Friday, February 22, 2008

Understanding Gary Taubes' ideas on obesity.

In his book Good Calories, Bad Calories and in some lectures Gary Taubes offers an alternative hypothesis about how and why we get fat. I have read the book, and some of the chapters several times, in an effort to understand the explanation of caloric balance and the conservation of energy. I think I finally get it. However, up until recently I have had a lot of difficulty explaining it to others. I invite you to follow along below, in the hope that at the end you will "get it" too.

In the beginning of his lecture at Stevens Institute of Technology, Taubes' invites the audience to think like scientists as he takes them on a tour of the observational data about obesity from a century ago to present. In this article I want to you to think not so much as a scientist, but more as an engineer.

To do this we are going to examine a very simple model a fluid supply system. The design goal is to supply a small but fairly stable supply at the output, so that irregular supplies at the input won't disturb the flow too much. Think of a car engine idling: a small trickle of fuel must be available at all times. The basic design idea is a storage tank, with a source and drain, and some way of monitoring the supply so we know when to fill it again.

Before we go further, let's take a look at a couple of water supply systems I have seen, one at a friend's country chalet and another at my family's old lakeside cottage. At the first, there was no electricity, and gasoline and propane were common fuels. Here is what was built to supply lake water to the house for showering, dish washing, and toilet flushing.

A small gasoline-powered pump takes water from the lake and pushes it up into the water tank on a platform tower. From the water reservoir, a supply line feeds back down to the household plumbing. When a tap is opened in the house, the water pressure supplied by gravity determines the flow rate. Now here is the clever part: a second little supply line goes back to the pump which can activate the on-off switch. The switch is pressure-sensitive. No water actually flows back into the pump, but the pressure can be measured. When the pressure drops below a defined amount, the pump will start. When the pressure rises to the designed maximum, it will turn the pump off. This clever arrangement is known in engineering as a feedback control system. It saves us the trouble of operating the switch manually: we could find a way to read the tank level ourselves and keep it somewhere between full and empty. This is how we attend to our cars; since they don't refuel themselves, their fuel supply relies on the owner to periodically fill it up. They rely on the visual feedback of the fuel gauge.

You may wonder why we bother with the trouble to construct a platform and tank. Why not connect the pump directly to the house supply? Just turn it on whenever you need the water. That's a legitimate design too, and it will work of course, but it makes for very inefficient use of our pump, as in a regular car in city traffic that stopped and restarted the engine at every red light and stop sign (the design of modern hybrid engines attempt to reduce that inefficiency).

Our pump is extremely over-powered for the typical flow we'd need in the house; probably hundreds of litres in a few minutes, so it makes sense to use the pump sparingly. It can replenish the tank quickly compared to our household usage, so it won't run as often, but it will run efficiently.

In this tower reservoir system, there are various things that the engineer will have to consider, such as the flow capacity of the pump, the diameter of the fill hose, the height of the tank (the level of the water above ground is called the"head"), the capacity of the tank, and the size of the house supply hose. Another critical setting is the regulation of the pump's pressure switch: it will determine the variation in the head. All of these things will determine the flow rate of the water at the tap. Later we'll see how adjusting these design variables affects the output.

In this system it will be near impossible to keep the flow exact, but we can design for an acceptable minimum and maximum. When it is working correctly, on average the tank will be partially full, and the variation in the head will determine the variation in flow at the tap. In order to understand this system, you must convince yourself that these two things are linked.

Here is a small experiment you can do at home. Get a plastic bottle or cardboard milk carton, and punch a small hole on the side, close to the bottom. Set it at the edge of the sink, and then fill it up (of course leaving the cap off). If you have managed to get a fairly clean round hole, the water will stream out of the bottle in a nice parabolic curve, very familiar to most beer-loving engineers. Watch where the stream hits the sink bottom. As the level in the bottle goes down, the stream will get weaker, on the point where the stream lands in sink will get closer to the bottle. This should convince you that pressure is directly in proportion to the level of the water. More important, you should also see that the amount of water, the rate of outflow, also lessens with reduced pressure. You can also play with the size of the hole: obviously a smaller one restricts the flow more than a larger one, but here is a key point to remember: the pressure from the head (the water level) is the same regardless of the hole size.

