Gray Matters

Migraine and marihuana

dahlem — Sun, 29 Aug 2010 08:06:20 +0200

I just read a comment about my visual migraine aura video in YouTube

The shaping and flashing of it is near perfect; however, it needs Color, and, some auras loop into a closed figure, while expanding outward. Your simulation seems most accurate near the end of it, when the aura is larger and wider. I'm very very pleased that so many people are doing simulated Auras for migraine sufferers, this is extremely important educational information. I wonder if anyone has studied to see if weed has any treatment effect on migraine? I would use it if so.

I guess that this questions was asked by many people and probably answered by some of them in a self-experiment.

30 minutes or 19 years—know your risk

The video shows a neural network simulation of a visual disturbance that lasts in migraine usually about 20 to 30 minutes. However, in rare cases migraine aura can be longer. If it lasts longer than 7 days, it is diagnosed as persistent migraine aura symptoms (aka visual snow).

In an internet survey initiated by Sofia Green, three people reported that persistent visual disturbances have occurred after using marijuana for the first time. All symptoms lasted many years, in one case for 19 years. You can read on the Migraine Aura Foundation more about this kind of Cannabis-induced persisting perception disorder.

Top down physiology

dahlem — Sat, 07 Aug 2010 08:24:02 +0200

Nature repeatedly reinvented certain control strategies shared among different body systems to maintain our physiological machinery. Each strategy not only works in a generic way and it also can fail in a generic way. Understanding these universal mechanisms can help to infer from symptoms the underlying pathology.

The two previous posts What is physiology? and Physiology organized by major body systems lay the basis. However, you don't have to read through these posts to understand this one.

Their distilled version is that in physiology we mainly study functioning of major human body systems. Like, for example, the respiratory system, and the blood and circulatory system. Just to name those systems that will also be mentioned in this post. Of course, there are several more human body systems and there is also non-human physiology.

These posts (initially I planned three, this being the last, but there will be more) were written during my preparation for a course "Dynamical Diseases". In this one, we will mainly learn that there are typical patterns how biological regulation systems work—and fail.

The 30,000-foot view

Physiology is the science of biological regulation, in technical terms, it is about closed-loop control systems. Pathophysiology is about the failure of such control systems. That’s the 30,000-foot view. This was correctly diagnosed in another blog. The question is, what can we see from far distance? Is it relevant for clinical reasoning?

In the previously reviewed editorial of Acta Physiologica we read [1]:

[T]here is [...] an underlying necessity for thorough knowledge and understanding of the basic sciences, like medical physiology. It is well appreciated that basic sciences support sound clinical reasoning and are indispensable for understanding pathological mechanisms [...]

I am convinced that this 30,000-foot view provides exactly this: an indispensable viewpoint for understanding certain pathological mechanisms, because it focuses on the overarching theme how physiological systems work and fail.

Physiological processes are dynamic

By their very nature, physiological processes are dynamic processes! The aim of these processes is to preserve a certain stable physical and chemical environment for the organs. Stable can mean constant, e.g., think about your body temperature. But more often it means a stable periodic oscillation, like a beating heart or a breathing pattern.

Even a seemingly stable situation is dynamic. Photo: thanks to Eckhard Pecher

Physiological control mechanisms keep the physiological quantities (e.g. body temperature, heart rate, etc) in a certain range. Let it be the amplitude range and/or frequency range. Furthermore, some quantities (e.g. body temperature) must stay within that range even if outer body conditions change, while others (e.g. heart rate) must adapt to changing conditions (e.g. running).

There are thousands physiological quantities that must be controlled within the human body. Yet their respective control strategies narrow down to far fewer. In other words, nature repeatedly reinvented generic control strategies and implemented these in various different body systems.

Even more important is the next point. A specific control method, say one that achieves a constant but adaptive period, for example, one that controls the heart rate, usually fails in only a few generic ways. The physiological target state can become unstable only in certain generic bifurcations. If, to stay with this example, the physiological heart rate becomes unstable, is is attracted to a new stable pathophysiological state that could cause fibrillation. An example for a failure due to a bifurcation in another major body system is the Cheyne-Stokes respiration, an abnormal crescendo-decrescendo breathing pattern.

