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.

Nonlinear mechanical property of tracheal cartilage: A theoretical and experimental study

Background: Despite being the stiffest airway of the bronchial tree, the trachea undergoes significant deformation due to intrathoracic pressure during breathing. The mechanical properties of the trachea affect the flow in the airway and may contribute to the biological function of the lung. Method: A Fung-type strain energy density function was used to investigate the nonlinear mechanical behavior of tracheal cartilage. A bending test on pig tracheal cartilage was performed and a mathematical model for analyzing the deformation of tracheal cartilage was developed. The constants included in the strain energy density function were determined by fitting the experimental data. Result: The experimental data show that tracheal cartilage is a nonlinear material displaying higher strength in compression than in tension. When the compression forces varied from -0.02 to -0.03 N and from -0.03 to -0.04 N, the deformation ratios were 11.03±2.18% and 7.27±1.59%, respectively. Both were much smaller than the deformation ratios (20.01±4.49%) under tension forces of 0.02 to 0.01 N. The Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. It underestimates the stability of trachea by exaggerating the displacement in compression. This study may improve our understanding of the nonlinear behavior of tracheal cartilage and it may be useful for the future study on tracheal collapse behavior under physiological and pathological conditions.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.