4772

Combined fractal and connected component analysis for characterization of cardiac fibrosis distribution in end stage renal disease patients on routine hemodialysis
Zeynep Ali1, Bonnie Lam1, and Moriel Vandsburger1

1Bioengineering, UC Berkeley, Berkeley, CA, United States

Synopsis

A magnetization transfer based MRI technique for measurement of cardiac fibrosis was applied to 34 end stage renal disease patients on routine hemodialysis and 19 controls. Short axis maps of changes in tissue magnetization transfer properties were combined to create 3D domains in which anatomical connectivity of voxels in the myocardium was linearized. Connected component analysis was used to isolate distinct spatially connected sub-regions of myocardium and fractal analysis of magnetization transfer changes was applied to the whole myocardium as well as these sub-regions. The measured fractal dimensions show tissue-level structural differences between the different tissue types and patient populations.

Introduction

End-stage renal disease (ESRD) patients suffer high mortality from fatal cardiac arrhythmias with an emerging link to myocardial fibrosis. Histological data probing diffuse fibrosis at the tissue level has shown a fractal spatial pattern1. In a prior study, we utilized magnetization transfer (MT) based imaging to quantify the global burden of cardiac fibrosis in ESRD patients2 (Figure 1). In this study, we applied fractal analysis and connected component analysis to previously acquired data in order to probe and characterize the morphology of fibrosis in ESRD patients on routine hemodialysis.

Methods

Preparation of 3D tissue space: Short axis maps of ΔS/So (Figure 1) spanning from the left ventricular base to the apex in ESRD (n = 34) and controls (n = 19) were previously contoured to define endo and epicardial borders. Myocardial voxels were subsequently translated from Cartesian to radial coordinates (Figure 2) and stacked based on longitudinal position. At each angle (θ), the radial value was redefined based on distance from the midwall such that voxels at identical radial positions (r, θ) and adjacent longitudinal positions (z1, z2) were physically connected in a domain termed HeartSpace.

Fractal Analysis: A 3D box-counting method3 was implemented in MATLAB and applied over the entire HeartSpace within four ΔS/So domains corresponding to healthy myocardium (ΔS/So < 150%), diffusely enhanced myocardium (150 < ΔS/So < 200%), enhanced myocardium (ΔS/So > 200%), and all enhanced myocardium (ΔS/So > 150%) based on prior studies that compared ΔS/So values to late gadolinium enhancement and gadolinium partition coefficient2. Fractal dimension (FD) of each domain was calculated by taking the slope of the best-fit line of a log-log plot of the box side length vs. the number of boxes required to cover all the entire tissue volume.

Connected Component Analysis: Voxels with ΔS/So above 150% were isolated and 26-neighbor connected component analysis (CCA) was used to isolate fibrotic clusters as connected components (CCs) based on existing Matlab CC algorithms. Fractal analysis was then repeated on each connected component composed of above 40 voxels within each patient.

Statistics: Two-tailed t-tests were used to determine significance.

Results

Fractal analysis yielded fractal dimensions (FDs), values that quantified the space-filling characteristics of the tissue being analyzed. Significant differences in FD within all three elevated ΔS/So domains were observed between the ESRD and control populations (Figure 3). In ESRD patients, elevated FD values in diffusely fibrotic (150% < ΔS/So < 200%) and densely fibrotic tissues (ΔS/So > 200%) reveal planar distributions within 3D space (Figure 3). The combination of these two domains (ΔS/So > 150%) resulted in FD values close to 2.5, indicative of a fractal 3D space-filling pattern that was not observed in either domain independently (Figure 3).

Use of connected component analysis enabled measurement of fractal dimension in distinct spatially connected sub-regions of myocardium (Figure 4). The average size of connected components was significantly higher in ESRD patients compared to healthy controls (321 ± 168 voxels Control vs. 2448 ± 3839 voxels ESRD, p = 0.0028). In comparison to values obtained over the entire ventricle, lower FD values for the diffusely and densely elevated myocardium were observed among individual connected components (Figure 5) that are consistent with patterns that fill 2D space with 1D line-like structures. The combination of these two tissues showed that the elevated myocardium on total was planar. Among ESRD patients, comparison of the average fractal dimension of a single connected component to the corresponding size revealed that both the diffusely elevated (150% < ΔS/So < 200%) and combined elevated (ΔS/So > 150%) domains consistently demonstrated fractal dimensions of approximately 2 regardless of connected component size. In contrast, the fractal dimension of densely fibrotic tissue (ΔS/So > 200%) increased from around 1 in smaller connected components (consistent with point elevations) to around 2 in larger connected components (consistent with planar fractal patterns).

