S.I. Loginov, professor, Dr.Biol.
J.S. Efimova, postgraduate student
Laboratory of biomechanics and kinesiology, Surgut state university of KhMAR-Ugra, Surgut

Shooter’s ability to control body vertical stability and limb tremor are the acute factors of shooting from any weapon [55; 53; 52]. Herewith, biophysical, biomechanical and physiological mechanisms of these factors are still insufficiently studied in such sports as biathlon and winter polyathlon.

The bibliographical retrieval of the data on the studies of the phenomenon and the mechanisms of vertical stability and human limb tremor while shooting was made using Sport Discus, MedLine databases, information sources of Russian state university of physical culture, sport and tourism (SCOLIPC) and resources of State central medical library and Russian state library (formerly V.I. Lenin state library of the USSR).

Limb tremor and shooting quality. Shooting from all kinds of weapons is known to depend on human voluntary motions and muscle tremor [42, 54, 56, 50] in particular. Tremor parameters are in the inverse relation with shooting, therefore the factors affecting the scope of tremor also influence the ability to point shooting. Adrenalin and local muscle warming essentially increase the scope of tremor, whereas its local cooling decreases it. Adrenoceptor beta-antagonists (betablockers – propranalol, metoprolol, atenolol) act the same, facilitating the increase of postural stability and shooting accuracy by decreasing heart rate and muscle tremor [44, 40], but are prohibited in sport. The intake of increased dosage of vitamins В₁, В₆ and В₁₂ increases shooting accuracy and decreases the value of postural tremor in shooters due to improved delicate control of slow moves with basal ganglions [36] taking part in it. Physiological mechanisms, provoking the noted changes in biathletes, are understudied [47].

Polyathlon has even more unresolved issues. Summer and winter polyathlon are assumed to be one of the hardest sports [6, 14, 15], conceding only modern pentathlon and athletic decathlon by complicacy of athletes’ training. The winter polyathlon program includes cross-country ski race, push-up and air rifle shooting. An athlete fires 20 shots standing in the kneeing position, trying not to move while shooting, be accurate in controlling the rifle and compete, coping with nerves by his will only [15]. The whole shot cycle is conditionally divided into 4 phases [29]. The phase 1 starts from loading a cartridge up to taking a ready position. In this time slot athlete depictures the structure of further actions, takes actions correlated with legs fixing, relaxation of non-active muscle groups and bears arms. In the phase 2 – the phase of preparing to fire a shot - athlete comes to the ready, puts his head on the butt, checks the relative position of body parts, makes respiratory movements, holds his breath and lays roughly. The phase 3 consists in shooter’s actions on pointing and holding the rifle in the center of the target and deciding to shoot or not at this moment. The phase is finished by the moment of the shot. The phase 4 – rest phase, starts from shot and is finished by started loading of the rifle.

Such a differentiation of the shot cycle is tight only for the shots made on the first try. However, a shot is frequently made on the second, third or more tries, with the athlete still holding the rifle and trying with the gun already held at the ready. In case of this shot 2-3 rough laying phases, 2-3 aiming phases, 1 phase of taking up the weapon (1^st) and 1 rest phase (4^th) take place [29]. Herewith, the effect of static load grows significantly.

Shooting is a specific example of sports activity requiring stability and accuracy [29]. All fired shots are not only to reach the target, but ideally hit the mark to the utmost. Accuracy can be improved by regular training [17, 12] and quality of arms. High-quality arms and ammunition are a must, since they ensure more accurate bullet flight path. Physiological and biophysical aspects of training are still unclear, yet sensor (visual control, relation of signal and noise of sensory canal) and locomotor aspects (set and pattern of involvement of synergist and antagonist muscles) are obviously important.

The relation of rifle design and shooting efficiency parameters were studied in the K. Yuan’s and Y.H. Lee’s research [59]. Twenty persons, experienced shooters, were subjected to experiments. In the first part of the experiment the effect of rifle weight and distance before the shot were studied, along with stability of work while doing the exercise. The data of hand angular changes, EMG of muscles under study, general centre of pressure, holding in the aiming point and subjective preferences were analyzed. Various rifle constructions were proved to result in changes in position and vary the level of muscle activation to balance the system, influencing thereby aiming stability. In the second part of the experiment the correlation of aiming and shooting stability (accuracy) was considered within battle shooting. The results of both of the experiments were shown to correlate significantly (R=0,92-0,94, р<0,0001). The authentically high aiming and shooting correlations (R=0.86-0.98, р<0,0001) testify to essential interrelation of aiming stability and shooting accuracy.

