Frank Niemeyer

Influence of the fixation stability on the healing time--a numerical study of a patient-specific fracture healing process.

BACKGROUND The healing outcome of long bone fractures is strongly influenced by the interfragmentary movement of the bone fragments. This depends on the fixation stability, the optimum value of which is still not known. The aim of this study was to simulate a patient-specific human healing process using a numerical algorithm and to retrospectively analyse the influence of the fixation stability on the healing time. METHODS The healing simulation was processed as an initial value problem. This was iteratively solved based on two mechanical (invariants of the strain tensor, calculated through a finite element analysis) and five biological state variables (local tissue composition and blood perfusion) using a previously published fuzzy logic algorithm. For validation purposes, the calculated interfragmentary movement was compared to in vivo measurements of this patient. By changing clinically adjustable parameters of the fixation device, the influence of the fixation stability on the healing time was analysed. FINDING The time course showed good agreement of the interfragmentary movement compared with the in vivo measurements. The predicted healing time was strongly influenced by the fixation stability, i.e. by changing the parameters of the fixation device, it was possible to significantly reduce the healing time. INTERPRETATION The time to heal could be greatly reduced by modification of the fixator design, i.e. increasing the fixation stiffness. When using external fixation devices, this could be achieved by decreasing the free bending length of the pins, using a stiff fixation body and a stiff connection between the pins and the body.

Internal forces and moments in the femur of the rat during gait.

The rat is of increasing importance for experimental studies on fracture healing. The healing outcome of long bone fractures is strongly influenced by mechanical factors, such as the interfragmentary movement. This movement depends on the stability of the fracture fixation and the musculoskeletal loads. However, little is known about these loads in rats. The musculoskeletal loads during gait were estimated using an inverse-dynamic musculoskeletal model of the right hindlimb of the rat. This model was based on a micro-CT scan of the lower extremities and an anatomical study using 15 rat cadavers. Kinematics were reconstructed from X-ray movies, taken simultaneously from two perpendicular directions during a gait cycle. The ground reaction forces were taken from the literature. The muscle forces were calculated using an optimization procedure. The internal forces and moments varied over the gait cycle and along the femoral axis. The greatest internal force (up to 7 times bodyweight) acted in the longitudinal direction. The greatest internal moment (up to 13.8 bodyweight times millimeter) acted in the sagittal plane of the femur. The validity of the model was corroborated by comparing the estimated strains caused by the calculated loads on the surface of the femoral mid-shaft with those from the literature. Knowledge of the internal loads in the femur of the rat allows adjustment of the biomechanical properties of fixation devices in fracture healing studies to the desired interfragmentary movement.

Prediction of fracture healing under axial loading, shear loading and bending is possible using distortional and dilatational strains as determining mechanical stimuli

Numerical models of secondary fracture healing are based on mechanoregulatory algorithms that use distortional strain alone or in combination with either dilatational strain or fluid velocity as determining stimuli for tissue differentiation and development. Comparison of these algorithms has previously suggested that healing processes under torsional rotational loading can only be properly simulated by considering fluid velocity and deviatoric strain as the regulatory stimuli. We hypothesize that sufficient calibration on uncertain input parameters will enhance our existing model, which uses distortional and dilatational strains as determining stimuli, to properly simulate fracture healing under various loading conditions including also torsional rotation. Therefore, we minimized the difference between numerically simulated and experimentally measured courses of interfragmentary movements of two axial compressive cases and two shear load cases (torsional and translational) by varying several input parameter values within their predefined bounds. The calibrated model was then qualitatively evaluated on the ability to predict physiological changes of spatial and temporal tissue distributions, based on respective in vivo data. Finally, we corroborated the model on five additional axial compressive and one asymmetrical bending load case. We conclude that our model, using distortional and dilatational strains as determining stimuli, is able to simulate fracture-healing processes not only under axial compression and torsional rotation but also under translational shear and asymmetrical bending loading conditions.

Effect of the fixator stiffness on the young regenerate bone after bone transport: Computational approach

Bone transport is a well accepted technique for the treatment of large bony defects. This process is mechanically driven, where mechanical forces play a central role in the development of tissues within the distracted gap. One of the most important mechanical factors that conditions the success of bone regeneration during distraction osteogenesis is the fixator stiffness not only during the distraction phase but also during the consolidation phase. Therefore, the aim of the present work is to evaluate the effect of the stiffness of the fixator device on the interfragmentary movements and the tissue outcome during the consolidation phase. A previous differentiation model (Claes and Heigele, 1999) is extended in order to take into account the different behaviors of the tissues in tension and compression. The numerical results that were computed concur with experimental findings; a stiff fixator promotes bone formation while the excessive motion induced by extremely flexible fixators is adverse for bony bridging. Experimental interfragmentary movement is similar to that computed numerically.

