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Influence of head constraint and muscle forces on the strain distribution within the intact femur
Medical Engineering & Physics 22 (2000) 453–459 www.elsevier.com/locate/medengphy
Influence of head constraint and muscle forces on the strain distribution within the intact femur J.A. Simo˜es
a,*
, M.A. Vaz b, S. Blatcher c, M. Taylor
d
a Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal Department of Mechanical Engineering and Industrial Management, University of Porto, 4200-465 Porto, Portugal c IRC in Biomedical Materials, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK Bioengineering Research Group, School of Engineering Sciences, The University of Southampton, Highfield, Southampton SO17 1BJ, UK b
d
Received 7 March 2000; received in revised form 25 July 2000; accepted 7 September 2000
Abstract The aim of this study was to analyse the influence of muscle action and a horizontally constrained femoral head on the strain distribution within the intact femur. The strain distribution was measured for three loading configurations: joint reaction force only, joint reaction force plus abductors, and joint reaction force plus the abductors, vastus lateralis and iliopsoas. In each case the strains were recorded from 20 uniaxial strain gauges placed on the medial, lateral, anterior and posterior aspects of the proximal femur. Application of the abductor muscle force produced a marginal decrease in the strain levels on all aspects of the femur as compared with the joint reaction force alone. This is in contrast with previous studies which have simulated an unconstrained femoral head. The inclusion of vastus lateralis and iliopsoas further reduced the strain levels. A horizontally constrained femoral head produces smaller variation in the strain levels when muscle forces are applied. In vivo data, demonstrating negligible movement of the femoral head in one-legged stance, support the results of this study and suggest that in the absence of comprehensive muscle force data, a constrained femoral head may provide a more physiologically relevant loading condition. 2001 IPEM. Published by Elsevier Science Ltd. All rights reserved. Keywords: Strain distribution; Loading; Intact composite femur; Strain gauge
1. Introduction Simulation of physiological loading of the hip is of considerable importance to improve prostheses design, bone remodelling simulations and mechanical testing of implants. There has been considerable debate in the literature as to how the femur is loaded. The majority of experimental and analytical studies assume the femur to be simplistically loaded, with the application of just a joint reaction force or the joint reaction force plus the abductors. This generates a characteristic bending stress/strain pattern within the diaphyseal femur. There is growing evidence to suggest that mechanisms exist which act to minimise bending to produce a predominately compressive stress/strain distribution. The various
* Corresponding author. Tel.: + 351-234-370830; fax: +351-234370953. E-mail address: [email protected] (J.A. Simo˜es).
mechanisms have been comprehensively reviewed by Pauwels [11], Frost [7] and Currey [6]. Many combinations of muscle forces have been modelled in vitro in an attempt to simulate femoral loading [2]. Telemetry studies of the implanted hip have given us reliable data for the magnitude and direction of the joint reaction force. Although the direction of the muscle forces can be estimated, their true magnitude during gait or any other activity has yet to be properly defined. The best estimates of the muscle forces have been supplied from muscle optimisation studies, such as those of Crowninshield et al. [5], Seireg et al. [15] and Ro¨hrle et al. [14]. All of the optimisation studies predict some abductor activity. Ro¨hrle et al. [14] predict significant abductor muscle activity, of approximately two times body weight. Apart from the abductors, there is little consensus on the other major muscles that are active during gait. However, other muscles which have been predicted as active somewhere in the gait cycle by at least two studies are: tensor fasciae latae, iliacus, semitend-
1350-4533/01/$ - see front matter 2001 IPEM. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 4 5 3 3 ( 0 0 ) 0 0 0 5 6 - 4
454
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
