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.

A method for optimal fit of patient-specific fracture fixation plates

Anatomically pre-contoured fracture fixation plates are a treatment option for bone fractures. A well-fitting plate can be used as a tool for anatomical reduction of the fractured bone. However, recent studies showed that some plates fit poorly for many patients due to considerable shape variations between bones of the same anatomical site. Therefore, the plates have to be manually fitted and deformed by surgeons to fit each patient optimally. The process is time-intensive and labor-intensive, and could lead to adverse clinical implications such as wound infection or plate failure. This paper proposes a new iterative method to simulate the patient-specific deformation of an optimally fitting plate for pre-operative planning purposes. We further demonstrate the validation of the method through a case study. The proposed method involves the integration of four commercially available software tools, Matlab, Rapidform2006, SolidWorks, and ANSYS, each performing specific tasks to obtain a plate shape that fits optimally for an individual tibia and is mechanically safe. A typical challenge when crossing multiple platforms is to ensure correct data transfer. We present an example of the implementation of the proposed method to demonstrate successful data transfer between the four platforms and the feasibility of the method.

Effects of anticoagulants on outcome of femoral neck fracture surgery

PURPOSE To review records of 330 patients who underwent surgery for femoral neck fractures with or without preoperative anticoagulation therapy. METHODS Medical records of 235 women and 95 men aged 48 to 103 years (mean, 81.6; standard deviation [SD], 13.1) who underwent surgery for femoral neck fractures with or without preoperative anticoagulation therapy were reviewed. 30 patients were on warfarin, 105 on aspirin, 28 on clopidogrel, and 167 were controls. The latter 3 groups were combined as the non-warfarin group and compared with the warfarin group. Hospital mortality, time from admission to surgery, length of hospital stay, return to theatre, and postoperative complications (wound infection, deep vein thrombosis, and pulmonary embolism) were assessed. RESULTS The warfarin and control groups were significantly younger than the clopidogrel and aspirin groups (80.8 vs. 80.0 vs. 84.2 vs. 83.7 years, respectively, p<0.05). 81% of the patients underwent surgery within 48 hours of admission. The overall mean time from admission to surgery was 1.8 days; it was longer in the warfarin than the aspirin, clopidogrel, and control groups (3.3 vs. 1.8 vs. 1.6 vs. 1.6 days, respectively, p<0.001). The mean length of hospital stay was 17.5 (SD, 9.6; range, 3-54) days. The overall hospital mortality was 3.9%; it was 6.7% in the warfarin group, 3.8% in the aspirin group, 3.6% in the clopidogrel group, and 3.6% in the control group (p=0.80). Four patients returned to theatre for surgery: one in the warfarin group for washout of a haematoma, 2 in the aspirin group for repositioning of a mal-fixation and for debridement of wound infection, and one in the control group for debridement of wound infection. The warfarin group did not differ significantly from non-warfarin group in terms of postoperative complication rate (6.7% vs. 2.7%, p=0.228) and the rate of return to theatre (3.3% vs. 1%, p=0.318). CONCLUSION It is safe to continue aspirin and clopidogrel prior to surgical treatment for femoral neck fracture. The risk of delaying surgery outweighs the peri-operative bleeding risk.

Understanding the relationship between interfragmentary movement and callus growth in fracture healing: A novel computational approach