Discussion

In contrast to replacement fibrosis that develops after ischemic injury, reactive fibrosis in ESRD patients is intrinsically diffuse and spatially heterogeneous. Subsequently, measurement of an average myocardial ΔS/So value in ESRD patients limits the ability to detect spatial patterns of elevation. In juxtaposition, measurement of the fractal dimension from MT based imaging of cardiac fibrosis provides a logical method for quantifying the spatial order of diffusely fibrotic myocardium. The further combination with connected component analysis provides additional detail of cardiac fibrosis in ESRD patients as an interconnection of diffuse and focal fibrotic tissue that fills 3D space in a fractal pattern.

Conclusion

Fractal analysis of the myocardium provides greater characterization of the spatial distribution of cardiac fibrosis in ESRD patients.

Acknowledgements

The American Heart Association National Affiliate (14CRP20380071) and National Institutes of Health (R01HL128592) to MV funded this work.

References

1. Zouein, F. A. et al. Applying fractal dimension and image analysis to quantify fibrotic collagen deposition and organization in the normal and hypertensive heart. Microsc. Microanal. 20, 1134–1144 (2014).

2. Stromp, T. A. et al. Gadolinium free cardiovascular magnetic resonance with 2-point Cine balanced steady state free precession. Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance 17, 90, doi:10.1186/s12968-015-0194-1 (2015).

3. Mandelbrot, Benoit B., and Roberto Pignoni. The fractal geometry of nature. Vol. 173. New York: WH Freeman (1983).

Figures

Figure 1. Magnetization transfer based imaging of cardiac fibrosis in ESRD patients (development and validation of this method can be found in Stromp et al.2). The normalized signal difference ΔS/So calculated from two differentially MT-weighted cine bSSFP images is consistently around 150% in healthy myocardium and over 200% in myocardium that enhances with gadolinium. In ESRD patients, this technique can be used to examine whether myocardium is healthy (A-D) or diffusely fibrotic (E-H) without using gadolinium. This imaging data was acquired across the entire left ventricle in ESRD patients and healthy controls.

Figure 2. Construction of HeartSpace. CMR images are masked to isolate the left ventricular tissue. The superior right ventricular insertion point is selected on each image from the patient and the centroid of the left ventricular blood pool is calculated. The image is translated from Cartesian to radial coordinates. Finally, each strip from each slice of the heart is justified based on distance from the centroid and stacked to represent the true connectivity of the voxels.

Figure 3. Box and whisker plots of the average fractal dimensions of the entire left ventricle. Based on our prior study in which ΔS/So were compared to gadolinium partition coefficient and LGE status, healthy tissue was defined as ΔS/So < 150 %, diffusely elevated tissue was defined as 150 <ΔS/So < 200 %, and focally enhanced tissue was defined as ΔS/So > 200%. Significant differences were observed in fractal dimensions of the diffusely elevated, focally elevated, and all elevated tissue groups when comparing ESRD patients to corresponding healthy controls.

Figure 4. Identification of Connected Components. Connected component analysis was performed on all voxels with ΔS/So > 150%. Division of the entire ventricle (left) into connected components (right) is shown for an ESRD patient with substantial diffuse fibrotic burden. Within each connected component the fractal properties of the focal and diffuse fibrosis are examined by repeating fractal analysis.

Figure 5. (Top) Boxplots of the average FD of connected components for each population and fibrotic domain. While fractal dimension was higher on average in ESRD patients compared to healthy controls across domains, values were lower than comparable values obtained across the entire left ventricle. (Bottom) However, comparison of fractal dimension to connected component size revealed a size dependent change in the fractal characteristics of densely fibrotic tissue.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)
4772