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Estimation of bone-on-bone contact forces in the tibiofemoral joint during walking

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Estimation of bone-on-bone contact forces in thetibiofemoral joint during walking
Ashvin Thambyah
a,
T
, Barry P. Pereira
a
, Urs Wyss
b
a
Musculoskeletal Research Laboratories, Department of Orthopaedic Surgery, Lower Kent Ridge Road, National University of Singapore, Singapore 119074, Singapore
b
Mechanical Engineering, Queen’s University, Kingston, Ontario, Canada
Received 3 November 2004; received in revised form 18 November 2004; accepted 27 December 2004
Abstract
In this study, the tibiofemoral contact forces were estimated from standard gait analysis data of adult walking. Knee angles, groundreaction forces, and external flexion–extension knee moments together with lines of action and moment arms of the force bearing structuresin the knee previously determined were used to obtain bone-on-bone contact forces. The heel strike, the onset of single limb stance andterminal extension before toe-off each corresponded to a significant turning point on the force versus gait cycle curve. The tibiofemoral bone-on-bone peak forces calculated reached an estimated three times bodyweight. The estimated joint loads are clinically relevant and can either be used directly for evaluation of subjects in a gait analysis, or indirectly in studies of the knee joint where models simulating loadingconditions are used to investigate various pathologies.
D
2005 Published by Elsevier B.V.
Keywords:
Biomechanics; Gait analysis; Physiological joint loading
1. Introduction
In vivo tibiofemoral contact forces were difficult tomeasure because the joint is encapsulated, articulating anddifficult to access. Even in the unlikely scenario where oneis able to access the joint, sensors that measure forces haveto be rugged, fast and accurate to capture forces in dynamicactivities. Many studies therefore resort to modeling the joint mathematically and calculating the forces, [1–5] or simulating articular joint mechanisms in vitro and usingsensors to measure the forces [6,7].Currently an accepted way to estimate in vivo tibiofe-moral contact forces is to incorporate data from severaldifferent experiments and then to calculate them. Standardmechanics can be used to model the knee joint as a series of rigid links, outlined in a typical free-body-diagram andforces calculated thereafter. As with any free-body-diagram,external forces and moments acting on the system need to beknown, as well as the dimensions and geometrical layout of the interconnecting rigid links. Morrison [2] used gait dataof human subjects and the morphometric data of one humancadaver to calculate the joint forces. The gait data provideinformation on the joint segment orientations as well asexternal forces and moments acting about the joint. Thecadaver study reveals the anatomical details necessary tocomplete the free-body-diagram of the joint; and thisincludes the moment arms of weight-bearing tendons andligaments and the tibiofemoral contact point, all of whichare involved in providing equilibrium to the joint inresponse to the external forces and moments acting on it.The accuracy and reliability of gait analysis for a particular subject have been discussed in great detail withthe conclusion that the joint angles and moments areacceptable for use in a standard fashion [8–11]. However,
the issue of bone-on-bone contact forces remains vague asthe action and moment arms of the major force-bearingstructures crossing the human knee joint of the subject are
0968-0160/$ - see front matter
D
2005 Published by Elsevier B.V.doi:10.1016/j.knee.2004.12.005
T
Corresponding author. Tel.: +65 68746521.
E-mail address:
ashvin@nus.edu.sg (A. Thambyah).The Knee 12 (2005) 383–388www.elsevier.com/locate/knee
not known. There are those that obtain these parametersfrom other means such as radiography [12–16] and
magnetic resonance imaging, [17–19] but it becomesobvious that medical imaging involves processes that arecostly and has its own inherent limitations.The lines of action and moment arms of the major force- bearing structures crossing the human knee joint have beenestimated based on cadaver studies [20] and verified inexperimental models [21]. The result is a series of relation-
ships for the lines of action and moment arms of the major force-bearing structures, with respect to the flexion angle of the knee, avoiding the use of additional data, such asmedical imaging or more cadaver studies. The idea tocombine the gait analysis data together with the lines of action and moment arms of the major force-bearingstructures crossing the human knee joint from the study of Herzog and Read [20] to estimate tibiofemoral contact forces therefore becomes an attractive proposition. Thismethod is not new as Zheng et al. [22] combined the datafrom these two sources to calculate tibiofemoral contact forces. However, the potential efficiency of this method-ology, especially for a quick and simple way to analyzemany subjects, may have not been highlighted enough in the previous study because of the emphasis of the use of additional inputs namely optimal muscle–length relation-ships [22]. While it is important to consider the role of
muscle inputs, the straightforwardness of this model inremaining such, via adopting a basic methodology as used by Morrison, [2] where a closed quasi-static system of balancing external forces and moments with internalstabilizing structures to calculate tibiofemoral joint forcesis an attractive option.
