Magnetic Resonance (MR) elastography is a method for measuring tissue elasticity via phase images acquired with an MR scanner. The propagation of periodic mechanical waves through the tissue can be captured by means of a modified phase contrast sequence. These waves are generated with a mechanical oscillator (actuator) and coupled into the tissue through the skin. The actuator must be capable of generating a sinusoidal excitation with excellent phase and amplitude stability, while not disturbing the MR imaging process. In this work, an actuator based on a piezoelectric principle was developed. Based on the imaging evaluation of several material samples, the housing for the piezoelectric ceramic was constructed of aluminum. Smaller parts of the housing were manufactured from brass and titanium to fulfill the mechanical constraints. A lever was used to transfer the oscillation generated by the piezoelectric ceramic to the point of excitation. The lever amplifies the piezoelectric motion, allowing for a more compact design. Three different lever designs were characterized by an acceleration sensor both outside and inside the magnet. It was shown that the rigidity of the lever, as determined by its material and form, was decisive in determining the resonant frequency of the system and therefore the maximum practical frequency of operation. It was also shown that the motion of the oscillator is unaffected by the electromagnetic fields of the MR imager. The final design can be placed directly in the magnet bore within a few centimeters of the tissue volume to be imaged without generating significant artifacts. An amplitude range of 0 -1 mm in the frequency range from 0 to over 300 Hz was achieved, sufficient for performing most MR elastography applications.

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_ _ -Mit dieser Apparatur kann man den S c h w e f e l g e h a l t a l l e r v e r b r e n n l i c h e n f e s t e n , f l u s s i g e n u n d quantitativ bestimmen. Durch entsprechende Abanderung der Absorptionsfliissigkeit ist es weiterhin moglich, auch die H a 1 o g e n e zu absorbieren und ihre Menge festzustellen. Da die Methode einfach und zuverlassig ist, halten wir sie nicht nur auf dem Gebiete der Analyse von Brennstoffen fur einen wesentlichen Fortschritt, sondern empfehlen sie auch allgemein an Stelle der langwierigen und nicht ungefahrlichen Carius-Methode.

Stability and cost optimality of power generation and supply systems must not be considered independently from one another. Simple examples show that optimizing cost without considering stability may result in modes of operation that, while economically optimal, are unstable. We demonstrate that stability, robustness, and optimality can be considered systematically and simultaneously by combining bifurcation theory and nonlinear optimization. Essentially, the proposed method enforces a backoff distance between the optimal point of operation and operational or stability boundaries in the space of the optimization variables, where bifurcation theory is used to describe nonlinear stability boundaries.We optimize a simple grid to demonstrate the features of the proposed approach. Our results show that the method can be applied to problems with both continuous and Boolean optimization variables, where the latter represent grid breakers in the example. The constraints for robust stability turn out to be crucial in that economically optimal but unstable modes of operation exist despite the small size of the illustrative example. Our results demonstrate that the robustness constraints can affect the optimal value of the Boolean variables. We show that the method provides a measure for the cost of stability and robustness.

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