This is what the concept of a dynamical disease is about. It is a top down description on the level of bifurcations, that is, rather abrupt transitions from a healthy into a diseased state.

Not all diseases are dynamical diseases. A physiological target state can drift, maybe because an antagonistic interaction is weakened, without causing an instability to occur. Usually, you can infer from the dynamics of the symptoms and physiological measurements whether the underlying disease is a dynamical one or not.

The details have to be worked out. This requires some knowledge in nonlinear dynamics. This is what my course at the TU Berlin is about, but it is clearly beyond a blog post.

(Just to be clear on this, knowledge in nonlinear dynamics is required to work this out—you don't need this to infer from symptoms the diseased state and the corresponding best therapy. I do not claim that all medical students must master complex mathematical tools. Quite the contrast, I prefer physicians who are extremely experienced and open minded. Usually I don't care about their math skills. Yet in medical research math matters.)

What is next

I will give later more examples, in particular, cardiac arrhythmias , the already mentioned Cheyne-Stokes respiration, seizure activity, migraine with aura, and others.

Furthermore, I will review the historical context and argue that the industrial revolution in the nineteenth century was the midwife when this mechanical view on the physiological machinery saw the light of day.

Literatur

[1] Luc Snoeckx, Minimum standard and learning outcomes in physiology required by the Bologna process: the Federation of European Physiological Societies end-terms of physiology in a medical curriculum, Acta Physiologica, 200:1-2, 2010.

Note

In German we should translate the word control as Steuerung or Regelung and not merely as Kontrolle.

Physiology organized by major body systems

dahlem — Thu, 05 Aug 2010 18:37:52 +0200

It may seems stubbornly self-centered, but it does make sense to organize physiology by the major human body systems. In fact in Europe, the minimum standard and learning outcomes in physiology will soon be organized this way thanks to the Bologna process.

What happened so far?

The previous post, this post today, and a third upcoming one all summarize my first lecture within the course "Dynamical Diseases". The complete course will be held the first time in the winter semester 2010 at the TU Berlin. Writing these posts is part of my preparation.

In my previous post "What is physiology", I reported on my search in various encyclopedias for an informative definition of physiology—I was really surprised how this failed.

You don't have to read through the previous post, but you should have a first idea what physiology is: namely the "study of the functioning of living organisms". Furthermore, "[p]hysiological processes are dynamic [...] aimed at preserving a constant [...] internal environment" (both citations are from the Encyclopædia Britannica). This post is mainly about living organisms and their constituent parts. The next post is about their dynamics.

It is all about functioning

Things living things do, have, or can be done with: all that is biology. Divided into branches it is morphology, taxonomy, embryology, genetics, ecology, and physiology.

Physiology—the white bubble within the gray biology bubble shown above—is about the functioning of living organisms. It is not about, for example, form and growth of living organisms (or parts thereof). That much we understand already. Well, form and growth may be closely related to functioning but this would be another story.

Let us try to take the easy road and keep things separated. Once we have order, we can start to soften boundaries. Thus, let us ask:

Which parts are functioning in living organisms?

I will only talk about humans. There is no good reason for this except for the self-centered stubbornness of human beings (including myself). Of course, there is also plant physiology, avian physiology, or even deep-sea diving physiology, just to name some exotic facets of this discipline. But let us start with ordinary humans.

What are the constituent parts of human beings? And keep in mind, we still only talk about functioning. Yes, I have a little toe, two actually, but as far as functioning is concerned, there is not much to say about these little guys. Frankly, they are useless. Function implies purpose.

What are my functioning parts, or yours for that matter? Sounds like a simple question, right?

Who can name the major body systems by heart? Heart, little hint here. Correct, one is the circulatory system. It consists of the heart, blood, and blood vessels. Eight more major body organ systems are missing. Come on, name them ...

I am honest with you. I could not. Now I can but not before I got prepared for the upcoming lecture.

One obvious way would be to open a (human or medical) physiology text book. Although again, it is surprisingly difficult to get right to this list. There is another source, thanks to the Bologna process.

