One elite female breaststroke swimmer (height: 1.78 m; weight: 69.8kg) who competes internationally in 50 m and 100m events was selected for in-depth analysis due to the presence of a consistent pattern of yawing motions. Her personal best time for 100m long course is 1.10.85. She is right side dominant (both arm and leg) and when training front crawl she breathes predominantly to the right. At the time of testing she was free of injuries but had, in the past, injuries to ankles, knees, and left intercostal muscle.

Dynamic strength data for shoulder flexion/extension, shoulder internal/external rotation, and knee flexion/extension were collected on a Biodex Dynamometer (Biodex®, Biodex Corporation, Shirley NY.). These actions are known to be prominent in swimming (Miyashita and Kanehisa, 1979; Payton et al., 1997; Payton et al., 2002). The Biodex was set to ‘isokinetic mode’ with constant speeds of 60°/s and 180°/s. A rotational speed of 60°/s is one of the most accepted to measure the peak torque of participants (Campenella et al., 2000; Girold et al., 2006; 2007; Lephart et al., 2002; Lund et al., 2005; McCleary and Andersen, 1992; Stickley et al., 2008). A rotational speed of 180°/s enables assessment of torques that can be applied at rotation speeds similar to those used in actual swimming where, for example, based on our data, the shoulder joints typically flex through approximately 90 degrees in approximately 0.5s in the trials of this breaststroke swimmer. While the knee joint angular velocities commonly exceeded 180°/s accuracy of the measures obtained on the Biodex dynamometer diminishes at speeds higher than 180°/s (Mayer et al., 2001) meaning that 180°/s is the upper limit of the speed range for obtaining accurate and reliable results.

Following familiarisation and warm-up, twelve repetitions of each exercise were performed at maximum effort, first at 60°/s followed by 180°/s conducted in accordance with the standard operating guidelines issued by Biodex Inc. The order with respect to right and left was randomised. Asymmetry in dynamic strength across right and left sides was indicated by a difference in average peak torque at each rotation rate and expressed as a percentage of the higher of the two values. Given that the swimmer’s results were to guide strength and conditioning and physiotherapy programs the swimmer was highly motivated to comply with the instructions ‘push as hard and as fast as you can for every repeat’. The Biodex is known to be reliable among motivated subjects with ICCs of 0.95 at 60°/s and 0.96 at 180°/s reported for peak torque during knee flexion and extension (Feiring et al., 1990).

The participant, wearing a one piece legless racing competition swimsuit complying with the new rules (i.e. not a body suit) was photographed simultaneously by two digital cameras at a distance of 10m capturing orthogonal front and side views of the subject in accordance with the ‘e-Zone’ method described by Deffeyes and Sanders (2005). A bespoke MATLAB program, based on Jensen’s (1978) ‘elliptical zone’ method, was used to determine the segment masses, segment centre of mass positions relative to the segment endpoints, and moments of inertia about transverse, antero-posterior, and longitudinal axes of each segment from the digitised landmarks. Briefly, masses segment masses and moments of inertia are based on the volume of the segment modelled as a series of ellipses with depth of 2cm. Using the diameters of the each ellipse obtained from the digitised front and side photographs in conjunction with estimates of density, the mass of each ellipse can be found. The position of the centre of mass of the segment relative to a meaningful landmark or segment endpoint can then be determined by summing moments and the moments of inertia about the three anatomical axes of the segment determined by summing the local and remote terms of the contributions of each ellipse by applying the parallel axis theorem (Hay, 1993). These methods have been applied in several three-dimensional studies of swimming (Psycharakis and Sanders, 2008; Psycharakis and McCabe, 2011; Sanders and Psycharakis, 2009).

The e-zone method enables the characteristics of the segments of the individual swimmer to be taken into account when calculating segmental contributions to torques about the three body axes. Reliability of repeated digitisations of the photographs has been assessed (paper under review). Coefficients of variation are less than 1% for segment centre of mass locations and masses of the trunk and thorax, less than 2% for the moments of inertia about the transverse and anteroposterior axes, and less than 3% for the moment of inertia about the longitudinal axis. CVs for the smaller body segments are larger, for example, the forearms have CVs of approximately 2% in segment centre of mass location, 5% in mass, and 8% in moments of inertia. However, due to their much smaller mass and moments of inertia, these have only small effects on the whole body net torques.

