The complex process of bone remodelling is strongly linked to the electric fields that naturally occur in the bone as a bioelectric tissue. Still, this process needs to be fully understood. Mechanical loading causes charge shifts in the bone, which are characterised by streaming potentials and the piezoelectric properties of the collagen matrix of the bone.

The biological structure of bone is multiscale. The entities on different spatial scales, such as osteoblasts/osteoclasts on the microscale, bone tissue on the mesoscale, and whole bone on the macroscale, show responses to endogenous electric fields in distinct time scales. Electrical stimulation aims to imitate these naturally occurring electrical signals to enhance bone regeneration. The design of innovative implants that employ electrical stimulation for accelerated bone regeneration is a fast-growing research area. In recent years, much research has been done to develop electrically stimulating implants for different applications, e.g., bone fractures, non-unions, or avascular necrosis. The stimulation parameters used in clinical and in vivo applications are mainly used empirically, and little is known about the actual field distribution inside the tissue. Numerical simulation can close this gap and help predict the tissue's electric field distribution, optimise stimulation parameters, and identify essential parameters, e.g. via Uncertainty Quantification.

On the macroscale, we will present different examples of finite element models of electrostimulating bone implants for bone defects, e.g., in the jaw region. More specifically, we will discuss practicable stimulation arrangements and electrode designs and optimise stimulation parameters (dimensions of the electrodes, stimulation voltage) with regard to the electric field strength as a target variable. Modelling parameters with an essential impact on the electric field distribution will be identified via sensitivity analysis. Furthermore, on the mesoscale, the electric fields experienced by the bone cells and their response affect bone remodelling. On this front, we present a mathematical model based on the mean-field analysis, which explains the effect of the electric field on bone cells in an in-vitro setup. In addition, on the microscale, each bone cell changes its shape and adhesion with the orientation of the electric field. The cell contractility affecting its shape and adhesion can be mathematically modelled as a multi-physics phenomenon, particularly a bio-chemo-electro-mechanical model.

With these phenomena that happen in distinct time scales across the spatial scales of the bone, it is necessary to implement a multiscale numerical simulation bridging these scales. Such a multiscale model helps provide a better understanding of the impact of electrical stimulation on bone regeneration. Further, such models can enhance the experimental characterisation of therapeutical electrical stimulation of bone. In this context, we present our approach to developing a multiscale framework for electrically active bone implants.

Bone can optimize its structure under the influence of mechanical loads. The macroscopic load acting on bone influences the bone cells, particularly osteocytes present in the lacunae canalicular network (LCN). These osteocytes respond to numerous physical signals, including substrate strain, interstitial fluid flow, and pore pressure. Cellular-level strains in vivo are considered too small to elicit a response from osteocytes. However, several studies suggest that load-induced interstitial fluid flow (IFF) in LCN may be a primary stimulus as it exerts shear and drags forces on osteocytes. Besides IFF, it has also been shown that pore pressure generated under physiological loading conditions is adequate to enable osteocytes to respond. Despite the importance of IFF and Pore pressure, relatively few studies explore their influence on bone adaptation. Motivated by the fact above, we investigated the role of interstitial fluid flow and fluid pore pressure on osteogenesis.

This work aims to predict new bone formation on both cortical bone surfaces under mechanical loading. We use dissipation energy density due to fluid flow and fluid pore pressure as a stimulus because, being a scalar quantity and having attributes similar to fluid motion, it is convenient to use. We hypothesize that the site-specific new bone distribution at the endocortical and periosteal surfaces is directly proportional to the square root of the summation of the dissipation energy density due to canalicular fluid flow and pore pressure. Accordingly, a poroelastic finite element model of a simplified geometric beam with a cross-section similar to the mid-cross-section of 16 weeks old C57BL/6J was subjected to the mid-strain axial loading protocol Barmen et al. [1]. The fluid velocity and pore pressure estimated from the above analysis is used to calculate the dissipation energy density. This model is coupled with a novel mathematical formulation, considering the summation of the dissipation energy density of poroelastic flow and pore pressure as a stimulus to predict cortical bone adaptation.

The bone formation rates (BFR) calculated by the model are 0.9986 µm³/µm²/sec and 0.6348 µm³/µm²/sec, respectively, at the periosteal and endocortical surfaces, which are not significantly different from the corresponding experimental BFR of 0.9257 ± 1.5855 µm³/µm²/sec (p-value = 0.9817, t-test) and 0.5964 ± 1.4285 µm³/µm²/sec (p-value = 0.9791, t-test). Additionally, the statistical significance of site-specific MAR was measured using Watson’s U² test. The computed MAR at both the cortical surfaces was not significantly different from the experimental MAR at the periosteal surface (p-value = 0.3417, Watson’s U² test) and at the endocortical surface (p-value = 0.94, Watson’s U² test).

Reference:

[1] A. G. Berman, C. A. Clauser, C. Wunderlin, M. A. Hammond, and J. M. Wallace, 2015, PLoS One, 10 (6), 1-16.

