Henning Dathe

High-resolution maps of magnetization transfer with inherent correction for RF inhomogeneity and T1 relaxation obtained from 3D FLASH MRI

An empirical equation for the magnetization transfer (MT) FLASH signal is derived by analogy to dual‐excitation FLASH, introducing a novel semiquantitative parameter for MT, the percentage saturation imposed by one MT pulse during TR. This parameter is obtained by a linear transformation of the inverse signal, using two reference experiments of proton density and T1 weighting. The influence of sequence parameters on the MT saturation was studied. An 8.5‐min protocol for brain imaging at 3 T was based on nonselective sagittal 3D‐FLASH at 1.25 mm isotropic resolution using partial acquisition techniques (TR/TE/α = 25ms/4.9ms/5° or 11ms/4.9ms/15° for the T1 reference). A 12.8 ms Gaussian MT pulse was applied 2.2 kHz off‐resonance with 540° flip angle. The MT saturation maps showed an excellent contrast in the brain due to clearly separated distributions for white and gray matter and cerebrospinal fluid. Within the limits of the approximation (excitation <15°, TR/T1 ≪ 1) the MT term depends mainly on TR, the energy and offset of the MT pulse, but hardly on excitation and T1 relaxation. It is inherently compensated for inhomogeneities of receive and transmit RF fields. The MT saturation appeared to be a sensitive parameter to depict MS lesions and alterations of normal‐appearing white matter. Magn Reson Med 60:1396–1407, 2008.

Quantitative FLASH MRI at 3T using a rational approximation of the Ernst equation

From the half‐angle substitution of trigonometric terms in the Ernst equation, rational approximations of the flip angle dependence of the FLASH signal can be derived. Even the rational function of the lowest order was in good agreement with the experiment for flip angles up to 20°. Three‐dimensional maps of the signal amplitude and longitudinal relaxation rates in human brain were obtained from eight subjects by dual‐angle measurements at 3T (nonselective 3D‐FLASH, 7° and 20° flip angle, TR = 30 ms, isotropic resolution of 0.95 mm, each 7:09 min). The corresponding estimates of T1 and signal amplitude are simple algebraic expressions and deviated about 1% from the exact solution. They are ill‐conditioned to estimate the local flip angle deviation but can be corrected post hoc by division of squared RF maps obtained by independent measurements. Local deviations from the nominal flip angles strongly affected the relaxation estimates and caused considerable blurring of the T1 histograms. Magn Reson Med 59:667–672, 2008.

Influence of thermoplastic appliance thickness on the magnitude of force delivered to a maxillary central incisor during tipping.

INTRODUCTION The aim of the study was to quantify the forces delivered by thermoplastic appliances made of 2 materials with 2 thicknesses to a maxillary central incisor during tipping. METHODS Two materials were tested, each in 2 thicknesses: Erkodur (Erkodent Erich Kopp GmbH, Pfalzgrafenweiler, Germany) 1.0 and 0.8 mm, and Biolon (Dreve Dentamid GmbH, Unna, Germany), 1.0 and 0.75 mm. For each material, 5 appliances were produced. To measure the forces applied, an isolated measuring tooth, part of a standardized resin model, was deflected in 0.05 degrees steps from 0 degrees to 0.42 degrees in the vestibular and palatine directions, after placing the respective appliance on the model. For statistical analysis, the force components Fx/tipping and Fz/intrusion at a displacement of +/- 0.151 mm from the incisor edge were selected. Means and standard deviations were calculated. The Wilcoxon 2-sample test for group pairings was used. RESULTS The norms for the mean Fx forces ranged from 1.62 (SD, 0.41) to 5.35 N (SD, 0.63). The mean Fz forces were between 0.07 (SD, 0.13) and -2.47 N (SD, 0.34). The highest intrusive forces were measured during vestibular displacement of the measuring tooth. The forces delivered by the thick appliances were overall significantly higher (P <0.0001) than those of the thin materials. The forces delivered by the Biolon appliances were generally significantly higher (P <0.0001) than those for the Erkodur materials. CONCLUSIONS The forces applied were mostly too high when compared with those stated in the literature as ideal. In addition to thickness, the thermoforming process influences the magnitude of the force delivered by a thermoformed appliance.

Modeling the influence of TR and excitation flip angle on the magnetization transfer ratio (MTR) in human brain obtained from 3D spoiled gradient echo MRI

Attempts to optimize the magnetization transfer ratio (MTR) obtained from spoiled gradient echo MRI have focused on the properties of the magnetization transfer pulse. In particular, continuous‐wave models do not explicitly account for the effects of excitation and relaxation on the MTR. In this work, these were modeled by an approximation of free relaxation between the radiofrequency pulses and of an instantaneous saturation event describing the magnetization transfer pulse. An algebraic approximation of the signal equation can be obtained for short pulse repetition time and small flip angles. This greatly facilitated the mathematical treatment and understanding of the MTR. The influence of inhomogeneous radiofrequency fields could be readily incorporated. The model was verified on the human brain in vivo at 3 T by variation of flip angle and pulse repetition time. The corresponding range in MTR was similar to that observed by a 4‐fold increase of magnetization transfer pulse power. Choice of short pulse repetition time and larger flip angles improved the MTR contrast and reduced the influence of radiofrequency inhomogeneity. Optimal contrast is obtained around an MTR of 50%, and noise progression is reduced when a high reference signal is obtained. Magn Reson Med, 2010.

