Magnetic Resonance Fingerprinting with short relaxation intervals

PurposeThe aim of this study was to investigate a technique for improving the performance of Magnetic Resonance Fingerprinting (MRF) in repetitive sampling schemes, in particular for 3D MRF acquisition, by shortening relaxation intervals between MRF pulse train repetitions.Material and methodsA calculation method for MRF dictionaries adapted to short relaxation intervals and non-relaxed initial spin states is presented, based on the concept of stationary fingerprints. The method is applicable to many different k-space sampling schemes in 2D and 3D. For accuracy analysis, T₁ and T₂ values of a phantom are determined by single-slice Cartesian MRF for different relaxation intervals and are compared with quantitative reference measurements. The relevance of slice profile effects is also investigated in this case. To further illustrate the capabilities of the method, an application to in-vivo spiral 3D MRF measurements is demonstrated.ResultsThe proposed computation method enables accurate parameter estimation even for the shortest relaxation intervals, as investigated for different sampling patterns in 2D and 3D. In 2D Cartesian measurements, we achieved a scan acceleration of more than a factor of two, while maintaining acceptable accuracy: The largest T₁ values of a sample set deviated from their reference values by 0.3% (longest relaxation interval) and 2.4% (shortest relaxation interval). The largest T₂ values showed systematic deviations of up to 10% for all relaxation intervals, which is discussed. The influence of slice profile effects for multislice acquisition is shown to become increasingly relevant for short relaxation intervals. In 3D spiral measurements, a scan time reduction of 36% was achieved, maintaining the quality of in-vivo T1 and T2 maps.ConclusionsReducing the relaxation interval between MRF sequence repetitions using stationary fingerprint dictionaries is a feasible method to improve the scan efficiency of MRF sequences. The method enables fast implementations of 3D spatially resolved MRF.     

Single-slice mapping of ultrashort T(2)

In this communication we present a method for single-slice mapping of ultrashort transverse relaxation times T(2). The RF pulse sequence consists of a spin echo preparation of the magnetization followed by slice-selective ultrashort echo time (UTE) imaging with radial k-space sampling. In order to keep the minimum echo time as small as possible, avoid out-of-slice contamination and signal contamination due to unwanted echoes, the implemented pulse sequence employs a slice-selective 180° RF refocusing pulse and a 4-step phase cycle. The slice overlap of the two slice-selective RF pulses was investigated. An acceptable Gaussian slice profile could be achieved by adjusting the strength of the two slice-selection gradients. The method was tested on a short T(2) phantom consisting of an arrangement of a roll of adhesive tape, an eraser, a piece of modeling dough made of Plasticine?, and a 10% w/w agar gel. The T(2) measurements on the phantom revealed exponential signal decays for all samples with T(2)(adhesive tape)=(0.5 ± 0.1)ms, T(2)(eraser)=(2.33 ± 0.07)ms, T(2)(Plasticine?)=(2.8 ± 0.06)ms, and T(2)(10%agar)=(9.5 ± 0.83)ms. The T(2) values obtained by the mapping method show good agreement with the T(2) values obtained by a non-selective T(2) measurement. For all samples, except the adhesive tape, the effective transverse relaxation time T(2)(?) was significantly shorter than T(2). Depending on the scanner hardware the presented method allows mapping of T(2) down to a few hundreds of microseconds. Besides investigating material samples, the presented method can be used to study the rapidly decaying MR-signal from biological tissue (e.g.: bone, cartilage, and tendon) and quadrupolar nuclei (e.g.: (23)Na, (35)Cl, and (17)O).     

Rapid and accurate measurement of transverse relaxation times using a single shot multi-echo echo-planar imaging sequence

Methods for making rapid and accurate measurements and maps of the transverse relaxation time from a single free induction decay (FID) are proposed. The methods use a multi-echo sequence in combination with B1 insensitive (hyperbolic secant or BIREF2b) refocusing pulses and rapid echo-planar imaging techniques. The results were calibrated against a single spin echo echo-planar imaging sequence using a phantom containing a range of CuSO4 concentrations. The mean percentage absolute difference between the multi-echo and single-echo results was 3% for the multi-echo sequence using the hyperbolic secant refocusing pulse, and 7% for the multi-echo sequence using the BIREF2b refocusing pulse, compared to 13% for a multi-echo sequence using a nonselective sinc refocusing pulse. The use of the sequences in vivo has been demonstrated in studies of gastric function, i.e., the measurement of gastric dilution and monitoring of formation of a raft of alginate polysaccharide within the stomach.     

