The mountainside: recovery after a challenge

The stress response is where a challenge is applied and either recovered from or pushed over a barrier. This page sets out what the model predicts about recovery, tests it in people, and reports what was found, including where the prediction failed and where our own measure misled us.

The idea

Picture the body's resting state as a ball in a valley. A challenge pushes the ball up the side and it rolls back; the time it takes is the recovery time. Steady demand tilts the landscape: the valley grows shallower and the ridge to a different, worse state comes closer, until near a tipping point (the fold) the valley all but vanishes.

Height on this page is a potential, so lower means more stable. That is the opposite of the Map, where higher ground means fitter (lower risk of death). The two views answer different questions: the Map says how good a place is, the potential says how firmly a person is held there. A stable valley can sit on high ground or low.

What the model predicts

Recovery time is flat over most of the range of demand and rises sharply only in a narrow band next to the fold (critical slowing down). Two things follow. People far from an edge should recover at about the same speed whatever their load. And averages over groups made mostly of such people should show little or no slowing, which is why comparing people near an edge with everyone else, inside the same wave of measurement, is the real test (below).

The project's own allostasis model, with load and capacity as two coupled states, has the same shape: its slowest mode is flat over most of the range of demand and lengthens close to the fold. The return after a short pulse also has a hump at moderate demand.

One published result sits awkwardly with the narrow band. Pyrkov and colleagues (Nature Communications 12:2765, 2021) report recovery time rising steadily across adulthood, not only near an edge. One possible reconciliation: ageing moves everyone slowly toward an edge, while acute disease moves some people there quickly. This is open, not resolved. Our own data point the other way within each wave (older people settled closer to rest), which leaves it more open, not less.

Where this has been seen

From the most controlled setting to the least. The signature is clear where the approach to the edge is controlled, and murky where it is not.

1. Yeast populations: a clean fold, dialled by the experimenter

   Yeast grow cooperatively on sucrose: cells break it down outside the cell and share the products, so a population too thin to feed itself collapses. That is a fold. Comparing populations held at higher and higher daily dilution, Dai and colleagues found that, approaching the tipping point, fluctuations in population density grew in size and duration, return after a disturbance slowed, and a salt shock that low-dilution populations survived drove high-dilution populations extinct. Dai, Vorselen, Korolev and Gore, Science 336:1175, 2012.

   The fold itself: which populations survive

   Where the survivors settle

   Left: each square is eight replicate populations started at one density (rows, halving downward) and held at one dilution (columns); filled means alive on day seven, and mixed squares give the count. Right: the survivors' density, mean and range over starting densities. As dilution rises, survivors settle lower while the smallest starting density that survives climbs: the stable state and the threshold approach each other, as at a fold. At the highest dilution some populations were still between alive and dead on day seven.

   Recovery after a salt shock

   Warning signs before collapse

   Replicates

   All replicates The authors' subset

   Population means across replicate cultures, computed here from the authors' open data (Dryad), not copied from the paper's figures. Left: the shock knocks every population down; at low dilution it returns at once, at higher dilution slowly, and at the highest dilutions it never returns (resampling the populations gives the same answer every time). Right: the spread between populations and the day-to-day autocorrelation rise overall as dilution approaches the point of collapse; bars are bootstrap intervals over populations. The spread rises cleanly; the autocorrelation is noisier and dips at one dilution. The authors' subset of replicates (described in their supplement) shows the same rise.

   Caveat: the same group later found that the link between stability and resilience that slowing indicators rely on can break down when several drivers change at once (Dai, Korolev and Gore, PNAS 112:10056, 2015; Dai's doctoral thesis). People are always in that situation.

2. Single cells: the attractor loosens before a fate decision

   Before blood progenitor cells (a mouse cell line) commit to a lineage, correlation between cells falls while correlation between genes rises. This is a warning read from snapshots of many cells, not a recovery time. Mojtahedi et al., PLoS Biology 14:e2000640, 2016.

   The index divides how strongly genes move together by how alike the cells are, so it rises as cells drift apart while genes act in concert. Recomputed here from the authors' open single-cell data (supplementary data, CC BY) with a simpler preprocessing than theirs, so the level differs; hollow markers are the authors' own values. In all three treatments the index peaks on day three, before the cells commit, and falls by day six. Bars are intervals from random halves of the cells. Day three has more cells than the other days, which if anything lowers its index. One cell line, one study.

3. Exercise intensity: a measurable edge in one person

   Oxygen uptake and blood lactate reach a steady state quickly at moderate intensity, after a delay at heavy intensity, and not at all above critical power. Jones et al., Physiological Reports 7:e14098, 2019 (full text; a review). This maps onto the model above: fast return, slow return, no resting state to return to.

