"The 33"-Road Bike Racing - Heart rate as a convolution of effort?

So, I was thinking on a ride yesterday about how heart rate relates to effort.

Say you are at a low, Z1 steady state. If you go 100% for 10 seconds, your heartrate hasn't even begun to catch up by the time you stop. It spikes, maybe 10 seconds after that and depending on your fitness it recovers after....some amount of time.

So, at any time, the heartrate that a monitor measures is affected by the work load you have put on your system over the last 1-2 minutes (plus a combination of your fitness and overall tired-ness. TSS or something for those of you with powermeters and too much time on your hands).

My idea is that your "effort" is much more consistent with your power output than your heartrate. I don't think that that's a stretch.

Ok, so you take your effort and convolve it with a Lorentz/Gaussian function centered some few seconds before now. The shape of this curve is determined by a number of things.
1) the number of seconds before now that most affects your HR is something I need to determine through testing
2) The long range tail will also be affected by your fitness. If you're in great shape, you recover faster and are therefore less affected by how hard you were working 2 minutes ago.


My theory:
http://i153.photobucket.com/albums/s240/jnoffsinger/conv.jpg

The whole point being, if you can deconvolve the measured heartrate against your personal recovery function, you get something that looks painfully like a power profile.

ta-da.

^ Buy a power meter.

Google "heart rate kinetics." Lots out there. Tricky problem.

You also have to factor in your training load over several days or weeks, your hydration level, your mental state (in a race your HR might be higher due to the mental stress), the ambient temperature, humidity and airspeed, what you ate for breakfast and the last tiime you had sex (with or without a partner). Add in terms for the above and you'll have a good equation for how HR relates to power output.

Your equations assume a purely Aerobic function right? How realistic is that? I am not sure if you can ignore the anerobic effort

It’s fun to play around with (for me at least), but it doesn’t work very well. HR just isn’t responsive enough for short efforts (t1/2 ~30s), and for longer efforts HR drift complicates things.

However, I agree that a lot more information can be gleaned from HR data than people think.

Your equations assume a purely Aerobic function right? How realistic is that? I am not sure if you can ignore the anaerobic effort

It will suffer greatly when P > PVO2max, but not that badly between FTP and PVO2max.

ok, as suggested by curveship, I did some googling
http://jap.physiology.org/cgi/reprint/81/6/2500

the above paper has some segments related to what I was thinking, although their mathematical methods leave something to be desired. It seems they just assume an exponential tail to steady-state, which may not be bad, but I was thinking fitting to a single (more complicated) function, not 3 simple tails.

cmh is just being contrary. whatever, man. Obviously there is training drift (see the comment on TSS in my OP), and the data isn't that useful IN THE FIELD. Where the real benefit would come would be post ride/race analysis.

If you want to gauge efforts for 1 minute intervals, then HR is not for you. For 5 minutes intervals, HR is probably not for you. 20 minute efforts....now we're talking. Also, you don't look at your HR in a race, so it would be VERY interesting to see the affect of adrenaline on the system. Obviously any testing, etc, would have to be done with a powermeter for calibration, and the analysis I would do would HOPEFULLY not look anything like everyone's least favorite powermeter, the iBike.

The idea, however, may not provide any real training benefit, but would be more of a study on the human
repiratory/aerobic system. I'm sure there is plenty of stuff out there, but whatever.

I'm not going to claim I am experienced in this field, and a bit of reading is necessary, but I think more of a correlation can be drawn than people think. At any rate, it's an interesting problem and something to think about. In my field we try to whittle a problem down to it's salient details and then model from there. After you have a baseline then you can start to include effects such as the last time the subject made passionate love to himself.

(plus a combination of your fitness and overall tired-ness. TSS or something for those of you with powermeters and too much time on your hands).


Um... I take about 10 minutes per day downloading and looking at my powerfiles. "TSS or something" reduces the amount of time I take to plan workouts.

You probably spent more time googling heart rate whatever than I'll take all week looking at my powerfiles.

VW

Um... I take about 10 minutes per day downloading and looking at my powerfiles. "TSS or something" reduces the amount of time I take to plan workouts.

You probably spent more time googling heart rate whatever than I'll take all week looking at my powerfiles.

VW

it was a flippant comment. no offense. I'm obviously spending more time on this than I really should.

I haven't looked at that kind of math since grad school, and I ain't gonna do it on BF.

