Simultaneous multislice refocusing via time optimal control.

A low radiation burden is essential during diagnostic procedures in pediatric patients due to their high tissue sensitivity. Using MR examination instead of the routinely used CT reduces the radiation exposure and the risk of adverse stochastic effects. Our retrospective study evaluated the possibility of using ultrafast single-shot (SSh) sequences and turbo spin echo (TSE) sequences in rapid MR brain imaging in pediatric patients with hydrocephalus and a programmable ventriculoperitoneal drainage system. SSh sequences seem to be suitable for examining pediatric patients due to the speed of using this technique, but significant susceptibility artifacts due to the programmable drainage valve degrade the image quality. Therefore, a rapid MR examination protocol based on TSE sequences, less sensitive to artifacts due to ferromagnetic components, has been developed. Of 61 pediatric patients who were examined using MR and the SSh sequence protocol, a group of 15 patients with hydrocephalus and a programmable drainage system also underwent TSE sequence MR imaging. The susceptibility artifact volume in both rapid MR protocols was evaluated using a semiautomatic volumetry system. A statistically significant decrease in the susceptibility artifact volume has been demonstrated in TSE sequence imaging in comparison with SSh sequences. Using TSE sequences reduced the influence of artifacts from the programmable valve, and the image quality in all cases was rated as excellent. In all patients, rapid MR examinations were performed without any need for intravenous sedation or general anesthesia. Our study results strongly suggest the superiority of the TSE sequence MR protocol compared to the SSh sequence protocol in pediatric patients with a programmable ventriculoperitoneal drainage system due to a significant reduction of susceptibility artifact volume. Both rapid sequence MR protocols provide quick and satisfactory brain imaging with no ionizing radiation and a reduced need for intravenous or general anesthesia.

The purpose of this study was to compare the relative usefulness of multishot turbo spin echo (TSE) and half-Fourier single-shot turbo spin echo (HASTE) for determination of optimal breath-hold fast T2-weighted technique in terms of lesion detection, lesion-to-liver contrast-to-noise ratio (CNR), and image quality. The images of TSE with and without fat suppression (FS) and of HASTE with and without FS were retrospectively reviewed for 49 patients with 128 lesions. Without FS, TSE and HASTE images allowed depiction of focal hepatic masses (112 of 128, sensitivity = 87.5%) at the same rate. TSE with FS depicted more focal lesions (115 of 128, 89.8%) than HASTE with FS (109 of 128, 85.2%), but the difference was not statistically significant (P > .05). The CNR of each lesion on HASTE sequences was greater (P < .01) than that on TSE sequences. The CNR of hemangioma was distinct from that of solid tumors and cystic lesions in all sequences, and the range of CNR in each group of pathologies overlapped less and were well separated in the HASTE sequences. HASTE sequences produced better image quality with fewer artifacts (P < .0001). The results of this study suggest that HASTE sequences allow differentiation between solid tumors, hemangiomas, and cystic lesions in terms of CNR, producing fewer image artifacts, with acceptable sensitivity in lesion detection.

Focal liver lesions: characterization with quantitative analysis of T2 relaxation time in TSE sequence with double echo time

Automatic Segmentation of Pelvic Structures From Magnetic Resonance Images for Prostate Cancer Radiotherapy

Magnetic resonance imaging (MRI) is the method of choice for the evaluation of spondyloarthritis (SpA). According to the guidelines of the Assessment of Spondyloarthritis International Society (ASAS) and Outcome Measures in Rheumatology (OMERACT), MRI findings in SpA of the spine and the sacroiliac joints (SIJ) are classified as inflammatory and structural alterations. Modern gradient-echo sequences (GRE) are recommended for optimized detection of structural alterations of the SIJ. We assess the benefit of GRE in the detection of structural alterations of the SIJ in comparison to conventional turbo spin-echo sequences (TSE). Retrospective study of 114 patients who received MRI of the SIJ for the evaluation of SpA. Structural alterations of the SIJ were assessed by two blinded readers separately for T1 TSE and T2* GRE. The findings were classified according to a previously published chronicity score separately for both sides and sequences. Interobserver reliability was calculated with Cohen's Kappa, and the significance of findings was assessed with the Wilcoxon test. P-values <0.05 were required for statistical significance. 68 of 114 (60%) patients showed SpA-typical findings of the SIJ. The average chronicity score for GRE (score 3.3) was significantly higher than for TSE (score 2.6), p=0.001. The Kappa-values for the interobserver reliability were 0.86-0.90 without any statistically significant differences between both sides and sequences. Both T1 TSE and T2* GRE showed a high interobserver reliability in the detection of structural alterations in patients with SpA. However, T2* GRE detected significantly more structural alterations than T1 TSE and should be an integral part of a modern MRI protocol for the diagnostic workup of patients with suspected SpA. T2* gradient-echo sequences are superior to T1 turbo spin-echo sequences in the detection of structural SI-joint alterations.

