On Spencer’s curve

2000px-znak_a-1-svg1In our recent ultrasound refresher course, I tried to give a talk on the vagaries of stenosis graduation (mainly) for extracranial stenoses. The gist of the talk is outlined in the following notes.

The Bernoulli principle

While Bernoulli’s equation is rather intricate, the underlying principle of conservation of flow along a stenosed tube is simple. Consider a tube with a short stenosis with laminar flow of a Newton fluid. Then the bigger area A1 multiplied with the flow  velocity v1 (take psv for simplicity, although this is not really correct) should be the same as the smaller area A2 multiplied with v2. Thus the increase of flow is proportional of A1 / A2, so that the reduction to a third of the area leads to an increase by the factor 3 of the flow velocity, a reduction to a tenth leads to ten times the flow velocity in the stenosis.img_7579

Adding friction

Since we usually don’t observe velocities higher than 5 m/sec, there must be a limiting principle and this is the resistance offered by the stenosis, which reduces flow in the whole vessel. This resistance can be approximated by the law of Hagen-Poiseuille and is proportional to the length of the stenosis, the inverse of r^4 and the inverse of viscosity. Again, this only holds for laminar flow and the case of blood offers some more complications, but the core message is: the longer the stenosis the higher the flow reduction. Also the flow reduction grows much more with decreasing vessel diameter than the flow velocity increase by Bernoulli’s principle can compensate. Very tight and long stenoses show a flow velocity reduction despite there high grade. If you  find a psv of only 2,4m/sec this might therefore mean either a mere medium grade stenosis or a very tight stenosis (near occlusion).img_7578

Spencer’s curve

Taking these two principles into account, Spencer and Reid (in their brilliant 1979 stroke article) deduced the famous curve now known as Spencer’s curve (see Alexandrov’s papers for a more detailled exposition).

Since at the time duplex sonography was technically not feasible, the Spencer curve is based on the theoretical assumption of a 2 mm stenosis and thus does not correct for the length of the stenosis (as well as the other factors mentioned below). This explains why the cw-doppler-data in their paper does not really fit the theoretical model. Still it is the best approximation we have to a theoretical foundation of stenosis quantification.

Measuring diameters

Diameter instead of area

Most of the studies have been done with angiographic imaging of stenoses or ultrasound measurements of the stenosis diameter rather than the area. Of course, the area could easily be calculated from the diameter (r^2 pi) if it were a circle, but then it isn’t. In ultrasound we could measure the area itself (if no shadowing artifacts are present), yet no one does really. Therefore you should remember that most of calculations of the stenosis area from the diameter are systematically invalid.

Where, when and how to measure diameters

For some absurd reason, Europeans kept to the local stenosis degree (i.e., diameter of perfused lumen divided by the original vessel diameter), at least in their ECST trial, while the NASCET trial used the more reasonable distal stenosis degree (i.e., minimal lumen diameter divided by non-stenosed distal ICA diameter). Since the ICA bulb varies in its bulbiness and distends with age and blood pressure (and with stenosis degree), the local stenosis degree is usually a shot in the dark. The distal (NASCET) degree suffers from pseudoocclusion, i.e., collapse of the distal vessel in very high grade stenosis. All attempts to calculate the NASCET stenosis degree from ECST and vice versa are irrational.

Being faithful to both traditions, I measure all the lumina (minimal lumen, original vessel lumen, distal lumen). The only really interesting number is the residual diameter (combined with the length of the minimal lumen), because this determines the hemodynamic compromise.

Other important factors


Neither is blood a Newton fluid, nor is all the viscosity (rarely measured today) explained by the hematocrit alone. Yet the hematocrit is an important number to factor into your interpretation of ultrasound data. You should note it.


Every vessel wall abnormality leads to small perturbations of flow and thus turbulence. Turbulence reduces anterograde flow and thus reduces the distal pressure after a stenosis. While very hard to quantify it is essential to mention turbulent flow when you see it. Remember that to distinguish retrograde (i.e. turbulent) flow from flow increase with aliasing you need to look at the color bar on the side of your duplex image, noting that flow increase jumps over the upper limit of the color spectrum while retrograd flow (usually) passes the black zero flow region.


decreases over the lifetime, even more if severe hypertension or calcification of vessel walls is present. This, again, is very hard to quantify, but often easy to recognize qualitatively in your duplex image, when you recognize the pulsation of the vessel wall. Reduced elasticity has to lead to increased flow velocities.


