Numerical modelling of an orthopedic brace with increased functional characteristics for the treatment of idiopathic scoliosis

2.1Boston brace as a research subject

The Boston brace, designed for non-surgical intervention for scoliosis, is predominantly successful in managing spinal deformities where the apex of the curve lies between the sixth thoracic and third lumbar vertebrae. This type of a brace is uniquely designed to be non-rigid at the top, resting under the patient’s armpits to maintain stability and reduce displacement [2, 8]. In this study, a Boston brace was designed for managing a left lumbar spine curvature. The brace shell was constructed from a 4 mm thick polypropylene sheet, and in this work the authors will focus only on the study of the brace shell.

Unlike complex braces like the Cheneau brace, which uses multiple corrective forces in a spatial system, the Boston brace utilizes a simpler three-point corrective force system [9]. Two forces, A and B, act on the spine by pressuring the ribs, with a third force, C, acting upon the pelvis (Fig. 1). A is the primary corrective force, while B and C provide counteracting support.

Figure 1.

Diagram of the Boston brace in frontal view-depicting the simplified correction mechanism for the left lumbar curve. Forces exerted by the brace: B and C – supporting forces, A – primary corrective force, D – extra load introduced following the pre-stressing of the brace with force, A, E – standard earth gravity.

The study aims to modify the design of the orthosis to increase its functionality without disturbing the distribution of corrective forces after optimization. This goal requires maintaining the distribution of pressure on the patient’s torso. The model used assumes point loads, although it is known that in real-world scenarios the corrective forces would be distributed over the corrective pads surfaces, while ensuring that the pressure is maintained within a safe range. It should be noted that modeling the pressure of brace on the torso is a complex issue and has been extensively researched [1, 5, 6]. However, in this study, the main goal is to optimize the structure and functionality of the orthosis shell, not to model the pressure of the orthosis on the torso.

2.2Finite element modeling

In this study, the parameters of a brace model were set, and a finite element method (FEM) based model was created by generating a FE mesh. In order to be consistent with the conditions used in previous publication [3], this computational model was designed to mimic the experimental tests, applying the same three-point system of forces using supports B and C, and a pre-loading force A. Two immobile supports were set, and a preliminary load of 36 N was applied, reflecting the actual force range in real-life braces. This initial load ensured the stability of the brace’s position on the experimental test stand, used in previous studies [3]. The gravitational force E, while minor, was also factored into the model for a more accurate representation [10].

Subsequently, an additional force D of 0.1 N was then introduced in the direction of force A, in line with the conditions of the experimental testing that employed an electronic speckle interferometer (ESPI) system [11]. This system, using optical interferometry, measured displacements along the camera lens axis – in the Z-axis of the computer model. Introducing a smaller force was a strategic move designed to facilitate the measurement of small displacements within the measurement range of the interferometer and ensuring the material’s linearity during testing. The final simulation result, which calculated the difference in shell displacements before and after the introduction of force D, was processed for further analysis.

Polypropylene, commonly used for orthoses, known for its durability and flexibility, was chosen as the shell material of the orthosis. It has a Young’s modulus (E) of 1,000 MPa and a Poisson’s ratio (v) of 0.2, making it an ideal choice for achieving the optimal balance of stiffness and flexibility needed in an orthosis [5, 12].

A 10-node tetrahedral element was used to develop the FEM model. This type of element is particularly useful for accurately representing complex geometries in 3D, and its excellent numerical performance in simulating elastic behavior is invaluable for modeling materials such as polypropylene.

An iterative mesh refinement process was applied until the von Mises stress changed by less than 3% with additional node density [13]. The final mesh consisted of 121,253 nodes and 86,187 finite elements with a maximum edge dimension of 10.0 mm.

In addition to the determination of von Mises stresses distribution, the field of principal stresses in the corset shell, represented by a system of vectors assigned graphically for each shell element, was also determined. The relatively dense distribution of principal stress vectors made it possible, in the next step, to plot principal stress trajectories in the most interesting areas of the corset, which were then used to implement structural changes aimed at improving the functional properties of the orthosis.

3.1Numerical tests of the original brace

Numerical model was subjected to tests under loads similar to those used in previous FEM studies described by Grycuk and Mrozek [3], specifically a 36 N load applied at point A in line with physiological loading conditions. The results generated a distribution of von Mises stress, as visualized in Fig. 2. Apart from the areas with minimal surface area where the loading force and supports were positioned, most of the orthosis achieved stress levels under 6.9 MPa (Fig. 2). This stress magnitude aligns with the linear portion of polypropylene’s stress-strain relationship [14]. This result substantiated the earlier assumptions about the linearity of the orthosis model.

Figure 2.

View of original brace with equivalent values of von Mises stress.

From Fig. 2, it can be seen that the identification of several isolated areas of higher von Mises stresses does not help define the working scheme of the orthosis shell. Much more useful for this purpose is to use the determined distribution of principal stress vectors, and in particular to use this distribution to construct the trajectories of these stresses. Figure 3 provides a representation of the principal stress vectors, specifically for maximum tensile stresses σ1. This diagram plots the pathways of principal stress σ1. Splines were drawn to match the directions of σ1 vectors, beginning and ending near the places where the external forces were applied. These paths shape splines were aligned tangentially with σ1 vectors.

Figure 3.

Distribution of the principal tensile stress vectors σ1 with trajectories of principal stress drawn on the original brace. Points of application of forces: force C exerted to the pelvis and forces A and B exerted on the thoracic region.

Based on the shapes of the principal stress σ1 trajectories obtained from the numerical analyses and the areas of the shell where these trajectories correspond to the stresses with the highest values, it can be hypothesized that these areas are mainly responsible for performing the corrective function of the brace. Thus, the other parts of the shell should only be responsible for performing ancillary functions, such as stabilizing the orthosis relative to the torso, and should not significantly affect the corrective tasks posed to the brace. These parts could be removed without significant negative effects on the shell stiffness.

Confirmation of this thesis can be obtained, for example, by removing from the original brace structure those parts of the shell where the principal stress trajectories correspond to σ1 stresses with relatively small values and performing a numerical analysis analogous to that obtained for an original orthosis. The postulate would be considered confirmed if the obtained mechanical characteristics of the modified brace, its nature of deformation under corrective loading and the level of stiffness would differ only little from the original structure. Thus, obtaining the characteristics most similar to the original brace would require only a slight corrections, for example, of the thickness of the shell in critical areas. Small corrections would be necessary due to the fact that the areas to be removed, however, have some small contribution to the load transfer of the shell, and some compensatory action would be required due to their removal.

3.2Modified brace numerical tests

In order to verify the thesis formulated in Section 3.1, the original geometry of the corset shell was modified. A significant portion of the front wall was removed, leaving only a relatively narrow strip within which the principal stress trajectories corresponded to σ1 stresses with relatively high values, as seen in Fig. 3. Small portions of the rear wall of the corset were also removed, but with the tension strap attachment locations retained. This was done in order to preserve areas coinciding with the originally determined trajectories of maximum principal stresses. The front wall of the modified corset was also thickened by 0.95 mm in order to compensate for the contribution of the removed shell fragments, which carried only small loads. The modified corset (Fig. 4) was subjected to forces identical to those applied to the original brace.

Figure 4.

View of modified brace with equivalent values of von Mises stress.

Figure 5.

Distribution of the principal tensile stress vector σ1 with trajectories of principal stress drawn on the modified brace. Points of application of forces: force C exerted to the pelvis and forces A and B exerted on the thoracic region.

Figure 6.

View of the displacement along the Z-axis of the original and modified brace. The cross-sectional lines A-A, which correspond to the transverse plane, are plotted in the figures. Points I to V correspond to the measured points in the comparative verification shown in Table 1.

A view of the modified corset shell, including the distribution of von Mises stresses is shown in Fig. 4. The distribution of principal stresses in the front wall of the corset is shown in Fig. 5. It can be seen that despite minor differences, the nature of the distribution of both von Mises stresses and the distribution of principal stresses is very similar for both the original and modified corsets. A similar conclusion can be drawn by comparing the displacement fields of the two corsets after the application of corrective forces, shown in Fig. 6. The results presented suggest that the mechanical characteristics of the two corsets are very similar.

The correction function of a corset is related to its stiffness, which can be further analyzed by determining the brace displacement field occurring in its fixed cross-section in the transverse plane due to applied correction forces. Figure 7 shows a comparison of the displacement fields of the two corsets in the same cross-sections. A comparison of the numerical values of displacements for selected points is shown in Table 1.

Figure 7.

View of 9.6x scaled displacements in cross-section A-A (in the transverse plane marked in Fig. 6) of the braces: gray color – original brace not loaded with corrective forces; red color – original brace loaded with corrective forces; blue color – modified brace loaded with corrective forces. B and C – supporting forces, A – primary corrective force, D – extra load introduced following the pre-stressing of the brace with force A.

Based on a comparison of the volume of the original and modified corset, it was calculated that the shell of the modified corset has a mass that is 39% lower than that of the original corset.