Date of Award


Document Type


Degree Name



Computer Science and Engineering

First Advisor

Paul J. Rullkoetter

Second Advisor

Peter J. Laz


Annulus, Disc, FEA, Lumbar, Nucleus, Probabilistic


Human lumbar spine mechanics are influenced by soft tissue structures. Understanding and properly modeling these structures can help determine pathology, treatment, and implant design and performance. Finite element models of the L4-L5 level of the lumbar spine are often used, which include a representation of the intervertebral disc and spinal ligaments. Validation of these models are typically based on torque rotation data from a single subject or the models use average properties reported in literature. However, experimental testing reports variation up to 40% in ligament stiffness and even greater variability for annulus fibrosis properties. Probabilistic approaches enable consideration of the impact of intersubject variability on model outputs. However, they often require lengthy computation times.

The first objective of this dissertation was to develop a methodology to better calibrate constitutive models of the disc using displacement data of intradiscal points across the mid-transverse plane of an L4-L5 lumbar spine disc in addition to kinematics. It was hypothesized that this will result in a more accurate constitutive model. The second objective was to develop a comprehensive probabilistic representation to characterize variability in the parameters describing the soft tissue structures and to develop efficient Monte Carlo simulations methods of a finite element model of the L4-L5 functional spinal unit.

The data used to calibrate constitutive models at intradiscal points across the disc was collected from compression, extension, flexion, and lateral bending. Optimization was used to calibrate the model parameters. Constitutive model types and the number of zones were compared. The best combination was a linear elastic constitutive model representing the nucleus pulposis and a Holzapfel-Gasser-Ogden model representing the annulus fibrosis divided into anterior, right lateral, left lateral, and posterior zones. The probabilistic representation of the ligaments and disc was determined based on direct mechanical test data as found in the literature. A single stiffness parameter was defined to characterize each ligament, with the anterior longitudinal ligament being the stiffest, while the posterior longitudinal ligament and interspinous ligament had the greatest coefficient of variation of 0.65 and 0.64, respectively. The posterior portion of the annulus fibrosis had the greatest stiffness and greatest variation up to 300% in circumferential loading. This probabilistic representation was used to evaluate the Sobol and descriptive variance reduction sampling methods, which were assessed for efficiency and accuracy in comparison to traditional random Monte Carlo sampling. Comparisons were based on output torque-rotation curves at the 10th and 90th percentile for flexion, extension, axial rotation, and lateral bending. The descriptive sampling technique best matched the random sampling technique, at the extremes of rotation, with a 3.6% mean difference. This was achieved with a 10X reduction in the number of iterations and computation time.

Applications of a more accurately calibrated constitutive model of the NP and AF could be the development of nucleus replacement materials that more closely match the natural NP and prediction of activities which could cause disc herniation. The resulting probabilistic representation can be utilized to include intersubject variability in biomechanics evaluations. The improvements in efficiency of Monte Carlo simulations enable intersubject variability to be considered in a variety of biomechanical evaluations, including design-phase screening of orthopedic implants.


Recieved from ProQuest

Rights holder

Dana Joseph Coombs

File size

155 p.

File format





Biomedical engineering, Mechanical engineering, Biomechanics