Mathematical rambling on the topic of altitude acclimatization

Well, you warned people, there’s a lot of math in that blog.  I could keep up with it just fine, and I think you’ve got the variables dialed in pretty well.  A bit conservatively, IME, but then I get less severe AMS less often than most people do.  I still get it and have spent decades pondering when it was worst, better, and how to minimize it.

What I may have learned from your presentation, is the potentially significant benefit of pausing at some moderate altitude, even for 4 hours.  I hadn’t thought of steps that short – more of days, maybe half-days at the least.  But again, I think your model is fairly accurate, so I’ll believe that your “what-if?” scenarios with and without the short stops are accurate, relative to each other.

One variable I’m not sure you’ve factoring in, other than in the pauses, is the level of exertion at elevation.  Living at sea level, getting to a 7,000-foot trailhead ASAP, and hiking with a heavy pack over a 10,500 pass: yeah, that will make your head pound and your guts puke.  But zooming up to 8,000-9,000 and sitting in a lawn chair reading a book – for me – doesn’t wipe me out.  And yet it seems to acclimatize me.  Hiking at a moderate pace with a UL pack is in between.  Not as risky as going heavy weight.

And a simple thing:

>”Drive up from the Bay Area in the early morning”

WTH do that?  Pack your bags in advance, and leave straight from work the previous evening.  Sure, there’ll be a traffic jam getting through Livermore and over the Altamont, but have a campground or inn picked out around 5,000 feet.  I’d say a bit higher, but that’s often the highest elevation I could park my car and sleep for free outside a national park.  Even leaving work at 5 pm, catching a bunch of traffic, then dinner in Oakdale or Big Oak Flat around 7:30 pm and I’d still be ready to get into bed at 9 pm, 10 pm at the latest.  No rush the next morning, I’m already almost there and there’s no traffic at 6 or 7 am when I drive into the park and get to the trail head.  Plug that into your model and the whole purple curve will be reduced greatly.

Short version: Don’t sleep at sea level if there’s ANY way you can sleep at 5,000 feet and get 8-10 hours more adjustment before hitting the trail.

fun read! though i skipped the equations / mostly just looked at the pictures and thought, ‘cool.’

here’s some math that you probably already know: how much diamox are/were you taking?

250mg 2x/day is what it will say on the bottle, but 1/2 that is common for hikers. fewer side effects and similar efficacy. and i’ve at least read about people taking 1/4 of the label (62mg 2x/day).

there’s a good facebook group about altitude run by a nurse. it’s pretty diamox-centric, but there are some smart people there as interested in this stuff as you!

ha, ha, good one : )

when people climb Mt Everest, they hike a few thousand feet higher, then back down and sleep over night.  Then back up to that altitude and sleep over night.  Then repeat with then next altitude higher.

how does that fit into your model.

I’m like you, 10,000 feet and I start getting headaches

I did South Sister.  Camped at trailhead 5000 feet.  Maybe 8 hours to summit a little higher than 10,000 feet, approximately constant slope.  I got a severe headache (maybe 1/4 of the way up your shittiness scale) so I immediately went back down 1000 feet and felt fine.  It seems like your model has a delay from getting to altitude and feeling shitty, but it seems pretty instant to me.  Maybe I’m misinterpreting that.

Very interesting. You may need to add another factor to your model though: very long-term acclimatisation. Sue and I pop up to almost 6,000′ on a regular basis and feel nothing at all. One time to 10,000′ briefly (Europe) was not a problem. Even 15,000′ for a night or two (Nepal) was OK. But those were after many years of up and down. You may find the same yourself.

On the other hand, there is some evidence that spending too long at high altitude trying to acclimatise may be counter-productive. Your red cell count climbs – but it can climb too far.

