本文將使用GPU來加速MATLAB運算環境中事件相關電位之動態因果模型的運算效能，事件相關電位之動態因果模型是近期發展出來的建模方法，主要的功能是用來研究神經元的有效性連接及大腦功能的推論。動態因果模型經由最大期望值演算法的遞迴估測運算找出一組最佳的參數模型讓輸出最貼近實驗所觀察到的腦波輸出，其中的原理是將模型的似然函數最大化。由於最大期望值演算法中的估測運算相當耗時，且會隨著資料量的增加而運算時間也隨之增加，本文提供了一個平行化的架構並使用GPU來提高最大期望值演算法的運算效能，藉此動態因果模型可以快速的估測出神經元的有效性連接。在本研究的平行架構中，我們將根據動態因果模型的模型複雜度(即需要被估測的參數數量)動態配置GPU執行緒的數量作分散式的平行運算。我們將改變資料長度以及模型複雜度並先使用電腦合成數據來呈現系統的平行效能及精準度的損失。研究結果顯示本研究所提供的GPU執行緒分配策略對MATLAB微分Hidden state的部分加速約達48.72倍且精準度高達99%。最後我們使用腦電波實驗數據評估GPU平行架構的加速效能並證明其實用性，GPU將整體MATLAB的運算時間從4527.8秒縮短至778.4秒，且在實驗結果中顯示兩者皆會篩選出相同的假設模型，但GPU和MATLAB所估算出的連接強度完全不同，這可能是因為動態因果模型屬於不適定問題(ill-posed problem)造成GPU和MATLAB估算出不同的區域最大值，因此我們將GPU的平行架構定義為快速掃描的工具，使用者可以先藉由GPU的快速運算來篩選假設模型，再使用MATLAB重複估算所選出假設模型的連接強度，最後再來比較哪個區域最大值為較佳的解。This thesis presents the use of graphic processing unit (GPU) to accelerate a brain-activity analytical tool, the Dynamic Causal Modelling for Event Related Potential (DCM for ERP) in MATLAB. DCM for ERP is a recently developed advanced method for studying neuronal effective connectivity and making inference about the brain functions. DCM utilizes an iterative procedure, the expectation maximization (EM) algorithm, to find the optimal parameters given a set of observed events (data) and the underlying probability model, such that the likelihood function is maximized. As the EM algorithm is computationally demanding, time consuming and largely data dependent, we propose a parallel computing scheme using GPUs to achieve a fast estimation of neural effective connectivity in DCM. The computational loading of EM was partitioned and dynamically distributed to either the threads or blocks according to the DCM model complexity (i.e. the number of parameters to be estimated). The performance of this dynamic loading arrangement in terms of execution time and accuracy loss were evaluated using synthetic data. The results show that our method can accelerate a Hidden state differential by about 48.72 times as fast as the MATLAB version and the accuracy is up to 99%. The experimental electroencephalogram (EEG) data were then used to evaluate the speedup factor and the estimation performance in terms of the model evidence in practice. The GPUs estimation could shorten the computing time from by 4527.8 to 778.4 seconds. The GPUs give qualitatively the same outputs as MATLAB does though quantitatively the estimates are not equal. This may be because of the ill-posed problem in the model and lead to different local maximization. Therefore, we consider this tool as a fast screen tool for users to select the most likely model and then the output results of the winning model should be double checked with MATLAB for re-assurance.
