Systematic Dimensional Analysis of the Scaling Relationship for Gradient and Shim Coil Design Parameters.

ABSTRACT:

Purpose

To demonstrate systematic, linear algebra-based, dimensional analysis to derive a scaling relationship among the design parameters of MRI gradient and harmonic shim coils.

Theory and methods

The dimensions of five physical quantities relevant for gradient coil design (inductance, gradient amplitude, inner diameter [ d$$ d $$ ], current, and the permeability of free space) were decomposed into fundamental units, and their exponents were arranged into a dimensional matrix. The resulting set of homogenous equations was solved using standard linear algebraic methods. Inclusion of the number of turns as an additional unit yielded a 5 × 5 dimensional matrix with a unique, nontrivial solution. The analysis was extended to harmonic shim coils. The gradient coil scaling relat

SUBMITTER: Lee SK 

PROVIDER: S-EPMC9893842 | biostudies-literature | 2022 Oct

REPOSITORIES: biostudies-literature