Morphometric measurement of the proximal tibia to design the tibial component of total knee arthroplasty for the Thai population

Purpose This study evaluates the morphology of the Thai proximal tibia based on three-dimensional (3D) models to design the tibial component. Methods The 3D models of 480 tibias were created using reverse engineering techniques from computed tomography imaging data obtained from 240 volunteers (120 males, 120 females; range 20–50 years). Based on 3D measurements, a digital ruler was used to measure the distance between the triangular points of the models. The morphometric parameters consisted of mediolateral length (ML), anteroposterior width (AP), medial anteroposterior width (MAP), lateral anteroposterior width (LAP), central to a medial length (CM), central to a lateral length (CL), medial anterior radius (MAR), lateral anterior radius (LAR), and tibial aspect ratio (AR). An independent t-test was performed for gender differences, and K-means clustering was used to find the optimum sizes of the tibial component with a correlation between ML length and AP width in Thai people. Results The average morphometric parameters of Thai proximal tibia, namely ML, AP, MAP, LAP, CM, and CL, were as follows: 72.52 ± 5.94 mm, 46.36 ± 3.84 mm, 49.22 ± 3.62 mm, 43.59 ± 4.05 mm, 14.29 ± 2.72 mm, and 15.28 ± 2.99 mm, respectively. The average of MAR, LAR, and AR was 24.43 ± 2.11 mm, 21.52 ± 2.00 mm, and 1.57 ± 0.08, respectively. All morphometric parameters in males were significantly higher than those of females. There was a difference between the Thai proximal tibia and other nationalities and a mismatch between the size of the commercial tibial component and the Thai knee. Using K-means clustering analysis, the recommended number of ML and AP is seven sizes for the practical design of tibial components to cover the Thai anatomy. Conclusion The design of the tibial component should be recommended to cover the anatomy of the Thai population. These data provide essential information for the specific design of Thai knee prostheses.

LOCATION AND STABILITY OF THE TRIANGULAR POINTS IN THE TRIAXIAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is generalized in the sense that the two primaries are considered as triaxial bodies. It was found that the locations of these points are affected by the triaxiality coefficients of the primaries and the eccentricity of orbits. Also, the stability regions depend on the involved perturbations. We also studied the periodic orbits in the vicinity of the triangular points.

Effects of Perturbations on the Stability of Equilibrium Points in the CR3BP with Luminous and Heterogeneous Spheroid Primaries

This paper studies the position and stability of equilibrium points in the circular restricted three-body problem (CR3BP) under the influence of small perturbations in the Coriolis and centrifugal forces when the primaries are radiating and heterogeneous oblate spheroids. It is seen that there exist five libration points as in the classical restricted three-body problem, three collinear Li(i=1,2,3) and two triangular Li(i= 4,5). It is also seen that the triangular points are no longer to form equilateral triangles with the primaries rather they form simple triangles with line joining the primaries. It is further observed that despite all perturbations the collinear points remain unstable while the triangular points are stable for 0 < µ < µc and unstable for µc ≤ µ ≤ ½, where µc is the critical mass ratio depending upon aforementioned parameters. It is marked that small perturbation in the Coriolis force, radiation and heterogeneous oblateness of the both primaries have destabilizing tendencies. Their numerical examination is also performed.

Unveiling Perturbing Effects of P-R Drag on Motion around Triangular Lagrangian Points of the Photogravitational Restricted Problem of Three Oblate Bodies

The perturbing effects of the Poynting-Robertson drag on motion of an infinitesimal mass around triangular Lagrangian points of the circular restricted three-body problem under small perturbations in the Coriolis and centrifugal forces when the three bodies are oblate spheroids and the primaries are emitters of radiation pressure, is the focus of this paper. The equations governing the dynamical system have been derived and locations of triangular Lagrangian points are determined. It is seen that the locations are influenced by the perturbing forces of centrifugal perturbation and the oblateness, radiation pressure and, P-R drag of the primaries. Using the software Mathematica, numerical analysis are carried out to demonstrate how the dynamical elements: mass ratio, oblateness, radiation pressure, P-R drag and centrifugal perturbation influence the positions of triangular equilibrium points, zero velocity surfaces and the stability. Our investigation reveals that, though the radiation pressure, oblateness and centrifugal perturbation decrease region of stability when motion is stable, however, they are not the influential forces of instability but the P-R drag. In the region when motion around the triangular points are stable an inclusion of the P-R drag of the bigger primary even by an almost negligible value of 1.04548*10-9 overrides other effect and changes stability to instability. Hence, we conclude that the P-R drag is a strong perturbing force which changes stability to instability and motion around triangular Lagrangian points remain unstable in the presence of the P-R drag.

Effect of Oblateness of the Secondary up to J4 on L4,5 in the Photogravitaional ER3BP

In a synodic-pulsating dimensionless coordinate, with a luminous primary and an oblate secondary, we examine the effects of radiation pressure, oblateness (quadruple and octupolar i.e. ) and eccentricity of the orbits of the primaries on the triangular points in the ER3BP. have been shown to disturb the motion of an infinitesimal body and particularly has significant effects on a satellite’s secular perturbation and orbital precessions. The influence of these parameters on the triangular points of Zeta Cygni, 54 Piscium and Procyon A/B are highlighted in this study. Triangular points are stable in the range and their stability is affected by said parameters.

Motion around triangular points in the restricted three-body problem with radiating heterogeneous primaries surrounded by a belt

The present paper studies the locations and linear stability of the triangular equilibrium points when both primaries are radiating and considered as heterogeneous spheroid with three layers of different densities. Additionally, we include the effects of small perturbations in the Coriolis and centrifugal forces and potential from a belt (circumbinary disc). It is observed that the positions of the triangular equilibrium points are substantially affected by all parameters (except a perturbation in Coriolis force) involved in the system.The stabilty of motion is found only when $$0 < \mu < \mu_{c}$$ 0 < μ < μ c , where $$\mu_{c}$$ μ c is the critical mass value which depends on the combined effect of radiation pressures and heterogeneity of the primaries, small perturbations and the potential from a belt.It is also seen that the Coriolis force and the belt have stabilizing effect,while the centrifugal force, radiation and heterogeineity of the primaries have destabilizing behaviour.The net effect is that the size of the region of stability decreases when the value of these parameters increases where $$\mu$$ μ is the mass ratio and $$k_{1} ,k_{2}$$ k 1 , k 2 characterize heterogeneity of both primaries. A practical application of this model could be the study of motion of a dust grain near the heterogeneous and luminous binary stars surrounded by a belt.Finally, we carried out and discuss numerical experiments aiming at computing the positions of triangular points and critical masses of three binary systems: Archid, Xi Booties and Kruger 60.

Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

In this paper, we present a comprehensive analytical study on the perturbed restricted three bodies problem. We formulate the equations of motion of this problem, in the event of the asteroids belt perturbation. We find the locations of equilibrium points (collinear and triangular points) and analysis their linear stability. Furthermore the periodic orbits around both collinear and triangular points are found.