Introduction & Aims Optimising fracture treatments requires a sound understanding of relationships between stability, callus development and healing outcomes. This has been the goal of computational modelling, but discrepancies remain between simulations and experimental results. We compared healing patterns vs fixation stiffness between a novel computational callus growth model and corresponding experimental data. Hypothesis We hypothesised that callus growth is stimulated by diffusible signals, whose production is in turn regulated by mechanical conditions at the fracture site. We proposed that introducing this scheme into computational models would better replicate the observed tissue patterns and the inverse relationship between callus size and fixation stiffness. Method Finite element models of bone healing under stiff and flexible fixation were constructed, based on the parameters of a parallel rat femoral osteotomy study. An iterative procedure was implemented, to simulate the development of callus and its mechanical regulation. Tissue changes were regulated according to published mechano-biological criteria. Predictions of healing patterns were compared between standard models, with a pre-defined domain for callus development, and a novel approach, in which periosteal callus growth is driven by a diffusible signal. Production of this signal was driven by local mechanical conditions. Finally, each model’s predictions were compared to the corresponding histological data. Results Models in which healing progressed within a prescribed callus domain predicted that greater interfragmentary movements would displace early periosteal bone formation further from the fracture. This results from artificially large distortional strains predicted near the fracture edge. While experiments showed increased hard callus size under flexible fixation, this was not reflected in the standard models. Allowing the callus to grow from a thin soft tissue layer, in response to a mechanically stimulated diffusible signal, results in a callus shape and tissue distribution closer to those observed histologically. Importantly, the callus volume increased with increasing interfragmentary movement. Conclusions A novel method to incorporate callus growth into computational models of fracture healing allowed us to successfully capture the relationship between callus size and fixation stability observed in our rat experiments. This approach expands our toolkit for understanding the influence of different fixation strategies on healing outcomes.

A semiautomatic method to identify vertebral end plate lesions (Schmorl's nodes)

Background Context There are differences in definitions of end plate lesions (EPLs), often referred to as Schmorl’s nodes, that may, to some extent, account for the large range of reported prevalence (3.8 to 76%). Purpose To develop a technique to measure the size, prevalence and location of EPLs in a consistent manner. Study Design/Setting This study proposed a method using a detection algorithm which was applied to five adolescent females (average age 15.1 years, range 13.0 to 19.2 years) with idiopathic scoliosis (average major Cobb angle 60°, range 55 to 67°). Methods Existing low-dose, computed tomography scans were segmented semi-automatically to extract 3D morphology of each vertebral endplate. Any remaining attachments to the posterior elements of adjacent vertebrae or endplates were then manually sectioned. An automatic algorithm was used to determine the presence and position of EPLs. Results EPLs were identified in 15 of the 170 (8.8%) endplates analysed with an average depth of 3.1mm. 11/15 of the EPLs were seen in the lumbar spine. The algorithm was found to be most sensitive to changes in the minimum EPL gradient at the edges of the EPL. Conclusions This study describes an imaging analysis technique for consistent measurement of the prevalence, location and size of EPLs. The technique can be used to analyse large populations without observer errors in EPL definitions.

Genome-wide association study using extreme truncate selection identifies novel genes affecting bone mineral density and fracture risk

Osteoporotic fracture is a major cause of morbidity and mortality worldwide. Low bone mineral density (BMD) is a major predisposing factor to fracture and is known to be highly heritable. Site-, gender-, and age-specific genetic effects on BMD are thought to be significant, but have largely not been considered in the design of genome-wide association studies (GWAS) of BMD to date. We report here a GWAS using a novel study design focusing on women of a specific age (postmenopausal women, age 55-85 years), with either extreme high or low hip BMD (age- and gender-adjusted BMD z-scores of +1.5 to +4.0, n = 1055, or -4.0 to -1.5, n = 900), with replication in cohorts of women drawn from the general population (n = 20,898). The study replicates 21 of 26 known BMD-associated genes. Additionally, we report suggestive association of a further six new genetic associations in or around the genes CLCN7, GALNT3, IBSP, LTBP3, RSPO3, and SOX4, with replication in two independent datasets. A novel mouse model with a loss-of-function mutation in GALNT3 is also reported, which has high bone mass, supporting the involvement of this gene in BMD determination. In addition to identifying further genes associated with BMD, this study confirms the efficiency of extreme-truncate selection designs for quantitative trait association studies. © 2011 Duncan et al.

