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Research Papers

Comparing Predictive Accuracy and Computational Costs for Viscoelastic Modeling of Spinal Cord Tissues

[+] Author and Article Information
Nicole L. Ramo

School of Biomedical Engineering,
Colorado State University,
1376 Campus Delivery,
Fort Collins, CO 80523
e-mail: Nicole.Ramo@colostate.edu

Kevin L. Troyer

Department of Mechanical Engineering,
Colorado State University,
1374 Campus Delivery,
Fort Collins, CO 80523
e-mail: kttroy@gmail.com

Christian M. Puttlitz

School of Biomedical Engineering,
Colorado State University,
1374 Campus Delivery,
Fort Collins, CO 80523;
Department of Mechanical Engineering,
Colorado State University,
1374 Campus Delivery,
Fort Collins, CO 80523;
Department of Clinical Sciences,
Colorado State University,
1374 Campus Delivery,
Fort Collins, CO 80523
e-mail: christian.puttlitz@colostate.edu

1Corresponding author.

Manuscript received October 11, 2018; final manuscript received February 17, 2019; published online March 25, 2019. Assoc. Editor: Brittany Coats.

J Biomech Eng 141(5), 051009 (Mar 25, 2019) (9 pages) Paper No: BIO-18-1446; doi: 10.1115/1.4043033 History: Received October 11, 2018; Revised February 17, 2019

The constitutive equation used to characterize and model spinal tissues can significantly influence the conclusions from experimental and computational studies. Therefore, researchers must make critical judgments regarding the balance of computational efficiency and predictive accuracy necessary for their purposes. The objective of this study is to quantitatively compare the fitting and prediction accuracy of linear viscoelastic (LV), quasi-linear viscoelastic (QLV), and (fully) nonlinear viscoelastic (NLV) modeling of spinal-cord-pia-arachnoid-construct (SCPC), isolated cord parenchyma, and isolated pia-arachnoid-complex (PAC) mechanics in order to better inform these judgements. Experimental data collected during dynamic cyclic testing of each tissue condition were used to fit each viscoelastic formulation. These fitted models were then used to predict independent experimental data from stress-relaxation testing. Relative fitting accuracy was found not to directly reflect relative predictive accuracy, emphasizing the need for material model validation through predictions of independent data. For the SCPC and isolated cord, the NLV formulation best predicted the mechanical response to arbitrary loading conditions, but required significantly greater computational run time. The mechanical response of the PAC under arbitrary loading conditions was best predicted by the QLV formulation.

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Figures

Grahic Jump Location
Fig. 1

Acute stress-relaxation response of SCPC to the 5% applied strain history; (a) MATLAB (color lines) predictions of average experimental data (black line); (b) errors of each prediction normalized to the experimental average value. Over this range, the RMSE of the NLV and QLV formulations were approximately equivalent while the LV error was greater.

Grahic Jump Location
Fig. 2

Acute stress-relaxation response of SCPC to the 3% applied strain history; (a) MATLAB (color lines) predictions of average experimental data (black line); (b) errors of each prediction normalized to the experimental average value. Over this range, the RMSE of the NLV formulation prediction was lower than the QLV and LV formulations.

Grahic Jump Location
Fig. 3

Acute stress-relaxation response of the isolated cord to the 5% applied strain history; (a) MATLAB (color lines) predictions of average experimental data (black line); (b) errors of each prediction normalized to the experimental average value. Over this range, the RMSE of the LV formulation prediction was lower than the QLV and NLV formulations.

Grahic Jump Location
Fig. 4

Acute stress-relaxation response of the isolated cord to the 3% applied strain history; (a) MATLAB (color lines) predictions of average experimental data (black line); (b) errors of each prediction normalized to the experimental average value. Over this range, the RMSE of the NLV formulation prediction was lower than the QLV and LV formulations.

Grahic Jump Location
Fig. 5

Acute stress-relaxation response of PAC to the 5% applied strain history; (a) MATLAB (color lines) predictions of average experimental data (black line); (b) errors of each prediction normalized to the experimental average value. Over this range, the RMSE of the LV formulation prediction was lower than the QLV and NLV formulations.

Grahic Jump Location
Fig. 6

Acute stress-relaxation response of PAC to the 3% applied strain history; (a) MATLAB (color lines) predictions of average experimental data (black line); (b) errors of each prediction normalized to the experimental average value. Over this range, the RMSE of the QLV formulation prediction was lower than the NLV and LV formulations.

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