2. Methods
Gait analysis data were obtained from the Clinical Gait Analysis Normative Gait Database (CGA) website (http:// www.univie.ac.at/cga/data) with their kind permission.These were of 10 young adults compiled by the HongKong Polytechnic University and offered to the Internet public domain. The dataset contained kinematic and kineticdata, including ground reaction force data.Knee flexion–extension angles, moments and groundreaction forces were used for the calculation to derive joint contact (reaction) forces [2,23]. The free body
diagram is shown (Fig. 1). To calculate the tibiofemoral
bone-on-bone contact forces the anatomical orientation of the force bearing structures in the knee was required.These structures were simplified to the sagittal plane andconsist of two opposite lines of action via the patellaligament and hamstrings tendon respectively. The lines of action of the patella ligament (
a
pt
) and biceps femoris(hamstrings) tendon (
a
bft
) and the respective moment arms (
d
) were derived from the equations of Herzog andRead [20] using the knee flexion angle (
h
) from gait analysis (Fig. 2):
Patella Ligament
a
pt
¼
0
:
744
E
þ
02
0
:
575
E
01
h
ð Þ
0
:
475
E
02
h
ð Þ
2
þ
0
:
309
E
04
h
ð Þ
3
d
pt
¼ þ
0
:
471
E
þ
01
þ
0
:
420
E
01
h
ð Þ
0
:
896
E
03
h
ð Þ
2
þ
0
:
477
E
05
h
ð Þ
3
Fig. 1. Moments and forces from gait analysis derived from rigid body analysis are used as input for the boundary conditions of the knee joint where thesemoments and forces are balanced by internal structures to maintain equilibrium.
A. Thambyah et al. / The Knee 12 (2005) 383–388
384
Biceps Femoris Tendon
a
bft
¼
0
:
275
E
þ
03
0
:
872
E
00
h
ð Þ
0
:
712
E
03
h
ð Þ
2
d
bft
¼
0
:
146
E
þ
01
0
:
926
E
02
h
ð Þþ
0
:
855
E
03
h
ð Þ
2
0
:
878
E
05
h
ð Þ
3
þ
0
:
238
E
07
h
ð Þ
4
:
The moment arm for the patella ligament (
d
pt
) and bicepsfemoris tendon (
d
bft
) are input into the force–moment equation to derive the force in the patella ligament (
F
pt
)and biceps femoris tendon (
F
bft
).
M
p
, is the external flexion(+) or extension (
) moment that was obtained from the gait analysis data using the previous model [11]. The following
equations were used to calculate the tibiofemoral bone-on- bone contact forces (FC) in the vertical (
x
) and horizontal (
y
)axes:If
M
p
is positive, then:
F
pt
d
pt
¼
M
p
FC
x
¼
F
pt
x
þ
F
x
FC
y
¼
F
y
þ
F
pt
y
sin
a
pt
If
M
p
is negative, then:
F
bft
d
bft
¼
M
p
FC
x
¼
F
bft
x
þ
F
x
FC
y
¼
F
y
þ
F
bft
y
sin
a
bft
Þð
F
x
and
F
y
are the reaction forces derived from the groundreaction forces with the positive
y
-axis being upwards andthe positive
x
-axis being perpendicular and pointing towardsthe line of forward progression (Fig. 1).
F
pt
is the tension in the patella ligament (assumed to arisefrom quadriceps contraction) that balances a positiveexternal flexion moment,
M
p
, acting about the knee; while
F
bft
is the tension in the hamstrings tendon that balances anegative external extension moment,
M
p
. The
x
and
y
subscripts denote the resolved forces in the horizontal (
X-
)and vertical (
Y-
) axes. These forces are resolved from theline of action values derived for the patella ligament (
a
pt
)and biceps femoris tendon (
a
bft
).
