Σήμανση στο μαγνητικό συντονισμό μέσω επιλεκτικής κωδικοποίησης - ειασαγωγή της μιγαδικής διέγερσης

Abstract

The aim of this doctoral thesis is to examine, evaluate and develop methods for the design of one-dimensional selective excitation pulses and sequences, with applications mainly in the field of magnetic resonance tagging. In this context, the thesis can be divided in two parts. The first one, consisting of chapter two, concerns selective excitation theory. The approach adapted is based on the Shinnar - Le Roux (SLR) algorithm, and concerns the nature of the pulse. It is proven that when the excitation characteristics, as defined by the Cayley-Klein parameters describing the rotation induced due to the pulse, are symmetric around the on resonance point, which means that they can be described by means of FIR filters with real coefficients, the resulting excitation waveform is also real. Thus, it can be implemented using simple amplitude modulation. On the computational part, this allows the derivation of a simplified version of the SLR algorithm, which involves only real quantities, and thus reduces computational complexity and cost. For the case when non-symmetric excitation characteristics are desired, the notion of complex excitation is introduced. Complex excitation is the result of the combination of the SLR algorithm with FIR filters with complex-valued coefficients. Since such filters allow frequency responses that are non-symmetric around the dc point, non-symmetric excitation characteristics can be achieved. Implementation cost of this approach lies both in the use of complex algorithms, like the complex Chebychev approximation based FIR filter design algorithms, as well as in the need for I/Q modulation in order to implement the waveform. In this thesis, the method proposed is exploited in order to yield tagging patterns that are non-symmetric with respect to the on-resonance point. Other possible applications include, but are not limited to, design of pulses with better control over the phase dispersion of the transversal magnetization component. A further topic discussed is the error introduced by the zero-order hold approximation used by most D/A converters in order to produce the excitation waveform, as well as ways to avoid it. The second part of the thesis, consisting of chapters three to six, concerns magnetic resonance tagging as an application of one-dimensional selective excitation theory. Chapter four deals with the problem of localized tagging based on the SPAMM 1-1 sequence. Localized tagging is achieved by combining periodic tagging sequences with selective excitation pulses. The analysis offered, based on the SLR framework, offers insight in the role of the selective pulses’ phase in the tagging process. It is shown that if two identical pulses are applied, their phase components approximately cancel out. This allows discarding refocus and pre-emphasis gradients, reducing gradient switching needs and sequence duration. Furthermore, non-linear phase pulses can be used, which allow a better selection profile to be achieved. By modifying the phase of the two pulses, “multirate” patterns with variable tagging grid density can be achieved. The proposed form of L-SPAMM 1-1 has the disadvantage of limited pulse duration, and thus poses a limit on the achievable quality of the selection profile. In order to overcome it, a variation of it, M-SPAMM 1-1 (multirate SPAMM 1-1) is proposed. The sequence, which can be used in order to produce symmetric selection profiles, uses a gradient of different sign during the application of the first rf pulse. Gradient reversal allows for unlimited pulse duration, at the expense of tagging sequence duration. The sequence can be used in order to produce localized tagging grid of both uniform and variable density. The method is better suited for the latter case, where its ability to produce a better selection profile becomes of value. Chapter five is concerned with variable tagging sequence design. The concept of periodicity and non-periodicity is discussed, the notion of the basic tagging pattern, i.e. the smallest pattern unit whose periodic repetition produces the desired grid, is introduced, and an algorithm is proposed that can be used in order to find it. SLR-based variable tagging sequence design is proposed. Resulting sequences consist of a train of alternating non-selective rf and gradient pulses. Its main advantage, apart from the better approximation, is that it can produce non-symmetric tagging patterns, using the complex excitation techniques discussed in chapter two. The proposed design method is complemented by a grid shifting technique using phase difference between subsequent rf pulses. Chapter six discusses constant gradient tagging. Tagging sequences based on periodicity rely on non-selective rf pulses, that in some cases, like the SPAMM sequence, are implemented with the gradient switched off during their application. The same approach is adopted, in order to limit peak rf power, in the case of the newer variable tagging sequences. However, gradient switching causes increased sequence duration, both due to constrains of the driving electronics as well as to concerns about patient exposure to low-frequency alternating magnetic fields. In this chapter, the approximation achieved by keeping the gradient constant is discussed. A mathematical analysis, based on the theory of tagging k- space, is derived, and design choices and their implications are discussed. It is demonstrated that constant gradient tagging is a realistic alternative that needs less time, even of the order of 3 ms for variable tagging sequences, and has the added advantage of being suitable even for older or less expensive scanners. The framework produced by the analysis is suitable for formulating a generic approach to localized tagging. The combination of SPAMM, DANTE and variable tagging sequences with selective excitation pulses is discussed and demonstrated, and the notion of overlapping pulses is introduced. The latter provide a way to significantly improve selection profile, and make the combination of selective excitation pulses with variable tagging sequences realistic. The chapter concludes with the introduction of the localized variable DANTE sequences. These are a combination of localized DANTE sequences of different periodicity that produce a variable density pattern. Five variations of the sequence are proposed: basic LV-DANTE, LV-DANTE with phase shift, LV-DANTE with modulation, complex LV-DANTE and hybrid LV-DANTE, each one dealing with different characteristics of the desired tagging grid. The sequences proposed have duration of about 3-5 ms. In the seventh chapter, the main points of the thesis, as well as its contribution, are discussed. Summarizing, the contribution of the thesis is focused on the following points: • The derivation of the relationship between amplitude modulation and profile symmetry, and the derivation of simplified, real-valued version of the SLR algorithm. • The introduction of complex excitation for non-symmetric excitation profiles. • The investigation of the role of pulse phase in the localized tagging process, the derivation of a simplified, faster version of the L-SPAMM 1-1 sequence, and the introduction of the M-SPAMM 1-1 sequence and of the notion of localized variable tagging. • The discussion of the role of periodicity in tagging, and the introduction of the notion of the basic tagging pattern. • The introduction of the use of the SLR algorithm for variable tagging sequence design. • The framework of constant gradient tagging and the introduction of the use of overlapping pulses. • The introduction of the family of localized variable DANTE tagging sequences.