But carry on...

It seems they just assume an exponential tail to steady-state, which may not be bad, but I was thinking fitting to a single (more complicated) function, not 3 simple tails.


An ever increasing number of terms is not the answer, trust me. :)



For 5 minutes intervals, HR is probably not for you. 20 minute efforts....now we're talking.

It works surprising well for intervals even as short as 2min. It should also come as no surprise to anybody that HR is highly correlated with average power for steady state efforts and for very short on/off intervals (eg 15s).

I got a nice little sample of this on my first lap around my neighborhood with a power meter...

http://www.photoscene.com/kimandsteve/images/3495.png

I got a nice little sample of this on my first lap around my neighborhood with a power meter...

http://www.photoscene.com/kimandsteve/images/3495.png

Wow. thanks UMD. If I look at the 10s spike around 1 minute as a delta function, it's pretty easy to see how the idea has some merit.

Integrating your power against some sort of lorentzian seems like it would give a result very nearly the HR. If someone wants to send me a data file or two (all i need is power, hr on a time axis), then I can play around.

thanks again.

UMD -- did you just get that? I figured you already had a PM

It’s pretty easy to predict the shape of the HR plot from power data. Use an exponentially weighted moving average with a half-life value of ~30s (alpha =0.0465).

EWMA
http://upload.wikimedia.org/math/5/8/d/58d7ee77df3201aa5ea95c7a380e2a45.png

This was a warm-up followed by 2x10min work periods that both average 250W -but differ significantly. The efforts were bracketed with 5min@250W for “calibration” purposes. All efforts were preceded with 5min@150W to establish baseline.

http://i168.photobucket.com/albums/u164/Enthalpic/PNworkload.jpg?t=1198473508

http://i168.photobucket.com/albums/u164/Enthalpic/PNHR.jpg?t=1198473464

http://i168.photobucket.com/albums/u164/Enthalpic/PNormalizations.jpg?t=1198473738

Ignore the 30s moving average plot; I was playing around with power normalization functions at the time. Just compare the shape of the HR plot and exponentially moving average power plots.

Ergometer + HR data recorder = tons of fun for a sports science geek.

I would be interested in a power prediction function that uses both the current HR value and at least the first derivative. Obviously if your HR is rising quickly you are working at a much higher power than the current HR would suggest.

P ~ c1 (HR) + c2 (d/dt HR)

You might also be interested in how a HR monitor can be used to monitor training status and even prescribe training intensities.
http://www.bikeforums.net/showthread.php?t=360040

ok
cmh is just being contrary. whatever, man.



Yeah, sorry. I was being contrary. Since I don't have a power meter, I do use HR to gauge long tempo rides and intervals down to about 10 minutes in length. And I allow a lag at the start of any interval for my HR to catch up to keep from starting out too hard. I suppose this is what you are getting at, but with a more formal approach. I still don't think you will get much useful training info out of it, but if it is fun for you, have at it.

enthalpic, good stuff, again.

I think the derivative is the crucial point, as you've suggested. I'm worried that the sampling rate of most HRMs is not fast enough to get a good value, especially since the function to be plotted depends heavily on the derivative. This is where post-processing would be helpful. Unfortunately, PP in the field is more or less a no-go.

I feel there is a lot of training info to be had, although clearly it wouldn't be as useful outright as a powermeter. Additionally, everyone likes to do "10 min at 105% FTP" and such. Just as has been suggested, what if you've got a wicked hangover and forgot to eat breakfast? Is your FTP the same?

I don't know, but if you get plot some sort of "effort number", that's the point of the intervals anyway. On days when you're feeling good the numbers would be similar, on bad days they might differ.

I also have no experience with the anaerobic side of HR data, so that's a factor that gets ugly. Maybe there is some way of quantifying it?

I've got something to sleep on, at least.

the analysis I would do would HOPEFULLY not look anything like everyone's least favorite powermeter, the iBike

The iBike works well. Probably an order of magnitude better than what you're attempting. There's HR drift within a ride, decreasing HR inertia in subsequent efforts, stroke volume changes between rides, etc etc.

On the macro scale, though, TRIMPS works pretty well as a replacement for TSS.