Clearly, further research and more data is needed. You will have to do many more trips up there … :-)

Cheers

I joke that most of my acclimatization these days is sitting, watching a movie, at 33,000 feet, and having another beer every time the flight attendant comes by with the beverage cart.  But I actually have noticed a slight benefit coming off of 2-3 days with lots of flights prior to something like a GCNP hike.  A few dozen hours at 7500-foot air-pressure (that’s what they pressurize passenger jets to) is better than none for those of us who live at sea level.  I certainly retain fluids after several flights just like I do after a Whitney trip.  By 2 days later, I’ve pissed it away, but I’m typically 4-5 pounds heavier after two nights of red eye connections (4 to 6 flights).

Thread drift

“Even leaving [The Bay Area] work at 5 pm, catching a bunch of traffic, then dinner in Oakdale or Big Oak Flat around 7:30 pm”

Maybe from Pleasanton. I live in the South Bay.  If I left at 500pm, I risk being barely past Tracy 2 hours later.

A few dozen hours at 7500-foot air-pressure (that’s what they pressurize passenger jets to) is better than none for those of us who live at sea level. 

Yes, some very serious things there. The air pressure for international flights used to be held at a somewhat higher altitude, and Sue found that very hard to handle. A few years ago they lowered the effective altitude (ie increased the cabin pressure), and since then Sue has not had nearly as much trouble. I commented on this to a flight attendant one time and she agreed, saying that they (the hosties) found it a lot less tiring as well.

The reason for the lower air pressure is simply the fuel cost of running the compressors; the reason for increasing the pressure is to attract more customers. But the airlines are very shy of talking about this – perhaps for fear of media attention or regulations requiring even higher pressures.

EDIT:
Wikipedia has an interesting article on this. It seems that within the USA air space planes are already subject to cabin pressure regulations, with the pressure requirements going up. And the airlines and manufacturers are getting the message:

The cabin altitude of the Boeing 767 is typically about 6,900 feet (2,100 m) when cruising at 39,000 feet (12,000 m). This is typical for older jet airliners. A design goal for many, but not all, newer aircraft is to provide a lower cabin altitude than older designs. This can be beneficial for passenger comfort. For example, the Bombardier Global Express business jet can provide a cabin altitude of 4,500 ft (1,400 m) when cruising at 41,000 feet (12,000 m). The Emivest SJ30 business jet can provide a sea-level cabin altitude when cruising at 41,000 feet (12,000 m). One study of 8 flights in an Airbus A380 aircraft found a median cabin pressure altitude of 6,128 feet (1,868 m), and 65 flights in a Boeing 747-400 aircraft found a median cabin pressure altitude of 5,159 feet (1,572 m).
(Source: Wikipedia)

Cheers

Roger, when did you notice a difference?  I’ve been seeing 7500-8000 density altitude for 15+ years now.  I haven’t checked recently but I’ll bring an altimeter on my next flight (which is really annoying to nerdy types who want to explain to me why it doesn’t work inside the plane and I don’t explain why/how I’m using it, so they get to remain annoyed).

But I’m almost always on 737s with only a dozen flights each year on Airbus products or on long-haul jets (that fly a bit higher, typically).  I’ll check it out on my next long flight.|

(Even further) thread drift:  Anyone know if oxygen concentrators are seeing use in the Himalayas?  They’ve reached a point that even with the battery weight, they give more hours of supplemental oxygen per weight than oxygen tanks do (plus you can recharge them yourself!) so they’ve taken over the home-health and increasingly the travel-oxygen markets.

David said:

What I may have learned from your presentation, is the potentially significant benefit of pausing at some moderate altitude, even for 4 hours.

That was really a surprise to me, too. I thought it would take >8 hours to have any measurable affect. But, perhaps not. Mathematically, there isn’t much acclimatization that occurs over that four hours (less than 1,000 feet). But my trips tend to take me just over the cusp of where problems begin to occur (in other words, I could go to 9,000 feet without problems, but just over 10,000 feet, and I definitely have problems). That extra 1,000 feet of acclimatization can be the difference, in those cases (or, so says the model).

