When threshold training isn't threshold training

Most runners are familiar with threshold training.  It's been the chief contribution to real-world training from the field of exercise physiology.  In principle, it's simple: there is a "tipping point," physiologically speaking, when incremental increases in speed become progressively more difficult.  Training right at this sweet spot should raise the threshold, moving that "tipping point" to a faster pace.  But there is not a unanimous understanding of what exactly "threshold training" is, or about how to properly apply it to training.  Threshold training is one of the topics du jour in any number of running magazines and websites, so I don't mean to unnecessarily repeat here what's been done to death elsewhere.  No, today's post is about my own peculiar interpretation of threshold training, and the consequences thereof.  In short, I think the real value of threshold training is that it involves practicing running fast and efficiently in a state of low metabolic stress.  I'll cover exactly what all that means shortly, but the consequences of this are surprising: "threshold" does not always have to correspond to one specific pace.  This opens up a lot of possibilities in training.

Introduction

First, though, a crash course in exercise physiology and a thought experiment to illustrate: In any athletic endeavor, almost all of your energy is derived from aerobic and anaerobic respiration.  You're probably familiar with these processes: both turn sugars into energy, either by burning them with oxygen (aerobic respiration) or without oxygen (anaerobic respiration).  There are no problems with sustaining aerobic respiration for a long time, but anaerobic respiration is a different story.  Metabolic byproducts like lactate and protons (H+) build up during anaerobic respiration, and eventually cause fatigue.  "Lactic acid buildup" is commonly blamed for the fatigue associated with anaerobic respiration, but this is technically a misnomer.  During an anaerobic effort, blood pH drops (indicating rising acidity) and blood lactate levels climb, but it turns out that these two are mostly independent processes, not the result of "lactic acid."  It seems that the acidity is the chief cause of fatigue, not the lactate. Regardless, except for a narrow window of time where the body's buffering system dampens the buildup of acidity but lactate levels rise (this is called the isocapnic buffering zone), lactate levels and blood pH mirror each other very closely.  In general, it's easier to measure blood lactate, so lactate levels are used as a proxy for how heavily an athlete is relying on anaerobic respiration.  In any case, the body only increases its baseline rate of anaerobic respiration when the energetic demands of an athletic effort exceed the body's aerobic capacity. 

Now, our thought experiment: let's say we take Sam, a hypothetical runner, and put him on a treadmill.  Sam is a reasonably fit runner who has recently set a 3200m PR of 10:00 and a (track) 5k PR of 16:05.  To measure his blood lactate levels, we insert a probe into a blood vessel.  The first thing we'll notice is that before we even start the treadmill, our lactate probe will show that there is a small amount of lactate circulating in Sam's blood, even at rest: about 1.0 millimoles of lactate per liter of blood, or mM for short (mM is just a measure of concentration).  This is because there's always some anaerobic respiration in your body, even at rest.  But there's more than enough oxygen circulating to "mop up" the metabolic byproducts, so the lactate level is stable.  So, we start up the treadmill.  Very slowly at first, say at 10min per mile pace.  Sam's lactate level will jump up a bit right away, perhaps to 1.5 mM, but it won't budge after that.  Even if we speed up the treadmill to 9min/mi, 8min/mi, or 7min/mi, his blood lactate level will move by 0.1 or 0.2 mM.  Furthermore, even if Sam runs on the treadmill for over an hour, his lactate level won't change.  That's because he's running at a steady state effort.  His body is getting all of the energy it needs from aerobic respiration.  

So we keep cranking up the speed on the treadmill, to 6:30 pace, then to 6:00 pace.  Sam's lactate level is probably 1.7 or 1.8 by now.  Just under 6min/mi, we'll see Sam's lactate level start to move up a bit more, reaching 2.0 mM for the first time.  If we stop changing the treadmill's speed, we won't see a change in lactate over time.  Sam is still at a steady state effort.  But if we increase the pace a little more, down to 5:50 or 5:45 pace, Sam will not be at a steady state anymore.  His blood lactate level will rise over time, even if we don't change the speed of the treadmill.  But at this pace, the increase in lactate concentration will be very slow.  Sam can probably sustain 5:50 or 5:45 pace for 80-90 minutes before having to stop due to exhaustion.  So we keep increasing the pace on the treadmill.  Sam's blood lactate will change a bit after each increase in pace.  Once we hit about 5:35, his blood lactate will be at about 4.0 mM.  If we continue to increase the pace, Sam's blood lactate level will start to jump more quickly with each change in pace.  Furthermore, the duration he could sustain a given pace before becoming exhausted will also drop sharply with each increase in pace.  Sam could maintain 5:35 pace for 50-60 minutes with a race-level effort.  But he could only maintain 5:25 pace for about half an hour.  And he could only maintain 5:15 pace for 17 or 18 minutes.  5:05 pace; perhaps 11 minutes.

