Preliminary Numerical Study on Electrical Stimulation at Alloplastic Reconstruction Plates of the Mandible. In: Langer U, Amrhein W, Zulehner W, editors. Scientific Computing in Electrical Engineering. Cham: Springer International Publishing; 2018. pp. 3-11. [DOI: 10.1007/978-3-319-75538-0_1]

Addressing Model Uncertainties in Finite Element Simulation of Electrically Stimulated Implants for Critical-Size Mandibular Defects

OBJECTIVE

Electrical stimulation is known to enhance bone healing. Novel electrostimulating devices are currently being developed for the treatment of critical-size bone defects in the mandible. Previous numerical models of these devices did not account for possible uncertainties in the input data. We present the numerical model of an electrically stimulated minipig mandible, including optimization and uncertainty quantification (UQ) methods that allow us to determine the most influential parameters.

METHODS

Uncertainties in the optimized finite element model are quantified using the polynomial chaos method that is implemented in the open-source Python toolbox Uncertainpy. The volumes of understimulated, beneficially stimulated, and overstimulated tissue are considered quantities of interest because they may significantly impact the expected healing success. Further, the current is a substantial quantity, limiting the lifetime of a battery-driven stimulation unit. With sensitivity analyses, the most critical parameters in the numerical model can be identified. Thus, we can learn which parameters are particularly relevant, for example, when conceptualizing the stimulation unit or planning the manufacturing process.

RESULTS

The results of this study show that the parameters of the electrode-tissue interface (ETI), as well as the conductivity within the defect volume, have the most significant impact on the model results.

CONCLUSIONS

The UQ results suggest that careful characterization of the ETI and the dielectric tissue properties is crucial to reduce these uncertainties.

SIGNIFICANCE

The numerical model regarding uncertainties yields important implications for reliable implant design and clinical translation.

PROVenance Patterns in Numerical Modelling and Finite Element Simulation Processes of Bio-electric Systems

The reproducibility of scientific results gains increasing attention. In the context of biomedical engineering, this applies to experimental studies of three different kinds: in-vivo, in-vitro, and in-silico. Numerical modelling and finite element simulation of bio-electric systems are intricate processes involving manifold steps. A typical example of this process is the electrical stimulation at alloplastic reconstruction plates of the mandible. During the bio-electric modelling and simulation process, diverse methods realised in various software tools are exploited. To comprehensibly render how the final model has been developed requires a thorough documentation. We exploit the W3C provenance model PROV to structure this process and to make it accessible for modellers and for automatic analyses. Different entity types, such as data, model, software, literature, assumptions, and mathematical equations are distinguished; roles of entities within an activity are revealed as well as the involved researchers. In addition, we identify five process patterns: 1) information extraction from the literature; 2) generation of a geometrical model which uses data as input; 3) composition of several geometrical or mathematical models into a combined model; 4) parameterisation, which augments the input model by additional properties; and, finally, 5) refinement, which uses a model in addition to an assumption and generates an enhanced model. By modelling provenance information of a typical bio-electric modelling and simulation process as well as identifying provenance patterns, we provide a first step towards a better documentation of academic investigations in that scientific field.

Establishment of a Numerical Model to Design an Electro-Stimulating System for a Porcine Mandibular Critical Size Defect

Electrical stimulation is a promising therapeutic approach for the regeneration of large bone defects. Innovative electrically stimulating implants for critical size defects in the lower jaw are under development and need to be optimized in silico and tested in vivo prior to application. In this context, numerical modelling and simulation are useful tools in the design process. In this study, a numerical model of an electrically stimulated minipig mandible was established to find optimal stimulation parameters that allow for a maximum area of beneficially stimulated tissue. Finite-element simulations were performed to determine the stimulation impact of the proposed implant design and to optimize the electric field distribution resulting from sinusoidal low-frequency ( f = 20 Hz ) electric stimulation. Optimal stimulation parameters of the electrode length h el = 25 m m and the stimulation potential φ stim = 0.5 V were determined. These parameter sets shall be applied in future in vivo validation studies. Furthermore, our results suggest that changing tissue properties during the course of the healing process might make a feedback-controlled stimulation system necessary.