Effects of alignment variables on thigh axial torque during swing phase in AK amputee gait
G. Ishai * A. Bar * Z. Susak *
Abstract
It is suggested that a major source of discomfort for aboveknee amputees during the swing phase of walking, is the thigh axial torque (TAT) transferred at the stumpsocket interface. The relation between TAT and variations in its six relevant alignment adjustments, has been investigated. A computerized routine has been established which indicates optimum choice of alignment setting, based on minimal TAT peaks. Feasibility for attenuating swing phase TAT has been demonstrated in three simulated patterns of amputee gait. As a conclusion, it is suggested that a useful clinical tool could be based on the presented alignment optimization procedure and may be expanded to include other factors associated with swing and stance phase comfort and performance.
Introduction
Dynamic effects which occur during the swing phase of walking, of aboveknee (AK) amputees frequently cause a sensation of discomfort which is closely related to the thigh axial torque (TAT) transferred at the stumpsocket interface, and to the associated shear stresses and angular displacement between the socket and the femur. Time characteristics of the TAT is a function of leg kinematics, mass properties of the prosthetic shank, and of kneebolt and shank alignment with respect to the socket. The susceptibility of the amputee to TAT during swing phase is higher than during the stance phase due to inertia and gravity loosening the stump socket attachment while the prosthetic leg is swinging forward.
The kinematics of the prosthetic leg during swing phase is governed by the amputee so as to fulfil functional requirements, such as cadence and ground clearance control. Because his ability to compensate for discomfort associated with TAT is limited, due to loss of voluntary knee control, it is the responsibility of the prosthetist to align the shank and kneebolt in an optimum manner satisfying both comfort and functional considerations.
New York University (1979) and Radcliffe (1955,1968), relate to the kinematic phenomenon associated with the TAT, namely, the internal or lateral "whips". Radcliffe states that an artificial leg must usually have the axis of its knee bolt rotated externally about the thigh axis by as much as 5 degrees to compensate for the tendency of the stump to rotate internally during the swing phase and to minimize whip. Two other adjustments which are referred to by Radcliffe (1968) as critical for proper alignment are the amount of abduction of the shank with respect to the socket, affecting both stance phase mediolateral stability and swing phase TAT, and the inset and outset of the foot which is mainly concerned with whip at the beginning and end of the stance phase. Clinical experience indicates that these guidelines are inapplicable in some complicated cases where final settings are arrived at after many trials. These tire the patient, and moreover, the end result may not fully satisfy the patient and the prosthetist. The source of the problem is mainly due to variability in amputees' gait pattern and in stump musculature as well as the intricate spatial motion of the prosthetic leg, which make achievement of an alignment optimum too complicated without the assistance of quantitative measurements and assessments. Objective measurements via appropriate tools or models may be useful in the clinic only if they determine the magnitude of kinetic variables most closely related to discomfort level and performance in walking, as well as indicate the desired changes in the alignment adjustments.
A previous study (Ishai and Bar, 1981) established a mathematical model, representing the relation between alignment setting and TAT, known to be one of the major causes of discomfort during swing phase. In the present work, TAT characteristics were investigated as a function of gait pattern, and an optimization routine was developed to indicate an alignment setting.
Determination of TAT
Mathematical model
A mathematical model of the swinging prosthetic leg (Ishai and Bar, 1981) determined TATtime variations. The principle of operation of the model is shown in Fig. 1. The values of the alignment variables together with the instantaneous knee flexion angle, determine shankthigh position at each instant of time. These relative positions together with the measured absolute kinematics of the thigh, are used to determine shank spatial kinematics. The force and moment exerted on the shank by the thigh, at the uppermost point of the shank axis, is calculated using the shank equations of motion. The resultant solution is the torque transferred from the shank to the thigh about the thigh axis (TAT).
Alignment variables
A set of six alignment variables has been defined, representing the relevant adjustments which affect the swingphase TAT (Fig. 2). An {X, Y, Z} system of coordinates is attached to the socket of the prosthesis. The Yaxis is the socket's central axis and the Zaxis is parallel to the instantaneous flexionextension axis of the thigh, referenced to the pelvis. A {1,2,3} system is attached to the prosthetic shank with the 2axis coinciding with the shank axis. In the "zeroalignment" state (Fig. 2a), where all alignment variables are set to zero, the two systems of coordinates are coincident.
