**Core Concept**
The Hering-Breuer inflation reflex and deflation reflex regulate breathing by sensing lung inflation and deflation, respectively. However, Head's paradoxical reflex is a distinct mechanism that allows the lungs to inflate further despite initial inflation, counterintuitive to the Hering-Breuer inflation reflex.

**Why the Correct Answer is Right**
Head's paradoxical reflex is a phenomenon where inflation of the lungs initially stimulates the Hering-Breuer inflation reflex, leading to a brief pause in inspiration. However, as inflation continues, the increased stretch receptors in the alveoli activate the Head's paradoxical reflex, causing an increase in the depth and rate of breathing. This is mediated by the activation of the vagus nerve, which releases neurotransmitters that stimulate the respiratory centers in the brainstem. The increased stretch receptors in the alveoli override the initial inhibitory response of the Hering-Breuer inflation reflex, allowing for further lung inflation.

**Why Each Wrong Option is Incorrect**
**Option A:** The Hering-Breuer inflation reflex is a protective mechanism that inhibits inspiration when the lungs are already inflated, preventing overinflation. It does not facilitate further inflation.
**Option B:** The Hering-Breuer deflation reflex is triggered by lung deflation, which stimulates inspiration to re-inflate the lungs. It is not related to further inflation during initial inflation.
**Option D:** The J-reflex is a vagally mediated reflex that inhibits the cough reflex and is not related to lung inflation or the Head's paradoxical reflex.

**Clinical Pearl / High-Yield Fact**
The Head's paradoxical reflex is an important mechanism that allows for deep and rapid breathing during exercise or stress, ensuring adequate oxygenation of the body. It is a classic example of how the respiratory system can adapt to changing demands.

✓ Correct Answer: C. Head's paradoxical reflex