It happened that I just read the editorial of the current issue of Acta Physiologica [1]. This is the official journal of the federation of European physiological societies. (It is always a good idea to read through the main current literature once you give a course on a subject!)

In this editorial, the minimum standard and learning outcomes in physiology are addressed. Such a standard is required by the Bologna process to achieve the harmonization of the European university systems. So members of a Task Force for Education have to construct a list of objectives in physiology, which can then be used as a guiding principle for physiology curricula. While this is still work in progress, these objectives, or end-terms that is how they name it, should be organized according to the major body systems. Eleven major body systems are identified:

the central and peripheral nervous system,
skeletal muscle system,
respiratory system,
blood and circulatory system,
water and salt homeostasis system,
urinary system,
endocrine system,
reproductive system,
gastrointestinal system,
metabolism, and
thermoregulation.

Of course I cross checked the list. And I found one missing major body system: the integumentary system (skin, sweat glands and stuff like that). Oups. I hope my skin still belongs to physiology and will not be sacrificed by the Bologna process.

If you read carefully till here, you noticed that I said above that there are nine major body organ systems. Now Acta Physiologica published a list of eleven plus one that is missing. There seem to be three too many.

Well, the water and salt homeostasis system, metabolism, and thermoregulation are not really related to organs. Actually, neither is the endocrine system related to (only) one organ. Moreover, metabolism could also be placed into the field of biochemsitry. But as I said, let us keep it simple. All these are functioning system of a human (and many more living organisms).

So the picture seems to me that we have eight major body organ systems, one multi-organ system and three major body systems that do not relate to organs explicitly. All are functioning systems and therefore are in the center of interest of physiologists.

I don't know about you, but I learned enough today. Only two more inter-related remarks.

Is it really self-centered?

First, well, you might correctly think this is heavily biased towards human physiology. That is true, but since this list is meant to be for physiology learing outcome within a medical curriculum, I guess this list is complete (except for the skin).

In North America, students can major in physiology, but—to the best of my knowledge—in Germany you either learn physiology as a medical student or as a biology student. There is no master in Physiology in Germany, yet, or is there?

Second, I got most information from the Encyclopædia Britannica and heavily using Amazons Look Inside feature on many Physiology text books. Furthermore, to defend, at least partly, the honor of Wikipedia the major body systems will also be found there. In the article on Human Physiology. If you think it would be too self-centered to have these systems being mentioned in the main article, that is ok with me. Yet the water and salt homeostasis system, metabolism, and thermoregulation, that is, the three non-organ systems are missing. Instead, you can read there that the immune system is part of physiology. This, although there is some logic behind it, is now one step too simple.

[read on]

Note (added Aug 13)

Luc Snoeckx, head of the Task Force for Education that is to construct the list of objectives in physiology, wrote me an email with the following explaination on whether the integumentary system is missing and if major body systems are organ systems:

Indeed, we did not consider the integumentum as a separate "organ" but preferred to make it part of the 'functional' systems Nervous system and Thermoregulation. It is a choice, and I agree that it is defendable to put all the functions of the skin under one denominator.
Your second remark is also correct if you consider the organs as anatomical organs, which we did not. We preferred the functional organs, and as such the approach of metabolism, homeostasis, and thermoregulation can be considered as "functional", more than organs, which is agreed upon.

Literatur

What is physiology?

dahlem — Wed, 04 Aug 2010 17:00:36 +0200

I am a physiologist. This is my outing in three parts. First, I will show that you cannot get easily an answer to What is physiology? In a second post, an answer is coming from the editorial of the current issue of Acta Physiologica, which aims at a harmonization between European physiology curricula. Finally, I will identify overarching concepts that define physiology. These concepts date back to the nineteenth centure but are still valid today.

Actually, I am a physicist—by training. I am a physiologist by heart.

Beginning with this posts, I will explain what physiology is. This and the subsequent posts are based on the first lecture that will be given in a new course called "Dynamical Diseases", which I am developing right now for the winter semester 2010 at the TU Berlin. I will start the course with the question:

What is physiology?

