Patellofemoral Stresses during Open andClosed Kinetic Chain ExercisesAn Analysis Using Computer Simulation

Zohara A. Cohen, MS, Hrvoje Roglic, MS, Ronald P. Grelsamer, MD, Jack H. Henry, MD,William N. Levine, MD, Van C. Mow, PhD, and Gerard A. Ateshian,* PhD

From the Orthopaedic Research Laboratory, Departments of Mechanical Engineering andOrthopaedic Surgery, Columbia University, New York, New York

ABSTRACT

Rehabilitation of the symptomatic patellofemoral jointaims to strengthen the quadriceps muscles while lim-iting stresses on the articular cartilage. Some investi-gators have advocated closed kinetic chain exercises,such as squats, because open kinetic chain exercises,such as leg extensions, have been suspected of plac-ing supraphysiologic stresses on patellofemoral carti-lage. We performed computer simulations on geomet-ric data from five cadaveric knees to compare threetypes of open kinetic chain leg extension exercises (noexternal load on the ankle, 25-N ankle load, and 100-Nankle load) with closed kinetic chain knee-bend exer-cises in the range of 20° to 90° of flexion. The exer-cises were compared in terms of the quadriceps mus-cle forces, patellofemoral joint contact forces andstresses, and “benefit indices” (the ratio of the quadri-ceps muscle force to the contact stress). The studyrevealed that, throughout the entire flexion range, theopen kinetic chain stresses were not supraphysiologicnor significantly higher than the closed kinetic chainexercise stresses. These findings are important forpatients who have undergone an operation and mayfeel too unstable on their feet to do closed chain kineticchain exercises. Open kinetic chain exercises at lowflexion angles are also recommended for patientswhose proximal patellar lesions preclude loading thepatellofemoral joint in deeper flexion.

The majority of patients who have patellofemoral jointmalalignment, dysplasia, osteoarthritis, or patellofemoral

pain syndrome are successfully treated nonoperativelywith appropriate rehabilitation programs.9,18,28,32,34,37 Aprimary goal in rehabilitating patients with these diag-noses is to condition the quadriceps muscles while main-taining moderate loads in the joint.14,23 High stresses onthe articular surfaces can exacerbate symptoms of painand perhaps damage the cartilage.21 Recently there hasbeen a significant interest in comparing open kinetic chainand closed kinetic chain exercises as they relate to lowerextremity rehabilitation. Open kinetic chain exercises,such as leg extension and straight-leg raises, are those inwhich there is no reaction force at the foot, whereas closedkinetic chain exercises, such as squatting and leg presses,are those in which there is force transmitted through thefoot to the tibia.

Studies have shown that closed kinetic chain exercisesare well suited for both rehabilitation and athletic train-ing.4,7,8,10,15,19,20,39,41 In contrast to open kinetic chainregimens, which strengthen only the quadriceps muscleswith no consistent firing of the hamstring muscle, closedkinetic chain exercises involve the hip, knee, and anklejoints simultaneously. Closed kinetic chain exercises arethought to improve general function by improving musclecoordination and physical performance.7,8,12,38,46 Fur-thermore, closed kinetic chain exercises have been advo-cated because of a concern that open kinetic chain reha-bilitation at low flexion angles exposes the patellofemoraljoint to supraphysiologic loads.27,40

Nevertheless, patients who have patellar subluxationoften have difficulty with closed kinetic chain regimens.23

Open chain exercises are generally better tolerated thanclosed chain exercises by patients in the postoperativeperiod, when many are unstable on their feet. Patientswho have lesions on the proximal aspect of their patellarsurface may not be able to perform closed kinetic chainexercises with the knee flexed in the 60° to 90° range; atthose angles, the proximal portion of the patella is incontact with the femoral trochlea.2,25,26 Studies have

*Address correspondence and reprint requests to Gerard A. Ateshian, PhD,Orthopaedic Research Laboratory, Columbia University, 630 West 168thStreet, Room BB 1412, New York, NY 10032.

No author or related institution has received any financial benefit fromresearch in this study. See “Acknowledgments” for funding information.

0363-5465/101/2929-0480$02.00/0THE AMERICAN JOURNAL OF SPORTS MEDICINE, Vol. 29, No. 4© 2001 American Orthopaedic Society for Sports Medicine

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shown open kinetic chain protocols in the range of 20° tofull extension to be particularly effective because the mus-cle effort of the quadriceps is highest in this range.16,45

Thus, there is good reason to explore more carefully thestresses associated with open kinetic chain exercises todetermine if they are in fact excessive.

