The Case of Preston Hughes III: Where's Willis?

In one episode of Married with Children ("Cheese, Cues, and Blood"), Al Bundy needed to raise money quickly. He did so by selling nine pints of his blood.

Kelly:  Daddy, you look so pale. 

Al:  Perhaps that's because I've been running all over town, selling pints of blood to nine blood banks. 

Jefferson:  Al, the human body only holds eight pints. 

Al:  Well, that's what they say, but the brain hides some.

Not much later in the episode:

Jefferson:  Well Al, you're looking better. You've stopped air-guitaring "It's a Small World". 

Al:  Yeah, it's the beer. Turns out, the brain doesn't need blood. Just gotta keep the brain wet.

Blood Volume

From The Physics Factbook:

In an average healthy adult, the volume of blood is about one-eleventh of the body weight. Most sources state the volume of blood in an average human adult, who is between 150 to 160 pounds, as between 4.7 and 5 liters, although the more recent sources state the volume of blood in an average adult as 4.7 liters.

There are 2.11 pints in a liter. The average healthy adult, weighing around 150 pounds, therefore has around ten pints of blood, not eight. I advise that you don't rely on Al Bundy (or any of The Married With Children cast) for medical advice. The human body can hold more than eight pints of blood, and the brain cannot survive on beer alone.

Shandra Charles weighed 127 pounds. I therefore estimate her blood volume was 4 liters, at least before someone used a double-edge knife to sever her carotid artery and jugular vein, then left her in that dark, overgrown lot to bleed out onto the trail. 

According to The Journal of Animal Science, a three-year-old, 156-pound sheep has a blood volume of 4.1 liters. That is coincidentally nearly identical to the blood volume I calculated for Shandra Charles.

Cardiac Output

From The Textbook of Medical Physiology, by Dr. John E. Hall

Note that the plateau level of this normal cardiac output curve is about 13 L/min, 2.5 times the normal cardiac output of around 5 L/min.This means that the normal human heart, functioning without any special stimulation, can pump an amount of venous return up to about 2.5 times the normal venous return before the heart becomes a limiting factor in the control of cardiac output.  ...

[M]aximal nervous excitation of the heart can raise the plateau level of the cardiac output curve to almost twice the plateau of the normal curve, as shown by the 25 L/min level of the uppermost curve ...

To be clear, author John Hall was discussing the cardiac output of humans. Assuming you want to know about the cardiac output of sheep, I recommend you read the mega-hit Anoxia, Oxygen Consumption and Cardiac Output in New-Born Lambs and Adult Sheep. Pay particular attention to Table 1 of that paper. It shows that adult sheep have a normal cardiac output of 5.2 liters per minute. That's remarkably close to Shandra's normal cardiac output of 5 liters per minute.

Now let's do some simple math. Assume a sheep with a blood volume of 4.1 liters and a cardiac output of 5.2 liters per minute. Assume further that the cardiac output would not change due to excitation (because the sheep would be anesthetized) or to changes in back-pressure or for any other reason. Given these assumptions, a sheep's heart could empty its body of blood in just 47 seconds.

Using a rule of thumb that someone (or somesheep) will die after losing half its blood, then the sheep assumed above would die in 24 seconds. Had the sheep's cardiac output been increased by a factor of 2 because it was suddenly aware it was about to die, then it would have died in just 12 seconds.

It's not surprising therefore that sheep (now plural) lose brain function just 15 seconds after both of their common carotids and both of their jugular veins have been severed.

The brain needs a continuous supply fresh blood. If instead the blood is pumped onto a lonely dirt trail in a dark, overgrown field, then the brain will quickly cease to function.

Quickly.

The Circle of Willis

In Pools of Blood, I explained that hockey players Clint Malarcuk and Richard Zednik survived cuts to their carotid arteries. They survived because they received prompt first aid. Someone nearby stopped blood from escaping from their carotid. While your brain clearly, absolutely, and unequivocally needs blood, it does not need that both carotid arteries supply that blood. In a pinch, if you excuse the pun, either will do

Due either to evolution or some really good, supernatural engineering (argue among yourselves), mammals such a humans and sheep are equipped with an interconnected plethora of arteries supplying the brain. This highly-evolved / well-engineered (argue among yourselves) collection of vessels is known as the Circle of Willis.

Here's a handy-dandy cross-section through someone's head showing the not-nearly-circular circle.

Check the upper-leftmost block of text. It says INTERNAL CAROTID ARTERIES. Follow the accompanying arrows. There they are: transected carotid arteries.

Somewhere above the upper portion of the neck, each common carotid artery divides into an internal and an external carotid artery. It is the internal carotid that is primarily responsible for supplying the brain with blood. In the image, you can see that the two internal carotids are connected to one another both front and rear, both anterior and posterior, by other arteries. Welcome to the Circle of Willis.

Shandra Charles died not because one of her common carotid arteries had been transected by a double-edged knife, at least not directly. She died because her blood spurted out of that transected artery onto a dirt path, and because there was no one there who could and would pinch that artery closed.

Shandra Charles did not die because her body had no intact pathway for supplying her brain with blood. She died because she ran out of blood.

The pathway was there, via the Circle of Willis.

The blood was not. It was soaking into the dirt beneath her neck. 

Time of Consciousness
We now have a pretty good upper limit on how long Shandra Charles feared for her life after having been stabbed. Based on the experimental data collected on sheep, and given that sheep and humans evolved from a common ancestor / were designed similarly (argue among yourselves), and because Shandra's blood volume and cardiac output were nearly identical to those of an adult sheep, we can be confident that Shandra Charles maintained brain function for no more than 90 seconds after having her common carotid artery transected by a double-edge blade.

Given that her cardiac output was probably elevated due to the dreadful "excitation" of the attack, it is likely that she lapsed into unconsciousness even more quickly.

It is impossible that she calmly provided Sgt. Hamilton with a dying declaration.

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