Of course I have a good idea what physiology is and I had it before I decided to develop this course. But once you teach, you need a thorough understanding of what you are talking about, even about short remarks within the introductory part of the first lecture. You never know what students might ask.

So I began a journey to better understand what others think physiology is.

From the meaning of the word physiology in ancient Greek we deduce that it is the study of nature. But so is physics. And clearly physics and physiology are different disciplines.

Physiology, Wikipedia (note that this post refers to the version in August)

Here is a simple answer from Wikipedia [1]:

Physiology is the science of the functioning of living systems.

As such it is a branch of biology. Biology includes also other things of living systems like their structure, growth, origin, evolution, distribution, and taxonomy. Yet, if you read on on Wikipedia, you are not learning much more than this, except for some—incomplete—history of physiology.

(Of course, I should complete the Wikipedia entry and not complain about it. I will do so, but one thing is writing for Wikipedia, another is writing my blog post. The latter goes first because I have to prepare my classes.)

Collage of Nobel Laureates in Physiology or Medicine. From NobelPize.org

Physiology is a major discipline in science. There is even a Nobel Prize in Physiology. Actually it is the Nobel Prize in Physiology or Medicine. And, of course, there is one in Physics. And in Chemistry, Literature, Economic Sciences, and Peace.

Well, I checked all these disciplines in Wikipedia and guess what, two articles have issues. Peace and Physiology. Peace? Ok, forget about it. But physiology? Why can't we have a decent Wikipedia article on physiology (as of August 2010)?

I looked into the Brockhaus, a German-language encyclopedia. Only a sixth part of a page is devoted to Physiology. I did not get more information than is given in the first sentence in Wikipedia citet above. Then I looked for the Physics entry: over 6 pages.

Really? There is 36 times more to say about physics than about physiology? I don't think so. Now I was really curious. There is the Encyclopædia Britannica. My favorite encyclopedia. Unfortunately, it is located only in our main library of the TU Berlin. I had to walk there 15min one way, but it was worth it. (Now I wonder whether I can effort the monthly membership of €8.99 to get the online version?)

I only checked the Micropædia, i.e., the short (fewer than 750 words) articles within the Britannica. I looked for physiology and physics. This time physiology clearly won by the amount of words. More important, I got confirmed what my intuition was in the first place. Physiological processes are dynamic processes that aim at preserving a constant physical and chemical internal environment. This is an important point. Physiology is much about regulation, that is, closed-loop control systems.

This matched what I learned in 1992 when I bought my first book on Physiology. Actually my first book that dealt with life sciences. It was called "Physiologie" and was edited by Peter Deetjen and Erwin-Josef Speckmann. The zeroth chapter was written by the editors, and introduced physiology as a science of biological regulation. A perfect introduction, if you ask me. Unfortunately somewhere on its way to the fourth edition, this introduction got exchanged for a rather meaningless chapter "Physiology – ein heißes Thema" (Physiology—a hot topic). Its is all bla bla bla now. Nice to read, but no information. Sorry to say this.

Before I can come back to physiology as a science of biological regulation (third post), in my next post, we will learn about current tendencies to harmonize the physiology curriculum at European universities. There, we will take a closer look at what major body systems actually need to be self-regulated.

For now, I invite you to comment here on what you think physiology is.

[read on]

Mathematical and computational neuroscience

dahlem — Wed, 16 Jun 2010 11:11:08 +0200

Jack Cowan had a profound impact on mathematical neuroscience. A large number of his pupils hold chairs today in the field of mathematical biology and computational neuroscience. What is actually the difference between mathematical and computational neuroscience, if there is any?

There is a difference between mathematical and computational neuroscience. Jack Cowan explains it being asked by Roger Bingham:

Do you have a simple explanation, something your mother could understand, to sort of explain what you’ve been doing these past 40 years?

