In a model of a narrowing coronary artery, the flow is proportional to the fourth power of the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a model of a narrowing coronary artery, the flow is proportional to the fourth power of the width of the lumen. The flow of a normal artery is .
- The deposits make the lumen narrower, so it is of its normal width. What is the flow?
- The lumen becomes narrower. What is the flow?
- Why can a person with a moderate narrowing have angina on effort?
Need a reminder? The key ideaShow
Normal blood pressure is mm Hg. A reading of mm Hg or higher is hypertension. The pulse pressure is the systolic pressure minus the diastolic pressure. In coronary artery disease, deposits narrow the coronary arteries. Angina is a chest pain from too little oxygen in the heart muscle. Heart failure is not cardiac arrest and not a heart attack.
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Flow per cent.
Plan. Find the width as a fraction, and raise it to the fourth power.
Step 1. narrower. Width . , so the flow is .
Step 2. narrower. Width . , so the flow is .
Step 3. Angina. In effort, the heart muscle needs more oxygen. A narrow artery cannot bring enough blood, and the muscle is short of oxygen. This gives the chest pain.
Answer: ; ; the narrow artery cannot meet the need of the working muscle.
Check. In the model, a small narrowing takes away much of the flow, because of the fourth power.
Watch out. This is a model of a narrow tube. A real artery is more complex, and the flow at rest stays near normal until the narrowing is severe.
Source. Gould, Lipscomb and Hamilton (1974), American Journal of Cardiology, 33, 87 to 94.
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