Welcome to today's exciting episode of "How Big a Dork Am I?" Today, we'll be discussing the making of unnecessary models:
In this graph, the blue points represent the average mass in grams of a fetus at a given week of gestation, while the red line is the mass predicted by a simple model treating the fetus as a sphere of uniform density with a linearly increasing radius.
The "model" was set up by taking the 40-week length reported at BabyCenter, and dividing by two to get an approximate radius for the spherical baby. Then I assumed that the actual radius increased linearly from zero to the final value, calculated the volume of the sphere, and multiplied by a constant density to get reasonable agreement between the model and the data.
If you take the numbers I put into this, and use them to estimate the mass of a cell in this model baby, you find that a cell with a volume of one cubic micron (10-18 m3) would have a mass of about 50 femtograms, which is kind of low, but remarkably good for such a silly model.
Oh, the things I will do to amuse myself...
Medicine & Health
Physical Science
Comments
That's some serious procrastination you've got going there. Grading? Writing up a paper?
Posted by: Aaron Bergman | May 20, 2008 2:43 PM
That's some serious procrastination you've got going there. Grading? Writing up a paper?
I was between a couple of meetings, and trying not to grade lab reports.
Posted by: Chad Orzel | May 20, 2008 3:48 PM
NERD!
(Also, there's no error bars.)
Posted by: John Novak | May 20, 2008 4:07 PM
Would this be a perfectly smooth, frictionless, spherical baby?
Posted by: dr. dave | May 20, 2008 4:36 PM
Inspired by the ultrasound pictures downblog:
What is the mass of the Star Child at the end of 2001: A Space Odyssey?
Posted by: Captain Button | May 20, 2008 5:00 PM
When is this kid due again? You have way too much time on your hands.
Posted by: Romeo Vitelli | May 20, 2008 5:02 PM
Here I am being an ambulance-chaser theorist. Why should the radius increase linearly with time? Here's my theory: because the rate at which nutrients can enter the fetus is proportional to the surface area (maybe). According to this theory, we would predict: (where M = mass, A = surface area, and t = time)
dM/dt = k A
where k is an empirically determined constant. Assuming that M scales as the cube of some characteristic length, R, and A scales as the square of R, then we have
k1 d/dt (R^3) = k k2 R^2
where k1 and k2 are two other constants. This
simplifies to
d/dt R = k k2/(3 k1)
We can absorb k1, k2 and the factor 3 into
the unknown constant k to get
d/dt R = k
Do I win? Isn't that even dorkier than your original post?
Posted by: Daryl McCullough | May 20, 2008 6:02 PM
Should reach 9.2 metric tons in 10 years. Hope your floors are reinforced.
Posted by: Anonymous | May 20, 2008 6:28 PM
Congrats, by the way. It's blissfully enjoyable until they learn to talk. Anyway, I actually think that is pretty darn cool, by the way.
Posted by: Ian Durham | May 20, 2008 8:42 PM
Congrats, by the way. It's blissfully enjoyable until they learn to talk. Anyway, I actually think that is pretty darn cool, by the way (the graph).
Posted by: Ian Durham | May 20, 2008 8:43 PM
John Novak: Also, there's no error bars.
They just don't show up on the graph...
The data are specified to +/- 1 gram. I'm sure that makes sense. Really.
dr. dave: Would this be a perfectly smooth, frictionless, spherical baby?
But of course. Can't you tell from the ultrasounds?
(Actually, Kate would probably beg to differ regarding the "frictionless" part...)
Daryl: Here I am being an ambulance-chaser theorist. Why should the radius increase linearly with time?
It's not, really. You can tell from the graph-- the slope of the model is too high early on, and too low later. A somewhat higher power would probably be a better fit-- taking out the early part (which is fairly close to exponential, almost doubling every week) and the last three points, weeks 16-40 fit pretty well to t^4.
Linear growth is the easiest thing to simulate, though.
Yes, I just cranked that into Excel and had it do a power-law fit. God, I'm a dork.
Posted by: Chad Orzel | May 20, 2008 9:04 PM
I would have tried to model it with the logistical equation.
Posted by: miller | May 21, 2008 12:16 AM
Since your baby is expanding linearly with time, Ω → 0. I'm sure you and your wife are glad that his/her self-gravity isn't significant.
Posted by: Luke | May 23, 2008 2:42 PM