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A direct measure of intramolecular chain diffusion is obtained by the determination of triplet-triplet energytransfer rates between a donor and an acceptor chromophore attached at defined points on a polypeptide chain. Single exponential kinetics of contact formation are observed on the nanosecond time scale for polypeptides in which donor and acceptor are linked by repeating units of glycine and serine residues. The rates depend on the number of peptide bonds (N) separating donor and acceptor and show a maximum for the shortest peptides (N ‫؍‬ 3) with a time constant ( ‫؍‬ 1/k) of 20 ns. This sets an upper limit for the speed of formation of the first side-chain contacts during protein folding.Protein folding starts from an ensemble of random coil conformations to finally reach the native state with well defined side-chain contacts. For many proteins, rapid chain collapse precedes formation of the native structure (1-3). In a number of small proteins, in contrast, collapse and formation of the native interactions occur simultaneously (4-8). In both scenarios, the search for energetically favorable conformations requires formation of interactions between parts of the polypeptide chain, which is limited by chain dynamics. Intrachain diffusion can thus be regarded as the elementary process that determines the maximum rate at which a protein can fold. Models for the rate-limiting steps and for the distance dependence of intrachain diffusion have been proposed in a number of theoretical studies (9-13), but to date no direct experimental data are available for the rates of contact formation between two defined points on a polypeptide chain.Triplet-triplet energy transfer provides an excellent tool to measure such rates of contact formation. Energy transfer between an electronically excited triplet donor (sensitizer) and an acceptor proceeds by an electron-exchange mechanism (Dexter mechanism), which requires van der Waals contact between the donor and acceptor. Rates of intermolecular exothermic triplet energy transfer approach, but do not exceed, the diffusion-controlled limit (14). The process is readily monitored by triplet-triplet absorption by using laser-flash photolysis. The fast formation and the long lifetimes of many triplet states allow measurements of processes in the range from nanoseconds to microseconds. MATERIALS AND METHODSThioxanthone (E T ϭ 265 kJ⅐mol Ϫ1) was used as a triplet donor, which can be excited selectively with an excimer laser pulse at 351 nm in the presence of naphthalene (E T ϭ 253 kJ⅐mol Ϫ1) as the acceptor (15). The amount of thioxanthone triplets was monitored by their strong triplet-triplet absorbance at max ϭ 620 nm. Fig. 1a shows the transient absorbance of triplet thioxanthone after excitation by a 351-nm laser flash of 20-ns duration. In the absence of acceptor, the thioxanthone triplets decay with a half-life of 30 s. The decay rate of the thioxanthone triplets increases on addition of naphthalene, because of the formation of triplet naphthalene (Fig. 1b). The secondor...

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Balanced steady state free precession (balanced SSFP) has become increasingly popular for research and clinical applications, offering a very high signal-to-noise ratio and a T2 /T1 -weighted image contrast. This review article gives an overview on the basic principles of this fast imaging technique as well as possibilities for contrast modification. The first part focuses on the fundamental principles of balanced SSFP signal formation in the transient phase and in the steady state. In the second part, balanced SSFP imaging, contrast, and basic mechanisms for contrast modification are revisited and contemporary clinical applications are discussed.

Balanced steady-state free precession (SSFP) completely compensates for all gradients within each repetition time (TR), and is thus very sensitive to any magnetic field imperfection that disturbs the perfectly balanced acquisition scheme. It is demonstrated that balanced SSFP is especially sensitive to changing eddy currents that are induced by stepwise changing phase-encoding (PE) gradients. In contrast to the linear k-space trajectory, which has small variations between consecutive encoding steps, other encoding schemes (e.g., centric, random, or segmented orderings) exhibit significant jumps in k-space between adjacent PE steps, and consequently induce rapidly changing eddy currents. The resulting disturbances induce significant image artifacts, such that compensation strategies are essential when nonlinear PE schemes are applied. Although direct annihilation of the induced eddy currents by additional, opposing magnetic fields has been investigated, it is limited by uncertainty regarding the time evolution of induced eddy currents. A generic (and thus system-unrelated) compensation strategy is proposed that consists of "pairing" of consecutive PE steps. Another approach is based on partial dephasing along the slice direction that annihilates eddy-current-induced signal oscillations. Both pairing of the PE steps and "through- Recent advances in MR hardware, and especially gradient coil and amplifier design have led to the increased importance and clinical use of balanced steady-state free precession imaging techniques (e.g., trueFISP, FIESTA, balanced FFE, and balanced SSFP) (1). In contrast to other gradient-echo methods, balanced steady-state techniques offer superior signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR); however, they suffer from artifacts resulting from any magnetic field imperfection that disturbs the perfectly balanced acquisition scheme. A major source of imperfections is off-resonant frequencies due to inhomogeneities of the magnetic field, such as susceptibility variations in the tissue (2). Furthermore, induced eddy currents within the conductive components of the MRI system generated by the timevarying magnetic fields of the phase-encoding (PE) gradient set have an important impact on the quality of balanced SSFP images. While a certain amount of dephasing (due to field inhomogeneities) can be refocused during steady-state, an abrupt change may generate sufficient deviations from the dynamic equilibrium to induce large signal fluctuations, and thus image artifacts. These types of rapid changes are mainly caused by eddy currents produced by varying PE gradients, and as a result currently available k-space encoding strategies are limited (3). Alternative view ordering schemes are often desirable in magnetization-prepared SSFP experiments to maximize signal contrast during acquisition, as was recently applied for contrast-enhanced MR angiography (CE-MRA) (4), or to accelerate cardiac 3D cine imaging (5); however, the applicable trajectories are considerably restricted due to ed...

