Explanation of simple harmonic motion as an example of problem based learning

After exams were over this term, students doing further maths in Abingdon have the opportunity of doing a maths project. Given two weeks, we are asked to find a topic related to maths that interests us, and that we can give a presentation on afterwards. I decided to choose a simple example of a dynamical system, because they are often used to model biological phenomenon. As it happens, the topic I chose wasn't as simple as I thought, but here's how it works, from basic maths upwards:
(warning: huge post)

Blood pressure continued

Part two: why do we need such high blood pressure?

So we have seen how blood pressure can be used as an indicator of largely chronic effects, and that it is a very useful measurement to keep track of. But what about the more acute side of medicine? 

I was lucky enough to stay in cardiothoracic critical care in my local hospital for a while as part of a work experience scheme with a consultant anaesthetist (a very underrated speciality, I have decided). While I was there, I noticed that they were measuring blood pressure on almost every patient. None of the people on the ward was there for chronic problems, so why were they bothering to measure the blood pressure? 

The answer is that they needed to see whether the heart was working properly, as almost everyone there had just been in or was about to go into surgery for a heart operation. If the heart is pumping blood around the body, it will push against the outside of the arterial walls, which is what we call blood pressure. If the pressure decreases, it is likely that the heart is not pumping the blood so well, and the patient might need to be looked at in more detail.

But that is a very crude way of getting a very vague answer. What I wanted to know was what the blood pressure actually signified about the heart that the doctors were interested in. When I asked the consultant this, he answered me with another question: why do we need such high blood pressure? I'll admit, I didn't understand the question when he first asked me it. 

My first thought was that some of the organs need high blood pressure, such as the kidneys: in the nephron, blood needs to be at high pressure in order to undergo ultrafiltration. But there are very few bits of the body that are like that, so it doesn't make sense to have the whole system running under unnecessary stress. What could be the advantage of having high pressure in the system? Does it have an advantage in itself? No. The advantage of running any fluid system at high pressure is to make the fluid move fast. That's what really matters: how quickly can the blood transport the necessary nutrients to the organs, and take away the waste products.

Again, I thought I'd got it, that we needed to run at such high pressure in order to move the blood around our body fast enough to work properly. Sadly for me, it turns out that the pressure needed to move the blood around our body is much lower than the average blood pressure. All I'd done was work out the question: why do we have such high blood pressure, when the same blood flow could be achieved with much lower pressure?

Looking at it from a purely physical standpoint, it makes no sense that two different pressures in the same system can provide the same blood flow. Where is the pressure being lost? There must be some kind of resistance that we are artificially providing in order to keep flow lower than its maximum. The pressure could be coming from the organs, or the arteries. We already know that only a few organs need the maximum pressure, so it must be coming from the arteries before the blood reaches the tissue it's going to. That can easily be provided by the muscle layer in the vessels, but I still hadn't worked out why it happened, just how it happened.

Why would the body have adapted to provide more resistance in the vascular system, making more work for the heart? Because it's not a fixed system: the muscles in the arteries can relax, reducing the pressure for various tissues, increasing the flow to those organs. This means when any tissue needs to increase the rate it gets its nutrients, the resistance of the vessels supplying that tissue can drop, which makes the flow spike immediately.

So to answer the question, we need high blood pressure so that blood flow to any part of the body can be increased straight away. That doesn't really explain why they measure blood pressure. That'll be in part three.

Blood pressure

Part one: problems with extreme blood pressures

As a culture, one of the facets of medicine we're obsessed with is blood pressure. This makes sense: hypertension in particular is a big problem in the obese western world, and hypotension can be equally as serious. It's also very easy to measure, using the fantastically named sphygmomanometer, or blood pressure cuff, of which every GP has at least one.

Hypertension (high blood pressure)

Blood pressure is defined as how hard the blood is pushing against the arteries as it is moved around the body. Arteries have adapted to compensate for being pushed against by developing a layer of elastic tissue, so they can stretch with different pressures. Unfortunately, these elastic layers are not adapted to deal with very high blood pressure, when they are being stretched constantly. Like an elastic band, if you stretch an artery too much and too often, it stops becoming elastic. In the case of arteries, they harden (ateriosclerosis, not to be confused with but similar to atherosclerosis, which is also to do with cholesterol and a build up of fatty substances). Because the arteries harden, the pressure of the blood continues to be high until it reaches the arterioles, which are not developed for that pressure at all, so they burst.
This is a problem particularly in organs like the brain, where a burst blood vessel increases the pressure of the whole cranium hugely, and can leave permanent damage.
Hypertension also leads to heart failure, because the coronary arteries harden, so when more blood to the heart is needed (e.g. running for the bus), they cannot expand to allow that amount of flow, so the heart doesn't get enough glucose or oxygen, so parts of it die; which is a heart attack. Obviously that's a problem. The other way high blood pressure leads to a heart attack is that the left ventricle has to work harder to pump the blood around the body at a higher pressure, so the muscle thickens (hypertrophy). Because the muscle is thicker, it requires more oxygen and gluscose, so the same thing happens as when above.

The reason this is important in the western world is because we are increasingly ticking more and more risk factor boxes: the population is aging, becoming fatter, drinking and smoking. It can also be unsymptomatic for a long time before a huge event happens, so it is important to measure even apparently healthy people.

