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Frontal motion analysis of the knee during a bicycle pedal revolution: Georgia State University, Atlanta, GA, Department of Kinesiology & Health [Biomechanics Lab.] Thesis Defense “A man should look for what is, and not for what he thinks should be!” - Albert Einstein

Frontal motion analysis of the knee during a bicycle pedal revolution 2011

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Page 1: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

Frontal motion analysis of the knee during a bicycle pedal revolution:

Georgia State University, Atlanta, GA, Department of Kinesiology & Health [Biomechanics Lab.]

Thesis Defense

“A man should look for what is, and not for what he thinks

should be!”- Albert Einstein

Page 2: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

Frontal motion analysis of the knee during a bicycle pedal revolution:

Georgia State University, Atlanta, GA, Department of Kinesiology & Health [Biomechanics Lab.]

Harry P Sowieja (Student PI)

Associated Research Personnel

Dr Mark D Geil (PI)Dr Jianhua Wu (Co-PI)Dr Christopher P Ingalls (Co-PI)

Page 3: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

INTRODUCTION

Correct position of the rider's lower extremity and proper transfer of forces to the crank is important to eliminate shear (transverse forces) which may cause injury to the ankle, knee and hip joints.

Do we know EFFECT of Seat Height???

Page 4: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

PURPOSE

Report the effect of three seat heights and two resistance loads (power output settings) on the knee's joint center, Medial - Lateral (M-L) displacement in the frontal plane throughout a bicycle pedal revolution.

What is the RATIONALE???

Page 5: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RATIONALE

1) It’s a Kinematic study from frontal plane vs. Kinetic study

2) Inform of a seat height selection for new cyclist that will result in the smallest amount of medial and lateral movement at the knee

3) Investigate pattern and repeatability in subjects with similar lower extremity physiology Height OK

???

Therefore :

Page 6: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

DEFINITIONS

a/p: Anterior/posterior BDC: Bottom Dead Center dK: Median Knee displacement LL: Leg Length M-L: Medial-Lateral PA: Pedal Axis

SDdK: Mean Std. Deviation of dK

SL: Seat Low (=94% of LL) SH: Seat High (=106% of LL) SN: Seat Neutral (=100% of LL) STA: Seat Tube Angle TDC: Top Dead Center V-V: Valgus-Varus

Page 7: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

HYPOTHESES

1) The mean of dK will be greatest for all subjects at the low seat height position

2) The maximum displacement (dKmax) for any seat height will occur during the 200W test of the pedal cycle

dK

Page 8: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD : At Subject Intake

10 male and 10 female recreational cyclists

Ages of 34±11.304

Intake Questionnaire on a laptop to determine

Subjects’ fitness and free of knee injury ?

Subjects’ experience in cycling ? (NOT > 3Hr/Wk)

Subjects’ Consent and Vicon Measuring System (VMS) calibration

Page 9: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD : Obtained Consent

After Intake : Each subject was asked to read and sign a CONSENT FORM

Procedure was verbally described to candidates as on CONSENT FORM

Page 10: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD : VMS setup

The study session began with taking anthropometric measurements

Anthropometric parameters are from the Plug-In Gait product guide

The required parameters in the setup procedure for the VMS with Vicon Nexus software v1.5.2 are presented in TABLE 1 :

Page 11: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD – TABLE 1:

Page 12: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD : Determine : Valgum, Varum or Normal and Left/Right leg dominance

Physical characteristics of the subjects’ knees was measured using calipers i.e., group 1, 2 or 3 (Akitoshi, Naoki et al. 2009)

Dominant Leg – Kick a tennis ball (RIGHT or LEFT leg)

Page 13: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD : 19 Markers

Reflective markers, 16 placed according to convention on selected anatomical features of Subject and 3 on the Velotron

Marker placement described in the VMS manual

19 Markers are as follows: – ASIS (LASI & RASI) – PSIS (LPSI & RPSI) – thigh (LTHI & RTHI)– knee (LKNE & RKNE)– tibia (LTIB & RTIB)– ankle (LANK & RNK)– heel (LHEE & RHEE) – toe (LTOE & RTOE) – Pedal Axis Wands (LPAW & RPAW), and – Center of the VELOTRON Pedal Reference (CVPR)

Page 14: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD : Seat Height

Matching geometry of the VELOTRON (stationary bicycle) to subject’s leg length (LL)

LL measured from the superior border of the greater trochanter to the floor [subject wearing sneakers]

LL used to set the seat height which is the distance measured from the center of the pedal axis (PA) to the top of the seat, along the crank and seat tube