Under normal loading conditions, weightbearing jointshave been found to experience forces as high as 10 timesbody weight, leading to maximum contact stresses vari-ously reported at 3.44 MPa,2 4.2 MPa,25 and 17 MPa.33

Impact stresses in the range of 15 to 20 MPa have beenshown to cause cell death, rupture of the collagen fibermatrix, and increase in tissue water content.43 Progres-sive degeneration of cartilage toward osteoarthritis mayoccur at stresses lower than failure-inducing impactstress; indeed, it is believed that once an initiating biome-chanical or biochemical event has compromised the integ-rity of the cartilage matrix, even normal stress levels mayprogressively lead to degeneration.6,11,22,36

This study simulated closed kinetic chain and threetypes of open kinetic chain exercises by employing previ-ously validated three-dimensional computer models gen-erated from cadaveric data. The simulations provide anestimate of patellofemoral joint contact stresses, quadri-ceps muscle forces, and other biomechanical values. Thehypothesis of this study is that open kinetic chain exer-cises do not cause excessively high stresses to the patel-lofemoral joint.

MATERIALS AND METHODS

In previous studies, we measured the kinematics of fivecadaveric knees, three from men and two from women,while the knee was extended from 90° to 0° in an openkinetic chain experimental configuration and a constantquadriceps muscle load was applied.1,30 The quadricepsmuscle forces were represented by three components: 1)the rectus femoris muscle, combined with vastus interme-dius and vastus medialis longus muscles; 2) the vastuslateralis muscle; and 3) the vastus medialis obliquus mus-cle (Fig. 1A). The groups were loaded in a 3:2:1 ratio on thebasis of values obtained from the literature2,17 and main-tenance of a total quadriceps muscle tension of 534 N.2

The quadriceps muscle forces were kept constant whilethe tibia was moved through the range of motion by con-straining its anterior-posterior position and allowing thetibia to find its natural center of rotation. A coordinatemeasurement machine was used to measure the three-dimensional position of triads that were rigidly attachedto the bones (Fig. 2). The kinematic data determined fromthe triad positions were used in conjunction with surfacetopography data that were acquired via stereophotogram-metry to provide a simultaneous analysis of joint kinemat-ics and contact areas.5 The coordinate measuring machinewas also used to digitize the bony contours of the patella,distal femur, and proximal tibia of these joints, as well asthe insertion points of the loaded muscle groups and thepatellar tendon.

The three-dimensional topographic data and kinematicdata acquired from these cadaveric studies were used in

our subsequent study to create three-dimensional multi-body models of each of the five joints (Fig. 1B).31 Eachmodel employed its corresponding cadaveric experimental

Figure 1. A, forces and contact area on the patella at 90° offlexion. RF, rectus femoris muscle plus the vastus interme-dius and vastus medialis muscles; VL, vastus lateralis mus-cle; VMO, vastus medialis obliquus muscle; PT, patellar ten-don. B, three-dimensional mathematical models of fiveknees.

Figure 2. The knee joint testing machine with a mountedknee. Precision triads were rigidly attached to the femur,patella, and tibia.

Vol. 29, No. 4, 2001 Patellofemoral Stresses during Exercises 481

data to describe the surface topography, location of muscleinsertions, muscle direction, and tibial kinematics; how-ever, values obtained from the literature were used toapproximate the muscle force magnitudes and the mate-rial properties of the cartilage and ligaments. The modelsemploy the fundamental equations of static force and mo-ment equilibrium to predict joint kinematics and contactareas under any muscle-loading configuration. Each of themodels was successfully validated by applying the samemuscle loads as in the earlier experimental study andcomparing the predicted kinematics of the patella with thecorresponding experimental measurements.30 The readeris referred to our previous publications for a more detaileddescription of the underlying experimental data30 and themodeling equations.31

