Numerical Study of Secant Method for Finding the Optimum RF Coil Length in MRI Systems Using Python

Tatik Juwariyah; Silvia Anggraeni; Henry Binsar Hamonangan Sitorus

doi:10.30871/jaic.v10i4.12989

Authors

Tatik Juwariyah Department of Industrial Engineering, Universitas Pembangunan Nasional Veteran Jakarta
Silvia Anggraeni Department of Electrical Engineering, Universitas Pembangunan Nasional Veteran Jakarta
Henry Binsar Hamonangan Sitorus Department of Electrical Engineering, Universitas Pembangunan Nasional Veteran Jakarta

DOI:

https://doi.org/10.30871/jaic.v10i4.12989

Keywords:

Python, Numerical simulation, Ideal solenoid, Nagaoka model, RF coil, Secant method, Wheeler model

Abstract

Determining the coil length l to achieve the desired target inductance Ltarget involves nonlinear and transcendental RF coil design equations. The ideal solenoid coil model does not align with real-world conditions, therefore, it is corrected using the Wheeler and Nagaoka models. From a mathematical perspective, these two models are nonlinear, making it highly difficult to determine the coil length analytically. This study presents the application of the Secant method to solve the coil length optimization across three models: Ideal Solenoid, Wheeler, and Nagaoka. By applying the Secant method with a case study involving a target inductance Ltarget = 10 µH, radius r = 5 cm, and number of coil turns N = 15, an optimum length of 17.71 cm was obtained with an error tolerance of 10-6. The convergence rates of the three models were evaluated to obtain error value data at each iteration. Based on the relationship between the convergence rate and iteration steps, the Wheeler and Nagaoka models yielded identical data at every iteration. The Secant method proved effective in solving nonlinear function root-finding cases, demonstrating a logarithmic convergence rate. This study is expected to provide a reliable computational framework for medical device engineers to ensure manufacturing accuracy in the design of RF coils in MRI systems.

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