2.1. Data and statistical analysis
The present study only focused on the data analysis for sagittal plane knee forces. Calculating the forces from theother planes is beyond the scope of this paper. Averagetibiofemoral sagittal plane forces, with standard deviations,were plotted against percent gait cycle. Turning points in thecurve were compared. Test for significant differences between the turning points and the mean force was performed using Analysis of Variance (ANOVA) followed by post hoc Tukey with a 0.05 level of significance.
3. Results
On average, peak external flexion moments occurred at 15% gait cycle, while peak external extension momentsoccurred at about 40% gait cycle (Fig 3A). This peak external flexion moment in the gait cycle corresponded tothe onset of single limb stance while the peak externalextension moment corresponded to terminal extension andtoe-off. From the ground reaction force data, it wasestimated that the stance phase ended at approximately60% gait cycle.The tibiofemoral bone-on-bone forces were reported ascompressive and shear forces (Fig 3B and C). For thecompressive forces, three points in the gait cycle wereobserved to correspond with three significant (
P
b
0.05)turning points in the force curves. These three turning pointsin the force curve corresponded with three turning points inthe moment curve relative to the gait cycle. The first turning point in the compressive force curve corresponded with a peak extension moment, the second turning point with aflexion moment and the third turning point with anextension moment again. The first turning point was at about 3% gait cycle at heel strike and the force was 1832-N(SD, 161-N). The second turning point occurred at 15% gait cycle. This phase corresponded approximately to the onset of single limb stance and the average peak force was 779-N(SD, 203-N). The third turning point in compressive forcesoccurred at about terminal extension and toe-off at the endof stance phase. The force was 2075-N (SD, 186-N). This
Fig. 2. Schematic showing the moment arm (
d
pt
) of the patella ligament assumed to be the perpendicular distance of the line of action to thetibiofemoral contact point. The orientation of the line of action of the patellaligament is an angle
h
relative to the local anatomical axis of the tibia asshown by the dotted lines. (Refer to Fig. 1 for notations used).
A. Thambyah et al. / The Knee 12 (2005) 383–388
385
final rise in compressive forces occurred at about 44% gait cycle.Turning points in the shear force curves were significant (
P
b
0.05) and occurred at similar points in the gait cycle asthat of the compressive forces and moments (Fig. 3C).These were at the onset of single limb stance and terminalextension before toe-off. The first turning point was at
132-N (SD, 34-N) and at 10% gait cycle. The negativevalue indicated that the force was one that was oriented pointing against the direction of forward progression in thesagittal plane, that is, from anterior to posterior relative tothe tibiofemoral joint. The next turning point in the shear force curve followed at about 44% gait cycle. The averageforce was 131-N (SD, 48-N).
4. Discussion
The tibiofemoral bone-on-bone contact forces for walk-ing calculated in the present study mainly agree with previously calculated forces [2] showing similarities albeit
some differences. (Fig. 4) Both, the previous and present
studies, report three distinct turning points or
peaks
in theforce curves. The first peak in the present study reachedapproximately 3 times body weight (if assuming average bodyweight of 650-N from t he ground reaction force data)and in the previous study [2] it was reported just at about 3
times body weight. Both the previous and present studiesshow the first peak to occur at about the same time in thegait cycle, that is, soon after foot contact. The second peak in the present study matches closely the second peak calculated in the previous study [2] in timing occurring at
about the onset of single limb stance phase. In the present study the peak reaches about one times body weight, againassuming 650-N bodyweight for the present study’s population while in the previous it was closer to two times body weight [2]. The third peak in the present study reached
about three times body weight at the end of stance phase just prior to toe-off, while in the previous study the third peak occurred at about the same time in stance phase reachingabout two and a half times body weight. The differences
Fig. 4. Comparison of the peak forces calculated in the present study with that of a previous study (Morrison JB 1970) [2]. Bodyweight in the cohort of the
present study for the calculation above is assumed to be 650-N.Fig. 3. Charts of (A) average external moments, (B) average tibiofemoral bone-on-bone contact forces (compressive), and (C) average shear forces.All are plotted against percent gait cycle. One standard deviation is shownfor each of the averaged curves.