In the current study, these validated models were usedto simulate closed and open kinetic chain exercises. Theforces on the patella were the three modeled quadricepsmuscle components (model input), two modeled patellartendon components (model output), and articular contactforce, calculated as the resultant of the contact stress(model output). The tibia was fixed in the positions ac-quired in the earlier experimental study, while the patellawas free to rotate and translate, guided by the forcesacting on it. In the model analysis, the articular contactstress is proportional to the compressive strain, which, inturn, is approximated by the overlap of the articular sur-faces as a fraction of the cartilage-layer thicknesses. Theeffective cartilage modulus (proportionality constant) em-ployed in the current study was 10 MPa, which reasonablyapproximates the dynamic modulus of cartilage incompression.29

Each of the following four exercises was simulated: 1)knee bend (denoted by CKC); 2) unloaded leg extension(OKC-0); 3) leg extension with an external force of 25 N atthe ankle, perpendicular to the tibia at all flexion angles(OKC-25); and 4) leg extension with an external force of100 N at the ankle (OKC-100). A schematic of the threeloading configurations is shown in Figure 3. Note that theclosed kinetic chain exercise is a standard knee bend, inwhich the person’s weight rests on the ball of the foot, andis not the modified squat, in which the heel remains incontact with the ground and the person’s torso leans an-teriorly.35 The loaded open kinetic chain simulations(OKC-25 and OKC-100) represent exercises that can only

be done with an exercise machine that can apply a force atthe ankle that remains perpendicular to the tibia, regard-less of the knee’s flexion angle. This simulation would notproperly represent an exercise that was performed with aweight placed at the ankle because such an exercise wouldlead to a flexion moment that varied with flexion angle.

The applied moments used to simulate the closed ki-netic chain exercise were based on experimental values forthe moments required by subjects rising from a chairreported by Andriacchi and Mikosz.3 Those peak momentswere measured to be 82.2 Nzm (60.4 foot-pounds) for menand 59.4 Nzm (43.7 foot-pounds) for women. Assumingthat the seat in that study was at or slightly above kneeheight, the subjects typically would not have attainedflexion angles greater than 90°. Because flexion momentdecreases with extension from 90° to 0°, the reported peakmoments are assumed to have occurred at approximately90° of flexion. Given the geometry of the deep knee bend,shown in Figure 4, at any flexion angle u, the flexionmoment is equal to the subject’s body weight (W) multi-plied by its moment arm to the joint’s center of rotation(Lzsin[u/2]), where L is the length of the tibial shaft). Giventhe reported peak moments, WzL would be 116.3 Nzm formen and 84.0 Nzm for women. Adjusting the moment armfor lower flexion angles, the moment at any angle u can begiven by 116.3zsin(u/2) Nzm and 84.0zsin(u/2) Nzm for menand women, respectively.

Figure 3. Simulated loading cases: A, closed kinetic chainor squatting (WB, body weight). B, open kinetic chain legextension (WT, tibia weight). C, open kinetic chain loaded(WT, tibial weight; M, external moment on tibia).

Figure 4. Free body diagram showing the derivation of theapplied flexion moments based on peak moments at 90° offlexion. The flexion moment balances the moment about theknee because of the subject’s body weight. W, body weight;L, length of the tibial shaft; u, flexion angle; d, moment arm tothe joint’s center of rotation; M, flexion moment.

482 Cohen et al. American Journal of Sports Medicine

To simulate unloaded leg extension, the first of the openkinetic chain exercises, the quadriceps muscles were cho-sen to balance just the weight of the lower leg. We derivedthe magnitudes of these weights as well as the body seg-ment dimensions and centers of mass needed for thissimulation from data obtained from anthropometric stud-ies for the tibia and ankle.13 For the loaded leg-extensionsimulations, constant external moments (not varying withflexion) were applied in addition to the moment due to theleg weight (varying with flexion). Loads of 25 N (5.6pounds) and 100 N (22.5 pounds) were applied to the anklein a direction perpendicular to the axis of the tibial shaftat the given flexion angle. These loads produced constantmoments of 10.2 Nzm (7.5 foot-pounds) and 40.9 Nzm (30.1foot-pounds) for men and 9.1 Nzm (6.7 foot-pounds) and36.3 Nzm (26.7 foot-pounds) for women, for the 25-N and100-N loads, respectively.

Table 1 lists the flexion moments for men and womenthat were applied to simulate the four loading schemes.The flexion moment increased from a minimum at fullextension to a maximum at 90° for the closed kinetic chainconfigurations, whereas it decreased from a maximum atfull extension for the open kinetic chain configuration. Inthe implementation of the model, the quadriceps muscleforces that would generate the designated flexion momentwere not known a priori because the patellar position,which influences the moment, was unknown. Thus, thequadriceps muscle forces were adjusted iteratively (main-taining a constant ratio between the muscle groups) at agiven flexion angle until the desired moment wasgenerated.

