Archive for February, 2018

Is weight homeostasis possible?

February 28, 2018

I am slightly obsessed with my weight. Forgive me: I am 58 and have spent many decades repeatedly putting on weight slowly, and then losing it rapidly.

For many years I have wondered why can’t I just eat modestly and trust my body to “sort itself out!”

My recent discovery of the Mifflin St Joer equations (link) has allowed me to  simulate my weight over time, and my calculations are allowing me to understanding my own experience.

But my calculations have also raised a profound question:

  • Is homeostasis of weight even possible?

Homeostasis

Homeostasis (or Homoeostasis) is the term given to physiological systems which conspire to keep something constant.

For example, we have systems that maintain our body temperature without any conscious effort. I don’t have to berate myself for being too hot and promise myself that in the future I will try to be cooler.

No. Our bodies sort out their internal temperature. I understand the system consists of temperature sensitive cells and nervous system reflexes that control blood flow, sweat glands, shiver reflexes, and our desire to undertake activity.

Hunger

And I have generally imagined that in a more perfect world, a similar kind of system would underpin my desire to eat.

In this ideal world, I would naturally maintain my weight without any obvious effort on my part – stopping eating when I had eaten ‘enough’.

I had thought such a system actually existed. One part of the system is supposed to arise from the competing actions of hormones such as ghrelin – which makes us experience hunger – and leptin – which makes us feel satiated.

Together, ghrelin and leptin are supposed to act as part of a system of energy homeostasis.

However, having run many simulations of my own weight versus time (see below) and reflected on this, I am sceptical.

“But I know a bloke who…”

We all know people who seem to be able to eat at their ease and not put on weight.

I have no explanation for that, but then I have never experienced that myself.

My experience is that my weight either increases or decreases over time. What I have never observed it to do in all my 58 years on Earth is to stay the same! (I have written about this before: story 1 or story 2.)

What’s the problem?

I programmed the Mifflin St Joer equations into a spreadsheet to see the predicted effect on my weight of various dietary and exercise choices.

You can download the spreadsheet here and perform calculations about yourself in the privacy of your own computer. 

I entered my current age (58.2 years) and weight (74 kg), and I used the MSJ equations to predict what would happen to my weight if I ate 1800 kiloCalories (kCal) a day.

The results are shown below together with the effect of eating 50 kCal/day more or less

Weight versus Age Projection

  • The red line suggests that if I eat 1800 kCal/day then my weight will gradually decline over the next couple of years stabilising at about 71 kg. That would be dandy.
  • However, the dotted green lines show what would happen if I got my calorific intake wrong by ± 50 kCal per day. This is plus or minus half of a small glass of wine, or a half a biscuit either eaten, or not eaten.

These ‘alternate realities’ predict that my weight in three years time might be anywhere between 64 kg and 77 kg – a range of 13 kg!

To be within a kilogram of the predicted weight, my average energy intake would need to match 1800 kCal/day within 10 kCal a day. That is less than a single mouthful of food!

I don’t believe that any autonomic system can achieve that level of control. 

Weight versus Age Projection 2

So what?

Reflecting on these simulations, I don’t believe that the systems within our bodies that mediate ‘energy homoeostasis’ operate well over many years.

At least they don’t operate well in an environment where calories are so easy to obtain.

So I think my experience of slow weight gain over time is not a fault with my autonomic nervous system, or a moral failing on my part. It is just the way things are.

Asking the thinerati

Asking several slim individuals around the coffee machine this morning confirmed my view. They all were either (a) young (b) self-conscious about fitting into clothes or (c) weighed themselves regularly.

Personally I have resolved to keep weighing myself and using this to provide manual feedback.

How is my weight doing? Thank you for asking. It’s been just about stable since Christmas and I intend to keep it that way!

SI at the RI

February 23, 2018

 

MdeP at the RI

On Monday 16th October 2017 I gave a talk at about the International System of Units (the SI) at the Royal Institution (the RI) in London.

It wasn’t a great talk, but it was at the RI. And I stood where Michael Faraday stood!

The RI have now processed the video and produced an edited version: enjoy 🙂

The RI have tended to retain the video of me talking rather than showing the animated PowerPoint slides. If you would like the full multimedia experience, you can download the presentation using the link below.

On the day

I was nervous and arrived ridiculously early with a couple of glass Dewars containing triple point of water cells.

I waited outside the lecture theatre for Martin Davies from the RI to arrive.

When he arrived, he noticed the Dewars and without hesitation he turned to the wall and pointed out the painting above where I was standing, and said:

“What a coincidence: your standing by a picture of Sir James Dewar lecturing in this theatre!”

