**1. Introduction**

Competitive alpine skiing is a physically demanding sport that requires a combination of strength, strength endurance, postural balance, and coordination [1,2]. It comprises a sequence of high-intensity isometric and concentric-eccentric contractions [3]. Recreational skiing is also considered a very intense activity, especially when viewing a recreational skier in terms of their physical abilities. In alpine skiing, the ground reaction force and, thus, the body load is the greatest in the steering phase of the turn after passing the fall line [4,5]. That is when the eccentric work of the muscles also occurs [3]. In competitive skiing, fatigue reduces the skiing speed, increases the turning radius [3], and debilitates the ability to maintain balance, which can result in a loss of skiing control, fall, or injury [6,7]. Indeed, alpine skiing is a sport with a high risk of injury, having an overall injury rate of approximately 2–4 injuries per 1000 skier-days in recreational skiing [8–10] and ~10 per 1000 runs in World Cup competitive skiing [11].

Fatigue may occur in the muscle itself (local or peripheral fatigue) and on the level of the nervous system (central fatigue). Local fatigue is related to the impaired transmission of an action potential, an impaired association between muscle stimulation and contraction, and inhibition of the contractile process [6], while central fatigue is connected to reduced initiation or transmission of motoneuron electrical activity [12]. The development of peripheral fatigue is progressive and depends on the duration of the activity and its intensity. Peripheral muscle fatigue is considered short-lived when it largely ends within 1 min, with phosphocreatine and strength recovery, and it is long-term when the effects of fatigue remain for at least 30 min after activity [13].

Static equilibrium is defined as the ability to maintain the center of mass (CoM) above the support surface [14]. When the center of pressure (CoP) of the ground reaction force is outside the support surface, the body loses balance or an appropriate human action (e.g., a step) occurs in order to maintain or restore equilibrium [15]. In upright standing, the body uses two main strategies to compensate for challenged balance. In anterior–posterior disturbances, an ankle strategy occurs in which most compensatory movements are performed by the ankle and foot [16]. In disturbances that act in the medial–lateral direction, the body responds with a hip strategy, in which more complex movements occur, especially in the hip joint and torso [16,17]. The contribution of the hip increases with a reduced support surface and with larger and faster disturbances. In skiing, the strategy of the ankle is not expressed because the ankle joint is in a sti ff ski-boot and, therefore, does not possess much freedom of movement. Thus, the skier uses predominantly knee and hip joint movements to maintain balance and to regulate the angle of the ski against the snow, from which the turning radius is determined (and, consequently, radial forces) in connection with carved turns [18].

Recently, skis have appeared on the market that are much wider than ordinary skis in the part under the ski boot (waist-width above 100 mm compared to 60 mm on classic skis). Such skis were originally designed for skiing o ff-piste. However, current skis with waist-widths between 80 and 90 mm are considered "allride skis" for on- and o ff-piste skiing, consequently often being used on hard or icy snow. In powder (o ff-piste) skiing, such skis have a wider support base and better flow on the snow. When wide skis are being used on icy/hard snow conditions, the outside and more loaded ski's point of application of the ground reaction force is farther away from the middle of the foot and shifted medially compared to when using narrower skis [19]. It was found that the knee-joint kinematics is consequently di fferent on wider skis than on narrower ones, with knee rotation being more a ffected than knee abduction/adduction. In a study that simulated a quasi-static equilibrium position in a ski turn, it was found that the kinematic changes in the knee were such that the torque in the joint remained unchanged, regardless of the width of the ski [20]. The possible explanation for this was that, by keeping the external torques relatively low, there was also less muscle e ffort.

From studies analyzing human gait, it is known that, as the antigravity muscles ge<sup>t</sup> fatigued, the total speed of movement of the CoM, the amplitude of movement in the mediolateral and anteroposterior directions, and the total range of motion of the CoM increase [21,22]. The purpose of the current research was to investigate the functional stability of the knee joint and balance in a quasi-static simulation of a ski turn when using skis of di fferent waist-widths in connection with fatigue, as the lower-limb muscle fatigue might be an injury risk factor in skiing [23]. In a broader context, the study examined hitherto unknown factors that could a ffect knee-joint injury, which was proven to be the most commonly injured joint in both recreational and competitive skiing [24,25].