Measuring pore connectivity by pulsed field gradient diffusion editing with hydrocarbon gases

Measurements of time-dependent diffusion are performed on a rock sample saturated first with water, then methane and finally ethane. The gases were selected because their increased diffusivities and relaxation times allow probing greater length scales than water and because of their practical relevance. The nuclear magnetic resonance measurements employed pulse field gradient diffusion editing pulse sequences, allowing analysis of D(t) as a function of relaxation time. Very different D(t) behaviors are observed for different relaxation times, including indications of connected pore networks at moderate relaxation times.     

Experimental validation of a T2rho transverse relaxation model using LASER and CPMG acquisitions

The transverse relaxation rate (R2=1/T2) of many biological tissues are altered by endogenous magnetized particles (i.e., ferritin, deoxyhemoglobin), and may be sensitive to the pathological progression of neurodegenerative disorders associated with altered brain-iron stores. R2 measurements using Carr-Purcell-Meiboom-Gill (CPMG) acquisitions are sensitive to the refocusing pulse interval (2taucp), and have been modeled as a chemical exchange (CE) process, while R2 measurements using a localization by adiabatic selective refocusing (LASER) sequence have an additional relaxation rate contribution that has been modeled as a R2rho process. However, no direct comparison of the R2 measured using these two sequences has been described for a controlled phantom model of magnetized particles. The three main objectives of this study were: (1) to compare the accuracy of R2 relaxation rate predictions from the CE model with experimental data acquired using a conventional CPMG sequence, (2) to compare R2 estimates obtained using LASER and CPMG acquisitions, and (3) to determine whether the CE model, modified to account for R2rho relaxation, adequately describes the R2 measured by LASER for a full range of taucp values. In all cases, our analysis was confined to spherical magnetic particles that satisfied the weak field regime. Three phantoms were produced that contained spherical magnetic particles (10 microm diameter polyamide powders) suspended in Gd-DTPA (1.0, 1.5, and 2.0 mmol/L) doped gel. Mono-exponential R2 measurements were made at 4T as a function of refocusing pulse interval. CPMG measurements of R2 agreed with CE model predictions while significant differences in R2 estimates were observed between LASER and CPMG measurements for short taucp acquisitions. The discrepancy between R2 estimates is shown to be attributable to contrast enhancement in LASER due to T2rho relaxation.     

Laser scattering with a rapidly tuned dye laser

A facility is described for the measurement of the total spectrum produced by laser radiation scattered from a plasma during one laser pulse. The dye laser is electrooptically tuned by a high frequency voltage applied to a modified Lyot filter within its cavity. The scattered spectrum is registrated together with the laser reference signal by a transient recorder and processed afterwards. Both measuring time and inaccuracy could be reduced drastically. Scattering experiments have been accomplished in a H₂ cascade of 5 mm diameter arc at atmospheric pressure, and at 14 and 20 A, respectively. For this arc very precise spectroscopic results are available for checking the accuracy of the scattering measurements. Both the spectroscopic line and continuum experiments yield a temperature which lies between electron and ion temperature if there is no local thermal equilibrium, whereas the pure electron temperature is provided by the scattered spectrum. The agreement between spectroscopic and scattering results within the high error limits is the experimental proof for the applicability of this new scattering technique which requires only about one hundredth of the measuring time, as compared with the usual shot-to-shot registration.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

MRI with the dipolar interaction refocusing techniques: analysis of the effectiveness for the solid-state polymers

The effectiveness of solid-echo and magic-echo phase-encoding solid-state magnetic resonance imaging methods was tested to determine possible improvement of sensitivity and spatial resolution for investigation of various types of solid polymers. The dipolar interaction refocusing pulse sequences have been used to elongate the possible phase-encoding period and to improve the signal sensitivity. The comparison of both dipolar refocusing techniques with conventional single point imaging method was made. The optimization of the phase-encoding time and magnetization recovery periods were performed basing on (1)H spectra and longitudinal relaxation measurements, respectively. The influence of imaging artifacts (intrinsic for each technique) on image quality was investigated. The effectiveness of the artifacts suppression methods was tested.     

