The Steampunk Satyricon

Thursday, May 5, 2011

Placenta is Awesome!

A few weeks ago, I picked up a free copy of what has to be one of the world's geekiest newsletters: Fields Notes, a magazine-style publication about the mathematical research and activities at the Fields Institute in Toronto. One small article caught my eye -- a short blurb about something called the Placenta Modeling Group. In a couple of paragraphs, one of the group members (all students, supervised by a mathematics professor) described how human placenta was being used to study something called "Murray's law" (not to be confused with Murphy's law) and how it was involved in creating mathematical models for blood flow and vascular branching -- basically, how blood vessels grow and spread throughout an organ. I admit, I had never imagined connecting placenta and math, but it made so much sense. Here's an organ, perfectly healthy in most cases, that is simply "ejected" by a woman at the end of her pregnancy, typically without a whole lot of fuss -- why not use it for research? It's not like anyone was planning on doing anything with it, right? I became so curious about the "placenta + math" concept that I had to look into it further.

I'd heard the terms "placenta" and "afterbirth" tossed around, but when they show a baby being born on television, usually the most you ever see is part of the umbilical chord and no one ever seems to talk specifically about the placenta. And since I have no interest in being a father or getting anyone pregnant, learning more hasn't exactly been on my "To Do" list. But I'm here t' tell ya:


Placenta is awesome!

Do you have any idea how *awesome* placenta is?? Why does no one ever talk about how awesome placenta is? Is it one of those things where men who aren't doctors dismiss it as unimportant because they don't have to deal with it directly? Or maybe it's because placentas look like bloody, disgusting raw liver when they come out a few minutes after the baby. Or maybe it's kind of like the Opening Act Syndrome: people only care about the headliner (the baby) and are off buying t-shirts when the opener is on stage (in the case of the placenta, I guess it would be Closing Act Syndrome).

And, as I'm sure you've heard, there really are people who eat it. More on that later.

The placenta is formed by the trophoblast, a layer of tissue that surrounds the fertilized embryo and also forms the outer membrane that the baby sits in. Lots of proteins working at the molecular level interact to dig into mom's uterine wall and anchor the little parasite into place. Tiny tendrils called microvilli reach out like tree roots and hook the fetus into the mothers plumbing. But the placenta does way more than just hold the fetus in place. If pregnancy were a car, the baby would be in the passenger seat... the placenta would be the driver.


The placenta is the first to let the woman's body know that she's pregnant. It produces a number of hormones including human chorionic gonadotropin (HCG) which triggers the release of progesterone, a hormone that stops menstruation. (If you've ever peed on a stick to find out if you're pregnant, what the test detects is the presence of HCG in your urine.) The placenta also produces corticotrophin-releasing hormone (CRH) that basically works like a biological oven timer. CRH is released -- which in turn causes the release of other hormones -- over the course of the pregnancy until there is so much CRH in the system that the alarms go off and the woman's body knows it's time to make the necessary adjustments and push the baby out.

The placenta continues to give instructions to the pregnant woman's body in the language of proteins while it's also busy keeping the baby alive. What no one's entirely sure about is how the infant, with all of its alien genetic material, isn't destroyed by the mother's immune system (which, apparently, does happen sometimes). The current popular theory is that mom's immune system reaction is suppressed by an endogenous retrovirus (ERV) present in the placenta. Humans are full of billions of viruses, most of which do nothing to us or for us, but here is one virus that might actually be helping us. "Placental ERV... could play a role in a localized maternal immunosuppression, permitting the initial trophoblastic attachment, invasion, and overall placental survival," according to biologist and immunologist, J. Robin Harris.

One thing that is certain: the placenta keeps blood from the mother and blood from the baby from ever mixing. Sure, some stray embryonic cells from the baby might wind up in mom's bloodstream, but mostly, the placenta only allows proteins and nutrients from the mother to go in and fetal waste to go out. According to In the Womb by Peter Tallack, the fetus receives its nutrients within an hour of the mother eating.

Admittedly, sometimes the placenta isn't so awesome. It can filter lots of harmful stuff and keep it away from the baby, but things like alcohol, nicotine and HIV (the virus responsible for AIDS) are able to slip through. Sometimes, the placenta embeds itself in such a way that, once it's at its full size, it blocks the birth canal, a condition known as placenta previa that can cause bleeding and requires an un-awesome cesarean to get the baby out safely. But, for the most part, the placenta is still pretty awesome... if only because of the mathematical and research awesomeness that goes along with it.

[[YES!! MATH IS AWESOME!!! DON'T BE A BIG COWARDLY ASSHOLE!!! FACE THE MATH!!!!]]