Seat height at 100% of LL is called seat neutral (SN)

Seat height at 94% of LL called seat low (SL) and

Seat height at 106% of LL called seat high (SH)

Page 15: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD : Cyclist position

a/p adjustment of the seat was found by having the subject sit on the seat in a common cyclist position

vertical projection of the subpatellar surface to the PA with the crank at 90° of rotation after TDC

Handle bar height was adjusted 10±5cm higher than the saddle height (aim was to achieve a comfortable back angle of approximately 45°)

Page 16: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

METHOD : Speed & Resistance

Manageable speed of 80±5rpm, indicated on a laptop screen, was easily achieved by all subjects at 50Watts resistance

Resistance was increased in steps of 50W to 100W or 200W

Subject given an opportunity to practice,

Six trials of steady state speed for 15s (SH, SL and SN randomly selected)

Captured with VMS, seven Vicon T-10 cameras (six 8.5mm and one 12.5mm)

Subject verbally told when data recording started, then encouraged to maintain constant speed and after 15seconds informed of completion

The laptop controls the constant load of 100 watts or 200 watts to the VELOTRON

Page 17: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS : 120 Trials

Raw data in VMS converted by Plug-In-Gait software to Comma Separated Files

RPAW and RKNE or LPAW and LKNE, were transferred to an Excel spreadsheet

Macros in Excel to find the BDC of each pedal revolution

=IF(AND(E6+F6>410,E6+F6<430),IF(AND(F6>124.256,F6<129.256),IF(OR(E6>E7,F6<F7),IF(AND(E6<308.924,E6>288.424),IF(E6>E7,K5+1,K5),K5),K5),K5),K5)

saved in a data file using a naming order as follows: – Group - Subject # - Seat height - Load (eg. 1F03SL100W = Valgum female - Third subject - Seat height low - 100 Watt load) -

Table1

18 right leg dominant subjects and 2 left leg dominant subjects

Page 18: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS : 120 Trials cont.

72 to 77 data points for a single pedal revolution = 80±5rpm

20 Revolutions = 1440 to 1540 data points

Macros to calculate the difference between the median of 20 maximum and minimum x-coordinates dK and Std. Deviation SDdK

TABLE 2 filled out and HYPOTHESES analyzed

Plots of the M-L displacement at the left and right knee joint center (y and z coordinates)

Page 19: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – Fig 13: SH100W for subject 3F07

Medial peak displacement

120°±30°

Lateral peak displacement

270°±30°

Page 20: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – Fig 14 : six trials of subject 3F07

Movement Pattern

“OVAL”

Page 21: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – Fig 15 : six trials of subject 3F11

Movement Pattern

“SICKLE”

Page 22: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – Fig 16 : six trials of subject 3M02

Movement Pattern

“LINEAR”

Page 23: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – Fig 17 : six trials of subject 3M20

Movement Pattern

“SCATTERED”

Page 24: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – Fig 18 : six trials of subject 2M17

Movement Pattern

“LINEAR”

Page 25: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – Fig 19 : six trials of subject 1F10

Movement Pattern

“OVAL”

Page 26: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS : M-L Movement Pattern

“Oval” – 3F07 (RKNE) and 1F10 (RKNE) i.e.,(Fig 14&19)

“Sickle” – 3F11 (LKNE) i.e.,(Fig 15)

“Linear” – 3M02 (RKNE) and 2M17 (RKNE) i.e.,(Fig 16&18)

“Scattered” – 3M20 (RKNE) i.e.,(Fig 17)

2/20 more experienced recreational cyclists (3M02 and 2M17) i.e., very active and spent 1-3 hours per week cycling

Page 27: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 2 :

TABLE 2: MAX M-L displacement of knee in frontal plane

@ LOW Seat (SL) @ NEUTRAL Seat (SN) @ HIGH Seat (SH)dK SDdK dK SDdK dK SDdK

12.103 3.823 13.655 4.114 23.794 7.97019.783 5.931 19.577 6.163 27.817 8.61128.469 9.035 20.432 6.154 19.761 6.37228.928 8.969 43.554 13.491 53.267 16.70524.899 8.177 19.795 5.898 22.500 7.14511.511 3.255 12.837 3.707 14.085 4.34421.526 6.944 20.538 6.347 10.655 2.96551.011 17.050 28.115 8.748 43.133 13.91516.229 5.208 15.238 4.684 17.396 5.89322.703 6.613 12.927 3.852 17.749 5.20027.224 8.945 16.477 5.043 21.272 6.73320.775 6.462 27.009 8.633 22.446 7.48216.905 5.438 16.827 5.279 25.271 7.93222.824 7.189 17.134 5.364 40.040 12.982