Cowan answers:

Well I’ve just been trying to apply the methods of mathematical physics to thinking about how the brain works. By that I mean that there is a way in which physicists approach the world, theoretical physicists, that I think really, really works and is really interesting. They don’t try to put in every detail of what the phenomenon is like. They, if they have good taste, they select only those details that are really important for the questions they want to answer. And they construct what are sometimes called toy models, which aren’t facing reality, to quote the title of a book by a friend of mine, Sir John Eccles, but they abstract from reality just what is needed to understand something. And I think that’s what I’ve been trying to do with respect to brain mechanisms: try to make toy models that contain enough details to answer questions about and give you ways to think about what’s going on in the brain. It’s not, I mean, it’s not something that’s commonly done. A lot of the time people do computational neuroscience where they put in a lot of details and make simulations and study what goes on. I don’t do that. I tend to put in as few details as possible and say things that are interesting with few details rather than put in a lot of details.

Computational neuroscience and mathematical modelling are not necessarily but quite often different approaches. Non is superior to the other. Sometimes, you need computational methods to solve even simple toy models.

I like both types of work. Mathematical modeling is much more satisfying for me because you gain a deeper understanding. Computational methods can be fun, too. Usually, you are closer to the experimental data and therefore it is easier to cooperate with experimental groups. This, of course, is essential, as only the experimental work can guide our mathematical theories.

Thinking out loud with Jack Cowan

The whole interview can be seen below and the transcript is here. There are many more comments on science today and in fomer times, e.g. rules how to publish if you want to become an amazingly successful scientist, or Jack Cowan's fascination with visual hallucinations.

Migraine - diagnostic criteria distilled

dahlem — Fri, 09 Apr 2010 14:54:50 +0200

Medical information is often given in the web. Although diagnosing yourself or even getting medical advice from the web is definately not a good idea, you can assume greater responsibility for your health by staying informed.

Over the years, people have contacted me because they recognized their visual migraine aura symptoms in my computer simulations of such visual field defects, which are presented on various web sites. Some people who contacted me had not even been diagnosed before with migraine, but later were. My impression is that quite a lot often deal with their problem alone using self-prescribed drugs for their headaches.

When a headache is a migraine

No doubt, the web has a significant impact on health care services. By providing access to medical information and advice it is possible to assume greater responsibility for your health. However, only a doctor can diagnose migraine. Having said that, the standardized diagnostic criteria that determine whether a headache is migraine or not, can be found in the web easily.

For example in less than 40 seconds, Dr. Susan Broner manages to summarize precisely these diagnostic criteria in this YouTube video.

According to the 2nd Edition of The International Headache Classification (ICHD-II) the migraine headache is a recurrent symptom manifesting in attacks that usually last 4-72 hours. Typical characteristics of the headache are unilateral location, pulsating quality, moderate or severe intensity, and worsening during physical activity.

I once summarized the diagnostic criteria in a single illustration.

Diagnostic criteria according to the International Headache Classification

A At least 5 attacks fulfilling criteria B-D

B Headache attacks (untreated) lasting 4-72 hours

C At least two of the following characteristics: unilateral location, pulsating quality, moderate or severe pain, intensity aggravation by physical activity

D At least one of the following: nausea and/or vomiting, photophobia and phonophobia

E Not attributed to another disorder

Read the complete list at the IHS website.

What if your headache attacks fulfill all but one of criteria A-E shown in the figure? It could still be a migraine. It is not that easy. There are many sub-types and a total of 23 diagnostic codes for migraine.

My advice is, go and see a doctor if you think you suffer from migraine. I am happy to talk with everybody who contacts me about visual patterns that they may see during a migraine attack. In particular, how people can provide valuable information on their symptoms for further research. But I am not a medical doctor. I cannot provide or comment on help in migraine treatment, in particular medication or other forms of migraine pain relief.

"This cannot happen"

dahlem — Sat, 27 Feb 2010 18:08:45 +0100

The statement made in the title often marks a major step in our understanding of something that happened but should not have. In a scientific context, this can result in a shift of paradigm.

This cannot happen ... unless, of course, my assumptions were wrong.

You may ask What cannot happen? I have indeed something in mind. But let me just for a little longer stay in the abstract and call it it.

It cannot happen. Three words that say so much more. Who ever said or wrote them obviously thought about the possibility of it, or was forced by someone else to think about it, but than asserts that it cannot happen.

So what is my actual topic? What is it?

Well, if you have read earlier posts, you know what will come: more about migraine research from the perspective of a physicist.

