**Core Concept**
The underlying condition in this patient is gout, a form of inflammatory arthritis characterized by deposition of monosodium urate (MSU) crystals in the joint space, leading to inflammation and potentially, the formation of tophi. Tophi are deposits of MSU crystals that can accumulate in various tissues, including the periarticular regions of joints.

**Why the Correct Answer is Right**
The nodular masses in this patient are likely tophi, which are characteristic of chronic gout. Tophi are formed when MSU crystals are deposited in the soft tissues, leading to a chronic inflammatory response. This process involves the activation of immune cells, such as macrophages and neutrophils, which release various cytokines and chemokines, resulting in tissue damage and the formation of tophi. The periarticular tissue of the proximal and distal interphalangeal joints is a common site for tophi formation in patients with chronic gout.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because tophi are not typically associated with rheumatoid arthritis (RA), which is characterized by the formation of rheumatoid nodules.
* **Option B:** This option is incorrect because osteophytes are bony growths that can occur in joints affected by osteoarthritis, but they are not typically associated with gout or tophi formation.
* **Option C:** This option is incorrect because ganglion cysts are benign, fluid-filled cysts that can occur in joints, but they are not typically associated with gout or tophi formation.

**Clinical Pearl / High-Yield Fact**
Tophi can be a diagnostic clue for chronic gout, and their presence can help differentiate gout from other forms of arthritis. Tophi can also be associated with other systemic conditions, such as hyperparathyroidism and kidney disease, which can lead to hyperuricemia.

**Correct Answer:** C.