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Flow Rate

I received an extra credit essay from one of my students based on a question from the textbook that I had to do a little modeling to understand. The question was one about patients with atherosclerosis that could be explained using Poiseuille’s Law. This Law describes the relationship between the flow rate, pressure, radius and viscosity of a liquid flowing through a vessel.

Basically, it is presented as:

Flow Rate = change in Pressure * pi * radius^4* Length of the vessel * viscosity

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The question asks, ‘why symptoms of myocardial ischemia do not usually occur until ~75% of a vessel has been occluded.’

The easy answer is that that is the cutoff after which the amount of blood required to provide Oxygen sufficient for the heart’s metabolism is insufficient. However, this can be visualized qualitatively simply by graphing the equation. To do this, I made up a quick spreadsheet and just plugged in ‘1’ for all the variables, then solved for the flow rate. From here, I simply plugged in fractions into the radius variable.

Here’s the raw data:

Screen Shot 2015-05-08 at 5.00.16 PM

1.00 – 0.75 (i.e. a 75% blockage) = 0.25 is the number from the question. Here’s the analysis:

Screen Shot 2015-05-08 at 5.02.20 PM

Note how the Flow Rate has dropped to essentially ZERO when the radius is occluded 75%.

There may be more to this, but I think that just looking at this analysis of the equation answers a lot.

ps – I just spent a hell of a lot of time and effort messing around in the terminal of my mac changing the screen capture file type all to realize that it wasn’t my mac that was the problem at all – I simply was not using the largest image type available in wordpress and then tried to scale up my image after it was inserted – don’t do this. You lose all of your image quality.

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Posted by on May 8, 2015 in Uncategorized


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A Press a Day …

ImageTaking a page from WordPress’ Daily Post eBook, 365 Days of Writing Prompts

Have you ever made a New Year’s Resolution that you kept?”

I can confidently say, yes.


This very year, I have kept my resolution to exercise by putting in workout #1 this afternoon.

Granted, that’s a little weak to claim that one day constitutes a kept resolution, but ask yourself, have you kept your resolution this long? Or are you already making excuses that you just haven’t gotten around to it yet?

And, if it makes you feel any better, you can rest assured that the only reason I’m claiming this year’s resolution as kept is because I don’t think I can say so about many other years in the past. I often find slips of paper that say things like,

1. Get three days of exercise in a week.

2. Restrict yourself to dessert only twice a week

3. Don’t drink beer on weeknights

4. Learn Latin … etc. etc.

Typically, I get to about the second week of January and start rationalizing that, ‘There’s no way I was ever actually going to learn latin any better than I did in 10th grade. And, I guess since I’m drinking a beer, that one’s out too. But it’s really just #1 and #2 that are actually important.’

Then, another week out, I’ll think, ‘There’s no way I can keep up this exercise schedule without some kind of reward. I’m going to have dessert tonight, and so long as I keep to resolution #1, it won’t matter. Thats the important one.’

Then, probably the next night, ‘Hmmm. I didn’t exercise today even though I was supposed to. I’m not going to get dessert then. Well, unless my wife does. I can’t sit here watching her have ice cream without me.’

I have gotten so few resolutions into February, it’s laughable.

The only time I actually can make a big change is when it’s with someone else – or, even better, AGAINST someone else. I can rise to a challenge like nobody’s business. I’ve won weight-loss bets (first person to lose 10% of their current body weight). I’ve won race challenges (OK, we’re both in bad shape, but I’ll bet I can beat you in a half marathon in March). But to go it alone? It’s like Chekhov says, “Any idiot can face a crisis, it’s the day-to-day living that wears you out.”


So, bring on the crisis. That, I can do.


Excerpt From: The Editors, “365 Days of Writing Prompts.” iBooks.

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Posted by on January 2, 2014 in Uncategorized


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