The placenta is basically a system of pipes, just like the rest of the human circulatory system or, for that matter, a sewage system or the plumbing in an apartment building. Suppose you're an engineer trying to design a system for transporting fluids or a medical researcher trying to understand how nutrients, medicines or toxins get carried through the body. Studying vascular systems like the one found in the placenta can lead to all kinds of useful discoveries that can even be applied to the planning and creation of fabricated systems. (Never forget: Guesswork is expensive. Math is cheap.)

Whether it's air moving through a filter, water moving through pipes or blood moving through your veins, people trying to understand a fluid-transferring system find mathematical models incredibly useful (nota bene: physicists often treat gasses -- like air -- as if they were fluids because under certain conditions they behave similarly). One of the principles governing the way fluids move, one that can be confirmed using placenta, is Murray's law, named after American scientist Cecil D. Murray who, around 1926, surveyed the data and crunched the numbers that allowed him to arrive at a deceptively simple relationship.

Nature is awesome... and lazy. Nature always tries to do the most with the least. It takes power to move blood through your body, and, as Murray knew, nature naturally seeks the optimal arrangement for accomplishing its goals using the least amount of energy. Knowing this allowed Murray to derive a mathematical relationship.

It was found that the total power requirement to keep our blood pumping could be expressed by the equation
Pt = Total power
f = volumetric flow rate
r = radius of a vessel
a = a constant dependent on the viscosity of the flowing fluid
b = a constant dependent on metabolism

A word here about mathematical derivations of equations: They are very, very, very important and not to be feared! Some scientists seem to live for them. And while they are almost always a good thing to study, personally, I've come to the conclusion that even more important to non-scientists than the detailed derivation of equations is the presentation of gratuitous beefcake.


So, just imagine our friend here marshalling his skills, taking the equation for the total power required to pump blood, using his calculus to take derivatives of the function with respect to the radius and then finding where total power is minimized.

Having total faith in his mathematical accumen, we note the results...
Where
Since we want totals for all of the little branching vessels involved, we write the equation as
since  "Σ" just means "All of these things added up." Then, we do some algebra and find


Bottom line: Murray's law says that the cube of the radius of a parent vessel is equal to the sum of the cubes of the radii of the smaller, branching vessels (called the daughter vessels). The math suggests that (Σr2)t is some constant value which suggests (accurately, as it turns out) that the cells that make up the walls of blood vessels can reshape themselves in ways predicted by Murray's law. It even works when you take into account the fact that blood isn't an ordinary fluid like water or alcohol. Human blood is a non-Newtonian fluid meaning how thick it is changes depending on how fast it's moving.

Some of the things scientists do are abstract it-might-be-useful-someday research, but some is hey-I-can-use-this-right-now research. Fluid-flow research falls into both categories: It has something for everyone. The energy required to pump blood throughout your body is connected to metabolism which is connected to how efficiently your body uses the calories you ingest which is connected to the shape of your body which is connected to whether or not people avert their eyes in horror when you're in a bathing suit. Short term or long view, it's all part of getting a better idea of how our bodies work and what's happening when things go wrong.

Which brings us back to the placenta because, just like the researchers looking for fluid flow models, other researchers can examine placenta in pursuit of their own goals... for example, as a way of making better babies and healthier adults.

Just because women have been giving birth for thousands of years doesn't mean we know everything about the process or that there's no room for improvement. That's what the folks at Placental Analytics (http://www.placentalanalytics.com) are interested in: figuring out the connections between baby health, grownup health and the health of the placenta. The researchers there will tell you: "Just as the pattern of roots reflects the underlying soil's fertility and predicts the health of plants that depend on those roots for sustenance, [vascular branching] reflects the health of the maternal environment and impacts on fetal health."

If the state of the placenta was neglected in the past, that is certainly no longer true. Doctors Carolyn Salafia  and Michael Yampolsky, two of the key researchers with Placental Analytics, are among the folks leading the way in the study of the workings of the placenta. As Dr. Yampolsky told me via email, "Our general aim is developing diagnostic techniques (i.e. medical applications), using the placenta as a diagnostic tool." Judging by the research they've published, Salafia, the founder of Placental Analytics who does medical research, and Yampolsky, a mathematics professor, have probably looked at more placentas than almost anyone in human history, but that is unconfirmed. One thing is certain: They know a good looking placenta when they see one.

A normal placenta is round(ish) with the umbilical cord stuck in the middle. According to one study, an average placenta is about 18 cm (7.1 in.) in diameter. There does appear to be a relationship between the mass of the placenta and the mass of the fetus (science literati like you and I always endeavor to use the proper term "mass" while the hoi polloi limit themselves to always using the occasionally inappropriate term "weight"). Dr. Salafia and her team at Placental Analytics analyzed a buttload of data from the National Collaborative Perinatal Project (which collected data from 26,000 births) and found that


PM = placental mass
FM = fetal mass
α constant = 1.03 ± 0.17
β constant = 0.78 ± 0.02

Everyone knows how much a baby weighs at birth, but not everyone weighs the placenta and they should. You need the PM and the FM to find the fetoplacental ratio (FPR) which can be used to help determine if something went wrong in the womb.