inosus, semimembranosus, sartorius, rectus femoris, adductor longus, adductor magnus, biceps femoris and vastus. However, prediction of muscle forces should be treated with caution due to the numerous assumptions made in their calculation. Ro¨hrle et al. [14] reported that a 5 mm displacement of the origin of the rectus muscle resulted in a 55% decrease in the predicted force of the adductors. Other sources of error include the location of the centre of mass of skeletal segments, the use of skin markers to track the motion of underlying bone during kinematic studies and the assumption of no antagonistic or synergistic muscle activity. Thus, there is a degree of uncertainty in the selection of which muscles are important, and their relevance to mechanical testing. The applied boundary conditions are of equal importance when modelling the femur as an isolated structure, but this has been rarely considered. The femoral head can be simulated as being either unconstrained or horizontally constrained. To the authors’ knowledge, all finite element analyses to date have assumed the femoral head to be unconstrained [1,8,12,16,17,19,18,20]. In contrast, the majority of experimental studies have assumed the femoral head to be horizontally constrained [2] except for Christofolini et al. [3] and Rohlmann et al. [13], who simulated the femoral head as unconstrained. The reason for this division between finite element studies and experimental studies, using unconstrained and horizontally constrained femoral heads, respectively, is not clear in the literature. Yet the effect on the strain distribution could be pronounced. An in vivo radiological study performed by Taylor et al. [16] suggested that there is minimal medial deflection of the loaded femoral head during one-legged stance (approximately 1.5 mm). Therefore, in an attempt to simplify experimental set-ups and in the absence of comprehensive muscle force data, the question arises whether it is reasonable to simulate the femoral head as horizontally constrained. The aim of this study was to analyse the influence muscle action and a horizontally constrained femoral head have on the strain distribution within the intact femur. The effect of three principal muscle groups, the abductors, the iliopsoas and the vastus lateralis, was investigated. The results were compared with a experimental study performed by Christofolini et al. [3], who conducted a similar study but with an unconstrained femoral head.
diaphysis (Fig. 1). All gauges had the axis of the grid aligned with the longitudinal axis of the femur and were positioned in an identical way to those in the studies of McNamara et al. [9] and Cristofolini et al. [3]. The strain gauges were bonded with an adhesive after preparing the surface of the femur model and connected to a dataacquisition system (Solartron SI 35951B IMP, Solartron Instruments). The signal stability of each gauge was measured for 2 h, and very small variations were observed. The tests were performed at room temperature, 22±1°C, and a relative humidity of 65%. Cristofolini et al. [4] have performed a detailed mechanical validation of composite femur models. An extensive experimental validation of the mechanical behaviour of 15 composite femurs (Pacific Research Labs) and comparison with four dried and rehydrated and four fresh-frozen human femurs was carried out. The behaviour under axial loading and the characterisation of the bending and torsional stiffness showed that composite femurs fall well within the range for cadaveric femurs, with no significant differences being detected between the synthetic femurs and the two groups of cadaveric femurs. The interfemur variability for the composite femurs was 20 to 200 times lower than for the cadaveric specimens. A jig, shown in Fig. 2, was designed and built to apply the joint reaction force and muscle forces to the femur. The load on the femoral head was applied through a screw connected to a polyethylene socket and monitored
2. Materials and methods For the purpose of this study, a synthetic composite femur (model 3103, Pacific Research Labs) was used. The composite femur was prepared with 20 uniaxial gauges (CEA-06-125UN-350, Measurements Group, Inc., Raleigh, NC) placed at five levels, namely on the lateral, medial, anterior and posterior sides of the
Fig. 1. Composite femur bone model prepared with 20 uniaxial strain gauges.
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
Fig. 2.
Experimental jig to apply the hip joint reaction and muscle forces.
by a load cell. The femur was distally fixed by the femoral condyles on a platform, which allowed us to position the femur in the desired position. The muscle forces were exerted by gravity through weights fixed to metallic straps that were connected to metallic plates on the femur as shown in Fig. 3. The jig was surrounded by a frame structure where pulleys were positioned in order
(a) Fig. 3.
455
to load the muscles in the required direction. Fig. 3 also shows how the femoral head movement was constrained. Three different loading conditions were analysed; the magnitudes and directions of the forces are shown in Table 1 (Fig. 4). In the first load configuration, load case 1, the femur was loaded with a joint reaction force positioning the femur 13° in adduction and 7° in flexion.