WNT16 influences bone mineral density, cortical bone thickness, bone strength, and osteoporotic fracture risk

We aimed to identify genetic variants associated with cortical bone thickness (CBT) and bone mineral density (BMD) by performing two separate genome-wide association study (GWAS) meta-analyses for CBT in 3 cohorts comprising 5,878 European subjects and for BMD in 5 cohorts comprising 5,672 individuals. We then assessed selected single-nucleotide polymorphisms (SNPs) for osteoporotic fracture in 2,023 cases and 3,740 controls. Association with CBT and forearm BMD was tested for ~2.5 million SNPs in each cohort separately, and results were meta-analyzed using fixed effect meta-analysis. We identified a missense SNP (Thr>Ile; rs2707466) located in the WNT16 gene (7q31), associated with CBT (effect size of -0.11 standard deviations [SD] per C allele, P = 6.2×10-9). This SNP, as well as another nonsynonymous SNP rs2908004 (Gly>Arg), also had genome-wide significant association with forearm BMD (-0.14 SD per C allele, P = 2.3×10-12, and -0.16 SD per G allele, P = 1.2×10-15, respectively). Four genome-wide significant SNPs arising from BMD meta-analysis were tested for association with forearm fracture. SNP rs7776725 in FAM3C, a gene adjacent to WNT16, was associated with a genome-wide significant increased risk of forearm fracture (OR = 1.33, P = 7.3×10-9), with genome-wide suggestive signals from the two missense variants in WNT16 (rs2908004: OR = 1.22, P = 4.9×10-6 and rs2707466: OR = 1.22, P = 7.2×10-6). We next generated a homozygous mouse with targeted disruption of Wnt16. Female Wnt16-/- mice had 27% (P<0.001) thinner cortical bones at the femur midshaft, and bone strength measures were reduced between 43%-61% (6.5×10-13<P<5.9×10-4) at both femur and tibia, compared with their wild-type littermates. Natural variation in humans and targeted disruption in mice demonstrate that WNT16 is an important determinant of CBT, BMD, bone strength, and risk of fracture. © 2012 Zheng et al.

Identifying vertebral end plate lesions (schmorl's nodes) using a semi-automatic method

INTRODUCTION There is a large range in the reported prevalence of end plate lesions (EPLs), sometimes referred to as Schmorl's nodes in the general population (3.8-76%). One possible reason for this large range is the differences in definitions used by authors. Previous research has suggested that EPLs may potentially be a primary disturbance of growth plates that leads to the onset of scoliosis. The aim of this study was to develop a technique to measure the size, prevalence and location of EPLs on Computed Tomography (CT) images of scoliosis patients in a consistent manner. METHODS A detection algorithm was developed and applied to measure EPLs for five adolescent females with idiopathic scoliosis (average age 15.1 years, average major Cobb 60°). In this algorithm, the EPL definition was based on the lesion depth, the distance from the edge of the vertebral body and the gradient of the lesion edge. Existing low-dose, CT scans of the patients' spines were segmented semi-automatically to extract 3D vertebral endplate morphology. Manual sectioning of any attachments between posterior elements of adjacent vertebrae and, if necessary, endplates was carried out before the automatic algorithm was used to determine the presence and position of EPLs. RESULTS EPLs were identified in 15 of the 170 (8.8%) endplates analysed with an average depth of 3.1mm. 73% of the EPLs were seen in the lumbar spines (11/15). A sensitivity study demonstrated that the algorithm was most sensitive to changes in the minimum gradient required at the lesion edge. CONCLUSION An imaging analysis technique for consistent measurement of the prevalence, location and size of EPLs on CT images has been developed. Although the technique was tested on scoliosis patients, it can be used to analyse other populations without observer errors in EPL definitions.

The vertebral venous system in healthy and scoliotic adolescent spines - a 3D MRI investigation