Initial Forces and Moments Delivered by Removable Thermoplastic Appliances during Rotation of an Upper Central Incisor

OBJECTIVE To determine the forces and moments delivered to a maxillary central incisor during rotation by three different thermoplastic appliances with identical thickness. MATERIALS AND METHODS Five identical appliances were manufactured from each of three materials (Ideal Clear 1.0 mm, Erkodur 1.0 mm, Biolon 1.0 mm). An upper central incisor fixed in a measuring device was rotated around its central axis in 0.5-degree steps to +/-2.5 degrees, +/-5 degrees, and +/-7.5 degrees (equivalent to an activation of +/-0.17 mm, +/-0.34 mm, and +/-0.51 mm of the incisor edge) in the clockwise and anticlockwise directions with the respective appliance fixed in place. For statistical analysis, the moments Tz (rotation) and forces Fz (intrusion) were tested. Means and standard deviations for Tz and median and 25% and 75% quantiles for Fz were calculated. An analysis of variance (ANOVA) was performed. RESULTS The minimal moment was determined at a rotation of -0.17 mm (-7.3 Nmm, +/-0.8), and the maximal moment at a deflection of -0.51 mm (-71.8 Nmm. +/-2.5) was recorded. The minimal value for Fz was measured at an activation of -0.17 mm (0.0 N), and the highest intrusive forces were evaluated for a rotation of -0.51 mm (-5.8 N). The particular material sometimes had a significant (P < .05) influence on the forces delivered and the moments. CONCLUSIONS During rotation with aligners, an intrusive force can also be observed. The direction of rotation, and the materials used all exert an influence on the force delivery properties of the appliance.

Initial forces generated by three types of thermoplastic appliances on an upper central incisor during tipping.

The force properties of thermoformed appliances have not been systematically investigated. Therefore, the aim of the present study was to quantify the forces delivered by thermoplastic appliances manufactured from three different materials, with the same thickness, on a central upper incisor, during tipping. Five identical appliances were manufactured from three different materials all with a thickness of 1.0 mm (Ideal Clear, Erkodur, and Biolon). For measuring the forces, an isolated measuring tooth, as part of a standardized resin model incorporated in a newly developed measuring device, was tipped in nine 2.7 arc minute (0.04629 degree) steps, from 0 to 0.416 degrees in the vestibular and palatal directions around a rotational axis through the virtual apex, after positioning an appliance on the model. For statistical analysis, the force components Fx/tipping and Fz/intrusion at a displacement of +/-0.151 mm from the incisor edge were determined. Means and standard deviations (SDs) were calculated. The Kruskal-Wallis test for overall effects and the Wilcoxon two-sample test for individual group pairings were used (P < 0.05 significance level). The mean Fx forces ranged from -2.82 N (SD 0.62) to 5.42 N (SD 0.56). The mean Fz forces were between -0.14 N (SD 0.52) and -2.3 N (SD 0.43). The highest intrusive forces were measured during vestibular displacement of the measuring tooth. The forces delivered by the Biolon appliance were found to be much greater (P < 0.01) than those of the other materials. The forces delivered by the materials investigated were mostly higher than those stated in the literature.

Identification of signal bias in the variable flip angle method by linear display of the algebraic ernst equation

A novel linear parameterization for the variable flip angle method for longitudinal relaxation time T1 quantification from spoiled steady state MRI is derived from the half angle tangent transform, τ, of the flip angle. Plotting the signal S at coordinates x = Sτ and y = S/τ, respectively, establishes a line that renders signal amplitude and relaxation term separately as y‐intercept and slope. This representation allows for estimation of the respective parameter from the experimental data. A comprehensive analysis of noise propagation is performed. Numerical results for efficient optimization of longitudinal relaxation time and proton density mapping experiments are derived. Appropriate scaling allows for a linear presentation of data that are acquired at different short pulse repetition times, TR << T1 thus increasing flexibility in the data acquisition by removing the limitation of a single pulse repetition time. Signal bias, like due to slice‐selective excitation or imperfect spoiling, can be readily identified by systematic deviations from the linear plot. The method is illustrated and validated by 3T experiments on phantoms and human brain. Magn Reson Med, 2011.

Exact algebraization of the signal equation of spoiled gradient echo MRI.

The Ernst equation for Fourier transform nuclear magnetic resonance (MR) describes the spoiled steady-state signal created by periodic partial excitation. In MR imaging (MRI), it is commonly applied to spoiled gradient-echo acquisition in the steady state, created by a small flip angle alpha at a repetition time TR much shorter than the longitudinal relaxation time T(1). We describe two parameter transformations of alpha and TR/T(1), which render the Ernst equation as a low-order rational function. Computer algebra can be readily applied for analytically solving protocol optimization, as shown for the dual flip angle experiment. These transformations are based on the half-angle tangent substitution and its hyperbolic analogue. They are monotonic and approach identity for small alpha and small TR/T(1) with a third-order error. Thus, the exact algebraization can be readily applied to fast gradient echo MRI to yield a rational approximation in alpha and TR/T(1). This reveals a fundamental relationship between the square of the flip angle and TR/T(1) which characterizes the Ernst angle, constant degree of T(1)-weighting and the influence of the local radio-frequency field.