In this paper, the bang–bang property and the existence of the solution for the time optimal control of a specific kind of microwave heating problem are studied. The mathematical model for the time optimal control problem (P) of microwave heating is formulated, in which the governing equations of the controlled system are the weak coupling system of Maxwell equations and the heat equation. Based on a new observability estimate of the heat controlled system, the controllability of the system is derived by proving the null controllability of an equivalent system. The existence of the time optimal control of microwave heating is acquired under some stated assumptions, enabling the bang–bang property of the time optimal control problem (P) to be achieved.

Clinical MRI patients typically experience elevated acoustic noise levels of 80-110 dB(A). In this study, standard clinical turbo spin echo (TSE) and gradient echo (GRE) sequences were optimized for reduced acoustic noise at preserved diagnostic image quality. The physical sources of acoustic noise generation in an MRI gradient coil were analyzed. A sequence conversion algorithm was derived that optimized the gradient time scheme for an arbitrary MRI sequence, preserving the governing spin physics. The algorithm was applied to generate "quiet" versions of standard clinical TSE and GRE sequences. The first volunteer images indicated that contrast-to-noise ratio and perceived diagnostic image quality remained on the same level for the algorithmic optimization. Additional careful TSE- and GRE-specific protocol adaptions yielded total acoustic noise reductions of up to 14.4 dB(A) for the TSE and up to 16.8 dB(A) for the GRE. A physical sound pressure reduction of 81% (TSE) and 86% (GRE) for MRI patients was achieved. The results can be used to render MRI scans more patient-friendly in clinical practice, particularly for patients who are young, scared, or elderly.

A fourth-order model is developed for a crane-load system. From this model a time optimal control scheme with input constraints is investigated for transferring the crane load with swing angle regulation. Rather than following a conventional numerical method approach for solving the two point boundary value problem, a rule-based approach inspired by the manual crane operation is proposed. It is shown that the time optimal control problem becomes the determination of the switching times. Based on the heuristics obtained, a set of expert rules is generated for the adjustment of the switching times. A simple iteration method for obtaining the optimal switching times is presented which provides an alternative solution when there is no analytical expression for a solution. From collected data a lookup table is generated. By incorporating an interpolation algorithm it is possible to transfer the crane load an arbitary distance without load pendulation at the destination in minimum time.

To investigate the impact of high-bandwidth radiofrequency (RF) pulses used in turbo spin echo (TSE) sequences or combined with slice encoding for metal artifact correction (SEMAC) on artifact reduction at 3 Tesla in the knee in the presence of metal. Local transmit/receive coils feature increased maximum B1 amplitude, reduced SAR exposition and thus enable the application of high-bandwidth RF pulses. Susceptibility-induced through-plane distortion scales inversely with the RF bandwidth and the view angle, hence blurring, increases for higher RF bandwidths, when SEMAC is used. These effects were assessed for a phantom containing a total knee arthroplasty. TSE and SEMAC sequences with conventional and high RF bandwidths and different contrasts were tested on eight patients with different types of implants. To realize scan times of 7 to 9 min, SEMAC was always applied with eight slice-encoding steps and distortion was rated by two radiologists. A local transmit/receive knee coil enables the use of an RF bandwidth of 4 kHz compared with 850 Hz in conventional sequences. Phantom scans confirm the relation of RF bandwidth and through-plane distortion, which can be reduced up to 79%, and demonstrate the increased blurring for high-bandwidth RF pulses. In average, artifacts in this RF mode are rated hardly visible for patients with joint arthroplasties, when eight SEMAC slice-encoding steps are applied, and for patients with titanium fixtures, when TSE is used. The application of high-bandwidth RF pulses by local transmit coils substantially reduces through-plane distortion artifacts at 3 Tesla.