Another thing to notice is that the size of the bottle does not affect the pressure. You could have a milk carton or a five gallon jug, but with the same size hole, the pressure is the same, and the arc of the stream will be the same. What does change is how much time will pass before it empties, as the pressure will fall more slowly with a larger bottle.

A variation of supply design existed at my old country house, where we had electricity but no running water. In this case, another option was available, a small electric pump with a metal compression tank attached. This type of tank had a much smaller capacity than the water tower, more like five gallons rather than five hundred. It had an internal membrane, like a inner tube in a tire. When the pump filled this small tank, it would compress the air between the inner balloon and the metal. When the pump was off, this air pressure could supply the force needed to push water out and into the house. The benefits of this system is the size, so this unit could be installed in a small pump house, was quieter, and could be installed closer to the taps. Ours was located under the cottage in a crawlspace. One of the main differences in this design is that the pump runs much more frequently, but electric pumps have different efficiencies than gas ones. For the same reasons, modern hybrid cars run better on electricity in stop-and-go traffic, whereas a gasoline engine performs best for longer steady runs like on the highway. As before, there was an automatic pressure switch to control the operation of the pump to keep the tank pressure within the desired range.

Now most engineers know that all the variables in these water pumping systems have analogous ones in other situations. An electrical engineer would recognize this as the periodic charging and discharging of a capacitor or battery. The common person recognizes this as the charging of a cell phone once a day -- the lake is the house AC, the pump is the AC adapter, the battery is the storage tank, and the tap is the electrical drain on the battery. A civil engineer would recognize this in any dynamic feedback system; the lay person might see this as a space heater in a room: again the lake is house current, the pump is the heating element, the tank is the radiator (or the air in the room if none), the thermostat sends the feedback signal to the heater, and the tap is the loss of heat through an open window or through the imperfect insulation. A biochemist might see this as the movement of a molecules across a membrane, where the lake is the organism's food, the tank is the concentration of the nutrient solution in a cell, the pump is osmotic pressure and the feedback is a hormone which controls the channels ("holes") in the membrane. The mathematics of all these things turns out to be the same. I chose to use the water/fuel pump example to illustrate the system dynamics because I think it is the easiest to visualize.

For our discussion, imagine we have a supply system like the one with the compression tank as above. Let's remove the outer metal shell and replace it with a big stretchy rubber bladder, a special balloon. As this bladder/tank fills we can observe its size easily. Remember that our design goal was to provide a regulated output, so we are going to keep the tap open, like the hole in the milk carton at the edge of the sink. As another change, instead of the bladder pressure controlling the pump, let us put a device at the tap to measure the flow, set it to signal at a certain range, and send that signal back to the pump.

Let's watch this system operate in our imaginations, starting from an an empty system. The flow meter will read below minimum, so it will send a signal to start the pump. Very shortly, some water will start coming out of the tap, and some will start to fill the bladder. Since our pump can move much more water than our tap can drain, the bladder will continue to expand. At a certain point, the flow meter will show that it is at maximum, and send a signal to stop the pump. At this point the bladder will be at its largest size, and highest pressure. As the water slowly drains out the tap, pushed by the pressure in the bladder, the bladder will start to shrink. But it will never empty completely, because when the pressure drops enough, the flow reduces and the pump will start the cycle again. After the initial start, the system will reach a state of cyclic regularity, what is called dynamic equilibrium. The pump will cycle at regular intervals, and the bladder will expand and contract. It would appear as if it were breathing, or as a heart pumping, although very slowly.