The computer models were used to calculate the kine-matic position of the patella for tibial positions between20° and 90° of flexion, in increments of 10°. Each flexionangle was tested under each of the loading conditionslisted in Table 1, yielding a total of 32 configurations foreach knee. The first two experimental positions, 0° and10°, could not be included in the model analysis because,within that range, the patella is in contact with the su-prapatellar fat pad and not the trochlear groove. Althoughthe model could be extended to include contact betweenthe patella and the fat pad as well as between the fat padand the cortical bone of the femur, this model refinementwas not employed here.

For each exercise simulation at each flexion angle, themodel yielded biomechanical variables including thequadriceps muscle force, the patellofemoral joint contactforce, the average patellofemoral joint contact stress, thepeak patellofemoral joint contact stress, and the force inthe patellar tendon. The ratio of the quadriceps muscleforce to the force in the patellar tendon was calculated byusing the model solution to evaluate the percentage of thequadriceps muscle force reaching the tibia. A ratio ofquadriceps muscle force to contact stress was also calcu-lated to serve as an index of the benefit of the exercise(benefit index) because the goal of patellofemoral jointexercises is to strengthen the quadriceps muscles whilekeeping the contact stress to a minimum. The statisticalsignificance of observed differences in quadriceps muscleforce, mean contact force, mean contact stress, peak con-tact stress, and benefit index between the exercise modelswas measured using two-factor analysis of variance withrepeated measures on each knee, at a significance level ofa 5 0.05. The two factors were exercise model and flexionangle, and both primary and interaction effects weresought. Duncan’s multiple range test was employed todetect any groupings of the models in terms of the meas-ured variables.

RESULTS

Simulation results were obtained for 10° increments be-tween 20° and 90° of knee flexion and averaged over thefive knees for presentation purposes. The quadriceps mus-cle force increased with flexion from 20° to 90° for the CKCexercise simulations (Fig. 5). The force also increased withflexion for the OKC-25 and the OKC-100 exercises, despitethe decrease in moment with flexion for those exercises.The CKC quadriceps muscle force, reaching 3994 N at 90°,increased at a faster rate than the quadriceps muscle forcefor any of the open kinetic chain simulations. The patel-lofemoral joint contact force (Fig. 6) and average contactstress (Fig. 7) showed similar trends: the average CKCstresses increased progressively from 20° to full flexion(going from 0.9 to 5.8 MPa), the OKC-0 and OKC-25 val-ues increased only slightly (OKC-0 increased from 0.4 to0.7 MPa; OKC-25 from 0.8 to 1.6 MPa), and the OKC-100simulation showed a small increase (1.7 to 2.2 MPa) in

TABLE 1Flexion Moments Applied to the Knees at Different Flexion Angles and for Different Exercises

Flexion momenta (Nzm)

CKC OKC-0 OKC-25 OKC-100

Angle (deg) Male Female Male Female Male Female Male Female

20 20.18 14.59 7.71 7.52 17.93 16.59 48.61 43.8230 30.08 21.74 7.31 7.10 17.54 16.17 48.21 43.4040 39.74 28.73 6.70 6.47 16.92 15.54 47.60 42.7750 49.11 35.50 5.88 5.64 16.10 14.71 46.78 41.9460 58.10 42.00 4.88 4.63 15.11 13.71 45.78 40.9370 66.65 48.18 3.73 3.49 13.96 12.57 44.63 39.7980 74.69 53.99 2.48 2.24 12.70 11.32 43.38 38.5490 82.17 59.40 1.14 0.93 11.37 10.00 42.04 37.23

a CKC, closed kinetic chain; OKC, open kinetic chain.

Vol. 29, No. 4, 2001 Patellofemoral Stresses during Exercises 483

stress over the low flexion angles, 20° to 50°, but increasedmore rapidly (2.2 to 4.0 MPa) from 50° to 90°. In the 20°-to-50° region, the CKC stress was higher than the OKC-25configuration, and the OKC-100 configuration stress washigher yet.

