Biomechanics of the ACL: Measurements of in situ force in the ACL and knee kinematics

22 Pages·1998·0.71 MB·English

TheKnee5(cid:14)1998.267]288
Biomechanics of the ACL: Measurements of in situ force
in the ACL and knee kinematics
U
Savio L-Y. Woo , Ross J. Fox,Masataka Sakane, Glen A. Livesay,
Theodore W. Rudy,Freddie H. Fu
MusculoskeletalResearchCenter,DepartmentofOrthopaedicSurgery,Uni¤ersityofPittsburghMedicalCenter,210LothropStreet,
Pittsburgh,PA15213,USA
Accepted10October1997
Abstract
Injuryofthe anterior cruciate ligament(cid:14)ACL.can leadtokneeinstability associated withdamagetootherkneestructures
and the increased risk of degenerative joint disease. This has led to the frequent use of intra-articular tissue grafts for ACL
reconstruction in an attempt to restore normal knee function. Despite moderate success, the continued failure of ACL
reconstruction to restore normal knee kinematics has led many investigators to study the role played by the ACL in normal
knee motion. At our research center, we have focused on the development of a new and innovative approach to measure
multiple degree of freedom (cid:14)DOF. knee kinematics and to determine the in situ forces within the ACL. A unique testing
system utilizing a 6-DOFrobotic manipulator anduniversal force]momentsensor (cid:14)UFS.has been developedsuch that these
measurementscanbemadeinanon-contactfashionwhileallowingaseriesofexperimentstobeperformedonthesameknee.
Inthismanuscript,wewilldescribethefunctional andmathematical developmentoftheroboticrUFSsystemanditsuseina
seriesofstudiesdesignedtogiveinsightintothefunctionoftheACLandACLgrafts.Ourfirststudyinvestigatedtheeffectof
constrained vs.unconstrained knee motionon anterior tibial translation and on the in situ force in the ACL.We found that
unconstrainedmultiple-DOFkneemotionsignificantlyincreasedanteriortibialtranslation.Whilethemagnitudeoftheinsitu
force remained similar to the more constrained condition, its direction, point of application and distribution between the
anteromedial(cid:14)AM.andposterolateral(cid:14)PL.bundleswerefoundtosignificantlychange.Thesefindingsledustoinvestigatethe
effect of knee flexion angle and magnitude of anterior applied tibial load on the in situ force in the ACL and its bundles
during unconstrained knee motion.We found the PL bundle of the human ACL to carry a greater proportionof the in situ
force than the AM bundle near knee extension. Also, the change in magnitude of the in situ force in the PL bundle with
changing knee flexion angle was similar to that of the entire ACL. This led us to conclude that the PL bundle must play a
significant role in ACL function and in resisting anterior tibial load and that it should receive more serious consideration
during ACL reconstruction. Lastly, we used our new testing system to examine two popular ACL reconstruction techniques:
bone]patellar tendon]bone (cid:14)BPTB. and quadruple semitendinosusrgracilis hamstring (cid:14)QSTrG. grafts. We compared them
in terms of restoration of anterior tibial translation and reproduction of the in situ force in the intact ACL. Each
reconstruction was performed on the same knee, allowing us to minimize interspecimen variability and take advantage of
pairedstatistical analysis.Wefoundthatwhilebothreconstructionseffectivelyreducedanteriortibialtranslationsecondaryto
anterior tibial loading to a level not significantly different from the ACL intact knee, use of a QSTrG graft may be
advantageous, as it reproduced the in situ forces of the intact ACL more closely. This series of three studies has garnered
quantitative datatofurther ourunderstandingofhowtheACLfunctions andhasyieldednewconceptstohelpimproveACL
reconstruction. Through the use of a robotic manipulator, our testing system has the capability to reproduce complex
physiologic loading conditions that allow us to evaluate the efficacy of various ACL reconstruction techniques and
UCorrespondingauthor.Tel.:q14126482000;faxq:14126482001.
0968-0160r98r$-seefrontmatterQ1998ElsevierScienceB.V.Allrightsreserved.
PIIS0968-0160(cid:14)98.00014-3
268 S.L.-Y.Wooetal.rTheKnee5(1998)267]288
rehabilitation protocolsinthe sameknee.Inthe future, weintendtoacquire invivokinematic dataofthe kneesecondaryto
various functional and sporting activities and reproduce them using our roboticrUFS system such that in vivo in situ forces
can be indirectly determined. We believe that such studies will provide a basis for the advancement of ACL reconstruction
and rehabilitation. Q 1998Elsevier Science B.V.All rights reserved.
