium, Phosphate, and PTH levels. This will confirm the diagnosis of hypocalcemia potentially related to changes in parathyroid function post-surgery.
Hence, the correct answer is Calcium, Phosphate, and PTH levels.