GAL and atrial fibrillation: In univariate logistic regression analysis with left ventricular ejection fraction, end-diastolic internal diameter, end-systolic internal diameter, PTFV1 < −0.03 mm s, gal-3, and TGF-β1 as independent variables, gal-3, and TGF-β1 were the risk factors for poor collateral circulation for stroke due to AF, and then included in the multifactorial logistic regression analysis, and neither was an independent risk factor.