The following hypotheses were set:

**Hypotheses H1a.** *Fatigue causes a statistically significant increase in external tibial rotation and knee abduction*/*valgus compared to prefatigue values.*

**Hypotheses H1b.** *The fatigue-induced change in the position of the knee joint (external rotation and abduction*/*valgus of the knee) is statistically significantly more pronounced in connection with wider skis compared to narrower ones.*

**Hypotheses H2a.** *Fatigue results in a statistically significant increase in the movement of the center of pressure on the ground (CoP) compared to prefatigue values.*

**Hypotheses H2b.** *The fatigue-induced increase in the movement of the CoP is statistically significantly more pronounced with wider skis compared to narrower ones and, consequently, the body balance and the knee-joint stability in the fatigue state are hampered more when using wide skis compared to narrow ones.*

#### **2. Materials and Methods**

Fifteen healthy male participants were included in the study (age 33.4 ± 8.6 years; height: 176.9 ± 7.9 cm; weight: 77.3 ± 13.2 kg). They were all physically fit and they were all skiers. None of them had any injury in the last year and no serious injury of any body part at any time in their life span. The study was approved by the responsible Ethics Committee at the University of Ljubljana (No. 1327/2017) and informed consent following the Declaration of Helsinki was obtained from all subjects.

## *2.1. Measurement System*

For three-dimensional photogrammetry, 11 reflective optical markers were placed in accordance with a standardized protocol [26]: six on the outer lower limb, two on the ski boot, and three on the movable plate of the simulator (Figure 1). The reflective markers were recorded using an optical kinematic system (Optitrack V120: Trio, Natural Point, USA), consisting of three calibrated infrared cameras (sampling rate: 120 Hz). With the manufacturer's software (Motive, version 1.5.0.), we obtained real-time information on the position of body segments and standard Euler's angles in the knee joint in three anatomical planes [27].

**Figure 1.** A ski turn simulator with a participant: (**a**) lateral supporting strap with pressure/tensile force gauge; (**b**) optical marker; (**c**) axis of rotation; (**d**) force plate.

The same ski simulator as in a previous study [20] consisted of a metal plate that was attached to the frame such that the plate could be tilted around the sagittal axis (Figure 1). With the help of three optical markers mounted on the simulator's plate, the ski-binding-boot (lower shell of the ski boot) coordinate system was determined. This coordinate system was used to calculate the Euler angles in the knee joint (flexion–abduction–rotation). The ski binding for fastening the ski boot moved freely in the plane of the plate transverse to the axis of rotation with the help of a stepper electric motor controlled by a computer. The ski waist-width was simulated by the displacement of the ski-binding-boot from the axis of rotation (imaginary ski-edge) as shown in Figure 2. The starting position, i.e., ski width = 0, was defined when the mid-sole of the ski-boot was aligned with the axis of rotation (nonrealistic ski width) and, thereafter, two realistic waist widths were simulated: narrow ski = 60 mm and wide ski = 120 mm.

**Figure 2.** A frontal-plane schematic of the apparatus that enabled simulating different ski waist-widths. The elliptic shapes represent the left/outside ski-boot in the simulated right ski-turn. The axis of rotation (pointed by the arrow) represents the inner edge of the left (outside) ski. The simulated width of the ski is equal to the doubled distance between the axis of the rotation (ski edge) and the mid of the boot. The positions "b" and "c" simulated the 60 and 120 mm ski waist-widths, respectively. The position "a" is nonrealistic and was used only to collect reference values. The computer-guided electromotor (not shown on the schema) moved the platform with the ski-boot-binding system between the presented positions.

The participant was strapped to the side via a pressure/tensile force gauge (HBM model: S9M/2 kN, Hottinger Baldwin Messtechnik GmbH, Darmstadt, Germany). The force gauge was connected to an analog-to-digital converter (DEWE 43, Dewesoft d.o.o., Trbovlje, Slovenia). With the help of the Dewesoft X program and the appropriate length of the rope, it was initially ensured that the radial force always represented approximately the same proportion of the force of gravity and, thus, the angle of inclination of the entire body was quasi-statically determined.

