Volumetric B1+ field homogenization in 7 Tesla brain MRI using metasurface scattering

Technical Summary: Volumetric B1+ Field Homogenization in 7 Tesla Brain MRI Using Metasurface Scattering

Problem Statement
Ultrahigh field (UHF) magnetic resonance imaging (MRI), particularly at 7 Tesla (7T), offers superior signal-to-noise ratio (SNR) and spatial resolution for diagnosing intractable brain diseases. However, increasing the static magnetic field ($B_0$) raises the Larmor frequency of the transmit radiofrequency (RF) magnetic field ($B_1^+$). At 7T, the wavelength of the $B_1^+$ field within human tissue becomes comparable to or smaller than the dimensions of the human head. This creates a biological resonator characterized by wavelength-scale footprints, random heterogeneous materials, and dissipative properties. Consequently, electromagnetic multimodes and complex interferences emerge, leading to detrimental mesoscopic challenges: severe $B_1^+$ field inhomogeneity and local heating. Traditional homogenization techniques, such as active parallel RF transmission (pTx) or passive high-permittivity materials (HPMs), face limitations regarding implementation complexity, increased electromagnetic absorption, or insufficient volumetric coverage due to the breakdown of effective medium theory in mesoscopic systems.

Methodology
The authors propose a semi-analytical design procedure based on scattering theory to achieve volumetric $B_1^+$ field homogenization using passive metasurfaces. The core of the method involves three steps:

1. Scattering Ansatz and Discretization: The problem is formulated using the Lippmann-Schwinger equation. The authors discretize the spatial domain into $N$ subspaces ($\Omega_n$) where metasurface objects can be placed. Instead of solving the recursive integral equation directly, they introduce "magnetic ansatz impulses" ($B_n$) for each domain. These impulses are derived from full-wave simulations (3D FDTD) of the RF coil with a single metasurface object at each location, assuming a fixed effective permittivity.
2. Weighted Optimization and Pruning: The total magnetic field is approximated as a linear superposition of the initial coil field and the weighted ansatz impulses ($B(r) \approx \sum c_n B_n(r)$). The complex weights ($c_n$) are optimized using a gradient descent method to minimize the coefficient of variation (CV) of the $B_1^+$ field within the region of interest (ROI). To ensure practical implementability and stability, a "pruning" technique is applied to reduce the number of active metasurface objects from $N$ to a minimal set $M$ ($M < N$), retaining only those with significant weights.
3. Refinement via Depth-First Search (DFS): Since the initial ansatz relies on a Born approximation that neglects multiple scattering interactions, the authors employ a DFS algorithm to fine-tune the effective permittivity values ($\varepsilon_m$) of the pruned metasurface objects. This step accounts for multiple scattering effects, aligning the actual simulated field with the ideal homogenized field.

Key Contributions

• Systematic Design Framework: Development of a non-invasive, systematic design recipe for metasurfaces in mesoscopic, heterogeneous environments, moving beyond empirical or heuristic approaches.
• Pruning Technique: Introduction of a pruning method to minimize the number of required metasurface elements, thereby reducing geometric complexity and enhancing implementation stability.
• Generalizability: Demonstration that the design is robust across different anatomical scales and heterogeneities, applicable to male, female, and infant head models.

Results
The method was validated using full-wave analysis on realistic human brain models: the Duke model (male), the MIDA model (female), and a modified Duke model (baby).

• Field Homogeneity: The optimized metasurfaces achieved a more than twofold improvement in field homogeneity. Specifically, the CV of the $B_1^+$ field was reduced by 40% for the Duke model (from 0.26 to 0.15), 46% for the MIDA model (from 0.37 to 0.20), and 44% for the reduced Duke model (from 0.31 to 0.17).
• Heating Suppression: The approach significantly suppressed local heating. On average, the method achieved a 22.98% reduction in average specific absorption rate (SAR) and a 23.58% reduction in peak SAR compared to head-only cases. The performance of the 7T MRI with metasurfaces approached that of commercial 3T MRI systems.
• Robustness: The design maintained stable field homogenization under dynamic conditions, including head rotations (flexion, extension, and lateral flexion), with CV reductions of at least 38.5% across all tested models and rotation types.

Significance
The paper claims that this work provides a universal methodology for noninvasive field homogenization in optical and electromagnetic mesoscopic environments. By treating the human brain as a correlated disorder system, the authors demonstrate that a simplified, pruned metasurface configuration can effectively manipulate wavefronts to achieve constant-intensity waves. This offers a pathway to stable and safe UHF MRI operations beyond 7T, addressing long-standing challenges in volumetric homogenization and safety without the complexity of active multi-channel systems. The results also suggest broader applicability to biophotonics and medical treatments requiring precise wave energy concentration or flattening in heterogeneous biological tissues.