On the geometric phases during radio frequency pulses with sine and cosine amplitude and frequency modulation.

In this work, we describe the formation of geometric phases during nonadiabatic frequency swept (FS) radio frequency (RF) pulses with sine amplitude modulation and cosine frequency modulation functions. The geometric phases during the FS pulse were analyzed using a Schrödinger equation formalism, and the unified analytical expression for the geometric phase was derived. We present the solutions for sub-geometric phase components incorporated in spinor wavefunctions for the RF Hamiltonian of spin ½ nuclei. We demonstrate that the geometric phases during sine/cosine RF pulses are opposite in signs for different initial conditions of the spinor and that geometric phases can accumulate in correspondence to different magnetization trajectories. The derived formalism could be extended for the evaluation of the geometric phases during a wide class of amplitude- and frequency-modulated pulses used in MRI and in high-resolution NMR.

Glioma cell density in a rat gene therapy model gauged by water relaxation rate along a fictitious magnetic field.

Longitudinal and transverse rotating-frame relaxation time constants, T(1) (ρ) and T(2) (ρ) , have previously been successfully applied to detect gene therapy responses and acute stroke in animal models. Those experiments were performed with continuous-wave irradiation or with frequency-modulated pulses operating in an adiabatic regime. The technique called Relaxation Along a Fictitious Field (RAFF) is a recent extension of frequency-modulated rotating-frame relaxation methods. In RAFF, spin locking takes place along a fictitious magnetic field, and the decay rate is a function of both T(1ρ) and T(2ρ) processes. In this work, the time constant characterizing water relaxation with RAFF (T(RAFF) ) was evaluated for its utility as a marker of response to gene therapy in a rat glioma model. To investigate the sensitivity to early treatment response, we measured several rotating-frame and free-precession relaxation time constants and the water apparent diffusion coefficients, and these were compared with histological cell counts in 8 days of treated and control groups of animals. T(RAFF) was the only parameter exhibiting significant association with cell density in three different tumor regions (border, intermediate, and core tissues). These results indicate that T(RAFF) may provide a marker to identify tumors responding to treatment.

MRI contrast from relaxation along a fictitious field (RAFF).

A new method to measure rotating frame relaxation and to create contrast for MRI is introduced. The technique exploits relaxation along a fictitious field (RAFF) generated by amplitude- and frequency-modulated irradiation in a subadiabatic condition. Here, RAFF is demonstrated using a radiofrequency pulse based on sine and cosine amplitude and frequency modulations of equal amplitudes, which gives rise to a stationary fictitious magnetic field in a doubly rotating frame. According to dipolar relaxation theory, the RAFF relaxation time constant (T(RAFF)) was found to differ from laboratory frame relaxation times (T(1) and T(2)) and rotating frame relaxation times (T(1ρ) and T(2ρ)). This prediction was supported by experimental results obtained from human brain in vivo and three different solutions. Results from relaxation mapping in human brain demonstrated the ability to create MRI contrast based on RAFF. The value of T(RAFF) was found to be insensitive to the initial orientation of the magnetization vector. In the RAFF method, the useful bandwidth did not decrease as the train length increased. Finally, as compared with an adiabatic pulse train of equal duration, RAFF required less radiofrequency power and therefore can be more readily used for rotating frame relaxation studies in humans.

Detection of neuronal loss using T(1rho) MRI assessment of (1)H(2)O spin dynamics in the aphakia mouse.

The loss of dopaminergic (DA) neurons in the substantia nigra pars compacta (SNc) is well characterized in Parkinson's disease (PD). Recent developments in magnetic resonance imaging (MRI) techniques have provided the opportunity to evaluate for changes in cellular density. Longitudinal relaxation measurements in the rotating frame (T(1rho)) provide a unique magnetic resonance imaging contrast in vivo. Due to the specificity of T(1rho) to water-protein interactions, the T(1rho) MRI method has strong potential to be used as a non-invasive method for quantification of neuronal density in the brain. Recently introduced adiabatic T(1rho) magnetic resonance imaging mapping methods provide a tool to assess molecular motional regimes with high sensitivity due to utilization of an effective magnetic field sweep during adiabatic pulses. In this work, to investigate the sensitivity of T(1rho) to alterations in neuronal density, adiabatic T(1rho) MRI measurements were employed in vivo on Pitx3-homeobox gene-deficient aphakia mice in which the deficit of DA neurons in the SNc is well established. The theoretical analysis of T(1rho) maps in the different areas of the brain of aphakia mouse suggested variation of the (1)H(2)O rotational correlation times, tau(c). This suggests tau(c) to be a sensitive indicator for neuronal loss during neurological disorders. The results manifest significant dependencies of the T(1rho) relaxations on the cell densities in the SNc, suggesting T(1rho) MRI method as a candidate for detection of neuronal loss in neurological disorders.