Keywords: Anterior cruciate ligament; Knee instability; ACLreconstruction
1. Introduction the forces in the ACL. These studies, primarily per-
formed under A-P loading, revealed that the antero-
The function of the knee joint is mediated by a medial (cid:14)AM. and posterolateral (cid:14)PL. bundles carry
complex interaction of its component parts. These unequal proportions of the ACL force w50]63x. This
component parts include the patella, femur and tibia; observation, besides providinginsight into the normal
the ligaments and capsule; the articular cartilage and function of the ACL, can serve as a basis for evaluat-
menisci; and the muscles. The interdependence of
ingreconstructive procedures.Specifically,bycompar-
these structures is such that injury or failure of any
ing this data tothat achieved by ACLgrafts, variables
one of them leads to deterioration of the overall
such as how,where, and under what tension the ACL
function of the joint. Ligaments are particularly vul-
graft should be placed intra-operatively can be evalu-
nerable as they are subject to low-degree sprains in
ated. Furthermore, the results of such comparisons
w x
virtually every injury of the knee 1,2, and in some
can also help in the determination of how to position
cases, are ruptured completely. Complete ligament
the knee to achieve the safest, most effective post-op-
ruptures, especially of the anterior cruciate ligament
erative rehabilitation protocol.
(cid:14)ACL., can lead to the clinical symptom of knee
In our research center, we have focused on the
instability w3]7x, which may be associated with tears
effect which different testing conditions can have on
and degeneration of the menisci and articular carti-
the measurement of the in situ forces in the ACL.
lage, as well as increased laxity of other knee liga-
Specifically, we have found that varying knee flexion
ments w8]14x.
angle, knee constraint (cid:14)or degree-of-freedom, DOF.,
Because the ACL also fails to heal with a quality
w x and the magnitude and direction of the applied tibial
that restores its function 15, numerous reconstruc-
load can result in different in situ forces in the ACL.
tive procedures have been developed for patients de-
Because the techniques we use to reconstruct the
manding high levels of knee performance. The most
ACL clinically are often based on the quantitative
commonreconstructive techniques utilizeintra-articu-
lar autografts w16]36x.While reconstruction has vastly data gathered in the laboratory, it is imperative that
improved patient outcome w34,37]42x, allowing suffi- the data be gathered accurately andin an appropriate
physiologic setting.
cient restoration of stability to permit some high-de-
This manuscript will briefly summarize what we
mand athletes to return to their sport of choice, it
have accomplished in assessing the in situ forces in
fails to completely restore normal knee kinematics or
the ACL in response to multiple-DOF knee motion,
to prevent the associated onset of joint degeneration
w x specifically during knee flexionrextension with ante-
43,44.
riortibial loading,andtheclinical applicationofthese
This failure to achieve an adequate restoration of
results. To achieve a more realistic experimental set-
normal knee kinematics has resulted in the need to
ting, we developed a new testing system } a robotic
improve upon our current understanding of ACL
function. Bylearning moreabout the role ofthe ACL manipulator in combination with a universal
in the intact knee, it is hoped that improved recon- force]moment sensor (cid:14)UFS. which can directly mea-
struction and rehabilitation protocols can be devel- sure the force in the ACL with simultaneous mea-
oped on a more scientific basis. This has motivated surement ofmultiple-DOFkneemotion.Weusedthis
many studies specifically aimed at the measurement technology to perform a series of studies examining
of knee motions (cid:14)kinematics. and of forces in the the effect of knee constraints, knee flexion angle, and
ACL in response to various external loads applied to magnitude of applied anterior tibial load on the in
the knee joint. situ forces in the ACL.This approach,also appliedto
Initially, studies focused on the measurement of objectively evaluating current bone]patellar
tibial translation in response to anterior tibial loading tendon]bone and semitendinosus]gracilis hamstring
and the concept of primary and secondary restraints ACL reconstruction procedures, has enhanced our
wasdevelopedw45]49x.TheACLwasshowntobe the understanding of the function of the ACL and ACL
w x
primary restraint to anterior tibial translation 47. grafts. It is hoped that with these and future studies,
More recently, efforts were focused on determining our methodology will lead to new and improved con-
S.L.-Y.Wooetal.rTheKnee5(1998)267]288 269
cepts of ACL reconstruction and post-operative re- force measuring device. These methods include the
habilitation. use of buckle transducers w60,63,75]78x, implantable
transducers w79]86x and the implantation of a steel
w x
2. What is the in situ force? prostheticcableinplaceoftheligament 87,88.While
these methodscan all measure the in situ force in the
The orthopaedic literature has provided a detailed ACL, they require instrumentation and contact with
description of the complex anatomic nature of the the ACL which may alter the in situ length of the
ACL w64]74x, theorizing that different fibers of the ACL and thus the in situ force measured.
