Angina Pectoris and Angina Decubitus are actually two separate clinical entities. Angina Pectoris is "cardiac pain" due to ischemia (reduced blood flow) to the heart muscle during exercise or exertion. Angina Decubitus, a less well understood phenomenon, occurs at rest but is a bit more complicated in its etiology (cause).
Angina Decubitus is generally associated with Left Ventricular Hypertrophy (LVH), which in most reported cases is caused by Hypertension. It also occurs with dilated Cardiomyopathies, particularly Left Ventricular Dilatation resulting from untreated or poorly controlled hypertension which leads to eventual thinning and enlargement of the left ventricle.
Some studies have shown that there is a rise in oxygen consumption, heart rate and stroke volume of the heart prior to the onset of symptoms from Angina Decubitus suggesting that it is also associated, although indirectly, with "exertional characteristics."
Angina Decubitus occurs primarily when the affected person assumes the Left Lateral Decubitus position or basically lying on the left side. With a hypertrophied heart, the muscle is already at risk of ischemia as the penetrating branches from the coronary arteries cannot perfuse the deeper portions of the muscle well. When blood flow is reduced significantly and/or interrupted pain or angina occurs. Some researchers believe the lateral decubitus position in the presence of a hypertrophied heart exacerbates the relative small vessel ischemia and thereby precipitates the pain or angina.
Many of the original articles describing Angina Decubitus can be found in the Archives of JAMA (Journal of the American Medical Association). Many were written in the early 1950's with sporadic articles appearing since then.
I hope this provides a starting point for your understanding of this interesting phenomenon!
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National Library of Medicine
Archives of JAMA