These e-zone data were then input to the MATLAB analysis program enabling calculation of whole body centre of mass, whole body velocity and acceleration, angular momentum and torque.

To enable identification of the endpoints of body segments when digitising the video recordings, black skin markers 1.5cm in diameter were applied to 19 anatomical landmarks. Marker locations were: the vertex of the head (using a swim cap), the right and left of the following: tip of the 3rd distal phalanx of the finger, wrist axis, elbow axis, shoulder axis, hip axis, knee axis, ankle axis, 5th metatarsophalangeal joint, and the tip of 1st phalanx (big toe). These markers defined a 13 segment body model for whole body CM calculation comprising the combined head and neck, thorax and trunk as a combined segment, right and left arms, forearms, hands, thighs, shanks, and feet. The head and neck was combined as a single segment for calculation of linear and angular kinematics and kinetics. Similarly the thorax and abdomen were combined as a single segment (referred to as the ‘trunk’) for calculation of linear and angular kinematics and kinetics. However, because the hips and shoulders rotate somewhat independently about the long axes of the thorax and abdomen respectively angular kinematics and kinetics of the thorax and abdomen about their longitudinal axes were calculated separately.

The swimmer performed her usual warm-up prior to the testing session for a period of five minutes. The testing required the swimmer to perform a ‘fatigue set’ comprising 4*100m maximum effort breaststroke swims from a push start with no pacing strategy. Successive 100m swims commenced 90 seconds apart ensuring short and diminishing rest time between 100m swims. This was designed to enable assessment of whether technique changed as a consequence of increasing fatigue.

The testing session was conducted in a 25m x 13.25m x 2m indoor level deck swimming pool (average pool temp 29.5° ± 0.2). The volume within which the data were sampled was calibrated using a rectangular prism frame 4.5m in length (X direction), 1.5m height (Y direction), and 1.0m width (Z direction) (Psycharakis, Sanders, and Mill, 2005). The frame was suspended so that half was below and half above the water surface with the X axis aligned with the swimming direction. The calibration frame was recorded by six gen-locked Elmo PTC-400C PTZ cameras (four cameras below and two above the water surface) and digitised to yield separate calibration files for the above and below water views using the Ariel Performance Analysis System (APAS) which incorporates the direct linear transformation (DLT) algorithms of Abdel-Aziz and Karara (1971). The heights of all cameras were adjusted so that the control points on the calibration frame were clearly distinguishable. All six cameras recorded the motion of the swimmer at a sampling frequency of 25 frames per second and an electronic shutter speed of 1/120s enabling sharp images of the moving limbs for digitising.

One breaststroke stroke cycle (SC), defined as the period between the instant of commencement of lateral movement of the hands (Z direction) for the out-sweep to the corresponding instant in the next stroke, was selected from the third lap of each 100m swim. The third lap was chosen as the calibrated space was further from the turning wall for the odd numbered laps than the even laps, thereby ensuring that the swimmer was well into their mid-pool phase and unaffected by the turn. Using the third lap rather than the first ensured that the sample was taken at a time when they were in the phase of the swim in which the pace is almost constant and intracyclic variability is small. APAS was used to manually digitise the nineteen body landmarks separately for above and below water views for every video field from all six camera views. The digitised data set comprised 10 frames prior to, and beyond, the defined SC to avoid subsequent endpoint errors when processing the data. Following DLT transformation of the data into 3D coordinates the above and below water coordinate data were then combined into one single file representing continuous coordinates throughout the SC. This file was input to a customised MATLAB analysis program to calculate all variables. During this process a 4th order Butterworth filter with a frequency cut off of 4 Hz was applied after extrapolating the data by reflection to an additional 20 points beyond the start and finish of the SC (30 fields of additional data at each end) as added insurance against distortion of the endpoints of the data set. The rationale for choosing 4 Hz as the cut-off was based on the Fourier spectral analysis indicating that little power (<1%) was contained in frequencies greater than 4Hz. Also, the frequency cut-off complies with the ‘rule of thumb’ to sample at least five times the highest frequency of interest to avoid aliasing. A Fourier transform and inverse transform was then used to interpolate the data to the equivalent of 200 samples per second to increase the precision of identifying the start and finish of the SC. After trimming the data to the period of the SC the data were then converted to 101 points, again by Fourier transform and inverse transform, representing percentiles of the SC. The use of the Fourier series transform is regarded as highly appropriate when analysing periodic data, such as in swimming (Bartlett, 1997).