(b)
(a) Plates and cables attached to the femur head for muscle force application and (b) device used to constrain the femur head horizontally.
456
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
Table 1 Muscle and joint reaction forces for the three load cases Load case
Resultant force (N)
Angle (degree)
f 1 Joint reaction force 2. Joint reaction force Abductors 3. Joint reaction force Abductors Iliopsoas Vastus lateralis
g
700
167
21
700 300
167 20
16 180
730 300 188 292
159 20 47 180
7 180 262 –
Load case 2 replicates the loading configuration used by several authors, consisting of a joint reaction force applied to the femoral head and an abductor muscle force applied at the great trochanter [8,12,16–18]. In load case 3, the angle of the joint reaction force was increased to 20° in the transverse plane to assess its effect on the overall strain distribution, and the action of the three major muscle groups, the abductors, the vastus lateralis and the iliopsoas, was applied [16]. The simulations were performed with the distal end of the femur rigidly constrained and, for each case, the axial strain distribution was obtained on the medial, lateral, anterior and posterior regions of the diaphyseal femur.
microstrain. The addition of iliopsoas and vastus lateralis, load case 3, resulted in a further reduction in the strains observed. In general, there was a 50–150 microstrain reduction on the medial aspect of the femur and a 100–250 microstrain reduction on the lateral aspect of the femur as compared with load case 2. On the anterior and posterior aspects of the femur there was little change in the strain magnitudes observed in the proximal femur. However, there was a progressive reduction in the strain to a peak reduction of 200 microstrain at the most distal location, as compared with load cases 1 and 2. There was a peak difference in strain of approximately 1500 microstrain, a reduction of nearly 50% as compared with load case 1.
3. Results 4. Discussion The axial strains on the medial, lateral, anterior and posterior aspects of the femur for the three load cases are shown in Fig. 5. Load case 1 displays a typical bending strain distribution, with high medial and lateral strains (⫺1500 and 1200 microstrain, respectively), and significantly lower strain values on the anterior and posterior surfaces of the femur (⫺850 and 500 microstrain, respectively). This resulted in a peak difference in strain of 2700 microstrain. The addition of the abductors’ muscle force in load case 2 produced a decrease of approximately 300 microstrain over the entire medial and lateral aspects of the femur. However, there was only a marginal decrease in the strains observed on the anterior and posterior aspects of the femur. For load case 2 there was a peak difference in strain of approximately 1800
The purpose of this study was to examine the influence of a horizontally constrained femoral head and muscle forces on the strain distribution within the intact femur. Cristofolini et al. [3] performed a similar study, except that they simulated the femoral head as unconstrained and studied the action of 10 muscles instead of three as in this study. Direct comparison of the strain magnitudes is difficult, as Cristofolini et al. used a cadaveric femur instead of the composite femur used in this study. The cadeveric femur was also 50 mm smaller than the composite femur that we used in our study. For similar load case 1, Cristofolini reported peak medial, lateral, anterior and posterior strains of ⫺900, 450, 250 and ⫺400 microstrain, respectively. In this study peak
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
457
3º
f JRF
JRF
Fabd
Fabd
20º
FIp
FIp
9º Fvl
47º
JRF - Joint Reaction Force Fabd - Abductors FIp - Iliopsoas Fvl - Vastus lateralis
y x Fig. 4.
y z
The applied joint reaction and muscle forces.
