**Core Concept**
The question is testing the understanding of the pathophysiology and clinical presentation of pyogenic liver abscess, specifically the common route of spread. Pyogenic liver abscess is a collection of pus in the liver parenchyma, often caused by bacterial infection. The liver's unique anatomy and blood supply play a crucial role in the spread of infection.

**Why the Correct Answer is Right**
The most common route of spread of pyogenic liver abscess is through the biliary tract. Bacteria from the gut can ascend through the biliary tree, invading the liver parenchyma and causing abscess formation. This is often seen in patients with biliary disease, such as cholangitis or cholelithiasis. The biliary tract provides a direct pathway for bacteria to reach the liver, making it the most common route of spread.

**Why Each Wrong Option is Incorrect**
* **Option A:** Hematogenous spread is a possible route of spread, but it is less common than biliary tract spread. This route involves the direct entry of bacteria into the bloodstream, which can then infect the liver.
* **Option B:** Direct inoculation is a rare route of spread, typically seen in cases of penetrating trauma or surgical procedures. This route involves the direct introduction of bacteria into the liver tissue.
* **Option C:** Peritoneal spread is not a common route of spread for pyogenic liver abscess. While the peritoneum is a potential space for abscess formation, this route is more commonly associated with other types of intra-abdominal infections.

**Clinical Pearl / High-Yield Fact**
Remember that pyogenic liver abscess is often seen in patients with biliary disease, and the biliary tract is the most common route of spread. This is an important clinical correlation to remember for exam purposes.

**Correct Answer: B. Biliary tract spread.**