How Can Biomechanical Multibody Models of Scoliosis Be Accurate in Simulating Spine Movement Behavior While Neglecting the Changes of Spinal Length?

This paper studies how biomechanical multibody models of scoliosis can neglect the changes of spinal length and yet be accurate in reconstructing spinal columns. As these models with fixed length comprise rigid links interconnected by rotary joints, they resemble polygonal chains that approximate spine curves with a finite number of line segments. In mathematics, using more segments with shorter lengths can result in more accurate curve approximations. This raises the question of whether more accurate spine curve approximations by increasing the number of links/joints can yield more accurate spinal column reconstructions. For this, the accuracy of spine curve approximation was improved consistently by increasing the number of links/joints, and its effects on the accuracy of spinal column reconstruction were assessed. Positive correlation was found between the accuracy of spine reconstruction and curve approximation. It was shown that while increasing the accuracy of curve approximations, the representation of scoliosis concavity and its side-to-side deviations were improved. Moreover, reconstruction errors of the spine regions separated by the inflection vertebrae had minimal impacts on each other. Overall, multibody scoliosis models with fixed spinal lengths can benefit from the extra rotational joints that contribute toward the accuracy of spine curve approximation. The outcome of this study leads to concurrent accuracy improvement and simplification of multibody models; joint-link configurations can be independently defined for the regions separated by the inflection vertebrae, enabling local optimization of the models for higher accuracy without unnecessary added complexity to the whole model.

Effects of root chord movement on thrust generation of oscillatory pectoral fins.

Fin kinematics is the key to thrust generation of oscillatory pectoral fins of manta rays. This could be one of the main reasons that fin designs of robotic manta rays are becoming more complex to simulate the fin kinematics more closely so as to generate high thrusts. However, as the trend suggests, the extent of improvement to thrust generation might not be worth the complexities added to the designs. Out-of-the-box design changes that favour the simplicity and yet improve the fin performance can be a sound replicate for the complicated fin design features. One aspect of manta rays' pectoral fins that influences the fin kinematics is the constraint imposed on the movement of their particularly long root chord that is entirely attached to the body of manta rays. Hypothetically, reducing such a constraint can promote the angle-of-attack during flapping, which can improve thrust generation. This paper aims to study if the simple idea of disengagement of the fin root chord from the body, which is obviously a deviation from the nature, can improve thrust generation. An experiment was conducted on thrust generation of four basic fin designs, where different portions of their chord was disengaged from the body step-by-step. The disengagement occurred for each quarter of the chord, starting from the trailing edge towards the leading edge. It was found that the fins with free root chord (minimal attachment to the body) could generate thrust slightly less than the fully constrained fins (full attachment). In addition, it was shown that thrust generation efficiency kept increasing while disengaging the chord further, and reached the maximum for free root chord. This may show that a powerful and yet more efficient fin can be produced with such a deviation from the nature.

Finding line of action of the force exerted on erect spine based on lateral bending test in personalization of scoliotic spine models.

In multi-body models of scoliotic spine, personalization of mechanical properties of joints significantly improves reconstruction of the spine shape. In personalization methods based on lateral bending test, simulation of bending positions is an essential step. To simulate, a force is exerted on the spine model in the erect position. The line of action of the force affects the moment of the force about the joints and thus, if not correctly identified, causes over/underestimation of mechanical properties. Therefore, we aimed to identify the line of action, which has got little attention in previous studies. An in-depth analysis was performed on the scoliotic spine movement from the erect to four spine positions in the frontal plane by using pre-operative X-rays of 18 adolescent idiopathic scoliosis (AIS) patients. To study the movement, the spine curvature was considered as a 2D chain of micro-scale motion segments (MMSs) comprising rigid links and 1-degree-of-freedom (DOF) rotary joints. It was found that two MMSs representing the inflection points of the erect spine had almost no rotation (0.0028° ± 0.0021°) in the movement. The small rotation can be justified by weak moment of the force about these MMSs due to very small moment arm. Therefore, in the frontal plane, the line of action of the force to simulate the left/right bending position was defined as the line that passes through these MMSs in the left/right bending position. Through personalization of a 3D spine model for our patients, we demonstrated that our line of action could result in good estimates of the spine shape in the bending positions and other positions not included in the personalization, supporting our proposed line of action.

A new method to approximate load-displacement relationships of spinal motion segments for patient-specific multi-body models of scoliotic spine.

Load-displacement relationships of spinal motion segments are crucial factors in characterizing the stiffness of scoliotic spine models to mimic the spine responses to loads. Although nonlinear approach to approximation of the relationships can be superior to linear ones, little mention has been made to deriving personalized nonlinear load-displacement relationships in previous studies. A method is developed for nonlinear approximation of load-displacement relationships of spinal motion segments to assist characterizing in vivo the stiffness of spine models. We propose approximation by tangent functions and focus on rotational displacements in lateral direction. The tangent functions are characterized using lateral bending test. A multi-body model was characterized to 18 patients and utilized to simulate four spine positions; right bending, left bending, neutral, and traction. The same was done using linear functions to assess the performance of the proposed tangent function in comparison with the linear function. Root-mean-square error (RMSE) of the displacements estimated by the tangent functions was 44 % smaller than the linear functions. This shows the ability of our tangent function in approximation of the relationships for a range of infinitesimal to large displacements involved in the spine movement to the four positions. In addition, the models based on the tangent functions yielded 67, 55, and 39 % smaller RMSEs of Ferguson angles, locations of vertebrae, and orientations of vertebrae, respectively, implying better estimates of spine responses to loads. Overall, it can be concluded that our method for approximating load-displacement relationships of spinal motion segments can offer good estimates of scoliotic spine stiffness.