strains of ⫺1500, 1200, 500 and ⫺850 microstrain were observed on the medial, lateral, anterior and posterior aspects of the femur, respectively, for an identical load case. Hence the strains observed in the composite femur used in this study were 1.7 to 2.5 times higher than those observed in the cadaveric femur used by Cristofolini et al. In Cristofolini’s study, the application of an abductor muscle force produced an increase of over 300% in the peak medial strains and an increase of over 400% in the lateral strain as compared with the femur loaded without muscles. This finding is contrary to those reported here, where there was a decrease of approximately 30% in the axial strains on both the medial and lateral aspects of the femur. Since only the vertical motion of the femoral head was allowed in this study, the action of the abductor force pulling the femoral head medially was resisted by the loading mechanism. In effect, the horizontal femoral head constraint increases the horizontal component of the joint reaction force and minimises femoral bending. However, it should be noted there are fundamental differences between the loads applied in Cristofolini’s study and those used here. In Cristofolini’s study, the abductor muscle force consisted of a resultant force of nearly four times body weight as opposed to just 1.3 times body weight used in this study. In Cristofolini’s study the addition of further muscles had only a small influence on the strain distribution on
the medial and lateral aspects of the femur; i.e., for a unconstrained femoral head simulation, it would appear that the strain distribution is dominated by the action of the abductors. In this study the application of iliopsoas and vastus lateralis produced a further decrease of 25% in the medial strain levels and a reduction of up to 50% in the lateral strain levels as compared with load case 2. Similar reductions in the strain values were seen in the distal femur for the anterior and posterior aspects of the femur. Therefore it would appear that the tension banding effect of vastus lateralis is still effective in a horizontally constrained femoral head experimental set-up. In vivo data suggest that there is negligible movement of the femoral head during one-legged stance [16] as compared with the unloaded femur. It has been proposed that muscles act to minimise bending during all activities to produce a predominantly compressive strain distribution within the intact femur [6,7,11,10]. If this is true, then it is also reasonable to assume that muscles also act to minimise the deflection of the femoral head during normal daily activities. If this is the case, then it is reasonable to simulate the femoral head as horizontally constrained. This study has shown that such a constraint acts to resist the horizontal loads applied by the abductors, thus reducing the degree of bending present in the femur. However, the use of a constrained head does not produce a predominately compressive strain distribution
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J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
Fig. 5. Strain distributions within the medial, lateral, anterior and posterior aspects of the femur.
alone and the application of further muscle forces, such as iliopsoas and vastus lateralis, are need to produce such a strain state. However, further work is required to see if the application other muscle forces will produce a more uniform strain distribution. The advantage of the constrained femoral head set-up is its simplicity. Complex experimental set-ups are required to simulate an unconstrained femoral head.
5. Conclusions The objective of this study was to analyse the influence of muscle simulation on the strain distribution within the diaphyseal of the femur. Femoral head boundary conditions have been shown to influence the strain distribution within the intact femur. An unconstrained
femoral head results in the abductor muscles significantly increasing the femoral bending strains. In vivo data appear to contradict the validity of this type of experimental set-up. In the absence of comprehensive muscle force data, a constrained femoral head may provide a more physiologically relevant loading condition. References [1] Bergmann G, Craichen F, Rohlmann A. Hip joint loading during walking and running measured in two patients. J Biomech 1993;26:969–90. [2] Colgan D, Trench P, Slemon D, McTague D, Finlay JB, O’Donnell P. et al. A review of joint and muscle load simulation relevant to in-vitro stress analysis of the hip. Strain 1994;May:47–61. [3] Cristofolini L, Viceconti M, Toni A, Giunti A. Influence of thigh muscles on the axial strains in a proximal femur during early stance in gait. J Biomech 1995;28(5):617–24.
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
[4] Cristofolini L, Viceconti M, Cappello A, Toni A. Mechanical validation of whole bone composite femur models. J Biomech 1996;29(4):525–35. [5] Crowninshield RD, Johnston RC, Andrews JG, Brand RA. A biomechanical investigation of the human hip. J Biomech 1978;11:75–85. [6] Currey JD. The mechanical adaption of bones. Princeton, NJ: Princeton University Press, 1984. [7] Frost HM. Bone remodelling and skeletal modelling errors. Springfield (IL): Orthopaedics Lecturers, 1973. [8] Huiskes R. The various stress patterns of press-fit, ingrown and cemented femoral stems. Clin Orthop Rel Res 1990;261:27–38. [9] McNamara BP, Viceconti M, Cristofolini L, Toni A, Taylor D. Experimental and numerical pre-clinical evaluation relating to total hip arthroplasty. In: Middleton J, editor. Proceedings of 2nd International Symposium on Computer Methods in Biomechanics and Biomedical Engineering. The Netherlands: Gordon & Beach, 1996:1–0. [10] Munih M, Kralj A, Bajd T. Bending moments in lower extremity bones for two standing postures. J Biomed Eng 1992;14:293–301. [11] Pauwels F. Biomechanics of the locomotor apparatus. Berlin/Heidelberg/New York: Springer Verlag, 1980. [12] Prendergast PJ, Taylor D. Stress analysis of the proximo-medial femur after total hip replacement. J Biomed Eng 1990;12:379–82.