So clearly there is something going on between 6:00 and 5:35 pace.  Whereas Sam could maintain 6:00 pace for well over two hours in a race situation, his ability to sustain paces for a long duration drops off significantly after 5:35 pace or so.  As you might guess, in this range is where Sam's aerobic system becomes insufficient to meet his energetic requirements.  As such, his anaerobic system needs to pitch in to help, resulting in higher blood lactate levels and an unstable metabolic situation.  Numerous physiological events occur in Sam's body between 6:00 and 5:35 pace, all of which have garnered a name and all of which vie for being called the "real" threshold.  At about 5:55 pace, Sam ceases to be at a metabolic steady state.  Any speed above this point will result in the gradual accumulation of lactate.  So some physiologists call this point the aerobic threshold.  Others think the most important event is when Sam's blood lactate levels cease to rise linearly and instead rise exponentially.  This happens at about 5:35 pace, and is often termed the anaerobic threshold.  Some physiologists are uncomfortable with the term "anaerobic" (since it implies that less oxygen is getting to muscles), so they term it the lactate threshold.  For others, even this isn't good enough: it has to be the onset of blood lactate accumulation (OBLA).  Even others prefer to measure the increase in ventilation, or breathing, and term the sharp increase the ventilatory threshold.  You can see how this has quickly gotten out of hand.

Problems arise

Once physiologists identified these points, they latched onto them like a man overboard onto a lifebuoy.  The lactate threshold (or anaerobic threshold or OBLA or ventilatory threshold, depending on who you ask) was fairly easily identifiable and predicted race performance fairly well too.  Additionally, it fit the aerobic/anaerobic model quite nicely: there was a portion where blood lactate was more or less flat, and then at an abrupt point, it started to grow exponentially.  Or at least it appeared so.

A quick gander on the internet will identify many sites boasting of the advantage of measuring and training at your lactate threshold.  And they have generated very nice lactate threshold curves that look just as described above: flat for a while, then a sharply defined point where lactate begins to rise sharply.

It should be fairly obvious to any scientist that these can't be real graphs from real experiments.  They're far too "nice."  Real data is messier.  So with a bit of snooping, we can find some results from real laboratory experiments.  Here are a few examples; a few have eagerly-circled or boxed "threshold" points:

 Now, at a first glance, these look pretty good.  And if we keep in mind our aerobic/anaerobic model, we can easily identify two distinct "zones," corresponding to the aerobic and and anaerobic contributions to metabolism.  The first image is from a Wisconsin lab which does of VO2 max and threshold tests for amateur cyclists and triathletes.  The second image above, with the two line segments drawn in to correspond to the aerobic and anaerobic portions, is from a PowerPoint presentation for a graduate-level exercise physiology class at a large public university in Illinois.  The third is from this research paper.  So this isn't stuff from uneducated internet hacks.

But even these are kind of messy.  Let's take a look at a cleaner plot and see if we can pinpoint the threshold.

Pretty simple, right? We could pretty easily draw a circle right around "8" on the horizontal axis, then draw two lines on either side, corresponding to the "aerobic" and "anaerobic+aerobic" portions of the graph.  But hold on...Hopefully, you've been a bit hesitant this whole time.  Something just isn't right with all these graphs.  This choosing of "threshold" points seems rather arbitrary.  And indeed, if we look up the literature, it is quite arbitrary.  Here are a few definitions I've lifted from an article by LV Billat (click for article citations):

     *"Onset of plasma lactate accumulation" is established as being exercise induced
       levels which are 1 mM/l [sic-using mM implies /l, so the /l is extraneous] 

       above baseline lactate values." 
     * "Maximal steady-state" is displayed when oxygen, heart rate, and/or treadmill
       velocity produce a lactate level that is 2.2 mM/l."
     * "Onset of blood lactate accumulation" (OBLA) occurs when continuous incremental
       exercise produces a lactate level of 4 mM/l."
     * "Individual anaerobic threshold" is the state where the increase of blood
       lactate is maximal and equal to the rate of diffusion of lactate from the
       exercising muscle. Values range from 2-7 mM/l."
     * "Lactate threshold" is the starting point of an accelerated lactate
       accumulation and is usually around 4 mM/l and is expressed as %VO2max."
     * "Maximal steady-state of blood lactate level" is the exercise intensity that
       produces the maximal steady-state of blood lactate level and ranges from
       2.2-6.8 mM/l."