20.075 6.621 22.309 7.530 30.669 10.31315.041 4.705 14.183 4.394 16.420 4.937

18.501 5.890 16.360 5.531 16.882 5.46917.956 6.018 11.515 3.910 20.653 6.24420.767 7.025 21.347 7.496 22.547 7.38537.769 12.654 36.338 12.638 26.661 9.296

NormalFemale14

@ LOW Seat (SL) @ NEUTRAL Seat (SN) @ HIGH Seat (SH)

NORMALNormalFemale07NormalFemale08NormalFemale09NormalFemale11NormalFemale13

VARUM

NormalFemale18NormalMale01NormalMale02NormalMale04NormalMale15NormalMale16NormalMale19NormalMale20

VALGUMValgumFemale05ValgumFemale10

VarumFemale12VarumMale03VarumMale06VarumMale17

@ NEUTRAL Seat (SN) @ HIGH Seat (SH)@ LOW Seat (SL)dK SDdK dK SDdK dK SDdK

7.868 2.356 9.665 2.864 22.390 7.24820.732 5.903 17.077 5.322 30.511 9.21138.400 12.184 25.993 8.011 39.851 12.46723.592 7.040 39.215 11.952 50.209 16.10130.746 9.906 21.462 6.189 19.086 5.82412.496 3.721 17.049 5.079 21.386 6.67223.749 7.926 28.003 9.192 29.702 9.29238.733 13.412 42.853 15.015 42.069 13.41720.698 6.917 22.502 7.685 24.746 8.72129.268 8.994 24.825 7.746 20.491 5.67926.859 8.863 15.891 4.914 28.588 9.18125.488 7.975 21.608 6.685 15.664 5.18115.292 4.679 12.378 3.767 20.270 6.19425.594 8.181 27.562 8.518 30.053 9.182

21.422 7.256 36.389 11.572 43.230 13.31413.678 3.862 20.075 6.330 19.144 5.804

23.148 7.074 19.324 6.071 15.263 4.87813.649 4.247 11.108 3.447 33.493 9.80728.079 9.053 17.730 5.475 25.479 7.50642.082 14.091 37.230 13.066 36.428 12.353

NormalFemale09

@ NEUTRAL Seat (SN) @ HIGH Seat (SH)

NORMALNormalFemale07NormalFemale08

@ LOW Seat (SL)

VALGUM

NormalFemale11NormalFemale13NormalFemale14NormalFemale18

NormalMale01NormalMale02NormalMale04NormalMale15NormalMale16NormalMale19NormalMale20

VarumMale17

ValgumFemale05ValgumFemale10

VARUMVarumFemale12

VarumMale03VarumMale06

Page 28: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 2 : cont.

dK SDdK dK SDdK dK SDdK

7.868 2.356 9.665 2.864 22.390 7.24820.732 5.903 17.077 5.322 30.511 9.21138.400 12.184 25.993 8.011 39.851 12.46723.592 7.040 39.215 11.952 50.209 16.10130.746 9.906 21.462 6.189 19.086 5.82412.496 3.721 17.049 5.079 21.386 6.67223.749 7.926 28.003 9.192 29.702 9.29238.733 13.412 42.853 15.015 42.069 13.41720.698 6.917 22.502 7.685 24.746 8.72129.268 8.994 24.825 7.746 20.491 5.67926.859 8.863 15.891 4.914 28.588 9.18125.488 7.975 21.608 6.685 15.664 5.18115.292 4.679 12.378 3.767 20.270 6.19425.594 8.181 27.562 8.518 30.053 9.182

21.422 7.256 36.389 11.572 43.230 13.31413.678 3.862 20.075 6.330 19.144 5.804

23.148 7.074 19.324 6.071 15.263 4.87813.649 4.247 11.108 3.447 33.493 9.80728.079 9.053 17.730 5.475 25.479 7.50642.082 14.091 37.230 13.066 36.428 12.353

NormalFemale09

200 Watts@ NEUTRAL Seat (SN) @ HIGH Seat (SH)

NORMALNormalFemale07NormalFemale08

@ LOW Seat (SL)

VALGUM

NormalFemale11NormalFemale13NormalFemale14NormalFemale18

NormalMale01NormalMale02NormalMale04NormalMale15NormalMale16NormalMale19NormalMale20

VarumMale17

ValgumFemale05ValgumFemale10

VARUMVarumFemale12

VarumMale03VarumMale06

Page 29: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 3 : General Linear Model for dK

Table 3: Within-Subjects Factors for dK

Seathgt ResistDependent Variable

MeanStd.