But apart from this, if we abstract the specifically migraine research content, I illustrate with examples a specific case of general interest. Namely observing something that should not have happened because it is unstable behavior (or rather an unstable solution in mathematical terms). Just look at the image above, and you will know what I mean.

Observing unstable behavior does not really contradict the theory you have, yet there clearly is a problem. Or would you ever pitch your tent near this rock?

Artefact or scientific revolution

Let me start with a simple example.

What if your are a scientist and you just have observed something that should not have happened according to current scientific believe? You are excited of course. This could manifest a shift of scientific paradigm and your are right in front of it.

To be more concrete, imagine you are interested in the theory of gravity. On a sunny day you hike through North Yorkshire, England and you see the rock shown in the image above. Intuitively, you may think:

This cannot happen. Unless, of course, the theory of gravity is wrong.

In view of the bizarre rock formation you start to ponder:

"... Maybe there is a difference between inertial mass and gravitational mass? No, that would not really explain this bizarre rock formation. Wait a minute, there may be actually nothing wrong with the theory of gravity. This rock formation is a perfectly valid solution of how rocks could behave within this theory. The only problem is that this solution is unstable! ..."

To me, unstable solutions create very interesting situations. In a different dress, such a problem puzzled me many years.

Unstable migraine waves

I was puzzling over waves in the brain that cause migraine. In particular, I investigated how are the chances that such waves can occur. You may ask How does that relate to the rock example? Well to see this, you need to replace the landscape of North Yorkshire with the landscape created by the phase space of waves described by a mathematical model.

Don't worry, if the last sentence did not make any sense.

You don't need to understand the details. Just try to imagine that we can identify within an abstract space valleys and hills, that is, stable and unstable states, respectively. This space results from a problem like the occurrence of waves in the brain. Once we have a mathematical model for such problems, that is, the migraine waves, we have also a landscape, much like in the picture below.

So the problem was that any of the observed waves in human brain during a migraine attack are more like the one shown in the middle part of the figure. Such spatially confined waves are unstable solutions and we should not observe them (unless, of course, the current model is too simple!).

Unstable solutions are not good solution to real life problems for the same reason why you would never pitch your tent near the bizarre rock. They collapse usually in no time. So I needed an extended theory like in the case of the weird rocks to explain spatially confined migraine waves.

The rocks are eroded by water and wind. This is obviously a delicate process. There is no direct analogy of the wind, water and erosion in the case of migraine waves. So I leave it at that and continue with the migraine waves.

Simply speaking, I believe the brain found a method to merge the stability of the wave shown in the left side, that is, a wave that engulfs all of one hemisphere and the spatially confined wave shown in the middle. This is a phenomenon, termed saddle-node bifurcation, that shows very universal behavior and is found in many dynamical systems. In other words, the brain found a clever way to avoid the global wave, that is, more damaging waves, and yet allow for a highly excitable medium, like the brain clearly is.

The main purpose of this blog is to explain in some loose way how mathematics and physics enters neurology. It is about creating models of the brain and investigate their descriptive and predictive power. Probably everyone is awestruck in view of the famous Brimham rocks. Unfortunately, it needs quite a bit of mathematical training to see what in a dynamical systems like our brain can and what cannot happen, or how the dynamics must be modified so that it can.

The goal is to make predictions based on such mathematical models. For instance, how to avoid unwanted behavior like migraine waves. If we can proof that the migraine waves are really created by such a saddle-node bifurcation, than we also can exploit the universal dynamics near such a phenomenon in migraine therapy.

EPILOG

If an assertion fails

It was in the early 90ties when I first read

This cannot happen.

I was, at most, only partly aware of the irony. The sentence was the message I read as a computer program crashed.

I only later learned what it meant. First, I thought this is just funny. But as I started to develop my own computer programs, I came in the situation to write programs that would crash more often than I wished. So I read books about programming, like Code Complete. One thing I learned was that this sentence was an assertion. And that such asserstions can help me to develop better programs.