The peak stress followed the same trends as the meanstress and is therefore not represented by a separategraph. The peak stress values ranged from 139% to 211%of the mean stress and reached a maximum of 8.1 MPa forthe CKC simulation at 90°. In the low flexion range (20° to50°), the OKC-100 exercise demonstrated the highestpeak stresses with values from 3.3 to 3.8 MPa, correspond-ing to 170% to 187% of the mean stress in that range.

The ratio of quadriceps muscle force to contact stress,the benefit index, is displayed in Figure 8. The benefit

index stayed relatively constant throughout the range ofmotion for the OKC-25 and OKC-100 exercises, exhibitingslight increases of 10% and 26%, respectively, for the20°-to-90° range. The index for the OKC-0 exercise fol-lowed a similar trend from 20° to 60°, demonstrating agradual increase in that range, but then, from 60° to 90°,it dropped by 45%. For the CKC simulation the indexincreased steeply between 20° and 60° of flexion, rising86% in that range, and continued to rise more graduallyfrom 60° to 90°. The OKC-100 exercise had the highestbenefit index of all the exercises at flexion angles from 20°to 50°, and the CKC exercise had the highest benefit from50° to 90°. The calculation of the ratio of the patellartendon force to the quadriceps muscle force demonstrateda continuous decrease with flexion angle (not shown). Theratio reached 0.5 at 90° of flexion, indicating that only halfthe quadriceps muscle force is transmitted to the tibia atthat flexion angle.

Figure 5. Quadriceps muscle force exerted in closed kineticchain (CKC) and open kinetic chain (OKC) exercises com-pared with flexion angle. OKC 0N, unloaded knee extension;OKC 25N, leg extension with 25-N external force at theankle; OKC 100N, leg extension with 100-N external force atthe ankle.

Figure 6. Patellofemoral joint (PFJ) contact forces duringclosed kinetic chain and open kinetic chain exercises com-pared with flexion angle. See legend at Figure 5 for expla-nation of abbreviations.

Figure 7. Average patellofemoral joint (PFJ) contact stresscompared with flexion angle. See legend at Figure 5 forexplanation of abbreviations.

Figure 8. Benefit index (ratio of quadriceps force to averagecontact stress) for each exercise at different flexion angles.See legend at Figure 5 for explanation of abbreviations.

484 Cohen et al. American Journal of Sports Medicine

The quadriceps muscle force, contact force, mean con-tact stress, peak contact stress, and benefit index all dem-onstrated a significant dependence on exercise (P ,0.0001). For all five of these variables Duncan’s multiplerange test demonstrated a significant difference betweenthe means of the different exercises. For the mean stress,for example, the CKC exercise had the highest mean at 2.8MPa, followed by the OKC-100 at 2.6 MPa, the OKC-25 at1.2 MPa, and the OKC-0 at 0.6 MPa. The other variablesdemonstrated the same ranking, except for the benefitindex, for which Duncan’s grouping showed CKC andOKC-100 to be nondistinct.

A significant interaction between exercise and flexionangle was observed for all the analyzed variables (P ,0.0001). At low flexion angles (below 50°) the quadricepsmuscle force, contact force, contact stress, peak stress, andbenefit index were the highest for the OKC-100 model andthen decreased, going from CKC to OKC-25 to OKC-0.This ordering changes at the higher flexion angles; therethe CKC was highest, followed by the OKC-100, OKC-25and, finally, the OKC-0. Thus, the effect of exercise wasmodulated by flexion angle; at low flexion angles CKC wasbest in terms of its low stresses and high quadricepsmuscle force, whereas at higher flexion angles the OKC-100 was best.

The interaction between exercise and flexion angleprompted us to explore the least squares means for theeffect of exercise at each flexion angle. The least squaresmeans analysis was done with a Bonferroni correction formultiple comparisons. A pair of means was consideredsignificantly distinct for P values less than 0.05. The mostnoteworthy finding of this analysis was that CKC andOKC-100 models were often nondistinct. Their meanswere not statistically distinct for quadriceps muscle forcein the 40°-to-60° range, patellofemoral joint contact forcefrom 20° to 60°, patellofemoral joint contact stress from20° to 70°, peak contact stress from 30° to 70°, and benefitindex throughout the entire range from 20° to 90°. Outsidethose ranges, the CKC exercise had lower forces and lowerstresses for the lower flexion angles, and the OKC-100exercise had lower forces and lower stresses for the higherflexion angles. Another noteworthy finding was that theOKC-0 and OKC-25 were in many cases nondistinct.There was no significant difference between them forquadriceps muscle forces from 20° to 50°, patellofemoraljoint contact force from 20° to 60°, contact stress from 20°to 80°, peak stress from 20° to 70°, and benefit index from20° to 50°. Outside those ranges, the OKC-25 simulationsdemonstrated significantly higher quadriceps muscleforces, contact forces, contact stresses, peak stresses, andbenefit indices. Finally, for most parameters, there wereno significant differences between the four models at 20°of flexion.

