Fatigue Model
A fatigue model describes how muscle force declines during repeated contractions or sustained activity because metabolic resources, ion balance, and excitation-contraction processes become progressively limited. A fatigue model calculator estimates the force remaining over time or repetitions, the percent decline from the starting force, the fatigue index, and the effect of optional recovery intervals.
Core definitions and formulas
A simple fatigue model treats force as decreasing step by step with a fatigue rate constant. When rest is included, part of the lost force can be recovered toward the initial value.
\[
\begin{aligned}
F_{n+1} &= F_n \cdot e^{-k}
\end{aligned}
\]
\[
\begin{aligned}
F_{\text{after rest}} &= F + r \cdot \left(F_{\text{initial}} - F\right)
\end{aligned}
\]
In these expressions, \(F_n\) is the force at a given contraction or time interval, \(k\) is the fatigue rate constant, \(r\) is the recovery factor, and \(F_{\text{initial}}\) is the starting force. A larger fatigue rate causes force to fall faster, while a larger recovery factor causes force to rebound more strongly during rest.
\[
\begin{aligned}
\text{Fatigue index} &= \frac{F_{\text{initial}} - F_{\text{final}}}{F_{\text{initial}}}
\end{aligned}
\]
How to interpret results
A larger force remaining at the end of the task means fatigue developed more gradually. A larger percent decline or fatigue index means the muscle lost a greater fraction of its original performance. If recovery intervals are included, the force curve may show partial rebounds between bouts instead of a purely continuous decline.
Results usually include force remaining after each interval, percent decline from the initial force, a fatigue index, and a label such as gradual fatigue or rapid fatigue. The main graph shows the decline pattern, while the recovery-adjusted graph shows how rest can partly restore force.
- A higher fatigue rate constant produces a faster drop in force.
- A higher recovery factor increases the rebound during rest.
- Percent decline and fatigue index describe related but not identical views of the same trend.
- Recovery does not necessarily restore full initial performance.
Example: if initial force is high but declines steadily over repeated contractions, the model shows progressive fatigue. If short rest intervals are added, the force may recover partially before declining again in the next bout.
This tool is most useful for studying repeated-effort performance, muscle fatigue, and recovery behavior in physiology or exercise contexts. A deeper next step would be metabolic fatigue mechanisms, calcium handling limits, or task-specific performance models.