Computational Hemodynamics

This is a quick update on salt, and a digression about computation and blood pressure control. Read all the way to the end for a grain of salt advisory on the carbohydrate-insulin hypothesis.

My salt experiment is progressing and I've completed a 6 day baseline period, followed by a 3 week salt restriction period during which I consumed approximately 800-1,000 mg of sodium per day. I am now half way through a 2 week salt loading phase where I am consuming about 6,000 mg of sodium per day. It is quite a challenge to eat this much salt, though my taste buds have now gotten used to it.

Results? There has not really been a noticeable change in blood pressure between the three phases. Blood pressure during salt loading is almost certainly the same as the baseline diet, which was fairly low in salt to begin with. I'm still reviewing the data on the salt restriction phase, as there may have been a small drop there. I will report in more detail later.

Severe salt restriction had some negative side effects, most significantly an impairment in my body's ability to maintain a stable core temperature. In a warm environment, I might experience an increase in heart rate, and ultimately an elevated core temperature (up to 100.5 in one case). I also noticed a substantial drop in exercise performance. I was clearly dehydrated during this period, as evidenced by a drop in body weight. According to a google book called The Interface of Neurology and Internal Medicine (2007), salt restriction and dehydration can result in impaired thermoregulation possibly leading to heat stroke. I believe dehydration and the resulting drop in blood volume limits cardiac output, thereby preventing the cardiovascular system from performing its temperature regulatory functions.

Infinite Gain

In a former incarnation I was an electrical engineer.

Beloved of electrical engineers the world over, the operational amplifier (a.k.a. the "op amp") has been a mainstay of circuit design at least since the mid-1960s, when the first integrated circuit operational amplifier was introduced. An op amp has two inputs and one output, with the output dependent on the difference in voltage between the inputs, multiplied by a gain factor.

An ideal op amp by itself has effectively an infinite gain. This means it is not going to make a very useful amplifier unless it is built into a circuit that incorporates negative feedback. In this configuration, as articulated by Paul Horowitz and Winfield Hill in "The Art of Electronics," the op amp will do "whatever is necessary to make the voltage difference between the inputs zero."

An operational amplifier in the inverting closed-loop configuration. Rf provides negative feedback such that the voltages at the (+) and (-) inputs become equal. The circuit designer can manipulate Rin and Rf to produce the desired relationship between Vin and Vout.

Since the op amp is so useful in engineering, one might expect to find something like it in evolved biological systems that incorporate regulatory elements and negative feedback. In fact, there does appear to be an "infinite gain" element in the human blood pressure regulation system.

Computational Hemodynamics

In 1966, Arthur Guyton and Thomas Coleman developed a computer model of blood pressure regulation. The model was put together based on prior research on the various systems that work together to regulate blood pressure, including hormones (renin, angiotensin, aldosterone, antidiuretic hormone), heart pumping parameters (including pulse and stroke volume), fluid dynamics, electrolytes, local blood flow control, and various other factors. In a paper published in 1990 in the journal Hypertension, Guyton discusses the discovery he made using this computer model of an infinite gain regulatory element.

1966 was a long time ago in the computing world. Guyton and Coleman may have needed one of these to program their blood pressure model. Image from "Introductory Computer Programming" by Fredric Stuart, John Wiley & Sons, Inc. 1966.

After Guyton and Coleman started playing around with their computer model (did I mention it was 1966!), they saw some unexpected results. They increased one variable -- namely total peripheral resistance -- that "everyone already understood" would cause chronic hypertension. Instead, as Coleman reported to Guyton, "the patient developed hypertension all right, but the pressure came back to normal after a few days." Guyton and Coleman saw that the kidney's ability to regulate fluid and electrolytes was effectively an infinite gain feedback system: like an op amp, the kidney would do whatever was necessary to maintain stable blood pressure. While this surprised them at first, they found that this property could explain earlier observations that had been difficult to understand.

As Guyton stated in the 1990 paper, "the infinite gain property of the kidney-fluid mechanism for pressure control is so dominating that it will not allow a factor from outside this mechanism to alter the blood pressure permanently unless the kidney-fluid mechanism is itself altered at the same time." In other words, if you are looking for a cause for a long term change in blood pressure, look for something that is affecting kidney function.

Here is an except of a schematic diagram of Guyton's 1972 blood pressure model (this may be a revised version of the original 1966 model). A shrunken version of the full diagram is included at the end of this post. It's so big that it is worth checking out the fill size image, which you can get here.

A small segment of the Guyton 1972 schematic.

Biology as Computation

I think this story is a good example of a successful computational approach to a biological question. We can view the human blood pressure regulatory system as a computational system. It reads a variety of inputs and "computes" the organism's blood pressure. If we can accurately model the system's individual elements (based on lots of reductionist basic science) we can try to simulate the whole thing in a computer.

This story also shows that a reductionist approach to biology can mislead. Viewed in isolation, it seemed obvious to everyone that an increase in "total peripheral resistance" would result in a long-term rise in blood pressure. This was consistent with the fact that patients with hypertension typically also show an increased total peripheral resistance. However, in other cases where there is a clear primary cause for a rise in total peripheral resistance (e.g. multiple amputations), scientists frequently observed no long term increase in blood pressure.

The computer model helped provide an answer to these riddles. Instead of relying on an intuitive understanding of a single element, it let us watch what happens when all of the computational elements are allowed to interact. It then became obvious to Guyton and Coleman that the kidney's fluid regulation mechanism was powerful enough to override other factors that might try to drive blood pressure up or down. It could then be hypothesized that the increased total peripheral resistance seen in hypertensives was in fact a consequence, and not a cause, of elevated blood pressure. Work could then proceed on how exactly this came about.

Beyond Blood Pressure

Some complex systems may sometimes exhibit simple and comprehensible behaviors, while other complex systems will not. Computational approaches might help us figure out which is which. Computational approaches may be required when purely reductionist thinking is not enough. In other cases, when the basic "computational units" of the system being modeled are not individually well understood, a computational approach might lead us absolutely nowhere. And as anyone who has ever tried to build a complex system can tell you, if it is not extensively validated, it is almost guaranteed to break.

Blood pressure regulation is complex, though it is probably quite simple compared to many other biological systems. To me the diagram below looks about as complex as this schematic for the Intel 4004 microprocessor, introduced in 1971. The infinite gain property of kidney fluid regulation, discovered because of a computer model, allows for a powerful simplification. If the kidney is really driving the blood pressure boat, we could safely ignore most of the complexity of the total system and look only at the kidney's health and its specific regulatory drivers. Many other complex systems will not be reducible in this way.

Grain of salt advisory.

Consider this next time someone says carbs drive insulin which drives fat storage. Insulin works in a complex web of biological computational elements, including the mother of all biological computers, the human brain. Insulin viewed in isolation may or may not give us the answer. This is why my ears glaze over a bit when I hear someone start talking about "<hormone du jour> resistance." I'm not interested in the behavior of a single wire in a complex web. I want to know how the whole thing works.

Blood pressure regulation. It's complicated. From Guyton 1972.