Introduction. The venous drainage system within vertebral bodies (VBs) has been well documented previously in cadaveric specimens. Advances in 3D imaging and image processing now allow for in vivo quantification of larger venous vessels, such as the basivertebral vein. Differences between healthy and scoliotic VB veins can therefore be investigated. Methods. 20 healthy adolescent controls and 21 AIS patients were recruited (with ethics approval) to undergo 3D MRI, using a 3 Tesla, T1-weighted 3D gradient echo sequence, resulting in 512 slices across the thoraco-lumbar spine, with a voxel size of 0.5x0.5x0.5mm. Using Amira Filament Editor, five transverse slices through the VB were examined simultaneously and the resulting observable vascular network traced. Each VB was assessed, and a vascular network recorded when observable. A local coordinate system was created in the centre of each VB and the vascular networks aligned to this. The length of the vascular network on the left and right sides (with a small central region) of the VB was calculated, and the spatial patterning of the networks assessed level-by-level within each subject. Results. An average of 6 (range 4-10) vascular networks, consistent with descriptions of the basivertebral vein, were identifiable within each subject, most commonly between T10-L1. Differences were seen in the left/right distribution of vessels in the control and AIS subjects. Healthy controls saw a percentage distribution of 29:18:53 across the left:centre:right regions respectively, whereas the AIS subjects had a slightly shifted distribution of 33:25:42. The control group showed consistent spatial patterning of the vascular networks across most levels, but this was not seen in the AIS group. Conclusion. Observation and quantification of the basivertebral vein in vivo is possible using 3D MRI. The AIS group lacked the spatial pattern repetition seen in the control group and minor differences were seen in the left/right distribution of vessels.

Variations in vertebral venous vasculature

INTRODUCTION Cadaveric studies have previously documented typical patterns of venous drainage within vertebral bodies (VBs) [1,2,3], comprised primarily of the basivertebral vein, a planar tree like structure at the mid-height of the VB. These studies, however, are limited in the number of samples available, and so have not examined any potential differences in this anatomy in conditions such as scoliosis. MRI is able to create 3D images of soft tissue structures in the spine, including the basivertebral vein without the use of contrast. As a non-invasive imaging technique this opens up the possibility of examining the venous network in multiple VBs within the same subject, in healthy controls as well as in subjects with abnormal anatomy such as adolescent idiopathic scoliosis (AIS). CONCLUSIONS High resolution MRI scans allow in vivo quantification of the vertebral venous system at multiple levels on healthy and scoliotic populations for the first time. The length of the basivertebral vein was seen to have a significant bias to the right hand side of the VB in both healthy and AIS adolescents. The spatial pattern of this vein showed large variations in branching both within and across individuals.

Fracture healing via periosteal callus formation requires macrophages for both initiation and progression of early endochondral ossification

The distribution, phenotype, and requirement of macrophages for fracture-associated inflammation and/or early anabolic progression during endochondral callus formation were investigated. A murine femoral fracture model [internally fixed using a flexible plate (MouseFix)] was used to facilitate reproducible fracture reduction. IHC demonstrated that inflammatory macrophages (F4/80+Mac-2+) were localized with initiating chondrification centers and persisted within granulation tissue at the expanding soft callus front. They were also associated with key events during soft-to-hard callus transition. Resident macrophages (F4/80+Mac-2neg), including osteal macrophages, predominated in the maturing hard callus. Macrophage Fas-induced apoptosis transgenic mice were used to induce macrophage depletion in vivo in the femoral fracture model. Callus formation was completely abolished when macrophage depletion was initiated at the time of surgery and was significantly reduced when depletion was delayed to coincide with initiation of early anabolic phase. Treatment initiating 5 days after fracture with the pro-macrophage cytokine colony stimulating factor-1 significantly enhanced soft callus formation. The data support that inflammatory macrophages were required for initiation of fracture repair, whereas both inflammatory and resident macrophages promoted anabolic mechanisms during endochondral callus formation. Overall, macrophages make substantive and prolonged contributions to fracture healing and can be targeted as a therapeutic approach for enhancing repair mechanisms. Thus, macrophages represent a viable target for the development of pro-anabolic fracture treatments with a potentially broad therapeutic window...

Risedronate in adults with osteogenesis imperfecta type I: Increased bone mineral density and decreased bone turnover, but high fracture rate persists