ACL are recruited at different flexion angles. As it is For this reason, many investigators developed non-
impossibletoexamineeach fiberinthe ACLindividu- contact approaches to determine the forces in the
ally, the ‘bundle theory’, based on an anatomic divi- ACL. These methods include the placement of strain
w x w x
sion of the ACL in the pig, goat, sheep and cow 67 gaugesnear the ligamentinsertion site 57,the place-
w x w x
and on a functional division in the human 68 has ment of in-line external force transducers 61,89 and
w x
established itself as a good compromise. This theory the use of X-rays to make kinematic calculations 58.
provides a method of consistently dividing the ACL These methods avoid the problems of the contact
into its component AM and PL bundles, allowing measurements, butarelimitedintheir ability toeasily
comparisons designed to give insight into its biome- vary flexion angle and applied load.
chanical nature, especially regarding the force dis- Whether a contact or non-contact method is used,
tribution within the ACL. Knowing this information the system design must also consider the number of
gives the surgeon an important goal to achieve when DOF through which the knee may move.Historically,
selecting such variables as graft type, placement, and studies on knee mechanics were performed allowing
tension for ACL reconstruction; i.e. to reproduce the the knee to move in only a single DOF, that is,
force present in the intact ACL. This force is called anterior translation of the tibia with respect to the
the in situ force. femur. In reality, the knee has the potential to move
By definition,the in situ force in a knee ligament is in 6DOF:three translations } proximal]distal (cid:14)PD.,
the force carried by the ligament in response to a anterior]posterior(cid:14)AP.andmedial]lateral(cid:14)ML.;and
given load applied to the knee while the knee (cid:14)and three rotations } internal]external (cid:14)IE., varus]
ligament. remains intact. The in situ force within a valgus (cid:14)VV. and flexion]extension (cid:14)FE.. The anterior
ligament characterizes the role that the ligament is drawer and Lachman tests done at a given knee
playing in resisting an external load applied to the flexion angle allow 5-DOF tibial motion, as demon-
intact knee. Because force,by definition,is a vector,a strated by studies that showed the tibia not only to
complete measurement of in situ force must include displace anteriorly but also to rotate internally
w x
its magnitude, direction, and point of application. In 45,90,91. Therefore modeling the anterior drawer in
theory, the force vector originates from a single point the laboratory using a setup allowingonly APtransla-
within the ligament insertion sites, and may be ori- tion (cid:14)1 DOF. may be toorestrictive. We hypothesized
ented in different directions within the substance of that the in situ forces in the ACL due to anterior
the ligament with changing externally applied load tibial loadingmeasuredatachosenkneeflexionangle
and knee flexion angle. This is especially important in under conditions of 1-DOF knee motion might not
the ACL, where different fibers are loaded at differ- represent the physiological situation of 5-DOF knee
ent knee positions, thus causing the net in situ force motion. While other investigators made similar hy-
vectortochangeitsdirectionandpointofapplication. potheses, developing testing systems to measure the
While the literature has traditionally reported only ACL in situ force under multiple-DOF knee motion
w x
the magnitude of the force, we contend that the 53,55,59,60,92, their systems often made indirect
direction and point of application of the in situ force measurements or lacked the ability to measure the in
are equally important and must also be considered. situ force at multiple flexion angles, under multiple
applied loads, or with complete determination of
3. Brief summaryof past testing systems magnitude, direction and point of application (cid:14)Fig.1..
Several techniques have been developed to de- 4. Development of the roboticrrrrrUFS system
termine the in situ force in the ACL which can be
roughlyclassified bywhether contact isorisnotmade Hence, we set out to develop a new technique with
withtheligament,theDOFthroughwhichthekneeis the explicit goal of finding a way to measure the in
allowed to move during testing, and the ease with situ force(cid:14)includingmagnitude,directionandpointof
which the flexion angle and applied external load can application.intheACLanditsbundlesinresponseto
be changed. Contact methods involve making direct external loading. Our goal was to directly measure
physical contact with the ligament midsubstance by a these forces without making ligament contact, while
270 S.L.-Y.Wooetal.rTheKnee5(1998)267]288
Fig.1. Akinematic linkage devicedesignedtomeasure the three translational andthree rotational degreesoffreedomofaknee (cid:14)adapted
fromw55x..
maintaining multiple-DOF knee motion. Further-
more,the system had to have the ability to repeat the
multiple-DOF knee motion after initial testing such
that numerous testing conditions could be evaluated
withinthe samekneeandthus interspecimen variabil-
ity eliminated.
