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Magnetic Resonance Imaging
Published in Suzanne Amador Kane, Boris A. Gelman, Introduction to Physics in Modern Medicine, 2020
Suzanne Amador Kane, Boris A. Gelman
Nuclear dipoles undergo a similar precession when a constant magnetic field is applied to atomic nuclei with a nonzero spin. As we discussed above, a nuclear dipole does not entirely orient along an external magnetic field, but rather, inclines at an angle relative to the field direction. The applied magnetic field exerts a torque on the nuclear dipole, just as gravity exerts a torque on the top. However, instead of aligning the dipole along the field lines, the magnetic field causes the nuclear dipole to precess around the field's direction (Figure 8.11b). The precession of a magnetic dipole in a magnetic field is called the Larmor precession, and the characteristic frequency (the number of revolutions per second about the field's direction) is the Larmor frequency.
Advantages and Limitations of RNAi Delivery for Cancer Biological Therapeutics Imaging
Published in Loutfy H. Madkour, Nanoparticle-Based Drug Delivery in Cancer Treatment, 2022
MRI is an important versatile technique that provides noninvasive imaging based on the principle of nuclear magnetic resonance (NMR), by using strong magnetic field and radiofrequency (RF) pulses to generate RF signal (relying on intrinsic physiological feature) for visualization (Figure 7.8a). Specifically, an atom nucleus consists of a number of protons and neutrons, each of which has a constant spin and produces angular momentum, which consequently leads to a net angular momentum in the nucleus. If there is an equal number of protons and neutrons in nucleus, net angular momentum is zero. If there is an unequal number of protons and neutrons, then the nucleus gives a specific net spin angular momentum. In the latter circumstances, the nuclear Larmor precession is gained when an external magnetic field is present, and the resonant absorption of RF pulses by nucleus will occur when the frequency of RF pulses equals to the Larmor precession rate. Finally, the RF signal is generated after the removal of external magnetic field [138]. In this regard, the 1H nucleus is particularly useful for MRI since it is abundant in aqueous physiological environment and is magnetically active to give a large magnetic moment to generate RF. However, the RF signal can only be detected from an excess of nuclei with spins aligned either parallel or anti-parallel direction, an equal number of nuclei spins pointing in opposite direction cannot generate detectable MR signals [129]. Therefore, MRI is limited by low sensitivity with long signal acquisition time. Nonetheless, MRI has a number of unique advantages including high spatial resolution, deep tissue penetration, and excellent soft tissue contrast. MRI has been widely used in the clinic to study the anatomy as well as function of tissues. In addition to the development of high field scanners, the design of contrast agents (CAs) plays an important role to improve the image quality by enhancing the contrast of diseased regions while sparing normal tissues. Generally, the CAs could be classified as T1 and T2 CAs due to their magnetic properties and relaxation mechanisms (Figure 7.8b).
A survey on quantum positioning system
Published in International Journal of Modelling and Simulation, 2021
Shiqi Duan, Shuang Cong, Yuanyuan Song
Positioning system can be divided into passive or active positioning system according to whether it interacts with outside environment or not. Passive positioning system adopts quantum sensor devices to realize attitude adjustment and positioning, which doesn’t need to receive real-time signals from on-orbit satellites for ranging and timing [25]. A typical representative of this technology is the atomic interferometer gyroscope based on the Sagnac effect [26–28]. The basic principle of atomic interferometer gyroscope is that cold atoms move in opposite directions along the same parabolic trajectory to form an atomic beam, and an interference loop is formed under the stimulation of the Raman laser. Since the phase shift difference of the double-loop interference is related to the rotation rate, so the angular velocity can be further extracted. The theoretical value of drift is much lower than the classical gyroscope [29]. As for the atom accelerometer, it is also based on the Sagnac effect of the atom, so its development trajectory is almost identical to that of the atomic interferometer gyroscope [30]. In addition to the interferometer gyroscope, the angular velocity sensing is achieved by using the spin of alkali metal atoms based on the Larmor precession rate of an atom. This kind of gyroscope is called the atomic spin gyroscope [31,32].
Magnetic field dependence of triplet-state ONP: theoretical analysis in terms of level anti-crossings
Published in Molecular Physics, 2019
Denis V. Sosnovsky, Konstantin L. Ivanov
Here is the secular HFC term, is the Larmor precession frequency of the nucleus. The notation of the states in Equation (18) is as follows. State corresponds to at high magnetic fields (i.e. ); state goes to at high fields; for the other states assignment is , and (correlation for states is omitted here, since they do not cross with any other states). The four states have the four relevant LCs at specific magnetic field positions. Instead of a single LC, we obtain four LCs; the LC points are the vertices of a ‘parallelogram’, see Figure 2(a). The relevant LCs in the system are the following ones: LC1 of and , LC2 of and , LC3 of and , LC4 of and . To determine the positions of all four LCs we need to solve quadratic equations, for instance, for the LC of and , LC1, the crossing point can be found from the expression:
Single-molecule spectroscopy of radical pairs, a theoretical treatment and experimental considerations
Published in Molecular Physics, 2019
Noboru Ikeya, Egor A. Nasibulov, Konstantin L. Ivanov, Kiminori Maeda, Jonathan R. Woodward
A single molecule in the ground state is excited to state by a continuous light source; the induced transitions are dynamic and occur at a frequency . However, unless one performs the experiment under special conditions (at cryogenic temperatures and special matrices or in the solid state), light excitation can be considered as an incoherent process [10]. Hence, except for the example shown in Figure 1, we chose the parameters ( and the decoherence time) such that the Rabi oscillations are completely suppressed. We also assume that there is a spontaneous transition , which gives rise to photon emission (fluorescence). The fluorescence rate is denoted as . In addition, we assume that from the excited state an RP can be formed in the singlet state, , at a rate . The singlet-state RP can recombine to the ground state, , at a rate . In addition, we take into account interconversion, i.e. singlet–triplet spin state mixing in the RP, which is of a coherent nature. For the sake of simplicity, we introduce only the mixing between the state and the central triplet state, , although can also be taken into account using the same theoretical formalism. This limitation is not of principal importance: where necessary, our treatment can be generalised to take into account transitions between any states of the RP. The approximation of mixing corresponds to high magnetic fields, where interconversion is due to the difference, , in the Larmor precession frequencies of the two radical centres. In turn, is due to hyperfine couplings with magnetic nuclei or due to the difference, , in the -factors of the radical centres [11]. Here we assume that RP is a ‘dark state’ of the system, (i) which gives no fluorescence and (ii) in which the system is trapped for a relatively long time. The latter assumption corresponds to the situation .