PEEK Biomaterials in Trauma, Orthopedic, and Spinal Implants

The flow of homogeneous fluids through porous media: analogies with other physical problems

Debris resulting from damage to the surface of polyethylene components of total joint replacements has previously been shown to contribute to long-term problems such as loosening and infection. Surface damage has been associated with fatigue processes due to stresses arising from contact between the metal and polyethylene components in these prostheses. In the present study, we used elasticity and finite-element solutions to determine these stresses for total hip replacements with head diameters of twenty-two and twenty-eight millimeters and for a condylar total knee replacement. We also examined the effect on these stresses of using carbon-fiber-reinforced polyethylene instead of plain polyethylene. Stresses associated with surface damage in the tibial component of the total knee replacement were much larger than those in the hip replacements. The analysis of contact stress as a function of thickness of the polyethylene insert for tibial components showed that a thickness of more than eight to ten millimeters should be maintained when possible. The contact stress in the tibial components was reduced most when the articulating surfaces were more conforming in the medial-lateral direction. Contact stresses were much less sensitive to changes in geometry in the anterior-posterior direction. For the hip components, the stresses were lower in the acetabular component of the twenty-eight-millimeter hip replacement than in the twenty-two-millimeter replacement. The use of carbon-fiber-reinforced polyethylene resulted in stresses that were higher by as much as 40 per cent. Because the contact area between articulating surfaces moves during flexion, portions of the surface will be subjected to cyclic stresses. The contact area for the knee replacements in flexion was smaller than for the hip replacements, and the range of the maximum principal stress was larger. Consequently, the combination of the higher stress and the moving contact area is more likely to cause surface damage due to fatigue in tibial components than in acetabular components, which is consistent with clinical observations.

The effect of conformity, thickness, and material on stresses in ultra-high molecular weight components for total joint replacement.

The purpose of this study was to examine the failure mechanisms and factors associated with failure of a nonmodular metal backed cemented tibial component. Out of 3152 total knee replacements done for osteoarthritis, 41 tibial components had been revised (1.3%). Four distinct failure mechanisms were

Tibial component failure mechanisms in total knee arthroplasty.

/pdf/encyclopedic-handbook-of-biomaterials-and-bioengineering-4yfiycworr.pdf

Encyclopedic handbook of biomaterials and bioengineering

Surface damage in polyethylene components for total joint replacement is associated with large contact stresses. An elasticity solution and finite element analyses were used to determine the influence of design parameters on the stresses due to contact in metal-backed components. For nearly conforming contact surfaces, it was found that the stresses in the plastic are very sensitive to clearance, that minimum plastic thickness of 4-6 mm should be maintained for metal-backed components, and that bonding the plastic to the metal backing reduces tensile stresses in the plastic at the edge of the contact zone.

The effect of conformity and plastic thickness on contact stresses in metal-backed plastic implants.

This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces. In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.

Timelike Minimal Surfaces via Loop Groups

Recent results using inverse scattering techniques interpret every solution φ(x, y) of the sine-Gordon equation as a nonlinear superposition of solutions along the axes x=0 and y=0. This has a well-known geometric interpretation, namely that every weakly regular surface of Gauss curvature K=−1, in arc length asymptotic line parametrization, is uniquely determined by the values φ(x, 0) and φ(0, y) of its coordinate angle along the axes. We introduce a generalized Weierstrass representation of pseudospherical surfaces that depends only on these values, and we explicitely construct the associated family of pseudospherical immersions corresponding to it.

Initial Value Problems of the Sine-Gordon Equation and Geometric Solutions

Our work is focused on certain theoretical aspects of non-linear non-Darcy flows in porous media, and their application in reservoir and hydraulic engineering. The goal of this paper is to develop a mathematically rigorous framework to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. Using fundamental geometric methods, we have proved the existence of a nonlinear scaling operator which relates constant mean curvature surfaces and time invariant pressure distribution graphs constrained by the Darcy–Forchheimer law. The hereby obtained properties of fast flows and their geometric interpretation can be used as analytical tools to evaluate important technological parameters in reservoir engineering.

Geometric framework for modeling nonlinear flows in porous media, and its applications in engineering

In [To], the author presented a method of constructing all weakly regular pseudospherical surfaces corresponding to given Weierstrass-type data. While the construction itself will appear later as a separate publication, this report contains a complete and detailed description of the Weierstrass representation for weakly regular surfaces with K = A1, in terms of moving frames and loop groups.

http://www.mathem.pub.ro/bjga/v07n2/B07-2-TODA.pdf

Magdalena Toda

Papers

The effect of conformity and plastic thickness on contact stresses in metal-backed plastic implants.

Timelike Minimal Surfaces via Loop Groups

Initial Value Problems of the Sine-Gordon Equation and Geometric Solutions

Geometric framework for modeling nonlinear flows in porous media, and its applications in engineering

Weierstrass-type Representation of Weakly Regular Pseudospherical Surfaces in Euclidean Space