With these aforementioned goals, we designed a
testing systemwhichincorporatedaroboticmanipula-
w x
tor and a UFS 93. The robot manipulator is a
six-joint series-articulated manipulator (cid:14)Unimate,
PUMA model 762.. It is a position-controlled device
with repeatability for position and orientation of less
than 0.02 mm and 0.028, respectively. It has a force
capacity of 450 N (cid:14)newtons. with the arm fully ex-
tended. In addition to position-control, the capability
of force-control is added by using the force]moment
data providedby the UFS(cid:14)JR3, model 4015. to guide Fig.2. Aschematicdiagramoftheroboticmanipulatoranduniver-
the robotic motion (cid:14)Fig. 2.. The full-force scales of salforce]momentsensor(cid:14)UFS.testingsystem.
the UFS are "900 N in its z direction, "450 N for
its other two directions, and "50 N m (cid:14)newton-me- tion. That is, the vector difference of the force as
ters. for moments. Repeatability is within the range measured by the UFS before and after modifying the
of0.2Ninforcesand0.01Nminmoments.Thus,the specimen equals the in situ force in the structure
robotic manipulator and UFS testing system are ade- removed from the specimen. In this manner, we can
quate to produce loads similar to those used during determine the magnitude, direction and point of ap-
clinical evaluation of the patient w46x. plication of the in situ forces of the ACL w50,93]99x.
The robotic manipulator is used to learn the com- The following section will describe the control theory
plex motion of the knee specimen in response to ofourtestingsystemandthemathematical arguments
external loads and then to reproduce this motion in on which it is based.
subsequent tests after the specimen has been modi-
fied (cid:14)e.g. removal of the ACL from the knee.. The 4.1. The joint coordinatedescription
UFS is used to record three forces and three mo-
ments in both cases. The ability to duplicate the The testing of cadaveric knee specimens is done
motion exactly before and after modifying the speci- with the tibia mounted to the UFS, which in turn is
men enables us to apply the principle of superposi- mountedon the end effector ofthe robotic manipula-
S.L.-Y.Wooetal.rTheKnee5(1998)267]288 271
tor (cid:14)Fig.2..The femur is mountedrigidlyto the robot Through the application of the principle of virtual
base. By ensuring a rigid body connection between work,a (cid:20)6=64 Jacobian matrix, J,can be obtained as
w x
the UFSand tibia, and the robot base and femur, the shown below 103:
UFS is able to record forces and moments applied to
the specimen. JsJ0
Tocharacterize the complex 6-DOFmotions of the d S S yd C C yC S yd S C 0 0
AP VV IE PD VV IE VV IE PD IE IE
knee joint in a clinically significant way, we use a d C S 0 0 0 1
AP VV VV
non-orthogonal joint coordinate description originally yd S C yd C S C C d C S 0 0
developedby Grood and Suntay w100x and Chao w101x yCAVPVSVIEV IE PD VV IE 0VV IE CPIED IE 0IE 0 0 ,
(cid:14)Fig. 3.. This system allows for the rigorous descrip- SVV 0 0 0 1 0
C C 0 S 0 0 0
tionofthe 6-DOFmotionofthe human knee andcan VV IE IE
be represented as a sequence of six serial links (cid:14)3.
w x
between the femur and tibia 95.
While the motion of the human knee is completely where the (cid:20)6=64 matrix J0 depends upon the rela-
described in this 6-DOF description, the associated tive positions of the sensor and tibia. The terms in
forces and moments are measured with respect to a this Jacobian matrix represent the displacements (cid:14)e.g.
Cartesian frame fixed with the UFS w95x. Therefore d sproximal]distaldisplacement.andthesinesand
PD
the three forces and three moments measured by the cosines of the angles (cid:14)e.g. S sthe sine of the VV
VV
UFS must be mathematically transformed into forces angle. in the joint coordinate description, as shown in
and moments along and about the non-orthogonal Fig. 3.
joint coordinate description. The details of this math- Because the sensor coordinate system is rigidly
ematical approach can be found in published works fixed to the tibial coordinate system, the Jacobian J0
w x
from our research center 96 and also in Paul et al. is constant and is determined by measuring the rela-
w x
102. tive positions and orientations of the two coordinate
Briefly, we define a (cid:20)6=14 force]moment vector, systems w103x.
