Mathematical modelling of intramembranous bone formation during fracture healing

During fracture healing, many complex and cryptic interactions occur between cells and bio-chemical molecules to bring about repair of damaged bone. In this thesis two mathematical models were developed, concerning the cellular differentiation of osteoblasts (bone forming cells) and the mineralisation of new bone tissue, allowing new insights into these processes. These models were mathematically analysed and simulated numerically, yielding results consistent with experimental data and highlighting the underlying pattern formation structure in these aspects of fracture healing.

Association study of genes related to bone formation and resorption and the extent of radiographic change in ankylosing spondylitis

Objective: To identify genetic associations with severity of radiographic damage in ankylosing spondylitis (AS). Method: We studied 1537 AS cases of European descent; all fulfilled the modified New York Criteria. Radiographic severity was assessed from digitised lateral radiographs of the cervical and lumbar spine using the modified Stoke Ankylosing Spondylitis Spinal Score (mSASSS). A two-phase genotyping design was used. In phase 1, 498 single nucleotide polymorphisms (SNPs) were genotyped in 688 cases; these were selected to capture >90% of the common haplotypic variation in the exons, exon-intron boundaries, and 5 kb flanking DNA in the 5' and 3' UTR of 74 genes involved in anabolic or catabolic bone pathways. In phase 2, 15 SNPs exhibiting p<0.05 were genotyped in a further cohort of 830 AS cases; results were analysed both separately and in combination with the discovery phase data. Association was tested by contingency tables after separating the samples into 'mild' and 'severe' groups, defined as the bottom and top 40% by mSASSS, adjusted for gender and disease duration. Results: Experiment-wise association was observed with the SNP rs8092336 (combined OR 0.32, p=1.2×10-5), which lies within RANK (receptor activator of NF?B), a gene involved in osteoclastogenesis, and in the interaction between T cells and dendritic cells. Association was also found with the SNP rs1236913 in PTGS1 (prostaglandin-endoperoxide synthase 1, cyclooxygenase 1), giving an OR of 0.53 (p=2.6×10-3). There was no observed association between radiographic severity and HLA-B*27. Conclusions: These findings support roles for bone resorption and prostaglandins pathways in the osteoproliferative changes in AS.

Modelling the effects of bone fragment contact in fracture healing

The fracture healing process is modulated by the mechanical environment created by imposed loads and motion between the bone fragments. Contact between the fragments obviously results in a significantly different stress and strain environment to a uniform fracture gap containing only soft tissue (e.g. haematoma). The assumption of the latter in existing computational models of the healing process will hence exaggerate the inter-fragmentary strain in many clinically-relevant cases. To address this issue, we introduce the concept of a contact zone that represents a variable degree of contact between cortices by the relative proportions of bone and soft tissue present. This is introduced as an initial condition in a two-dimensional iterative finite element model of a healing tibial fracture, in which material properties are defined by the volume fractions of each tissue present. The algorithm governing the formation of cartilage and bone in the fracture callus uses fuzzy logic rules based on strain energy density resulting from axial compression. The model predicts that increasing the degree of initial bone contact reduces the amount of callus formed (periosteal callus thickness 3.1mm without contact, down to 0.5mm with 10% bone in contact zone). This is consistent with the greater effective stiffness in the contact zone and hence, a smaller inter-fragmentary strain. These results demonstrate that the contact zone strategy reasonably simulates the differences in the healing sequence resulting from the closeness of reduction.

Executive control of working memory in schizophrenia

There is considerable evidence that working memory impairment is a common feature of schizophrenia. The present study assessed working memory and executive function in 54 participants with schizophrenia, and a group of 54 normal controls matched to the patients on age, gender and estimated premorbid IQ, using traditional and newer measures of executive function and two dual tasks—Telephone Search with Counting and the Memory Span and Tracking Task. Results indicated that participants with schizophrenia were significantly impaired on all standardised measures of executive function with the exception of a composite measure of the Trail Making Test. Results for the dual task measures demonstrated that while the participants with schizophrenia were unimpaired on immediate digit span recall over a 2-min period, they recalled fewer digit strings and performed more poorly on a tracking task (box-crossing task) compared with controls. In addition, participants with schizophrenia performed more poorly on the tracking task when they were required to simultaneously recall digits strings than when they performed this task alone. Contrary to expectation, results of the telephone search task under dual conditions were not significantly different between groups. These results may reflect the insufficient complexity of the tone-counting task as an interference task. Overall, the present study showed that participants with schizophrenia appear to have a restricted impairment of their working memory system that is evident in tasks in which the visuospatial sketchpad slave system requires central executive control.

