MRI is powered by mathematics—but that mathematics is often hidden behind scanner presets, formulas, and terminology that professionals are expected to memorize without fully understanding.
MRI Mathematics Textbook changes that.
Built specifically for MRI technologists, radiologic technology students, imaging professionals, and learners entering medical physics or biomedical engineering, this comprehensive guide takes you from foundational mathematics to the calculations that shape real MRI acquisition, reconstruction, image quality, and safety.
Inside, you'll learn to:
• Strengthen essential math skills through MRI-focused arithmetic, algebra, ratios, unit conversions, scientific notation, and equation solving.
• Understand trigonometry and vectors through flip angles, precession, magnetization components, gradient directions, and RF-induced rotation.
• Master exponential mathematics behind T1 recovery, T2/T2* decay, relaxation curves, inversion times, and signal prediction.
• Make sense of complex numbers and phasors, connecting magnitude, phase, quadrature detection, and rotating reference frames.
• Build a practical understanding of Fourier analysis, including frequency-domain thinking, sampling, Nyquist principles, and image reconstruction.
• Decode k-space mathematically, from sampling density and trajectories to partial acquisition, central versus peripheral data, and resolution.
• Calculate image-quality trade-offs, including SNR, CNR, voxel dimensions, bandwidth effects, averaging, and scan time.
• Work through quantitative MRI calculations, including diffusion, T1/T2 mapping, flow, SAR, field inhomogeneity, and other applied problems.
No advanced mathematics background is assumed. Concepts are introduced progressively and tied directly to the MRI problem they help solve. The manuscript's worked examples are designed to turn formulas into usable reasoning rather than memorized rules.
Stop treating MRI mathematics as something happening invisibly inside the scanner—build the mathematical confidence to understand what the numbers actually mean.