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Influence of head constraint and muscle forces on the strain distribution within the intact femur
Medical Engineering & Physics 24 (2002) 243 www.elsevier.com/locate/medengphy
Letter to the editor Influence of head constraint and muscle forces on the strain distribution within the intact femur The authors responded to my letter to the editor (Medical Engineering and Physics 23 (2001) 435-436. Readers should be aware that although, as the authors say, finite element analysis will allow the determination of an indeterminate force (in this case the horizontal component of force which the authors apply in their test rig) any such calculation must take account of the support conditions for the assembly tested. The authors state that the fermoral component is “fixed” at its distal end. This is an easy situation for analysis. In fact the component is in a test rig in which absolute fixation will be difficult to achieve. In an analysis of the type proposed the value of an indeterminate force action is particularly sensitive to elastic deflection of the supports. For the above reasons I take the liberty of repeating “It is important that it is recognised that no conclusions on structural loading stresses and strains can be drawn from test set-ups, which are statically indeterminate”. The authors may wish to be aware of a simple approximate method of determining the load actions on the head of femur due to tension in the iliopsoas tendon. In figure 4 of the original article if the line of the force vector is drawn at the 9 degree angle to the vertical which the authors specify it would be found to pass very close to the centre of the head of the femur allowing the medio lateral force component to be neglected. In the sagittal plane view in the right hand part of the figure the iliopsoas tendon, if it had been drawn in, would pass
vertically upwards in contact with the left anterior margin of the femoral head as it is shown. It is a realistic assumption that the coefficient of friction between the tendon and the head of femur would be negligibly small. Thus the force in the proximal part of the tendon would be the same as that in the distal. The force vectors will then form an isosceles triangle with the angle between them 47°. The resultant force transmitted to the head of femur FFHIP is given by: FFHIP ⫽ 2FIPsin23.5 ⫽ 0.8FIP The force acts on the femur in a direction 66.5 degrees from the vertical upwards and to the right in the view shown in the right hand part of the authors Figure 4. If the pelvis tilts forward or the femur flexes or extends the angle subtended at the centre of the femoral head by the part of the iliopsoas in contact with the head should be amended. If the femur is flexed beyond a certain amount (here approximatey 40°) there will be no contact between the tendon and femoral head. This, however, is unlikely to occur in walking on a level surface. If a stress analysis of the whole femur is to be undertaken the free body diagram should include this FFHIP force as well as the FIP force at the lesser trochanter. J.P. Paul, University of Strathclyde, Bioengineering Unit, Wolfson Centre, Glasgow G4 0NW, UK E-mail address: [email protected]
1350-4533/02/$22.00 2002 IPEM. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 4 5 3 3 ( 0 2 ) 0 0 0 0 7 - 3
Letter to the editor Influence of head constraint and muscle forces on the strain distribution within the intact femur The authors responded to my letter to the editor (Medical Engineering and Physics 23 (2001) 435-436. Readers should be aware that although, as the authors say, finite element analysis will allow the determination of an indeterminate force (in this case the horizontal component of force which the authors apply in their test rig) any such calculation must take account of the support conditions for the assembly tested. The authors state that the fermoral component is “fixed” at its distal end. This is an easy situation for analysis. In fact the component is in a test rig in which absolute fixation will be difficult to achieve. In an analysis of the type proposed the value of an indeterminate force action is particularly sensitive to elastic deflection of the supports. For the above reasons I take the liberty of repeating “It is important that it is recognised that no conclusions on structural loading stresses and strains can be drawn from test set-ups, which are statically indeterminate”. The authors may wish to be aware of a simple approximate method of determining the load actions on the head of femur due to tension in the iliopsoas tendon. In figure 4 of the original article if the line of the force vector is drawn at the 9 degree angle to the vertical which the authors specify it would be found to pass very close to the centre of the head of the femur allowing the medio lateral force component to be neglected. In the sagittal plane view in the right hand part of the figure the iliopsoas tendon, if it had been drawn in, would pass
vertically upwards in contact with the left anterior margin of the femoral head as it is shown. It is a realistic assumption that the coefficient of friction between the tendon and the head of femur would be negligibly small. Thus the force in the proximal part of the tendon would be the same as that in the distal. The force vectors will then form an isosceles triangle with the angle between them 47°. The resultant force transmitted to the head of femur FFHIP is given by: FFHIP ⫽ 2FIPsin23.5 ⫽ 0.8FIP The force acts on the femur in a direction 66.5 degrees from the vertical upwards and to the right in the view shown in the right hand part of the authors Figure 4. If the pelvis tilts forward or the femur flexes or extends the angle subtended at the centre of the femoral head by the part of the iliopsoas in contact with the head should be amended. If the femur is flexed beyond a certain amount (here approximatey 40°) there will be no contact between the tendon and femoral head. This, however, is unlikely to occur in walking on a level surface. If a stress analysis of the whole femur is to be undertaken the free body diagram should include this FFHIP force as well as the FIP force at the lesser trochanter. J.P. Paul, University of Strathclyde, Bioengineering Unit, Wolfson Centre, Glasgow G4 0NW, UK E-mail address: [email protected]
1350-4533/02/$22.00 2002 IPEM. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 4 5 3 3 ( 0 2 ) 0 0 0 0 7 - 3