Numerical simulation of thermal bone necrosis during cementation of femoral prostheses

Abstract

The implant of a femoral prosthesis is a critical process because of the relatively high temperature values reached at the bone/cement interface during the cementation of the infibulum. In fact, the cement is actually a polymer that polymerizes in situ generating heat. Moreover, the conversion of monomer into polymer is never 100%; this is dangerous because of the toxicity of the monomer. In this paper, we present a 3-D axisymmetric mathematical model capable of taking into account both the geometry of the implant and the chemical/physical properties of the cement. This model, together with its numerical simulation, thus represents a useful tool to set up the optimal conditions for the new materials developed in this orthopaedic field. The real complex geometry is assumed to be a bone/cement/metallic system having cylindrical symmetry, thus allowing the model to be reduced to two space variables. The cementation process is described by the Fourier heat equation coupled with a suitable polymerization kinetics. The numerical approximation is accomplished by semi-implicit finite differences in time and finite elements in space with numerical quadrature. The full discrete scheme amounts to solve linear positive definite symmetric systems preceded by an elementwise algebraic computation. We present various numerical simulations which confirm some critical aspects of this orthopaedic fixing technique such as thermal bone necrosis and the presence of unreacted residual monomer.

Biocompatibility and other properties of acrylic bone cements prepared with antiseptic activators

“…They produced osseous necrosis and impair the blood stream through the bone tissue 15,16 mainly attributed to the high polymerization exotherm 17 and also to the leakage of toxic unreacted residuals. 18,19 Taking all these factors into account, the aim of the present study has been to improve the biocompatibility of acrylic bone cements by using activators of reduced toxicity without impairing mechanical properties. The activators used, DMOH and BZN, have lethal dose 50 values 3-4 times higher than that of DMT, and they are less cytotoxic against polymorphonuclear leucocytes.…”

Effect of cementing technique and cement type on thermal necrosis in hip resurfacing arthroplasty—a numerical study

“…To model the amount of heat generated during polymerization, we used the relation: da=dt ¼ 1=DH tot ðdH=dtÞ, 13 where da/dt is the polymerization rate (with a being the fraction of polymerized cement), DH tot is the maximum polymerization heat, and dH/dt is the rate of heat generation. The polymerization kinetics was expressed as da=dt ¼ KðTÞa m ð1ÀaÞ n , where a is the fraction of polymerized cement, m and n are fitting parameters, and K(T) is defined by the Arrhenius relation KðTÞ ¼ Z 0 expðÀE a =RTÞ.…”

“…8,11 Another factor affecting the temperature rise is the polymerization properties of the cement. 12,13 A fast polymerizing cement will cause a higher peak temperature that will last for a short time, while slower polymerizing cement will cause a lower peak temperature that will be maintained for a longer time. Both peak temperature and exposure time are important for the viability of the surrounding tissue.…”

Research of Mechanical Characteristics of Bone Tissues By Means Of the Developed Automated System of Medical Appointment

“…Для решения тепловых задач используется уравнение: Для спонгиозного слоя костной ткани значение теплопроводности было принято 0.26 Вт/(м·K), для эндопротеза из титана ВТ1-00 -6.7 Вт/(м·K), для цемента -0.17 Вт/(м·K), для окружающей среды костной ткани -0.0398 Вт/(м·K) [14][15][16][17].…”