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR

Protein backbone 15N NMR spin relaxation rates are useful in characterizing the protein dynamics and structures. To observe the protein nuclear-spin resonances a pulse sequence has to include a water suppression scheme. There are two commonly employed methods, saturating or dephasing the water spins with pulse field gradients and keeping them unperturbed with flip-back pulses. Here different water suppression methods were incorporated into pulse sequences to measure 15N longitudinal T1 and transversal rotating-frame T1ρ spin relaxation. Unexpectedly the 15N T1 relaxation time constants varied significantly with the choice of water suppression method. For a 25-kDa Escherichiacoli. glutamine binding protein (GlnBP) the T1 values acquired with the pulse sequence containing a water dephasing gradient are on average 20% longer than the ones obtained using a pulse sequence containing the water flip-back pulse. In contrast the two T1ρ data sets are correlated without an apparent offset. The average T1 difference was reduced to 12% when the experimental recycle delay was doubled, while the average T1 values from the flip-back measurements were nearly unchanged. Analysis of spectral signal to noise ratios (s/n) showed the apparent slower 15N relaxation obtained with the water dephasing experiment originated from the differences in 1HN recovery for each relaxation time point. This in turn offset signal reduction from 15N relaxation decay. The artifact becomes noticeable when the measured 15N relaxation time constant is comparable to recycle delay, e.g., the 15N T1 of medium to large proteins. The 15N relaxation rates measured with either water suppression schemes yield reasonable fits to the structure. However, data from the saturated scheme results in significantly lower Model-Free order parameters (=0.81) than the non-saturated ones (=0.88), indicating such order parameters may be previously underestimated.     

Maximizing MR signal for 2D UTE slice selection in the presence of rapid transverse relaxation

Ultrashort TE (UTE) sequences allow direct visualization of tissues with very short T2 relaxation times, such as tendons, ligaments, menisci, and cortical bone. In this work, theoretical calculations, simulations, and phantom studies, as well as in vivo imaging were performed to maximize signal-to-noise ratio (SNR) for slice selective RF excitation for 2D UTE sequences. The theoretical calculations and simulations were based on the Bloch equations, which lead to analytic expressions for the optimal RF pulse duration and amplitude to maximize magnetic resonance signal in the presence of rapid transverse relaxation. In steady state, it was found that the maximum signal amplitude was not obtained at the classical Ernst angle, but at an either lower or higher flip angle, depending on whether the RF pulse duration or amplitude was varied, respectively.     

Quality assessment of localization technique performance in small volume in vivo 1H MR spectroscopy

A new phantom and evaluation method for experimental evaluation of 1H-magnetic resonance spectroscopy single volume localization techniques regarding signal contamination (C), defined as the part of the signal originating outside the volume of interest, is presented. The quality assessment method is based on a spherical phantom with an oil/water interface in order to reduce susceptibility effects, and applied for stimulated-echo acquisition method (STEAM) and spin-echo (SE) sequences, echo times of 270, 135, and 10 ms, and cubic volumes of interest (VOI) of 1(3), 1.5(3), 2(3), 2.5(3), and 3(3) cm3. To be able to mimic measurements of the contamination in three dimensions the physical gradients representing the three orthogonal directions for slice selection were shifted in the pulse sequences. Contamination values in one dimension differed between 6.5% and 8.4% in SE sequences, and between 0.7% and 13.8% in STEAM sequences. In STEAM sequences a decrease of C with increasing VOI size was observed while SE sequences showed comparable C values for the different VOI sizes tested. The total contamination in three dimensions were 19% and 18% in SE and STEAM sequences with a TE of 270 ms, and 7% in a STEAM sequence with a TE of 10 ms, respectively. The presented evaluation method is easily applied to the new phantom and showed high reproducibility.     

The analysis of excite and probe measurements of relaxation times with fluctuating pulse duration

The effect of fluctuations in the pulse duration of synchronously pumped modelocked pulse trains on excite and probe measurements is discussed. Relaxation times comparable with the pulse durations can be measured even when large pulse-to-pulse fluctuations in duration exist. The pump and probe pulse durations are assumed to be correlated. When the probe pulses are the second harmonic of the pump, or vice versa, the third harmonic must also be generated to permit deconvolution of experimental excite and probe data. When the pump and probe pulses have the same time dependence, the excite and probe curves consist of the desired response function convolved with the time-averaged second harmonic autocorrelation function which is easily measured. Deconvolution yields the relaxation time but fluctuations in pulse duration increase the root-mean-square voltage fluctuation at the output of the detector system and limit the accuracy with which the relaxation time can be calculated.     