Since blood flow is not continuous but pulsatile and this in varying shapes, we should really be using mean flows in our stenosis calculations. This has historically not been done. As a consequence, valve abnormalities (aortic stenosis, insufficiency) have to be factored in, when we try to calculate the stenosis degree from peak systolic velocities.

Blood pressure and atrial fibrillation

The (pulsating) blood pressure is the driving force of cerebral blood flow, trying to overcome venous and intracerebral pressure as well as the distal blood pressure offered by collaterals (see below). At least, you should note the blood pressure and relativize your stenosis graduation in cases of extreme values. When the patient has atrial fibrillation, you probably should use an “average” heartbeat rather than the extreme values. But bear in mind that absolute arrhythmia is a risk factor for arterioarterial embolization in itself.

The geometry of the stenosis

usually is far from being that of a tube. Rather, the blood flow curves around plaques, rotating and hitting small plaques on the distal wall. Again, the effects are impossible to quantify, but at least the geometry should be noted. The shape of the stenosis area should be remarked upon, if it isn’t circular.

The role of collaterals

The pressure difference along a stenosis is not only determined by the resistance of the stenosis itself, but also by the collateral blood flow which leads to an increase of distal pressure (mostly but not only in diastole). This leads to a reduction of the blood flow velocity in the case of good collateralization, thus also reduced flow velocities.

The danger of a stenosis

In the neurovascular clinic, I try to estimate four risks of a stenosis: the hemodynamic risk (what happens if the stenosis were to increase?), the embolic risk (how high is the risk of an embolic event from the stenosis?), risk factors and other risks.

Hemodynamic risk

The hemodynamic risk is determined by

  • the current hemodynamic compromise (jet flow velocity, CCA flow vs. ICA flow, pulsatilities, MCA flow, CO2 reserve)
  • the dynamics of the stenosis (how long has this been going on? was there time to develop collaterals?)
  • the completeness of the circle of Willis (variations such as A1 hypoplasia, Pcomm hypoplasia)
  • secondary stenoses in the collateral circulation.

The problem is that we cannot foresee whether the stenosis will be slowly progressive or suddenly close up (as in plaque rupture). At least in asymptomatic stenoses I require CT- or MR-angiography to determine the completeness of the circle of Willis.

Embolic risk

The embolic risk is determined by

  • Plaque morphology and
  • Plaque type
  • Whether the atherosclerotic process is active or burnt out.
    As in coronaries, it is not reasonable to revascularise every severe asymptomatic stenosis. But in a patient where the overall atherosclerotic process is currently active (after an NSTEMI, say), we can expect the plaques to rupture.
  • Previous embolic events can be noted on MRI.
  • Emboli detection
  • Is the anti-platelet medication working? Multiplate or similar tests.

Risk factors

  • Did the patient stop smoking? How long ago?
  • Can we use high dose statins in this patient? Statins are highly effective against plaque deterioration, but also have serious side effects (less exercise tolerance, diabetes, muscle problems), especially in the high doses we like to use for severe stenosis.
  • Is the patient’s blood pressure controllable? Note that severe stenosis lead to very labile blood pressures as one of the most important sensors of the system is damped.
  • Exercise? Although this has not been studied properly in carotid artery stenosis, I surmise that health by fitness should improve the prognosis of carotid artery stenosis.

Other risks

  • Central or mixed sleep apnea syndrome – very prevalent among ICA stenosis patients, leading to a bag of systemic problems, not the least being poor blood pressure control.
  • Bad blood pressure control (see above)
  • Development of secondary stenoses in the collateral vessels (contralateral, ECA, …)
  • Development of a collateral rete with its danger of bleeding


I don’t see any better physical theories coming. Also, we can never expect better data than NASCET and this is a bad foundation. Therefore you have to tackle all the complexities outlined above and refrain from simplifying an ICA stenosis to a mere number (always the worst approach).





