Error estimation for the automated multi‐level substructuring method

In this study, we propose an effective method to estimate the reliability of finite element models reduced by the automated multi‐level substructuring (AMLS) method. The proposed error estimation method can accurately predict relative eigenvalue errors in reduced finite element models. A new, enhanced transformation matrix for the AMLS method is derived from the original transformation matrix by properly considering the contribution of residual substructural modes. The enhanced transformation matrix is an important prerequisite to develop the error estimation method. Adopting the basic concept of the error estimation method recently developed for the Craig–Bampton method, an error estimation method is developed for the AMLS method. Through various numerical examples, we demonstrate the accuracy of the proposed error estimation method and explore its computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison of osteoconductivity and absorbability of beta-tricalcium phosphate and hydroxyapatite in clinical scenario of opening wedge high tibial osteotomy

The purpose of this study was to compare the osteoconductivity, and absorbability of hydroxyapatite or beta-tricalcium phosphate in clinical scenario of opening wedge high tibial osteotomy Total 41 knees of 40 patients with follow up period of more than 1 year were enrolled. These patients were divided into two groups, Group I (22 knees, 21 patients) used hydroxyapatite and Group II (19 knees, 19 patients) used beta-tricalcium phosphate as a substitute in the opening gap. According to proven method, the osteoconductivity was assessed radiographically by the extent of new bone formation at osteotomy space and absorbability was evaluated by measuring the area occupied by substitute at immediate postoperative, postoperative 6 months and 1 year. Regarding preoperative demographic data, no significant differences were found between two groups. No statistically significant differences were found between two groups regarding lower limb alignment (mechanical femorotibial angle, weight-bearing line%) and posterior tibial slope at postoperative and final follow up radiographs. Concerning the osteoconductivity, there were no significant differences between two groups in any zone. However, the absorption rate was significantly greater in the Group II than in Group I at 6 months (Group I: 13.7?±?6.8, group II: 35.3?±?15.8, P?=?0.001) and 1 year (Group I: 24.2?±?6.3, Group II: 49.6?±?14.3, P?<?0.0001). The complications related to bone substitutes were not observed. Both hydroxyapatite and beta-tricalcium phosphate showed satisfactory gap healing without complications and can be successfully used as alternative healing materials in opening wedge high tibial osteotomy. Our study showed that beta-tricalcium phosphate has superior absorbability than hydroxyapatite. But osteoconductivity showed no significant difference.