Rapid MRI method for mapping the longitudinal relaxation time

A novel method for mapping the longitudinal relaxation time in a clinically acceptable time is developed based on a recent proposal [J.-J. Hsu, I.J. Lowe, Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization, J. Magn. Reson. 169 (2004) 270-278] and the speed of the spiral pulse sequence. The method acquires multiple curve-fitting samples with one RF pulse train. It does not require RF pulses of specific flip angles (e.g., 90 degrees or 180 degrees ), nor are the long recovery waiting time and the measurement of the magnetization at thermal equilibrium needed. Given the value of the flip angle, the curve fitting is semi-logarithmic and not computationally intensive. On a heterogeneous phantom, the average percentage difference between measurements of the present method and those of an inversion-recovery method is below 2.7%. In mapping the human brain, the present method, for example, can obtain four curve-fitting samples for five 128 x 128 slices in less than 3.2s and the results are in agreement with other studies in the literature.     

Feasibility of fast MR imaging of the liver at 1.5 T

A phantom with T1 and T2 relaxation times encompassing normal liver and liver lesions was constructed to evaluate fast magnetic resonance pulse sequences using TR from 21-100 milliseconds, TE 12-60 milliseconds and flip angles from 5 degrees-90 degrees. Ten of these fast MR sequences were then selected and compared with conventional spin-echo sequences in normal volunteers (n = 3) and in patients with liver lesions (n = 6). Subjectively, the fast MR sequences eliminated motion artefacts. Objectively, 8 of 10 fast sequences had signal-to-noise ratios comparable to spin-echo imaging whereas only 2 of 10 had contrast-to-noise ratios that were similar to spin-echo imaging. This preliminary study, performed at 1.5 Tesla, does not show any clear-cut advantage of fast imaging over spin-echo imaging in the detection of liver lesions. The use of a liver tissue equivalent phantom provides a rapid, practical approach in evaluation of fast scans.     

Quality assessment of localization technique performance in small volume in vivo H MR spectroscopy

A new phantom and evaluation method for experimental evaluation of ¹H-magnetic resonance spectroscopy single volume localization techniques regarding signal contamination (C), defined as the part of the signal originating outside the volume of interest, is presented. The quality assessment method is based on a spherical phantom with an oil/water interface in order to reduce susceptibility effects, and applied for stimulated-echo acquisition method (STEAM) and spin-echo (SE) sequences, echo times of 270, 135, and 10 ms, and cubic volumes of interest (VOI) of 1³, 1.5³, 2³, 2.5³, and 3³ cm³. To be able to mimic measurements of the contamination in three dimensions the physical gradients representing the three orthogonal directions for slice selection were shifted in the pulse sequences. Contamination values in one dimension differed between 6.5% and 8.4% in SE sequences, and between 0.7% and 13.8% in STEAM sequences. In STEAM sequences a decrease of C with increasing VOI size was observed while SE sequences showed comparable C values for the different VOI sizes tested. The total contamination in three dimensions were 19% and 18% in SE and STEAM sequences with a TE of 270 ms, and 7% in a STEAM sequence with a TE of 10 ms, respectively. The presented evaluation method is easily applied to the new phantom and showed high reproducibility.     

Measurements of RF heating during 3.0-T MRI of a pig implanted with deep brain stimulator

Purpose

To present preliminary, in vivo temperature measurements during MRI of a pig implanted with a deep brain stimulation (DBS) system.

Materials and Methods

DBS system (Medtronic Inc., Minneapolis, MN) was implanted in the brain of an anesthetized pig. 3.0-T MRI was performed with a T/R head coil using the low-SAR GRE EPI and IR-prepped GRE sequences (SAR: 0.42 and 0.39 W/kg, respectively), and the high-SAR 4-echo RF spin echo (SAR: 2.9 W/kg). Fluoroptic thermometry was used to directly measure RF-related heating at the DBS electrodes, and at the implantable pulse generator (IPG). For reference the measurements were repeated in the same pig at 1.5 T and, at both field strengths, in a phantom.

