Numerical simulation of cross-country skiing

A program for numerical simulation of a whole ski race, from start to finish, is developed in MATLAB. The track is modelled by a set of cubical splines in two dimensions and can be used to simulate a track in a closed loop or with the start and finish at different locations. The forces considered in the simulations are gravitational force, normal force between snow and skis, drag force from the wind, frictional force between snow and ski and driving force from the skier. The differential equations of motion are solved from start to finish with the Runge–Kutta method. Different wind situations during the race can be modelled, as well as different glide conditions on different parts of the track. It is also possible to vary the available power during the race. The simulation program's output is the total time of the race, together with the forces and speed during different parts of the race and intermediate times at selected points. Some preliminary simulations are also presented.     

Biomechanics of simulated versus natural cross-country sit skiing

The purpose of this study was to investigate the biomechanics of cross-country sit-skiing in simulated and natural skiing. Thirteen international level athletes participated in a ski ergometer test (simulated conditions) and a test on snow in a ski-tunnel (natural conditions) using their personal sit-ski. Tests in both conditions were performed at individual maximal speed. When comparing the two conditions the main results were: (1) maximal speed in simulated conditions was lower (p < 0.05) but correlated well with the natural condition (r = 0.79, p < 0.001); (2) no differences in pole force variables were found; peak force (r = 0.77, p < 0.01) and average force (r = 0.78, p < 0.01) correlated well; (3) recovery time and time to peak did not differ and time to impact correlated with each other (r = 0.88, p < 0.01); (4) no differences were found in peak electromyography (EMG) and average EMG for Triceps, Pectoralis, and Erector Spinae; Rectus Abdominis did not differ in peak. EMG peak and average EMG of all muscles were correlated between the two conditions (r = 0.65–0.94; p < 0.05–0.01). Although some differences were observed, this study demonstrated that technical skill proficiency in natural and simulated cross-country skiing is comparable from a force production and muscle activation perspective.     

Kinematics of cross-country sit skiing during a Paralympic race

The study had three purposes: to verify a hypothesized speed decrease during the 15 km cross-country sit skiing (CCSS) race; documenting this possible fatigue effect (speed decrease), to evaluate changes among the four laps in kinematics parameters (cycle speed, cycle duration, cycle length, duty cycle (percentage ratio between pushing and total cycle duration), pole inclination, trunk inclination and shoulder–hand distance); to compare the kinematics parameters in cross-country sit skiers of different level. Video recordings were carried out during the 2006 Turin Winter Paralympic Games with two conventional digital video-cameras positioned on a flat and an uphill (8.3°) track, respectively. Better performing skiers (G1) had significantly higher speeds than worse performers (G2) both in the flat (6.54 ± 0.13 vs. 5.89 ± 0.50 m s^?1 and 5.55 ± 0.14 vs. 4.62 ± 0.22 m s^?1 in the first and last lap, respectively) and in the uphill track (3.67 ± 0.45 vs. 3.05 ± 0.59 m s^?1 and 3.20 ± 0.36 vs. 2.26 ± 0.36 m s^?1 in the first and last lap, respectively). The G1 athletes were able to maintain the high-speed better than the G2 over the entire race. Significant differences in cycle length and duty cycle between groups would be justified by the higher physical fitness of G1 skiers.     

Effects of fatigue on inter-cycle variability in cross-country skiing

The aim of the study was to examine the inter-cycle variability in cross-country skiing gait and its evolution with fatigue. Both issues were investigated to understand the flexibility capabilities of the neuromuscular system. Four women and four men skied on a treadmill, up to exhaustion. The angular displacements of the arms and legs movements were obtained for 40 s period at the beginning and end of the skiing test. Mean inter-cycle standard deviation (SD_c), largest Lyapunov exponent (λ₁) and correlation dimension (D_c) were computed for each time series and surrogate counterpart to evaluate the magnitude and nature of the variability. For any experimental time series, λ₁ was positive, D_c greater than 1 and both were found to be different from their surrogate counterparts, confirming that the temporal variations of the data had a deterministic origin. More, larger SD_c, D_c and λ₁ values were observed at the end of the test, indicating more variability, noise and local dynamic instability in the data with fatigue. Hence, the fluctuations of limb angular displacements displayed a chaotic behavior, which reflected flexibility of the neuromuscular system to adapt to possible perturbations during skiing. However, such chaotic behavior degraded with fatigue, making the neuromuscular system less adaptable and more unstable.     