One variable I’m not sure you’ve factoring in, other than in the pauses, is the level of exertion at elevation.

Yeah, that’s true. My data is pretty much limited to reasonably consistent behavior; hikes in which I pretty go at a constant (and relatively high-level) effort. It’s probably not very accurate if you deviate from that significantly.

”Drive up from the Bay Area in the early morning”

WTH do that?  Pack your bags in advance, and leave straight from work the previous evening.

It’s great advice; in fact, this year, I started to do more of that. The thing that’s time constraining for me isn’t solely work, though–it’s family. There’s getting the little ones ready fed and in bed each night, and get dressed and out the door each the morning. Those are the windows of time that I’m trying to maximize. So, if I go right after work, I miss essentially another half-day with them (compared to driving up early). What I have done is leave around 8:00pm or thereafter, just after they’re in bed. That works pretty well. Sometimes, it’s still not quite enough acclimatization to be completely liberated–but it definitely helps.

Ben said:

here’s some math that you probably already know: how much diamox are/were you taking?

250mg 2x/day is what it will say on the bottle, but 1/2 that is common for hikers.

On the first trip, I took 250mg per day, although I took it 2x per day at 125mg each. The second time, I was planning on halving that, but it was after the first dose that the chest pain ramped up pretty significantly, and I decided I was bailing before the time for the next dose came around.

Next time I try it, I’ll probably try 125mg per day, to see how it goes.

Jerry said:

when people climb Mt Everest, they hike a few thousand feet higher, then back down and sleep over night. Then back up to that altitude and sleep over night. Then repeat with then next altitude higher.

how does that fit into your model.

Yeah, that’s the best way to do it, so long as when you come back down, you come back down below the threshold of … lousiness accumulation (something makes me feel as though I should be a little less cavalier with my language here). That way, you force a large delta between acclimated and actual altitude during the day, which forces your body to acclimate more quickly. If you accumulated any … lousiness … during the day, it will dissipate. I’ll make a plot that demonstrates this later, and post it here.

It seems like your model has a delay from getting to altitude and feeling shitty, but it seems pretty instant to me. Maybe I’m misinterpreting that.

No, you’ve got that right. My experience has been just that: I can go to pretty high elevations from sea level (I’ve got from sea level to 11k multiple times, and 12k a few times) without any immediate symptoms (well, sometimes a little wooziness or lightheadedness, but hey–it’s like getting high for free). However, it’s after I linger for a few hours that I start to feel lousy. And lousier. And lousier. Even if I stopped ascending long ago.

That said, we all know that people have diverse physiological responses to altitude. I’m definitely on the more sensitive end, but undoubtedly there are others who are more sensitive. Likewise, the symptoms I develop (and the rate and order in which they develop) likely vary from person to person.

That’s what makes this model perhaps interesting to others, but probably not applicable–at least not directly.

Roger said:

You may need to add another factor to your model though: very long-term acclimatisation. Sue and I pop up to almost 6,000′ on a regular basis and feel nothing at all. One time to 10,000′ briefly (Europe) was not a problem. Even 15,000′ for a night or two (Nepal) was OK. But those were after many years of up and down. You may find the same yourself.

On the other hand, there is some evidence that spending too long at high altitude trying to acclimatise may be counter-productive. Your red cell count climbs – but it can climb too far.

Yeah, I think the phenomena that this model is useful for explaining is limited to the narrow band of scenarios that I expose myself to: A sea-level dude goes up to 9k – 13k rapidly, frequently enough that the problem is vexing, but infrequently enough that there’s little to no residual acclimatization between trips (probably–not sure how settled the medical science is on this).

Clearly, further research and more data is needed. You will have to do many more trips up there … :-)

I joked about this with my wife: “I’m really close to a breakthrough. But, the data set is not convincing. I’m going to take a sabbatical next July through October in order to gather data. For science!”

Of course, a good data set would consist of trips that went pretty far over the line–there would be a lot of “lousiness”. Kind of reminds be of the entomologist who intentionally got bit/stung by dozens of different kinds of insects so that he could semi-objectively rate the pain of each.

