Influences of age and mechanical stability on volume, microstructure, and mineralization of the fracture callus during bone healing : Is osteoclast activity the key to age-related impaired healing?

Earlier studies have shown that the influence of fixation stability on bone healing diminishes with advanced age. The goal of this study was to unravel the relationship between mechanical stimulus and age on callus competence at a tissue level. Using 3D in vitro micro-computed tomography derived metrics, 2D in vivo radiography, and histology, we investigated the influences of age and varying fixation stability on callus size, geometry, microstructure, composition, remodeling, and vascularity. Compared were four groups with a 1.5-mm osteotomy gap in the femora of Sprague–Dawley rats: Young rigid (YR), Young semirigid (YSR), Old rigid (OR), Old semirigid (OSR). Hypothesis was that calcified callus microstructure and composition is impaired due to the influence of advanced age, and these individuals would show a reduced response to fixation stabilities. Semirigid fixations resulted in a larger ΔCSA (Callus cross-sectional area) compared to rigid groups. In vitro μCT analysis at 6 weeks postmortem showed callus bridging scores in younger animals to be superior than their older counterparts (pb0.01). Younger animals showed (i) larger callus strut thickness (pb0.001), (ii) lower perforation in struts (pb0.01), and (iii) higher mineralization of callus struts (pb0.001). Callus mineralization was reduced in young animals with semirigid fracture fixation but remained unaffected in the aged group. While stability had an influence, age showed none on callus size and geometry of callus. With no differences observed in relative osteoid areas in the callus ROI, old as well as semirigid fixated animals showed a higher osteoclast count (pb0.05). Blood vessel density was reduced in animals with semirigid fixation (pb0.05). In conclusion, in vivo monitoring indicated delayed callus maturation in aged individuals. Callus bridging and callus competence (microstructure and mineralization) were impaired in individuals with an advanced age. This matched with increased bone resorption due to higher osteoclast numbers. Varying fixator configurations in older individuals did not alter the dominant effect of advanced age on callus tissue mineralization, unlike in their younger counterparts. Age-associated influences appeared independent from stability. This study illustrates the dominating role of osteoclastic activity in age-related impaired healing, while demonstrating the optimization of fixation parameters such as stiffness appeared to be less effective in influencing healing in aged individuals.

Effect of surgical approach on bone vascularisation, fracture and soft tissue healing : comparison of less invasive to open approach

Over the past ten years, minimally invasive plate osteosynthesis (MIPO) for the fixation of long bone fractures has become a clinically accepted method with good outcomes, when compared to the conventional open surgical approach (open reduction internal fixation, ORIF). However, while MIPO offers some advantages over ORIF, it also has some significant drawbacks, such as a more demanding surgical technique and increased radiation exposure. No clinical or experimental study to date has shown a difference between the healing outcomes in fractures treated with the two surgical approaches. Therefore, a novel, standardised severe trauma model in sheep has been developed and validated in this project to examine the effect of the two surgical approaches on soft tissue and fracture healing. Twenty four sheep were subjected to severe soft tissue damage and a complex distal femur fracture. The fractures were initially stabilised with an external fixator. After five days of soft tissue recovery, internal fixation with a plate was applied, randomised to either MIPO or ORIF. Within the first fourteen days, the soft tissue damage was monitored locally with a compartment pressure sensor and systemically by blood tests. The fracture progress was assessed fortnightly by x-rays. The sheep were sacrificed in two groups after four and eight weeks, and CT scans and mechanical testing performed. Soft tissue monitoring showed significantly higher postoperative Creatine Kinase and Lactate Dehydrogenase values in the ORIF group compared to MIPO. After four weeks, the torsional stiffness was significantly higher in the MIPO group (p=0.018) compared to the ORIF group. The torsional strength also showed increased values for the MIPO technique (p=0.11). The measured total mineralised callus volumes were slightly higher in the ORIF group. However, a newly developed morphological callus bridging score showed significantly higher values for the MIPO technique (p=0.007), with a high correlation to the mechanical properties (R2=0.79). After eight weeks, the same trends continued, but without statistical significance. In summary, this clinically relevant study, using the newly developed severe trauma model in sheep, clearly demonstrates that the minimally invasive technique minimises additional soft tissue damage and improves fracture healing in the early stage compared to the open surgical approach method.

A two-compartment mechanochemical model of the roles of transforming growth factor-beta and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor-beta (TGF-beta) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGF-beta and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGF-beta in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGF-beta significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures.

