## 2 Materials and Methods
### Materials and Measurements  
Each woman was tested at 3 points in her menstrual cycle: (1) bleeding phase (day 2.4 \(\pm\) 0.7); (2) follicular phase (day 10.4 \(\pm\) 2.2); and (3) luteal phase (day 21.8 \(\pm\) 2.1). In each of these phases, each participant performed a maximal test and, 48-72 h later, a submaximal test.  
The maximal test provided peak and average heart rate, maximum speed, blood lactate concentration at the end of the test (as well as 1, 3, 5, and 7 min after the test), and the kinetic variables of the running exercise. The start of the maximal test was 5-6 km/h slower than each participant's (most recent) best 10 km run time. It is an incremental test where every 1', the speed was increased by 1 km/h. The treadmill was always at a 1% gradient. The test ends when the participant cannot maintain the speed. Heart rate was measured continuously with the Garmin Forerunner 735 XT (Garmin, Olathe, KS, USA) wrist-worn device, connected to the Garmin HRM-Pro chest strap. Lactate concentration was measured from a right earlobe puncture using the Lactate Scout+ (EFK Diagnostic, Barleben, Germany) system and Lactate Scout Sensors test (HaB direct, Southam, UK) strips. Analysis of the kinetic variables of running was continuously performed using the RunScribe (Red Gait Lab (Foot) v. 2.4.0) system via two pods, one on the left foot and one on the right foot. RunScribe is a comprehensive running analysis platform that provides a detailed view of running mechanics by capturing data from both feet at every stride. RunScribe has been validated in several studies [12; 23; 24; 25], showing good-excellent concurrent validity for variables as maximum promotion velocity, contact time, cycle time, or foot-strike measures. At the end of each test, participants completed a questionnaire assessing their perceived level of fatigue before, during, and after the test on a scale of 0-5.  
The submaximal test was performed at 3 intensities: (1) 50% of the maximum speed of the maximum test; (2) 60% of the maximum speed of the maximum speed of the maximum test; (3) 80% of the maximum speed of the maximum test. The submaximal test made it possible to determine the peak and average heart rate at each of the 3 intensities, the blood lactate concentration at the end of each of the intensities, and the kinetic variables of the running exercise (shock (G), braking (G), peak vertical ground reaction force (F(Bw)), vertical and horizontal ground force rate (N/kg/s), swing force rate and total force rate (N/kg/s), leg and vertical spring stiffness (kN/m), and power (w)).  
The timing of the different phases of the menstrual cycle was tracked using an app called Clue, which was downloaded to each woman's mobile phone. They were also connected to the lead researcher via the same app, which synchronized information regarding their menstrual cycles. Clue is a period-tracking app, a science-based menstrual and reproductive health resource. It has a database of 378,000 users and 4.9 million natural cycles. Using self-reported tracking data, it can reveal statistically significant associations between cycle length variability and self-reported qualitative symptoms [26; 27; 28].