Sunday, August 17, 2008

More on the Shape of Weight Loss Curves

This installment about weight loss will focus on data for David (age 53, height six ft even). By way of background, I weighed about 160–172 lb in college (early 1970s), then tended to be in the 170s in my 20s, 180s in my 30s, 190s in my 40s, following the typical sort of pound-per-year pattern of adult male weight gain. I ballooned to close to 220 at the end of the holiday season at year-end 2007. My weight over the previous 2–3 years had become more erratic, fluctuating from about 205 to 220.

At the beginning of 2008, I adopted a non-calorie-restricted low-carbohydrate diet. If anything, I reversed the Atkins-recommended pattern of an “induction phase” of extremely low carbohydrates followed by a maintenance phase. Rather, I phased out carbohydrates from a previous life of 60% carbs (10% protein, 30% fat) to more like 15% carbs (25% protein, 60% fat) over a month or so by slowly finishing off leftover holiday sweets and breads and then not replacing them. Eating to satiety also occurred with an estimated total daily calorie reduction from about 2700 to about 2100 (all very rough numbers). The resulting weight loss is shown on the graphs of weight versus time (date).

I saw an initial weight loss rate of about 2 lb/wk for the first 2–3 weeks, similar to a typical induction phase. Thereafter the rate of loss dropped off to about 1 lb/wk, slowing perhaps to 0.75 lb/wk. It was starting to look like a possible exponential decay from an initial state to a final state resulting from a step change in diet, with a time constant of 8–14 months depending on what I chose as a likely asymptote. (Until there is measurable curvature in the data, it’s not possible to reliably fit a specific value to the asymptote.) I was trying to model the weight loss as a simple exponential decay, assuming that there was a single step change to account for. This would result in a linear fit on a semi-log plot of weight above assymptote versus time. This exponential approach to an asymptote (slowing of weight loss) might be expected because as body mass decreases, less total caloric intake is required just to maintain the body’s metabolic needs. Without further modifying the diet to decrease calories in, one would expect the weight loss to slow. You can see on the graphs that the data could be fit nicely to either an exponential model (straight line on the semi-log plot) or to a piece-wise linear model (set of straight lines on the linear plot) through July. The exponential fit shown assumes an asymptote of 165 lb. The linear plot has the exponential fit shown in orange. The light blue linear fit is drawn through the data from about February through May. The green line is a piece-wise linear fit with segments for the first two weeks, then mid-January through mid-March, mid-March through July, and a separate line for early-July through mid-August. The dashed dark green lines delimit a ±2 lb tolerance band about the mid-March through July fit line.

By mid to late July, it was still difficult to clearly identify which model fit the data best given the normal daily scatter in the data (even with some care to always measure under the same conditions, first thing in the morning). Certainly, a piecewise linear model where there was presumed to be some sort of “induction” phase for the first couple of months followed by a slower linear weight loss rate thereafter fit the data at least as well as the exponential fit.

Then, around the beginning of August, I was starting to get a cluster of data points that were looking unusually low, even though I hadn’t specifically made any major change in diet or lifestyle that I was particularly conscious of. Now, in mid-August, looking back, one can model the last six weeks of data as exhibiting a linear loss of about 1.5 lb/wk, about double what it had been for quite a while! So much for any simple linear or exponential fit to the data! Where will it go from here? And why? I’m not at all sure. Stay tuned for the next exciting episode!

I probably also eat somewhat less as my weight has decreased, although since I haven’t been keeping a careful food diary, that’s hard to prove. It’s clear that eating more dense calories helps you adjust to eating less food total, since you achieve satiety with smaller piles of food on your plate and fewer second helpings.

So, what’s going on in my life besides the low-carb diet? What could have caused the weight loss to accelerate? Clearly, life is more complicated than simple step changes and rapid return to a new equilibrium or steady-state.

A couple of things that may be different in the last 6 weeks with respect to diet are that I am probably eating a smaller late evening meal (meaning usually no second helpings), and about 3–4 days per week, my breakfast is now a protein shake, consisting of a couple of cups of whole milk with soy protein and/or whey protein plus low-caloric flavorings. My best estimate is that the number of calories in that breakfast is about the same as the typical cheese omelette or similar that I often eat otherwise, but there probably is a shift toward more total protein and less fat in the meal.

I’m now down about 30 lb in 33 weeks. I expect to be able to comfortably lose at least another 10 if not 20–25 lb before I reach a stable healthy weight. I suspect that I have more upper-body musculature than I had in my 20s, which may limit me from reaching my minimum athletic college weight, but I’m not sure. My waist circumference was about 34" in college, increasing to about 38" until recently when it got up to about 41". I’m back down to 36" now, and still have a little bit of a “spare tire.” I expect to get back down to 34". Almost all of my excess weight seems to have been stored as visceral fat in the abdomen and above the beltline for most of my pants—none of the weight gain or loss ever made all that much difference to the fit of most of my clothes, one of the reasons that my pattern of weight gain was rather insidious and easy to ignore. (This is probably true for most men.) Many of the symptoms of metabolic syndrome that I had have now gone away or abated (more on that after the next physical exam.)

Part of what had resulted in the relatively rapid weight gain in the last 2–3 years were some major changes in my life that made me more sedentary after a period of higher activity, along with an appreciative eating audience who enjoyed and encouraged my baking habits. (We have yet to find or develop a new bread recipe that is an acceptable low carb substitute, though we’re making progress.) One always tends to reduce eating more slowly than one reduces activity, so in principle, the weight could have accumulated simply because of excess calories. (Or was it excess carb consumption?)

In the last few years, I have eaten more of my calories late in the day, if that makes any difference. (I think it did, if for no other reason, than because I was more likely to need extra snacks to hold me until a late evening meal. Previously, I ate an earlier dinner, so I didn’t need an afternoon snack, and rarely ate anything for several hours before sleeping.) But I was hardly leading a couch-potato lifestyle while gaining weight. I was typically running at least 25–30 mi/wk on hilly terrain, if not always very fast. The running certainly seemed to be getting harder as I got either older or heavier or both. For my weight (averaging about 210 during this time), this amount of exercise should translate into 3300 kcal expended each week, or an average of 472 kcal/day (assuming no additional caloric expenditure for the hills—my best estimate is that our particular hills added another ~60 kcal/day). I estimate I was eating an average of about 2700 kcal/day during this time, which is about as much as the Runner’s World diet page says is needed to maintain my weight with only light exercise. Without getting into a critique of the Runner’s World diet recommendations (another posting), I should not have been gaining weight on this amount of calories with the amount of exercise I was getting!

Not surprisingly, my running ability has improved significantly with 30 fewer pounds to cart around. My breathing is easier and slower. My heart rate is slower and recovers faster. I can run uphill again, where I previously pretty much slowed to a walk most of the time. Longer runs (12–18 miles) don’t wipe me out anymore. I’m probably logging closer to 40 mi/wk than 30 mi/wk right now, though I’m still not going to win any races.

Regardless, what I am doing works! I’m not struggling at all to lose weight. I never feel like I am starving myself, and except for the usual carb temptations in the world at large, I am finding the diet easy and comfortable to live with and sustain.

No comments: