Optimization of bone fracture treatment

Source: Dynardo

With increasing life expectancies, the number of femoral fractures among elderly patients due to osteoporosis is expected to rise. To restore mobility in these patients as rapidly as possible, fracture treatment that takes into account the material properties of osteoporotic bone is essential.

The focus of this study was the treatment of femoral shaft fractures. These are commonly treated with plate osteosynthesis, which involves bringing the ends of a fractured bone together and fastening them with a metal plate and screws. Although there are a variety of different plate types, locking compression plates have been widely applied in recent years. Among patients with osteoporosis, the stable fixation of the plate is a big challenge for the surgeon since the bone often lacks the desired stability. This may lead to a high complication rate due to loosening of screws or breakage of the plate.

The aim of this study was to support surgeons in deciding where to place the screws to achieve optimal fracture healing and to prevent implant failure after a femoral shaft fracture. For this purpose, hundreds of different screw arrangements were evaluated and optimized using Dynardo’s optiSLang controlling an automated workflow. The procedure involved:

  • Use of computed tomography data for patient-specific modeling of the inhomogeneous material properties of the bone.
  • Evaluation of biomechanical parameters with finite element analysis.
  • Optimization of the screw arrangement under given constraints.

Optimization constraints included the number of screws, the inter-fragmentary movement, the distance between plate and bone, as well as the yield material properties of bone, plate and screws.

Automating this process offered a whole new perspective compared with currently used approaches for investigating the influence of position and number of screws on fracture healing. Without an automated process, only a small number of different layouts can be evaluated and compared. But the proposed automated system made it possible to select the best layout from hundreds of designs without unreasonable effort.

Fig. 1: Fracture movement on the near cortex is limited compared with the far cortex. Source: Dynardo

Materials and methods—A partly automated workflow (Fig. 2) was developed to select the best screw arrangement and position for plate osteosynthesis. Some tasks had to be executed manually for every patient, including bone segmentation, repositioning of bone fragments as well as the initial positioning of the plate. The majority of tasks, however, were controlled by optiSLang and performed automatically. These tasks included mesh generation, assignment of material properties and boundary conditions, finite element analysis and optimization. The model consisted of bone fragments, a locking compression plate and a varying number of screws. These objects were either generated or adapted for use in a finite element analysis.

Fig. 2: Procedure for the optimization of fracture treatment. Source: Dynardo

The CT dataset of a 22-year-old female was supplied by the Department of Radiology at the Technische Universitat Munchen. Materialise’s Mimics software was used for segmentation of the three-dimensional CT data sets. Finally, a three-dimensional geometry of the femur was created. The surface of the bone was smoothed and any small holes, tunnels and peaks on the surface were removed with Geomagic software. In this study, a healthy femur was used as an example, and an artificial transverse fracture with a fracture gap of 3mm was created using the Blender Version 2.67 software (Fig. 3).

Fig. 3: A transverse fracture with a fracture gap of 3mm was artificially added to a segmented femoral bone. Source: Dynardo

In this simulation, a Locking Compression Plate (LCP, article number 422 258) manufactured by Synthes was used. This plate was designed for treatment of distal femoral fractures. The compression plate had seven screw holes on the distal end and 13 screw holes for fixation along the bone shaft. The plate was designed to match the mean shape of femoral bones of a cohort and allow secure attachment. The plate was positioned relative to the femur following the recommendations of surgeons. The screws were automatically generated using the Blender software at the beginning of each optimization loop. An input file containing information about each screw as a discrete variable was generated automatically by optiSLang. The value “0” represented the state “no screw,” “1” a monocortical screw, and “2” a bicortical screw.

To demonstrate the functionality of this model, four screw designs were chosen. The layouts differed with respect to the bridging length, which is the distance between fracture gap and the first screw on either side of the fracture. The bridging length is known to have a large influence on the stability of the plate-bone construct. Four different designs were evaluated: In design a, the screws were placed directly next to the fracture. In designs b and c, the bridging lengths were composed of two or five unoccupied screws holes respectively. Design d had the largest bridging length, with ten empty screw holes (Fig. 4).

Fig. 4: Four screw layouts with varying bridging length. The bridging length is the distance between fracture gap and the first screw on either side of the fracture. Source: Dynardo

The finite element mesh was created with ICEM CFD from ANSYS. The mesh was generated (Fig. 5) automatically reading a script in the programming language TCL (Tool Command Language) using the following procedure:

  • Import STL files.
  • Create intersection lines and intersection points between objects.
  • Create material points.
  • Mesh generation.
  • Smoothing of mesh surface.
  • Export data as input file for ANSYS Classic.

Since the arrangement of screws was different for every optimization run, the TCL file was regenerated during every optimization run by a Python program.

Fig. 5: Meshed bone with plate and screws. Source: Dynardo

The material properties for bone, plate and screws were set in the preprocessor in ANSYS. Plate and screws were considered as homogeneous materials made of either the titanium alloy Ti-6Al-7Nb or stainless steel 316L. Bone was modeled as an inhomogeneous material consisting of 72 different materials depending on the HU value of the element. Cortical bone properties were chosen as the material property for the homogeneous bone to assess the difference between modeling the bone as a homogeneous object compared with an inhomogeneous object. All materials were assumed to be linear elastic and isotropic. Patient-specific bone material properties, such as Young’s modulus, were derived from Hounsfield Units contained in CT data. The mechanical properties were mapped onto the mesh using an algorithm programmed in Python.

Fig. 6: Physiological loading case—force application from distal. Source: Dynardo
Fig. 7: Determination of inter-fragmentary movement using the relative displacement of two points on the far cortex and on the near cortex of the bone. (Pp,xxx = Displacement of node on proximal bone fragment, Pd,xxx = Displacement of node on distal bone fragment, d = Relative displacement between two points). Source: Dynardo
Fig. 8: Assigning HU as temperatures on the finite element model of bone. Left side: CT scan (top) and finite element model with HU distribution (bottom) of femoral shaft bone. Right side: Two parallel longitudinal sections of the finite element model of femoral bone. Cortical bone (red) was mainly located along the bone shaft. The femoral epiphyses primarily consisted of cancellous bone (green). The dark blue array of the bone indicated the bone marrow. No HU were assigned to the plate and screws. Source: Dynardo

Optimization—The sensitivity analysis and optimization were performed using the software optiSLang v4 (Fig. 9). New designs were created using an evolutionary algorithm. The objective of the optimization was to minimize the number of screws. The parametric model consisted of 21 design parameters. Twenty design parameters were responsible for generating the screws. These parameters could take on one of three discrete states: 0 representing no screw, 1 representing a monocortical screw and 2 representing a bicortical screw. As the subject bone showed no signs of osteoporosis, the same outcomes would be expected no matter whether monocortical or bicortical screws were applied. Therefore, only two discrete states were permitted (0 = no screw, 2 = bicortical screw). The remaining design parameter represented the distance between plate and bone. This parameter could take on a continuous value between 0mm and 5mm.

Fig. 9: Upper panel: sensitivity workflow with metamodeling. Middle panel: optimization workflow. Lower panel: solver chain. Source: Dynardo

The optimization constraints were chosen according to findings from the literature. To maintain a stable attachment of the plate to the bone fragments, at least two screws had to be placed in every fragment. The inter-fragmentary movement was considered an important boundary condition for optimizing the number of screws and their position. Due to the bending load, the inter-fragmentary movement on the near cortex was generally smaller than on the far cortex. Two constraints were specified to take this behavior into account. To prevent failure of the implant under overloading the stress levels in the bone, plate and screws had to remain below the yield stress for the corresponding material. Overload was defined as three times the recommended load.

Fig. 10: Relationship between bridging length and inter-fragmentary movement on the far cortex. A linear correlation between the bridging length and the relative movement of the far cortex was observed. Source: Dynardo

The bridging length had a significant impact on the inter-fragmentary movement. A larger bridging length resulted in a linear increase in relative movement on the near cortex (Fig. 10). A positive linear relationship between bridging length and relative movement was observed on the far cortex. The objective of the optimization was to minimize the total number of screws. A design with four screws was selected as the optimal design by the evolutionary optimization algorithm (Fig. 11). The design had a medium bridging length of four unoccupied screw holes which equaled a distance of 100mm. There was a 0.5mm distance between plate and bone. A total of 180 designs were evaluated in order to select the best design. Designs with up to 16 screws were evaluated during the random sampling period. Primarily designs with four screws were tested toward the end of the optimization.

Fig. 11: Optimal design after optimization under predefined constraints. The optimal design consisted of four screws in total, two screws on the distal segment and two screws on the proximal segment. The bridging length measured 100mm. Source: Dynardo

Results—This study developed a general procedure for the optimization of fracture treatment. The aim was to improve the healing process by determining the optimal screw configuration under certain biomechanical constraints. The developed workflow enabled the selection of an optimal screw layout out of several thousand possible arrangements. For this purpose, the finite element mesh generation and the finite element analysis were successfully automated. This is the first procedure which allows for more than the comparison between individual FEAs of different plate osteosynthesis.

The optimization process required minimal user input. The user only needed to segment the bone, position the plate relative to the bone and select a couple of specific points on the model. These points included the material points of bone and plate, the measurement points for the inter-fragmentary movement as well as the points for force application and constraints. In future, user input may be further reduced by an automated segmentation procedure.

The rest of the procedure was performed automatically through a batch file. The selection of an optimal design, based on more than 150 other designs, using an evolutionary algorithm was completed within 24 hours. Additional parallelization of the computation process may be able to further decrease this computation time.

Read the full case study: “Optimization of Fracture Treatment,” M. Schimmelpfennig (Dynardo GmbH); C. Wittkowske, S. Raith, J. Jalali, A. Volf, L. Kovacs (Research Group CAPS, TU Munchen); A. Nolte (CADFEM GmbH); B. Konig, S. Dobele (Berufsgenossenschaftliche Unfallklinik Tubingen); J. Bauer, E. Grande Gracia (Institut fur diagnostische und interventionelle Radiologie der TU Munchen).