DeviationN

Low 100WattsLow100W 22.06 9.480 20

200WattsLow200W 23.66 9.895 20

Neutral 100WattsNeut100W 20.10 8.405 20

200WattsNeut200W 22.07 9.054 20

High 100WattsHigh100W 23.22 9.885 20

200WattsHigh200W 27.86 9.656 20

Mean Comparisons of dK – High200W greatest

Page 30: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 6 : General Linear Model for SDdK

Table 6: Within-Subjects Factors for SDdK

Seathgt ResistDependent Variable

MeanStd.

DeviationN

Low 100Watts Low100W 7.30 3.107 20

200Watts Low200W 7.67 3.151 20

Neutral 100Watts Neut100W 6.45 2.710 20

200Watts Neut200W 7.45 3.301 20

High 100Watts High100W 7.89 3.389 20

200Watts High200W 8.90 3.196 20

Mean Comparisons of SDdK – High200W greatest

Page 31: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 4 : Effect for dK

Table 4: Tests of Within-Subjects Effects for dK

Source Type of TestSum of Squares

df Mean Square F Sig.

Seathgt Greenhouse-Geisser 402.925 1.545 260.720 3.159 .069

Resist Greenhouse-Geisser 224.932 1.000 224.932 7.933 .011

Seathgt * Resist Greenhouse-Geisser 55.097 1.899 29.016 1.513 .234

Error(Seathgt) Greenhouse-Geisser 2423.697 29.363 82.542

Error(Resist) Greenhouse-Geisser 538.756 19.000 28.356

Error(Seathgt*Resist) Greenhouse-Geisser 691.954 36.078 19.179

Seathgt : p = 0.069 (NO significant effect)

Resist : p = 0.011 (YES significant effect)

Page 32: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 4 : Effect for SDdK

Seathgt : p = 0.045 (YES significant effect)

Resist : p = 0.028 (YES significant effect)

Table 7: Tests of Within-Subjects Effects for SDdK

Source Type of TestSum of Squares

df Mean Square F Sig.

Seathgt Greenhouse-Geisser 43.011 1.564 27.499 3.760 .045

Resist Greenhouse-Geisser 19.001 1.000 19.001 5.635 .028

Seathgt * Resist Greenhouse-Geisser 2.540 1.977 1.285 .589 .558

Error(Seathgt) Greenhouse-Geisser 217.336 29.718 7.313

Error(Resist) Greenhouse-Geisser 64.066 19.000 3.372

Error(Seathgt*Resist) Greenhouse-Geisser 81.864 37.563 2.179

Page 33: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

DISCUSSION – 1st HYPOTHESES

1) The mean of dK will be greatest for all subjects at the low seat height position

Tests of Within-Subjects Effect for dK indicated that there is no significance in seat height, (p>0.05)

The Tables 3&6 with box graphs for dK and SDdK show the High seat height has the greatest mean displacement

dK

Page 34: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 5 : Pairwise dK

Table 5: Pairwise Comparisons of Seat Height & Resistance for dK

(I) SeathgtOr

(I) Resist

(J) SeathgtOr

(J) Resist Mean Difference (I-J)

Std. Error Sig.(a)

95% Confidence Interval for Difference(a)

Lower Bound Upper Bound

Low Neut 1.779 1.603 .843 -2.429 5.988

High -2.679 2.213 .723 -8.488 3.130

Neut Low -1.779 1.603 .843 -5.988 2.429

High -4.458(*) 1.449 .019 -8.262 -.654

High Low 2.679 2.213 .723 -3.130 8.488

Neut 4.458(*) 1.449 .019 .654 8.262

100W 200W -2.738(*) .972 .011 -4.773 -.703

200W 100W 2.738(*) .972 .011 .703 4.773

Based on estimated marginal means* The mean difference is significant at the .05 level.a Adjustment for multiple comparisons: Bonferroni.

Page 35: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 8 : Pairwise SDdK

Based on estimated marginal means* The mean difference is significant at the .05 level.a Adjustment for multiple comparisons: Bonferroni.

