Fractal Analysis of Cardiac Fibrosis Patterns Derived From Magnetization Transfer Contrast MRI in Patients With End-Stage Renal Disease

OBJECTIVE. The purpose of this study is to use fractal analysis to characterize diffusely fibrotic, focally fibrotic, and healthy myocardium in patients with end-stage renal disease (ESRD) on the basis of previously published magnetization transfer (MT) contrast images. MATERIALS AND METHODS. The MT ratio values of patients with ESRD (n = 34) and healthy control subjects (n = 19) were used to construct anatomically faithful 3D left ventricular reconstructions. Established MT ratio threshold values were used to define healthy, diffusely enhanced, focally enhanced, and total enhanced tissue domains. The fractal dimension (FD) for reach domain was calculated using a 3D box-counting algorithm. RESULTS. Patients with ESRD showed a higher FD across all fibrotic domains compared with control subjects, in whom diffusely and focally enhanced myocardium showed largely planar distributions (mean [± SD] FD, 2.12 ± 0.02 and 1.92 ± 0.09, respectively), whereas the combined domain was fractal in 3D (mean FD, 2.41 ± 0.04). The FD and volume of fibrotic tissue were logarithmically correlated in the population with ESRD. Fractal analysis of MT-weighted cardiac MRI data revealed that the geometric characteristics of cardiac scar in patients with ESRD transition from fractal in 2D to planar in 2D to fractal in 3D as scar volume increases. CONCLUSION. Fatal arrhythmias in individuals with ESRD are increasingly attributed to cardiac fibrosis. Histologic analysis reveals that fibrosis progresses via a fractal expansion pattern. The method presented in this study can be applied to characterize the irregular space-filling morphometry of any pathologic substrate identified by contrast enhancement across noninvasive imaging modalities.