# Heart Rate Dynamics and Quantifying Physical Fatigue in Canadian Football
## 2 Materials and Methods
then taken as the absolute value of the largest minimum value in the HR derivative signal; larger values of HRRpk indicate faster return towards baseline post-exertion, while smaller values of HRRpk indicate a slower return. Both HRmax and HRRpk were computed for all bouts and series. In order to characterize whether HRmax and HRRpk measures change over the course of a session, the time of each running event was binned according to its occurrence in the first (start), second (middle), or final (end) of the session. Two 3-way mixed analyses of variance (ANOVA) were run to examine the effect of athlete group (between), running intensity (within), and time (within) on HRmax and DHRpk for running efforts, and another two 3-way mixed ANOVAs were run to determine the effects of the same factors on HRmax and DHRpk for running series. Additionally, a more continuous measure of HR dynamics and physical effort was explored, without the need for detecting running events with adequate recovery which occur infrequently during a session. Physical effort was considered as the total distance covered (in meters) within a window of time, and cardiovascular load was taken as the total number of heartbeats in that window. Total heartbeats were computed by dividing the HR signal (beats per minute) by 60 to obtain the number of beats per second and then taking the sum over the number of seconds in the time window. The number of heartbeats was then divided by the total distance covered as a measure of cardiovascular cost (CVC). A sliding window of 60 s was used to compute the CVC over the course of each session (Figure 3). In order to remove large spikes in the CVC time series due to a small denominator (i.e., small distance covered), a threshold of 2 km/h was used (similar to the bout detection) to remove time windows where the athlete was walking at a slow speed. A linear regression was fit to each CVC time series to evaluate the general trend in the metric, then the first and last regression values were extracted for comparison for each session. In order to analyze changes to CVC within a performance, a two-way mixed-measures ANCOVA was run to examine the effect of athlete group (between) and time (within) on CVC values, with a covariate of BMI to account for the differences in physical running efforts between athlete groups. Additionally, in order to evaluate the potential of CVC to capture long-range trends of fatigue, the mean CVC from each performance was correlated with the number of days from the start of the season using a Pearson correlation coefficient. Data for the correlation were taken only from athletes who had performed over the entirety of the season, resulting in 28 performances analyzed from 3 skilled players and 10 performances from 1 lineman. Significance levels for all statistical tests were set at \(p\) = 0.05, and all tests were run in R 4.1.2 [25]. Bonferroni corrections were performed for all post hoc pairwise comparison tests, and effect sizes were calculated using Cohen's d with thresholds of 0.2 (small), 0.5 (medium), and 0.8 (large) [26]. Figure 3: Cardiovascular cost (CVC) for (**a**) a skilled player and (**b**) a lineman. Top subplot shows velocity (blue) and heart rate (red) signals over time. Bottom subplot shows CVC (black solid) with walking period discontinuities removed; overall CVC trend represented by linear regression (black solid) and starting (green) and ending (red) regression values are highlighted.