**Core Concept**
Heparin is a commonly used anticoagulant in clinical practice, particularly in patients with atrial fibrillation, deep vein thrombosis, and pulmonary embolism. It works by activating antithrombin III, which inhibits the coagulation cascade, specifically the conversion of prothrombin to thrombin.

**Why the Correct Answer is Right**
The complication of heparin is due to its potential to cause heparin-induced thrombocytopenia (HIT). This occurs when heparin binds to platelet factor 4 (PF4), forming a complex that activates platelets, leading to platelet activation, aggregation, and ultimately, thrombocytopenia. The thrombocytopenia is often accompanied by a paradoxical increase in thrombin formation, resulting in arterial or venous thrombosis.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it is not a recognized complication of heparin. While heparin can cause bleeding, it is not a direct result of heparin therapy.
* **Option B:** This option is incorrect because it is not a known side effect of heparin. Osteoporosis is a potential side effect of long-term warfarin therapy, not heparin.
* **Option C:** This option is incorrect because it is not a direct complication of heparin. While heparin can cause anaphylaxis, it is a rare and distinct entity from HIT.

**Clinical Pearl / High-Yield Fact**
Heparin-induced thrombocytopenia (HIT) is a potentially life-threatening complication of heparin therapy, and prompt recognition and discontinuation of heparin are critical in preventing further thrombotic events. A platelet count should be checked regularly in patients receiving heparin, especially if they have a history of HIT or are at high risk for developing it.

**Correct Answer:** C. Heparin-induced thrombocytopenia (HIT).