Fracture healing is a complex process that involves numerous biological and mechanical factors. Understanding this process is crucial for healthcare professionals involved in the treatment and management of fractures, but also, for students pursuing careers in fields such as medicine, physical therapy, and biomechanics. Learning about fracture healing can provide them with a foundation for understanding musculoskeletal injuries and developing effective interventions and implant designs. In addition, gaining knowledge of fracture healing can inspire future research and innovation in the field, leading to improved treatments and outcomes for patients. However, with advancements in technology and increasing accessibility of simulation models, there is potential for a wider range of individuals to gain hands-on experience through simulation and digital learning methods. But up to date, simulation of fracture healing is limited to research institutes and highly trained professionals.

On the basis of the Ulm fracture healing model (Shefelbine et al. 2005, Simon et al. 2011), we developed a software platform (OSORA Medical Fracture Analytics), which is able to be used for educational purpose as well as for research questions.

We used the software in a course on fracture healing, where computational science and engineering students were exposed to different questions as the influence on the healing performance of:

• Fracture gap size
• Fracture angle
• Osteosynthesis stiffness

Into the web-based tool, we implemented a wizard to generate simulation input by students in an intuitive manner. Adjustable parameters where: AO-fracture class, geometrical bone and fracture dimensions, osteosynthesis material and loading conditions. Simulations were then automatically started and results available online.

The learning objectives for the students were the research of suitable literature data on experiments and studies to corroborate the simulation results, simulation performance and result interpretation.

Deriving qualitative and quantitative results from the web-based tool allowed a detailed comparison with literature data on those influences for the students.

The influence of fracture gap size was compared with in vivo data from Claes et al. 1997, Meeson et al. 2019 and Markel/Bogdanske 1994. Trends in the influence of the fracture angle where compared with Park et al. 1998 and Yamagishi et al. 1955. Literature data of simulations from Steiner et al. 2014 were used to explain and compare the influences of intramedullary nail stiffness behavior on the healing outcome.

Quantities as the interfragmentary motion, bone formation tissue volume over time and longitudinal fracture stiffness where analyzed and compared to the experimental findings.

With this web-app the students were able to in deep discuss on healing patterns and quantitative comparisons with literature data. The platform offers a flexible and engaging learning experience that was integrated into traditional classroom instruction, providing an efficient and effective means of enhancing biomechanical and medical education with computer simulation.

Introduction: While Wolff’s law established bone’s adaptation to mechanical environment, Frost’s mechanostat theory predicted a mechanical threshold (such that strain, strain energy density etc.) for such adaptation [1,2]. Such threshold (for example, strain) was, however, found to vary with forcing frequency [3]. Moreover, strain or strain energy density alone does not predict new bone formation [4]. Evidence of involvement of interstitial fluid flow in bone adaptation has been increasing in the literature [5]. Accordingly, bone adaptation models based on poroelastic dissipation energy density have been developed by various researchers [6-8]. The present work advances the poroelastic model by establishing the strain threshold and bone formation rate (BFR) as a function of forcing frequency.

Methods: Biot’s poroelastic model has been studied in frequency domain, and dissipation energy density has been calculated for a sinusoidal forcing frequency using standard methods [9]. Data from the literature have been used to establish relation among strain threshold, BFR and forcing frequency [3].

Results: BFR was found to be proportional to “square-root of dissipation energy density” minus a corresponding threshold value (of the “square-root of dissipation energy density”). The expression is similar to that obtained by the authors in previous study based on different experimental data, which were for non-sinusoidal waveform of loading on mouse tibia [8]. Dissipation energy threshold was found to be constant that does not depend on forcing frequency. On the other hand, the corresponding strain threshold was found to be a function of frequency. There is a frequency predicted for which the strain threshold is the minimum and that frequency is around 20 Hz, which agrees with the literature [10]. The strain threshold needed for new bone formation monotonously increases beyond this forcing frequency.

Conclusions: This work establishes that the rate of change of BFR with respect to square root of dissipation energy density is a constant, regardless of forcing frequency. The strain threshold has also been expressed in terms of frequency, which can easily determine the simple sinusoidal loading regimen (peak strain and frequency) to maintain a bone mass and mitigate bone loss arising due to bed-rest, space-flight, muscle paralysis etc.

References:
[1] Wolff, 1870, Arch. Für Pathol. Anat. Physiol. Für Klin. Med. 50, 389–450.
[2] Frost, 1987, Anat. Rec. 219, 1–9.
[3] Hsieh & Turner, 2001, Journal of Bone and Mineral Research, 16(50), 918-924.
[4] Tiwari & Prasad, 2017, Biomech. Model. Mechanobiol. 16, 395–410.
[5] van Tol, Schemenz, Wagermaier, Roschger, Razi, Vitienes, Fratzl, Willie, & Weinkamer, 2020, Proc Natl Acad Sci, 117(51):32251-32259.
[6] Kumar, Jasiuk, & Dantzig, 2011, Journal of Mechanics of Materials and Structures, 6(1-4), 303-319.
[7] Pereira, Javaheri, Pitsillides, & Shefelbine, 2015, J. R. Soc. Interface, 12, 20150590.
[8] Singh, Singh, & Prasad, 2021, Proceedings of the ASME IMECE2021, 71220.
[9] Biot, 1941, Journal of Applied Physics, 12, 155-164.
[10] Rubin, & McLeod, 1994, Clin Orthop, 298, 165–174.