Geometric Influence of the Sagittal and Vertical Apical Base Relationship on the ANB Angle

Objective:The objective of this study consisted in determining the variability of the ANB angle in relation to the position of the A- and B-points in the sagittal vertical plane.Materials and Methods:Using a theoretical model, we varied the position of the cephalometric points A and B in the sagittal vertical plane while its sagittal relationship was kept constant (Wits value = 0 mm). For this purpose, seven lines were erected perpendicular to the occlusal plane on a lateral cephalogram. The position of points A and B were determined on each of the vertical lines by calculating one anterior and one posterior angle in each case. In this way, the positions of all A- and B-points were clearly defined in the sagittal vertical plane.Results:The characteristic of the ANB angle in the sagittal vertical plane was graphically represented by determining both points A and B using two angles instead of one. This revealed that the ANB angle for the same sagittal base relationship was characterized by major variations depending on the position of the A- and B-points in relation to the anterior cranial base. The larger the SNA and SNB angles were, the larger the corresponding ANB angle. At the same time, the absolute value of ANB increased with the length of the vertical distance between the points A and B.Conclusion:The ANB angle is strongly influenced by geometric factors. Accurate diagnosis of the sagittal base relationship should thus take the individual character of the ANB angle into account.ZusammenfassungZiel:Das Ziel der Studie bestand darin, die Variabilität des ANB-Winkels in Abhängigkeit der Lage des A- und B-Punktes in der Sagittal-Vertikal-Ebene zu bestimmen.Material und Methode:Anhand eines theoretischen Modells wurde die Position der kephalometrischen Punkte A und B in der Sagittal-Vertikal-Ebene variiert, während ihre sagittale Relation konstant gehalten wurde (Wits-Wert = 0 mm). Hierfür wurden auf einem Fernröntgenseitenbild sieben Linien senkrecht zur Okklusionsebene konstruiert. Die Position der Punkte A und B wurde jeweils auf den senkrechten Linien bestimmt, indem jeweils ein anteriorer und ein posteriorer Winkel berechnet wurde. Auf diese Weise konnte die Lage der Punkte A und B in der Sagittal-Vertikal-Ebene eindeutig definiert werden.Ergebnisse:Die Eigenschaft des ANB-Winkels in der Sagittal-Vertikal-Ebene konnte graphisch dargestellt werden, in dem die Punkte A und B durch jeweils zwei statt durch einen Winkel berechnet wurden. Es zeigte sich, dass der ANB-Winkel für dieselbe sagittale Basenrelation in Abhängigkeit der Lage des A- und B-Punktes zur vorderen Schädelbasis große Variationen aufwies. Je größer der SNA- und SNB-Winkel waren, umso größer wurde der dazugehörige ANB-Winkel. Gleichzeitig vergrößerte sich der Betrag des ANB-Winkels mit zunehmendem vertikalen Abstand zwischen den Punkten A und B.Schlussfolgerung:Der ANB-Winkel wird in hohem Maße von geometrischen Faktoren beeinflusst. Für eine genaue Diagnose der sagittalen Basenrelation sollte aus diesem Grund die individuelle Natur des ANB-Winkels berücksichtigt werden.

The influence of occlusal forces on force delivery properties of aligners during rotation of an upper central incisor

OBJECTIVE To determine the forces and moments delivered to a maxillary central incisor during rotation with aligners when a simulated occlusal force generated during swallowing acts on the appliance. MATERIALS AND METHODS Five identical appliances were manufactured from four different starting materials (Erkodur 0.8 mm and 1.0 mm; Biolon 0.75 mm and 1.0 mm). An upper central incisor fixed in a measuring device was rotated around its central axis in 0.5-degree steps up to ±10 degrees with the appliance fixed in place. An occlusal force of 30 N generated during swallowing was simulated with a weight positioned on the appliance. For statistical analysis, the moments Tz (rotation) and forces Fz (intrusion) at a deflection of ±0.34 mm to the incisor edge (±5 degrees rotation) were tested. Means and standard deviations for Tz and median and 25% and 75% quartiles for Fz were calculated. An analysis of variance was performed. RESULTS The simulated occlusal force increased the measured intrusive force Fz (maximum with a weight, -3.7 N [-3.7, -2.4]; minimum without a weight, -1.3 N [-1.4, -1.1]) and the rotary moment Tz (maximum with a weight, -50.8 Nmm [±0.8]; minimum without a weight, 18.2 Nmm [±0.9]) significantly in all cases (P < .01). This was found for all materials measured and for both directions of rotation. CONCLUSION During rotation with aligners, a simulated occlusal force increases the intrusive force and the rotary moment. The biological adverse side effects of these phenomena remain unclear, especially in patients with periods of bruxism.