Like I said, quite arbitrary.  But what about our graphs? There's still something going on, isn't there? And it sure looks like there's a definite threshold right around 8, above.  I didn't label the y-axis (shame!) but it'd be pretty easy to draw a horizontal line at one of the arbitrary values described above (say, 4.0 mM).  Observe:

Easy.  LT equals 8.0 for this runner.  We could even do some statistics and get pretty good R² values for our lines.  Now what does that mean?  Like I said, physiologists latched onto the LT/AT/VT/OBLA pretty quick after it was discovered.  A flurry of studies followed, in which a few principles were established:

• The LT can be maintained by a trained runner for approximately 50-60 minutes in an all-out race.  This is usually 15k-20k depending on the ability of the runner.  
• When running at the LT, blood lactate levels are fairly stable for about 20min, after which they start rising fairly quickly
• Training at the LT 1-3 times a week will result in the curve "shifting" to the right, so the LT occurs later (and hence, a faster pace can be sustained without relying on anaerobic respiration).  This "shift" is illustrated in the graph with the blue background, above.

So, if you were wondering where the "tempo runs are once a week, 20min at the lactate threshold" idea came from, now you know.  Seeing that all of this stuff works (i.e. results in better race performances) might've caused you to write off your previous hesitation about the ambiguity of identifying precisely the "turning point" is on the lactate curve.  But really, you've been had! The graph above is completely made up.  Generated by a mathematical function.  And our "two line" model is completely misleading.  Here's the truth:

And that's why I didn't label the axes. This is a completely unmodified exponential equation, not a two-piece linear function.  And if we take a look back at our graphs from real tests, they look an awful lot like this exponential function.  Furthermore, if we try to find a "threshold" or "inflection point," we'll be completely incapable of doing so, because the e^x function has constant curvature, meaning that it's always increasing at the same rate.  One thing I was taught very early on in chemistry is that it is a cardinal sin in science to fit a curve with a simple model and call it "close enough."  You can see from the phoney two-part graph I concocted above that our two-part fit is actually pretty good. Like I said, I bet we could even get pretty good R² values.  But it's just plain WRONG! 

Rethinking threshold

So is the lactate threshold useless? Not quite...we do know both from research in the lab and real experience on the track and on the roads that training at the pace that elicits about 4.0 mM of lactate produces a good training effect, and can "shift" the lactate curve to the right, allowing faster paces to be run more aerobically.  Our model just doesn't quite correspond to the data.  I'm not an exercise physiologist, so I won't go in depth on the exact reason for the shape of the lactate curve, or whether it's an exponential, parabolic, or cubic curve.  Rather, I'd like to "reset" our notion of threshold, basing our understanding only on phenomena we can directly observe.  Then we'll look at the implications of that and some alternative explanations for what's going on.

Let's revisit our hypothetical runner Sam.  I calculated Sam's predicted aerobic and anaerobic/lactate thresholds using a chart from Jack Daniels Running Formula, a best-selling book by esteemed coach Dr. Jack Daniels (no relation to the whiskey distillery, by the way).  Daniels' premise is twofold: 1) training at specific paces (including the anaerobic threshold) allows for highly effective training (good "bang for your buck") and 2) these paces can be predicted by a runner's recent race times.  Most coaches find that Daniels' formula is pretty accurate.  For example, he predicts a 4:30 miler should be able to run 8:55 for 3k, 15:29 for 5k, and 32:11 for 10k.  My freshman year track PRs from college were 4:30, 8:56, 15:45, and 32:30.  So not too far off.  This curve can be extrapolated to predict the aerobic threshold ("marathon pace") and anaerobic/lactate threshold.  But let's forget any notion of threshold or physiology for a moment.  Since it appears that Daniels' formula is pretty accurate at predicting race performance for a given fitness level, let's just translate that into a curve showing the pace sustainable for a given race distance.

