Estimating fiber orientation in ultrasound imaging through correlation and multivariate Granger causality

Estimating myocardial fiber orientation is essential for understanding the heart's microstructure and diagnosing conditions like arrhythmias or heart failure. While Diffusion Tensor Imaging (DTI) is the current gold standard, it is often unavailable in many clinical settings due to cost and accessibility. Ultrasound offers a promising alternative, especially through methods that analyze the spatial coherence of RF signals, such as Backscatter Tensor Imaging (BTI). However, most existing techniques rely on correlation, which can miss important directional dependencies in the signals. In this work, we investigate the use of multivariate Granger causality (GC) as a complementary tool for estimating ultrasound-based fiber orientation. We first develop a simulation framework based on vector autoregressive models that allows independent control of correlation and causality. This framework enables systematic evaluation of correlation, time-domain GC, and frequency-domain GC under different signal regimes, including the effect of preprocessing such as bandpass filtering. We show that correlation performs well in correlation-dominant conditions, and GC is more effective when causal dependencies dominate. Frequency-domain GC in particular demonstrated robustness to filtering, whereas time-domain GC was more sensitive to preprocessing. The methodology was further validated experimentally using an in vitro nylon-fiber phantom, imaged with a 1024-element matrix array probe and a Verasonics Vantage 256 system. Coherent plane-wave compounding with 25 tilted transmissions was applied, and fiber orientations were varied from -60^∘ to 60° using a rotation stage. Analysis of the compounded RF data confirmed the simulation findings: correlation provided stable estimates in regions dominated by instantaneous dependencies, while GC better captured directional patterns and was more sensitive to local structure. Balanced cases, observed both in simulation and experiment, suggested that real myocardial signals may arise from a mixture of correlated and causal interactions. Finally, fusing correlation and GC outputs through consensus and averaging improved robustness and accuracy of orientation estimation, especially in noisy or heterogeneous regions. While simulations relied on linear Gaussian VAR models, the phantom was more homogeneous than real tissue, and only in-plane orientations were studied, the results provide a foundation for future extensions toward 3D analysis, ex vivo validation, and real-time implementation. Overall, this study establishes multivariate Granger causality as a valuable complement to correlation for ultrasound-based fiber orientation estimation, demonstrating feasibility and promise as a cost-effective alternative to DTI with potential impact in cardiac diagnosis and monitoring.