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[13] Rohlmann A, Mossner U, Bergmann G, Kolbel R. Finite-elementanalysis and experimental investigation of stresses in a femur. J Biomed Eng 1982;4:241–6. [14] Ro¨hrle H, Scholten R, Sigolotto C, Sollbach W, Kellner H. Joint forces in the human pelvis–leg skeleton during walking. J Biomech 1984;17:409–24. [15] Seireg A, Kempke W. Behaviour of in vivo bone under cyclic loading. J Biomech 1975;2:455. [16] Taylor M, Tanner E, Freeman MAR, Yettram AL. Stress and strain distribution within the intact femur: compression or bending? Med Eng Phys 1996;18(2):122–31. [17] Tensi HM, Gese H, Aschrel R. Non-linear three dimensional finite element analysis of a cementless hip prosthesis. Proc Instn Mech Engrs 1989;203H:215–22. [18] Verdonschot NJJ, Huiskes R, Freeman MAR. Pre-clinical testing of hip prosthetic designs: a comparison of finite element calculations and laboratory tests. Proc Instn Mech Engrs 1993;207H:149–54. [19] Weinans H, Huiskes R, Grootenboer HJ. Trends of mechanical consequences and modeling of a fibrous membrane around femoral hip prostheses. J Biomech 1990;23:991–1000. [20] Yettram AL. Effect of interface conditions on the behaviour of a Freeman hip endoprosthesis. J Biomed Eng 1989;11:520.
Influence of head constraint and muscle forces on the strain distribution within the intact femur J.A. Simo˜es
a,*
, M.A. Vaz b, S. Blatcher c, M. Taylor
d
a Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal Department of Mechanical Engineering and Industrial Management, University of Porto, 4200-465 Porto, Portugal c IRC in Biomedical Materials, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK Bioengineering Research Group, School of Engineering Sciences, The University of Southampton, Highfield, Southampton SO17 1BJ, UK b
d
Received 7 March 2000; received in revised form 25 July 2000; accepted 7 September 2000
Abstract The aim of this study was to analyse the influence of muscle action and a horizontally constrained femoral head on the strain distribution within the intact femur. The strain distribution was measured for three loading configurations: joint reaction force only, joint reaction force plus abductors, and joint reaction force plus the abductors, vastus lateralis and iliopsoas. In each case the strains were recorded from 20 uniaxial strain gauges placed on the medial, lateral, anterior and posterior aspects of the proximal femur. Application of the abductor muscle force produced a marginal decrease in the strain levels on all aspects of the femur as compared with the joint reaction force alone. This is in contrast with previous studies which have simulated an unconstrained femoral head. The inclusion of vastus lateralis and iliopsoas further reduced the strain levels. A horizontally constrained femoral head produces smaller variation in the strain levels when muscle forces are applied. In vivo data, demonstrating negligible movement of the femoral head in one-legged stance, support the results of this study and suggest that in the absence of comprehensive muscle force data, a constrained femoral head may provide a more physiologically relevant loading condition. 2001 IPEM. Published by Elsevier Science Ltd. All rights reserved. Keywords: Strain distribution; Loading; Intact composite femur; Strain gauge
1. Introduction Simulation of physiological loading of the hip is of considerable importance to improve prostheses design, bone remodelling simulations and mechanical testing of implants. There has been considerable debate in the literature as to how the femur is loaded. The majority of experimental and analytical studies assume the femur to be simplistically loaded, with the application of just a joint reaction force or the joint reaction force plus the abductors. This generates a characteristic bending stress/strain pattern within the diaphyseal femur. There is growing evidence to suggest that mechanisms exist which act to minimise bending to produce a predominately compressive stress/strain distribution. The various
* Corresponding author. Tel.: + 351-234-370830; fax: +351-234370953. E-mail address: [email protected] (J.A. Simo˜es).