ICU fever

Differential for (new, resistant) fever in the acute care ward aka ICU.

  • Wrong site:
    • The obvious five: lung, lines, abdomen, skin, urine
    • The hidden five: endocarditis, meningitis, translocation, sinusitis, abscess
    • The weird fevers: drug, central
  • Wrong bug – viruses, fungi
  • Wrong antibiotic – wrong spectrum, MDR pathogens

DNI/DNR and what it means

As you probably know, doctors love DNI/DNRs and everything that clearly prescribes what to do. So the first thing we try to establish with an elderly seriously sick patient is whether intensive care or resuscitation is really an option.

Yet a DNI/DNR label might signify many things to the team:

  1. In an emergency, don’t tube, don’t CPR
  2. Avoid advanced and invasive treatments, such as operations for intracerebral hematoma
  3. If in doubt, don’t try to cure the patient, prefer comfort measures in a palliative setting.
  4. The prognosis is judged to be bad, either mortality-wise or with respect to quality of life.

Although meaning 1 is usually what is intended and agreed upon, meanings 2 and 4 are often used as reasons, and meaning 2 is sometimes implied, even if – as in our house – the difference is made explicit even by SOPs.

Concerning prognosis, we know that

  • Neurological emergencies are very hard to prognosticate in the first 24, even 72 hours
  • Even epidemiological data is scarce – the best evidence exists for mortality of intracerebral hemorrhage (e.g. ICH score) and proximal occluded cerebral arteries; quality of life is a different beast altogether.
  • Stating a prognosis early leads to self-fulfilling prophecies

Our discussion of the subject does not lead to clear procedural standards, but it sensitizes…




Even in the most advanced discussions of modern times’ patient management, I have not once met a colleague who understood p-values. Not that I do.

In last Friday’s session we did the classical experiment (described e.g. in this article) of offering various choices of an explanation of how to interpret p-values to the audience, with actually none of them correct. Which is funny. Then we discussed the core definition. Which is simple. And worked through the examples on the Wikipedia entry (by the way: Wikipedia provides excellent articles on statistics!), such as computing p for simple random variables (such as the number of heads in n tosses of a coin). Which is hard.

Just for completeness: the p-value is the probability of obtaining the data’s test statistics or more extreme values, assuming the null hypothesis to be true.

Unfortunately we did not get far enough to discuss the Bayesian alternatives to p values and their decision theoretic applications.

Here are my take home messages:

  • p-values are a statistical property of the data.
  • You require a statistical model and have to assume the null hypothesis to be true to be able to compute them.
  • They say nothing about the truth of the null hypothesis or (even less so!) any alternative hypothesis.
  • They may increase with effect size yet small effect sizes may have the tiniest ps and vice versa.
  • They cannot be compared among studies.


Central venous access

Have you ever experienced the following: you instruct a peer in how to do a particular procedure while he is doing it, but then realize that you cannot really presuppose knowledge about the theoretical facts, such as indications, anatomy and so on?

We use the case of central venous catheter access to review the most important indications, anatomy, differential access site indications and so forth, then go through the basic steps and try to list details that you could never explain if doing a live instruction.

References: any modern ICU book. I use Irwin & Rippe’s, which is rather conservative. For some cool facts, I can recommend the book Evidence-based critical care.

Blink reflex

Starting with a patient with probable Fisher syndrome, we discuss the various ways to electrically image the brainstem. Here is what we came up with (there are other tests for research purposes, but this is what we routinely can or should be able to do):

  • Blink reflex
  • AEP
  • Calorics or rotating chair, or better: quantitative Halmagyi
  • VEMPs (we don’t do these, but they are easy to perform)
  • of course: long tracts (SEP, MEP)

We plough throught the neuroanatomy of the blink reflex, it’s technical aspects and various lesions with their typical and atypical blink reflex pathologies.

The blink reflex used to be an issue in the seventies and eighties, then with MRI we rediscovered it’s localizing potential (as opposed to – say – the masseter reflex). But it is really only useful if the MRI is negative, i.e., in those MRI-negative strokes and inflammatory lesions as well as cranial neuropathies. In the case of the latter I have to admit that a proper examination is often more effective than a good blink reflex.