Table 8: Pairwise Comparisons of Seat Height & Resistance for SDdK

(I) SeathgtOr

(I) Resist

(J) SeathgtOr

(J) Resist Mean Difference (I-J)

Std. Error Sig.(a)

95% Confidence Interval for Difference(a)

Lower Bound Upper Bound

Low Neut 0.543 0.470 0.786 -0.690 1.776

High -0.908 0.661 0.556 -2.643 0.826

Neut Low -0.543 0.470 0.786 -1.776 0.690

High -1.451(*) 0.448 0.013 -2.627 -0.275

High Low 0.908 0.661 0.556 -0.826 2.643

Neut -1.451(*) 0.448 0.013 0.275 2.627

100W 200W -0.796(*) 0.335 0.028 -1.498 -0.094

200W 100W 0.796(*) 0.335 0.028 0.094 1.498

Page 36: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

DICUSSION

Pairwise Comparisons of dK

Significance exists only between SN and SH

Pairwise Comparisons of SDdK

Significance exists only between SN and SH

Pairwise Comparisons of dK and SDdK

Overall - Significance exists between SN and SH and NOT at other seat heights

Page 37: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

DISCUSSION – 2nd HYPOTHESES

2) The maximum displacement (dKmax) for any seat height will occur during the 200W test of the pedal cycle

A 3 x 2 repeated measures ANOVA was calculated for dKmax and the results show the 3rd hypothesis is true (TABLE 9)

Page 38: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

RESULTS – TABLE 9 : General Linear Model for dKmax

Low100W < Low200W,

High100W < High200W

Neut100W < Neut200W,

Table 9: Within-Subjects Factors for dKmax

Seathgt ResistDependent Variable

MeanStd.

DeviationN

Low 100Watts Low100W 36.14 13.371 20

200Watts Low200W 36.29 14.071 20

Neutral 100Watts Neut100W 28.83 9.478 20

200Watts Neut200W 37.23 15.827 20

High 100Watts High100W 41.85 21.757 20

200Watts High200W 42.20 13.343 20

Therefore 3rd hypothesis is true because there is a significant

effect between the 100W and 200W grouping

Page 39: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

DISCUSSION

The Pilot study showed -

The Medial peak displacement occurred at 120°±30°

100W or 200W ≠ consistent variance in knee motion

Consistent quadriceps loading = cyclist experience

3 subjects (4=3F11, 8=3M01 and 20=2M17) out of range

The Lateral peak displacement at 270°±30°

Page 40: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

Main References

Gregor, R. J., Cavanagh P. R., et al. (1985). – "Knee flexor moments during propulsion in cycling--A creative solution to

Lombard's Paradox." Lombard’s Conjecture (1903)– Opposing Two-Joint muscles can reinforce each other

Hull and Jorge (1985). – "A method for biomechanical analysis of bicycle pedalling.”

McCoy, R. W. (1989). – “The effect of varying seat position on knee loads during cycling.”

Page 41: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

Foot Note : References

Akitoshi, S., M. Naoki, et al. (2009). "Influence of knee alignment on quadriceps cross-sectional area." Journal of biomechanics 42(14): 2313-2317.

Bressel, E. and J. Cronin (2005). "Bicycle seat interface pressure: reliability, validity, and influence of hand position and workload." Journal of biomechanics 38(6): 1325-1331.

Brouwer, G. M., A. W. Van Tol, et al. (2007). "Association between Valgus and Varus alignment and the development and progression of radiographic osteoarthritis of the knee." Arthritis & Rheumatism. 56(4): 1204-1211

Liebersteinerab, M. C., C. Ssubskiac, et al. (2008). "Frontal plane leg alignment and muscular activityduring maximum eccentric contractions in individuals with and without patellofemoral pain syndrome." The Knee. 15(3): 180-186

Martin, J. C. and N. A. T. Brown (2009). "Joint-specific power production and fatigue during maximal cycling." Journal of biomechanics 42(4): 474-479

Page 42: Frontal motion analysis of the knee during a bicycle pedal revolution 2011

Additional References :

Mesfar, W. and A. Shiraz-Adl (2005). "Biomechanics of the knee joint in

flexion under various quadriceps forces." The Knee. 12: 424–434.

Ricard, M. D., P. Hills-Meyer, et al. (2006). "The effects of Bicycle frame geometry on muscle activation and power during a Wingate anaerobic test." Journal of Sports Science and Medicine. 5: 25-32.

Ruby, P. and M. L. Hull (1993). "Response of intersegmental knee loads to foot/pedal platform degrees of freedom in cycling." Journal of biomechanics 26(11):

1327-1340.

Umberger, B. R., K. G. M. Gerritsen, et al. (2003). "A Model of Human Muscle Energy Expenditure." Computer Methods in Biomechanics & Biomedical Engineering 6(2): 99.

von Eisenhart-Rothe, R., M. Siebert, et al. (2004). "A new in vivo technique for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint." Journal of biomechanics 37(6): 927-934.

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THANK YOU!!!......QUESTIONS ???