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Slide track analysis of the relative motion between femoral head and acetabular cup in walking and in hip simulators
Journal of Biomechanics 36 (2003) 889
Letter to the editor
Slide track analysis of the relative motion between femoral head and acetabular cup in walking and in hip simulators In their article (Journal of Biomechanics 35 (2002) 455–464) the authors make useful contributions to the comparison of the functional mechanics of wear testing machines for hip joint replacement implants of the swash plate type. However, for analysis of the movements complying with ISO 14242–1 and for normal human locomotion, the analysis is incomplete. The authors derived a matrix specifying the relative angular movement of points on the articulating surface of the femoral head and the acetabulum and they state that the third term in the matrix is not relevant. In fact, this term corresponds to relative rotation Q between the acetabulum and the femoral head about the axis of the force vector. If it is assumed that the area of contact between the head and the acetabulum corresponds to a circle of radius R in a plane perpendicular to the force vector, the rotational term Q will result in relative tangential movement of the two surfaces in contact. For an element at radius R this will result in a tangential movement of value RQ: The tangential velocity at this point must be combined with the velocity of the point representing the force vector to get the resultant velocity at any point within the area of contact. If the area of contact between the two surfaces extends to the periphery of the acetabulum the pressure in this region will be augmented since the resultant pressure must be centered on the axis of the force vector. In their Fig. 2, the authors reproduced part of Fig. 4 from Paul (1976). This shows the inclination in the coronal plane of the hip joint force vector relative to the axis of the femur, i.e. relative to the line joining the centre of the femoral head and the centre of the knee. The direction of this force vector corresponds to the instant in the loading cycle at the first maximum in the force/time curve. The figure in Paul (1976) shows a second force vector corresponding to the inclination at the instant of the second maximum in the force–time relationship. Likewise, the figure from Paul (1976) shows also the two corresponding angles of the force vector in the sagittal plane. Brown et al. (1984) and Paul (1999) indicate the changes in the inclination of the hip
joint force vector relative to the hip/knee axis during the walking cycle obtained from a number of investigations into normal and hip joint replacement patients. These clearly indicate that the direction of the force vector varies during the walking cycle both relative to the femur and relative to the acetabulum by angles of between 10 and 25 . In the test protocol described in ISO 14242–1, a simplification to this situation is indicated by having the force vector in a fixed direction relative to the polar axis of the acetabulum although this is obviously not the case in normal body function. The data of Bergmann et al. (2001) clearly shows the varying inclination of the force vector both to the femur and to the pelvis. In the wear test machines analysed by the authors, the direction of the joint force vector is taken to be along the polar axis of the acetabular cup. In normal body function this is not the case. Depending on the diameter of the femoral head and the area of contact between the head and the acetabulum, the area transmitting load may extend up to the rim of the of the acetebular cup and in this circumstance as indicated previously, the pressure transmitted at the contact surface will be augmented in the region between the position of the force vector and the rim of the cup possibly leading to augmented wear.
References Bergmann, G. (Ed.), 2001. Hip 98 (compact disc). ISBN.3–9807848–0– 0, Berlin. Paul, J.P., 1976. Force actions transmitted by joints in the human body. Proceedings of the Royal Society of London B 192, 163–172. Paul, J.P., 1999. Strengh requirements of internal and external prostheses. Journal of Biomechanics 32, 381–393.
0021-9290/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0021-9290(03)00074-5
J.P. Paul Bioengineering Unit, Wolfson Centre, University of Strathclyde, Glasgow, G4 ONW, UK E-mail address: [email protected]
Letter to the editor
Slide track analysis of the relative motion between femoral head and acetabular cup in walking and in hip simulators In their article (Journal of Biomechanics 35 (2002) 455–464) the authors make useful contributions to the comparison of the functional mechanics of wear testing machines for hip joint replacement implants of the swash plate type. However, for analysis of the movements complying with ISO 14242–1 and for normal human locomotion, the analysis is incomplete. The authors derived a matrix specifying the relative angular movement of points on the articulating surface of the femoral head and the acetabulum and they state that the third term in the matrix is not relevant. In fact, this term corresponds to relative rotation Q between the acetabulum and the femoral head about the axis of the force vector. If it is assumed that the area of contact between the head and the acetabulum corresponds to a circle of radius R in a plane perpendicular to the force vector, the rotational term Q will result in relative tangential movement of the two surfaces in contact. For an element at radius R this will result in a tangential movement of value RQ: The tangential velocity at this point must be combined with the velocity of the point representing the force vector to get the resultant velocity at any point within the area of contact. If the area of contact between the two surfaces extends to the periphery of the acetabulum the pressure in this region will be augmented since the resultant pressure must be centered on the axis of the force vector. In their Fig. 2, the authors reproduced part of Fig. 4 from Paul (1976). This shows the inclination in the coronal plane of the hip joint force vector relative to the axis of the femur, i.e. relative to the line joining the centre of the femoral head and the centre of the knee. The direction of this force vector corresponds to the instant in the loading cycle at the first maximum in the force/time curve. The figure in Paul (1976) shows a second force vector corresponding to the inclination at the instant of the second maximum in the force–time relationship. Likewise, the figure from Paul (1976) shows also the two corresponding angles of the force vector in the sagittal plane. Brown et al. (1984) and Paul (1999) indicate the changes in the inclination of the hip
joint force vector relative to the hip/knee axis during the walking cycle obtained from a number of investigations into normal and hip joint replacement patients. These clearly indicate that the direction of the force vector varies during the walking cycle both relative to the femur and relative to the acetabulum by angles of between 10 and 25 . In the test protocol described in ISO 14242–1, a simplification to this situation is indicated by having the force vector in a fixed direction relative to the polar axis of the acetabulum although this is obviously not the case in normal body function. The data of Bergmann et al. (2001) clearly shows the varying inclination of the force vector both to the femur and to the pelvis. In the wear test machines analysed by the authors, the direction of the joint force vector is taken to be along the polar axis of the acetabular cup. In normal body function this is not the case. Depending on the diameter of the femoral head and the area of contact between the head and the acetabulum, the area transmitting load may extend up to the rim of the of the acetebular cup and in this circumstance as indicated previously, the pressure transmitted at the contact surface will be augmented in the region between the position of the force vector and the rim of the cup possibly leading to augmented wear.
References Bergmann, G. (Ed.), 2001. Hip 98 (compact disc). ISBN.3–9807848–0– 0, Berlin. Paul, J.P., 1976. Force actions transmitted by joints in the human body. Proceedings of the Royal Society of London B 192, 163–172. Paul, J.P., 1999. Strengh requirements of internal and external prostheses. Journal of Biomechanics 32, 381–393.
0021-9290/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0021-9290(03)00074-5
J.P. Paul Bioengineering Unit, Wolfson Centre, University of Strathclyde, Glasgow, G4 ONW, UK E-mail address: [email protected]