Prediction of adjacent vertebral fracture risk associated with vertebroplasty : a computer-based simulation study

Vertebrplasty involved injecting cement into a fractured vertebra to provide stabilisation. There is clinical evidence to suggest however that vertebroplasty may be assocated with a higher risk of adjacent vertebral fracture; which may be due to the change in material properties of the post-procedure vertebra modifying the transmission of mechanical stresses to adjacent vertebrae.

An experimental and finite element investigation of the biomechanics of vertebral compression fractures

Osteoporosis is a disease characterized by low bone mass and micro-architectural deterioration of bone tissue, with a consequent increase in bone fragility and susceptibility to fracture. Osteoporosis affects over 200 million people worldwide, with an estimated 1.5 million fractures annually in the United States alone, and with attendant costs exceeding $10 billion dollars per annum. Osteoporosis reduces bone density through a series of structural changes to the honeycomb-like trabecular bone structure (micro-structure). The reduced bone density, coupled with the microstructural changes, results in significant loss of bone strength and increased fracture risk. Vertebral compression fractures are the most common type of osteoporotic fracture and are associated with pain, increased thoracic curvature, reduced mobility, and difficulty with self care. Surgical interventions, such as kyphoplasty or vertebroplasty, are used to treat osteoporotic vertebral fractures by restoring vertebral stability and alleviating pain. These minimally invasive procedures involve injecting bone cement into the fractured vertebrae. The techniques are still relatively new and while initial results are promising, with the procedures relieving pain in 70-95% of cases, medium-term investigations are now indicating an increased risk of adjacent level fracture following the procedure. With the aging population, understanding and treatment of osteoporosis is an increasingly important public health issue in developed Western countries. The aim of this study was to investigate the biomechanics of spinal osteoporosis and osteoporotic vertebral compression fractures by developing multi-scale computational, Finite Element (FE) models of both healthy and osteoporotic vertebral bodies. The multi-scale approach included the overall vertebral body anatomy, as well as a detailed representation of the internal trabecular microstructure. This novel, multi-scale approach overcame limitations of previous investigations by allowing simultaneous investigation of the mechanics of the trabecular micro-structure as well as overall vertebral body mechanics. The models were used to simulate the progression of osteoporosis, the effect of different loading conditions on vertebral strength and stiffness, and the effects of vertebroplasty on vertebral and trabecular mechanics. The model development process began with the development of an individual trabecular strut model using 3D beam elements, which was used as the building block for lattice-type, structural trabecular bone models, which were in turn incorporated into the vertebral body models. At each stage of model development, model predictions were compared to analytical solutions and in-vitro data from existing literature. The incremental process provided confidence in the predictions of each model before incorporation into the overall vertebral body model. The trabecular bone model, vertebral body model and vertebroplasty models were validated against in-vitro data from a series of compression tests performed using human cadaveric vertebral bodies. Firstly, trabecular bone samples were acquired and morphological parameters for each sample were measured using high resolution micro-computed tomography (CT). Apparent mechanical properties for each sample were then determined using uni-axial compression tests. Bone tissue properties were inversely determined using voxel-based FE models based on the micro-CT data. Specimen specific trabecular bone models were developed and the predicted apparent stiffness and strength were compared to the experimentally measured apparent stiffness and strength of the corresponding specimen. Following the trabecular specimen tests, a series of 12 whole cadaveric vertebrae were then divided into treated and non-treated groups and vertebroplasty performed on the specimens of the treated group. The vertebrae in both groups underwent clinical-CT scanning and destructive uniaxial compression testing. Specimen specific FE vertebral body models were developed and the predicted mechanical response compared to the experimentally measured responses. The validation process demonstrated that the multi-scale FE models comprising a lattice network of beam elements were able to accurately capture the failure mechanics of trabecular bone; and a trabecular core represented with beam elements enclosed in a layer of shell elements to represent the cortical shell was able to adequately represent the failure mechanics of intact vertebral bodies with varying degrees of osteoporosis. Following model development and validation, the models were used to investigate the effects of progressive osteoporosis on vertebral body mechanics and trabecular bone mechanics. These simulations showed that overall failure of the osteoporotic vertebral body is initiated by failure of the trabecular core, and the failure mechanism of the trabeculae varies with the progression of osteoporosis; from tissue yield in healthy trabecular bone, to failure due to instability (buckling) in osteoporotic bone with its thinner trabecular struts. The mechanical response of the vertebral body under load is highly dependent on the ability of the endplates to deform to transmit the load to the underlying trabecular bone. The ability of the endplate to evenly transfer the load through the core diminishes with osteoporosis. Investigation into the effect of different loading conditions on the vertebral body found that, because the trabecular bone structural changes which occur in osteoporosis result in a structure that is highly aligned with the loading direction, the vertebral body is consequently less able to withstand non-uniform loading states such as occurs in forward flexion. Changes in vertebral body loading due to disc degeneration were simulated, but proved to have little effect on osteoporotic vertebra mechanics. Conversely, differences in vertebral body loading between simulated invivo (uniform endplate pressure) and in-vitro conditions (where the vertebral endplates are rigidly cemented) had a dramatic effect on the predicted vertebral mechanics. This investigation suggested that in-vitro loading using bone cement potting of both endplates has major limitations in its ability to represent vertebral body mechanics in-vivo. And lastly, FE investigation into the biomechanical effect of vertebroplasty was performed. The results of this investigation demonstrated that the effect of vertebroplasty on overall vertebra mechanics is strongly governed by the cement distribution achieved within the trabecular core. In agreement with a recent study, the models predicted that vertebroplasty cement distributions which do not form one continuous mass which contacts both endplates have little effect on vertebral body stiffness or strength. In summary, this work presents the development of a novel, multi-scale Finite Element model of the osteoporotic vertebral body, which provides a powerful new tool for investigating the mechanics of osteoporotic vertebral compression fractures at the trabecular bone micro-structural level, and at the vertebral body level.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