SF, consisting of the three forces (cid:14)f ,f ,f . and three This transformation relates the two force]moment
x y z
moments (cid:14)m ,m ,m . measured by the UFS (cid:14)Fig. 4., vectors, JF and SF, such that
x y z
SFs(cid:14)f ,f ,f ,m ,m ,m .T. (cid:14)1. JFsJT?SF. (cid:14)4.
x y z x y z
Thus, all forces and moments measured with re-
We then similarly define another (cid:20)6=14 force]mo- spect to the sensor coordinate system can be ex-
ment vector, JF, with respect to the 6-DOF joint pressed with respect to the joint coordinate descrip-
coordinate description as defined above, i.e. three tion (cid:14)Fig. 3..
forces (cid:14)f ,f ,f . and three moments (cid:14)m ,
ML AP PD FE
m ,m . such that 4.2.Combinationofposition-andforce-controlledmodes
VV IE
The followingiteration procedure was developedto
JFs(cid:14)m ,f ,m ,f ,m ,f .T. (cid:14)2.
FE ML VV AP IE PD operate the robotic manipulator in a force-controlled
Fig. 3. The joint coordinate description of the knee: (cid:14)a. equivalent serial-linkage system, with the UFS; (cid:14)b. relationship between the
orthogonalcoordinatesystemsofeachlink,where dandurepresentthelinearandangulardisplacements,respectively,alongandabouteach
linkand C representstherespectivecoordinatesystem.
272 S.L.-Y.Wooetal.rTheKnee5(1998)267]288
Fig. 4. Schematic of the transmission of an external force through a body to the UFS, and the rotation of the sensor coordinate system
(cid:14)x,y,z..The z-axisoftherotatedcoordinatesystem(cid:14)x9,y9,z9.isparalleltotheexternalforce.Theforces(cid:14)Fx, Fy, Fz.andmoments(cid:14)Mx, My,
Mz.measuredbytheUFSareshown(cid:14)adaptedfromw96x.
mode. The controller reads the position and orienta- The general procedure to test knees consists of the
tionfromtheroboticmanipulatorandreadstheforces following steps:
andmomentsfromthe UFS.After the effects oftares
and the fixture gravitational force are removed, the
results are translated to the specific movementcenter 1. Under force]moment control, the robotic manip-
location and the resultant forces and moments are ulator learns the 6-DOF path of the knee joint
compared to the target values. Utilizing the instanta- between the selected end points of flexion, e.g.
neous load-deflection information, the movements 0]908 of knee flexion.
neededtoreduce the errors are calculated, initially in 2. Theknee is then tested in 5 DOF(cid:14)at a fixedknee
the tibial coordinate system, transformed into the flexion angle. while the controller, subjecting the
robotic movement system, and finally, the motion specimen to a specified external load at a speci-
increment is commanded. fied rate, records the positions via the robotic
In passive knee flexion and extension, the target manipulator and records forces and moments via
forces and moments are specified to be zero (cid:14)residual the UFS. (cid:14)In practice, this process is repeated 10
force and moment magnitudes less than 2 N and 0.2 times per test to allow pre-conditioning of the
N m, respectively.. Once equilibrium is reached knee and thus minimize ligament viscoelastic ef-
through the iterative process, the position is recorded fects..
as a control point and an increment of rotation is 3. A ligament or other soft tissue is surgically cut.
effected, in order to cause a change in flexion angle, 4. After the knee specimen is thus modified, the
and this process is repeated. The path of flexion]ex- robotic manipulator repeats the identical 5-DOF
tension is thus a series of the final positions, which knee position while the UFSis used to record the
are stored for later use to duplicate the positioningof forces and moments.
the joint. In practice, a preliminary flexion]extension 5. The in situ force within the removed ligament or
path is determined, and the range of flexion is re- soft tissue is then calculated (cid:14)superposition. as
peated 10 times to precondition the knee, at which the difference between the UFS measurements
point the neutral path positions are refined to their taken before and after removal of the ligament.
final values. To apply a loaded condition (cid:14)AP, VV, Although the UFS is part of the control system
etc.., the same process is used with target forces when a path of motion is being learned under
andror moments being non-zero, while the flexion force]moment control, it is used only for data
angle is held at one of the selection alternatives. acquisition when the path of motion is repro-
S.L.-Y.Wooetal.rTheKnee5(1998)267]288 273
duced,the motion then being under position con- accuracy. A slight measurement error will result in a
trol. large error in the location of the point p.
