Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how AIS affects bone density distribution within the vertebrae. Existing pre-operative CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. This study demonstrated that AIS patients have a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. To the best of our knowledge, the only previous studies of bone density distribution in AIS are those of Périé et al [1,2], who reported a coronal plane ‘mechanical migration’ of 0.54mm toward the concavity of the scoliotic curve in the lumbar apical vertebrae of 11 scoliosis patients. This is comparable to the value of 0.8mm (4%) in our study, especially since our patients had more severe scoliotic curves. From a bone adaptation perspective, these results suggest that the axial loading on the scoliotic spine is strongly asymmetric.

Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how scoliosis affects bone density distribution within the vertebrae. In this study, existing CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. Five key bone density profile measures were identified from each normalised bone density distribution, and multiple regression analysis was performed to explore the relationship between bone density distribution and patient demographics (age, height, weight, body mass index (BMI), skeletal maturity, time since Menarche, vertebral level, and scoliosis curve severity). Results showed a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. At the apical vertebra, mean bone density at the left side (concave) cortical shell was 23.5% higher than for the right (convex) cortical shell, and cancellous bone density along the central 60% of the lateral path from convex to concave increased by 13.8%. The centre of mass of the bone density profile at the thoracic curve apex was located 53.8% of the distance along the lateral path, indicating a shift of nearly 4% toward the concavity of the deformity. These lateral bone density gradients tapered off when moving away from the apical vertebra. Multi-linear regressions showed that the right cortical shell peak bone density is significantly correlated with skeletal maturity, with each Risser increment corresponding to an increase in mineral equivalent bone density of 4-5%. There were also statistically significant relationships between patient height, weight and BMI, and the gradient of cancellous bone density along the central 60% of the lateral path. Bone density gradient is positively correlated with weight, and negatively correlated with height and BMI, such that at the apical vertebra, a unit decrease in BMI corresponds to an almost 100% increase in bone density gradient.

Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

Background The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell-to-cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell-to-cell adhesion, despite the fact that cell-to-cell adhesion is thought to play an important role. Results We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell-to-cell adhesion strength, q, and cell proliferation rate, ?, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and ?. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell-to-cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D = 161 - 243 ?m2 hour-1, q = 0.3 - 0.5 (low to moderate strength) and ? = 0.0305 - 0.0398 hour-1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony. Conclusions Our systematic approach to identify the cell diffusivity, cell-to-cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Investigation of the effects of the fatty acid profile on fuel properties using a Multi-Criteria Decision Analysis

The structural features of fatty acids in biodiesel, including degree of unsaturation, percentage of saturated fatty acids and average chain length, influence important fuel properties such as cetane number, iodine value, density, kinematic viscosity, higher heating value and oxidation stability. The composition of fatty acid esters within the fuel should therefore be in the correct ratio to ensure fuel properties are within international biodiesel standards such as ASTM 6751 or EN 14214. This study scrutinises the influence of fatty acid composition and individual fatty acids on fuel properties. Fuel properties were estimated based on published equations, and measured according to standard procedure ASTM D6751 and EN 14214 to confirm the influences of the fatty acid profile. Based on fatty acid profile-derived calculations, the cetane number of the microalgal biodiesel was estimated to be 11.6, but measured 46.5, which emphasises the uncertainty of the method used for cetane number calculation. Multi-criteria decision analysis (MCDA), PROMETHEE-GAIA, was used to determine the influence of individual fatty acids on fuel properties in the GAIA plane. Polyunsaturated fatty acids increased the iodine value and had a negative influence on cetane number. Kinematic viscosity was negatively influenced by some long chain polyunsaturated fatty acids such as C20:5 and C22:6 and some of the more common saturated fatty acids C14:0 and C18:0. The positive impact of average chain length on higher heating value was also confirmed in the GAIA plane

Site and gender specificity of inheritance of bone mineral density

Differences in genetic control of BMD by skeletal sites and genders were examined by complex segregation analysis in 816 members of 147 families with probands with extreme low BMD. Spine BMD correlated more strongly in male-male comparisons and hip BMD in female-female comparisons, consistent with gender- and site-specificity of BMD heritability. Introduction: Evidence from studies in animals and humans suggests that the genetic control of bone mineral density (BMD) may differ at different skeletal sites and between genders. This question has important implications for the design and interpretation of genetic studies of osteoporosis. Methods: We examined the genetic profile of 147 families with 816 individuals recruited through probands with extreme low BMD (T-score < −2.5, Z-score < −2.0). Complex segregation analysis was performed using the Pedigree Analysis Package. BMD was measured by DXA at both lumbar spine (L1-L4) and femoral neck. Results: Complex segregation analysis excluded purely monogenic and environmental models of segregation of lumbar spine and femoral neck BMD in these families. Pure polygenic models were excluded at the lumbar spine when menopausal status was considered as a covariate, but not at the femoral neck. Mendelian models with a residual polygenic component were not excluded. These models were consistent with the presence of a rare Mendelian genotype of prevalence 3–19 %, causing high BMD at the hip and spine in these families, with additional polygenic effects. Total heritability range at the lumbar spine was 61–67 % and at the femoral neck was 44–67 %. Significant differences in correlation of femoral neck and lumbar spine BMD were observed between male and female relative pairs, with male-male comparisons exhibiting stronger lumbar spine BMD correlation than femoral neck, and female-female comparisons having greater femoral neck BMD correlation than lumbar spine. These findings remained true for parent-offspring correlations when menopausal status was taken into account. The recurrence risk ratio for siblings of probands of a Z-score < −2.0 was 5.4 at the lumbar spine and 5.9 at the femoral neck. Conclusions: These findings support gender- and site-specificity of the inheritance of BMD. These results should be considered in the design and interpretation of genetic studies of osteoporosis.