Quantum Mechanics of Semantic Space

Presentation about information modelling and artificial intelligence, semantic structure, cognitive processing and quantum theory.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Adherence to nutrition supplements among patients with a fall-related lower limb fracture

Background The purpose of this study was to provide a detailed evaluation of adherence to nutrition supplements by patients with a lower limb fracture. Methods These descriptive data are from 49 nutritionally“ at-risk” patients aged 70+ years admitted to the hospital after a fall-related lower limb fracture and allocated to receive supplementation as part of a randomized, controlled trial. Supplementation commenced on day 7 and continued for 42 days. Prescribed volumes aimed to meet 45% of individually estimated theoretical energy requirements to meet the shortfall between literature estimates of energy intake and requirements. The supplement was administered by nursing staff on medication rounds in the acute or residential care settings and supervised through thrice-weekly home visits postdischarge. Results Median daily percent of the prescribed volume of nutrition supplement consumed averaged over the 42 days was 67% (interquartile range [IQR], 31–89, n = 49). There was no difference in adherence for gender, accommodation, cognition, or whether the supplement was self-administered or supervised. Twenty-three participants took some supplement every day, and a further 12 missed <5 days. For these 35 “nonrefusers,” adherence was 82% (IQR, 65–93), and they lost on average 0.7% (SD, 4.0%) of baseline weight over the 6 weeks of supplementation compared with a loss of 5.5% (SD, 5.4%) in the “refusers” (n = 14, 29%), p = .003. Conclusions We achieved better volume and energy consumption than previous studies of hip fracture patients but still failed to meet target supplement volumes prescribed to meet 45% of theoretical energy requirements. Clinicians should consider alternative methods of feeding such as a nasogastric tube, particularly in those patients where adherence to oral nutrition supplements is poor and dietary intake alone is insufficient to meet estimated energy requirements.

An epidemiological study of the relationship between time to surgery and health status for elderly patients with a hip fracture

A hip fracture causes permanent changes to life style for older people. Further, two important mortality indicators found post operatively for this group include, the time until surgery after fracture, and pre-operative health status prior to surgery, yet no research is available investigating relationships between time to surgery and health status. The researchers aimed to establish the health status risks for patients aged over 65 years with a non-pathological hip fracture to guide nursing care interventions. A prospective cohort design was used to investigate relationships between time to surgery and measures on pre-operative health status indicators including, skin integrity risk, vigor, mental state, bowel function and continence. Twenty-nine patients with a mean age in years of 81.93 (SD,9.49), were recruited. The mean number of hours from time 1 assessment to surgery was 52.72 (SD,58.35) and the range was 1 hour to 219 hours. At Time 2, the mean scores of vigor and skin integrity risk were significantly higher, indicating poorer health status. A change in health status occurred but possibly due to the small sample size it was difficult to relate this result to time. However the results informed preoperative care prior to surgery, for this group.

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.

An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

CYR61 (CCN1) protein expression during fracture healing in an ovine tibial model and its relation to the mechanical fixation stability

The formation of new blood vessels is a prerequisite for bone healing. CYR61 (CCN1), an extracellular matrix-associated signaling protein, is a potent stimulator of angiogenesis and mesenchymal stem cell expansion and differentiation. A recent study showed that CYR61 is expressed during fracture healing and suggested that CYR61 plays a significant role in cartilage and bone formation. The hypothesis of the present study was that decreased fixation stability, which leads to a delay in healing, would lead to reduced CYR61 protein expression in fracture callus. The aim of the study was to quantitatively analyze CYR61 protein expression, vascularization, and tissue differentiation in the osteotomy gap and relate to the mechanical fixation stability during the course of healing. A mid-shaft osteotomy of the tibia was performed in two groups of sheep and stabilized with either a rigid or semirigid external fixator, each allowing different amounts of interfragmentary movement. The sheep were sacrificed at 2, 3, 6, and 9 weeks postoperatively. The tibiae were tested biomechanically and histological sections from the callus were analyzed immunohistochemically with regard to CYR61 protein expression and vascularization. Expression of CYR61 protein was upregulated at the early phase of fracture healing (2 weeks), decreasing over the healing time. Decreased fixation stability was associated with a reduced upregulation of the CYR61 protein expression and a reduced vascularization at 2 weeks leading to a slower healing. The maximum cartilage callus fraction in both groups was reached at 3 weeks. However, the semirigid fixator group showed a significantly lower CYR61 immunoreactivity in cartilage than the rigid fixator group at this time point. The fraction of cartilage in the semirigid fixator group was not replaced by bone as quickly as in the rigid fixator group leading to an inferior histological and mechanical callus quality at 6 weeks and therefore to a slower healing. The results supply further evidence that CYR61 may serve as an important regulator of bone healing.