Henry Dewar at the RI

It’s hard to convey the historical significance of Royal Institution without sounding trite. So I won’t try.

But it is a special place for chemists and physicists alike, and I feel honoured to have even had the chance to stand on that spot.

================

Thanks to Chris Brookes and Martin Davies for a memorable day.

Why is it so hard to lose weight?

February 21, 2018

After several years of looking, I think I have finally found the answer.

So if people follow a calorie-controlled diet based on government guidelines, almost everyone will put on weight.

Let me explain…

Mifflin St Jeor

The minimal basal metabolic requirements (BMR) of a human being have been the subject of scientific study for more than a century.

The best estimate of our requirements are the Mifflin St Jeor (MSJ) Equations which state that the calorific requirements for men and women are given by:

Men:     BMR = 10 × [Weight in kg] + 6.25 × [Height in cm] – 5 × [Age in years] – 5

Women:     BMR = 10 × [Weight in kg] + 6.25 × [Height in cm] – 5 × [Age in years] – 161

This is the amount of food (expressed as kiloCalories (kCal) per day) required to maintain a given weight and do nothing else: no exercise at all.

A sedentary male lifestyle

The MSJ equations are generally multiplied by a factor to reflect the amount of physical activity one undertakes during the day. And there is considerable uncertainty about which factor applies to any particular individual!

The factor 1.2 is commonly chosen to represent a “sedentary lifestyle”. In a moment I’ll come back to whether this factor is justified or not.

But based on this factor, the blue line on the graph below shows how the actual calorific requirements of a man of my weight and height vary with age. The equivalent graph for women is shown in the next section.

Calories versus Age

The most striking thing about this graph is that the actual amount of calories I need to maintain my weight (1860 kCal/day) is 25% less than the government recommend (2500 kCal/day).

The difference is not a rounding error – it amounts to 640 kCal/day which is a reasonably-sized meal!

A man of my age living a sedentary lifestyle and following government guidelines would put on weight at a rate of several kilograms per year.

The second striking feature of the graph is reduction in calorific requirements with age. The slope of the graphs is 50 kCal/day per decade.

This means that if I was maintaining my weight in my forties, then unless I changed either my eating habits or my exercise habits, I would slowly begin to put on weight.

Eating 50 kCal/day too much amounts to putting on weight at around 2 kg per year.

Is the sedentary lifestyle factor 1.2 appropriate?

One way to assess whether the factor 1.2 applied to the MSJ equations is appropriate is to consider the calorific equivalent of some exercise.

For a man of my weight and height, running 1 kilometre uses up about 74 kCal.

So if I were to run 25 km per week, then this would allow me to eat about another 260 kCal/day and still maintain my weight. This is shown as the red line on the graph above.

Most people would consider running 25 km per week to be quite serious exercise. Comparing this amount of exercise to the work done in a sedentary day makes me think that the factor 1.2 is probably about right.

Women

The equivalent graph for women is shown below

Calories versus Age Women

It shows a similar disparity between government recommendations and actual metabolic requirements, but not quite as dramatically wrong as for men.

Government Guidelines

The reason I searched out the MSJ equations was because I know from experience that if I eat anything close to 2500 kCal per day I put on weight.

Calorific intake is notoriously difficult to estimate with an uncertainty better than about 10%,  but the MSJ figure of about 1860 kCal/day for a man of my age weight and height seems about right.

The UK Government guidelines are – frankly – nonsense, and given that the UK has something of a problem with obesity – not least with people of my age – it would seem a sensible first step to just get this simple factual message about right.

One important step would be to emphasise the reducing calorie requirements with age.

Government guides in the US such as this one are closer to reality, but if you want real information I recommend this helpful calculator.

Mugging

February 18, 2018

IMG_6849

After writing about ‘singing glasses’ previously, I was discussing the effect with my friend and colleague Andrew Hanson.

Have you done the mug thing?” he asked. And proceeded to hit the rim of a mug with a spoon.

As he moved the location at which he struck the mug, the pitch of the note changed.

And then he explained. Looking from the top, if the handle of the mug is at 12 O’clock, then:

  • Striking the mug at 3, 6, 9, or 12 produces one note – a lower note.
  • Striking the mug between 1 & 2, between 4 & 5, between 7 & 8 and between 10 & 11 produced a second note – a higher note.

Mug Vibrations 01

Andrew said the explanation was that in a mug, there are two types of flexural oscillations, and the frequency of the oscillations depends on whether the handle moves or not.