Summary Bisphosphonates can increase bone mineral density (BMD) in children with osteogenesis imperfecta (OI). In this study of adults with OI type I, risedronate increased BMD at lumbar spine (but not total hip) and decreased bone turnover. However, the fracture rate in these patients remained high. Introduction Intravenous bisphosphonates given to children with OI can increase BMD and reduce fracture incidence. Oral and/or intravenous bisphosphonates may have similar effects in adults with OI. We completed an observational study of the effect of risedronate in adults with OI type I. Methods Thirty-two adults (mean age, 39 years) with OI type I were treated with risedronate (total dose, 35 mg weekly) for 24 months. Primary outcome measures were BMD changes at lumbar spine (LS) and total hip (TH). Secondary outcome measures were fracture incidence, bone pain, and change in bone turnover markers (serum procollagen type I aminopropeptide (P1NP) and bone ALP). A meta-analysis of published studies of oral bisphosphonates in adults and children with OI was performed. Results Twenty-seven participants (ten males and seventeen females) completed the study. BMD increased at LS by 3.9% (0.815 vs. 0.846 g/cm 2, p=0.007; mean Z-score, -1.93 vs. -1.58, p=0.002), with no significant change at TH. P1NP fell by 37% (p=0.00041), with no significant change in bone ALP (p=0.15). Bone pain did not change significantly (p=0.6). Fracture incidence remained high, with 25 clinical fractures and 10 major fractures in fourteen participants (0.18 major fractures per person per year), with historical data of 0.12 fractures per person per year. The meta-analysis did not demonstrate a significant difference in fracture incidence in patients with OI treated with oral bisphosphonates. Conclusions Risedronate in adults with OI type I results in modest but significant increases in BMD at LS, and decreased bone turnover. However, this may be insufficient to make a clinically significant difference to fracture incidence.

Genetic determinants of bone density and fracture risk: State of the art and future directions

Context: Osteoporosis is a common, highly heritable condition that causes substantial morbidity and mortality, the etiopathogenesis of which is poorly understood. Genetic studies are making increasingly rapid progress in identifying the genes involved. Evidence Acquisition and Synthesis: In this review, we will summarize the current understanding of the genetics of osteoporosis based on publications from PubMed from the year 1987 onward. Conclusions: Most genes involved in osteoporosis identified to date encode components of known pathways involved in bone synthesis or resorption, but as the field progresses, new pathways are being identified. Only a small proportion of the total genetic variation involved in osteoporosis has been identified, and new approaches will be required to identify most of the remaining genes.

Genome-wide meta-analysis identifies 56 bone mineral density loci and reveals 14 loci associated with risk of fracture

Bone mineral density (BMD) is the most widely used predictor of fracture risk. We performed the largest meta-analysis to date on lumbar spine and femoral neck BMD, including 17 genome-wide association studies and 32,961 individuals of European and east Asian ancestry. We tested the top BMD-associated markers for replication in 50,933 independent subjects and for association with risk of low-trauma fracture in 31,016 individuals with a history of fracture (cases) and 102,444 controls. We identified 56 loci (32 new) associated with BMD at genome-wide significance (P < 5 × 10−8). Several of these factors cluster within the RANK-RANKL-OPG, mesenchymal stem cell differentiation, endochondral ossification and Wnt signaling pathways. However, we also discovered loci that were localized to genes not known to have a role in bone biology. Fourteen BMD-associated loci were also associated with fracture risk (P < 5 × 10−4, Bonferroni corrected), of which six reached P < 5 × 10−8, including at 18p11.21 (FAM210A), 7q21.3 (SLC25A13), 11q13.2 (LRP5), 4q22.1 (MEPE), 2p16.2 (SPTBN1) and 10q21.1 (DKK1). These findings shed light on the genetic architecture and pathophysiological mechanisms underlying BMD variation and fracture susceptibility.

Studies on elastic coupling parameters of fracture modes in orthotropic materials

The characterisation of cracks is usually done using the well known three basic fracture modes, namely opening, shearing and tearing modes. In isotropic materials these modes are uncoupled and provide a convenient way to define the fracture parameters. It is well known that these fracture modes are coupled in anisotropic materials. In the case of orthotropic materials also, coupling exists between the fracture modes, unless the crack plane coincides with one of the axes of orthotropy. The strength of coupling depends upon the orientation of the axes of orthotropy with respect to the crack plane and so the energy release rate components associated with each of the modes vary with crack orientation. The variation, of these energy release rate components with the crack orientation with respect to orthotropic axes, is analyzed in this paper. Results indicate that in addition to the orthotropic planes there exists other planes with reference to which fracture modes are uncoupled.