The dynamical problems of shock formation and star formation in normal spiral galaxies are investigated. The motion considered is that of the continuum of turbulent gas composing the gaseous disk moving m a gravitational field consisting of a two-armed spiral field superposed on the Schmidt model for the Milky Way system. The possible^ existence of a stationary two-armed spiral shock pattern is demonstrated. It is suggested that galactic shock waves may very well form the triggering mechanism for the gravitational collapse of gas clouds, leading to star formation. If an upper bound of 30 million years is assumed for the process of formation and evolution of relatively massive stars initiated at the shock, it is shown that the possible locations of the regions of luminous, newly born stars and the H n regions he on the inner side of each observable gaseous spiral arm of H i, extending from the sharp H i peak at the shock on the inner edge to approximately the center of the arm. in general agreement with obsérvations. < I. INTRODUCTION Many spiral galaxies have multiple spiral arms; however, two principal arms can generally be traced to the central region and sometimes to the very center of the system (see Sandage 1961). Often the spiral arms show a very high resolution into "knots" that are generally interpreted as H xi regions and associations of stars. While the young stars practically always appear in stellar associations, the young stellar associations with their corresponding brilliant H n regions often occur in chains and spiral arcs within the larger grand design of spiral structure. The contiguity of H n regions and spiral arms was first recognized by Baade and Mayall (1951) in their study of the H n regions of M31. It was Morgan, Sharpless, and Osterbrock (1952) who first detected spiral structure in our Galaxy and who showed that the young stars and H xx regions appear like strings of beads. In recent observational studies of our Galaxy, Westerhout (1968) has found that the young stellar associations and brilliant H n regions actually lie along the inner sides of the observed gaseous spiral arms. In view of these observational studies, a basic problem stands out, namely, what physical mechanism could trigger star formation along a grand design of spiral structure in such an orderly fashion. M. S. Roberts (1967) has shown for a number of Sc-type galaxies that the circumferential bands with highest H x distribution not only do not coincide with but lie significantly outside the circumferential bands containing the most prominent newly born stars and H xx regions. It would seem obvious a priori that star formation would most probably take place in those regions where the mass of neutral hydrogen is the largest. To have little or no star formation in the regions of highest H x distribution seems indeed perplexing. This is just one further aspect of star formation that must be considered. a) Grand Design of Spiral Structure Two different spiral theories have been suggested to account for the grand design feat...

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This pulsed cavitational ultrasound system is capable of transcutaneous nonthermal destruction of renal tissue. Refinement of this technology for noninvasive ablation of small renal masses is currently under way.

Purpose In high intensity focused ultrasound (HIFU) therapy, an ultrasound beam is focused within the body to locally affect the targeted site without damaging intervening tissues. The most common HIFU regime is thermal ablation. Recently, there has been increasing interest in generating purely mechanical lesions in tissue (histotripsy). This paper provides an overview of several studies on the development of histotripsy methods toward clinical applications. Material and Methods Two histotripsy approaches and examples of their applications are presented. In one approach, sequences of high-amplitude, short (microsecond-long), focused ultrasound pulses periodically produce dense, energetic bubble clouds that mechanically disintegrate tissue. In an alternative approach, longer (millisecond-long) pulses with shock fronts generate boiling bubbles and the interaction of shock fronts with the resulting vapor cavity causes tissue disintegration. Results Recent pre-clinical studies on histotripsy are reviewed for treating benign prostatic hyperplasia (BPH), liver and kidney tumors, kidney stone fragmentation, enhancing antitumor immune response, and tissue decellularization for regenerative medicine applications. Potential clinical advantages of the histotripsy methods are discussed. Conclusions Histotripsy methods can be used to mechanically ablate a wide variety of tissues, whilst selectivity sparing structures such as large vessels. Both ultrasound and MR imaging can be used for targeting and monitoring the treatment in real time. Although the two approaches utilize different mechanisms for tissue disintegration, both have many of the same advantages and offer a promising alternative method of noninvasive surgery.

We follow the perturbations in the flow of interstellar gas which result from steady forcing by spiral gravitational fields of various strengths. The density response is quite nonlinear even if the amplitude of the spiral field maintained by the disk stars is only a small fraction of the basic axisymmetric field. An analytical study of the properties of slightly nonlinear flows yields certain results which are qualitatively similar to those found numerically for fully nonlinear flows. Galactic shocks arise naturally, indeed necessarily, if the strength of the underlying spiral gravitational field exceeds a certain critical value. The breadth of the zone of high gas compression depends critically on whether the Dopplershifted phase-velocity of the stellar density wave is greater than or less than the "effective acoustic speed" of the gas. In the former case, very narrow compression zones result; in the latter, quite broad zones. This distinction may explain why some galaxies have narrow optical arms while others have broad optical arms. In addition, a certain range of values for the intrinsic frequency of the wave gives rise to ultraharmonic resonances which can introduce secondary compressions of the interstellar gas. This result may relate directly to the origin of the Carina spiral feature in our own Galaxy as well as to the phenomena of branches, spurs, and feathers which are often seen in external spiral galaxies. Subject headings: galactic structure-interstellar matter