Validation of physiological tests in relation to competitive performances in elite male distance cross-country skiing

The purpose of the present study was to establish which physiological test parameters reflects the distance performances in the Swedish National Championships in cross-country skiing (SNC) and the International Ski Federation's ranking points for distance performances (FISdist). The present study also aimed to create multiple regression models to describe skiing performance for the SNC distance races and International Ski Federation's (FIS) ranking. Twelve male, Swedish, national elite, cross-country skiers (maximal oxygen consumption [·VO?max] = 5.34 ± 0.34 L·min?1) volunteered to participate in the study. Their results in the 2008 SNC (15 km race [SNC15] and 30 km race [SNC30]) and FISdist points were used as performance data. On the week preceding the Championship, subjects completed a test battery consisting of 7 physiological tests: isokinetic knee extension peak torque (PT), vertical jumps (VJ), lactate threshold (LT), ·VO?max, and 3 double poling tests of different durations (DP20, DP60, and DP360). Correlations were established using Pearson's correlation analysis, and models to describe skiing performance were created using standard multiple linear regression analysis. Significant correlations were found between the performance parameters and test parameters derived from LT, ·VO?max, and DP60 tests. No correlations with any performance parameter were found for PT, VJ, DP20, and DP360 tests. For FISdist and SNC15, the models explain 81% and 78% of the variance in performance, respectively. No statistically valid regression model was found for SNC30. The results of this study imply that the physiological demands in male elite distance cross-country skiing performances are different in different events. To adequately evaluate a skier's performance ability in distance cross-country skiing, it is necessary to use test parameters and regression models that reflect the specific performance.     

The energy cost of level cross-country skiing and the effect of the friction of the ski

Oxygen consumption [(VO2) in ml.kg-1.min-1], blood lactate concentration ([La] in mM) and dynamic friction of the skis on snow [(F) in N] were measured in six athletes skiing on a level track at different speeds [(v) in m.min-1] and using different methods of propulsion. The VO2 increased with v and F, the latter depending mostly on snow temperature, as did [La]. The VO2 was very much affected by the skiing technique. Multiple regression equations gave the following results: with diagonal stride (DS), VO2 = -23.09 + 0.189 v + 0.62 N; with double pole (DP), VO2 = -30.95 + 0.192 v + 0.51 N; and with the new skating technique (S), VO2 = -32.63 + 0.171 + 0.68 N. In terms of VO2 DS is the most expensive technique, while S is the least expensive; however, as F increases, S, at the highest speed, tends to cost as much as DP. At speeds from 18 to 22 km.h-1, the speeds measured in the competitions, the F for DS and DP can represent from 10% to 50% of the energy expenditure, with F ranging from 10 to 60 N; with S this range increases to 20%-70%. This seems to depend on the interface between the skis and the snow and on the different ways the poles are used.     

Training effects of cross-country skiing and running on maximal aerobic cycle performance and on blood lipids

Two experiments were carried out to compare the cardiorespiratory and metabolic effects of cross-country skiing and running training during two successive winters. Forty-year-old men were randomly assigned into skiing (n = 15 in study 1, n = 16 in study 2), running (n = 16 in study 1 and n = 16 in study 2) and control (n = 17 in study 1 and n = 16 in study 2) groups. Three subjects dropped out of the programme. The training lasted 9-10 weeks with 40-min exercise sessions three times each week. The training intensity was controlled at 75%-85% of the maximal oxygen consumption (VO2max) using portable heart rate metres and the mean heart rate was 156-157 beats.min-1 in the training groups. In the pooled data of the two studies the mean increase in the VO2max (in ml.min-1.kg-1) on a cycle ergometer was 17% for the skiing group, 13% for the running group and 2% for the control group. The increase in VO2max was highly significant in the combined exercise group compared to the control group but did not differ significantly between the skiing and running groups. The fasting serum concentrations of lipoproteins and insulin did not change significantly in any of the groups. These results suggested that training by cross-country skiing and running of the same duration and intensity at each session for 9-10 weeks improved equally the cardiorespiratory fitness of untrained middle-aged men.     

