Development and validation of a computational multibody model of the elbow joint

Abstract

Computational multibody models of the elbow joint can provide a powerful tool to study joint biomechanics, examine muscle and ligament function, soft tissue loading, and the effects of joint trauma. Such models can reduce the cost of expensive experimental testing and can predict some parameters that are difficult to investigate experimentally, such as forces within ligaments and contact forces between cartilage covered bones. These parameters can assist surgeons and other investigators to develop better treatments for elbow injuries and thereby increase patient care. Biomechanical computational models of the elbow exist in the literature, but these models are typically limited in their applicability by artificially constraining the joint (e.g. modeling the elbow as a hinge joint), prescribing specific kinematics, simplifying ligament characteristics or ignoring cartilage geometries.The purpose of this thesis was to develop anatomically correct subject specific computational multibody models of elbow joints and validate these models against experimental data. In these models, the joints were constrained by three-dimensional deformable contacts between articulating geometries, passive muscle loading, and multiple bundles of non-linear ligaments wrapped around the bones. iv In this approach, three-dimensional bone geometries for the model were constructed from volume images generated by computed tomography (CT) scans obtained from cadaver elbows. The ligaments and triceps tendon were modeled as spring-damper elements with non-linear stiffness. Articular cartilage was represented as uniform thickness solids covering the articulating bone surfaces. Finally, the model was validated by placing the cadaver elbows in a mechanical testing apparatus and comparing predicted kinematics and triceps tendon forces to experimentally measured values. A small improvement in predicted kinematics was observed compared to experimental values when the lateral ulnar collateral and annular ligament were wrapped around the bone. Some reductions of RMS error were also observed when a non-linear toe region was modeled in the ligament compared to models that had only a linear force-displacement relationship. None of these changes were statistically significant (ANOVA p-value was greater than 0.05).

Lateral collateral ligament deficiency of the elbow joint: A modeling approach

“…Multibody computational models can predict important parameters that are difficult or not possible to capture experimentally such as ligament forces and cartilage contact pressures. A previously developed anatomically correct computational multibody model was used for this study . The model includes discretized humerus cartilage that allows computation of contact pressure distribution and contact area.…”

“…A previously developed anatomically correct computational multibody model created from a cadaver sample (61 years, male, right arm) was used as the basis of the model in this study . Discretized cartilage representation was added to allow for calculation of contact characteristics.…”

“…The stiffness parameter k was obtained from the literature (Table ). The zero‐load length, l 0 , which is the ligament length where the ligament first becomes taut, was based on a laxity test performed in a previous cadaveric study . Briefly, to determine l 0 , the humerus was held in a fixed position while the lower arm was manually moved through its full range of motion with minimal force applied (as judged by the experimenter).…”

“…The resulting bone kinematics were measured with Optotrak rigid body motion markers. The l 0 , for each ligament bundle was estimated by computing the maximum straight‐line distance between origin and insertion sites of the ligament throughout the range of motion and then multiplying by a correction factor of 0.8 . The correction factor was applied to reduce the error inadvertently introduced by the experimenter during the laxity test by applying a small load on the ligaments .…”

“…Inputs to the subroutine were the ligament stiffness and strain, damping coefficient, ligament length at the constructed position, and the ligament zero‐load length. Ligament wrapping was employed to better represent the ligament force's lines of action by dividing the ligament into multiple elements attached in series through via points . For example, to simulate wrapping around the radius for the annular ligament, two line arcs were placed along the perimeter of the radius head together with the non‐linear force elements.…”