mechanisms have been comprehensively reviewed by Pauwels [11], Frost [7] and Currey [6]. Many combinations of muscle forces have been modelled in vitro in an attempt to simulate femoral loading [2]. Telemetry studies of the implanted hip have given us reliable data for the magnitude and direction of the joint reaction force. Although the direction of the muscle forces can be estimated, their true magnitude during gait or any other activity has yet to be properly defined. The best estimates of the muscle forces have been supplied from muscle optimisation studies, such as those of Crowninshield et al. [5], Seireg et al. [15] and Ro¨hrle et al. [14]. All of the optimisation studies predict some abductor activity. Ro¨hrle et al. [14] predict significant abductor muscle activity, of approximately two times body weight. Apart from the abductors, there is little consensus on the other major muscles that are active during gait. However, other muscles which have been predicted as active somewhere in the gait cycle by at least two studies are: tensor fasciae latae, iliacus, semitend-
1350-4533/01/$ - see front matter 2001 IPEM. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 4 5 3 3 ( 0 0 ) 0 0 0 5 6 - 4
454
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
inosus, semimembranosus, sartorius, rectus femoris, adductor longus, adductor magnus, biceps femoris and vastus. However, prediction of muscle forces should be treated with caution due to the numerous assumptions made in their calculation. Ro¨hrle et al. [14] reported that a 5 mm displacement of the origin of the rectus muscle resulted in a 55% decrease in the predicted force of the adductors. Other sources of error include the location of the centre of mass of skeletal segments, the use of skin markers to track the motion of underlying bone during kinematic studies and the assumption of no antagonistic or synergistic muscle activity. Thus, there is a degree of uncertainty in the selection of which muscles are important, and their relevance to mechanical testing. The applied boundary conditions are of equal importance when modelling the femur as an isolated structure, but this has been rarely considered. The femoral head can be simulated as being either unconstrained or horizontally constrained. To the authors’ knowledge, all finite element analyses to date have assumed the femoral head to be unconstrained [1,8,12,16,17,19,18,20]. In contrast, the majority of experimental studies have assumed the femoral head to be horizontally constrained [2] except for Christofolini et al. [3] and Rohlmann et al. [13], who simulated the femoral head as unconstrained. The reason for this division between finite element studies and experimental studies, using unconstrained and horizontally constrained femoral heads, respectively, is not clear in the literature. Yet the effect on the strain distribution could be pronounced. An in vivo radiological study performed by Taylor et al. [16] suggested that there is minimal medial deflection of the loaded femoral head during one-legged stance (approximately 1.5 mm). Therefore, in an attempt to simplify experimental set-ups and in the absence of comprehensive muscle force data, the question arises whether it is reasonable to simulate the femoral head as horizontally constrained. The aim of this study was to analyse the influence muscle action and a horizontally constrained femoral head have on the strain distribution within the intact femur. The effect of three principal muscle groups, the abductors, the iliopsoas and the vastus lateralis, was investigated. The results were compared with a experimental study performed by Christofolini et al. [3], who conducted a similar study but with an unconstrained femoral head.