Noninvasive determination of the anaerobic threshold in canoeing, cross-country skiing, cycling, roller, and ice-skating, rowing, and walking

The relationship between velocity (V) and heart rate (HR) was determined in four canoeists, 42 cross-country skiers, 73 cyclists, nine ice-skaters, 10 roller-skaters, 32 rowers, and 20 walkers. The athletes were asked to increase their work intensity progressively, from low to submaximal velocities; HRs were determined by ECG in roller-, ice-skating, and walking, or read on a cardiofrequency meter in canoeing, cross-country skiing, cycling, and rowing. In all the athletes examined the linearity of the V-HR relationship was maintained up to a submaximal speed (deflection velocity, Vd), beyond which the increase in work intensity exceeded the increase in HR. Vd and anaerobic threshold (AT), determined through blood lactate measurements, were coincident in 19 athletes (6 cross-country skiers, 3 cyclists, 2 roller-skaters, 3 rowers, and 5 walkers). Vd was correlated with the average speeds maintained in walking (20 km, n = 13, r = 0.88), cross-country skiing (15 km, n = 20, r = 0.80; 30 km, n = 8, r = 0.82; 12 km, n = 7, r = 0.86; 11 km, n = 7, r = 0.86) and cycling (1,000 m flying-start, n = 68, r = 0.83), thus showing that AT is a limiting factor in these aerobic events.     

Numerical simulation of aldolase tetramer stability

A theoretical study of aldolase tetramer stability, conducted by finite difference Poisson-Boltzmann (FDPB) and modified Tanford-Kirkwood (MTK) techniques using the atomic coordinates of human aldolase, is described. A method for calculating the interaction energy between subunits is proposed. An analysis of the contribution of different energy terms to the stability and oligomeric equilibria (monomer ⇔ dimer ⇔ tetramer) of aldolase is made. It is shown that the loss of solvation energy and electrostatic interactions at very high and low pH-s destabilise the oligomers. These energy terms are compensated over a wide pH range by the stabilization energy due to hydrophobic interactions. It is shown that the aldolase tetramer is energetically more preferable than other oligomers in the pH range from 5 to 11. Subunit-subunit interactions within the tetramer suggest one dimeric form to be the most stable of the possible sub-parts. For this reason the tetramer can be thought of as a “dimer of dimers”. A comparison between our theoretical results and available experimental data shows that the dissociation of the aldolase tetramer below pH 3–4 cooperatively leads to acid denaturation. A second dissociation is predicted to occur at high pH (>12) in addition to the well known acidic dissociation. The analysis suggests that a mutation of His20 or Arg257 to a neutral residue could decrease the pH of the acidic dissociation by approximately 1 pH unit. Received: 16 February 1998 / Revised version: 8 April 1998 / Accepted: 19 April 1998     

Numerical simulation of the cardiovascular system

In this article, we aim at giving a non-technical overview of some mathematical models currently used in the numerical simulation of the cardiovascular system. A hierarchy of models for blood flows in large arteries is briefly described as well as an electromechanical model for the heart. We discuss some possible applications of the numerical simulations of such models, for example the optimization of prostheses. We also address the issue of the data assimilation for the calibration of the models.     

Numerical simulation of microneedles' insertion into skin

Microneedles have recently received much attention as a novel way for transdermal drug delivery. In this paper, a numerical simulation of the insertion process of the microneedle into human skin is reported using the finite element method. A multilayer skin model consisting of the stratum corneum, dermis and underlying hypodermis has been developed. The effective stress failure criterion has been coupled with the element deletion technique to predict the complete insertion process. The numerical results show a good agreement with the reported experimental data for the deformation and failure of the skin and the insertion force. The influences of the mechanical properties of the skin and the microneedle geometry (e.g. tip area, wall angle and wall thickness) on the insertion force are discussed. The numerical results are helpful for the optimum design of the microneedles for the transdermal drug delivery system.     

