Shalom Michaeli

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.

Type I mucopolysaccharidosis (MPS I) is an autosomal recessive lysosomal storage disorder with neurological features. Humans and laboratory animals with MPS I exhibit various white matter abnormalities involving the corpus callosum and other regions. In this study, we first validated a novel MRI technique, entitled Relaxation Along a Fictitious Field in the rotating frame of rank n (RAFFn), as a measure of myelination and dysmyelination in mice. We then examined differences between MPS I mice and heterozygotes using RAFF5 and histology. RAFF5 (i.e., RAFFn with n = 5) relaxation time constants were highly correlated with histological myelin density (R2 = 0.68, P<0.001), and RAFF5 clearly distinguished between the hypomyelinated and dysmyelinated shiverer mouse and the wild-type mouse. Bloch-McConnell theoretical analysis revealed slower exchange correlation times and smaller exchange-induced relaxation rate constants for RAFF4 and RAFF5 compared to RAFF1-3, T1ρ, and T2ρ. These data suggest that RAFF5 may assess methylene protons in myelin lipids and proteins, though other mechanisms (e.g. detection of myelin-bound water) may also explain the sensitivity of RAFF5 to myelin. In MPS I mice, mean RAFF5 relaxation time constants were significantly larger for the striatum (P = 0.004) and internal capsule (P = 0.039), and marginally larger for the fornix (P = 0.15). Histological assessment revealed no differences between MPS I mice and heterozygotes in myelin density or corpus callosum thickness. Taken together, these findings support subtle dysmyelination in the brains of mice with MPS I. Dysmyelination may result from myelin lipid abnormalities caused by the absence of α-L-iduronidase. Our findings may help to explain locomotor and cognitive deficits seen in mice with MPS I.

Diffuse abnormalities are known to occur within the brain tissue of multiple sclerosis (MS) patients that is "normal appearing" on T1-weighted and T2-weighted magnetic resonance images. With the goal of exploring the sensitivity of novel MRI parameters to detect such abnormalities, we implemented an inversion-prepared magnetization transfer (MT) protocol and adiabatic T1ρ and T2ρ rotating frame relaxation methods. Nine relapsing-remitting MS patients and seven healthy controls were recruited. Relaxation parameters were measured in a single slice just above the lateral ventricles and approximately parallel to the AC-PC line. The MT ratio of regions encompassing the normal-appearing white matter (NAWM) was different in MS patients as compared with controls (p = 0.043); however, the T1 measured during off-resonance irradiation (T1sat) was substantially more sensitive than the MT ratio for detecting differences between groups (p = 0.0006). Adiabatic T1ρ was significantly prolonged in the NAWM of MS patents as compared to controls (by 6%, p = 0.026), while no differences were found among groups for T2ρ. No differences among groups were observed in the cortical gray matter for any relaxation parameter. The results suggest degenerative processes occurring in the NAWM of MS, likely not accompanied by significant abnormalities in iron content.

The purpose of our study was to determine if sectioning the canine fibular collateral ligament, popliteus tendon, and popliteofibular ligament would result in residual posterolateral instability and produce measureable evidence of early-onset arthritis on ultra-high field MRI. The fibular collateral ligament, popliteus tendon, and popliteofibular ligament were surgically sectioned in six canines. Six months postoperatively, both limbs were biomechanically tested involving 3.25 Nm varus and 1.25 Nm internal and external rotation torques at 28.5° (mean full extension), 60°, and 90° of flexion. A 7.0-tesla MRI scanner acquired T (1ρ)-weighted images, and relaxation time constants were calculated. Compared to the non-operative knees, varus angulation significantly increased by 2.0°, 8.0°, and 12.4° in the operative knees at full extension, 60° flexion, and 90° flexion, respectively. External rotation was significantly increased by 8.1° at full extension, 12.2° at 60°, and 8.2° at 90°. Internal rotation was significantly increased by 9.1° at full extension and 12.4° at 60°. T (1ρ) MRI mapping revealed a significant increase in relaxation times in the medial compartment of the surgical knees compared to controls. This study validated that grade III surgically created posterolateral knee injuries do not heal and that the canine knee developed early-onset changes of the medial compartment, indicative of early-onset osteoarthritis, developed in the operative knees.

Measurements of chemical-exchange processes by NMR are widely used to obtain valuable information about molecular dynamics and structure. Here, a computational method is introduced to assess the influence of chemical exchange on spin relaxation rates. The method is based on the inclusion of a random exchange process in product operator calculations on a microscopic level. This product operator approach can be applied to estimate exchange contributions when using sophisticated pulse sequences that cannot be easily described analytically. The method applies to the full range of exchange times measurable by NMR and can incorporate interference effects between exchange and other processes such as scalar coupling. To demonstrate its utility, simulated relaxation data were compared with theoretical predictions of spin-locking and Carr-Purcell spin-echo sequences with hard and adiabatic pulses, using different time scales for a two-site chemical-exchange process. Finally, simulations were used to examine a system in which a second random process is superimposed on a simple two-site exchange process. The method was found to provide a simple and robust tool to analyze pulse sequences and equations commonly used to study exchange-induced relaxation.

ABSTRACT Transverse relaxation in the rotating frame (T2ρ) is the dominant relaxation mechanism during a train of adiabatic full passage (AFP) radiofrequency (RF) pulses with no interpulse time intervals placed after the 90° excitation pulse. The magnetization components remain transverse to the time-dependent effective field and undergo relaxation with the time constant T2ρ. Longitudinal relaxation in the rotating frame (T1ρ) is the dominant relaxation mechanism during a train of AFP RF pulses placed prior to an excitation pulse. Here, magnetization is aligned along the time-dependent effective field during adiabatic rotation undergoes relaxation with the time constant T1ρ. A detailed description of rotating frame relaxations due to dipolar interactions and exchange during adiabatic pulses is presented herein. The exchange-induced and dipolar interaction contributions depend on the modulation functions of the adiabatic pulses used. The intrinsic rotating frame relaxation rate constant is sensitive to fluctuations at the effective frequencey (ωeff) in the rotating frame, and this is modulated differently during the two types of AFP pulses. This may lead to the possibility to assess T1ρ and T2ρ relaxation influenced by dipolar relaxation pathways and exchange in human brain tissue and provide a means to generate T1ρ and T2ρ contrasts in MRI.