**Core Concept:**
The soap bubble appearance on a mandible radiograph is indicative of a lytic lesion, which is a type of bone tumor. The presence of blood on aspiration suggests that the lesion is vascular, as blood is drawn into the space due to pressure differences. The whirring sound and the connection with the heart suggest that the lesion is adjacent to or communicating with the heart.

**Why the Correct Answer is Right:**
Given the clinical presentation, the correct next investigation would be to perform a cardiac catheterization or cardiac angiography. This is because the whirring sound and the ability to feel the heartbeat in the lesion suggest that the lesion is either an arteriovenous malformation (AVM) or an arteriovenous fistula (AVF) adjacent to or communicating with the heart. These conditions are characterized by the abnormal shunting of blood between arteries and veins, leading to the described clinical findings.

**Why Each Wrong Option is Incorrect:**
A. Computed tomography (CT) scan: Although CT can provide detailed anatomic information, it doesn't address the hemodynamic connections between the lesion and the heart.
B. Magnetic resonance imaging (MRI): MRI can provide detailed soft tissue imaging, but it does not address the hemodynamic connections between the lesion and the heart.
C. Fine-needle aspiration cytology: This investigation focuses on the cellular nature of the lesion, not its hemodynamic connection to the heart.
D. Bone scan: A bone scan would likely show increased uptake in the lesion, but it does not address the hemodynamic connections between the lesion and the heart.

**Correct Answer:**
The correct investigation to perform is cardiac catheterization or cardiac angiography (Option D). This is because it directly addresses the hemodynamic connections between the lesion and the heart, which is essential for understanding the clinical presentation described in the question.