Runx2 overexpression in bone marrow stromal cells accelerates bone formation in critically-sized femoral defects

The repair of large non-unions in long bones remains a significant clinical problem due to high failure rates and limited tissue availability for auto- and allografts. Many cell-based strategies for healing bone defects deliver bone marrow stromal cells to the defect site to take advantage of the inherent osteogenic capacity of this cell type. However, many factors, including donor age and ex vivo expansion of the cells, cause bone marrow stromal cells to lose their differentiation ability. To overcome these limitations, we have genetically engineered bone marrow stromal cells to constitutively overexpress the osteoblast specific transcription factor Runx2. In the present study, we examined Runx2-modified bone marrow stromal cells, delivered via poly(caprolactone) scaffolds loaded with type I collagen meshes, in critically-sized segmental defects in rats compared to unmodified cells, cell-free scaffolds and empty defects. Runx2 expression in bone marrow stromal cells accelerated healing of critically-sized defects compared to unmodified bone marrow stromal cells and defects receiving cell-free treatments. These findings provide an accelerated method for healing large bone defects which may reduce recovery time and the need for external fixation of critically-sized defects.

Enhancing in vivo vascularized bone formation by cobalt chloride-treated bone marrow stromal cells in a tissue engineered periosteum model

The periosteum plays an indispensable role in both bone formation and bone defect healing. In this study we constructed an artificial in vitro periosteum by incorporating osteogenic differentiated bone marrow stromal cells (BMSCs) and cobalt chloride (CoCl(2))-treated BMSCs. The engineered periostea were implanted both subcutaneously and into skull bone defects in SCID mice to investigate ectopic and orthotopic osteogenesis and vascularization. After two weeks in subcutaneous and four weeks in bone defect areas, the implanted constructs were assessed for ectopic and orthotopic osteogenesis and vascularization by micro-CT, histomorphometrical and immunohistochemical methods. The results showed that CoCl(2) pre-treated BMSCs induced higher degree of vascularization and enhanced osteogenesis within the implants in both ectopic and orthotopic areas. This study provided a novel approach using BMSCs sourced from the same patient for both osteogenic and pro-angiogenic purposes in constructing tissue engineered periosteum to enhance vascularized osteogenesis.

Distributed control of gait for a humanoid robot

This paper describes a walking gait for a humanoid robot with a distributed control system. The motion for the robot is calculated in real time on a central controller, and sent over CAN bus to the distributed control system. The distributed control system loosely follows the motion patterns from the central controller, while also acting to maintain stability and balance. There is no global feedback control system; the system maintains its balance by the interaction between central gait and soft control of the actuators. The paper illustrates a straight line walking gait and shows the interaction between gait generation and the control system. The analysis of the data shows that successful walking can be achieved without maintaining strict local joint control, and without explicit global balance coordination.

Enhancing vascularized bone formation using tissue engineered periosteum

Objectives: The periosteum plays an indispensable role in both bone formation and bone defect healing. The aim of this project is to produce tissue engineered periosteum for bone defect treatment. Methods: In this study we constructed an artificial in vitro periosteum by incorporating osteogenic differentiated bone marrow stromal cells (BMSCs) and cobalt chloride (CoCl2)-treated BMSCs. The engineered periostea were implanted both subcutaneously and into skull bone defects in SCID mice to investigate ectopic and orthotopic osteogenesis and vascularisation. After two weeks in subcutaneous and four weeks in bone defect areas, the implanted constructs were assessed for ectopic and orthotopic osteogenesis and vascularisation by micro-CT, histomorphometrical and immunohistochemical methods. Results: The results showed that CoCl2 pre-treated BMSCs induced higher degree of vascularisation and enhanced osteogenesis within the implants in both ectopic and orthotopic areas. Conclusion: This study provided a novel approach using BMSCs sourced from the same patient for both osteogenic and pro-angiogenic purposes in constructing tissue engineered periosteum to enhance vascularized osteogenesis.

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.

Size and habit of mineral particles in bone and mineralized callus during bone healing in sheep

Bone healing is known to occur through the successive formation and resorption of various tissues with different structural and mechanical properties. To get a better insight into this sequence of events, we used environmental scanning electron microscopy (ESEM) together with scanning small-angle X-ray scattering (sSAXS) to reveal the size and orientation of bone mineral particles within the regenerating callus tissues at different healing stages (2, 3, 6, and 9 weeks). Sections of 200 µm were cut from embedded blocks of midshaft tibial samples in a sheep osteotomy model with an external fixator. Regions of interest on the medial side of the proximal fragment were chosen to be the periosteal callus, middle callus, intercortical callus, and cortex. Mean thickness (T parameter), degree of alignment (ρ parameter), and predominant orientation (ψ parameter) of mineral particles were deduced from resulting sSAXS patterns with a spatial resolution of 200 µm. 2D maps of T and ρ overlapping with ESEM images revealed that the callus formation occurred in two waves of bone formation, whereby a highly disordered mineralized tissue was deposited first, followed by a bony tissue with more lamellar appearance in the ESEM and where the mineral particles were more aligned, as revealed by sSAXS. As a consequence, degree of alignment and mineral particle size within the callus increased with healing time, whereas at any given moment there were structural gradients, for example, from periosteal toward the middle callus.