Interference, capable of changing significantly shooter’s work result, is an alternative to stability. Interference can be environmental (wind, air temperature, attention deconcentration) and internal (breathing actions, response at heartbeat, arteriopalmus). Interference can occur due to changes in shooting technique [13].

Interference in the muscles incapable due to morphophysiological and biomechanical features of long-term stabilization of vertical or other body position and its kinematic units, such as free hands and shoulder girdle while holding arms in a certain position  [42; 21; 47] is also essential.  

Postural or physiological tremors normally mean a subtle limb trembling. In the classic experiment tremor is estimated by recording voluntary limb motions (usually hand), when a testee tries to constantly hold it in the forefront suspended position. If hand tremor is registered by an ordinary accelerometer, a more or less rhythmic component can be marked, commonly with the peak frequency of 7-11 Hz (Fig. 1). Orthostatic leg tremor with the frequency of 13-18 Hz is pathologic, common for elderly people and is associated with instability while standing [43].

Proceeding from numerous researcg works, the range of human physiological tremor changes occasionally [7, 8, 9, 11, 2, 18, 3, 32, 25], but the oscillation frequency is much more stable. So, according to Martin Lakie, researcher from School of Sport and Exercise Sciences University of Birmingham (England), who wrote in the mid-‘90s of the last century: “Tremor frequency cannot be changed by any popular physiological or pharmacological interferences. Mechanical muscle load is the only known experimental method of changing tremor frequency. Tremor frequency can be reduced by increasing inertia” [47, p. 443]. Proceeding from the experiment with the participation of 245 persons, the peak of tremor frequency for the majority of testees was in the range of 7 to 11 Hz (Fig. 1, A).

Fig. 1. Left hand tremor, measured by accelerometer in an average man within 60 sec. A – amplitude-frequency distribution. B – average spectrum of frequency versus acceleration; С – spectrogram (see А) with the light band representing frequency when the acceleration value is maximum and reflects chance time variation (here frequency is 7,8 Hz at acceleration of 17 × 10−3g). (M. Lakie, 2010, р. 443) [47].

Based on the quoted researches, the author suggests that muscle acts as a resonator or a vibration source tend to fluctuate with the widest range and frequency close to its natural one, testifying to the preference given to the rate of motion rather than its stability [48]. The divergence in tremor frequency between single individuals is very small. Moreover, the fact that the peak tremor frequency correlates with visually motor reaction latency is not proved by any data. Therefore, in shooting the dominating specific peak tremor frequency has no advantage and fails to influence the result [48].

The reason of rhythmic oscillations with the rate of 7-11 Hz is still unknown. Partly, this acceleration can result from repeated impulses made by working neuromotor units. Even in case of complete desynchronization of activity of motor units, a slight trend to force modulation still remains, showing the activity of the most active motor units. In the event of growing frequency summation occurs, activity potential patterns are being generated, capable of keeping lower the basic oscillation frequency [17]. A random input signal from motor units can excite the muscle-tendon system that can provoke limb oscillations close to its natural rate. Partly, rhythmic activity can be stipulated by synchronized motor units [39]. As proved by some data, these two mechanisms work even in isoperimetric constraints [38].

As opposed to frequency, the amplitude of tremor (AT) varies essentially in different people. As shown by the study made by M. Lakie [128], AT differed approximately in 100 times in the sample of 245 persons. Sick people with intensely shaking hands cannot paint or write, hardly eat or drink from tableware. AT was proved to increase with age. The oldest participants had on the average a ten times bigger AT than the youngest participant. Moreover, human amplitude of tremor changes is spontaneous and chaotic, decreasing or growing twice or three times without any notable cyclicity [58, 10].

The amplitude of tremor can be increased or reduced by many ways. β – receptor antagonists are known to increase the AT level along with emotions (anger, fear) by means of adrenaline release. Peripheral β2-receptors are indirectly correlated with tremor through control of sodium-potassium metabolism (general Na⁺-K⁺ pump stimulation) and affect directly muscular contractility.

The increase of AT occurs at thyrotoxicosis. Thyrotoxic tremor results from synergizing the effect of thyroid hormones on adrenaline sensitivity, since tremor is known to be stopped by β-blockers, decreasing the К⁺ plasma level or increasing the concentration of extracellular Na⁺.

Local hand heating increases AT, whereas local cooling – reduces. Alcohol and lithium intake and physical exercises decrease the amplitude of tremor. But, it is to be marked that ischemia effects tremor only when muscles are active [47].

The amplitude of physiological tremor can change influenced by neurogenic and myogenic factors. Alcohol is a typical neurogenic factor. The decrease of AT influenced by alcohol is of central character (stipulated by CNS), since infusion of diluted ethanol directly into a muscle failed to decrease tremor [46]. The way of action is unknown, but as follows from some data, alcohol is capable of suppressing thalamic and cerebellar brain centers [35]. E.g. decrease of muscle temperature by putting a hand into cold water represents a myogenic effect due to reduction of the tetanus amplitude in active motor units, slowing down muscle contraction and relaxation. And an absolutely opposite effect takes place in case of local muscle heating, that is considered as a stimulator of AT [46]. Inadequate blood supply (ischemia) provokes rapid (within approximately 30 seconds) decrease of AT. But ischemia is known not to affect AT in case of still relaxed muscle [45]. The joint effect of ischemia and slight residual contractive activity of muscles responsible for contraction is likely. In its turn, this combination results in metabolite accumulation or depletion in muscle, provoking decrease of AT. Proceeding from the experiments Marti Lakie et al. [45] suggested that locally high extracellular К⁺ concentration related to intracellular K⁺ concentration can directly block tremor influencing T-tubules of skeletal muscle. The blocking damages the transfer of action potential and disturbs the contractive process. Thus, any effects, provoking increase of extracellular K⁺ (e.g. β – blocking), reduce the amplitude of physiological tremor while β2-receptor agonists, facilitating the K⁺ inflow into cells, increase AT. Meanwhile, the supposition of the dominating metabolic changes in the amplitude of tremor is still disputable.

The effect of physical exercises on the amplitude of tremor on the general body level is accompanied by the growth of AT due to adrenaline release of the proved tremorogenic β2-adrenergic effect. However, the quoted effect is realized with a 5-10-minute delay between the peak of preparation blood concentration and peak of increase of AT [47]. If physical exercises are done with the intensity adequate for arising of ischemia in muscles, the significant reduction of AT will be an immediate effect. Therefore, isometric exercises temporarily decrease AT, but the amplitude of tremor is heard to grow after strenuous extensional trainings [109]. Heart work and breathing actions affect the amplitude of physiological tremor, where the latter can be suppressed by will power. Oscillations associated with heart work are noticeable on relaxed hand, but invisible on tense hand. They are concealed by the postural tremor, caused by muscular work. The amplitude of oscillations of ballistocardiographic tremor is approximately 2-10 % of the common postural tremor. Tremor arises due to arterial pulsation, spreading all over the body, and shock wave caused by rapid blood expulsion from heart ventricles. The rise of blood stroke volume provokes growth of both of the components and, consequently, the increase of ballistocardiographic tremor.

Capacities of tremor control. As follows from the foregoing data, changes in postural stability and tremor are central and stipulated by the state of nervous system. Therefore, change in the functional state of central nervous system is assumed to be capable of modifying tremor frequency and amplitude characteristics. The method of formation and activation of artificial stable interactions, optimizing human psychophysiological state, is known to be effective in control of the CNS functional state [30]. So, e.g. rhythmic photostimulation promotes generation of artificial cerebral functional interactions. Matrix of long-term memory with a frequency selective sensor input and output into certain receptor structures of intracentral cerebral regulation, modeling its tonic and phasic activation processes lays the basis of artificial cerebral functional interactions. Its use is effective to improve human exercise performance in extreme conditions. Artificial cerebral functional interactions activated by photostimulation provoke system changes in psychophysiological status and affect mental, vegetative and somatic functions, reserved for several hours after a single activation [27]. However, it is yet to find out on the use of photostimulation of visual analyzer to improve shooters’ postural stability.

Proceeding from the development of new approaches to studies of musculoskeletal system and the ways of use of eddy-current sensors along with measuring systems on its base, V.V. Kozlova studied the effect of static physical load on amplitude frequency indices of pupils’ tremor. The increase of load from 1 kg up to 2,5 kg was proved to result in lower amplitude of oscillations in the range of 8-10 Hz, i.e. high frequency constituents (not exceeding 2,5-5 c.u. in amplitude), up to its almost complete leveling. Herewith, the amplitude of oscillations grows in the area of low frequency band and a shift to the area of lower frequencies takes place (from 3-4 Hz to 1-1,5 Hz).

Stability of holding hand or leg with a rifle was investigated with the use of frequency and statistic analysis of cinematograms in the group of polyathletes and non-athletes [2, 3, 4]. Even prior shooting the amplitude of oscillations in the range of 0,8-1,7 Hz is lower in the groups of athletes, and after shooting the intergroup divergence is more evident (due to increase of the amplitude of oscillations in the group of non-athletes).

Some researchers [37] speak on the importance of the long-term final focus on the purpose before finishing aiming. The authors offered an innovative method of interference in education, meant to improve effectiveness in rifle shooting.

