一種用于fMRI的快速動(dòng)態(tài)因果模型反演方法

摘" 要： 針對動(dòng)態(tài)因果模型（DCM）在分析大腦有效連接時(shí)面臨的高計(jì)算成本問題，提出一種結(jié)合廣義線性模型（GLM）和稀疏DCM的算法，即廣義稀疏DCM（GSD）算法。該算法在以下三個(gè)方面進(jìn)行優(yōu)化：首先，利用傅里葉變換的對稱性將頻域DCM的復(fù)數(shù)計(jì)算轉(zhuǎn)換為實(shí)數(shù)計(jì)算，降低計(jì)算復(fù)雜度；其次，應(yīng)用GLM和濾波技術(shù)減少觀測信號的干擾，提高參數(shù)估計(jì)的準(zhǔn)確度；最后，定義新的代價(jià)函數(shù)來優(yōu)化變分推斷參數(shù)和濾波器參數(shù)，進(jìn)一步提升參數(shù)估計(jì)的精度。該研究采用兩組公開的功能核磁共振成像（fMRI）數(shù)據(jù)對GSD算法進(jìn)行驗(yàn)證，包括仿真的史密斯小世界網(wǎng)絡(luò)數(shù)據(jù)和運(yùn)動(dòng)與注意力實(shí)測數(shù)據(jù)。實(shí)驗(yàn)結(jié)果表明，GSD算法在保持與傳統(tǒng)方法相近的參數(shù)估計(jì)性能的同時(shí)，能將計(jì)算時(shí)間降低50%以上。該研究成果為平衡模型的解釋力和計(jì)算效率提供了新的視角，有望推動(dòng)DCM在更廣泛領(lǐng)域的應(yīng)用。

關(guān)鍵詞： 廣義線性模型； 動(dòng)態(tài)因果模型； 稀疏算法； 有效連接； 計(jì)算復(fù)雜度； 模型解釋力

中圖分類號： TN919?34； TP301.6" " " " " " " " " "文獻(xiàn)標(biāo)識(shí)碼： A" " " " " " " " " " 文章編號： 1004?373X（2025）07?0146?09

Fast dynamic causal modeling regression method for fMRI

HU Xinhang1， WU Haifeng1， 2， 3， ZENG Yu1， 2， 3

（1. School of Electrical and Information Engineering， Yunnan Minzu University， Kunming 650504， China;

2. Yunnan Provincial Key Laboratory of Unmanned Autonomous Systems， Kunming 650504， China;

3. Yunnan Provincial Colleges and Universities Intelligent Sensor Network and Information System Technology Innovation Team，

Yunnan Minzu University， Kunming 650504， China）

Abstract： In view of the high computational cost faced by dynamic causal modeling （DCM） when analyzing brain effective connectivity， an algorithm that combines the generalized linear model （GLM） and sparse DCM， namely the combined generalize?linear?model and sparse DCM （GSD） algorithm， is proposed. The algorithm is optimized in the following three aspects： firstly， the symmetry of Fourier transform is used to convert the complex number calculation of frequency domain DCM into real number calculation， reducing the computational complexity; secondly， GLM and filtering techniques are applied to reduce the interference of observed signals and improve the accuracy of parameter estimation; finally， a new cost function is defined to optimize the variational inference parameters and filter parameters to further improve the accuracy of parameter estimation. In this study， two sets of public functional magnetic resonance imaging （fMRI） data are used to verify the GSD algorithm， including the simulated Smith small?world network data and the motion and attention measured data. The experimental results show that the GSD algorithm can reduce the calculation time by more than 50% while maintaining parameter estimation performance similar to that of the traditional methods. The research results of this paper provide a new perspective for balancing the explanatory power and computational efficiency of the model， and are expected to promote the application of DCM in a wider range of fields.

Keywords： GLM; DCM; sparse algorithm; effective connectivity; computational complexity; model explanatory power

0" 引" 言

隨著腦成像技術(shù)的不斷發(fā)展，出現(xiàn)了許多結(jié)合功能核磁共振成像（Functional Magnetic Resonance Imaging， fMRI）技術(shù)來研究有效連接的方法，例如結(jié)構(gòu)方程模型、多變量回歸模型、格蘭杰因果模型（Granger Causality Modeling， GCM）和動(dòng)態(tài)因果模型（Dynamic Causal Modeling， DCM）等[1]，其中GCM和DCM最具代表性。DCM基于動(dòng)態(tài)系統(tǒng)理論和狀態(tài)空間模型[2]，不僅能夠更全面地考慮大腦網(wǎng)絡(luò)的動(dòng)態(tài)調(diào)節(jié)過程，也可以根據(jù)神經(jīng)科學(xué)先驗(yàn)知識(shí)對腦活動(dòng)進(jìn)行解釋，這使得DCM成為了研究有效連接更主流的方法，并涌現(xiàn)出了許多與之相結(jié)合的新方法[3?5]。……