Data on the magnitude and direction of the ground reaction force were captured using the Kistler 5691 force plate (Kistler, Winterthur, Switzerland) on which the ski simulator was placed and the accompanying Kistler MARS software (Kistler, Winterthur, Switzerland).

#### *2.2. Measurement Protocol*

The subject was bonded to a robotic ski simulator with his left ski-boot, while the other ski-boot was lifted from the ground throughout the measurement (simulation as if all the weight is on one leg during the turn). The computer-controlled system randomly changed the position of the ground reaction force four times every 10 s, simulating three ski waist-widths: 0 mm (used as a reference value), 60 mm ("narrow ski"), and 120 mm ("wide ski"). The subject had to maintain 60◦ of flexion in the knee joint and 25◦ inclination of the plate for 10 s after each ski-width change on the simulator. These predefined values of knee flexion and ski inclination were set to avoid other influences on knee kinematics and to focus only on ski width, as well as to enable a skiing-like body position and ground reaction forces [20]. Both knee flexion and ski inclination conditions were monitored in real time using on-screen visual feedback. Sets lasting 40 s were repeated three times with a 2 min resting interval. This was followed by a fatigue protocol, during which the subject performed three series of one-legged squats in a ski-boot to a knee flexion angle of 70◦. The knee angle during squats was monitored on the screen in real time by the participant. The participants were loudly encouraged to perform the squats until failure, i.e., until no additional squat could be performed, which enabled us to meet one of the most common definitions of muscle fatigue: "the exercise-induced decrease in the ability to produce force" [28]. During each series of squats, the subject had 30 s of rest. The fatigue phase was followed by three additional 40 s random "waist-width" load sequences on the simulator: the first immediately after fatigue, the second 2 min after fatigue, and the third 4 min after fatigue.

#### *2.3. Data Processing*

For each 10 s measurement on the simulator under di fferent simulated waist-widths, data from the last 5 s before the new waist-width position occurred were used. Thus, the subject had su fficient time for each simulated waist-width to occupy a quasi-static balanced position.

From the kinematics system, flexion, abduction, and rotation in the knee joint [27] were obtained. The force transducer enabled monitoring the magnitude of the radial force in the simulated turn. From the force plate, the following data were obtained:


The mean frequency (MF) of the power spectrum of CoP in both directions (anteroposterior: MFAP, mediolateral: MFML), defined as the frequency of the oscillations of the CoP calculated as the mean frequency of the power spectrum in a given direction. The peak frequency (PF) of the power spectrum of motion CoP in both directions (anteroposterior: PFAP, mediolateral: PFML), calculated as the peak frequency of the power spectrum in a given direction.

Frequency was calculated as CoP changes in a direction (i.e., signal local extremes or peaks) divided by the measurement time (FP) for both directions (anteroposterior: FPAP, mediolateral: FPML).

First, the baseline value of the parameters was determined by calculating the average of the first three measurements for all CoP parameters at a reference waist-width of 0 mm. In the next step, these CoP prefatigue reference values were compared with the values obtained immediately after fatigue, 2 min after fatigue, and 4 min after fatigue on simulated skis of di fferent widths.

#### *2.4. Statistical Analysis*

SPSS.20 (IBM Corporation, New York, NY, USA) and MS Excel 2013 were used for statistical analysis. Data were presented as mean and standard deviation.

The normality of the distribution was first tested using Kolmogorov–Smirnov test and then the homogeneity of variances was tested using the Leven test. Analysis of variance for repeated measurements was used to test the di fferences between the dependent variables. In the post hoc analysis, the di fference between individual pairs was tested with paired-sample *t*-tests.

A two-way analysis of variance for repeated measurements (measurement time (4) × ski waist-width (3)) was used to determine whether there were statistically significant di fferences in parameters at the measurement time factor (before fatigue, immediately after fatigue, 2 min after fatigue, and 4 min after fatigue), with the ski waist-width factor (neutral, narrow, and wide) and with the interaction of both factors (measurement time × ski waist-width). To separately determine whether the groups differ from each other, in terms of ski waist-width (narrow vs. wide ski) and in terms of measurement time, a one-way analysis of variance was performed. Effect sizes were calculated as η2 for variance analysis, as well as for pairwise comparisons using the Cohen's *d* measure [29]. The level of statistical significance was determined at *p* < 0.05.