Toresolvethisdifficulty,weuseaforcetransforma-
tion scheme by rotating the sensor coordinate system
4.3. The in situ force¤ector mathematically such that the z-axis of the new Carte-
sian coordinate system (cid:14)z9. is parallel to the direction
4.3.1. Magnitudeand direction of the measured in situ force (cid:14)Fig.4..As described by
The magnitude of the in situ force, F, in the Fujie et al. w96x, this results in a point p9s
transected ligament is determined as follows: (cid:14)p 9,p 9,p 9.T along the line of action of the in situ
x y z
force described with respect to the rotated coordinate
’
<F<s f2qf2qf2 . (cid:14)5. system as
x y z
terTmhieneddiraesctfioolnlowcso:sine of the in situ force is de- px9symf y99, py9smf x99 and pz9sarbitrary.
z z
(cid:14)9.
f f f
axs<Fx< ays<Fy< and azs<Fz<. (cid:14)6.
In essence, this is a parametric equation of the line
of action, which is parallel to the z9-axis. That is,
Forease ofdescription,the direction ofthe force is choosing any two arbitrary values for coordinate p 9
transformed from a representation using Cartesian will result in twopoints, p9,such that a line is formezd
coordinatestooneusing spherical coordinates.In this
between them. Once the line of action is determined
representation, elevation, termed alpha (cid:14)a., physi-
with respect to the new, primed coordinate system, it
cally represents the angle the force makes with the
can be mathematically rotated back to its original
tibial plateau; and deviation, termed beta (cid:14)b., repre- w x
orientation using a transformation matrix 96. The
sents the angle between the force and the sagittal
parametric equationofthe line ofactionofthe insitu
plane as viewed from the posterior aspect of the tibia force with respect to the sensor coordinate system (cid:14)x,
(cid:14)Fig. 5.. Both aand bare determined as follows: y, z. is then determined as
assiny1(cid:15) <Ffy< /, bstany1(cid:15) ffzx /. (cid:14)7. p syfzmyqfymzqfx’fx2qfy2qfz2s
x f2qf2qf2
x y z
’
4.4. Point of application p syfxmzqfzmxqfy fx2qfy2qfz2s , (cid:14)10.
y f2qf2qf2
x y z
The point of application of the in situ force in the
’
ACL is defined as the point where the line of action yf m qf m qf f2qf2qf2s
of the in situ force passes through the tibial insertion p s y x x y z x y z
z f2qf2qf2
site of the ACL. This is determined in a two-step x y z
process. First, we determine the line of action of the
in situ force in the ligament, and then we determine where s is a parameter that indicates a location along
the location of the tibial insertion site in space. The the line of action of the in situ force with respect to
point where these two intersect is the point of appli- the sensor coordinate system w96,104x.
cation of the in situ force on the tibial plateau. Because the parametric equations that describe the
To locate the line of action of the in situ force, we line of action of the in situ force vector are symmet-
firstdeterminethepoint ps(cid:14)p ,p ,p .T wherethein ric, there is no dependence upon the direction of the
x y z
situ force vector intersects the surface of the sensor in situ force. The error remains quite small even
(cid:14)i.e. the x]y plane of the sensor coordinate system.. when the measured force is parallel to the surface of
This requires us to divide the moments by f , and the UFS. This mathematical manipulation enables
z
accurate determination ofthe line ofthe in situ force.
p symy , p smx and p s0. (cid:14)8. Next, we determine the location of the tibial inser-
x f y f z tionsiteoftheACLwithrespecttothesensorcoordi-
z z
nate system. To do this, elastin stain is used to mark
If the direction of the force is nearly parallel to the sixlocationsaroundthe tibial insertion ofthe ACL.A
surface oftheUFS,andthus f isverysmall,then the compressive force of approx. 15 N is applied to the
z
determination of its line of action will diminish in first marker with a 1-mm diameter pin while the
274 S.L.-Y.Wooetal.rTheKnee5(1998)267]288
4.5. Knee kinematics
If one considers the determination of the in situ
force in a ligament to be the engineer’s approach to
evaluating the ligament, then the determination of
tibial translation following ligament injury would be
the clinician’s approach w105,106x. The roboticrUFS
system has the ability to evaluate the knee specimen
in this fashion also. Following knee specimen alter-
ation (cid:14)e.g. cutting the ACL., the knee is subjected to
the same external load as before specimen alteration
and the new position recorded. By comparing this
knee position with the position recorded prior to
specimen alteration, the change in tibial translation
due to the specimen’s alteration can be determined.
For the case of analyzing ACL transection, only the
anterior tibial translation is considered from the 5-
DOFtibial motion.In this way,measurements can be
considered to be equivalent to those made in the
Fig. 5. Schematic of the right tibial plateau as viewed from the
clinic using measuring devices such as the KT-1000.
poterioraspectshowing aand banglesdescribingthedirectionof
theACLinsituforce.