The whole body centre of mass (CM) was determined by taking moments about the X, Y, Z reference axes of the segment centres of mass obtained using the digitised endpoint coordinates in conjunction with the segment masses and proportional segment centre of mass locations obtained from the e-Zone program.

Paths of the hands, represented by the wrists, and paths of the feet, represented by the ankles, were expressed relative to the CM. Linear and angular segmental kinematics were determined from the digitised segment endpoint coordinates using standard inverse dynamics approaches.

The angle of yaw of the trunk was determined as the angle between the projection onto the XZ plane of the position vector (v) of the midpoint of the shoulders with respect to the midpoint of the hips and the X axis. Computationally this was: (Eq 1) Where v_i(z) and v_i(x) are the Z and X components of v respectively at the ith time percentile.

The angular momentum vector (H) of each segment (s) was calculated as the sum of local (HL) and transfer (HT) terms calculated using the methods of Dapena (1978). The components of the angular momentum vector represent rotations about the external horizontal X axis (roll), the vertical Y axis (Yaw) and the horizontal Z axis (pitch). To calculate the local angular momentum contribution (HL) the angular momentum of the segment about an instantaneous axis of rotation perpendicular to the long axis of the segment was determined as: (Eq 2) Where HL_trsi is the local angular momentum of segment s about its own transverse axis at the ith time percentile expressed in the external reference system; I_trs is the moment of inertia of segment s about its transverse axis obtained from the e-Zone program (Deffeyes and Sanders, 2005) and y_si is the angular velocity vector of segment s at the ith time percentile.

To obtain the angular velocity vector an orientation vector was defined as the unit vector (R) in the direction of the long axis of the segment. The magnitude of the angular velocity of the segment was: (Eq 3) Where t_i is the time at the ith percentile. The angular velocity vector was then (Eq 4)

This yields an angular velocity vector perpendicular to the plane determined by R_i+1 and R_i-1. Angular momentum of the limb segments about their longitudinal axes was regarded as negligible relative to the magnitude of the angular momentum about their transverse axis and therefore ignored in accordance with Dapena (1978).

Given that the upper and lower torso are large segments that rotate about their longitudinal axis in swimming (albeit not deliberately in breaststroke swimming) angular momenta of those segments about their long axes were calculated. The same process described above was applied except that the orientation vectors were the line between the shoulders for the upper torso and between the hips for the lower torso. It was deemed necessary to treat the trunk as two segments comprising upper torso (including the head and neck) and lower torso when assessing angular momentum about the long axis due to the relative independence of hip and shoulder rotation in swimming (Cappaert, 1998; Payton et. al., 1999; Psycharakis and Sanders, 2008). The anatomical division of the upper and lower torso was the plane perpendicular to the long axis of the body passing through the xiphoid process. Moments of inertia of these segments about their long axes were obtained from the output of the e-Zone program. The angular momentum of the whole trunk (including the head and neck) was then the vector sum of local and transfer terms of the combined trunk segment about its instantaneous transverse axis, and the local and transfer terms of the upper and lower torso about their long axes.

The contributions of the transfer components to angular momentum about each of the orthogonal axes of the external reference frame were computed using: (Eq 5) Where HT_si is the transfer term of the angular momentum of segment s at the ith time percentile and v_si is the vector obtained by subtracting the location of the segment centre of mass from the CM.

Torque at the ith time percentile acting on each segment s was determined as: (Eq 6)

To provide an indication of how consistent the normalised time series were across the fatigue set a repeatabililty coefficient (r) was calculated (Kadaba et al., 1989).

The average peak torque obtained from the Biodex Dynamometer for each exercise and speed are shown in Table 1. The right knee was stronger than the left in knee extension at both 60°/s (9%) and 180°/s (15%). The right side was stronger than the left in knee flexion at 60°/s (17%) but not at 180°/s. Differences between right and left sides in shoulder internal and external rotation were small except for internal rotation at 180°/s (8.1%). The right shoulder was stronger than the left in flexion and extension at both speeds by magnitudes between 5% and 10%. These differences need to be considered in the light of what is common in terms of asymmetry.