As for references I turn to my beloved book on neurophysiology, which is now available in a new edition.

Windows 8

This is not really about medicine, but filled some of my weekend – so here it is, my Windows 8 experience.

Maybe I am not cut out for using modern operating systems. I just managed the switch from Win7 and XP to OS X – worked like a charm (no pun intended). Then I was so annoyed with the waiting time in Windows 7 that I upgraded to Windows 8. I expected many problems with the UI, the start screen, but the speed increase promised so much relief that I went online to buy Win8 for our living room all-in-one touch Medion computer (not too fast, not too slow, running Win7 with Media Center for TV).

This blog entry reflects my first 20 hours.

I download the upgrade manager from the home page and start it – so far, no problems. A “compatibility check” opens, shows this neat little half circle of circling dots that replaces our old hourglass. Nice.

After about 5 minutes I begin to wonder what my computer is doing. No progress bar in sight. Frozen? What happened to the splash screens of good old Windows 98, providing you with information about new features in every step of the installation? But no, this is a modern computer with a sleek no-nonsense no-information designed UI, beautifully colored empty space without text.

After about 10 minutes it comes up with some questions and then requests me to buy the upgrade with my credit card. Then it starts downloading which is quicker than I thought. After about an hour it awakes and starts – after a few questions and an EULA – to prepare the preparatory steps (this is their lingo, not mine). As it discovers that my Bluetooth driver (which came with the computer) is not Win8 compatible, it commanda me to uninstall the driver. I call up the deinstallation goody and deinstall. After 17 minutes I become suspicious: progress of 17%. It turns out that you cannot deinstall, if an upgrade is ongoing. Yet the upgrade can’t continue with the old driver on board. You can’t kill the process. So I reboot the machine and restart the upgrade, after the compatibility check and some more questions (I have signed 3 license agreements on my computer and a few online up to this point), I am led to the purchase page for Win8. But wait, I have done that already, right?

Google reveals that you can find a secret installation directory on your C drive under C:/ESP – you can restart from there.

This time, somehow the Bluetooth driver (still happily residing in my programs list) is not so harmful, so the installation continues, requiring two more license agreements to be signed. Interestingly, each has a new list of small print texts to be exhaustively read. We end up with a check of installation readiness (“Installationsbereitschaft”) – mine is steadily decreasing, the system dies again for about half an hour without any sign of life, but we are used to that. Then a question pops up: “Do you want to install [this and that]?” I thought, I’d have signaled my wishes clearly, but yes I do. Then a message: your PC is going to reboot a few times, which can take a while. OK. Let’s see. I would watch a video, but then my TV computer is rebooting currently, so I take out my Mac and reminisce about the upgrade to Mountain Lion a few weeks ago, which took exactly 15 minutes.

A few alarms later, Windows 7 is rebooting, asking five times, whether it really should reboot. It seems to be reluctant to give up. Then it doesn’t reboot, it just hangs. I kill the PC with the power button and restart. It hangs for one hour. So far so good. Then the happy half circle, thank God, it is alive. “Preparation is going on…” No progress bar, of course. Then, after 10 minutes: “2%”. Progress. Speed. Technology. This is a new era of user friendly operating systems.

I’ll spare you the next 2 hours. It eventually came up and asked me for my email address. I know that from OS X, so I supply my information and can login. Somehow my user has been morphed from my former Win7 login to this user. The other ones have been thrown away. I start the marvelous UI, get the new start menu and there are plenty of tiles, moving and changing beautifully. So I click on Fotos to see my old fotos. But the library I had is gone. Let us reconfigure. But wait, how? Of course, change to the desktop. No problem. Win + D still works. My libraries of images, videos and stuff are gone. My media center is gone. Still, the files remain. So I add my external foto drive to the image library again and switch into Metro. Neat. Yet there are no pictures in my library. Sad. But then, after about 5 minutes: a picture. One. Only. Of about 1033. Why has it chosen this one? Is it because people are smiling on it and this is the new UI? Only smiling people.