Forgive my small brain and lack of advanced math skills. Can't comment on the formula or Enthalpic's always cogent insight. But in layperson's experiential verbiage:

A powermeter is absolute relative to it's inherent accuracy (+/- factor and calibration). FTP IS a moving target, but it's a comparatively easy power over time determination. And it can, for the most part, be plotted over a broad curve (hangovers excepted). And those FTP exceptions usually give
ample physical notice.

HR is much more of a guess. It's a huge leap over PE training, but still much more a shot in the dark. This thread actually sparked me to review some ride files; there are times when there's a very linear HR/P relationship, there are other times when I'm left scratching my head. Sometimes my HR is quite high relative to P, other times I can push the wattage while my HR is lower than expected.

This, BTW, is usually a good tip off that I'm heading on the wrong side of a peak; the other cause seems to be a short warm up.

But without the power data, it's much more of a guess.

HR is much more of a guess. It's a huge leap over PE training, but still much more a shot in the dark. This thread actually sparked me to review some ride files; there are times when there's a very linear HR/P relationship, there are other times when I'm left scratching my head. Sometimes my HR is quite high relative to P, other times I can push the wattage while my HR is lower than expected.

This, BTW, is usually a good tip off that I'm heading on the wrong side of a peak; the other cause seems to be a short warm up.

Are you saying that you are heading off the peak when you can push wattage while your HR is lower than expected, or when it is high relative to power?

Coffee is one variable that changes my HR (higher) even with the same power output.

Pushing hard w/o a proper warmup also gets my HR higher for a given power output.

Are you saying that you are heading off the peak when you can push wattage while your HR is lower than expected, or when it is high relative to power?

Lower HR. Really becomes evident in TT's, it might take me 10 minutes into the event to see the HR I would normally expect. It's an odd sensation, kind of a disconnect between the muscles and the aerobic system, where my legs will feel like I'm pushing more watts than I am, but my HR and breathing pattern will indicate a lower wattage.

Lower HR. Really becomes evident in TT's, it might take me 10 minutes into the event to see the HR I would normally expect. It's an odd sensation, kind of a disconnect between the muscles and the aerobic system, where my legs will feel like I'm pushing more watts than I am, but my HR and breathing pattern will indicate a lower wattage.

I guess that is where I'm confused. Do your legs feel like you are pushing more watts, or are you actually pushing more watts. I've certainly had the feeling where I was pushing hard with a low HR but my speed disagreed with my legs. Now in the short time I've had the power meter I've watched it happen (low HR and less power than it felt like I was producing), but I've also seen the opposite where my HR was lower and I actually was producing more power. It seems that would be a good thing, no?

I guess that is where I'm confused. Do your legs feel like you are pushing more watts, or are you actually pushing more watts. I've certainly had the feeling where I was pushing hard with a low HR but my speed disagreed with my legs. Now in the short time I've had the power meter I've watched it happen (low HR and less power than it felt like I was producing), but I've also seen the opposite where my HR was lower and I actually was producing more power. It seems that would be a good thing, no?

That's the difference between the "no chain" feel of a peak and the "wow, this hard but I must be putting out some wattage here...nope" feeling when you're falling off the peak.

Both tend to show a lower heart rate relative to PE. Aside from the "yesterday's news" effect.

Which is why racing on a HRM is, for me, a bad option.

And other than the first 10 minutes or so of a TT, my PM is pretty much a black box flight recorder to be examined later too. But the PM is a huge training aid, and HR data is good stuff to review.

That's the difference between the "no chain" feel of a peak and the "wow, this hard but I must be putting out some wattage here...nope" feeling when you're falling off the peak.

Both tend to show a lower heart rate relative to PE. Aside from the "yesterday's news" effect.

Which is why racing on a HRM is, for me, a bad option.

And other than the first 10 minutes or so of a TT, my PM is pretty much a black box flight recorder to be examined later too. But the PM is a huge training aid, and HR data is good stuff to review.

Gotcha... if I manage to get my Quarq onto my race bike, I'll have to figure out if I want to leave power on the display or take it off...

Lower HR. Really becomes evident in TT's, it might take me 10 minutes into the event to see the HR I would normally expect. It's an odd sensation, kind of a disconnect between the muscles and the aerobic system, where my legs will feel like I'm pushing more watts than I am, but my HR and breathing pattern will indicate a lower wattage.

I get a disconnect on longer rides. At > 2hrs I often see a lower HR for a given speed, meaning im more efficient when tired? Dont have watts to back this up, its gotten a little more pronounced with age.