If we subvert the feedback mechanism manually, what happens? Let's say we run the pump a little too long occasionally, or a little less. As long as the average intake is the same, our system will stabilize itself. In the case of over-pumping, the bladder will stretch, and our output will remain at a high flow longer than usual until things settle down. If we let the feedback system function, all will be in balance.

Now we're ready to look at some of the ways the different components can affect operation. Here are some things that we may observe:

  • pump runs too hot
  • pump cycles too often
  • bladder expansion and contraction is too great or little
  • average bladder size is too big or too small
  • output flow varies too much
  • output flow average is too high or too low

Of all these possible problems, I want to look at one in particular, which is the bladder being a different size than our operating specification. Remember our bottle-over-the-sink experiment: when the hole is small, the flow is reduced. There are two ways to change the design here: we can either enlarge the hole, or increase the head. In our water tower example, if we install a smaller diameter pipe to the house, we would have to keep our water level higher, by pumping more initially, putting the same tank on a higher platform. These are familiar trade-offs for engineers. In the compression tank, we could build it to withstand a higher pressure. Finally in our bladder example, we would have to put in a higher pressure skin if we want to keep its operating size the same, or else we would have to allow room for extra expansion and capacity. And of course we would not want to install a pump so powerful that it could explode our bladder!

Let's watch our system running again, but this time, in the laboratory of our minds, we are going to put a wider pipe between the bladder and the flow meter. On this pipe we'll put a valve so that we can control the output flow from fully open to fully shut. By adjusting this valve setting we can watch the system. First we'll close it a bit. As usual, the output flow will reduce and the the pump will start. The bladder will expand until it reaches a higher pressure, and then the pump will stop. Once this new plateau is reached our system settles down as before: same pump cycle, same pressure variation (but higher average pressure) in the bladder, same output flow. Similarly, if we open our control valve, flow is increased temporarily. The bladder will contract, and push out its excess water. During this time, the pump will be off longer than usual, but once again, after an adjustment period the system will stabilize around the desired flow. You can seen how the size of the output pipe directly affects what kind of storage tank can be used. If we play with the valve settings, we can "tune" our tank for an optimum size/pressure trade-off. This could be important depending on the application. In our water tower example we could design a huge tank. In a car, which carries around its own fuel, you have to be concerned about the weight of the fuel and the size of the tank (this is critical in airplane design). In hydrogen fuel car prototypes, the size of the tank has been a major engineering problem, certainly not the weight of the fuel. There are always trade-offs.

Now let's imagine two identical pumping systems out in the field: same pumps, bladders, pipes and output flow needs (but no valve, it was used in the lab as a design aid, and is not necessary in production models). We install these two systems, and let them run merrily away in their feedback-regulated stable environments. The pumps cycle, the bladders expand and contract, the output flow is regulated as required. They are fuel pumps bringing a steady supply to a complex system of engines which need a regulated fuel supply in order to function.

Now, unfortunately, one of our systems has a little problem. In the same place where our lab valve was, a bit of corrosion and rust begins to build. Over five years, the rust builds up ever so slowly, until the pipe is half-blocked. As we learned from our lab, the system still functions perfectly because our super-stretchy bladder has expanded over time to compensate for this reduced output flow.

We are now going to play metaphorical god and give life and consciousness to our two pumping systems, Arnold Dogma and his poor inflated friend, Rusty Taubes.

Arnold: "Whoa, dude, you're carrying a bit of extra weight, aren't you?"

Rusty: "Cripes yeah. Why am I fat, Arnold?"

Arnold: "Well, I hate to say it, Rusty, but you just eat too much -- you run your pump too often!"

A few days later Rusty says, "You know Arnie, I don't think I pump any more than you do. Look at our cycle times, they're identical." "Trust me, Rusty," says Arnold. "You're fooling yourself, or you're in denial. You must pump more than me, otherwise you wouldn't be fat. That's the first law of thermodynamics. You know that signal you get to pump? Just ignore it once in a while. You'll slim down. Just don't pump so much."