Figures 1 and 2 show the Z positions with respect to the midline of the body (line from midpoint of the hips to midpoint of the shoulders) of the wrists and ankles respectively plotted against time normalised to percentiles of the SC defined as the period between the first instant of outward movement of the wrist until the same instant in the next SC. These figures are useful in showing the differences in the width of the pull and kick between right and left sides, the timing of the phases of the stroke, and the differences in timing between right and left sides with successive 100m swims.

The timing of the transition between the out-sweep and in-sweep of the hands coincides with the instant of attaining the widest points and the commencement of recovery is evident as the time when the wrists stop moving rapidly towards the midline (Figure 1). The swimmer slowed as the set progressed due to the effect of fatigue reflected in the times for each 100m (Ist: 1:16.60; 2nd: 1:19.19; 3rd: 123.22; 4th: 127.65). The actual duration of the SCs were 1.49s, 1.46s, 1.62s, 1.73s, with the differences due primarily to an increase in the time from commencement of the kick to the start of hand separation as the swimmer became fatigued. Thus, when represented as normalised time, the events in the 3^rd and 4^th 100m swims occur at a smaller percentage of the SC than the events in the 1^st and 2^nd swims. Despite the changes in duration of the SC the patterns remain very similar within sides of the body (right wrist: r = 0.985; left wrist: r = 0.986; right ankle: r = 0.956; left ankle: r = 0.967)

Figure 3 shows the trunk yaw profiles across normalised time of the sampled SC for each of the 100m swims. Patterns of trunk yaw were similar across the fatigue set (r = 0.900). The pattern comprised a slight yaw to the left (indicated by positive yaw angles corresponding to anti-clockwise rotation) during the out-sweep of the hands, a yaw to the right (indicated by negative yaw angles corresponding to clockwise rotation) during the in-sweep, a rotation to the left during recovery of the upper limbs followed by a rotation to the right to realign the trunk with the line of swimming direction during flexion of the hips and knees in preparation for the kick.

Taking into account the change in duration of the SC across the four swims the yaw patterns were very similar except that the yaw to the left in the second half of the stroke cycle was less in the 3^rd and 4^th swims than in the 1^st and 2^nd swims.

Figure 4 shows the whole body angular momentum across the sampled SC for each of the 100m swims. Apart from the timeline differences associated with the increased duration of the glide following arm recovery, the patterns were very similar (r = 0.859). However, angular momentum reflecting yawing motion to the left during the arm recovery diminished with fatigue.

Figure 5 shows the net torque acting on the whole body. The timing of the torques indicates the link between the actions and the changes in angular momentum. Common trends were apparent across the fatigue set (r = 0.786). During the out-sweep of the hands, the torques were generally positive and therefore developed angular momentum to produce some yaw to the left. During the in-sweep the torques became strongly negative, changing the angular momentum to negative and consequent yaw to the right. A large positive torque coincided with the commencement of the recovery of the upper limbs and eventually reversed the direction of rotation. A negative torque acting to bring the body back into alignment occurred during the recovery of the lower limbs in preparation for the kick. The torques became smaller in the 3rd and 4th 100m swim than in the first two 100m swims.

Through application of the methods described in this paper, the causes of rotations in aquatic activities of individuals, in this case yaw of an elite breaststroke swimmer, can be traced. Asymmetries in technique were shown to be linked to the torques causing the yaw.

Once the technique asymmetries have been identified, programs to ameliorate the asymmetries can be implemented. In this case, habituation of movement patterns, in particular, the left upper limbs being different from the right upper limbs, may be linked to several causes including injury to an intercostal muscle on the left side, right side dominance, and strength differences. It is unclear whether the pattern of lower limb motion emanates from the yawing actions created by the technique asymmetries of the upper limbs. It may be, for example, that the right lower limbs swinging wider than the left in preparation for the kick may be due in part to the yaw to the left that occurs in response to the asymmetrical recovery of the upper limbs.

While further dry land training can be done to ensure that strength asymmetries are corrected, it appears that in this case work must be done to change the asymmetrical movement pattern. In the first instance this should focus on the arm action to eliminate the yaw that occurs prior to the recovery of the lower limbs for the kick. It may be that improvement of the arm action leads naturally to improvement in the asymmetries observed with respect to the preparation and performance of the kick.

It is evident that the approach described may be used in the diagnosis of the causes of misalignments during swimming that reduce performance potential of individual swimmers. This will enable the design of sound interventional strategies to correct technique and establish bilateral symmetry in strength and flexibility.