Results

At 3.0 T, the maximal temperature elevations at DBS electrodes were 0.46 °C and 2.3 °C, for the low- and high-SAR sequences, respectively. No heating was observed on the implanted IPG during any of the measurements. Measurements of in vivo heating differed from those obtained in the phantom.

Conclusion

The 3.0-T MRI using GRE EPI and IR-prepped GRE sequences resulted in local temperature elevations at DBS electrodes of no more than 0.46 °C. Although no extrapolation should be made to human exams and much further study will be needed, these preliminary data are encouraging for the future use 3.0-T MRI in patients with DBS.     

Fiber-to-field angle dependence of proton nuclear magnetic relaxation in collagen

Longitudinal and transverse proton relaxation times were measured on pig tendon. For T₁, dispersion curves and more accurate measurements at 20 MHz are presented. Values of T₂ were obtained from CPMG pulse sequences, at 20 MHz. The dependence of relaxation times against the fiber-to-field angle was particularly investigated. Longitudinal relaxation rate was found to be almost orientation independent, and presented quadrupolar peaks between 1 and 4 MHz. On the contrary, transverse relaxation, that was well fitted by the sum of four exponentials, was highly orientation dependent. Deconvolution showed that the exponentials decaying most quickly are most orientation dependent. For those two fractions, a cross-relaxation model allowed explaining the fiber-to-field angle dependence, and the specially low rate corresponding to the magic angle of 55°. Finally, each decaying mode was assigned to a fraction of protons localized in the macromolecular structure and characterized by particular dynamics.     

Errors in the Measurement of Cross-Correlated Relaxation Rates and How to Avoid Them

Cross-correlated relaxation rates Γ are commonly obtained from constant time experiments by measuring the effect of the desired cross-correlated relaxation on an appropriate coherence during the constant time T. These measurements are affected by systematic errors, which derive from undesired cross-correlated relaxation effects taking place before and after the constant time period T. In this paper we discuss the sources and the size of these errors in an example of two pulse sequences. Higher accuracy of the measured data can be obtained by recording a set of experiments with different T values. Cross-correlated relaxation rates are measured in constant time experiments either from the differential relaxation of multiplet components (J-resolved Γ experiments) or from the efficiency of magnetization transfer between two coherences (quantitative Γ experiments). In this paper we calculate analytically the statistical errors in both J-resolved and quantitative Γ experiments. These formulae provide the basis for the choice of the most efficient experimental approach and parameters for a given measurement time and size of the rate. The optimal constant time T for each method can be calculated and depends on the relaxation properties of the molecule under investigation. Moreover, we will show how to optimize the relative duration of cross and reference experiments in a quantitative Γ approach.     

Application of linear optimization techniques to MRI phase contrast blood flow measurements

The goal of this study was to use linear optimization techniques as a systematic method of cine phase contrast pulse sequence design and to apply this technique to the measurement of blood flow in vivo. The optimized waveforms were validated in a constant flow phantom with average velocities ranging from 5 to 50 cm/s. The same optimized sequence was also run in a segmented k-space variation with five phase encoding lines per segment. The magnetic resonance (MR) derived velocity measurements were accurate over the entire range of velocities tested (p < .05) in both cases. The same optimized pulse sequence was applied to the measurement of flow in the main pulmonary artery of five normal volunteers and compared with stroke volumes and cardiac outputs calculated from right ventricular volume measurements. These measurements showed a mean difference between the MR phase contrast calculated stroke volume and the volumetric stroke volume measurement of 9.8 ± 11.6%. The mean difference between the calculated phase contrast cardiac output and the volumetric cardiac output was 4.4 ± 10%. These results imply that optimization techniques are an efficient method for designing cine phase contrast pulse sequences.     

Influence of the electron-hole density profile on the reflectivity of laser irradiated silicon

We study the influence of the spatial extension of the electron-hole plasma created by a pump pulse on the reflectivity of a probe pulse. We show that the density deduced from reflectivity measurements is the surface density value with a very good accuracy, except very close to the plasma resonance. We also show that the resonance broadening due to the spatial inhomogeneity can be larger than the one due to free carriers absorption and has to be included in the usual experimental determination of the plasma relaxation time.