diaphysis (Fig. 1). All gauges had the axis of the grid aligned with the longitudinal axis of the femur and were positioned in an identical way to those in the studies of McNamara et al. [9] and Cristofolini et al. [3]. The strain gauges were bonded with an adhesive after preparing the surface of the femur model and connected to a dataacquisition system (Solartron SI 35951B IMP, Solartron Instruments). The signal stability of each gauge was measured for 2 h, and very small variations were observed. The tests were performed at room temperature, 22±1°C, and a relative humidity of 65%. Cristofolini et al. [4] have performed a detailed mechanical validation of composite femur models. An extensive experimental validation of the mechanical behaviour of 15 composite femurs (Pacific Research Labs) and comparison with four dried and rehydrated and four fresh-frozen human femurs was carried out. The behaviour under axial loading and the characterisation of the bending and torsional stiffness showed that composite femurs fall well within the range for cadaveric femurs, with no significant differences being detected between the synthetic femurs and the two groups of cadaveric femurs. The interfemur variability for the composite femurs was 20 to 200 times lower than for the cadaveric specimens. A jig, shown in Fig. 2, was designed and built to apply the joint reaction force and muscle forces to the femur. The load on the femoral head was applied through a screw connected to a polyethylene socket and monitored
2. Materials and methods For the purpose of this study, a synthetic composite femur (model 3103, Pacific Research Labs) was used. The composite femur was prepared with 20 uniaxial gauges (CEA-06-125UN-350, Measurements Group, Inc., Raleigh, NC) placed at five levels, namely on the lateral, medial, anterior and posterior sides of the
Fig. 1. Composite femur bone model prepared with 20 uniaxial strain gauges.
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
Fig. 2.
Experimental jig to apply the hip joint reaction and muscle forces.
by a load cell. The femur was distally fixed by the femoral condyles on a platform, which allowed us to position the femur in the desired position. The muscle forces were exerted by gravity through weights fixed to metallic straps that were connected to metallic plates on the femur as shown in Fig. 3. The jig was surrounded by a frame structure where pulleys were positioned in order
(a) Fig. 3.
455
to load the muscles in the required direction. Fig. 3 also shows how the femoral head movement was constrained. Three different loading conditions were analysed; the magnitudes and directions of the forces are shown in Table 1 (Fig. 4). In the first load configuration, load case 1, the femur was loaded with a joint reaction force positioning the femur 13° in adduction and 7° in flexion.
(b)
(a) Plates and cables attached to the femur head for muscle force application and (b) device used to constrain the femur head horizontally.
456
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
Table 1 Muscle and joint reaction forces for the three load cases Load case
Resultant force (N)
Angle (degree)
f 1 Joint reaction force 2. Joint reaction force Abductors 3. Joint reaction force Abductors Iliopsoas Vastus lateralis
g
700
167
21
700 300
167 20
16 180
730 300 188 292
159 20 47 180
7 180 262 –
Load case 2 replicates the loading configuration used by several authors, consisting of a joint reaction force applied to the femoral head and an abductor muscle force applied at the great trochanter [8,12,16–18]. In load case 3, the angle of the joint reaction force was increased to 20° in the transverse plane to assess its effect on the overall strain distribution, and the action of the three major muscle groups, the abductors, the vastus lateralis and the iliopsoas, was applied [16]. The simulations were performed with the distal end of the femur rigidly constrained and, for each case, the axial strain distribution was obtained on the medial, lateral, anterior and posterior regions of the diaphyseal femur.
microstrain. The addition of iliopsoas and vastus lateralis, load case 3, resulted in a further reduction in the strains observed. In general, there was a 50–150 microstrain reduction on the medial aspect of the femur and a 100–250 microstrain reduction on the lateral aspect of the femur as compared with load case 2. On the anterior and posterior aspects of the femur there was little change in the strain magnitudes observed in the proximal femur. However, there was a progressive reduction in the strain to a peak reduction of 200 microstrain at the most distal location, as compared with load cases 1 and 2. There was a peak difference in strain of approximately 1500 microstrain, a reduction of nearly 50% as compared with load case 1.