Numerical simulation of noninvasive blood pressure measurement

In this paper, a simulation model based on the partially pressurized collapsible tube model for reproducing noninvasive blood pressure measurement is presented. The model consists of a collapsible tube, which models the pressurized part of the artery, rigid pipes connected to the collapsible tube, which model proximal and distal region far from the pressurized part, and the Windkessel model, which represents the capacitance and the resistance of the distal part of the circulation. The blood flow is simplified to a one-dimensional system. Collapse and expansion of the tube is represented by the change in the cross-sectional area of the tube considering the force balance acting on the tube membrane in the direction normal to the tube axis. They are solved using the Runge-Kutta method. This simple model can easily reproduce the oscillation of inner fluid and corresponding tube collapse typical for the Korotkoff sounds generated by the cuff pressure. The numerical result is compared with the experiment and shows good agreement.     

Numerical simulation of microneedles' insertion into skin

Microneedles have recently received much attention as a novel way for transdermal drug delivery. In this paper, a numerical simulation of the insertion process of the microneedle into human skin is reported using the finite element method. A multilayer skin model consisting of the stratum corneum, dermis and underlying hypodermis has been developed. The effective stress failure criterion has been coupled with the element deletion technique to predict the complete insertion process. The numerical results show a good agreement with the reported experimental data for the deformation and failure of the skin and the insertion force. The influences of the mechanical properties of the skin and the microneedle geometry (e.g. tip area, wall angle and wall thickness) on the insertion force are discussed. The numerical results are helpful for the optimum design of the microneedles for the transdermal drug delivery system.     

A dynamic model of Nordic diagonal stride skiing,with a literature review of cross country skiing

The forces during the kicking phase in Nordic diagonal stride skiing are described by differential equations and the results are compared with experiments. The difference between static and dynamic friction, interacting with characteristics of the skier such as weight, velocity and the kicking force's angle with the terrain, are essential for high-velocity diagonal striding. Analytical results for relationships between glide length, friction and kicking force are shown. Aerodynamic drag and gravity are accounted for. A propulsion force based on the Hill (1970) equation for muscle contraction velocity and activation is constructed. The model shows a feasible tool for studying the effects of ski stiffness, the kicking force and the amount of waxing during diagonal stride skiing.     

Structural biology: alive and skiing

Structural biologists of all shapes and sizes gathered recently in Breckenridge, Colorado to discuss recent developments in the field. If we are to believe what they said, the future of structural biology is very bright.     

Does off-trail backcountry skiing disturb moose?

The advancement of recreational activities into wildlife habitat calls for a better knowledge about the effects of human-induced disturbances, particularly in systems where humans dominate wildlife mortality. We exposed nine adult free-ranging female moose repeatedly to off-trail backcountry skiing to study moose behavior and habituation using a controlled field experiment in Northern Sweden. Moose response was short-term, but distinct. Moose moved 33-fold faster during the first hour following disturbance, resulting in almost a doubling of the energetic usage per kilogram body weight. Movement rates increased 3 h following disturbances, came along with enlarged activity ranges at the day of disturbance, and resulted in moose leaving the original area. We found no evidence for habituation. Because of the short-term response, the effect of single skiing disturbance events on the overall energy budget of large-bodied animals in good body condition is likely to be negligible. We recommend off-trail skiers to avoid following wildlife tracks because such disturbances bear risk for more severe consequences on wildlife's energy budget if wildlife resists habituation, if an animal's risk perception is high, or when the frequency of disturbance increases.     

Numerical simulation of a surface barrier discharge in air

The development of a surface barrier discharge in air at atmospheric pressure under the action of a constant voltage of different polarity is simulated numerically. When the polarity of the high-voltage electrode is negative, the discharge develops as an ionization wave that moves along the dielectric surface. When the polarity is positive, the discharge develops as a streamer that first moves above the dielectric surface and then comes into contact with and continues to develop along it. In the case of a high-voltage electrode of positive polarity, the discharge zone above the dielectric surface is approximately five times thicker than that in the case of negative polarity. The characteristic aspects of numerical simulation of the streamer phase of a surface barrier discharge are discussed. The numerical results on the density of the charge stored at the dielectric surface and on the length of the discharge zone agree with the experimental data.