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ObjectiveTo compare mono- and bi-exponential T2* analysis in healthy and degenerated Achilles tendons using a recently introduced magnetic resonance variable-echo-time sequence (vTE) for T2* mapping.MethodsTen volunteers and ten patients were included in the study. A variable-echo-time sequence was used with 20 echo times. Images were post-processed with both techniques, mono- and bi-exponential [T2*m, short T2* component (T2*s) and long T2* component (T2*l)]. The number of mono- and bi-exponentially decaying pixels in each region of interest was expressed as a ratio (B/M). Patients were clinically assessed with the Achilles Tendon Rupture Score (ATRS), and these values were correlated with the T2* values.ResultsThe means for both T2*m and T2*s were statistically significantly different between patients and volunteers; however, for T2*s, the P value was lower. In patients, the Pearson correlation coefficient between ATRS and T2*s was −0.816 (P = 0.007).ConclusionThe proposed variable-echo-time sequence can be successfully used as an alternative method to UTE sequences with some added benefits, such as a short imaging time along with relatively high resolution and minimised blurring artefacts, and minimised susceptibility artefacts and chemical shift artefacts. Bi-exponential T2* calculation is superior to mono-exponential in terms of statistical significance for the diagnosis of Achilles tendinopathy.Key Points• Magnetic resonance imaging offers new insight into healthy and diseased Achilles tendons• Bi-exponential T2* calculation in Achilles tendons is more beneficial than mono-exponential• A short T2* component correlates strongly with clinical score• Variable echo time sequences successfully used instead of ultrashort echo time sequences

Balanced steady-state free precession (bSSFP) has become increasingly important in clinical applications. Its signal properties have been investigated over several years by many groups, and various critical factors for bSSFP signal intensity and stability, such as off-resonances, flow, and eddy currents, have been identified. It is generally accepted that bSSFP signal intensity is a function of relaxation times, excitation angles, and spin densities only. While this is true for simple phantoms, it appears that signals from tissues are significantly less intense than predicted by theory. This work demonstrates that the molecular origin of this apparent signal reduction is due to on-resonance magnetization transfer (MT). High flip angles in combination with very short repetition times (TRs), as commonly used for bSSFP, lead to a considerable saturation in the fraction of macromolecular (MM) pool protons. As a result, bSSFP signal is strongly attenuated by up to a factor of 2 in the human brain compared to the signal expected from theory. The signal behavior of balanced SSFP (bSSFP; also known as TrueFISP, FIESTA, and balanced FFE) has been investigated in detail over the last several years by several research groups. This includes the analysis and modification of bSSFP's frequency response function to generate frequency-selective images, such as water-only images; investigations of the transient phase and its off-resonance behavior, and possible preparation or starter schemes; and the modification of the somewhat artificial T 2 over T 1 contrast using magnetization preparation techniques. It is commonly accepted that under certain conditions the signal intensity of steady-state bSSFP is proportional to the ͱT 2 /T 1 , as can be derived from the Freeman-Hill formula (1) for TR Ͻ Ͻ T 1 ,T 2 (2). This contrast can be clearly recognized in clinical applications such as cardiac or abdominal imaging, where signals from muscles or liver are low, whereas those from blood, cerebrospinal fluid (CSF), and fat are bright.Theoretical signal intensities derived from the FreemanHill formula (1) and signals from experiments on dopedwater phantoms are in excellent agreement. On the other hand, no detailed and quantitative comparison between theoretical and measured signals in biological tissues has been performed to date. However, subtle deviations from the theoretical formula have been recognized in some studies (3-5), indicating further mechanisms of contrast generation in bSSFP.An introductory 2D bSSFP example of this behavior is presented in Fig. 1a. In this figure vessels and CSF appear bright, whereas gray matter (GM) and white matter (WM) show low signal intensities. The contrast ratio of CSF to GM or WM yields a factor of about 6. However, according to the Freeman-Hill formula, which is a function of the flip angle ␣, microscopic relaxation rates T 1 and T 2 , spin density 0 , and repetition time (TR), the contrast ratio should only be a factor of ϳ3, instead of 6. Thus signals from experiments and predictions deviate by a...