And the side-topic:

Even leaving [The Bay Area] work at 5 pm, catching a bunch of traffic, then dinner in Oakdale or Big Oak Flat around 7:30 pm

Maybe from Pleasanton. I live in the South Bay. If I left at 500pm, I risk being barely past Tracy 2 hours later.

I have a pretty hard time making it past the Black Bear Diner in Tracy without a stop, regardless of traffic. But I’m in Livermore–a quick escape from the Bay Area *should* be easy for me.

Hi David
Roger, when did you notice a difference?  
Maybe about 5-6 years ago? But note: my data set is fairly restricted: Cathay Pacific long-haul Australia to Europe. (We fly CP because their business class seating arrangements beat the hell out of most other airlines, and I will NOT fly coach class any more. Sorry, but I just won’t! Not for a 24 hr flight.)

Adam – I am sure there is a whole lot more to it. I do remember us climbing slowly up to some small peak in Nepal – puff puff puff. Sue was not real happy on top and wanted to go down fairly soon. She RAN down the hill! Very clearly, the level of exertion has something to do with it. Maybe the slowly increasing air pressure is also significant?

Cheers

“Your red cell count climbs – but it can climb too far.”

And thicken your blood to a dangerously high level.

One thing that hasn’t been mentioned so far is how you train for rapid ascents to the relatively high altitudes of the Sierra. My personal experience based on 36 years of going over the high passes of the Eastern Sierra, for what it may be worth, is that training to make the maximum use of what O2 is available as you ascend rapidly from 4-6K feet to 11.5-12K feet is well worth the effort, and may be done while living at sea level. I have found a combination of endurance training well within my aerobic zone combined with relatively extended efforts, 1-1.5 hours near my anaerobic threshold has allowed me to make ascents over passes/cols such as Shepherd, Taboose, Baxter, and Lamarck in one day without ill effect and keep on going from there. I hypothesize that the key is to develop not only cardiac endurance, but also higher stroke volume, denser capillary networks in the working muscles, and more and larger mitochondria, the idea being to get whatever O2 is available to the mitochondria efficiently enough to produce the ATP necessary to keep moving in an O2 constrained environment. Other factors of importance are carrying a lighter load and moderating the pace, both already mentioned, as also staying hydrated, and ingesting only simple carbohydrates, which require minimal digestion and far less O2 to metabolize than either fat or protein. I am only an experiment of one, but this approach has made a major difference for me since I adopted it. Like many, I started out with heavy loads, far less rigorous training that I now do, more complex food, and less attention to pace and hydration, and suffered accordingly. My 2 cents. FWLIW.

Edited: One other factor, again already mentioned, it the benefits resulting from spending at least a few hours at 4-5K feet to prime the acclimatization pump, so to speak. In my case, I typically fly from Seattle to Reno, which is at an altitude of 4400′, drive down to Bishop, CA, which is at an altitude of 4000′, and spend a day there acclimatizing before I start a hike. The drive down takes ~4 hours at an average elevation of ~6000′. So, all in all, I will have spent ~40 hours at an elevation of at least 4000′. Having come from sea level in Seattle, this no doubt stimulates the body to begin making the biochemical adjustments to the higher altitudes I will rapidly encounter once I begin my hikes. For acclimatization, the most difficult of the passes I have hiked on the East Side is Lamarck Col, with good reason. Not only is it at an altitude of 12,990+ feet, but the trail head is at 9400′, reached by driving up from Bishop(elev. 4000′) in ~30 minutes. That is a step function increase in the demands placed on the body by the rapid increase in altitude, and requires special attention to pace and hydration. I ran into trouble the first two times I did it by hiking too fast. This is probably the situation most similar to the one Adam faced when driving up to Tuolumne Meadow from sea level and immediately trying to hike up to Vogelsang with a heavy pack, FWIW.

