An optimization‐based method for prediction of lumbar spine segmental kinematics from the measurements of thorax and pelvic kinematics

Abstract

Given measurement difficulties, earlier modeling studies have often used some constant ratios to predict lumbar segmental kinematics from measurements of total lumbar kinematics. Recent imaging studies suggested distribution of lumbar kinematics across its vertebrae changes with trunk rotation, lumbar posture, and presence of load. An optimization-based method is presented and validated in this study to predict segmental kinematics from measured total lumbar kinematics. Specifically, a kinematics-driven biomechanical model of the spine is used in a heuristic optimization procedure to obtain a set of segmental kinematics that, when prescribed to the model, were associated with the minimum value for the sum of squared predicted muscle stresses across all the lower back muscles. Furthermore, spinal loads estimated using the predicted kinematics by the present method were compared with those estimated using constant ratios. Predicted segmental kinematics were in good agreement with those obtained by imaging with an average error of ~10%. Compared with those obtained using constant ratios, predicted spinal loads using segmental kinematics obtained here were in general smaller. In conclusion, the proposed method offers an alternative tool for improving model-based estimates of spinal loads where image-based measurement of lumbar kinematics is not feasible.

Trunk muscle forces and spinal loads in persons with unilateral transfemoral amputation during sit-to-stand and stand-to-sit activities

“…A detailed description of the modeling procedures can be found in our earlier studies (Hendershot et al, 2018;Shojaei et al, 2015;Shojaei et al, 2016a). Briefly, a non-linear finite element model of the spine was used to estimate trunk muscle forces required to complete the activity and the resultant spinal loads using an optimization-based iterative procedure (Bazrgari et al, 2007;Shojaei et al, 2015). The finite element model composed of six rigid elements, representing the thorax (T1-T12) and each lumbar vertebra (L1-L5), and six flexible non-linear beam elements characterizing the non-linear stiffness of each lumbar motion segment between T12 and S1 vertebrae (Fig.…”

“…While the kinematics of pelvis and thorax were readily available from measurement, kinematics of the lumbar vertebrae had to be estimated. Given that contributions of lumbar motion segments to the total deformation of lumbar spine change with posture and loads in hands (Shojaei et al, 2015), we did not use the traditional method of using fixed ratios to distribute lumbar deformation, obtained from measurements, between its segments. Instead, we have developed and validated a heuristics optimization procedure in MATLAB (The MathWorks Inc., Natick, MA, USA, Version 8.6) wherein the finite element model is used to find a set of lumbar segmental kinematics that when prescribed to the model results in prediction of muscle forces that minimizes the cost function of the optimization procedure (i.e., sum of squared muscle stress across all lower back muscles) (Shojaei et al, 2015).…”

Human body modeling method to simulate the biodynamic characteristics of spine in vivo with different sitting postures

“…So material of muscle was modeled as passive material in present study. However, future study should consider the active property of muscle, such as kinematics‐driven model …”

Persons with unilateral transfemoral amputation experience larger spinal loads during level-ground walking compared to able-bodied individuals

“…Since only kinematics of the thorax and the pelvis were available from the experimental measurements, a heuristic optimization procedure (Figure 2) was used in the biomechanical model to determine a set of segmental kinematics in the lumbar region (i.e., from L1 to L5) such that the corresponding set of estimated muscles forces minimized a cost function (Shojaei et al, 2015). The cost function used for this heuristic optimization procedure was the sum of squared muscle stress across all lower back muscles.…”

“…In summary, the global optimization is conducted to determine a set of lumbar segmental kinematics that is associated with minimal sum of squared stress across the entire lower back muscles. Meanwhile, for each possible set of lumbar segmental rotations within the global optimization procedure, a local optimization is conducted for the redundant equilibrium problem at each spinal level to determine the set of muscle forces that optimize the cost function of the local optimization at that specific level (Shojaei et al, 2015). The muscle forces associated with the optimal local kinematics (i.e., the output of the global optimization procedure) were then used to estimate spinal loads at all lumbar levels.…”