The sampling of 20 world-class skeet shooters was distributed equiprobably into one of the two possible groups in view of scored points in preliminary firing. The ones who studied in groups significantly increased their mean time of fixing their look (397 versus 423 ms). Higher assessments of shooting accuracy were registered, namely 62% (before) versus 70% (after). Proceeding from the results, shooting accuracy improved thanks to work of more effective ways of control of visual-motor strategy.

The purpose of the research by A. Baca, P. Kornfeind [34] was to analyze stability while biathletes are aiming. 9 athletes fired four series of five shots at single target and at the target close to each other in a rifle range. The system reconstructed horizontal and vertical moves of the foresight based on the video record. The time period was divided into 10 equal intervals starting from coming to the ready till finish with a shot. Eight kinematic parameters, describing moves in these intervals, were calculated. Proceeding from the values received, a special variant of artificial neural network of the SOM type (Kohonen self-organizing map) was received. Similar neurons were united in clusters. It was followed by comparison with the corresponding neurons for each shot in 10 databases describing aiming. A number of correlated clusters were used in the relevant order as a complex showing target motion. On the second of processing of shot types the secondary neural network was identified. A more stable pattern was revealed in the members of the national team compared to biathletes a class lower by the shooting level. The significant conclusion of the work was the proved chaotic character of conditions of two series of shots.

The effect of rifle design on shooting parameters was studied in the research by C.K. Yuan, YH. Lee [59]. Twelve experienced shooters were involved in the experiments. In the first part of the experiment the effect of rifle weight and length was considered in the model to allocate stability. Changes in hand angles, EMG of selected muscles, fluctuations of centre of pressure, changes in the target and subjective preferences were analyzed. Various rifle constructions were proved to provoke changing position and muscle activation levels to maintain the system of vertical stability, influencing thus aiming stability. The second part of the experiment was devoted to consideration of the correlations between aiming, stability and accuracy of shooting in conditions of combat firing. The data changed in the same direction in both of the experiments and closely correlated with each other (R = 0.92-0.94, р <0,0001). The high correlation of fluctuation of aiming and dispersion of group shooting effectiveness (г = 0.86-0.98, р <0,0001) testifies to body stability while aiming as a determinant of success in shooting.

Shooting is a variety of human skill to be trained and mastered. Despite the stipulated above biophysical and physiological peculiarities, training standard and shooter’s school within the stages of perennial training is acute while coping with tremor [17, 12, 26]. Training standard is understood to be a combination of serial actions associated with taking a certain position (coming to the ready), aiming and firing a shot. Dozens of methods and methodical details are being realized within this rough algorithm, acquired within perennial and hours-long trainings in the special footwear and costume. In one of the researches, devoted to studies of tremor in 38 shooters, performing in the British National shooting championship and 120 non-shooters, the indices of physiological tremor, were recorded (Fig. 2).

Fig. 2. Comparison of hand tremor of 38 shooters and 120 non-shooters. Average data and its standard deviates in each of the 9 frequency bands are adduced. The amplitude of tremor: dark columns – for shooters, light columns – for non-shooters (M. Lakie, 2010, р. 446) [47].

As follows from the data adduced on Fig. 3, the shooters’ postural tremor in each of the 9 bands is almost half lower than in non-shooters from the control group, testifying to the capacity of control of involuntary movements.

Long before these suppositions the ideas on tremor control had been stated by V.M. Es’kov et al. [7, 8, 9, 10, 11]. The data received by O.V. Klimov are quite interesting [18] in the work devoted to studies of voluntariness in organization of limb involuntary micromovements, i.e. postural tremor. In the experiment with the use of eddy-current sensor cinematograms of finger micromovements at rest were recorded, followed by (still recording) the task given to a testee to actively hold the position – “aiming” and in several seconds – the “Stop” command, while recording limb micromovements.

Fig. 3. A contains a part of the record of finger micromovements at rest with shown oscillations of low frequency on a large scale, modulated by the oscillations of higher frequency. On Fig. 3. B the amplitude frequency characteristic of micromovements on the corresponding time interval is adduced. The cinematogram clearly shoes the peaks close to the frequencies of 1 Hz, 3 Hz, 6 Hz, 8 Hz и 10 Hz with the amplitude of 30, 25, 14, 5 and 4 c.u, correspondingly. Thus, prior to aiming low frequency oscillations dominate in the amplitude frequency characteristics along with a very feebly marked frequency close to 10 Hz.