Other factors of importance are carrying a lighter load and moderating the pace, both already mentioned, and also staying hydrated, and ingesting only simple carbohydrates, which require minimal digestion and far less O2 to metabolize than either fat or protein. 
Just so. At very high altitudes, or  at lower ones with a heavy load, even sugar and water can be quite tasty :-) But fats … difficult.
Cheers

“And thicken your blood to a dangerously high level.”

Which is solved (for males) by frequent blood donations.  If you don’t consistently injury yourself and eat tasty critters (moose, caribou, red salmon), IME your “crit” can exceed desired levels.

Giving blood drops it several points and they give you cookies and juice!

“I’m going to take a sabbatical next July through October in order to gather data. For science!”

Good idea : )

Adam,

As a geezer I am not as subject to altitude sickness as younger backpackers. In fact I’ve never experienced it, even at 12,000 ft. All I experienced was fatigue.

But… when above 8,000 ft. every morning I always take 3 tablets of NO2 Red (from GNC). This stuff is really time-released L-Arginine, an amino acid that creates Nitric Oxide in your bloodstream. NO in turn dilates all blood vessels. This includes the capillaries in your lung’s alveoli sacs, permitting greater O2 uptake. It’s fairly well known among mountaineers going above 20,000 ft. that they take Cialis or Viagra for the same reason. Plus it helps move lactic acid away from your muscles faster.

So give this a try. It would appear that O2 deprivation is the major cause of your problem. This may help.I know I can readily tell when I have forgotten to take my NO2.

And remember to hydrate well first thing in the morning. Studies have shown it’s almost impossible to “catch up” on hydration later in the day.

Tom–excellent points, and great advice. Over the past few years, I’ve found myself following much of the advice you listed, although it was more in the general pursuit of the hiking style I’ve come to enjoy, not specifically to minimize the effects of elevation. One crime I’m still guilty of is going too fast, particularly on the first day–if I don’t focus on it, I’ll hike/climb at my sea-level pace.

However, speed can be a two-edged sword: I suspect that heavy exertion both increases the rate at which you acclimate, as well as the rate at which you accumulate lousiness. My gut tells me that going faster is–in general–a losing battle (you’ll feel worse for having done it). However, if you can go fast enough to get over the high obstacles and down to a moderate elevation for camping, you have a solution. I suspect the challenge here is in ensuring that you have the appropriate cardiovascular fitness to go “fast” without undue exertion. You also require a lower-elevation landing spot to camp at for that approach. In addition to being a nasty step-function, Lamarck Col lacks easily obtained low-elevation camping on the south side (unless one is heading down into Evolution Valley). After going over Lamarck Col, neither a northbound hiker (headed over Glacier Divide) nor a southbound hiker (headed into Evolution Basin) will see much in the way of camping below 10,500 feet for quite a few miles. I have a trip I’ve been thinking about over Lamarck, but the only solution I’ve come up with is to spur down to Evolution Valley for camping.

Eric,

As a geezer I am not as subject to altitude sickness as younger backpackers.

See, there’s something to look forward to! My knee has been acting up for the last few years, and just yesterday I was literally annoyed by some kids on my lawn. So, perhaps I’m mature for my age, and perhaps that will extend itself to my susceptibility to AMS?

I appreciate the suggestion on NO2 Red! I’ll look into it. Anything that helps is a good tool to have.

I’m not “mature” enough to go see my doctor for a Viagra prescription, FWIW.

“heavy exertion both increases the rate at which you acclimate, as well as the rate at which you accumulate lousiness. “

I’ve got anecdotal, “n of 1” data that exertion immediately after a quick assent increases feeling lousy.  I also have multiple experiences of being high up but taking it easy making later exertion much easier.

“Very interesting. You may need to add another factor to your model though: very long-term acclimatisation.”