Exploring the Potential of Generative Adversarial Networks for Synthesizing Radiological Images of the Spine to be Used in In Silico Trials

In silico trials recently emerged as a disruptive technology, which may reduce the costs related to the development and marketing approval of novel medical technologies, as well as shortening their time-to-market. In these trials, virtual patients are recruited from a large database and their response to the therapy, such as the implantation of a medical device, is simulated by means of numerical models. In this work, we propose the use of generative adversarial networks to produce synthetic radiological images to be used in in silico trials. The generative models produced credible synthetic sagittal X-rays of the lumbar spine based on a simple sketch, and were able to generate sagittal radiological images of the trunk using coronal projections as inputs, and vice versa. Although numerous inaccuracies in the anatomical details may still allow distinguishing synthetic and real images in the majority of cases, the present work showed that generative models are a feasible solution for creating synthetic imaging data to be used in in silico trials of novel medical devices.

Simulating lateral distraction osteogenesis

Distraction osteogenesis is an effective method for generating large amounts of bone in situ for treating pathologies such as large bone defects or skeletal malformations, for instance leg-length discrepancies. While an optimized distraction procedure might have the potential to reduce the rate of complications significantly, our knowledge of the underlying mechanobiological processes is still insufficient for systematic optimization of treatment parameters such as distraction rate or fixation stiffness. We present a novel numerical model of lateral distraction osteogenesis, based on a mechanically well-controlled in vivo experiment. This model extends an existing numerical model of callus healing with viscoplastic material properties for describing stress relaxation and stimuli history-dependent tissue differentiation, incorporating delay and memory effects. A reformulation of appositional growth based non-local biological stimuli in terms of spatial convolution as well as remeshing and solution-mapping procedures allow the model to cope with severe mesh distortions associated with large plastic deformations. With these enhancements, our model is capable of replicating the in vivo observations for lateral distraction osteogenesis in sheep using the same differentiation rules and the same set of parameters that successfully describes callus healing in sheep, indicating that tissue differentiation hypotheses originally developed for fracture healing scenarios might indeed be applicable to distraction as well. The response of the model to modified distraction parameters corresponds to existing studies, although the currently available data is insufficient for rigorous validation. As such, this study provides a first step towards developing models that can serve as tools for identifying both interesting research questions and, eventually, even optimizing clinical procedures once better data for calibration and validation becomes available.

Mathematical and Finite Element Modeling

Abstract Mathematical modeling and finite element analysis have been widely used for the investigation of the biomechanics of the spine, and are considered to be one of the pillars of spine research together with in vitro testing and in vivo studies. Hundreds of finite element models aimed at predicting the biomechanical response of the spine under both healthy and pathological conditions as well as after the implantation of surgical devices have been discussed in the literature. In this chapter, after providing a historical perspective on how mathematical and numerical modeling became an integral part of biomechanics research, the basic principles of finite element modeling are described. Then a selection of the most relevant finite element models of the spine, which had a major influence on contemporary studies, is briefly illustrated.

Modelling the fracture-healing process as a moving-interface problem using an interface-capturing approach

Abstract We present a novel numerical model of the fracture-healing process using interface-capturing techniques, a well-known approach from fields like fluid dynamics, to describe tissue growth. One advantage of this method is its direct connection to experimentally observable parameters, including tissue-growth velocities. In our model, osteogenesis, chondrogenesis and revascularisation are triggered by mechanical stimuli via mechano-transduction based on previously established hypothesis of Claes and Heigele. After experimentally verifying the convergence of the numerical method, we compare the predictions of our model with those of the already established Ulm bone-healing model, which serves as a benchmark, and corroborate our results with existing animal experiments. We demonstrate that the new model can predict the history of the interfragmentary movement and forecast a tissue evolution that appears similar to the experimental results. Furthermore, we compare the relative tissue concentration in the healing domain with outcomes of animal experiments. Finally, we discuss the possible application of the model to new fields, where numerical simulations could also prove beneficial.