Mathematical model of mechanical testing of bone-implant (4.5 mm LCP) construct

Abstract

The study deals with the possibility of substituting time- and material-demanding mechanical testing of a bone defect fixation by mathematical modelling. Based on the mechanical model, a mathematical model of bone-implant construct stabilizing experimental segmental femoral bone defect (segmental ostectomy) in a miniature pig ex vivo model using 4.5 mm titanium LCP was created. It was subsequently computer-loaded by forces acting parallel to the long axis of the construct. By the effect of the acting forces the displacement vector sum of individual construct points occurred. The greatest displacement was noted in the end segments of the bone in close proximity to ostectomy and in the area of the empty central plate hole (without screw) at the level of the segmental bone defect. By studying the equivalent von Mises stress SIGMAeqv on LCP as part of the tested construct we found that the greatest changes of stress occur in the place of the empty central plate hole. The distribution of this strain was relatively symmetrical along both sides of the hole. The exceeding of the yield stress value and irreversible plastic deformations in this segment of LCP occurred at the acting of the force of 360 N. These findings are in line with the character of damage of the same construct loaded during its mechanic testing. We succeeded in creating a mathematical model of the bone-implant construct which may be further used for computer modelling of real loading of similar constructs chosen for fixation of bone defects in both experimental and clinical practice.

The study deals with the possibility of substituting time- and material-demanding mechanical testing of a bone defect fixation by mathematical modelling. Based on the mechanical model, a mathematical model of bone-implant construct stabilizing experimental segmental femoral bone defect (segmental ostectomy) in a miniature pig ex vivo model using 4.5 mm titanium LCP was created. It was subsequently computer-loaded by forces acting parallel to the long axis of the construct. By the effect of the acting forces the displacement vector sum of individual construct points occurred. The greatest displacement was noted in the end segments of the bone in close proximity to ostectomy and in the area of the empty central plate hole (without screw) at the level of the segmental bone defect. By studying the equivalent von Mises stress SIGMAeqv on LCP as part of the tested construct we found that the greatest changes of stress occur in the place of the empty central plate hole. The distribution of this strain was relatively symmetrical along both sides of the hole. The exceeding of the yield stress value and irreversible plastic deformations in this segment of LCP occurred at the acting of the force of 360 N. These findings are in line with the character of damage of the same construct loaded during its mechanic testing. We succeeded in creating a mathematical model of the bone-implant construct which may be further used for computer modelling of real loading of similar constructs chosen for fixation of bone defects in both experimental and clinical practice.