The alignment variables are:
a and b which define knee centre location in the XZ plane: a represents the location along the X and b, along the Z direction (Fig. 2b and c)
alpha and beta which define the orientation of the knee bolt relative to the thigh system (Fig. 2 d and e): alpha represents the external rotation angle of the kneebolt about the Yaxis, and beta the angular inclination of the kneebolt with relation to the XZ plane.
c and gamma define the position of the shank with respect to the thigh system (Fig. 2 b and f): the c adjustment is achieved by shifting the shank forward with respect to the knee bolt. The angle gamma is formed by the shank axis relative to the XY plane while standing (theta_{K} = 0).
It should be noted that some alignment systems do not allow the adjustment of all the 6 parameters mentioned, and that each alignment parameter does not necessarily correspond to a single degree of freedom in the alignment device.
Leg kinematics and mass properties of the prosthesis
Due to the unavailability of spatial kinematic data of AK amputees' gait, the kinematic inputs introduced to the model were based on normal gait data published by Lamoreux (1971). In cases where amputees' typical gait patterns were investigated, the normal data were modified: to simulate a case where the amputee has an abducted stump, a constant abduction was added to the normal abductionadduction angle between thigh and pelvis, at each instant of time. The simulation of circumducted gait was carried out by multiplying the normal thigh abductionadduction data by a constant factor.
Geometrical dimensions and mass properties of the prosthetic shank are similar to a USMC AK prosthesis type U.S. Universal Multiplex Mark V.
TAT optimization
The TAT simulation based on the mathematical model in Fig. 1, may be used in the clinic in the search for an optimum alignment setting which causes minimal peak values in TAT characteristic during swing phase. Using measured leg kinematics and mass properties of the prosthetic shank, the mathematical model may be used to estimate the time change of the TAT for all possible combinations of alignment setting. The setting which results in minimal peak values of TAT is chosen as optimum. The foregoing procedure was found to be time consuming and impractical for clinical use, because it demanded excessive computer time to determine TAT at each alignment setting. In the search for a shorter optimization procedure the relation between TAT and the alignment variables was investigated.
The TAT at zero alignment in the normal, abducted and circumducted gait patterns, are shown in Fig. 3. TAT sensitivity to unit variations in the alignment variables about the zero alignment state (1 degree in alpha,beta,gamma and 1 cm in a, b, c), is depicted in Fig. 4, for each of the walking patterns. There is a fundamental difference between the effects on the swing phase TAT of changes in the gamma and b adjustments and of changes in alpha and beta. gamma and b cause the shank axis to lie outside the XY plane during walking. Both the orientation of the shank axis and the distance of the shank centre of mass from this plane remain constant during the whole walking cycle. On the other hand, alpha and beta cause the orientation of the shank axis with relation to the XZ plane to change as a function of the magnitude of knee flexion. The greater the knee flexion, the larger the angular deviation of the shank axis relative to the XZ plane. This difference is expressed in TAT characteristics at the beginning and end of swing phase where TAT values are noticeably higher for a change in gamma and b as compared to those obtained by changes in alpha and beta. It should be noted that a numerical filter with a 7 Hz cutoff frequency was used to smooth the kinematic information during data processing and may have filtered out the expected high frequency contents at knee full extension impact near the end of the swing phase. It is expected that contributions to TAT of the gamma and b deviations from zero adjustment, would be even larger than those obtained by the simulation.
It is evident that while the sensitivities to alpha, beta, gamma and b variations are practically invariant with the investigated walking patterns, the sensitivity of TAT to variations in the a and c adjustments is largely influenced by the investigated gait patterns. This is explained by the a and c adjustments affecting the anteroposterior (Xdirection) placement of mass elements of the shank relative to the thigh, thus influencing the magnitude of the momentarm about the thigh axis, and of mediolateral (Zdirection) "inertiaforces" acting on the shank. Since the walking patterns mentioned above differ in mediolateral character of motion, and subsequently in the characteristics of mediolateral inertia force acting on the shank, the TAT sensitivity to variations in the a and c adjustments is largely affected by the walking patterns. Conversely, since alpha, beta, gamma and b adjustments influence the positioning of mass elements of the shank in the Zdirection, the TAT sensitivity to these alignment variables is practically unaffected by the changes in the walking patterns.