   Illustration Shapes only, not measured data. Caveat: the delayed steady state may come from a second process (the slow component of oxygen uptake) rather than from slowing of the same recovery. We found no openly licensed dataset that records oxygen uptake in all three intensity domains, so this stays a sketch.

   The experiment we propose: graded constant-work-rate bouts below and above each person's critical power, with oxygen-uptake and heart-rate recovery kinetics measured after every bout. Work rate plays the part of the yeast dilution: the edge is located per person, and recovery is measured at known distances from it. It is the human analogue of the yeast series above. The open problem sets out the design; collaborators with a metabolic cart are welcome.

4. Human populations: free-living, mixed signal

   In blood counts followed over time, the autocorrelation time of an ageing index rises with age, and daily step counts from wearables show the same. Pyrkov et al., Nature Communications 12:2765, 2021. The authors' extrapolation to a fixed limit on human lifespan is speculative. Most authors work for or hold shares in the company that funded the study.

5. Older adults: resilience read from repeated measurements

   Resilience in people can be estimated from the pattern of small recoveries in ordinary time series, not only from deliberate challenges (Scheffer et al., PNAS 115:11883, 2018). Physical resilience in older adults has been defined as the ability to resist functional decline or recover health after a stressor (Whitson et al., Journals of Gerontology A 71:489, 2016), and repeated measurements around a stressor have been proposed for the clinic (Gijzel et al., Journal of the American Geriatrics Society 67:2650, 2019). In daily self-rated health, frail older adults showed higher variance, but not higher autocorrelation, the classic slowing signal (Gijzel et al., Journals of Gerontology A 72:991, 2017). So far the human signal is mostly variance, not slowing.

   The last rung is this page's own test in MIDUS: see below.

Cautionary notes

• Mood: rising autocorrelation and variance in daily emotions came before transitions into and out of depression (van de Leemput et al., PNAS 111:87, 2014).
• Chronic disease: slower recovery proposed as a general risk marker for acute attacks in episodic conditions such as asthma, arrhythmia and migraine; a review without new data (Olde Rikkert et al., Critical Care Medicine 44:601, 2016).
• Heart cells: noise amplification before a switch to an alternating rhythm in clusters of heart cells, but that transition is a period doubling, not a fold (Quail, Shrier and Glass, PNAS 112:9358, 2015).
• Epilepsy: long recordings found no sign of slowing before most seizures (Wilkat, Rings and Lehnertz, Chaos 29:091104, 2019; Milanowski and Suffczynski, International Journal of Neural Systems 26:1650053, 2016). Not every transition is a fold, so slowing is not a universal warning.

Testing it in people

A measured recovery: heart rate after a stress test

Heart rate of young adults in the minutes around the end of a standard social-stress test, from the WESAD wearable study: it is high during the test and falls back within minutes once it ends. Group mean with its standard-error band.

Wearable studies: per-person fits

Young adults only, so they say nothing about age; they show how recovery time depends on the kind of challenge, including exercise, the prototypical physical challenge. Every row gives the number of people whose recovery could be fitted.

MIDUS: what the recovery measure is made of

MIDUS ran a seated baseline, a maths and a Stroop task, each followed by a six-minute seated recovery, at two visits about a decade apart. It records one average per period, not a recovery curve. So recovery time here is not fitted to a curve: it is read from three averages. The response is the rise from baseline to the tasks; the shortfall is how far above baseline the recovery periods still sit; the recovery fraction is the share of the response that has gone, one minus the shortfall over the response. Recovery time (τ) is the time constant of the exponential return whose average over the recovery window leaves that shortfall.

Heart rate, beta-blocker users left out; group means, not people. People: those with every period measured, out of everyone in the group. "Full recovery" means the recovery periods sat at or below baseline, so τ is too short to estimate; "no recovery" means they sat at or above the task level. A dagger marks τ at or beyond the six-minute window, which is extrapolated. "Share defined" is the share of bootstrap resamples in which τ could be computed at all. Heart-rate variability and the perceived-stress breakdown shown here before are dropped: variability does not dip reliably during these tasks, so its τ has no meaning, and the stress tertiles did not order consistently, which reads as noise. How recovery time is computed.

Men settled further above baseline than women at a similar rise, so their recovery reads slower. In the earlier wave the gap holds after allowing for age and response (the gradient table below); in the later wave it is smaller and not clear. We do not interpret it further.

Cortisol across the same protocol

Median saliva cortisol at the samples MIDUS takes: on arrival, at baseline, after both thinking tasks and their recoveries, after a standing challenge, and half an hour later. In nanomoles per litre, by age band. Group medians, not people.