As you can see, it's a curve.  If you don't believe me, plot your own PRs at all distances, translating the time into minutes per km.  Even if you are opposed to using formulas to predict race performance, you can understand that the difference between 6:30 and 6:00 is not as significant as the change from 5:00 to 4:30.  If we plot this out on our graph, it becomes obvious:

Each red segment (change in pace) is about 10 seconds per km

If we take 10k pace as an example, it's easy to see that your ability to sustain 10 seconds per km slower than 10k pace is a much greater than your ability to sustain 10 seconds per km faster than 10k pace.  Furthermore, it's clear that there is a "zone" of paces that are relatively easy to maintain: To run 21km, for example, you only have to slow down by about 10sec/km relative to 10k pace.  Likewise for 21km to 42km.  Even if there's no EXACT moment where everything gets more difficult, we could vaguely say there's a "threshold zone" somewhere between 15k and 42k (marathon) pace. In this range, we have a rather large window where we can cover significantly longer distances by slowing down only a small amount. This will prove useful in a minute.

Returning to physiology (or not)

So, does real physiology have any role to play? Some naysayers think that any concept of "threshold" is useless due to the inconsistencies in definition and the inability to pin the term to any particular pace, and runners should instead focus only on race-relevant paces or VO₂ max.  But I don't think we should throw the baby out with the bathwater, and I don't mean to bash the field of physiology (though I've probably stepped on a few toes in the last few paragraphs).  Indeed, even if curve-fitting isn't an exact science, many of our findings still hold: on a pace-per-km basis, there is a significant change in metabolic requirements, and it occurs somewhere between marathon and 15k pace.

We also know that if you train around where the dotted line is (2.0 mM in this graph), this curve will shift to the right over time.  We also know that if your lactate curve is shifted further to the right, you tend to race faster.  As far as whether there is an exact threshold, I'd like to defer to this quote on threshold training from LetsRun.com coaching "guru" John Kellogg:

Of course it [the lactate threshold] exists as a zone. Pinpointing it as a precise value of blood lactate concentration is iffy.

It's kind of like identifying the "blue" region of the visible spectrum. Obviously it exists, but where does "blue" precisely occur - at a wavelength of 450 nanometers or 475 nm or 500 nm? It just depends on which shade of blue you want to label "exactly blue." As far as we're concerned, agreeing on an exact wavelength or shade to call "blue" ought to take a back seat to being able to recognize the basic color of blue from its neighbors, green and violet. Same deal in running. A runner should be able to recognize by effort when he's entering the basic zone in which the "threshold" somewhere lies.

If a guy said the color blue didn't exist, we'd know right away he was either totally blind or unable to distinguish blue from any other color. And when we see a wall painted with a color in the blue region of the spectrum, we don't think, "Oh, look at that 495-nanogram-wavelength wall over there!" We just call it blue without really thinking about what kind of quantitative definition "blue" ought to have. Being able to recognize the color of the wall in the first place is the idea. Knowing off the top of the head what wavelength of light is being reflected off it doesn't change the look of it one bit.

Since shorter wavelengths are more penetrative than longer ones, blue is a more intense color than green, but isn't as intense as violet. Ultraviolet or shorter wavelengths are potentially damaging to human cells. Carrying that analogy over to running, the entire "aerobic spectrum" is like the visible spectrum, which is comprised of wavelengths from about 400 nanometers (violet) to 700+ nm (red). Jogging might be somewhere in the "red" end, while extremely high-intensity aerobic work (near max VO2, which also requires a significant anaerobic contribution if sustained) is at the other end, near ultraviolet. The "comfortably fast" aerobic efforts lie in the green and blue regions, with the "threshold zone" somewhere in the blue. It doesn't matter what exact wavelength it occurs at, but it does matter that you can recognize a basic shade of blue when you see it. As a runner, you'd like to be able to tell when you're crossing from the softer green zone into the strong blue zone and you should learn how it feels when you get into the more intense violet zone so you can figure out what shade of blue is the right one for you to look at more often without "damaging your eyes." Precisely identifying a wavelength value for "blue" is just mentally punching the clown.

Even if we can't pinpoint an exact number, and even if we aren't exactly sure what's going on at the cellular level, threshold training is still useful.  We can run a "steady-state" pace like marathon pace, where lactate doesn't accumulate over time at all, to directly stimulate our body's aerobic system, and we can run a more traditional "lactate threshold" pace to stimulate both the aerobic system and the body's ability to process lactate as a fuel (without going into oxygen debt). This "threshold zone" seems to fall between 2.0 and 4.0 mM of lactate on a blood lactate curve, or between 15km and 42km race pace.  And we know that both of these are useful training schemes.

Why does threshold training work?

