Step 1: Fix the valve's position in the circuit.
The mitral valve sits between the left atrium and left ventricle. Blood leaving the left ventricle goes straight into the aorta, the main artery feeding the whole body.
Step 2: Follow a broken-off vegetation.
If part of the vegetation on the mitral valve breaks free, it gets pushed out with the blood into the aorta. From there it can travel to any organ fed by the aorta's branches, such as the brain, the spleen, or the kidney, and lodge in a small artery there, cutting off blood flow to that patch of tissue.
Step 3: Ask where the right side of the heart fits in.
The lung is fed differently. Blood reaches the lung through the pulmonary artery, which carries blood from the right ventricle, not the left. A clot or vegetation piece from the left-sided mitral valve simply has no pathway into the pulmonary artery.
Step 4: Compare with a right-sided lesion.
If the vegetation were instead on the tricuspid or pulmonary valve (right side of the heart), then the pieces breaking off would indeed end up in the lung, since that is exactly the vessel the right heart pumps into. But this question is about the mitral valve, which is left-sided.
Step 5: Conclude.
Brain, spleen and kidney are systemic organs reachable through the aorta, but the lung is only reachable from the right heart, so it is the one site the mitral valve embolus cannot reach.
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