When I first started backpacking at high elevations I had some brutal experiences that forced me to end trips early even after plenty of acclimatization prior to the trip. I thought that I would never be able to successfully hike at high elevations. After pushing myself through the misery for a few years, I am now much, much better at high elevations. It’s still rough on me but this summer I was able to reach a 12,700 foot pass after 3 days of gradual elevation gain. It was slow going but I did it without any complications. I had no idea that repeated exposure, even months apart, could help me build up a tolerance to high elevations but it seems to be working…. or is that not how it really works?

Hi Justin
As David put it, “n of 1”, but I think so. Just keep going (up) gently.

Cheers

I’ve scanned through your article and I like your idea of trying to map to your misery index.

As far as modeling human body adaptation, I suspect you’ll have better overall fits/results if you model adaptation more in tune with existing published data.  See for example the figures in Zubieta-Calleza, et al. at http://zuniv.net/pub/AdaptationJPP.pdf .  One approach might be to model adaptation to altitude increases with an RC (capacitor) charge-up type equation and altitude decreases with a linear degradation equation.

David,

Thanks for the link to the article–interesting. As you’re probably aware, the model that I chose for adapting to increases in elevation does exhibit behavior akin to an RC circuit (with a time constant of 1/0.027 = 37 hours, to be precise).

The challenge I have with modeling adaptation to decreases in altitude is that I have no data for those–in other words, I didn’t do any trips that consisted of significant descents, followed by significant time passing, followed by significant ascents, followed by AMS symptoms.

One drawback to my approach is that I have a single, qualitative diagnostic: how crappy I feel. So, I have to model two serialized processes (acclimation, then accumulation of lousiness). I was able to choose parameters in both of those processes such that the output agrees reasonably well with my data, but my choice of parameters (or, my choice of the mathematical description of those processes) is almost certainly not a unique solution for obtaining agreement.

So–in terms of modeling the acclimation along descents, I could certainly change the form of the function I use, but I wouldn’t be able to make any meaningful statements about how it affects agreement with the data, since there is no data affected by de-acclimation.

A good data point for me to take would be to do a trip for several days, get nice and acclimated, then come down for 3-4 days, and head straight back up to >10k feet. If I accumulate some lousiness, I can start to bound the de-acclimation by stating that for all practical purposes, I completely de-acclimated over those 3-4 days. If I don’t accumulate lousiness, I can try again, with a 5-6 window, etc. I see a lot of driving in my future–for science!

Last point, and bigger picture: I’m not sure if red blood cell count alone is descriptive of the process of acclimation, particularly the “prompt” response that occurs within the first 48 hours (and which is the one that I have the most data on). I’m sure red blood cell count is a large part of our bodies’ response, but is it the only (or the most important) factor related to the development of symptoms of AMS, which is the only thing I purport to be able to say ANYTHING about)? I say this from a position of ignorance: I have a very incomplete understanding of the human body and how it works.

Well, a complete enough understanding to procreate. Twice.

Hi Adam
It would be valuable research, but you might need a permanent arterial tap for all the blood samples?

Cheers

“the model that I chose for adapting to increases in elevation does exhibit behavior akin to an RC circuit (with a time constant of 1/0.027 = 37 hours, to be precise).”

Thanks for the time constant.  I hadn’t gleaned that from my first reading.  That seems about right for the short-term acclimatization effects (breathing rate, tidal volume, blood pH, etc.  It clearly doesn’t address red blood cell counts which is on a much long time frame. That doesn’t mean your equations don’t model short-term acclimatization well -, I think they do.   But 6 weeks at elevation will leave you more acclimatized than your model suggests.  From my extensive reading of many years ago, 6 weeks was when you get to 90% of how far our red blood cells would go.

>”A good data point for me to take would be to do a trip for several days, get nice and acclimated, then come down for 3-4 days, and head straight back up to >10k feet.”

A better data point would be for a Denver (or Leadville!) resident to do some timed event (440m ?) at home, spend a few days low, return home and repeat the event.  I suspect there’s data on that, certainly in the hands of US Olympic coaches and maybe in the literature.