5. Experimental studies
forces and moments developed in the UFS are Utilizing this technology, we have performed a se-
recorded. A second compressive force of approxi- ries of three experimental studies on porcine and
mately the same magnitude is then applied to the human cadaveric knees. The first study was designed
same marker from a different direction. As for the in to verify the validity of the roboticrUFS system and
situ force described above, the line of action of each to evaluate the effect of varying joint constraint on
compressive force is determined. The point where the measurement ofin situ forces. Thesecondexperi-
these two lines intersect with respect to the sensor ment was designed to evaluate the effect of knee
coordinate system is the elastin stain marker’s posi- flexionangleandappliedanterior tibial loadonthe in
tion in 3-D space. By repeating this process for each situ force in the human ACL and its distribution
ofthe six elastin stain markers, a plane describing the between the AMandPLbundles.Thethirdevaluated
ACL tibial insertion site in 3-D space is defined the efficacy of bone]patellar tendon]bone and semi-
relative to the sensor coordinate system. tendinosus and gracilis ACL reconstruction proce-
dures.
With this geometrical definition of the ACL tibial
In each experiment, comparison of the magnitude
insertion and the line of action of the in situ force in
of the in situ force between groups was made using
theACLwithrespecttothesensorcoordinatesystem,
analysis of variance (cid:14)ANOVA. followed by Fisher’s
the point of intersection between the two can be
PLSDpost-hoctests.Thedirectionandpointofappli-
determined. That is, the plane representing the tibial
cation data were compared through the construction
insertion site of the ACL is generically represented
of multivariate confidence intervals determined using
by:
the means and standard deviations of the normalized
w x
data 52.Lastly,toevaluate theeffect ofvaryingknee
axqbyqczsd, (cid:14)11. flexion angle and applied anterior tibial load on the
magnitude of the ACL in situ force, the data were
where x can be substituted for with p (cid:14)s., y substi- compared using general linear modeling techniques
x
tuted for with p (cid:14)s., and z substituted for with p (cid:14)s.. with Student’s t-test evaluation. In all cases, signifi-
Solvingfor s giveysthe unique pointwhichsatisfieszthe cant differences were set at P-0.05.
geometric plane and the line of action (cid:14)i.e. their
intersection..Thensolving p (cid:14)s., p (cid:14)s.and p (cid:14)s.with 5.1. Study 1: In situ forces and knee kinematics under
x y z
the aforementioned s gives the point in the sensor multiple-DOF knee motion
coordinatesystemwhichrepresents thepointofappli-
cation of the ACL in situ force on the tibial plateau 5.1.1. Goals and hypotheses
w x
96,104. We hypothesized that there was a significant dif-
S.L.-Y.Wooetal.rTheKnee5(1998)267]288 275
ference between the in situ forces in the ACL and The robot then applied AP loading to "100 N at a
between kinematic knee motions measured with dif- rate of 20 mmrmin to the joint at 308, 608 and 908
ferent constraint conditions placed on the knee, e.g. while allowing unconstrained, 5-DOF knee motion.
5-DOF vs. 1-DOF. To do this, we chose to study Joint kinematics (cid:14)i.e. position and orientation. during
porcine knees because of their uniform size, age and each loading were recorded for later use (cid:14)Fig. 7..
bone quality. Specifically, we compared the in situ The test was then repeated with the robot con-
forceswithintheACL,distributionofthisforcewithin strained to moving the joint in only 1-DOF (cid:14)i.e. only
the two bundles of the ACL, and the anterior tibial AP. motion. AP loading to "100 N at a rate of 20
translation secondary to applied anterior tibial loads. mmrmin was applied to the joint at 308, 608 and 908.
By using the roboticrUFS system, we were able to As for the 5-DOF case, the joint positions and orien-
perform both the 1-DOF and 5-DOF tests (cid:14)Fig. 6. on tations under load were recorded.
each knee, allowing us to eliminate inherent inter- Next, all tissues around the knee were removed
specimen variability and take advantage of paired except the ACL,leaving a femur]ACL]tibia complex
statistical analysis techniques. (cid:14)FATC.. The specimen was checked to ensure that
only the ACL provided resistance to anterior tibial
5.1.2. Methods and results loading. The 5-DOF path of tibial motion for the
Eight porcine knee joints were dissected free of intact knee under anterior tibial loading was then
musculature, leaving the joint capsule and knee liga- reproduced by the robot while the forces and mo-
mentsintact. Thetibia andfemurwerecuttoalength ments applied to the tibia were recorded by the UFS.
