Measuring Exertion

What exactly is it in exertion that triggers the flu-like sickness in CFS patients? In real life, we normally associate exertion with muscular force, but muscular exertion usually does not cause sickness in healthy people. So we don't know what exertion really means in the context of CFS physiology; exertion is as problematic as fatigue to define and measure.

In the paper Evidence for sensitized fatigue pathways..., Staud et. al. had CFS patients perform grip exercise with and without the cuff. Healthy controls did not feel any difference. CFS patients, on the other hand, felt fatigue when their arms were cuffed. They surmised from this that CFS patients were more sensitive to metabolites. This suggests the possibility of exertion being the effort against the metabolite load in CFS patients. Though the fatigue from the metabolite accumulation is immediate (or with some delay till the metabolites get into the bloodstream from the muscles), the higher effort required to work through the amplified perception of the metabolite load could be causing the flu-like sickness the next day.

The metabolites in blood stream dissipates exponentially as they get filtered out by the body. The metabolite concentration at time t, or the residual, is express with the equation of:

C(t) = C0*e^-kt

With ongoing exercise, the total build-up will be then the sum of all Ci(t) from t = 0 to t:

Q(t) = ∫C(t)*e^-ktdt

This can be approximated with summation of all residuals of C.

Q(t) = C0*e^-kt + C1*c^-k(t-1)...

It would be reasonable to assume that the metabolites produced are proportional to the calories spent, since the metabolites are by-products of burning fuel. We can also assume that there is no metabolite accumulation in the resting state. Then we could use activity calories as the proxy for the metabolite concentration at time t. And the cumulative concentration of metabolites at time t can be computed in R as:

q = Reduce(
    function(a,b) a*(1-k) + ifelse(b-C<0,0,b-C), 
    as.vector(fintraday$calories), 
    0, 
    accumulate=T,
)

fintraday$calories is a time series of calories spent at each minute of the day and q is the accumulation of exponentially aged calories standing in as the metabolite load at each given minute. The plot for calories spent vs. metabolite load looks like this:

To maintain the same walking speed against this load, the body has to work harder by increasing the "effort". And when this effort going above certain threshold could be causing the sickness. So, we can take the highest metabolite load and use that as the proxy of the effort.

Note that the metabolite load will dissipate rather quickly if you take the rest, substantially lessening the effort required to move after the rest. And this could be why CFS patients like Bruce Campbell reported being able to go much further when they incorporated rests in their walk. This is also confirmed by my own experience. Reducing the speed by 5-10%  also allows you to go about twice as further without triggering the post-exertional sickness. Conversely, increasing the speed by 5-10% will half the distance you can walk without triggering the post-exertional sickness.

Walking faster means not only building up the load exponentially faster, but also working harder against the load. A double whammy, if you will. Increasing the speed just by a couple more steps per minute when walking 1km triggers the sickness for me the next day, and this is probably why.

There is also the cumulative effect of exertion. As I noted before, the same exertion that normally does not trigger the post-exertional sickness can when I am weakened by activities of previous days. So, I summed up the metabolite stress over N days, with the metabolite stress being max(q), to see if that more accurately predicts the fatigue rating. It turned out that 4 day sum (d4) yields the best correlation. Here is the graph from Aug. 2015:

The cumulative effect of exertion may not be time-invariant. For the past 9 months, the d4's correlation to fatigue has been steadily decreasing over months while the maxq's correlation has been steadily increasing.  It's as if the cumulative effect of exertion has been diminishing and the fatigue has become more heavily influenced by the exertion the day before.

Still, d4 and maxq predicts the fatigue substantially better than raw calories or steps taken. So I might be onto something here. To be continued..