**Core Concept**
Vasa previa is a rare but serious condition where fetal blood vessels are present in the membranes covering the cervix, making them vulnerable to rupture during labor or membrane rupture. The diagnosis of vasa previa requires a thorough ultrasound examination to identify the fetal blood vessels in the membranes.

**Why the Correct Answer is Right**
The investigation of choice for diagnosing vasa previa is Doppler ultrasound. This is because Doppler ultrasound can detect the blood flow in the fetal blood vessels in the membranes, allowing for early identification of vasa previa. The Doppler ultrasound machine uses high-frequency sound waves to detect the movement of red blood cells in the vessels, creating a characteristic "whooshing" sound that indicates blood flow. This is particularly useful in identifying vasa previa, as it can help differentiate it from other conditions such as placenta previa.

**Why Each Wrong Option is Incorrect**
**Option A:** Magnetic Resonance Imaging (MRI) is not the investigation of choice for diagnosing vasa previa. While MRI can provide detailed images of the fetal anatomy, it is not as sensitive as Doppler ultrasound for detecting blood flow in the fetal blood vessels in the membranes.
**Option B:** B-mode ultrasound is not specific enough for diagnosing vasa previa. While B-mode ultrasound can provide images of the fetal anatomy, it does not have the sensitivity to detect blood flow in the fetal blood vessels in the membranes.
**Option C:** Fetal echocardiogram is not relevant to the diagnosis of vasa previa. A fetal echocardiogram is used to evaluate the fetal heart, and is not indicated for diagnosing vasa previa.

**Clinical Pearl / High-Yield Fact**
A key aspect of diagnosing vasa previa is the presence of fetal blood vessels in the membranes, which can be identified by Doppler ultrasound. The classic sonographic finding of vasa previa is the presence of vessels crossing the internal cervical os, which can be detected by Doppler ultrasound.

**Correct Answer:** C. Doppler ultrasound.