Is recovery time measuring recovery?

Every headline on this page once rested on τ, so we tested the measure itself. We built synthetic groups with a known recovery time and passed them through exactly the steps used on MIDUS, with the measured noise of a single period's average and a range of response sizes.

With noise alone the measure is sound once the response is more than a beat or two per minute; below that, groups often read as "full recovery". But if recovery settles a fixed amount above baseline whatever the response (sitting after talking, a baseline still settling, the room), τ is biased upward, and more so the smaller the response. Two groups with the same true recovery time and responses a factor of two apart then differ in τ by about as much as the two MIDUS waves do. τ cannot tell slow recovery from a fixed offset; one recovery period per task is not enough to separate them.

So the comparisons below use a second measure: the shortfall at equal response, the difference between two groups in how far above baseline they settle, after allowing for how much each person rose. The response here is measured against the second half of the baseline, so its noise is not shared with the shortfall. In the simulation this measure stays close to zero when two groups differ only in response size.

The wave effect

Several hundred MIDUS participants did the same protocol at the second and the third wave, about a decade apart. τ was longer at the later visit, which at first looks like slowing with age. It is not. In the same people, the rise during the tasks halved, while the shortfall, how far above baseline heart rate still sat in the recovery periods, barely changed. A similar leftover divided by a smaller rise gives a longer τ: the pattern the simulation above produces with no change in recovery at all. The halved response points to the visit (equipment, procedure or setting), not ageing: it is about the same at every age.

Same people at both waves, beta-blocker users left out. Change: later minus earlier, with its bootstrap interval. The response is what moved; the shortfall did not move clearly. In systolic pressure the shortfall may have grown a little; its interval just reaches zero.

τ by group as first published, kept for comparison. Change: later minus earlier recovery time, with its bootstrap interval. These τ changes are mostly the smaller response, not slower recovery (above).

Same age, different wave

Within each wave, τ falls with age: older people read as recovering faster. That runs against Pyrkov and colleagues and against a naive reading of the model. It is not a response-size artefact: the rise during the tasks changes little with age until the oldest band, and the gradient is in the shortfall itself, after allowing for the rise (second table). Older people's heart rate settled closer to, or below, its resting level. Why is open. Candidates: the oldest people who completed the protocol are the healthiest survivors, or there is less tonic arousal in the recovery periods with age. The interval on the gradient is wide in the later wave.

Shortfall per decade of age and between women and men, each allowing for the other and for the response; and the response per decade of age. Within each wave, beta-blocker users left out, with bootstrap intervals.

Markers that shift with the wave

Shifts of about the same size at every age look like a change in the laboratory, not in the people. The MIDUS documentation records changes that fit. C-reactive protein moved from a plasma nephelometric assay to a serum electrochemiluminescence assay, and the documentation gives an equation to convert between them; urine cortisol and catecholamines moved from the Mayo Clinic laboratories to the University of Wisconsin with lab-developed methods and no conversion equation; saliva cortisol moved laboratory and assay, and from four samples to five, so the samples are not numbered alike across waves. The psychophysiology sites, tasks and period structure were the same at both waves, but the recording system changed, and continuous blood pressure was added partway through the second wave. We found no documented change to the tasks that would halve the heart-rate response. Sources: MIDUS 3 Biomarker Project, Blood, Urine and Saliva Data Documentation, Section C; MIDUS 2 and MIDUS 3 Psychophysiology Protocol Documentation.

Near the edge: the real test

The model predicts slowing only close to a tipping point, so the test is to compare people near an edge with everyone else, inside the same wave so the wave effect cancels. If the model is right, each near-edge group should sit above zero: slower than its reference group.

This tests two things at once: the model, and the assumption that high allostatic load, high blood pressure or diabetes puts someone near a fold in the system being measured. Each condition is an edge in its own system. Heart rate after a thinking task is a weak proxy for most of them, so a null in heart rate rejects only "near an edge in any system means slower heart-rate recovery", not the model itself. The test has to be matched to the system: blood pressure for high blood pressure (below), glucose for diabetes (not yet done), posture for frailty.

Observed: the shortfall at equal response, near-edge group minus its reference group in the same wave, in beats per minute or millimetres of mercury, with its ninety-percent bootstrap interval. Above zero means settling further from rest, as slower recovery would. The tick on each row marks the smallest slowing of interest: the extra shortfall a slowing of one minute would add at the reference group's response. The model gives no size for this without placing each group on its demand axis, which there is no validated way to do, so the minute is our stated choice. Beta-blocker users left out, all ages. Group means, not people.

