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.

Comparison of eight published lumbar spine finite element models

Due to its ability to represent intricate systems with material nonlinearities as well as irregular loading, boundary, geometrical and material domains, the finite element (FE) method has been recognized as an important computational tool in spinal biomechanics. Current FE models generally account for a single distinct spinal geometry with one set of material properties despite inherently large inter-subject variability. The uncertainty and high variability in tissue material properties, geometry, loading and boundary conditions has cast doubt on the reliability of their predictions and comparability with reported in vitro and in vivo values. A multicenter study was undertaken to compare the results of eight well-established models of the lumbar spine that have been developed, validated and applied for many years. Models were subjected to pure and combined loading modes and their predictions were compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges; their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with previously published median in vitro values. However, the ranges of predictions were larger and exceeded the in vitro ranges, especially for facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with in vivo values. The simulations yielded median facet joint forces of 0 N in flexion, 38 N in extension, 14 N in lateral bending and 60 N in axial rotation that could not be validated due to the paucity of in vivo facet joint forces. In light of high inter-subject variability, one must be cautious when generalizing predictions obtained from one deterministic model. This study demonstrates however that the predictive power increases when FE models are combined together. The median of individual numerical results can hence be used as an improved tool in order to estimate the response of the lumbar spine.

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.

Compressive and shear force generated in the lumbar spine of female rowers

Rowers have and accrue greater lumbar spine bone mineral density (BMD) associated with mechanical loading produced during rowing. The aim of this study was to estimate the mechanical loading generated at the lumbar spine (LS) that is apparently providing an osteogenic benefit. The cohort comprised 14 female rowers (average age: 19.7yrs; height: 170.9 cm, weight: 59.5 kg) and 14 female matched controls (average age: 20.9 m yrs; height: 167.5 cm; weight: 58.1 kg). BMD was assessed using the Hologic QDR 2000+ bone densitometer, indicating higher lumbar spine BMD in the rowers compared to the control subjects (1,069 +/- 0.1 vs. 1,027 +/- 0.1 g/cm2). No significant difference existed for BMD at any other site. All rowers performed a six-minute simulated race on a Concept II rowing ergometer. Mechanical loading generated at the lumbar spine during this task was assessed using a two-dimensional model of the spine, enabling the calculation of the compressive and shear forces at L4/L5. The shear force was the joint reaction force perpendicular to the spine at the L4/L5 joint. Peak compressive and shear force at the lumbar spine of the rowers were 2,694 +/- 609 (N) and 660 +/- 117 (N), respectively. Peak compressive force at the LS relative to body weight was 4.6 times body weight. The literature would suggest that forces of this magnitude, generated at the LS during maximal rowing, may be contributing to the site specific higher LS BMD found in the rowers.

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.

Development of a new ultrasound-based system for tracking motion of the human lumbar spine: Reliability, stability and repeatability during forward bending movement trials

The aim of this study was to develop a new method for quantifying intersegmental motion of the spine in an instrumented motion segment L4–L5 model using ultrasound image post-processing combined with an electromagnetic device. A prospective test–retest design was employed, combined with an evaluation of stability and within- and between-day intra-tester reliability during forward bending by 15 healthy male patients. The accuracy of the measurement system using the model was calculated to be ± 0.9° (standard deviation = 0.43) over a 40° range and ± 0.4 cm (standard deviation = 0.28) over 1.5 cm. The mean composite range of forward bending was 15.5 ± 2.04° during a single trial (standard error of the mean = 0.54, coefficient of variation = 4.18). Reliability (intra-class correlation coefficient = 2.1) was found to be excellent for both within-day measures (0.995–0.999) and between-day measures (0.996–0.999). Further work is necessary to explore the use of this approach in the evaluation of biomechanics, clinical assessments and interventions.

