# Heart power and ischemic heart disease

Ischemic heart disease is caused basically by an imbalance between $\mathrm{O}_2$ (which is translated into energy) demand and consumption by the heart. Therefore let us investigate how much energy the heart spends per unit of time and what factors contribute to such a demand.

As the blood flows out of the heart it is impelled against a pressure $p$ (the afterload). If the area of the exiting artery (the aorta) is $A$, then the force the heart must be exerting is

$F = p \cdot A.$

If the mean velocity the blood exits the heart is $v$ and the heart takes a time $t$ to do it, then we can multiply both sides of the last equation by $vt$ resulting in

$Fvt = p \cdot (Avt).$

Observe that $vt$ is also the distance travelled by the blood expelled by the heart in one pump. Therefore $Avt = V$ (in the right side of the equation) is the stroke volume (volume of blood expelled per beat) and $Fv = \Omega$ is the mean heart power. Therefore

$\Omega \cdot t = p \cdot V.$

The last thing to notice is that $t$ is the time of a full-cycle. Therefore if $f$ is the cardiac frequency, then $t = 1/f$ and we can finally write

$\Omega = pVf.$

This means that the energy used by the heart increases linearly with the afterload, the stroke volume and the heart frequency. This explains why unstable anginas happen when we exercise, for exemple.

Some medications such as nitrates decrease the heart power by decreasing the heart's stroke volume by accumulating blood in the veins (therefore less blood reaches the heart). Other medications such as beta-blockers decrease the heart power by blocking beta-1 receptors and therefore decreasing the heart frequency.

The most important thing to notice is that the percentage of decrease in heart power is exactly the same as the percentage decrease in the mechanism the medication is working on.

Note by Lucas Tell Marchi
3 weeks, 1 day ago

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