Hypotension (low blood pressure)

In some people, who exercise a lot, low pressure is a sign of good health and fitness. It can also be caused temporarily by alcohol, other drugs, or a postural change, among others. Mostly, it is harmless.

However, in acute and extreme circumstances, where hypotension is caused by blood loss or heart failure, it becomes very harmful. The brain (as well as other organs) doesn't get enough blood, which contains the glucose and oxygen it needs to survive, so it begins to die. This is a state called shock, which can be life-threatening. The loss of volume of blood is not always as obvious as a bleed; dehydration by diarrhoea or insufficient fluid intake can also cause hypotension, but this is likely to be less serious.

GP Work Experience

This is Wallingford Medical practice. It's a building on the side of a small stream in a town just a few miles from a train station which is two stops from my station. To the right of the picture, there's a community hospital, including a maternity ward. My week's work experience was spent mainly in the consultation rooms, but I did get to see the hospital too; thanks to everyone's hospitality, I managed to see pretty much everything.

Work starts early in GP practices; I knew that already in theory, but the reality is coffee and morning discipline. Which I actually enjoyed - getting up to do something you are really looking forward to is a great feeling.

One difference between salary doctors and partners is that partners have to work the hours to finish the work, and salary doctors only have to work the hours they're paid. I was shadowing a partner, so I was in bright and early, and was allowed to sit in on the practice meeting. Practice meetings are great at showing the business side of the general practice, something that is not so prevalent in other areas of the NHS, and it gave me an insight into how everyone worked as a team, despite spending most of their days shut off from each other in their rooms. The other thing I gleaned from the meetings was that no matter how many years you've been a doctor, there's always more to learn. In the practice meeting, two doctors were asking for study leave to go on different courses to learn about more in fields they're interested in, and in another meeting, a consultant physiotherapist came and talked about what she did and how GPs can help (when to refer, what to expect etc.).

Each day is split into morning surgery, then coffee, then visits, then lunch (meetings and paperwork), then afternoon surgery. There is also ward rounds of the hospital (which I got to shadow on the last day) in the morning, to check up on patients in the wards and reissue any drugs that needed a new prescription for.

It's hard to pick a favourite part of GP work, because each patient is so different that it's difficult to generalise. I'll probably post one or two of the cases I thought were the most interesting as individual blog posts, but the thing I noticed the most, in visits and in consultations, and in the hospital, was how much the atmosphere was moulded around the patient. Every person was different - an excited visit from an expecting young mum, a calm talk about testicles with a nervous teenage boy, a veeeerryy sloowww conversation with a depressed woman -  I could go on. 

The relationship with the doctor is also different each time, and that's one of the challenges of general practice, I think, because you don't only have to have gone through umpteen years of medical training and have the responsibility of looking after all of your patients, but also you have to be able to communicate with whoever walks through that door. Communication is different to making friends with, as well. In a lot of cases, it would be easy to let the patient tell you what they think is wrong with them and exactly what drugs they want, write a prescription, and let them go. But often, that's not what's needed, and it can be hard to tell someone that they need nothing at all, or a different treatment, or tests. Cooperation is important, and the needs of the patient come first, but a confident, misinformed person could be more of a danger to themselves than the disease they have.

I'll post more about GP work later, but this post is long enough. Bite sized work experience!

WOOO!

Finally finished my 2011 in science series. That took a LOT longer than expected. But now that means I am free to post whatever I want!
I have just finished a week's work experience in a GP surgery, which was fantastic, so I'm sure the next few posts will be devoted to that. Also making an Easter resolution to add pictures to my blags so they look less boring.

December: Microbots and Mutants

Okay, so the title is a bit of a lie. Again. But scientists did manage to grow eyes on the side of tadpoles' heads. Which pretty much makes them mutants. Why did they do this to the poor baby frogs? Well, it revealed an entirely new form of control over the formation of organs in the body. By altering voltage gradients, they were able to produce eyes in parts of the body that would never normally have eyes. While this may not have any clinical applications, it is an interesting find in the world of embryology.

Nanorobots were also new to the world in December. These are small (<1mm) machines that can be steered using magnets to the right place in the giant 3D maze of the circulatory system to detect disease and deliver the drugs needed. They have been in the pipeline since 2007, but development started in December last year.

In other science: 2 earth size exoplanets and 1 hospitable exoplanet in the Kepler system (Kepler-20e, 20f, and 22b respectively); engineers at MIT make a camera with 1 trillion frames per second, fast enough to capture light travelling across surfaces, and a potential vaccine for HIV goes into production.

November: elderly embryos and erotica

This month in stem cell news: induced pluripotent cells were created from people as old as 101, a feat which was previously thought impossible due to the ageing process of living organisms. The elderly stand to gain the most from therapies involving stem cells, so the news that they might be able to culture their own could open up new doors in regenerative medicine. Or it could confuse us even more about ageing. Stem cells were also coaxed into specialising into the dopamine producing cells that are damaged in Parkinson's disease early in the month.

On the slightly less serious side of medicine, a woman masturbated in an MRI scanner. Kayt Sukel stimulated herself to orgasm while held still in the device so that her brain activity could be monitored. It's hoped that the data might help both men and women who have problems climaxing, and also that it might offer an insight into how we feel happy.

In other science: a one molecule "car" is built; Scottish engineers start to sell their bionic legs, and the six men put into isolation 520 days previously to simulate a trip to Mars are released.