PET動態造影是將發射正子的放射性藥物注射入活體後，以連續時間掃描的方式，記錄藥物分佈和變化的過程。藉由動態模型擬合於組織的時間-活度曲線，評估具有生理或生化意義的動態參數，提供功能性資訊，作為臨床診斷的重要依據。假設三隔室模型 (3-Compartmental Model) 可以描述 FDG在活體的代謝機制，並由四個動態參數代表FDG在隔室間的運輸與代謝的速率常數。當活體細胞狀態改變，進而影響葡萄糖的代謝時，可以經由定量分析計算速率常數異常的環節。進行動態模型的參數評估時，需使用非線性迴歸分析法，其中Levenberg-Marquardt (LM) 演算法是最常使用的方法之一。然而，在雜訊較高的情況下，使用LM會有無法計算或收斂的現象，因此限制了LM在臨床的實用性。本研究除了沿用LM以殘差平方總合作為調整修正步伐的方法外，另外還考量動態參數個別收斂的情況。本研究提出之Weighted Levenberg-Marquardt (WLM) 演算法，改變LM的鬆弛係數形式，以加權的方式，強調各速率參數收斂的獨立性，期望達到有效收斂的目的。模擬實驗的結果顯示，利用WLM在低雜訊時有良好的計算結果，在高雜訊時可以克服LM無法計算的問題；應用於臨床影像參數評估時，也能有效的收斂。

Dynamic PET scan is capable of describing kinetics of the activity distribution of radiopharmaceuticals inside an object in vivo. Typically, by fitting the time-activity curve from dynamic PET images based on a given kinetic model, the corresponding estimated kinetic parameters can provide functional and physiological information. In this work, we consider three-compartmental model to describe the FDG metabolism in a living body. This model consists of 4 kinetic parameters which represent the rate constants of FDG transport and metabolism between plasma and tissues. Conventionally, Levenberg-Marquardt (LM) algorithm is used to estimate the parameters of nonlinear model. However, LM algorithm suffers some problems such as divergence or incapable estimation at high noise level. Based on the least square criteria and to ensure the convergence of kinetic parameter estimation, we suggested a weighted Levenberg-Marquardt (WLM) algorithm which introduces a relaxation parameter to prevent estimation procedure from divergence. The experimental results indicate that WLM can estimate kinetic parameters accurately as LM at low noise level, and still maintain estimation accuracy and stability at high noise level where LM algorithm becomes divergent. When applied to clinical images, WLM algorithm can also converge efficiently, while LM algorithm diverges once again.

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