DISCUSSION

The painful patellofemoral joint has been successfullytreated either with nonoperative measures14,23,42,44,47 orwith surgical intervention followed by physical therapy.45

Over the last decade controversy has increased regarding

the preferred nonoperative treatment for patellofemoraljoint pain: open or closed kinetic chain exercises. Somestudies have raised the concern that open kinetic chainexercises may actually exacerbate the patients’ symp-toms,27,40 particularly when the knee is near full exten-sion. We addressed this question using a biomechanicalanalysis that employs experimentally generated multi-body models of cadaveric knees.

Because the model input consisted of flexion momentsapplied across the knee, the amount of quadriceps muscleforce necessary to produce those moments was an outcomeof the analysis. It was found that the quadriceps muscleforce (Fig. 5), like the contact force (Fig. 6), increased withflexion for the closed kinetic chain exercise, as was ex-pected from the increase in the applied flexion moment.For the OKC-0 simulation, the force increased slightlyfrom 20° to 60° and then decreased, yielding an overalldecrease of 75 N, from 137 N to 62 N. The increase inquadriceps muscle force indicates that some of it wasabsorbed by the contact between the patellar and femoralsurfaces. This explanation was corroborated by the in-crease in patellofemoral joint contact force with flexion, asshown in Figure 6. The OKC-25 exercise generated quad-riceps muscle forces that were not significantly differentfrom those generated from the OKC-0 exercise for the20°-to-50° range of flexion. These two exercises were notdistinct in terms of contact stresses and benefit indices.

Leg extension did not lead to undue stresses in thepatellofemoral joint, even at low flexion angles. The mosthighly loaded open kinetic chain exercise, OKC-100,showed no significant difference from the closed kineticchain exercise in terms of the contact stress produced from20° to 70°. Furthermore, the closed kinetic chain exercisedemonstrated higher stress from 80° to 90° (Fig. 7). Gen-erally, the CKC and OKC-100 exercises were very similarand exhibited nondistinct benefit indices throughout theentire range of flexion (Fig. 8). The OKC-0 and OKC-25exercises demonstrated lower contact stress than did theclosed kinetic chain exercise for all flexion angles from 20°to 90°. For the open kinetic chain exercises, both mean andpeak stress levels were all within the previously citedrange of values for maximum stress during normal load-ing conditions (3.44 MPa,2 4.2 MPa,25 and 17 MPa33),suggesting the safety of open kinetic chain regimens.Thus, the study’s hypothesis was confirmed; open kineticchain-generated stresses were found to be neither signif-icantly different from those generated by closed kineticchain exercises nor supraphysiologic.

As the knees flexed from 20° to 90°, the patellar contactareas were noted to move from the distal to the proximalpart of the patellar articular surfaces (Fig. 9), in agree-ment with reports in the literature2,12,13,26,33 and ourown previous experimental findings.1 This finding is clin-ically important because it suggests that pain related tochondral lesions in the proximal patella can be avoided byexercise performed with the knee flexed 20° to 30° (in thisrange, contact occurs over the distal part of the patella).The results of this study demonstrated that, in that range,the quadriceps muscles can be strengthened equally wellwith either squatting or constant moment leg extension,

Vol. 29, No. 4, 2001 Patellofemoral Stresses during Exercises 485

since the stresses they produced were not statisticallydifferent. For patients with distal lesions, exercises in the45° to 90° knee flexion range are indicated, and openkinetic chain exercises may be preferable because they donot require the patient to stand in an unstable positionand because their stresses can be lower than those of theclosed kinetic chain exercises. An exercise regimen can bechosen on these grounds only if the locations of the lesionsare known, via arthroscopy or MRI. Even without knowl-edge of the lesion locations, if a patient identifies therange in which he or she feels the most pain, the physicaltherapist can adjust the exercise routine accordingly, withthe knowledge that both closed and open kinetic chainexercises are beneficial.