RAFFn relaxation rate functions.

In the present study we derive expressions for relaxation rate functions due to dipolar interactions between identical spins in the rotating frames of rank greater than or equal to 3. The rotating frames are produced due to fictitious magnetic field as generated by amplitude and frequency modulated radiofrequency (RF) pulses operating in non-adiabatic regime. This solution provides a means for description of the relaxations during method entitled Relaxation Along a Fictitious Field (RAFF) in the rotating frame of rank n (RAFFn), in which a fictitious field is created in a coordinate frame undergoing multi-fold rotation about n axes (i.e., rank n). We validate the proposed model by comparison with the accepted trigonometric relations for relaxation rates between tilted frames. The agreement between the proposed model for RAFF3 and the trigonometric model is excellent.

The time-dependence of exchange-induced relaxation during modulated radio frequency pulses.

The problem of the relaxation of identical spins 1/2 induced by chemical exchange between spins with different chemical shifts in the presence of time-dependent RF irradiation (in the first rotating frame) is considered for the fast exchange regime. The solution for the time evolution under the chemical exchange Hamiltonian in the tilted doubly rotating frame (TDRF) is presented. Detailed derivation is specified to the case of a two-site chemical exchange system with complete randomization between jumps of the exchanging spins. The derived theory can be applied to describe the modulation of the chemical exchange relaxation rate constants when using a train of adiabatic pulses, such as the hyperbolic secant pulse. Theory presented is valid for quantification of the exchange-induced time-dependent rotating frame longitudinal T1rho,ex and transverse T2rho,ex relaxations in the fast chemical exchange regime.

T1rho MRI contrast in the human brain: modulation of the longitudinal rotating frame relaxation shutter-speed during an adiabatic RF pulse.

Longitudinal relaxation in the rotating frame (T1rho) is the dominant mechanism during a train of adiabatic full passage (AFP) RF pulses with no interpulse intervals, placed prior to an excitation pulse. Asymptotic apparent time constants (T1rho') were measured for human occipital lobe 1H2O at 4T using brief imaging readouts following such pulse trains. Two members of the hyperbolic secant (HSn) AFP pulse family (n=1 or 4; i.e., arising from different amplitude- and frequency-modulation functions) were used. These produced two different non-monoexponential signal decays during the pulse trains. Thus, there are differing contrasts in asymptotic T1rho' maps derived from these data. This behavior is quite different than that of 1H2O signals from an aqueous protein solution of roughly the same macromolecular volume fraction as tissue. The ROI-averaged decays from the two acquisitions can be simultaneously accommodated by a two-site-exchange model for an equilibrium isochronous process whose exchange condition is modulated during the pulse. The model employs a two-spin description of dipolar interaction fluctuations in each site. The intrinsic site R1rho(identical with T1rho(-1)) value is sensitive to fluctuations at the effective Larmor frequency (omegaeff) in the rotating frame, and this is modulated differently during the two types of AFP pulses. Agreement with the data is quite good for site orientation correlation time constants characteristic of macromolecule-interacting water (site A) and bulk-like water (site B). Since R1rhoA is significantly modulated while R1rhoB is not, the intrinsic relaxographic shutter-speed for the process (identical with /R1rhoA-R1rhoB/), and thus the exchange condition, is modulated. However, the mean residence time (67 ms) and intrinsic population fraction (0.2) values found for site A are each rather larger than might be expected, suggesting a disproportionate role for the water molecules known to be "buried" within the large and concentrated macromolecules of in vivo tissue.

Transverse relaxation in the rotating frame induced by chemical exchange.

In the presence of radiofrequency irradiation, relaxation of magnetization aligned with the effective magnetic field is characterized by the time constant T1rho. On the other hand, the time constant T2rho characterizes the relaxation of magnetization that is perpendicular to the effective field. Here, it is shown that T2rho can be measured directly with Carr-Purcell sequences composed of a train of adiabatic full-passage (AFP) pulses. During adiabatic rotation, T2rho characterizes the relaxation of the magnetization, which under adiabatic conditions remains approximately perpendicular to the time-dependent effective field. Theory is derived to describe the influence of chemical exchange on T2rho relaxation in the fast-exchange regime, with time constant defined as T2rho,ex. The derived theory predicts the rate constant R2rho,ex (= 1/T2rho,ex) to be dependent on the choice of amplitude- and frequency-modulation functions used in the AFP pulses. Measurements of R2rho,ex of the water/ethanol exchanging system confirm the predicted dependence on modulation functions. The described theoretical framework and adiabatic methods represent new tools to probe exchanging systems.

Exchange-induced relaxation in the presence of a fictitious field.