Solutions to optimal control problems obtained via direct methods are usually of low resolution. As the desired resolution becomes higher, the number of parameters in the resulting parameter optimization problem increases nonlinearly. A concatenated approach to trajectory optimization previously introduced by the authors to obtain high resolution optimal solutions with low storage requirements is applicable only to a specific class of problems, such as minimum time and minimum energy optimal control problems. The hodograph ballooning approach introduced in this paper generalizes the concatenated approach to the most general optimal control problem. Introduction The development of powerful nonlinear programming software [1, 2] has made direct approaches to trajectory optimization the method of choice for most practical applications [3-5]. The discretization of an optimal control problem to a finite dimensional parameter optimization problem avoids many of the troublesome pathologies that are typical for the optimization over infinite dimensional function spaces [6-8]. Furthermore, direct approaches usually do not. require guessing the switching structure, and the dynamical system is devoid of the nonintuitive costate variables. However, to achieve good resolution it is usually necessary to refine some type of discretization mesh, and, ultimately, to use a large number of design parameters. For typical gradient search methods, this increase in the dimension of the optimization problem has nearly always a negative effect on the convergence rate and the robustness. Additionally, CPU time and RAM requirements for each iteration increase with the second power of the number of parameters (third power for non-sparse solvers) so that direct optimization approaches can become quite expensive. In [9], a method was introduced that achieves excellent resolution without solving high-dimensional nonlinear programming problems. This was achieved by lo'Senior Engineer, Member AIAA. t Supervising Engineer, Member AIAA. 117 Research Drive, Hampton, VA 23666. Copyright ©1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved cally optimizing the trajectory on an iterative sequence of short, partly overlapping subarcs. However, this approach is not applicable to the most general problem formulation. Loosely sneaking, it was required in [9] that the cost state does not appear explicitly in the right-hand side of the equations of motion. The present paper introduces a method through which the approach introduced in [9] becomes applicable to the most general problem formulation. Application of this method, however, requires a priori knowledge of the optimal cost. In practice it is observed that the optimal cost can be obtained with very high precision with reasonably low order discretizations. Once a good guess for the optimal cost is obtained presented in this paper can be applied to refine the trajectory, or, if the optimal cost value is not known a priori with sufficient precision, it can be applied iteratively with the prescribed cost value adjusted in an outer loop. Problem Formulation Let us consider the following simple optimal control problem stated in Mayer form: ^ 4 ( x ( t f ) , t f ) (1 )

Time-varying bang–bang property of time optimal controls for heat equation and its application

Multi-slice 2D turbo spin echo (TSE) sequences are widely used for T2-weighted MR imaging of the liver. On the other hand, there is a demand for 3D imaging to enable the observation of thinner slices, though 3D TSE has often been associated with a high SAR (specific absorption rate) which is caused by repeated 180-degree refocusing pulses. The high SAR has been a limiting factor for 3D TSE, especially with 3.0 Tesla scanners. We carried out free-breath 3D SPACE T2-weighted MR imaging of the liver to yield TSE contrast. This is a variant of 3D TSE that employs specially-designed refocusing pulses to reduce the SAR. The PACE (prospective acquisition correction) technique was used to eliminate motion artifacts that appear conspicuously at 3 Tesla as compared with 1.5 Tesla. The 3D SPACE parameters were as follows; FOV=384mm and base matrix size=320, effective slice thickness=1.2mm. Five volunteers were examined with this sequence on a 3.0-Tesla whole-body scanner. The acquired isotropic 3D image data set was processed with both multi-planar reconstruction (MPR) and volume rendering technique (VRT) to yield images with high quality and very distinct continuity. Such processing was possible due to the isotropic 1.2-mm resolution made feasible by the 3D SPACE sequence. 3D T2-weighted imaging of the liver was performed successfully and safely by combining 3D SPACE and PACE, and the high-resolution isotropic image data assured the continuity of blood vessels and the cystic duct of the liver. I.

