Referring to the law of Laplace as applied to cardiac preload, the formula for the total radius of the left ventricle is r = , where r is total radius, Rin is inner radius, w is wall thickness.
Cardiac preload is one of the main factors that influence how much blood the heart pumps out with each heartbeat, or stroke.
Now, remember that the heart has two upper chambers: the left atrium, which receives oxygenated blood from the lungs via the pulmonary veins; and the right atrium, which receives deoxygenated blood from all of our organs and tissues via the superior and inferior vena cava.
From the atria, the blood flows into the lower chambers of the heart: the left ventricle, which pumps oxygenated blood to all our organs and tissues via the aorta; and the right ventricle, which pumps the deoxygenated blood back to the lungs via the pulmonary arteries.
Alright, now, each heartbeat consists of two phases: systole, which is when the heart contracts and pumps the blood out of the ventricles; and diastole, which is when the heart relaxes and ventricles fill with blood.
And as the left ventricle fills with blood during diastole, the pressure within it rises.
Another way to say this is that cardiac preload is directly proportional to the end-diastolic pressure and radius of the left ventricle, and indirectly proportional to two times the ventricular wall thickness.
To visualize this, let’s look at a cross-section of the left ventricle, which looks a bit like a doughnut, with little dough. A diet doughnut, if you will.
Now, the little dough circle represents the wall of the left ventricle, and its thickness is the ventricular wall thickness, or W. Pressure, or P, on the other hand, is determined by the volume of blood inside the ventricle at the end of diastole.
And finally, the radius, is the distance from the center of the ventricle to the outer edge. So...actually, the radius, or R, comprises of an inner radius, or Rin, which is the radius of the ventricular cavity, and the full radius is Rin plus the ventricular wall thickness.
And if you thought we were done with math, hold your horses. There’s one more formula we need to calculate the inner radius, which is: Rin=3 square root 3V / 4π, where V is the volume of the left ventricle at the end of diastole, or Rin = (3V/4π)⅓.
And then we can add wall thickness to the inner radius to determine the left ventricular end-diastolic radius, or R.
So let’s zoom in on the wall of the left ventricle. The bulk of these walls is made up of short, branched cardiac muscle cells packed one next to the other.
Zooming in further, if we look inside the muscle cells, we see bundles of myofibrils, or long chains of sarcomeres.
The sarcomere is the smallest structure in the muscle that is capable of contracting so it's considered the basic contractile unit of the muscle.
Zooming in further, you can see that the sarcomere has two Z discs that form its boundary and an M line in the middle.
Attached to the Z disc are thin filaments made of actin protein.
These actin filaments have structural polarity which means the end of the filament look different from one another.
We can think of it like an arrow with the pointed end being the “minus end,” pointing towards the M line, and the tail end being the “plus end,” attached to the Z disc.
Just like an arrow, the actin filament can only move in one direction: the direction it’s pointed at.
Attached to the M line are the myosin filaments which are thick bundles of myosin proteins with two globular heads.
During a muscle contraction, the myosin heads grab onto the actin filaments, and pull them towards the M line which brings the two Z discs closer together.
So, the length of the sarcomere is important because the force of contraction during systole depends on the number of myosin heads that bind to actin.
This number directly depends on the length of the overlapping section between actin and myosin filaments.
And the length of the overlapping section depends on the overall length of the sarcomere.
But, no matter how we choose to define cardiac preload, the problem is that these measurements are not possible in practice.
Imagine trying to measure the length of sarcomeres in vivo!
Therefore, in clinical practice, a surrogate for cardiac preload is used - specifically, the volume of blood within the left ventricle at the end of diastole that stretches out the overall muscle wall and each sarcomere within it.
It’s important to note that the end-diastolic left ventricular volume is not the same as cardiac preload; but it can be measured with an echocardiogram, so it’s easier to use this parameter in practice.
Now, the left ventricular end-diastolic volume and therefore preload is affected by five factors: venous pressure and rate of venous return, atrial contraction, resistance from valves, ventricular compliance, and heart rate.
Now, venous tone is determined by vasodilating and vasoconstricting factors. Vasodilating factors relax smooth muscle cells within the vein walls, thereby decreasing the vascular tone of the vein.