Steinkamp and coworkers40 reported extremely highstresses near full extension for leg-extension exercise, buttheir protocol imposed a flexion moment of 200 Nzm, whichis 400% of our maximum of 49 Nzm. They chose the weightto apply in the open kinetic chain case such that themaximum moment from the open kinetic chain configura-tion matched the maximum moment in the closed kineticchain exercise. However, they did not consider that, unlikethe closed kinetic chain case, for which the maximummoment occurs at 90° of flexion, the maximum moment foran open kinetic chain configuration occurs when the kneeis near full extension. In other words, they applied forcesappropriate for a flexion angle with high congruence be-tween the patellar and femoral surfaces to a joint position

exhibiting only a small region of contact. We believe theloads applied in our study are more reasonable for an openkinetic chain rehabilitation regimen.

The decrease in patellar tendon-to-quadriceps force ra-tio with flexion angle is consistent with the trend observedby Hirokawa24 for an open kinetic chain configuration.However, Hirokawa found a smaller decrease in the ratio,reaching only 0.8 at 90°. In other words, the quadricepsmuscles in his study transmitted a greater portion of theirforce to the patellar tendon than did the quadriceps mus-cles in our study, which transmitted 50%. This discrep-ancy may be explained by the fact that Hirokawa modeledhis quadriceps muscle forces as two lines that approxi-mately followed the vastus intermedius muscle. All thequadriceps muscle force in that model acted to extend theknee, with no medial-lateral force stabilizing the patella,and thus a larger percentage of it might have been trans-mitted to the tibia.

Although this study showed open kinetic chain exercisesto be useful in terms of quadriceps muscle strengtheningand safe in terms of the contact stress in the patellofemo-ral joint, it should be noted that strengthening is only oneof the goals of physical therapy. Another goal is simulationof sports and everyday activities, for which closed kineticchain exercise may be superior. Our study looked exclu-sively at one type of closed kinetic chain exercise, the kneebend, and we have shown that open kinetic chain exer-cises do not cause greater cartilage stresses than thisclosed kinetic chain exercise. There are other closed chainexercises, namely leg presses, which are used in patel-lofemoral joint rehabilitation and which have not beenexplored explicitly in this study.

Our study used biomechanical simulations based oncadaveric data rather than performing direct experimen-tation on cadavers, yielding two levels of uncertainty inour findings: 1) the inherent uncertainty in analyzing asmall sample (five knees) of a large population and 2) theuncertainty in the predictions of the model simulations.The uncertainty due to the small sample size is common toall experimental studies and is addressed by using stan-dard analysis of variance statistics. The accuracy of thesimulations can be inferred, although not ascertained un-equivocally, from our earlier validation study on thesesame models,31 which used comparable muscle loadingconfigurations. More qualitatively, the good agreementobserved in the contact areas and stress magnitudes pre-dicted by the models with experimental findings reportedin the literature serves to increase our confidence in themodel predictions. A limitation of the current implemen-tation of the modeling algorithm was its inability to testflexion angles lower than 20° without further model re-finements. This limitation, however, is not of great signif-icance because the fat pad provides the patella with a softand congruent bearing surface in the 0°-to-20° flexionrange. The benefit of performing computer simulations isthe ability to simulate far more loading configurations (inthis case, 4 exercises at 8 flexion angles each means 32testing configurations per joint) than would otherwise bepractical under the constraint of cadaveric tissuedegradation.

Figure 9. Contact areas on the patella and femur in openkinetic chain exercise at 30° (a), 50° (b), 70° (c), and 90° (d)of flexion.

486 Cohen et al. American Journal of Sports Medicine

CONCLUSIONS

Open kinetic chain exercises have not been found to causesupraphysiologic stresses. With flexion moments equiva-lent to as much as 100 N (or 22.5 pounds) applied at theankle, open kinetic chain exercises appear to be safe withregard to patellofemoral articular cartilage contactstresses. An exercise regimen should be chosen on thebasis of the patient’s comfort, as neither open nor closedkinetic chain regimens exhibited unphysiologic stresses.

ACKNOWLEDGMENTS

The authors thank Dr. J. Richard Steadman for insightfuldiscussion of this study and the Tahoe Research Instituteof Denver, Colorado, for partial funding of this work.

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