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.
Kinematics tracking is the process by which the motion of the joints is studied. This motion consists of relative rotation and translation of the joint bones. Joint motion analysis is used in diagnosis of joint pathology, as well as studying the normal joint function. Currently, fluoroscopy is used in joint kinematics tracking. We are researching the use of pulse-echo A-mode ultrasound for the bone motion tracking instead of the fluoroscopy to avoid its radiation. In this work we performed feasibility study using simulation, and concluded that it is feasible to perform knee motion tracking with accuracy of 2 mm. The idea of the proposed system is to attach a number of single-element ultrasound transducers to a brace as shown in Figure 1. This brace will have a commercially available optical or electromagnetic tracking system's probe attached to it to track the global motion of the brace. The ultrasound transducers will be responsible for transcutaneously detecting points over the surface of the bone. The bone's echo extracted from each signal at each transducer will be registered in the optical or electromagnetic tracker's coordinate frame to create a set of points acquired over the surface of the bone. These points represent the bone's position at that point of time. A 3D model of the bone is then registered to these points using the iterative closest point method (ICP) to estimate the bone's position. At each tracking step, the 3D model will be at a position close to the new position of the points set, because this process will be repeated at a rate of 100 Hz or more in order to ensure that the change in the bone's position between every two successive tracking steps is small enough to guarantee high tracking accuracy. In this work we simulated the mentioned process using real kinematics data obtained for a patient using fluoroscopy. 3D models of the proximal tibia and distal femur were segmented from CT scans of the patient's knee. These models were then moved using the kinematic data in incremental steps. Simulated points over the surface of the bones (simulating the points on the bone's surface to be acquired using ultrasound) were used to track the bones' simulated motion using another set of the bones 3D models which move only according to the registration with the simulated points. In other words, the tracking models follow the simulated points' motion. Simulation was performed using deep knee bend kinematics data.Introduction
Methods
Numerous studies have been conducted to investigate the kinematics of the lumbar spine, and while many have documented its intricacies, few have analyzed the complex coupled out-of-plane rotations inherent in the low back. Some studies have suggested a possible relationship between patients having low back pain (LBP) or degenerative conditions in the lumbar region and various degrees of restricted, excessive, or poorly-controlled lumbar motion. Conversely, others in the orthopedic community maintain there has been no distinct correlation found between spinal mobility and clinical symptoms. The objective of this study was to evaluate both the in-plane and coupled out-of-plane rotational magnitudes about all three motion axes in both symptomatic and asymptomatic patients. Ten healthy, 10 LBP, and 10 degenerative patients were CT scanned and evaluated under fluoroscopic surveillance while performing flexion/extension of the lumbar spine. Three-dimensional, patient-specific bone models were created and registered to fluoroscopic images using a 3D-to-2D model fitting algorithm. Introduction
Methods
Low back pain (LBP) in the region of the lumbar spine is a significant problem among individuals, and efforts focused on treating both the symptoms and causes of LBP have proven to be difficult. Aside from conservative treatments, the predominant surgical approach for treating degenerative spine conditions has been to fuse the vertebral bodies at the symptomatic level. Even today, surgical fusion and its effect on adjacent levels are still not fully understood. Therefore, the objective of this study was to use fluoroscopy and mathematical modeling techniques to identify the in vivo kinematics and kinetics in subjects having either a normal, degenerative or fused condition of the lumbar spine. Twenty-five subjects (ten normal, ten degenerative, and five fusion) were evaluated under fluoroscopic surveillance while performing flexion/extension of the lumbar spine. Subjects within the normal and degenerative groups were analyzed only once, while subjects from the fusion group were analyzed both pre-operatively and at a minimum of six months post-operative. The fusion group consisted of three subjects symptomatic at L4/L5, with the remaining two subjects symptomatic at L5/S1. In vivo kinematics data were derived using a 3D-to-2D model fitting algorithm and served as input into a 3D mathematical model of the lumbar spine. The parametric, inverse dynamics mathematical model was created to allow for the determination of the bearing surface contact and muscle forces at each level of the lumbar spine. Three-dimensional kinematics analyses revealed that subjects classified as having a normal lumbar spine experienced a more uniform motion pattern compared to those observed in the degenerative and fusion groups. Alternatively, the degenerative and fusion subjects demonstrated a more coupled motion pattern in order to perform in plane flexion/extension. Compared to the normal group, rotations in the sagital plane decreased by an average of 28% at the pathological level in the degenerative group, while in the fusion group segmental motions slightly increased at the adjacent levels. Results from the mathematical model also revealed higher out-of-plane forces and increased loading at symptomatic and adjacent levels in both the degenerative and fused groups compared to forces observed in the normal spine. The abnormal motion patterns, which result from decreased or loss of motion at pathological levels in the degenerative and fusion groups, are believed to result in higher resultant forces in the spine. This may be subjecting the intervertebral discs to increased stresses, and as a consequence may be linked to more rapid degeneration at levels where the abnormal kinematics are occurring.