No evidence of slower recovery. What differs is how much people react: high allostatic load, and diabetes in the earlier wave, go with a smaller heart-rate response. In blood pressure the picture is the one the model draws for the rise but not for the return: in the earlier wave, people with high blood pressure react more, as a flatter valley would, yet settle no further from rest. In the later wave the groups are small and the comparisons mostly inconclusive; the margin there is also small, because the later wave's responses are small.

Verdict: "ruled out" when the upper end of the ninety-percent interval is below the smallest slowing of interest (an equivalence test); "slower" when the whole ninety-five-percent interval is above zero; otherwise "inconclusive", and the upper end is the largest slowing the data still allow. Confounders: beta-blockers are left out throughout, but other blood-pressure drugs (ACE inhibitors, angiotensin-receptor blockers, calcium-channel blockers, clonidine) and diabetes drugs also change heart-rate and pressure responses, and diabetic cardiovascular autonomic neuropathy is a known cause of a blunted heart-rate response. The sensitivity rows leave out every user of a cardiovascular or antidiabetic drug. That removes the treated blood-pressure groups and most of the diabetes group entirely, so those groups have no such row.

In heart rate the observed points sit left of centre, toward a smaller response, with no rise. In blood pressure, in the earlier wave, the high-pressure groups sit to the right, a bigger response, still with no rise. A one-dimensional valley model predicts neither pattern.

The smaller heart-rate response near an edge fits an established literature. Low, or blunted, cardiovascular and cortisol reactions to acute stress go with obesity, depression and poorer self-rated health, so both ends of the reactivity range can signal poor health (Phillips, Ginty and Hughes, International Journal of Psychophysiology 90:1, 2013; Carroll et al., Neuroscience and Biobehavioral Reviews 77:74, 2017; Lovallo, Biological Psychology 86:121, 2011). In type two diabetes, Steptoe and colleagues found blunted blood-pressure and cortisol reactions and, unlike our MIDUS heart-rate result, impaired recovery, in a protocol that followed people for longer after the tasks (Steptoe et al., PNAS 111:15693, 2014). For blood pressure the literature runs the other way: larger pressure reactions predict later hypertension (Carroll et al., Psychosomatic Medicine 73:737, 2011), in line with the larger pressure responses of the high-pressure groups here. We found no study that tests laboratory reactivity against an allostatic-load score.

This reframes the open problem. Near an edge a system may lose gain, its sensitivity to input, not only the depth of its valley. The project's two-variable load and capacity model can test that directly: does the measured variable respond less to the same challenge as capacity falls? The open problem now asks this.

The standing challenge

MIDUS also stands people up after the baseline: the posture rung. It records no period after standing, so this is a response, not a recovery, and it cannot test slowing. Heart rate rises less with age and systolic pressure rises more.

An early warning?

Critical slowing should come before a transition. Among people without hypertension at the earlier wave, those whose heart rate recovered most slowly were more likely to have hypertension a decade later. The comparison of the slowest with the fastest quarter was not specified in advance: an earlier version of this page used thirds, and the result moves with the grouping. The continuous test, adjusted for age, sex, starting blood pressure, resting heart rate and the size of the response, is the one to trust, and it is weaker. There is no link for diabetes.

Adjusted odds ratio of each quarter of recovery at the earlier wave against the fastest quarter, with its interval, on a log scale. People in both waves, beta-blocker users left out, people whose heart rate rose by at least two beats per minute.

A first check elsewhere found nothing, but with a much weaker measure. The English Longitudinal Study of Ageing has no stress task; the nearest thing is how far the pulse settles across three seated readings taken a minute apart at a nurse visit. How far it settled did not predict hypertension or diabetes eight years later, from either of two starting waves.

What we found

• The longer recovery time at the later MIDUS wave is a smaller response at that visit, not slower recovery, and not ageing.
• Within each wave older people settled closer to their resting heart rate, at a similar response. The measure was checked for this; the reason is open.
• The predicted slowing near an edge was not seen within waves, in heart rate or in blood pressure. For most groups a slowing of a minute is ruled out; for the rest the table gives the largest slowing the data still allow.
• What differs near an edge is the size of the response: smaller in heart rate with high allostatic load or diabetes, larger in blood pressure with high blood pressure, clearest in the earlier wave. A one-dimensional valley model does not predict that. It suggests the landscape near an edge changes its sensitivity to input, not only its depth. This is an open problem.
• Slow recovery may come before hypertension. It was a hint with a grouping chosen after the fact; It needs a cohort with a real challenge protocol; a proxy check in ELSA found nothing.
• The system-matched glucose test is still to do.