**Core Concept**
Osmostat refers to the regulation of serum osmolality, which is crucial in managing patients with head injuries and rapidly increasing intracranial tension. The osmostat is a mechanism that helps maintain serum osmolality within a narrow range despite changes in fluid balance and solute intake. In patients with head injuries, the osmostat can be disrupted, leading to cerebral edema and increased intracranial pressure.

**Why the Correct Answer is Right**
The drug of choice for initial management in patients with head injuries and rapidly increasing intracranial tension without hematoma is **mannitol**. Mannitol works by creating an osmotic gradient, which helps to reduce cerebral edema and decrease intracranial pressure. This is achieved through the movement of water out of the brain cells and into the bloodstream, thereby reducing cerebral edema. The mechanism of action of mannitol involves the inhibition of sodium and water reabsorption in the renal tubules, which leads to increased sodium and water excretion in the urine.

**Why Each Wrong Option is Incorrect**
**Option A:** **Furosemide** is a loop diuretic that can increase intracranial pressure and is not indicated in the initial management of head injuries with rapidly increasing intracranial tension. Furosemide can cause a significant increase in serum osmolality, which can exacerbate cerebral edema.

**Option B:** **Nitroglycerin** is a vasodilator that can increase cerebral blood flow and intracranial pressure, making it contraindicated in patients with head injuries and rapidly increasing intracranial tension.

**Option C:** **Hypertonic saline** can be used to manage patients with head injuries and rapidly increasing intracranial tension, but it is not the drug of choice for initial management. Hypertonic saline works by creating an osmotic gradient, similar to mannitol, but it is typically used when mannitol is contraindicated or ineffective.

**Clinical Pearl / High-Yield Fact**
Mannitol is most effective when administered intravenously in a dose of 0.5-1 g/kg body weight over a period of 10-15 minutes. The effect of mannitol can be monitored by measuring the decrease in intracranial pressure and the improvement in cerebral edema.

**Correct Answer:** C. Mannitol.