So Rusty tries this. A few days later his bladder has indeed gotten smaller! He continues for a few more weeks like this and slims down more. Meanwhile, the more he slims, the more frequent that pump signal stays on, and for longer periods of time. Finally Rusty gives in to the signal, runs his pump, balloons to his previous size and the output flow is reestablished.

"Geez, Arnie, I tried hard, but that signal was so incessant. What else can I try?"

The naive Arnie says, "Here is something else you can try. You can have them run more engines at your tailpipe, just spend more fuel than you take in! You've got to waste some fuel. That'll slim you right down!" "But Arnie, look at our outputs, they're the same!" protests Rusty. "My flow is the same as yours and I fuel the same kind of engines. We both take in and put out the same amounts. But me -- I'm fat!" bemoans the inflated Rusty. But desperate is he, so some of the output gets siphoned off and burned. After a few weeks Rusty says, "Arnie, that's not working either, the important engines have slowed down, there is less of my output available for them since I've been fueling extra stuff. I'm not functioning to spec like this."

"I just don't know any more, Rusty," says Arnold Dogma. "Maybe you were just designed to have a bigger bladder, " he offers. But he still thinks to himself, "That Rusty just pumps too much. Yeah, he must pump when I'm not looking, or at least if he's not lying, he's fooling himself about his intake. Maybe he needs a psychologist."

Fortunately for Rusty Taubes, the problem was eventually fixed. A new output pipe was fitted, proper flow was restored, Rusty's balloon shrunk back to its original size, and he pumped happily ever after.

At this point the fable ends. Astute readers would not forgive me were I not to address Arnold's point about thermodynamics. Arnie was right of course. Over five years, Rusty did pump more. He must have. But the excess gathered so slowly. No tool exists that could have measured so accurately to see a difference in intake between Rusty and Arnie on any given day. Once the problem was fixed, that extra energy was released.

Now this is a very simple fuel supply system, and it cannot represent the human body, which is an incredibly complex machine consisting of dozens of interrelated feedback loops, and has many different fuels available. Before you protest too much, keep in mind that most people consider the human body as an even simpler machine: fuel intake goes in, gets burned, leftovers go to fat storage. This model considers that our output fuel flow is completely variable (which I think is a mistake), and also assumes that human waste has no caloric value.

Our simple feedback pumping system is very simple, yet it explains several observations about real bodies that the simpler model doesn't:

  • Many people don't continue to gain weight, they tend to plateau. It is like they have a set-point which they maintain. The weight creeps up over the years, and then they stay there. We all know friends and acquaintances that have a certain body type, which they maintain over the years.
  • Heavy people may not by lying or deluded when they say they eat the same amount as lean people
  • Fat people can be just as active as well, and hit the gym more that a sedentary lean person, and stay fat
  • Reducing intake or increasing expenditure does not work in the long run, it tries to consciously subvert the design of the body. The demand for fuel by the body's metabolism can crack the willpower of 95% of the people who use this method. The successful 5% learn to live with hunger and fatigue.
  • It shows why counting calories doesn't work, the accuracy needed is beyond our perception
  • It shows how daily fluctuations in intake and expenditure balance out naturally
  • It does not break any laws of thermodynamics
  • Obesity is the symptom of an underlying problem, not the cause
Now I'm not saying that fuel release is the only thing can go wrong, but it explains a lot. In a future post I hope to discuss that the human body has more than one type of fuel, and that it is perhaps not the quantity of fuel which is important in regulation but the fuel mixture. In the fable above it might serve to think that Rusty represented only the fat tissue in the body; the fuel is the circulating fatty acids in the bloodstream. We will see that the hormone insulin acts as the signaling mechanism which can start the pump, and also shut off the output, causing the fat stores to expand.

1 comment:

Jeff Erno said...

Very clever analogy.