Functional and structural of the erector spinae muscle during isometric lumbar extension

Study Design Cross-sectional study. Objectives To compare erector spinae (ES) muscle fatigue between chronic non-specific lower back pain (CNLBP) sufferers and healthy subjects from a biomechanical perspective during fatiguing isometric lumbar extensions. Background Paraspinal muscle maximal contraction and fatigue are used as a functional predictor for disabilities. The simplest method to determine muscle fatigue is by evaluating the evolution during specific contractions, such as isometric contractions. There are no studies that evaluate the evolution of the ES muscle during fatiguing isometric lumbar extensions and analyse functional and architectural variables. Methods In a pre-calibrated system, participants performed a maximal isometric extension of the lumbar spine for 5 and 30 seconds. Functional variables (torque and muscle activation) and architecture (pennation angle and muscle thickness) were measured using a load cell, surface electromyography and ultrasound, respectively. The results were normalised and a reliability study of the ultrasound measurement was made. Results: The ultrasound measurements were highly reliable, with Cronbach’s alpha values ranging from 0.951 0.981. All measured variables shown significant differences before and after fatiguing isometric lumbar extension. Conclusion During a lumbar isometric extension test, architecture and functional variables of the ES muscle could be analised using ultrasound, surface EMG and load cell. In adition, during an endurance test, ES muscle suffers an acute effect on architectural and functional variables.

Ability to discriminate between healthy and low back pain sufferers using ultrasound during maximum lumbar extension

Objective To analyze the ability to discriminate between healthy individuals and individuals with chronic nonspecific low back pain (CNLBP) by measuring the relation between patient-reported outcomes and objective clinical outcome measures of the erector spinae (ES) muscles using an ultrasound during maximal isometric lumbar extension. Design Cross-sectional study with screening and diagnostic tests with no blinded comparison. Setting University laboratory. Participants Healthy individuals (n=33) and individuals with CNLBP (n=33). Interventions Each subject performed an isometric lumbar extension. With the variables measured, a discriminate analysis was performed using a value ≥6 in the Roland and Morris disability questionnaire (RMDQ) as the grouping variable. Then, a logistic regression with the functional and architectural variables was performed. A new index was obtained from each subject value input in the discriminate multivariate analysis. Main Outcome Measures Morphologic muscle variables of the ES muscle were measured through ultrasound images. The reliability of the measures was calculated through intraclass correlation coefficients (ICCs). The relation between patient-reported outcomes and objective clinical outcome measures was analyzed using a discriminate function from standardized values of the variables and an analysis of the reliability of the ultrasound measurement. Results The reliability tests show an ICC value >.95 for morphologic and functional variables. The independent variables included in the analysis explained 42% (P=.003) of the dependent variable variance. Conclusions The relation between objective variables (electromyography, thickness, pennation angle) and a subjective variable (RMDQ ≥6) and the capacity of this relation to identify CNLBP within a group of healthy subjects is moderate. These results should be considered by clinicians when treating this type of patient in clinical practice.

Comparison of silicate-substituted calcium phosphate (Actifuse®) with rhBMP-2 (Infuse®) in posterolateral instrumented lumbar fusion

Study Design This was a randomised controlled trial in patients with degenerative disc disease (DDD) who underwent instrumented posterolateral lumbar fusion (PLF) surgery. Objective The aim of this study was to assess the efficacy of the bone grafting substitute, silicate-substituted calcium phosphate (SiCaP) compared with bone morphogenetic protein (rhBMP-2) and to evaluate clinical outcomes over a period of two years. Methods Patients undergoing PLF surgery for DDD at a single centre were recruited and randomised to one of two groups; SiCaP (n=9) or rhBMP-2 (n=10). One patient withdrew prior to randomisation and another from the rhBMP-2 group after randomisation. The radiological and clinical outcomes were examined and compared. Fusion was assessed at 12 months with computed tomography (CT) and plain radiographs. Clinical outcomes were evaluated by recording measures of pain, quality of life, disability and neurological status from six weeks to two years postoperatively. Results In the SiCaP and rhBMP-2 groups, fusion was observed in 9/9 and 8/9 patients respectively. Pain and disability scores were reduced and quality of life increased in both groups. Leg pain, disability and satisfaction scores were similar between the groups at each postoperative time point, however, back pain was less at six weeks and quality of life was higher at six months in the SiCaP group than the rhBMP-2 group. Conclusions SiCaP and rhBMP-2 were comparable in terms of achieving successful bone growth and fusion. Both groups similarly alleviated pain and improved quality of life, neurological, satisfaction and return to work outcomes following PLF surgery.