TAT sensitivity to alignment variations was investigated in a wide range of simulated alignment adjustments: alpha, beta and gamma, 8 to +8 degrees, a and c 5 to +5 cm, and b from 8 to +8 cm. By introducing unit variations to the alignment variables within these ranges, it was found that deviations of the alpha, beta, gamma and b sensitivities from the respective zeroalignment sensitivities, were less than 5 %. Conversely, the sensitivity to unit variations in a and c was found to vary significantly within the alignment range. Since the values of the a and c adjustments are usually predetermined from stance phase considerations (as they play an important role in achieving knee stability), their values may not be changed in the optimization of swingphase TAT.
TAT (denoted by T) is a function of time t and of the six alignment variables :
Equation
The total differential of T for constant t is given by:
Equation
Since the sensitivity of TAT to variations in alpha, beta, gamma and b is practically constant throughout the alignment range and as a and c are constrained by stancephase considerations and are kept constant in the optimization process:
Equation
where S_{alpha}(t), etc., denote the sensitivity characteristics of TAT to unit variations in alpha, beta, gamma and b, which are independent of the values of the alignment variables. The TAT, therefore, may be determined by:
Equation
The meaning of equation 4 is that the TAT for any combination of the alignment variables (alpha',beta',gamma',a,b',c) may be estimated from a given TAT and its sensitivities at another setting (alpha, beta, gamma, a, b, c), providing that a and c are kept the same at the two settings. This equation replaces the mathematical model of Fig. 1 in the iterative process of TAT optimization. As a result, the optimization procedure is significantly shortened (only a few minutes), because the lengthy calculations involved in the mathematical model are carried out for just the determination of TAT sensitivities and characteristic at the initial setting.
Results
The TATsimulation of Fig. 1 and the optimization routine of equation 4, were used to test their feasibility in optimizing prosthetic alignment in three cases, each representing a different simulated gait pattern.
Case 1. Normal hip and knee kinematics; 7 cm effective shank valgus
In the conventional alignment procedure, adjustment of y and b both serve to control the mediolateral position of ground reaction relative to the hip joint during the stance phase of walking. These control mediolateral stability and regulate load transfer characteristics to the stump. The result of the b and y deviations from the zeroadjustment is, therefore, an "effective valgus (or varus)", defined as the resulting mediolateral shift of the foot from the XY plane. An effective valgus may be achieved by an alignment device located immediately above the knee bolt ("lowerthigh device"), or alternatively, by a device located just below the knee ("uppershank device"). For the former, in addition to shin abduction (gamma), the knee bolt is angularly tilted by beta = gamma; in the latter, the knee bolt remains perpendicular to the thigh axis (beta = 0). For example, an effective valgus of 7 cm may be achieved by a lowerthigh device, having beta = gamma = 1.2 degrees, at a shank length of 55 cm. Stance requirement for knee stability usually dictates a negative setting of a, while the shank axis coincides with the thigh axis at standing, i.e. : c = a. In the present example a and c were 1.5 and +1.5 cm, respectively. The resulting TAT, which is depicted in Fig. 5, shows peak values of +2.31 and 1.61 Nm. The same effective valgus may be obtained by setting beta = 0 and gamma = 72 degrees, using an uppershank device. It is clear from Fig. 5 that the uppershank device is preferred, as it gives a markedly lower positive peak value of 0.82 Nm (in the direction of outward rotation about the thigh axis). Using the optimization routine based on equation 4, the setting of alpha = 2 degrees, beta = 7 degrees, gamma = 7.2 degrees and b = 0.0 cm, gave even lower peaks. In the optimization procedure alpha, beta and gamma were varied in 1 degree increments over a range of ± 8 degrees, b was determined by the constraint equation :
Equation
where EV is the effective valgus of 7 cm, and l the shank length of 55 cm. b was limited to the range of ±5 cm.
