Towards an effective medium theory for in-vivo Magnetic Resonance: Characterizing Admissible Magnetization Dynamics
Abstract
The classical Bloch equation forms the foundation of magnetic resonance theory but may be insufficient to capture the complex effective dynamics observed in heterogeneous materials such as biological tissue. Here an effective-medium strategy is proposed to describe magnetic resonance dynamics from observations at macro-scale (order 1 mm3). In this framework, the classical Larmor torque is retained while the relaxation term is replaced by a general nonlinear field (i.e. the effective medium term). This field is required to preserve key physical properties, including rotational symmetry, global stability of thermal equilibrium, and dissipativity. These requirements lead to a complete characterization of admissible relaxation fields and provide a constructive framework for generating nonlinear relaxation models. The resulting theory recovers classical Bloch dynamics as a special case and provides a principled foundation for effective-medium descriptions of magnetic resonance phenomena.
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BibTeX
@misc{sbrizzi2026towards,
title = {{Towards an effective medium theory for in-vivo Magnetic Resonance: Characterizing Admissible Magnetization Dynamics}},
author = {Alessandro Sbrizzi and Miha Fuderer and Ray Sheombarsing},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30401},
eprint = {2608.30401},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30401},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Towards an effective medium theory for in-vivo Magnetic Resonance: Characterizing Admissible Magnetization Dynamics
AU - Alessandro Sbrizzi
AU - Miha Fuderer
AU - Ray Sheombarsing
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30401
UR - https://arxiv.org/abs/2608.30401
AB - The classical Bloch equation forms the foundation of magnetic resonance theory but may be insufficient to capture the complex effective dynamics observed in heterogeneous materials such as biological tissue. Here an effective-medium strategy is proposed to describe magnetic resonance dynamics from observations at macro-scale (order 1 mm^3). In this framework, the classical Larmor torque is retained while the relaxation term is replaced by a general nonlinear field (i.e. the effective medium term). This field is required to preserve key physical properties, including rotational symmetry, global stability of thermal equilibrium, and dissipativity. These requirements lead to a complete characterization of admissible relaxation fields and provide a constructive framework for generating nonlinear relaxation models. The resulting theory recovers classical Bloch dynamics as a special case and provides a principled foundation for effective-medium descriptions of magnetic resonance phenomena.
ER -