## 2 Materials and Methods
### Experimental Design  
The experimental protocol adhered to the Declaration of Helsinki principles and was approved by the department institutional review board. All the subjects were informed about the aims of the study and the methods adopted.  
We outlined a cross-sectional design (Figure 1) in which three different gymnastic balls were tested (Ledragomma Srl, Osoppo, Italy). Two out of three gymnastic balls were spherical with a diameter of 53 (Gym 53) and 65 (Gym 65) centimeters, respectively (Figure 1A). The third one had an ovoid shape with a diameter of 65 cm (Eggball, Figure 1A). All the gymnastic balls were inflated until they reached the circumference reported in the manufacturer's guidelines. The postural balance control was assessed through a computerized force platform (AMTI BP400600, Watertown, MA, USA), recording the CoP trajectory at a sampling frequency of 100 Hz (Figure 1B). The force platform had the following characteristics: average CoP accuracy typically less than 0.2 mm; crosstalk values typically \(\pm\) 0.05% of the applied load; measurement accuracy typically \(\pm\)0.1% of the applied load (minimum applied load of 22.6 kg). The CoP signal was analyzed with the software Balance Clinic 1.4.2. The core-muscle activation was recorded with a BTS FREEEMG (BTS Bioengineering, Milan, Italy). The device resolution was 16 bit, and the sampling frequency was set to 1 kHz. The analyzed muscles were the rectus abdominis (RA), the abdominal external oblique (EO), and erector spinae (ES) of both the right and left sides of each participant (Figure 1B). Ag/AgCl pre-gelled electrodes were applied with an interelectrode distance of 24 mm. The skin preparation, sensor location, and orientation on the muscle bellies followed previous studies [16; 17]. All the gymnastic balls were employed in three different experimental conditions: bipedal seated (BS), unipedal seated (US), and during a dynamic exercise involving both upper and lower limbs (EX). The three experimental conditions are sketched in Figure 1C. Before recording the trials, all the subjects were familiarized with the tasks to perform on the gymnastic balls.  
In the BS condition, the barefooted subjects were instructed to sit on the gymnastic ball with hands naturally resting on their knees and the trunk in an upright position. Both feet were placed on the force platform. In the US condition, the barefooted subjects were instructed to sit on the gymnastic ball with hands naturally resting on their knees and the trunk in an upright position. The nondominant lower limb was raised parallel to the ground with the knee fully extended. In the EX condition, the barefooted subjects, starting from a seated position, were asked to perform alternate leg extensions and sidearm lateral raises while gripping two 1-kg kettlebells. The velocity of both leg extensions and arm lateral raises was standardized by setting a metronome at 50 beats per minute. The support surface on the force platform was enlarged by screwing a wooden board (length 1.50 m; width 0.80 m; depth 0.03 m) on it, allowing both the feet and the gymnastic ball allocation. The distance between the feet and the gymnastic balls' posterior margin was standardized to the length of the right lower limb of the subjects, measured from the anterior superior iliac spine to the ankle's medial malleolus. Subjects were instructed to gaze at a thin line vertically placed on a white wall in front of them, at 0.8 m. For each experimental condition, three trials lasting 30 s were performed with opened eyes.  
Figure 1: Experimental design of the cross-sectional study. (**A**) Gymnastic balls employed in the experimental trials; (**B**) details of the force platform and sensor location on the left, and experimental setup on the right; (**C**) visual representation of the tasks performed by the subjects. From left to right: bipedal seated (BS), unipedal seated (US), and dynamic exercise (EX).