In computer programming, an assertion is a programmed condition that the developer thinks is clearly true. It is good style to place assertions at routines to document what your assumtions are. Not as comments, which do not get executed, but as actual code that stops the program if an assertion fails. This should not be mistaken as error handling. Assertions check for things that should never happen, while error handling deals with, for example, the situation that the file you tried to open is defect. So, erros can happen.

To cut a long story short, if an assertion fails, something is very wrong. In a computer program, it means you should not trust the program at all. From this point on, the behavior is unpredictable, as the programmer obvioulsly did not thought about this to happen. That is why the program must stop.

The actual message in this case could be more diagnostic, i.e., describing the condition that should have been true but was not, but this is not the point here. This epilog emphasizes what assertions are good for and that it helps us to make our assertions explicit, not only in programming.

Math Matters, Apply It To Neurology

dahlem — Sat, 30 Jan 2010 22:21:17 +0100

Mathematics is as sharp as a scalpel and cuts brain malfunctioning into pieces.

The first part of my title is copied from an awareness campaign of the Society for Industrial and Applied Mathematics, better known as SIAM.

In this campaign, mathematics behind everyday life is explained on 16 posters, such as "The Math behind Stopping and Preventing Fires" or "The Math behind Cardiology and Heart Attacks".

In some sense my blog is surely also an awareness campaign:
The Math behind Neurology.

In which way do I think math matters in neurology?

The Math behind neurology

Mathematics certainly matters in many ways in neurology, but most are, in fact, not specific to neurology. Take statistics or other mathematical techniques to analyse data. Tomographic reconstruction is a good example. It is the basis of non-invasive medical imaging like CT or MRI. Without CT and MRI neurology would be quite different today. But so would cardiology.

So, which mathematical concepts are more specific to neurology? To get to this point, we should take a closer look at the brain and its functions, or rather by which means these functions are accomplished. The brain and its functions make us what we are, at least more than any other of our organs and their functions.

The brain consists of neurons that form networks, in which the neurons can synchronize their activity in infinite many ways. This neural activity in the brain forms complex spatial and temporal patterns. These pattern formation processes are to some extent amenable to mathematical analysis. Similarly, if brain functions fail to work normally, there are specific neural activity patterns that have caused this malfunctioning, e.g., neurological diseases.

Bifurcations into diseased brain states

I don't think we have mathematical concepts for what finally results from normal brain functioning, that is, for the mind. And my guess is we will never have. But we have mathematical concepts for the dynamical behavior of single cells and their activity in small networks, like reflex loops or circuits that can perform edge or motion detection tasks in our visual cortex. And there are many more such examples.

We also have mathematical concepts describing the onset of neural activity in neurological diseases, like epilepsy, migraine, essential tremor, and others. For example, how a healthy state of the brain becomes unstable and bifurcates into a diseased state.

Math can tell you whether certain states of your brain are stable or not.

Bifurcation theory is the name of this mathematical field. It provides precise definitions for transitions into diseased brain states. We can apply these mathematical concepts because these transitions, or rather bifurcations in the language of mathematics, occur in rather simple networks with simple dynamics. Such a bifurcation can be, for example, the emergence of a synchronization in the firring pattern of cells in a neural population.

Brain disorders

Why did I mention only neurology, what about psychiatric diseases? There are also mathematical concepts of neural activity related to psychiatric diseases. But, in general, psychiatric diseases are more closely related to the mind. There is almost never a simple network, as far as I know, that is exclusively affected. Mental states, diseased or not, are said to have neural correlates but they never have a clear one to one association with neural network activity, such as focal epileptiform activity causing seizures.

I am deliberately provocative at the following point. I would go as far as suggesting that if we understand a diseased state of the brain in terms of bifurcation theory or, at least, we see a chance to achieve this, it should be considered neurological by definition and otherwise psychiatric. Thus, math can be used to define a non-stigmatizing wall between neurology and psychiatry. I shall reserve that as another post to elaborate further.

Math can help recognizing symptoms

Let me give an example and consider visual hallucinations. They can be classified as simple or complex. An example of a simple visual hallucination is seeing moving zigzag lines. An example of a complex visual hallucination is seeing your high school math teacher talking to you. In the former case, you should consult a neurologist, in the latter a psychiatrist (unless, of course, your math teacher is present, than you should pay attention).

