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Research Papers

Neural Network Optimization of Ligament Stiffnesses for the Enhanced Predictive Ability of a Patient-Specific, Computational Foot/Ankle Model

[+] Author and Article Information
Ruchi D. Chande

Department of Biomedical Engineering,
Virginia Commonwealth University,
401 West Main Street,
PO Box 843067,
Richmond, VA 23284-3067

Jennifer S. Wayne

Department of Biomedical Engineering,
Virginia Commonwealth University,
401 West Main Street,
PO Box 843067,
Richmond, VA 23284-3067
e-mail: jwayne@vcu.edu

1Corresponding author.

Manuscript received December 16, 2016; final manuscript received June 8, 2017; published online July 7, 2017. Assoc. Editor: Guy M. Genin.

J Biomech Eng 139(9), 091003 (Jul 07, 2017) (8 pages) Paper No: BIO-16-1524; doi: 10.1115/1.4037101 History: Received December 16, 2016; Revised June 08, 2017

Computational models of diarthrodial joints serve to inform the biomechanical function of these structures, and as such, must be supplied appropriate inputs for performance that is representative of actual joint function. Inputs for these models are sourced from both imaging modalities as well as literature. The latter is often the source of mechanical properties for soft tissues, like ligament stiffnesses; however, such data are not always available for all the soft tissues nor is it known for patient-specific work. In the current research, a method to improve the ligament stiffness definition for a computational foot/ankle model was sought with the greater goal of improving the predictive ability of the computational model. Specifically, the stiffness values were optimized using artificial neural networks (ANNs); both feedforward and radial basis function networks (RBFNs) were considered. Optimal networks of each type were determined and subsequently used to predict stiffnesses for the foot/ankle model. Ultimately, the predicted stiffnesses were considered reasonable and resulted in enhanced performance of the computational model, suggesting that artificial neural networks can be used to optimize stiffness inputs.

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Figures

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Fig. 1

General artificial neural network architecture, multilayer feedforward network with single hidden layer. Inputs feed into the hidden layer with h hidden neurons; outputs of the hidden layer then feed into the neurons of the output layer. Interconnections among neurons are depicted as arrows with w representing their weights. (Adapted from Ref. 24).

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Fig. 2

Major tasks. The flowchart depicts the major steps implemented in the current work. ANN refers to artificial neural network, and all the relevant ANN steps apply to each type of neural network described in the research (i.e., feedforward network and radial basis function network).

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Fig. 3

Kinematic measures, right foot (medial view—left and dorsal view—right). Measures included talo-first metatarsal (θT1MT) and talonavicular (θTN) angles, and navicular (δNav) and first cuneiform (δ1st-CN) heights.

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Fig. 4

Percent difference, stiffness predictions relative to assigned. Each bar represents the percent difference of a given output element relative to the target (assigned stiffness) values of the original patient-specific, AAFD computational model. The “zero” line represents the target stiffnesses, and the 14 output elements (stiffnesses of AAFD implicated ligaments) are listed along the vertical axis. Absolute maximum differences (indicated by the white and black arrows for the FFN and RBFN, respectively) of approximately 6% and 12% were calculated for the FFN and RBFN, respectively. (Note: Negative percentages indicate a “less stiff” ligament relative to the target).

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Fig. 5

Percent difference, model kinematics relative to patient X-ray. Each bar represents the percent difference of a given kinematic measure relative to the patient-radiograph. The “zero” line represents the X-ray measures; and therefore, the closer a bar is to this line, the more closely the indicated model matches with the X-ray data. (Note: Negative percentages indicate an overprediction of the X-ray measure).

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