Fundamentals of Magnetic Resonance Imaging with image reconstruction simulated by MATLAB

Some basic and important topics of MRI may not be well-discussed in the available books and websites. Many formulas are not derived or not derived correctly. The explanation of several well-known phenomena is even not correct. In this book, starting from the observed free induction decay (FID) and the recovery (together they are called signal-FID), we expect that there is a magnetization-FID. From these two FIDs, we establish a framework for MRI. Traditional topics and some new topics are described. Every formula is derived step by step. The essence of MRI is discussed thoroughly. Each concept is explained in detail. How to explain the important concepts or how to derive the necessary formulas correctly is still a problem. The book discusses some important concepts or formulas at length. For instance, the book derives the important basic formula: FOVx * dKx = 2*pi between image and k-spaces based on data quadrature acquisition and Nyquist sampling rule. If T2 = ∞, the book indicates that the acquisition of discrete FID and the acquisition of discrete echo lead to discrete FT (Fourier Transform) automatically if a linear gradient field is applied. Inverse FT to the acquired signals leads to images. This discussion is similar to the available literatures. However, the pair of FT is not correct in MRI if T2 ≠ ∞. We will use FT for image reconstruction, but the FT is not an inverse FT in its traditional definition. In the book, continuous FT is used only as a heuristic step. But it is not necessary for the discussion of MRI. As the example from FID to MR image, simulated images are obtained for a graphic phantom by using MATLAB. The MATLAB method explains the blood image with pulsatile ghost correctly. In appendix, MATLAB codes for image reconstruction and some frequency selective pulses are included. Based on the established 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 with an application in perceptual alternation; etc. Also, the book indicates that raw data symmetry (Hermitian symmetry) does not hold for normal k-space. In addition to the traditional topics, further discussions indicate that several common topics may not be discussed correctly in literatures. These include that the artifacts of pulsatile ghost in blood flow; traditional explanation of flow mis-registration; the profile of laminar flow inside of a circular tube 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. Furthermore, Bloch equation with the terms T1, T2, diffusion, flow, etc. is derived by adding independent contributions to dM/dt with the only assumption that T2 decay occurs only in the x-y plane. A lengthy appendix is included to discuss many fundamental topics in physics and engineering that are relevant to MRI. The appendix includes the detailed derivations of 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 might be a joy. It is of value to beginners. Perhaps it may be valuable other readers as well.