As mentioned above, there are mathematical models of the neural circuits that can perfom edge detection tasks. These circuits can be directly driven by endogenous brain activity under certain pathological conditions and thus causing visual zigzag hallucinations. A zigzag pattern is nothing but a combination of edges. Therefore, a few edge detectors, that is, certain neural circuits going mad is a rather simple explanation. Zigzag hallucinations typically occur in migraine.

I have never experienced these zigzag hallucination myself, but I built about ten years ago a mathematical model of it. That clearly was more fun than having migraine. It was a small piece of math applied to a problem in neurology. The result is seen in this video.

So applying math can help in neurology in many ways, in this example, it helped patients to recognize and communicate their neurological symptoms during migraine.

I will report in this blog mostly about my own work. And, like in this post, about the context of my research and why it matters.

Migraine light?

dahlem — Wed, 27 Jan 2010 00:37:57 +0100

Can the application of appropriate light during a migraine attack reduce its severity?

An article in Nature Neuroscience, published online two weeks ago, presents "A neural mechanism for exacerbation of headache by light" (so its title). Bright light can worsening headaches. This is known to many of us from "memories of the painful mornings after the night before", so we read in the accompanying News and Views. That is correct.

The article is about migraine headaches. It proposes a mechanism how migraine headaches can be modulated by retinal input. If light can worsening a headache, can it also help? Many sufferers escape to a dark room. Is there an alternative? A question I would like to address is, which, if any, spatial or temporal frequencies attenuate a migraine attack? That would allow us to design much simpler medical devices than the migraine zapper is.

Read on about the migraine zapper [more].

The migraine zapper

dahlem — Thu, 21 Jan 2010 04:07:31 +0100

Therapeutic magnetic stimulation in migraine is widely discussed. Known as the migraine zapper, a transcranial magnetic stimulator became an FDA approved investigational medical device. But what about other external stimulation techniques, like electrical currents or light flashes? Should we invent migraine frizzlers and migraine scintillators, too, or is that all fringe science?

The application of transcranial stimulation at the beginning of a migraine attack may abort the attack or reduce its severity significantly for same patients. This is tested in a randomized, sham stimulation controlled investigation to assess the safety and to demonstrate that the method is effective as an add-on therapy in reducing attacks.

I think the idea is great. However, more important than the actual device is, to my mind, the stimualtion technique, i.e., the software that comes with the device. Like the very same computer (hardware) can run different operating systems, such as Windows, Mac, or Linux (software), the migraine zapper can be programmed in many different ways. Software can make a huge difference, as we all know.

Migraine frizzler and migraine scintillator

We might even investigate other devices that utilize other stimulation pathways into the brain. Animal data (Liebetanz et al. Neurosci. Lett. 398, 2006) suggests that anodal transcranial direct current stimulation (tDCS)—by increasing cortical excitability—increases the probability of migraine attacks even beyond the end of its application. Techniques adopted from chaos control can predict by which means it is possible to reverse the effect and abort an attack (Dahlem et al., Chaos 18, 2008). The tDCS-based device could be called the migraine frizzler instead of zapper. Even simpler would be to use a flashing light with certain good frequencies, the migraine scintillator. Here, too, we know spatial and temporal frequencies to increase cortical excitability. One can even elicte a migraine attack using light flashes. I firmly believe that it could work both ways, that we can also abort an attack or reduce its severity by external stimulations.

For any such device, my vision is a strategy I often have paraphrased as

From bifurcation to bench and bedside.

I want to understand neurological diseases, such as migraine but also stroke and epilepsies, as emergent transient states close to nonequilibrium phase transitions in the brain. Such transitions are in nonlinear dynamics called bifurcations.

Once we understand the theoretical concepts in terms of bifurcation theory, this should tell us how to program devices like the one shown in the video.

As Vivien Williams said in the video:

It's like something you'd see on Star Trek

But I guess we still need at least a five-year mission: to explore strange new therapies; to boldly go where no man has gone before. This can probably only be done by a multi-center international group of clinical and basic scientists working together on migraine and feedback therapy.