A. Thambyah et al. / The Knee 12 (2005) 383–388
386
between the forces obtained in the present study and that from the previous [2] may have some implications on thecalculation of peak stresses in the joint, for which forces arenormalised to contact area. In the onset of single limb stancewhere the difference in forces calculated is most obvious between the present and previous study [2], the smaller forces calculated in the present study suggest that peak stresses may be reduced. In a recent study by the present author [24] contact area in single limb stance correspondingto peak pressures of about 14 MPa was estimated to beabout 75 mm
2
. In that study [24] peak forces of almost twotimes body weight were simulated. If the current forces of about only one times body weight was used, then the peak pressure can reasonably be estimated to be correspondinglymuch less.Using the current method the accuracy and consistencyof the calculations are limited to that of the moment andground reaction force data. As the shear force calculationsuse the data from the shear ground reaction forcemeasurement, it becomes apparent that the calculation will be limited by any inconsistency in this measurement.However there is little doubt on the direction of the shear force in the tibiofemoral joint. Of particular interest is the posterior-directed shear force at the onset of single limbstance. At this point the external moment is one that tendsto flex the knee and much of the rest of the body andweight is behind the vertical axis of the knee. The knee isalso partially flexed (about 15
8
) positioning the femur to be susceptible to rolling and sliding over the tibia, which islargely prevented in stability by muscle and ligamentousactivity and restraint. The posterior-pointing shear forcecalculated in the present study therefore makes sense, andthis would also be an indication of the reaction necessaryto prevent sliding.In the present study, several assumptions for the modelhave been made to facilitate the calculation, including thereduction of the problem to a statically determinate one.These assumptions are as follows: – Although surface motion occurs in three planes simulta-neously, the sagittal plane motion is greatest by far [25].In this model, all motions in the other planes arenegligible. – The axis of flexion–extension rotation, perpendicularlyintersecting the sagittal plane, is assumed to coincidewith the instant center of zero velocity of the femur relative to the tibia; a point where the cruciates wouldintersect [21]. – The articulation of the tibia and femur is akin to that between two rigid bodies. – The articulation vis-a`-vis congruency, involves a meansurface of the tibia plateau versus a mean surface of thefemoral condyles [12]. – The tibiofemoral contact point coincides with the point where there is the shortest distance between the meanfemoral condyles and tibial plateau. – The tibiofemoral contact point also coincides with the perpendicular line drawn from the flexion–extension axisdown to the tangent of the tibial plateau surface [26]. – Knee ligaments and tendons are modeled as uniaxialtension vectors whose insertion points are fixed anddirections relative to the neutral position determined bythe relationships provided by Herzog and Read [20]. – An individual fibre in a ligament or tendon whose fibrelength and insertion point may vary is not considered.The ligament or tendon is taken to be a uniform wholestructure. – The length of the ligaments and tendons can changeaccording to the position of the knee, but the differencesin tension as a result of the effects of any inherent length–tension property in the soft tissue are assumed to be negligible. – All external forces and moments acting on the joint areassumed to be balanced by internal muscle forces and joint reactions. – External moments tending to
flex
the knee are assumedto be balanced by internal moments generated via
quadriceps
contraction. External
extension
momentsare assumed to be balanced by inter nal momentsgenerated via
hamstrings
contraction [23]. – The weight of the shank and foot is negligible as it constitutes less than one-tenth body weight and changesin velocities during walking and squatting are expectedto be relatively small. – Anatomical variations play an important role in t he linear measure of moment arms and lines of action [27], but
were not considered in the present study. Scaling of these parameters may be achieved by using an anatomicalmeasure, such as the femoral width [27].Only net external moments were considered. Henceresolving the muscle forces during co-contractions will beconsidered to be beyond the scope of this model. Also beyond the scope of this model was the distributed load intothe various individualized force bearing components of a particular muscle group. Hence the knee extensor (quad-riceps) force was combined into one force vector via the patella ligament, and the knee flexor (hamstrings) force wascombined into one force vector via the biceps femoristendon.The simplification to reduce the number of unknowns began with the initial step of reducing the problem to acoplanar one where three forces cancel each other out. Thisis similar to the assumptions made when modeling lever systems. A load, effort and fulcrum constitute the threeforces that maintain equilibrium. In the knee joint, the bodyweight negotiated (load) is balanced by the (effort of the)muscles and ligaments over the tibiofemoral contact (fulcrum). For the sagittal plane tibiofemoral contact kine-matics and kinetics, it is therefore relevant to note at this point that although knee motion occurs simultaneously inthree planes, the motion in the sagittal plane is so great that
A. Thambyah et al. / The Knee 12 (2005) 383–388
387

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