3. Results 4. Discussion The axial strains on the medial, lateral, anterior and posterior aspects of the femur for the three load cases are shown in Fig. 5. Load case 1 displays a typical bending strain distribution, with high medial and lateral strains (⫺1500 and 1200 microstrain, respectively), and significantly lower strain values on the anterior and posterior surfaces of the femur (⫺850 and 500 microstrain, respectively). This resulted in a peak difference in strain of 2700 microstrain. The addition of the abductors’ muscle force in load case 2 produced a decrease of approximately 300 microstrain over the entire medial and lateral aspects of the femur. However, there was only a marginal decrease in the strains observed on the anterior and posterior aspects of the femur. For load case 2 there was a peak difference in strain of approximately 1800
The purpose of this study was to examine the influence of a horizontally constrained femoral head and muscle forces on the strain distribution within the intact femur. Cristofolini et al. [3] performed a similar study, except that they simulated the femoral head as unconstrained and studied the action of 10 muscles instead of three as in this study. Direct comparison of the strain magnitudes is difficult, as Cristofolini et al. used a cadaveric femur instead of the composite femur used in this study. The cadeveric femur was also 50 mm smaller than the composite femur that we used in our study. For similar load case 1, Cristofolini reported peak medial, lateral, anterior and posterior strains of ⫺900, 450, 250 and ⫺400 microstrain, respectively. In this study peak
J.A. Simo˜es et al. / Medical Engineering & Physics 22 (2000) 453–459
457
3º
f JRF
JRF
Fabd
Fabd
20º
FIp
FIp
9º Fvl
47º
JRF - Joint Reaction Force Fabd - Abductors FIp - Iliopsoas Fvl - Vastus lateralis
y x Fig. 4.
y z
The applied joint reaction and muscle forces.
strains of ⫺1500, 1200, 500 and ⫺850 microstrain were observed on the medial, lateral, anterior and posterior aspects of the femur, respectively, for an identical load case. Hence the strains observed in the composite femur used in this study were 1.7 to 2.5 times higher than those observed in the cadaveric femur used by Cristofolini et al. In Cristofolini’s study, the application of an abductor muscle force produced an increase of over 300% in the peak medial strains and an increase of over 400% in the lateral strain as compared with the femur loaded without muscles. This finding is contrary to those reported here, where there was a decrease of approximately 30% in the axial strains on both the medial and lateral aspects of the femur. Since only the vertical motion of the femoral head was allowed in this study, the action of the abductor force pulling the femoral head medially was resisted by the loading mechanism. In effect, the horizontal femoral head constraint increases the horizontal component of the joint reaction force and minimises femoral bending. However, it should be noted there are fundamental differences between the loads applied in Cristofolini’s study and those used here. In Cristofolini’s study, the abductor muscle force consisted of a resultant force of nearly four times body weight as opposed to just 1.3 times body weight used in this study. In Cristofolini’s study the addition of further muscles had only a small influence on the strain distribution on
the medial and lateral aspects of the femur; i.e., for a unconstrained femoral head simulation, it would appear that the strain distribution is dominated by the action of the abductors. In this study the application of iliopsoas and vastus lateralis produced a further decrease of 25% in the medial strain levels and a reduction of up to 50% in the lateral strain levels as compared with load case 2. Similar reductions in the strain values were seen in the distal femur for the anterior and posterior aspects of the femur. Therefore it would appear that the tension banding effect of vastus lateralis is still effective in a horizontally constrained femoral head experimental set-up. In vivo data suggest that there is negligible movement of the femoral head during one-legged stance [16] as compared with the unloaded femur. It has been proposed that muscles act to minimise bending during all activities to produce a predominantly compressive strain distribution within the intact femur [6,7,11,10]. If this is true, then it is also reasonable to assume that muscles also act to minimise the deflection of the femoral head during normal daily activities. If this is the case, then it is reasonable to simulate the femoral head as horizontally constrained. This study has shown that such a constraint acts to resist the horizontal loads applied by the abductors, thus reducing the degree of bending present in the femur. However, the use of a constrained head does not produce a predominately compressive strain distribution
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Fig. 5. Strain distributions within the medial, lateral, anterior and posterior aspects of the femur.
alone and the application of further muscle forces, such as iliopsoas and vastus lateralis, are need to produce such a strain state. However, further work is required to see if the application other muscle forces will produce a more uniform strain distribution. The advantage of the constrained femoral head set-up is its simplicity. Complex experimental set-ups are required to simulate an unconstrained femoral head.
5. Conclusions The objective of this study was to analyse the influence of muscle simulation on the strain distribution within the diaphyseal of the femur. Femoral head boundary conditions have been shown to influence the strain distribution within the intact femur. An unconstrained
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