To accurately assess the symmetry of motion, the side differences should be assessed throughout the entire movement cycle [33]. Such a method may be the dynamic symmetry function (SF), based on commonly used symmetry index [2], which was previously used to assess the gait of patients after unilateral total hip replacement [28]. The symmetry index is a standard measure of asymmetry and quality of walking and can be seen as an essential topic in gait analysis. In particular, it increases the energy cost of walking and agrees with the dynamic balance deficits. The asymmetry can affect all aspects of gait, for example, spatially, by unequal step lengths between right and left, or temporally, by dissimilarity in time spent in the stance or swing phase between the two feet [26], and finally, by inequality in the joint kinematic characteristics and ground reaction forces [11,16].
Many authors point out that asymmetric gait patterns and the resulting increase in hip joints of transfemoral amputees may be associated with a higher risk of lower back pain (LBP) and hip osteoarthritis of the intact limb [33,39]. Reducing gait asymmetry through effective rehabilitation reduces the degree of stutter and, consequently, reduces the possibility of faster occurrence of degenerative changes in the contralateral knee joint and a decrease in the incidence of the LBP. The registered mechanism of changes in the range of motion of the pelvis and hip joint is an expression of compensatory movements aimed at alignment of the asymmetrical gait pattern. Investigations show that transfemoral amputation is not always the cause of the LBP. Morgen and coauthors [40] analyzed the kinematics of gait in TFA people with and without LBP. Transfemoral amputees with LBP showed higher transverse plane rotation in their lumbar spine during walking compared to amputees without LBP. The reason may be associated with intervertebral disc degeneration, suggesting that increased transverse plane rotation, secondary to walking with a prosthetic limb, may be a factor in the etiology of low-back pain in transfemoral amputees [40]. Risk of LBP events appears to vary by TFA etiology. Obesity did not correlate significantly with increased frequency of LBP events or time to the events. Phantom limb pain correlated with decreased time to LBP events after amputation. The association between prosthesis receipt and LBP events is ambiguous [41].
Moreover, prolonged time asymmetric loading of the lower limb may result in atrophy of stump muscles and degenerative changes in the joints [25]. The main challenge is to choose the adequate calculation of asymmetry depending on what aspect of gait one wants to assess. Usually, the easiest way is to calculate the difference between two sides, either with raw or absolute values, with or without reference to the average range. Different formulas were adopted, such as symmetry ratio, symmetry index, logarithmic transformation of the ratio or angle of symmetry [16,20,31–33], to objectively quantify the assessed phenomenon. These mathematical methods have been utilized in various clinical applications with different diagnostic values in relation to kinematic data [42]. Each approach demonstrated a similar advantage in terms of discriminative ability and has some significant disadvantages or shortcomings. The index is a single value which strongly depends on selected data points and reference values [42].
The symmetry analysis in our study assessed differences in the whole measured range and very accurately specified the areas where the symmetry was the largest or the smallest. Moreover, a symmetry function (SF) close to zero represented perfect symmetry, and the positive/negative sign indicated the direction of the asymmetry, while the value indicates the magnitude of asymmetry. The SF not only estimated symmetry values in the region of maximum value occurrence for which symmetry is most often assessed but also checked the proximity of these areas. The SF designated sections that were similar or not and indicated their degree of differentiation (difference?). The method is precise (for both large and small values) objective and standardized. Its values represent the degrees of similarity (symmetry) or difference (asymmetry) of the compared graphs. The correspondence with the scalar values is also confirmed by the statistical analysis between the peak values for the extracted parameters of time courses of articular angles. It is better to use tools already established and well known as the formulas for symmetry functions to compare successive evaluations or several subjects.
In the present study, gait of patients after unilateral TFA was characterized by an asymmetric range of motion in the main body joints. The pelvis and hip movements had the highest SF value, which was confirmed by statistical tests and the largest asymmetric areas revealed by the function. The most significant differences in pelvic obliquity were recorded during midstance (approximately 25 percent of cycle time (%CT)) and at initial- and mid-swing, where SF values reached more than 20%. In the sagittal plane, the pelvis tilted asymmetrically at the beginning of step initiation. The SF value reached more than 20%. Subsequently, in middle stance, movement was symmetrical, and in terminal stance, movement was again asymmetrical. The highest SF value was more than 25% at 60 %CT. In the transverse plane, the pelvis was even more asymmetrically positioned throughout the entire gait cycle. The size of the asymmetry was approximately 50% throughout the whole movement. Movements in the hip joint essentially mirrored the movements of the pelvis. The differences between the involved and uninvolved sides in topmost values were also statistically significant. In the frontal plane, the differences in SF reached 60% throughout the first part of the cycle. Movements in the sagittal plane were mostly symmetrical. Nevertheless, one of the most significant differences occurred in the transversal plane. Throughout the gait, the involved limb had significantly higher angle values than the uninvolved, and the symmetry function value oscillated from approximately 25% to 60% throughout the swing phase. Movements in the other studied joints had a repeatable pattern, e.g., the knee flexion-extension angle did not differ by more than 4% throughout the entire walking task, and the ankle plantar-dorsiflexion angle reached the value of -19.2% only during the swing phase. Similarly, no statistically significant differences between the peak values were present.