of 20 cm from the joint line and secured within This was done with the knee at 308, 608 and 908 of
thick-walled aluminum cylinders and rigidly fixed to flexion. Given the identical path of motion for the
the robot as described in Section 4 (cid:14)Fig. 2.. intact knee and the ACL-only knee, the forces and
Using force]moment control, the robotic manipu- moments measured during the second test represent
lator was used to first determine and record the those in the ACL in the intact knee under 5-DOF
6-DOF path of intact joint motion between 308 and anterior tibial loading w52,96x. The magnitude, direc-
908 of passive knee flexion w93,95x. This was done to tionandpointofapplicationoftheinsitu forceinthe
determine the path of passive flexion of a particular ACL were then determined, as detailed in Section 4.
knee specimen and to allow subsequent repositioning To determine the in situ forces in the ACL under
of the joint at any desired flexion angle by the robot. anterior tibial loading during 1-DOF knee motion,
Specific flexion angles along this path later provided the previously recorded 1-DOF tibial motion path of
the starting point (cid:14)zero reference. for externally ap- the intact knee was repeated on the ACL-only knee.
plied tibial load tests. The knee was placed in 308 Again, as the path of 1-DOFmotion was identical for
flexion and preconditioned with anterior]posterior the intact and ACL-only knee, the in situ forces
(cid:14)AP.loadingto100Natarate of50mmrminforfive developedin the ACL were determined and the mag-
cycles to minimize ligamentous viscoelastic effects. nitude, direction and point of application calculated.
A similar procedure was used to determine the
distribution of in situ forces between the AM and PL
bundles of the ACL. To examine the 5-DOF in situ
force in the PL bundle, the AM portion of the ACL
was bluntly transected, and the 5-DOF path of intact
knee motion under AP tibial loading was repeated at
308, 608 and 908 of knee flexion. The UFS outputs
were measured and the in situ forces in the PL
bundle determined. The in situ forces in the AM
portion of the ACL were then calculated using vector
algebra. Similarly,the test wasrepeatedwiththe knee
restricted to 1-DOF anterior tibial motion (cid:14)Fig. 7..
As documented by previous investigators, uncon-
strained, 5-DOF anterior tibial loading resulted in
significantly greater anterior tibial translation in the
intact knee when compared to the 1-DOF case (cid:14)1.4
times, P-0.05.. Associated with this translation was
anotabletotaltibialrotationof13"48(cid:14)mean"S.D...
However, the magnitudes of the in situ forces de-
Fig. 6. Diagrams detailing the joint motions allowed under (cid:14)a. veloped in the ACL were not significantly different;
1-DOFand(cid:14)b.5-DOFanteriortibialload. under 100 N anterior load, the in situ forces were
276 S.L.-Y.Wooetal.rTheKnee5(1998)267]288
Fig.7. FlowchartdetailingthesequenceoftestinganddataobtainedfromStudy1:1DOFvs.5DOF.
98.4"7.8Nand105.3"9.2N,for5-DOFand1-DOF, a was noted to decrease slightly in both cases, while
respectively, at 308 flexion.This trend was also true at bremained almost constant.
608 and 908 of flexion, although the magnitudes of in Under 5-DOF anterior tibial loading, the point of
situ force were slightly reduced. application of the in situ force in the entire ACL was
On the other hand, the constraint condition was located near the center of the ACL insertion site.
foundtosignificantly affect the directionofthe insitu This is shown on a representative specimen (cid:14)Fig. 9.,
force in the ACL at all knee flexion angles. The with the point of application of ligament force (cid:14)repre-
directionoftheinsituforceintheACLcorresponded senting the centroid of ligament loading.. The more
approximately with the direction in which the AM constrained, 1-DOF testing case resulted in the point
portion of the ACL inserted in the tibia. Specifically, ofapplicationoftheinsitu forceintheentire ACLto
under 5-DOF anterior tibial loading of 100 N at 308 be located more anteriorly in the posterior region of
knee flexion, the elevation (cid:14)a. and deviation (cid:14)b. of AM portion of the tibial insertion site (cid:14)Fig. 9..
the in situ force in the ACL were 15.7"4.48 (cid:14)a. and The distribution of force within the ACL was also
4.9"2.18 (cid:14)b.. This direction changed with 1-DOF found to be significantly affected by the constraint
anterior tibial loadingof100N,to26.8"4.18(cid:14)a.and condition. For the 5-DOF case, the distribution of
11.0"3.28(cid:14)b.(cid:14)Fig.8..Astheappliedloadincreased, forces between the AM and PL bundles of the ACL