In coronary artery disease, the coronary arteries that carry oxygen-rich blood to the heart muscle are narrowed due to the accumulation of fatty deposits known as plaque. This buildup of plaque is known as artherosclerosis. Plaque may be hard and stable, leading to narrow and hardened arteries, or it may be soft and likley to break open, causing blood clots. Whether hard or soft, plaque can cause angina by narrowing the artery, severely impeding blood flow, and by causing clots that can partially or completely obstruct the artery.

...are less flexible and walls are thicker, because deposits of fatty acids and minerals ...

It is the calcium deposits of atherosclerosis that make the arteries "stiff" or hard.

Here is an extract from a little booklet on heart surgery issued by the Escorts Heart Institute and Research Centre in New Delhi. My brother was recently admitted there for the same problem, and I have become something of an expert on the subject after going through the experience of witnessing his bypass surgery :)

Corornary artery disease causes a narrowing of the coronary arteries that restricts the flow of blood through these vessels. It is the result of the process called atherosclerosis. Atherosclerosis, or hardening of the arterteris, is a build up fatty substances within the walls of the arteries. The lining of the arteries become thickened and roughened by these fatty substances. When the coronary artery becomes narrowed or blocked, the heart muscle does not receive enough blood which can lead to angina or heart muscle damage or "heart attack".

The book is by Dr Naresh Trehan, who is one of the foremost heart surgeons of the world.

If you happen to be in New Delhi, you can pick this booklet from the Escorts hospital. Its full of information about heart diseases and their treatment. It is also available in Hindi.

This makes it clear that hardening does not refer to the hardness of the substance, but to the blockage of the artery, in other words, the narrowing of the artery supplying blood to the heart muscle.

Your sentence simply describes the condition known as atherosclerosis (sclerosis = hardness):
“Atherosclerosis (ath"er-o-skleh-RO'sis) comes from the Greek words athero (meaning gruel or paste) and **sclerosis (hardness)**. It's the name of the process in which deposits of fatty substances, cholesterol, cellular waste products, calcium and other substances build up in the inner lining of an artery. This buildup is called plaque.” http://www.americanheart.org/presenter.jhtml?identifier=4440

In advanced stages, atherosclerosis or the “hardening of the arteries” may lead to the narrowing or constriction of an artery (stenosis) or to arterial obstruction:

“These plaques cause a gradual, progressive narrowing of the the lumen of the artery, and thus make blood flow through the artery progressively more difficult. In addition, these plaques are subject to sudden rupture. When the plaques rupture, they trigger a clotting event within the artery that can cause acute obstruction of the lumen.” http://heartdisease.about.com/cs/coronarydisease/a/CAD1.htm

So in your context “hardening” means just that – hardening, loss of flexibility. It cannot be translated as “blockade” or “obstruction”.