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# Fundamentals of Magnetic Resonance Imaging: with image reconstruction simulated by MATLAB

**Author: ** Jintong Mao

**ISBN/ASIN: ** 1701655349

Starting from complex free induction decay (FID), this book establishes a logical framework for the discussion of the principles of MRI. Based on the framework, traditional topics and some new topics are described. Every formula is derived step by step. The essence of MRI is thoroughly discussed. Each concept is explained in detail. The book discusses at length for some concepts or formulas that are not very easy to grasp for a novice. Some readers may already get used to these concepts or formulas, but they may also not fully understand how to explain these concepts or how to derive the formulas correctly. ------ The book emphasizes that the acquisition of discrete FID leads to a discrete FT (Fourier transform) and also the acquisition of discrete echo leads to a discrete FT automatically in both cases if a linear gradient field exists. Inverse FT to acquired signals leads to images. Continuous FT is used as a heuristic step only in this book. But it is not necessary for the discussion of MRI. As the example from FID to MR image, simulated images are obtained for graphical phantoms by using MATLAB. In appendix, MATLAB codes for image reconstruction and for some frequency selective pulses are included. ------ Based on the framework, the traditional topics include basic pulse sequences; pulse train; image contrasts; signal to noise ratio; ringing artifacts; aliasing artifacts; improvement of slice profile; fat suppression; magnetization transfer; diffusion; flow image; fMRI for an application: perceptual alternation; etc. ------ Inside of the framework, additional topics include the artifacts of pulsatile ghost in flow that is explained incorrectly in literature; experiments show that traditional explanation of flow mis-registration is not correct; the experiment also shows that the profile of laminar flow looks like a long needle, instead of the commonly recognized ellipsoid; Stejskal-Tanner formula for b-value can be obtained by a wrong derivation, thus, the correctness of the formula may be in question; etc. ------In addition to above topics, Bloch equation with the terms T1, T2, diffusion, flow, etc. is derived by adding independent contributions to dM/dt with the assumption that T2 decay is at x-y plane only. A lengthy appendix is included to discuss many fundamental topics in physics and engineering that are relevant to MRI. The appendix includes detailed derivations for the formulas cited in the text. In order to discuss the concept of spin and thermal noise, basic concepts in physics such as special relativity and Boltzmann factor are reviewed. The appendix includes the detailed discussions of FT, Nyquist sampling, and Nyquist thermal noise, etc. The appendix allows readers to follow the discussion without significant extra efforts to derive the formulas themselves or to consult other sources for formula derivation.------It is the hope that the book is readable. It is also the hope that the journey through the book, particularly some portions of the first part of the book, might be a joy. It is of value to beginners. Perhaps it may be valuable to more readers as well.