The course of bone healing is influenced by the initial shear fixation stability

Fracture healing is influenced by fixation stability and experimental evidence suggests that the initial mechanical conditions may determine the healing outcome. We hypothesised that mechanical conditions influence not only the healing outcome, but also the early phase of fracture healing. Additionally, it was hypothesised that decreased fixation stability characterised by an increased shear interfragmentary movement results in a delay in healing. Sixty-four sheep underwent a mid-shaft tibial osteotomy which 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 callus was analysed using radiological, biomechanical and histological techniques. The tibia treated with semi-rigid fixation showed inferior callus stiffness and quality after 6 weeks. At 9 weeks, the calluses were no longer distinguishable in their mechanical competence. The calluses at 9 weeks produced under rigid fixation were smaller and consisted of a reduced fibrous tissue component. These results demonstrate that the callus formation over the course of healing differed both morphologically and in the rate of development. In this study, we provide evidence that the course of healing is influenced by the initial fixation stability. The semi-rigid fixator did not result in delayed healing, but a less optimal healing path was taken. An upper limit of stability required for successful healing remains unknown, however a limit by which healing is less optimal has been determined.

Bone tissue engineering : reconstruction of critical sized segmental bone defects in the ovine tibia

Well-established therapies for bone defects are restricted to bone grafts which face significant disadvantages (limited availability, donor site morbidity, insufficient integration). Therefore, the objective was to develop an alternative approach investigating the regenerative potential of medical grade polycaprolactone-tricalcium phosphate (mPCL-TCP) and silk-hydroxyapatite (silk-HA) scaffolds. Critical sized ovine tibial defects were created and stabilized. Defects were left untreated, reconstructed with autologous bone grafts (ABG) and mPCL-TCP or silk-HA scaffolds. Animals were observed for 12 weeks. X-ray analysis, torsion testing and quantitative computed tomography (CT) analyses were performed. Radiological analysis confirmed the critical nature of the defects. Full defect bridging occurred in the autograft and partial bridging in the mPCL-TCP group. Only little bone formation was observed with silk-HA scaffolds. Biomechanical testing revealed a higher torsional moment/stiffness (p < 0.05) and CT analysis a significantly higher amount of bone formation for the ABG group when compared to the silk-HA group. No significant difference was determined between the ABG and mPCL-TCP groups. The results of this study suggest that mPCL-TCP scaffolds combined can serve as an alternative to autologous bone grafting in long bone defect regeneration. The combination of mPCL-TCP with osteogenic cells or growth factors represents an attractive means to further enhance bone formation.

Application of a human bone engineering platform to an in vitro and in vivo breast cancer metastasis model

Breast cancer in its advanced stage has a high predilection to the skeleton. Currently, treatment options of breast cancer-related bone metastasis are restricted to only palliative therapeutic modalities. This is due to the fact that mechanisms regarding the breast cancer celI-bone colonisation as well as the interactions of breast cancer cells with the bone microenvironment are not fully understood, yet. This might be explained through a lack of appropriate in vitro and in vivo models that are currently addressing the above mentioned issue. Hence the hypothesis that the translation of a bone tissue engineering platform could lead to improved and more physiological in vitro and in vivo model systems in order to investigate breast cancer related bone colonisation was embraced in this PhD thesis. Therefore the first objective was to develop an in vitro model system that mimics human mineralised bone matrix to the highest possible extent to examine the specific biological question, how the human bone matrix influences breast cancer cell behaviour. Thus, primary human osteoblasts were isolated from human bone and cultured under osteogenic conditions. Upon ammonium hydroxide treatment, a cell-free intact mineralised human bone matrix was left behind. Analyses revealed a similar protein and mineral composition of the decellularised osteoblast matrix to human bone. Seeding of a panel of breast cancer cells onto the bone mimicking matrix as well as reference substrates like standard tissue culture plastic and collagen coated tissue culture plastic revealed substrate specific differences of cellular behaviour. Analyses of attachment, alignment, migration, proliferation, invasion, as well as downstream signalling pathways showed that these cellular properties were influenced through the osteoblast matrix. The second objective of this PhD project was the development of a human ectopic bone model in NOD/SCID mice using medical grade polycaprolactone tricalcium phosphate (mPCL-TCP) scaffold. Human osteoblasts and mesenchymal stem cells were seeded onto an mPCL-TCP scaffold, fabricated using a fused deposition modelling technique. After subcutaneous implantation in conjunction with the bone morphogenetic protein 7, limited bone formation was observed due to the mechanical properties of the applied scaffold and restricted integration into the soft tissue of flank of NOD/SCID mice. Thus, a different scaffold fabrication technique was chosen using the same polymer. Electrospun tubular scaffolds were seeded with human osteoblasts, as they showed previously the highest amount of bone formation and implanted into the flanks of NOD/SCID mice. Ectopic bone formation with sufficient vascularisation could be observed. After implantation of breast cancer cells using a polyethylene glycol hydrogel in close proximity to the newly formed bone, macroscopic communication between the newly formed bone and the tumour could be observed. Taken together, this PhD project showed that bone tissue engineering platforms could be used to develop an in vitro and in vivo model system to study cancer cell colonisation in the bone microenvironment.