As for why training in the "threshold zone" is useful, the science is less conclusive.  If there is not a distinctive point at which the body "switches" to anaerobic metabolism, what is it about running in the "threshold zone," the range of paces in which lactate levels are fairly stable, that is so effective? I'd like to propose a simple solution: threshold training is effective because it trains your body to sustain a fast pace with very little effort.  Since the buildup of lactate and other metabolic byproducts is slow or nonexistent at paces in the "threshold zone," there isn't a whole lot of metabolic stress on the body, even as you're cruising along at 86-92% of 5k pace (which should correspond to blood lactate levels of about 2.0 to 4.0 mM).  This is important, because it's (surprisingly) an example of specificity: the idea that the body will become good at what it practices.  So shoot free-throws and you'll get better at shooting free-throws.  And in this case, practice running fast with little effort and you'll get better at it.  And who wins a race? The person who runs the fastest.  Not the person who runs the hardest, nor the person with the most "guts."  So if you want to win (or just set a PR), you should train to run fast, not hard.

Implications

If the key to threshold training is running a fast pace continuously or nearly continuously without much lactate/metabolic waste buildup, there are some interesting consequences.  All of the "regular" threshold workouts still make sense: a tempo run at "aerobic threshold," say 45 minutes at 86% of 5k (~2.0 mM of lactate); a tempo run at "anaerobic threshold," say 20 minutes at 92% of 5k pace (~4.0 mM); a cruise interval workout consisting of 6-8x1200m at 92% of 5k with 60 seconds recovery (~4.0 mM).  But we could also conceivably achieve blood lactate levels of 2-4 mM (the "threshold zone") by doing repeats at high speeds, but keeping each repetition short enough so blood lactate only rises to 2-4 mM.  Then take a very short rest, just enough to allow lactate to drop back down, and then have at it again.

So we could do a workout like 16x400m at 8k to 10k pace with a 20-30sec shuffle/jog recovery and call it a "threshold" workout, even though the pace is well above the theoretical lactate threshold.  We could even go faster: 30x150m at 3k to mile pace with a 25-30 second walk recovery.  In college, my team used to do a workout that was essentially this second workout.  We called them "dungeons" because we did them on the old indoor track underneath our track stadium.  It was a 220yd track with very long straightaways (probably 70m) and extremely tight, steeply banked turns.  We'd run a straightaway, the turn, and a straightaway, which was allegedly 165 yards, at mile effort, then walk the curve and start again about 25-30 seconds after the last one finished.  The intensity of each repeat was quite high, but the workout never got progressively more difficult.  It seemed like you could do "dungeons" all day long.  I imagine our blood lactate during that workout looked something like this:

Of course you can't sustain this forever, but for the bulk of the workout, the effort approximates the lactate levels of a traditional "tempo run," despite the pace being much faster.

My theory is somewhat radical, but at least I'm in good company.  Steve Prefontaine's famous "30-40" workout, consisting of three miles' worth of continuous 400s with the first 200m in 30 sec and the second in 40 sec, achieves a similar end.  While it sounds incredible, when translated into relative paces is not so bad.  For Prefontaine, a 3:54 miler and 13:21 5k runner, the 30 second 200s were a full second slower per 200 than mile pace, and the 40 second 200s were 3 and a half seconds slower per 200 than his predicted marathon pace.  So it was, in effect, a threshold workout!  Of course, when runners tried for a "record" of 16 or 18 laps (Prefontaine allegedly did 20 laps of these once; Galen Rupp recently did 24), the workout ceased to be a threshold workout (just like doing a 45min run at the anaerobic/lactate threshold would be too strenuous to call it a threshold workout). 

John Kellogg, mentioned earlier, also advocates what he calls "high density LT repeats" faster than the traditionally-defined "threshold":

The PACE may be FASTER than the "laboratory GXT definition" of LT pace as "approximately one hour race pace", but the lactate levels THEMSELVES are what we are concerned with, NOT necessarily the PACE. For example, a runner who is in CURRENT shape for a 15:00 for 5,000m may have a theoretical LT pace of 5:15-5:20 [Daniels predicts 5:14-jd] per mile and might on one day perform 10 x 3 min. on/30-60 secs. off (so-called "high density") at an average of 5:15 mile pace for the 3 min. runs [...] Or the workout might consist of 20 x 400 in around 75, with 20-25 secs. rest periods - another high density session but run at a different pace than the first high density session.

Kellogg also advocates "low density" threshold sessions like  3 x 8 min. on/5 min. off at a tad slower than 5k pace.  While he claims these accomplish the same things any other threshold session, I'm not convinced.  To me, they seem more akin to "aerobic power" intervals done at 8k or 10k pace with long recovery, which stimulate the body's ability to PRODUCE lactate and function at a high percentage of maximal heart rate.  Regardless, I'm getting off-topic again.

Anyhow, there are several occasions where these different threshold workouts can be very useful.  For one, they allow for much more variety during base-phase training.  Instead of doing a 20min tempo run at 92% of 5k pace every Monday, you can mix it up with slower (longer at 85% 5k) and faster (intervals at 95%, 100%, or even 110% of 5k pace).  The high-speed sessions are also more useful and race-relevant than traditional threshold training for a pure middle-distance runner (say, an 800m/1500m specialist).  A workout like 30x150m at 3k to mile pace with 25-30sec walking recovery allows a middle distance runner to work closer to familiar and useful paces without neglecting aerobic development.

Conclusion

For proper long-term aerobic development, you really need to set aside a block of two or three months in a six-month training cycle to dedicate at least largely to aerobic development.  Mileage plays a big part in increasing your aerobic capacity, but targeted high-end aerobic running plays an important part too.  "Threshold" training is highly effective because it is a very efficient mode of training: you get a strong stimulus from fast running without a whole lot of metabolic stress.  Additionally, the various types of threshold workouts all function because of a single principle: they teach your body to run fast without working very hard.  I've always maintained that this is the real key to long-term improvement.  Once we partially separate the notion of "threshold" training from its physiological constraints, it becomes a more versatile and useful training tool.  The "classic" threshold workouts, like a 20min tempo run or a cruise interval workout, are still very useful, but we can add in less-traditional workouts like very short high-speed intervals with short recovery and longer steady-state "aerobic threshold" runs to mix up the pace while still accomplishing the same purpose, both mentally (learning to run fast) and physiologically (maintaining a fast pace continuously or nearly-continuously with low metabolic stress, i.e. low blood lactate levels).  This is especially good news for milers and 800m runners who often scoff at slogging through 4-mile tempo runs over hill and dale.  Finally, you should always keep in mind the purpose of the workout.  A threshold workout should never really be "hard"—it might be tiring due to the volume, but you should never get the tied-up knee-grabbing feeling that goes along with workouts like mile repeats at 5k pace or 400s at mile pace.  The whole point of threshold is to AVOID doing that.

This is not the last time we'll go over lactate threshold and energy metabolism in regards to training and racing.  There is still a lot I have yet to read on the subject, so expect more posts as soon as I get around to that.  There are some seminal papers by Dr. George Brooks on his "lactate shuttle" theory which show how lactate is moved around the body and burned as fuel (so much for being a waste product!) during exercise.  Additionally, Dr. Tim Noakes in South Africa has a very interesting alternative theory of fatigue.  Once I've waded into his 930-page tome The Lore of Running, I'll report back!  I've also probably made a few hasty generalizations in this post, so any corrections from real physiologists would be quite welcome.  I do my best, of course, but I'm not perfect.

Appendix: formulas for predicting threshold

Every coach probably has his or her own formula for predicting aerobic and anaerobic/lactate threshold.  I've found Jack Daniels' formulas to be reasonably good.  In any case, you should never rely fully on a formula: the point of threshold workouts is the feeling, not the pace.  Most runners I know do their threshold workouts too fast.  Use formulas only as guidelines, and always remember that you're supposed to feel like you aren't quite going as fast as you could.

Aerobic threshold: ("Marathon pace")
~82% of current 3200m/2mi fitness
~ 86% of current 5k fitness
~90.5% of current 10k fitness

Anaerobic/lactate threshold (50-60min race pace):
~87.5% of current 3200m/2mi fitness
~91.5% of current 5k fitness
~ 95.5% of current 10k fitness

These percentages change slightly based on race fitness (because a 5k is effectively a longer event, duration-wise, for a less-fit runner) but they are close enough for me.  If you want to devise an advanced quadratic formula to predict AT and LT from race times, go ahead, but perhaps your time would be better spent rethinking the reason you're doing threshold training to start with.  Also keep in mind that these formulas assume everything is on a track in ideal conditions.  So if your 5k PR is from a track race but you are doing intervals on a cross-country course, of course you'll have to adjust your times to take that into account. 

Lastly, keep in mind that I use "Renato Canova percents," so 86% of 5k pace is NOT 5k pace divided by 0.86.  Rather, it really means "14% slower than 5k pace" or (5k pace /100 + 5k pace) (or 5k pace * 1.14).  You might hate this system but if it's good enough for Canova, it's good enough for me.