有限元素生物力學分析:表面網格最佳化及納氏漏斗胸手術之力學分析

Abstract

本論文之目的，在於研究有限元素法於生物力學分析上之應用，研究內容包括了表面網格最佳化以及納氏漏斗胸手術之生物力學分析。對於生物力學分析研究而言，建立一個合適之有限元素網格，是一個非常重要的步驟，其中又以表面網格的建立最為重要，一般而言，表面網格乃建立於預先定義之模型表面上，但對於大部分之生物力學分析研究而言，其分析模型通常經由量測或斷層掃描資料建立而成，因此無法利用數學模式完整定義整個模型表面，例如脛骨、脊椎以及胸腔模型等研究，為了改善上述分析模型之表面網格品質，我們提出了一套表面網格最佳化方法，其中包括了三角形網格與四邊形網格之轉換、C1連續之表面方程式建立，以及微基因演算法表面網格平滑化處理，本方法可應用於模型表面網格之最佳化，而不需預先提供模型之表面方程式，因此可適用於生物力學分析模型之應用。 漏斗胸是一項常見的先天性胸廓畸形，其病症為患者之胸骨，以及肋軟骨向患者體內凹陷，而於患者前胸形成漏斗狀之變形。納氏手術為目前常用之漏斗胸微創手術，它的手術方式為，將矯形金屬板植入於漏斗胸患者之胸骨凹陷處，將患者前胸之凹陷處頂高，以達到矯正之目的。在手術過程當中，患者之胸廓會隨著胸骨之頂高而變形，然而，經由該變形所引發之應力，也同時產生並作用於患者胸腔骨骼上。在本論文中，我們利用半自動化方式，建立了五個漏斗胸患者之胸腔模型，並分析它們在經過納氏手術矯正之後，患者胸腔骨架上之應力與應變之分佈情形。根據分析結果發現，患者於手術後，其背部靠近脊椎附近，有大量的應力產生，其中大多集中在第三到第七對肋骨上，這個現象可用來解釋，某些漏斗胸病患，於納氏手術後產生背痛之原因，並且可能與少部分患者，於手術後發生脊柱側彎之原因有關。此外，我們利用有限元素分析結果，建立兩套肺容積估測方法，藉由量測患者胸腔容積之變化，可用來估測肺容積之變化，根據量 測結果發現，這五位患者之胸腔容積，分別增加了2.72%到8.88%不等的容積。

The purposes of this thesis are focused on the finite element biomechanical analysis, which contains surface mesh optimization and biomechanical analysis of Nuss pectus excavatum repair. For a biomechanical research, one of the significant problems is to create an appropriate finite element volume mesh and the surface mesh generation plays a crucial role in finite element volume mesh generation. Usually surface meshing methods in three dimensions generate meshes relying on prescribed patch interpolation. For some biomechanical researches, the analyzed models, which were usually reconstructed based on measured data or computer tomography scan data, do not have well defined surface function, such as tibia, spine and rib cage models. In order to improve the surface mesh quality of the reconstructed geometrical models, an approach of surface meshing optimization procedure is developed, which consists of a conversion scheme for primary triangular and quadrilateral surface meshes, a C1 continuous surface function reconstruction and a micro-genetic algorithm (MGA) mesh smoothing procedure. This procedure performs surface mesh optimization without pre-defined surface function. The practical cases are given to demonstrate its successful performance and its versatility. Pectus excavatum (PE) is one of the commonly found congenital chest wall deformity. It is characterized by depression of the sternum and the lower costal cartilages, producing a concave appearance to the anterior chest wall. The Nuss procedure is a minimal invasion technique that corrects pectus excavatum by inserting a pre-bent bar under the depressed sternum to elevate the sternum. After the Nuss procedure, the chest wall is deformed with the raised sternum and a reasonable amount of stress is induced on the chest wall. In this thesis, five patient-specific finite element models were generated to analyze the stress and the strain distributions induced on the chest wall after the Nuss procedure. The finite element models were reconstructed by applying a semiautomatic procedure based on patients’ computer tomography slices. The simulation results show that there are greater stresses occurred over the back and concentrated on the third through seventh ribs bilaterally, near the vertebral column. These phenomena might explain back pain on some patients after insertion of pectus bar and sporadically reported thoracic scoliosis after Nuss procedure. Moreover, we developed two thoracic volume measurement procedures to estimate the thoracic volume change of postoperative PE patients. The thoracic volume measurement procedure was performed based on the finite element analysis results and the increase of lung volume is estimated by measuring the increase of thoracic volume. The estimated results shown that the thoracic volume is increased about 2.72% to 8.88%.