On Fig. 3. B fragment of the cinematogram of micromovements during target limb holding is presented. As shown in the data adduced in this fragment, hand makes a slow drift from the line of sight, but than comes back to it. The corresponding to this record the cinematogram on Fig. 3. B shows that low frequency tremor components close to 1 Hz and 2 Hz decreased to 18 c.u. and 12 c.u., correspondingly. The amplitude of the 10-Hz-constituent, on the contrary, increased from 4 to 8 c.u.

Fig. 3. Cinematograms and amplitude frequency characteristics of limb micromovements at rest (A, B) and while aiming (C, D). A and B fragments show absolute limb oscillation (finger/ toe) with a response plate from the surface of eddy-current sensor marked vertically. On the X-line – time in seconds. The advisable distance between the response plate and eddy-current sensor, corresponding to the optimal limb position to eddy-current sensor, is indicated by a dotted line. Fragments B and C on the Y-line – amplitude of oscillations (c.u.), on the X-line – oscillation frequency, Hz. (O.V. Klimov, 2004) [18].

The results of studies of the structure of limb micromovements by amplitude frequency characteristics after aiming (relaxation phase) are shown on Fig. 4. C, D. Fragment 4, C shows a cinematogram of micromovements after the “Stop” command. Oscillation with the frequency of approximately 4 Hz arise, with the value reaching 10 c.u. The more thoroughly an athlete aims, the more intensively low frequency oscillations in the range of amplitude frequency characteristics arise (Fig. 4, D).

As shown by the frequency analysis of limb micromovements at rest, voluntary changes can be recorded during and after target holding in the amplitude frequency characteristics of postural tremor, which properties can be changed intentionally. Despite the fact that the testee managed to suppress partly by his will the low frequency tremor, occurring while holding limb, he failed to eliminate it completely. On the contrary, the amplitude of oscillations close to 10 Hz even slightly increased. In the author’s opinion, elite athletes (biathletes, polyathletes) can intentionally affect even more significantly the high frequency tremor indices.

In the study by N.G. Serebryakova et al. [31] the correlation of functional state of neuromuscular system and structure of the range of finger or toe micromovements is defined. The authors allocated the most informative constituents of the tremor range at varied regimes of muscle work. Correspondingly, “tonic” and “phasic” constituents were allocated in the tremor frequency structure (7,5-10,5 Hz and 10,5-12,.5 Hz). At rest “tonic constituent” is dominating, whereas at insignificant muscle tension “phasic constituent” is activated. In case of long-term and pathologic muscle tension the range power increases in the band of 12,5-22,0 Hz, correlating with clinical observations of states accompanying formation of muscle compensatory processes.

Nevertheless, in conditions of polyathlon postural tremor is being realized combined with breathing exercises, return ballistics at heart beat, arteriopalmus, developing fatigue, effect of external and numerous internal neurogenic and myogenic factors. The combination of these factors is chaotic, preventing from confident forecasting of shooting results [23].

The natural-climatic conditions of Ugra, distinguished by frequent changes of temperature, atmospheric pressure and other abiotic and chronobiological factors, affect the chaotic nature of shooting [16, 33, 28, 5]. The influence of dynamic and static physical loads is shown in Ugra in another way [18, 24, 22, 20, 25].

Hence, as follows from the adduced works, body verticality is controlled by integrating the information environment set up by cortex based on the input from visual, somatosensory, vestibular systems and afferent input from motoneuron pools of spinal cord and working muscles. The problem of control of multiple-unit, redundant systems was first settled using the concept of synergies [1, 56]. In the recent researches synergies are defined as the neuron ensembles, promoting low variability of performance characteristics of variables by synchronizing time of samplings in the phase space of elementary variables [49].

The above-stated logically requires studies of the stipulated problems in view of the chaos theory and self-organization of complex systems within methodology of multidimensional phase state spaces. Recently several works have been carried out dedicated to the use of the multidimensional phase spaces in estimation of the properties of physiological and psychophysiological functions of Ugra pupils [5, 85], in studies of behavior of human body state vector in the phase space at physical loads [25], in analysis of efficacy of graduated physical loads on human body by calculating matrices of interattractor distances [19], as well as in the analysis of vertical stability and tremor in polyathletes [24].

Therefore, the analysis of the subjected works testifies to serious attention of researchers paid to the problem of regulation of vertical stability and human tremor in daily life and while making exercises in various sports, especially in the complex kinds with shooting.

Regarding winter polyathlon the problem of vertical stability and hand tremor at shooting is hardly studied. Moreover, there exist very few works devoted to the studies of the features of shooters’ vertical stability and postural tremor influenced by static physical load and various stimulation methods by means of multidimensional phase spaces. This very circumstance prompted in a certain measure to write the present paper.

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Author’s contacts: apokin_vv@mail.ru