Development of a 3-dimensional human skin equivalent wound model for investigating novel wound healing therapies

Numerous difficulties are associated with the conduct of preclinical studies related to skin and wound repair. Use of small animal models such as rodents is not optimal because of their physiological differences to human skin and mode of wound healing. Although pigs have previously been used because of their human-like mode of healing, the expense and logistics related to their use also renders them suboptimal. In view of this, alternatives are urgently required to advance the field. The experiments reported herein were aimed at developing and validating a simple, reproducible, three-dimensional ex vivo de-epidermised dermis human skin equivalent wound model for the preclinical evaluation of novel wound therapies. Having established that the human skin equivalent wound model does in fact “heal," we tested the effect of two novel wound healing therapies. We also examined the utility of the model for studies exploring the mechanisms underpinning these therapies. Taken together the data demonstrate that these new models will have wide-spread application for the generation of fundamental new information on wound healing processes and also hold potential in facilitating preclinical optimization of dosage, duration of therapies, and treatment strategies prior to clinical trials.

A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique.

Decoupled trajectory planning for a submerged rigid body subject to dissipative and potential forces

This paper studies the practical but challenging problem of motion planning for a deeply submerged rigid body. Here, we formulate the dynamic equations of motion of a submerged rigid body under the architecture of differential geometric mechanics and include external dissipative and potential forces. The mechanical system is represented as a forced affine-connection control system on the configuration space SE(3). Solutions to the motion planning problem are computed by concatenating and reparameterizing the integral curves of decoupling vector fields. We provide an extension to this inverse kinematic method to compensate for external potential forces caused by buoyancy and gravity. We present a mission scenario and implement the theoretically computed control strategy onto a test-bed autonomous underwater vehicle. This scenario emphasizes the use of this motion planning technique in the under-actuated situation; the vehicle loses direct control on one or more degrees of freedom. We include experimental results to illustrate our technique and validate our method.

Controlling a submerged rigid body : a geometric analysis

In this paper we analyze the equations of motion of a submerged rigid body. Our motivation is based on recent developments done in trajectory design for this problem. Our goal is to relate some properties of singular extremals to the existence of decoupling vector fields. The ideas displayed in this paper can be viewed as a starting point to a geometric formulation of the trajectory design problem for mechanical systems with potential and external forces.

Mathematical modelling of chronic wound healing

Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.

Instability prolongs the chondral phase during bone healing in sheep

In this sheep study, we investigated the influence of fixation stability on the temporal and spatial distribution of tissues in the fracture callus. As the initial mechanical conditions have been cited as being especially important for the healing outcome, it was hypothesized that differences in the path of healing would be seen as early as the initial phase of healing. ----- ----- Sixty-four sheep underwent a mid-shaft tibial osteotomy that was treated with either a rigid or a semi-rigid external fixator. Animals were sacrificed at 2, 3, 6 and 9 weeks postoperatively and the fracture calluses were analyzed using radiological, biomechanical and histological techniques. Statistical comparison between the groups was performed using the Mann–Whitney U test for unpaired non-parametric data. ----- ----- In the callus of the tibia treated with semi-rigid fixation, remnants of the fracture haematoma remained present for longer, although new periosteal bone formation during early healing was similar in both groups. The mechanical competence of the healing callus at 6 weeks was inferior compared to tibiae treated with rigid fixation. Semi-rigid fixation resulted in a larger cartilage component of the callus, which persisted longer. Remodeling processes were initiated earlier in the rigid group, while new bone formation continued throughout the entire investigated period in the semi-rigid group. ----- ----- In this study, evidence is provided that less rigid fixation increased the time required for healing. The process of intramembranous ossification appeared during the initial stages of healing to be independent of mechanical stability. However, the delay in healing was related to a prolonged chondral phase.

Mechanical conditions in the initial phase of bone healing

Background: Bone healing is sensitive to the initial mechanical conditions with tissue differentiation being determined within days of trauma. Whilst axial compression is regarded as stimulatory, the role of interfragmentary shear is controversial. The purpose of this study was to determine how the initial mechanical conditions produced by interfragmentary shear and torsion differ from those produced by axial compressive movements. ----- ----- Methods: The finite element method was used to estimate the strain, pressure and fluid flow in the early callus tissue produced by the different modes of interfragmentary movement found in vivo. Additionally, tissue formation was predicted according to three principally different mechanobiological theories. ----- ----- Findings: Large interfragmentary shear movements produced comparable strains and less fluid flow and pressure than moderate axial interfragmentary movements. Additionally, combined axial and shear movements did not result in overall increases in the strains and the strain magnitudes were similar to those produced by axial movements alone. Only when axial movements where applied did the non-distortional component of the pressure–deformation theory influence the initial tissue predictions. ----- ----- Interpretation: This study found that the mechanical stimuli generated by interfragmentary shear and torsion differed from those produced by axial interfragmentary movements. The initial tissue formation as predicted by the mechanobiological theories was dominated by the deformation stimulus.

The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing : a finite element study based on sheep experiments

During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification.