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Research Papers

Using a Statistically Calibrated Biphasic Finite Element Model of the Human Knee Joint to Identify Robust Designs for a Meniscal Substitute

[+] Author and Article Information
Erin R. Leatherman

Department of Statistics,
West Virginia University,
Morgantown, WV 26506
e-mail: erleatherman@mail.wvu.edu

Hongqiang Guo

Department of Biomechanics,
Hospital for Special Surgery,
New York, NY 10021
e-mail: GuoH@hss.edu

Susannah L. Gilbert

Department of Biomechanics,
Hospital for Special Surgery,
New York, NY 10021
e-mail: GilbertS@hss.edu

Ian D. Hutchinson

Department of Biomechanics,
Hospital for Special Surgery,
New York, NY 10021
e-mail: ihutchin@wakehealth.edu

Suzanne A. Maher

Department of Biomechanics,
Hospital for Special Surgery,
New York, NY 10021
e-mail: MaherS@hss.edu

Thomas J. Santner

Department of Statistics,
The Ohio State University,
Columbus, OH 43210
e-mail: tjs@stat.osu.edu

1Corresponding author.

Manuscript received October 11, 2013; final manuscript received March 31, 2014; accepted manuscript posted April 28, 2014; published online May 15, 2014. Assoc. Editor: Tammy L. Haut Donahue.

J Biomech Eng 136(7), 071007 (May 15, 2014) (8 pages) Paper No: BIO-13-1483; doi: 10.1115/1.4027510 History: Received October 11, 2013; Revised March 31, 2014; Accepted April 28, 2014

This paper describes a methodology for selecting a set of biomechanical engineering design variables to optimize the performance of an engineered meniscal substitute when implanted in a population of subjects whose characteristics can be specified stochastically. For the meniscal design problem where engineering variables include aspects of meniscal geometry and meniscal material properties, this method shows that meniscal designs having simultaneously large radial modulus and large circumferential modulus provide both low mean peak contact stress and small variability in peak contact stress when used in the specified subject population. The method also shows that the mean peak contact stress is relatively insensitive to meniscal permeability, so the permeability used in the manufacture of a meniscal substitute can be selected on the basis of manufacturing ease or cost. This is a multiple objective problem with the mean peak contact stress over the population of subjects and its variability both desired to be small. The problem is solved by using a predictor of the mean peak contact stress across the tibial plateau that was developed from experimentally measured peak contact stresses from two modalities. The first experimental modality provided computed peak contact stresses using a finite element computational simulator of the dynamic tibial contact stress during axial dynamic loading. A small number of meniscal designs with specified subject environmental inputs were selected to make computational runs and to provide training data for the predictor developed below. The second experimental modality consisted of measured peak contact stress from a set of cadaver knees. The cadaver measurements were used to bias-correct and calibrate the simulator output. Because the finite element simulator is expensive to evaluate, a rapidly computable (calibrated) Kriging predictor was used to explore extensively the contact stresses for a wide range of meniscal engineering inputs and subject variables. The predicted values were used to determine the Pareto optimal set of engineering inputs to minimize peak contact stresses in the targeted population of subjects.

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Figures

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Fig. 1

A schematic diagram of the 2D axisymmetric knee joint

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Fig. 2

ISO 2009 dynamic axial force during gait. This profile was used in runs of the bFEM; the profile, scaled to 10 s, was used in the cadaver model.

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Fig. 3

The smoothed surface connecting the discrete set of bFEM-determined contact stresses across radial position and time when run at meniscal design inputs (hm, hc, Erm, Ecm, km) = (6.128, 2.980, 10.376, 108.800, 2.202) and patient inputs (ht, hf, Ec, kc) = (2.073, 2.044, 6.709, 5.289). The radial position of 0 mm corresponds to the center of the lateral compartment of the knee.

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Fig. 4

(a) The tibial component with attached sensor; note the box depicting the line of interest. (b) The experimental setup: during loading the tibia was aligned with the femoral component which was fixed to the crosshead of the MTS. The load profile in Fig. 2, scaled to 10 s, was applied to represent the axial force profile that occurs during gait.

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Fig. 5

(a) Contact stress data from a representative, experimentally tested, specimen. A line of interest was identified and the region covered by the meniscus was identified. (Each square represents a 2 × 2 mm sensing element.) (b) The contact stress, as a function of radial distance from the edge of the tibial spine, was plotted for both sensors and for the computational model; the data shown is from a representative knee at 14% of the loading cycle. The vertical line near 12 mm in (b) marks the inner edge of the meniscus.

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Fig. 6

ME plots for inputs hm (left), ht (center), and Ec (right) on the peak contact stress predictions at 14% of the axial loading profile

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Fig. 7

The distribution of predicted peak contact stress at 14% (left) and 45% (right) of the axial loading profile for 10,000 different patient conditions, for the meniscal design (hm, hc, Erm, Ecm, km) = (4.513, 1.698, 9.352, 83.065, 1.750)

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Fig. 8

Means and standard deviations of peak contact stress predictions at 14% of the axial loading profile for the 10,000 different patient conditions corresponding to 50 fixed meniscal designs. Desirable meniscal designs (those with low mean and low standard deviation) are marked with a filled circle.

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Fig. 9

Distributions of the peak contact stresses at 14% of the axial loading profile over the 10,000 draws of patient cartilage values for the four optimal meniscal designs listed in Table 3. The filled circles mark the 95th-percentile of the peak contact stresses, and the open circles mark the 99th-percentile of these stresses.

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Fig. 10

2D projections of 50 fixed meniscal designs corresponding to the designs used to construct Fig. 8. Desirable meniscal designs (those corresponding to low mean and low standard deviation) are marked with a filled circle.

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