In the present study we derive a solution for two site fast exchange-induced relaxation in the presence of a fictitious magnetic field as generated by amplitude and frequency modulated RF pulses. This solution provides a means to analyze data obtained from relaxation experiments with the method called RAFFn (Relaxation Along a Fictitious Field of rank n), in which a fictitious field is created in a coordinate frame undergoing multi-fold rotation about n axes (rank n). The RAFF2 technique is relevant to MRI relaxation methods that provide good contrast enhancement for tumor detection. The relaxation equations for n=2 are derived for the fast exchange regime using density matrix formalism. The method of derivation can be further extended to obtain solutions for n>2.

Relaxation dispersion in MRI induced by fictitious magnetic fields.

A new method entitled Relaxation Along a Fictitious Field (RAFF) was recently introduced for investigating relaxations in rotating frames of rank ≥ 2. RAFF generates a fictitious field (E) by applying frequency-swept pulses with sine and cosine amplitude and frequency modulation operating in a sub-adiabatic regime. In the present work, MRI contrast is created by varying the orientation of E, i.e. the angle ε between E and the z″ axis of the second rotating frame. When ε > 45°, the amplitude of the fictitious field E generated during RAFF is significantly larger than the RF field amplitude used for transmitting the sine/cosine pulses. Relaxation during RAFF was investigated using an invariant-trajectory approach and the Bloch-McConnell formalism. Dipole-dipole interactions between identical (like) spins and anisochronous exchange (e.g., exchange between spins with different chemical shifts) in the fast exchange regime were considered. Experimental verifications were performed in vivo in human and mouse brain. Theoretical and experimental results demonstrated that changes in ε induced a dispersion of the relaxation rate constants. The fastest relaxation was achieved at ε ≈ 56°, where the averaged contributions from transverse components during the pulse are maximal and the contribution from longitudinal components are minimal. RAFF relaxation dispersion was compared with the relaxation dispersion achieved with off-resonance spin lock T(1ρ) experiments. As compared with the off-resonance spin lock T(1ρ) method, a slower rotating frame relaxation rate was observed with RAFF, which under certain experimental conditions is desirable.

Assessment of brain iron and neuronal integrity in patients with Parkinson's disease using novel MRI contrasts.

Postmortem demonstration of increased iron in the substantia nigra (SN) is a well-appreciated finding in Parkinson's disease (PD). Iron facilitates generation of free radicals, which are thought to play a role in dopamine neuronal loss. To date, however, magnetic resonance imaging (MRI) has failed to show significant in vivo differences in SN iron levels in subjects with PD versus control subjects. This finding may be due to the limitations in tissue contrasts achievable with conventional T(1)- and T(2)-weighted MRI sequences that have been used. With the recent development of novel rotating frame transverse (T(2rho)) and longitudinal (T(1rho)) relaxation MRI methods that appear to be sensitive to iron and neuronal loss, respectively, we embarked on a study of 8 individuals with PD (Hoehn & Yahr, Stage II) and 8 age-matched control subjects. Using these techniques with a 4T MRI magnet, we assessed iron deposits and neuronal integrity in the SN. First, T(2rho) MRI, which is reflective of iron-related dynamic dephasing mechanisms (e.g., chemical exchange and diffusion in the locally different magnetic susceptibilities), demonstrated a statistically significant difference between the PD and control group, while routine T(2) MRI did not. Second, T(1rho) measurements, which appear to reflect upon neuronal count, indicated neuronal loss in the SN in PD. We show here that sub-millimeter resolution T(1rho) and T(2rho) MRI relaxation methods can provide a noninvasive measure of iron content as well as evidence of neuronal loss in the midbrain of patients with PD.

Exchange-influenced T2rho contrast in human brain images measured with adiabatic radio frequency pulses.

Transverse relaxation in the rotating frame (T(2rho)) is the dominant relaxation mechanism during an adiabatic Carr-Purcell (CP) spin-echo pulse sequence when no delays are used between pulses in the CP train. The exchange-induced and dipolar interaction contributions (T(2rho,ex) and T(2rho,dd)) depend on the modulation functions of the adiabatic pulses used. In this work adiabatic pulses having different modulation functions were utilized to generate T(2rho) contrast in images of the human occipital lobe at magnetic field of 4 T. T(2rho) time constants were measured using an adiabatic CP pulse sequence followed by an imaging readout. For these measurements, adiabatic full passage pulses of the hyperbolic secant HSn (n = 1 or 4) family having significantly different amplitude-and frequency-modulation functions were used with no time delays between pulses. A dynamic averaging (DA) mechanism (e.g., chemical exchange and diffusion in the locally different magnetic susceptibilities) alone was insufficient to fully describe differences in brain tissue water proton T(2rho) time constants. Measurements of the apparent relaxation time constants (T(2) (dagger)) of brain tissue water as a function of the time between centers of pulses (tau(cp)) at 4 and 7 T permitted separation of the DA contribution from that of dipolar relaxation. The methods presented assess T(2rho) relaxation influenced by DA in tissue and provide a means to generate T(2rho) contrast in MRI.