This paper presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal time control problems, and optimal norm control problems. Controlled systems in this study are internally controlled heat equations. With the aid of this theorem, we establish an optimal norm feedback law and build up some explicit algorithms for solutions of optimal norm and optimal time control problems.

In magnetic resonance imaging, transverse relaxation time (T2) mapping is a useful quantitative tool enabling enhanced diagnostics of many brain pathologies. The aim of our study was to test the influence of different sequence parameters on calculated T2 values, including multi-slice measurements, slice position, interslice gap, echo spacing, and pulse duration. Measurements were performed using standard multi-slice multi-echo CPMG imaging sequence on a 1.5 Tesla routine whole body MR scanner. We used multiple phantoms with different agarose concentrations (0 % to 4 %) and verified the results on a healthy volunteer. It appeared that neither the pulse duration, the size of interslice gap nor the slice shift had any impact on the T2. The measurement accuracy was increased with shorter echo spacing. Standard multi-slice multi-echo CPMG protocol with the shortest echo spacing, also the smallest available interslice gap (100 % of slice thickness) and shorter pulse duration was found to be optimal and reliable for calculating T2 maps in the human brain.

Previous article Next article The Closed-Loop Time Optimal Control. II: StabilityPavol BrunovskýPavol Brunovskýhttps://doi.org/10.1137/0314013PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe problem, to which extent does the closed-loop time-optimal control of a linear system fulfill its task if the system is subject to small perturbations, is studied.[1] Pavol Brunovský, The closed-loop time-optimal control. I. Optimality, SIAM J. Control, 12 (1974), 624–634 MR0355719 (50:8193) 0301.49004 LinkISIGoogle Scholar[2] Pavol Brunovský, On the best stabilizing control under a given class of perturbations, Czechoslovak Math. J., 15 (90) (1965), 329–369 MR0181518 (31:5747) 0154.10005 Google Scholar[3] H. Hermes, J. Hale and , J. LaSalle, Discontinuous vector fields and feedback controlDifferential Equations and Dynamical Systems (Proc. Internat. Sympos., Mayaguez, P. R., 1965), Academic Press, New York, 1967, 155–165 MR0222424 (36:5476) 0183.15905 Google Scholar[4] T. Ważewski, On an optimal control problem, Differential Equations and Their Applications (Proc. Conf., Prague, 1962), Publ. House Czechoslovak Acad. Sci., Prague, 1965, 229–242 MR0201758 (34:1640) 0133.06005 Google Scholar[5] B. N. Pšeničnyj, Line jny je differencial'ny je igry, Avtomat. i Telemeh., (1968), 65–78 Google Scholar[6] A. F. Filippov, On certain questions in the theory of optimal control, Vestnik Moskov. Univ. Ser. I Mat. Meh., (1959), 25–32, English transl., this Journal, 1 (1962), pp. 76–84 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Discrete and Continuous Dynamical Systems, Vol. 35, No. 9 | 2015 Cross Ref Measurement stability of time-optimal feedback control of two-input strictly normal linear systemsJournal of Differential Equations, Vol. 86, No. 1 | 1 Jul 1990 Cross Ref Local Time-Optimal Feedback Control of Strictly Normal Two-Input Linear SystemsSIAM Journal on Control and Optimization, Vol. 27, No. 1 | 14 July 2006AbstractPDF (3497 KB)Sensitivity Analysis of Time Optimal Control SystemsIFAC Proceedings Volumes, Vol. 17, No. 2 | 1 Jul 1984 Cross Ref Multivalued mappingsJournal of Soviet Mathematics, Vol. 24, No. 6 | 1 Mar 1984 Cross Ref Stability with regime switchingJournal of Economic Theory, Vol. 29, No. 1 | 1 Feb 1983 Cross Ref Measurement stability of third-order time-optimal control systemsJournal of Differential Equations, Vol. 36, No. 1 | 1 Apr 1980 Cross Ref Discontinuous differential equations, IIJournal of Differential Equations, Vol. 32, No. 2 | 1 May 1979 Cross Ref Volume 14, Issue 1| 1976SIAM Journal on Control and Optimization1-188 History Submitted:20 July 1973Published online:03 August 2006 InformationCopyright © 1976 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0314013Article page range:pp. 156-162ISSN (print):0363-0129ISSN (online):1095-7138Publisher:Society for Industrial and Applied Mathematics