The asymmetry of the hip (resulting directly from a reduction of the hip angle at foot strike during the contact phase) may result from keeping the knee prosthesis straight at the beginning of the support phase [22]. However, the symmetry varied depending on the socket type and gait speed – the stability of interlimb coordination increases with walking velocity, and the prosthesis-induced asymmetry diminishes at higher walking velocities [21]. Moreover, the pelvis is significantly more anterior tilted at foot strike for the uninvolved limb. The increased pelvic tilt in sync with hip flexion for the uninvolved side is a compensating strategy adopted to obtain a functional step length and symmetrical thigh inclinations [18]. For the intact, uninvolved limb, hip range of motion in the sagittal and frontal planes turned out to be significantly larger than for the residual, prosthetic limb [13], which demonstrated the role of the intact limb in compensating for reduced or absent muscles and joint function in the residual limb of TFA patients during walking.
The timing of extreme values (minimum and maximum) for the range of motion most often did not coincide with the time of occurrence of the extreme values of the SF function. The single agreement was observed in pelvic movements for the time of maximum value in tilting the pelvis. The timing of events for other analyzed movements was significantly different.
The maximum value of the vertical ground reaction force (GRF) component assessed throughout the entire gait cycle was usually the highest in the supporting phase of the TFA gait pattern, and its value for the amputated limb was significantly lower than that for the uninvolved limb [29,43,44]. Our previous research showed that variables describing GRF behavior were statistically smaller for the amputated limb regarding values for healthy controls by almost 7.7 percent of body weight (%BW) in the supporting phase, 12.3 %BW in terminal stance, and 12.0 %BW for the posterior braking force at initial stance [25]. Values of the vertical component of GRF during underweight in middle stance were on average 5.8 %BW higher for the amputated limb. In our study, all the components of the ground reaction force (GRF) showed a difference between sides, as revealed by the SF function. The value of symmetry seldom exceeded 5% in the supporting area. The involved limb was characterized by less value of reaction force in the weight acceptance phase, especially between 5-40 percent of the stance time (%ST). The mean value of symmetry function in the entire anteroposterior range was -1.0 ± 1.1% and oscillated from the smallest value (Min) of approximately -7% at the beginning (at approximately 10 %ST) and at the end of the support phase (at approximately 85 %ST) and the highest value (Max) of approximately 7% in the middle support (at 60 %ST). These areas are marked in red in Figure 3. At the same time, the differences in the Min and Max extreme values between the involved and uninvolved sides were not statistically significant. The mediolateral GRF component was characterized by the largest asymmetry, and the areas with the largest differences occurred at the beginning of the support (between 10 and 40 %ST) and in the propulsive phase at the end of the support (between 80-90 %ST). The average value of symmetry function throughout the entire cycle of movement was 0.4 ± 1.3% and varied from the smallest value (Min) of approximately -9% to 12% (Max). Similarly, differences in the Min and Max extreme values between the involved and uninvolved sides were not statistically significant.
The dynamic symmetry function proved to be a good tool to localize the regions of asymmetry and their positive or negative direction in the full gait cycle of transfemoral amputee gait. In the study group, there were differences in anteroposterior GRF forces between limbs, expressed as a change in their value. The amputated limb carried a higher load than the healthy limb. In addition, areas of increased pelvic and hip joint asymmetry were registered in the study group, mainly in the transverse and frontal planes. For this reason, there is a justified risk of bearing a higher load on the thigh stump of the amputated limb inside the socket. This is due to the lower protection of the amputated stump in the funnel for rotational movements (in the transverse plane) than for flexion-extension movements (in the sagittal plane). In rehabilitating people after TFA, overturning the maximum possible gait function determines the patient's future quality of life. Thus far, the use of the results of comprehensive movement analysis and their results in the daily practice of the rehabilitation team has been limited, influenced by the need to have appropriate training to interpret the results and to provide time for their analysis. In addition, the conclusions of the analysis were challenging to apply in daily therapy. By using the SF symmetry measure, data analysis is more accessible by detecting areas of asymmetry. The ability to interpret and use the results obtained is easier, which, in turn, enables more precise development of therapy goals. Imaging of asymmetry areas, in addition to information for the rehabilitation team, has additional functions for the person after TFA subject to improvement on the basis of feedback: the ability to assess the progress of improvement, by both the team and the patient, positively affects the active participation of the patient in rehabilitation.