I was fascinated. How had I never noticed that before? And why was the note that sounded when the mug was struck ‘on the quarter hours’ lower?

This is a very long article, and I apologise. But the physics of this phenomenon is complex and it took me a long time to get to the bottom of it.

Investigations

I picked 5 mugs from our domestic collection which were as straight-sided as possible, and which had walls which were as thin as possible. I thought these choices would make the vibrational spectrum simple.

First I measured the mugs: their diameter and the wall thickness, and then I picked a wooden striker and started hitting the mugs. (Speadsheet)

The place where one strikes the mug produces an oscillation with the striking location as a local maximum of the oscillation.

For a glass, it wouldn’t matter where one struck – any location on the rim is equivalent to any other. But for mugs, the striking position matters because of the handle.

Mug Vibrations 02

To see if I could understand what was going on I arranged the mugs in size order, from the smallest radius to the largest and struck each one three times at each location.

You can hear the sound here.

I also recorded the ‘spectrogram’ using the wonderful Spectrum View app for the iPhone. A screenshot from the app is shown below together with the mugs which made the noise.Mug Vibrations 03.png

A spectrogram shows:

  • time along the horizontal axis
  • frequency along the vertical axis
  • and the loudness of a sound at a particular frequency and time is shown by the colour: blue is quiet and yellow and red are loud.

On the spectrogram above one can see vertical lines which result from the ‘impulse’ sound of me hitting the mugs. This dies away quickly and one is just left with the ‘ringing’ of the mugs which I have outlined with dotted lines.

One can see that each mug rings at two closely-spaced frequencies. The two notes differ in frequency by between 5% and 15%.

Hitting the rim at either location produces mainly one mode of oscillation, but also a little of the other.

Let’s get numerical!

I used the app to locate the frequency of each note and plotted it on a graph of the frequency versus the mug diameter. I plotted each ringing note as a red dot, and their average as a black dot.

mug-vibrations-04.png

There was a general trend to lower frequency for the larger mugs, but the Toronto mug didn’t fit that trend.

I noticed that the walls of the Toronto mug were much thicker than the other mugs. So I wondered whether I could compensate for this by dividing the frequency by the thickness of the wall.

I did this based on the idea that the speed of the wave would be proportional to the  rigidity of the mug wall against bending. And that rigidity might be roughly proportional to the wall thickness. This seemed to be confirmed because the formerly ‘anomalous’ mug frequency now sat quite sweetly on a smooth trend.

Mug Vibrations 05

Now that the data seemed to fit a trend, I felt I was getting a handle on this problem. Could I understand the dependence of the resonance frequency on diameter?

Frequency

All waves obey the wave formula v = f λ. That is, the speed of the wave, v, is the product of the frequency of the wave, f, and its wavelength  λ.

For the waves on these mugs, the wavelength of the wave which runs around the rim of the cup is just half the perimeter i.e.  λ = π D/ 2 where D is the diameter of the mug.

  • So if all the waves travel with the same speed, then the resonance frequency should vary with diameter as f = 2 v / (π D) i.e. inversely proportional to the diameter.
  • However, for flexural waves, the material supporting the wave becomes floppier at longer wavelengths, and the speed of a flexural wave should fall with increasing wavelength. If this were the case we would expect the resonance frequency to vary inversely as the diameter squared.

Which of the above cases described the data best? I have plotted the two predictions on the graph below.

Mug Vibrations 06

I adjusted the speeds of the waves to match the data for large mugs and then calculated how it should vary for smaller diameter mugs.

Overall I think it is the theory in which the  speed of the flexural wave changes with wavelength that matches the data best.

Test

So now I had a theory that the speed of a flexural wave that runs around the rim of a mug is:

  • Proportional to the wall thickness
  • Inversely proportional to the diameter
    • So the resonance frequencies are inversely proportional to the diameter squared.

After I had finished all these measurements I came across another mug that I could have included in the study – my wife’s ‘Do more of what makes you happy‘ mug.

I decided to see if I could predict its resonant frequency from measurements of its wall thickness and diameter.

I have plotted data on this mug as crosses (×) on the graphs above and I think that overall it fits the trends rather well.

The two notes

If you belong to the minority who have read this far, then well done. It is only you who get to understand the final point about why the ‘quarter hour’ notes are lower.

What is the role of the handle? There are two possibilities.

  • Does it act as an extra mass which slows down the wave?
  • Or does it provide extra stiffness, which would speed up the wave?

Since the quarter hour notes are lower, it seems that it is the extra mass which appears to dominate in the mugs I have examined.

mug-vibrations-07.png


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