I’ll have to google that. I start the Internet Explorer and am taken away from the beautifully animated Metro world into Desktop hell. Somehow IE doesn’t know how to live in Metroland yet. But it can search. Unfortunately, it only searches in Bing. What the heck, they must know the world even better than Google. Bing comes up with a news entry in a blog that tells me how to get IE into Metro: you have to declare it your standard browser. You cannot do that in Metro. It turns out that you can change at most 4 settings in the settings charm menu in Metro – the rest is over on the Desktop. But how do you reach settings there? You right-click on the non-existent Start menu. Then a disordered list of leftovers appears, containing good old system preferences, where you can change settings. I activate IE as the standard for all HTML and throw in a few of other file types – we are generous today. Somehow, this is not enough. I close System Preferences, restart it and – voila – you can make IE the tile explorer as well. Switch back to Metro (this is really simple, as the Start Menu is just below where it was in Win7), start it. Sadly, the search engine here is a different one than in Desktop land. So switch back into Desktop Internet options – there is a lot to change. Fiddle around with the search engines, kill Bing as an option. That’s it.

Back to Metroland. Type in Media Center. Gone. Where has it gone? Right, it is still there, but not licensed. So fire up a browser, type your email into the homepage and obtain a license key for free. Great opportunity. But the email doesn’t arrive. In Junk mail? No. Just no email.

So now I sit here without TV. Might just as well get used to all the new gestures. My touch screen, it turns out, is not perfect for Win8, because the margin is not continuous with the screen (4 mm difference). So it is not always possible to call up the task list. But you can use the mouse for it, moving it into the SW corner and down, where it shows the tasks. The SE corner is for charms, but only every third try actually opens the charm menu. The other ones just didn’t work. I also cannot close windows with gestures, but what is ALT-F4 for, anyway? The browsing experience is great, though. Nearly as good as on my IPad. Yet I cannot edit the favorites. To switch to a new tab, I need to what? Right-click the upper margin. This is not too bad, I can do that.

What is wonderful that there are always preferences at hand, in the charms menu. The choice is a bit weird, though. For instance you cannot change what you want to. Also, the search gadget doesn’t find the preferences entries.

Next, I try what actually was my reason for the upgrade. Wake-up time. Let us through the thing into sleep mode. But how? No start menu, no sleep. I might press the power button, but remember that I used that for hibernation. So reconfigure? Too much of a hassle, takes forever to find the place where you configure that. No, the answer is the Charms menu. There, hidden under Settings is a way to send the computer to sleep. Only 3 mousemoves. That is impressive. So it goes to sleep. Some flickering. Gone. Press a key on the keyboard (my touch screen is too much asleep), a beautiful homescreen comes up. How do I get rid of that? No instructions. Try some swipes. Down, left, right. Up is the answer. Than a password is required. But wait, I booted this computer without password, because otherwise my wife wouldn’t be able to watch TV without knowing my password and I have to keep those secret. So a new login for my wife? No, this would require adapting the settings once more and this takes to much time. I erase the Email and change the password. Of course, this can’t be done in Gagaland, have to switch to System Settings once more.
You know what. The Desktop actually looks the same as in Win7. Even the unique new task bar is nearly the same. The only thing is: I cannot spawn the Start Menu with my touch screen any more. Icons have grown smaller everywhere, maybe because Aero is gone. Thus I cannot use the Desktop with Touch at all.
What remains though, is the awkward way, the Desktop behaves if you have a Beamer installed, but not running. Windows appear in the virtual space of the Beamer Desktop, but are nearly impossible to pull back onto the visible Desktop.

Next step in Desktopland: inspect the System Settings. All is well, here. The backup machinery stopped to work. It nowadays only backs up your personal files and settings, because you can always pull your software out of the Internet. Haha, very funny. But finally, they reinvented Time Machine of OS X. Marvelous idea, so much innovation.
What else could they copy from OS X: the copy manager is revamped. After 20 years of despair when copying more than one object, the system doesn’t forget the rest of the copy task, if one fails. This is really brilliant. I’d probably pay for the upgrade just for that. If I hadn’t lost the TV functionality.

I’ll wait for one more day and play around. But it might be easier to buy an iMac.