Development of a Patient-Specific Mathematical Modeling Approach for Determination of in Vivo Lumbar Spine Loading Conditions

Mathematical modeling provides an efficient and easily reproducible method for the determination of joint forces under in vivo conditions. The need for these new modeling methodologies is needed in the lumbar spine, where an understanding of the loading environment is limited. Few studies using telemetry and pressure sensors have directly measured forces borne by the spine; however, only a very small number of subjects have been studied and experimental conditions were not ideal for giving total forces acting in the spine. As a result, alternative approaches for investigating the lumbar spine across different clinical pathologies are essential. Therefore, the objective of this study was to develop of an inverse dynamic mathematical model for theoretically deriving in-vivo contact forces as well as musculotendon forces in patients having healthy, symptomatic, pathological and post-operative conditions of the lumbar spine. Fluoroscopy and 3D-to-2D image registration were used to obtain kinematic data for patients performing flexion-extension of the lumbar spine. This data served as input into the multi-body, mathematical model. Other inputs included patient-specific bone geometries, recreated from CT, and ground reaction forces. Vertebral bones were represented as rigid bodies, while massless frames symbolized the lower body, torso and abdominal wall (Figure 1). In addition, ligaments were selected and modeled as linear spring elements, along with relevant muscle groups. The muscles were divided into individual fascicles and solved for using a pseudo-inverse algorithm which enabled for decoupling of the derived resultant torques defining the desired kinetic trajectory for the muscles. The largest average contact forces in the model for healthy, symptomatic, pathological, and post-operative lumbar spine conditions occurred at maximum flexion at L4L5 level and were predicted to be 2.47 BW, 2.33 BW, 3.08 BW, and 1.60 BW, respectively. The FE rotation associated with these theoretical force values was 43.0° in healthy, 40.5° in symptomatic, 44.4° in pathological, and 22.8° in post-operative patients. The smallest forces occurred as patients approached the upright, standing position, followed by slight increases in the contact force at full extension. The theoretically derived muscle forces exhibited similar contributory force profiles in the intact spine (healthy, symptomatic, and pathologic); however, surgically implanted spines experienced an increase in the contribution of the external oblique muscles accompanied with decreased slope gradients in the muscle force profiles (Figure 2). These altered force patterns may be associated with the decrease in the predicted contact forces in post-operative patients. In addition, the decreased slope gradients in surgically implanted patients corresponds with the observed difficulty of performing the prescribed motion, possibly due to improper muscle firing, thereby leading to slower motion cycles and less ranges-of-motion. On the contrary, patients having an intact spine performed the activity at a faster speed and to greater ranges-of-motion, which corresponds with the higher contact forces derived in the model. In conclusion, this research study presented the development of a mathematical modeling approach utilizing patient-specific data to generate theoretical in-vivo joint forces. This may serve to help progress the understanding for the kinetic characteristics of the native and surgically implanted lumbar spine.