Case 2. Abducted stump
A typical case often met in the clinic requiring special attention, visąvis TAT attenuation, is that of the abducted stump amputee. For example, a 12 degrees of abduction was simulated as previously described where a and c were set to 1.5 and +1.5 cm, respectively, to fulfil stance requirements. Fig. 6 is the resulting TAT, for the case where all other alignment variables are set to zero. Unfortunately, this setting is usually unacceptable for both stance and swing phase considerations, and it being necessary to medially shift the foot with respect to the thigh. A 7 cm shift results by making gamma = 7 degrees utilizing the uppershank alignment device. The resulting TAT (Fig. 6), has peak values of +2.2 and 1.45 Nm. Using the lowerthigh device, instead of the uppershank device, to obtain the same medial shift of the foot, i.e., beta = gamma = 7 degrees, results in a TAT peak reduction to +18 and 10 Nm (18% and 28% attenuation in the positive and negative peaks respectively). Further attenuation of the positive TAT peak to 15 Nm, which occurs at the end of the swing phase, is obtained by using optimization routine, as in case 1. Nevertheless, it should be noticed that the further reduction of 14% in TAT peaks (having the gamma = 7 degrees as reference) causes a significant increase of TAT magnitude near midswing.
Case 3. Circumducted gait
Another pattern of amputees' gait associated with high TAT magnitudes, is circumducted gait, e.g., the exaggerated mediolateral movements of the leg in this gait pattern were simulated by multiplying thigh abduction by a factor of 2.0. The resulting TAT (Fig. 7), demonstrates high peak values of +1.8 and 3.5 Nm, at the reference setting of alpha = beta = gamma = b = 0.0, a = 1.5 cm and c = +1.5 cm. In this case the high TAT magnitude cannot be significantly reduced by the limited available adjustment range of alpha, beta, gamma and b, because of low TAT sensitivity to these parameters. The peak values can be attenuated by shifting the knee centre forward, together with the shank, i.e., by making a more positive and setting c to zero ; as depicted in Fig. 7, by setting alpha, beta, gamma = 0, a = 5 cm, b = 3 cm and c = 0 cm, a 22% and 34% attenuation is obtained in the positive and negative peaks, respectively. This alignment is unacceptable in commonly used prostheses, because it contradicts the stance phase stability requirement. However, it may be beneficial for amputees with circumducted gait to have a knee mechanism which allows a positive asetting. One possibility is a control system which ensures knee locking during the weightbearing phase, even for a positive asetting. An alternative is a polycentric knee design having a negative asetting at full extension which becomes positive with knee flexion.
Discussion and conclusion
A mathematical model estimates the thigh axial torque (TAT) during the swing phase of walking, for measured leg kinematics and alignment setting. The model, together with the optimization routine, potentially form a clinically efficient "tool", quickly predicting a final optimum alignment setting.
Where determination of TAT may be accomplished by a "pylon transducer" (Berme, 1976) installed in the prosthetic shank and knee goniometer, alignment optimization is made simpler. The reference TAT and the four sensitivity curves (S_{alpha}, S_{beta}, S_{gamma} and S_{b}) are obtained from five successive gait trials. The required changes in alignment are subsequently predicted by the optimization routine, using equation 4. It should be noted that, in this case, the initial alignment setting is not involved in the optimization process and, therefore, need not be measured.
The results obtained in cases 1 and 2 indicate that both lowerthigh and uppershank alignment devices should be used to achieve optimum setting.
Because of an absence of rigorous definition of the interaction between TAT and patient comfort, the present paper bases optimum alignment in terms of TAT peak reduction. When defined, an expanded form of optimization criteria, presumably involving parameters such as TAT derivatives and integral, may be incorporated in the optimization procedure.
Modified simulated kinematics for normals were introduced to the model of the swinging leg. The optimization procedure will be verified in clinical alignment routines, using measured amputee data in the model. The procedure will be expanded to include other swing and stance phase considerations.
Acknowledgements
The authors wish to thank Mr. E. Lewy from Protesia Lewy Co., TelAviv, for his assistance and advice.
The study was made possible by a grant from the MEP Fund, Women's Division, American Technion Society, N.Y., U.S.A.
References:
 Berme, N., Lawes, P., Solomonidis, S., Paul, J. P. (1976). A shorter pylon transducer for measurement of prosthetic forces and moments during amputee gait. Eng. Med., 4(4), 68.
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 Radcliffe, C. W. (1955). Functional considerations in the fitting of aboveknee prostheses. Artif. Limbs, 2(1), 3560.
 Radcliffe, C. W. (1968). Alignment of the aboveknee artificial leg. In Klopsteg, P. E. and Wilson, P. D. (eds.), Human limbs and their substitutes. Hafner, New York, p. 676692.
