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Research Papers

The Effect of Knee Model on Estimates of Muscle and Joint Forces in Recumbent Pedaling

[+] Author and Article Information
Michael J. Koehle

Biomedical Engineering Program and Department of Mechanical Engineering, University of California, Davis, CA 95616

M. L. Hull1

Biomedical Engineering Program and Department of Mechanical Engineering, University of California, Davis, CA 95616mlhull@ucdavis.edu

1

Corresponding author.

J Biomech Eng 132(1), 011007 (Dec 17, 2009) (8 pages) doi:10.1115/1.3148192 History: Received November 28, 2007; Revised March 03, 2009; Published December 17, 2009; Online December 17, 2009

The usefulness of forward dynamic simulations to studies of human motion is well known. Although the musculoskeletal models used in these studies are generic, the modeling of specific components, such as the knee joint, may vary. Our two objectives were (1) to investigate the effects of three commonly used knee models on forward dynamic simulation results, and (2) to study the sensitivity of simulation results to variations in kinematics for the most commonly used knee model. To satisfy the first objective, three different tibiofemoral models were incorporated into an existing forward dynamic simulation of recumbent pedaling, and the resulting kinematics, pedal forces, muscle forces, and joint reaction forces were compared. Two of these models replicated the rolling and sliding motion of the tibia on the femur, while the third was a simple pin joint. To satisfy the second objective, variations in the most widely used of the three knee models were created by adjusting the experimental data used in the development of this model. These variations were incorporated into the pedaling simulation, and the resulting data were compared with the unaltered model. Differences between the two rolling-sliding models were smaller than differences between the pin-joint model and the rolling-sliding models. Joint reactions forces, particularly at the knee, were highly sensitive to changes in knee joint model kinematics, as high as 61% root mean squared difference, normalized by the corresponding peak force of the unaltered reference model. Muscle forces were also sensitive, as high as 30% root mean squared difference. Muscle excitations were less sensitive. The observed changes in muscle force and joint reaction forces were caused primarily by changes in the moment arms and musculotendon lengths of the quadriceps. Although some level of inaccuracy in the knee model may be acceptable for calculations of muscle excitation timing, a representative model of knee kinematics is necessary for accurate calculation of muscle and joint reaction forces.

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Figures

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Figure 1

The right leg of the pedaling model. Coordinate systems are shown for the femur (F), tibia (T), patella (P), and talus (Ta) segments.

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Figure 2

The contact, four-bar, and pin-joint models. The origins are shown relative to the femur for different angles of flexion, ranging from 0 deg to 120 deg in 10 deg increments.

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Figure 3

Simulation results for the three knee models and experimental results. The gray area is the experimental data +/−1 standard deviation. At 0 deg crank angle, the crank arm is vertical. Positive radial force is toward the crank axis. Positive tangential force is forward.

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Figure 4

Muscle excitations generated from computed muscle control for variations in the kinematics of the patellotibial (PT) and patellofemoral (PF) models. −2 TF and +2 TF are the −2 standard deviation and +2 standard deviation tibiofemoral model variations, respectively. −2 PT and +2 PT are the −2 standard deviation and +2 standard deivation patellotibial model variations respectively. 0 SD is the unaltered reference model. For comparison, the experimental on-off timing of the EMG activity +/−1 standard deviation is given for muscles for which this data was available (30).

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Figure 5

Muscle forces over a complete crank cycle for the reference contact model and for variations in the kinematics of the tibiofemoral (TF) and patellotibial (PT) models. −2 TF and +2 TF are the −2 standard deviation and +2 standard deviation tibiofemoral model variations, respectively. −2 PT and +2 PT are the −2 standard deviation and +2 standard deviation patellotibial model variations, respectively. 0 SD is the unaltered reference model. Forces were sensitive to the kinematic variations over the second half of the crank cycle. Only results for extreme kinematic variations are shown. The vastus intermedius and vastus lateralis are not shown, but behaved similarly to the vastus medialis.

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Figure 6

Joint reaction forces over a complete crank cycle for the reference model and for variations in the kinematics of the tibiofemoral (TF) and patellotibial (PT) models. −2 TF and +2 TF are the −2 standard deviation and +2 standard deviation tibiofemoral model variations, respectively. −2 PT and +2 PT are the −2 standard deviation and +2 standard deviation patellotibial model variations, respectively. 0 SD is the unaltered reference model.

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