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.

Genome-wide association study for radiographic vertebral fractures: A potential role for the 16q24 BMD locus

Vertebral fracture risk is a heritable complex trait. The aim of this study was to identify genetic susceptibility factors for osteoporotic vertebral fractures applying a genome-wide association study (GWAS) approach. The GWAS discovery was based on the Rotterdam Study, a population-based study of elderly Dutch individuals aged >55years; and comprising 329 cases and 2666 controls with radiographic scoring (McCloskey-Kanis) and genetic data. Replication of one top-associated SNP was pursued by de-novo genotyping of 15 independent studies across Europe, the United States, and Australia and one Asian study. Radiographic vertebral fracture assessment was performed using McCloskey-Kanis or Genant semi-quantitative definitions. SNPs were analyzed in relation to vertebral fracture using logistic regression models corrected for age and sex. Fixed effects inverse variance and Han-Eskin alternative random effects meta-analyses were applied. Genome-wide significance was set at p<5×10-8. In the discovery, a SNP (rs11645938) on chromosome 16q24 was associated with the risk for vertebral fractures at p=4.6×10-8. However, the association was not significant across 5720 cases and 21,791 controls from 14 studies. Fixed-effects meta-analysis summary estimate was 1.06 (95% CI: 0.98-1.14; p=0.17), displaying high degree of heterogeneity (I2=57%; Qhet p=0.0006). Under Han-Eskin alternative random effects model the summary effect was significant (p=0.0005). The SNP maps to a region previously found associated with lumbar spine bone mineral density (LS-BMD) in two large meta-analyses from the GEFOS consortium. A false positive association in the GWAS discovery cannot be excluded, yet, the low-powered setting of the discovery and replication settings (appropriate to identify risk effect size >1.25) may still be consistent with an effect size <1.10, more of the type expected in complex traits. Larger effort in studies with standardized phenotype definitions is needed to confirm or reject the involvement of this locus on the risk for vertebral fractures.

Suggestive linkage of 2p22-25 and 11q12-13 with low bone mineral density at the lumbar spine in the Irish population

Osteoporosis is a disease characterized by low bone mineral density (BMD) and poor bone quality. Peak bone density is achieved by the third decade of life, after which bone is maintained by a balanced cycle of bone resorption and synthesis. Age-related bone loss occurs as the bone resorption phase outweighs the bone synthesis phase of bone metabolism. Heritability accounts for up to 90% of the variability in BMD. Chromosomal loci including 1p36, 2p22-25, 11q12-13, parathyroid hormone receptor type 1 (PTHR1), interleukin-6 (IL-6), interleukin 1 alpha (IL-1α) and type II collagen A1/vitamin D receptor (COL11A1/VDR) have been linked or shown suggestive linkage with BMD in other populations. To determine whether these loci predispose to low BMD in the Irish population, we investigated 24 microsatellite markers at 7 chromosomal loci by linkage studies in 175 Irish families of probands with primary low BMD (T-score ≤ -1.5). Nonparametric analysis was performed using the maximum likelihood variance estimation and traditional Haseman-Elston tests on the Mapmaker/Sibs program. Suggestive evidence of linkage was observed with lumbar spine BMD at 2p22-25 (maximum LOD score 2.76) and 11q12-13 (MLS 2.55). One region, 1p36, approached suggestive linkage with femoral neck BMD (MLS 2.17). In addition, seven markers achieved LOD scores > 1.0, D2S149, D11S1313, D11S987, D11S1314 including those encompassing the PTHR1 (D3S3559, D3S1289) for lumbar spine BMD and D2S149 for femoral neck BMD. Our data suggest that genes within a these chromosomal regions are contributing to a predisposition to low BMD in the Irish population.

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...