A strong wave manifestation may be a dominant constituent of the bar structure in barred spiral galaxies : large-scale gaseous density waves and shocks are identified as important phenomena in the gas flow. We generalize the steady-state gas-dynamical studies, previously limited to tightly wound normal spirals, to include barred and open-armed normal spirals. The steady-state response of the gas (non-self-gravitating) to a 5-107 o perturbing potential that is barlike in the inner parts and spiral-like in the outer parts is found to be strong and capable of inducing the formation of large-scale gaseous density waves and shocks in the bar and along the spiral arms. Highly oval streamlines characterize the gas circulation in the inner regions of the disk where large noncircular motions are of the order of 50 km s _1 to 150 km s-1. Strong velocity gradients in the gas flow are particularly pronounced across the bar near the shock. Two types of shocked gas flow are found to be possible in the inner regions of barred spirals. In one type, a shock-focusing phenomenon is discovered which focuses gas in the inner parts outward and gas in the outer parts inward, in the region of convergence where the spiral arm bends from the bar. This shock-focusing phenomenon is thought to account in part for the enhanced star formation activity observed at the ends of the bar structure in many barred spirals. Our analysis constitutes an essential complement to the recent time-evolutionary, numercial hydrodynamical calculations which lack the resolution necessary to compute the detailed structure of the shock and the gas streamlines in the bar region. The present study provides this resolution together with the critical forcing amplitude required to produce offset shocks along the bar. The dark, narrow dust lanes observed along the leading edges of the bar structure in many barred spirals are identified in this study as tracers of such shocks. The interstellar gas-itself a tracer and an important factor influencing the formation of stars and other tracers (e.g., offset dust lanes)-actually provides an outstanding interconnecting link between the overall appearance of a barred spiral and the underlying dynamics of its stellar component. Interpretation of the observed velocity field of one sample barred spiral, NGC 5383, through the application of the theoretical velocity field derived in this steady-state gas flow study indicates that a deeper understanding of barred spirals is obtained. Subject headings: galaxies : internal motions-hydrodynamics-shock waves

Histotripsy is a non-invasive tissue ablation method capable of fractionating tissue by controlling acoustic cavitation. To determine the fractionation susceptibility of various tissues, we investigated histotripsy-induced damage on tissue phantoms and ex vivo tissues with different mechanical strengths. A histotripsy bubble cloud was formed at tissue phantom surfaces using 5-cycle long ultrasound pulses with peak negative pressure of 18 MPa and PRFs of 10, 100, and 1000 Hz. Results showed significantly smaller lesions were generated in tissue phantoms of higher mechanical strength. Histotripsy was also applied to 43 different ex vivo porcine tissues with a wide range of mechanical properties. Gross morphology demonstrated stronger tissues with higher ultimate stress, higher density, and lower water content were more resistant to histotripsy damage in comparison to weaker tissues. Based on these results, a self-limiting vessel-sparing treatment strategy was developed in an attempt to preserve major vessels while fractionating the surrounding target tissue. This strategy was tested in porcine liver in vivo. After treatment, major hepatic blood vessels and bile ducts remained intact within a completely fractionated liver volume. These results identify varying susceptibilities of tissues to histotripsy therapy and provide a rational basis to optimize histotripsy parameters for treatment of specific tissues.

Quasi-steady flows of interstellar gas in a spiral gravitational field are followed for the purpose of investigating galactic shocks and the resultant processes of the formation of stars and interstellar clouds. We model the interstellar medium with two stable phases in which thermal balance is maintained through heating by low-energy cosmic rays. The problem, including transitions between the two phases, is given a general formulation but is solved in an approximation which ignores the difference in fluid velocities of the two phases. We also assume that the cosmic-ray flux is uniform in circles about the center of the Galaxy and that the relative abundances of the chemical elements are "normal." For a spiral gravitational field with strength equal to 5 percent that of the axisymmetric field at 10 kpc from the galactic center, the density ratio at maximum and minimum compressions is 9:1 for the intercloud medium while it is 40:1 for the gas in a typical cloud. During the decompression phase of the flow, a small percentage of the mass of the clouds evaporates to become intercloud material, but this small amount is recovered in the shock. As a by-product of phase transitions, the properties of the clouds in the regions between spiral arms are such as to make their detection in 21-cm absorption very difficult. In the absence of the cloud phase, we determine the thickness of the shock layer in the intercloud medium to be typically 50 pc. An interstellar cloud immersed as a test particle in the intercloud medium experiences a dynamic rather than a quasi-static compression as it passes through the shock layer. The critical mass for the gravitational collapse of a cloud is reduced by a large factor because of the compression in the shock. I. INTRODUCTION The problems discussed in this paper are motivated by the desire to understand the detailed mechanisms which trigger the formation of stars in normal spiral galaxies. Central to our discussion are two fundamental ideas: (i) spiral galactic shocks and (ii) the two-phase model of the interstellar medium. Within this context, we concentrate on the roles played by gravitational and thermal mechanisms. We avoid the vexing problem of the magnetic-field geometry by ignoring at the very outset the effects of the interstellar magnetic field. We do this not because we feel these effects to be unimportant, but because we wish to keep the present discussion as simple as possible. a) Basic Concepts On a small scale the main obstacle to star formation is that most of the interstellar clouds would not be even remotely bound by their self-gravitation if the clouds were * Now at the State University of New York at Stony Brook.