FPR is calculated from measurements taken at the time of birth and includes an important fudge factor research-yielded scaling exponent (k = 0.75).

When the placenta isn't the nice, round pancake shape, it could be an indication that something is wrong with the baby or the mother. If the shape is really distorted, it can effect the way the placenta functions and spell problems for the baby. When that kind of significant deformation is visible, it's a sign of "fetal-placental environmental pathology" and "variable arborization" of the placental vascular tree -- literally a flaw in the way the blood vessels of the placenta are branching out.

There are common ways the placenta gets deformed that doctors don't seem to worry about as much. Familiar shapes, like a star(ish) shape, that are less worrisome for those who know. But, as the folks at Placental Analytics have found, "deviations from symmetric fractal expansion out from the umbilical cord insertion are associated with reduced placental functional efficiency, i.e., a smaller birth weight for the given placental weight." Problems for the baby can mean problems for the adult she grows up to become, but early analysis can help nip those problems in the bud. Studying the placenta is like looking at tea leaves to see the future. Large, squishy tea leaves covered in blood.

And, yes, some people eat it... but not just people. Placental mammals, animals that don't have pouches or lay eggs, are known to biologists and zoologists as eutherians. Non-human mammal moms -- like mares and (normally vegetarian) cows -- routinely eat their own placenta after giving birth. Humans get a bit more creative. In some cultures, the placenta is dried, turned into a powder and used as a medicine. Some cultures treat the placenta as a sort of failed twin -- an underachieving fetus that didn't come into its own but kept the successful baby company in the womb -- and the expelled organ is buried near the home for good luck. One young lady told me she keeps the placenta of one of her children in her freezer. And then there are those who eat it.

The proper name for it is placentophagy. No numbers on how many people partake, but one thing is clear: It takes quite a lot of work to prep placenta for cooking. A kinda-fun-but-slightly-gross web page to look at belongs to Lord Manly who offers a richly detailed cooking lesson on how to execute his recipe for Placenta Casserole (as well as an abundance of the kinds of gory pictures of the placenta that I have opted to exclude from this blog post). For Lord Manly's recipe and instructions on prepping the bloody thing, check out his blog at http://havingapoo.blogspot.com/2007/07/placenta-party.html

A baby minder. A hormone factory. A research tool. A tasty entrée. Didn't I tell you? Placenta is awesome!



Sources
  • How Life Begins: The Science of Life in the Womb by Christopher Vaughan, © 1996, published by Times Books/Random House, Inc.
  • In the Womb by Peter Tallack, © 2006, published by the National Geographic Society.
  • Making Babies: The Science of Pregnancy by David Bainbridge, © 2000, published by Harvard University Press.
  • Vital Circuits: On Pumps, Pipes, and the Workings of Circulatory Systems by Steven Vogel, © 1992, published by Oxford University Press.
  • The Journal of General Physiology, Vol. 78, October, 1981. "On Connecting Large Vessels to Small: The Meaning of Murray's Law" by Thomas F. Sherman. The Rockefeller University Press.
  • Theoretical Biology and Medical Modeling, August 2006. "Pulsatile blood flow, shear force, energy dissipation and Murray's Law" by Page R. Painter, Patrik Edén and Hans-Uno Bengtsson. BioMed Central Ltd.
  • Theoretical Biology and Medical Modeling, May 2009. "Extension of Murray's law using a non-Newtonian model of blood flow" by Rémi Revellin, François Rousset, David Baud and Jocelyn Bonjour. BioMed Central Ltd.
  • BioEssays, Volume 20, Issue 4, pages 307–316, April 1998. "Placental endogenous retrovirus (ERV): structural, functional, and evolutionary significance" by J. Robin Harris. http://www.ncbi.nlm.nih.gov/pubmed/9619102
  • "Modeling the variability of shapes of a human placenta" by Michael Yampolsky, Carolyn M. Salafia, Oleksandr Shlakhter, Danielle Haas, Babara Eucker, John Thorp. December 20, 2007. http://www.math.toronto.edu/yampol
  • "Metabolic scaling law for fetus and placenta" by Carolyn M. Salafia and Michael Yampolsky. Published June 1, 2008
  • "Mean surface shape of a human placenta" by M. Yampolsky, O. Shlakhter, C.M. Salafia and D. Haas. http://www.placentalanalytics.com

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