Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan and thus cannot initiate or re-initiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis - a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division - we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.

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The effect of local structure on the characteristics of the regional phases Pg and Lg was investigated by analyzing events at epicentral distances less than 10° from the Nevada Test Site. The stations used are on markedly different geological structures; three on granitic intrusions, two on Pahute Mesa, a feature overlaying a buried volcanic caldera, and, finally, four on Yucca Flats, a deep alluvial valley. The crustal effect on amplitudes is quite significant for both Lg and Pg; Yucca Flats gives amplitudes as much as a full order of magnitude higher than the stations on granite, while Pahute Mesa stations are 0.7–0.8 magnitude units higher in amplitude than the granite sites. Besides gross amplitude effects, the local crust also induces prolonged ringing at Yucca Flats, resulting in the lengthening of the signal wave trains. The observed site amplification effects show no clear dependence on the azimuths of arrivals, indicating that the phenomenon is due to local structures and is not caused by lateral refraction of surface wave modes. The observed amplification is similar in magnitude for the vertical component of both Pg and Lg, thus not affecting the Pg/Lg amplitude ratio, a possible discriminant between earthquakes and explosions at regional distances. Finite difference theoretical simulations using two‐dimensional models of the Yucca basin reproduce, in a qualitative sense, the ringing effect observed at the Yucca Flats. Any attempt at matching characteristics of Pg and Lg with synthetic seismograms computed for laterally homogeneous layered structures is apt to lead to false conclusions about the source and path properties unless the recording sites used are carefully chosen for small crustal effects.

Ð During the period from 1975 to 1979, the former Soviet Union conducted a series a six nuclear explosions in a water-®lled cavity in salt which was created in 1968 by a tamped 27 kt explosion at a depth of 597 m at the Azgir test site at the north end of the Caspian Sea. Broadband, near-regional seismic data recorded from these tests have been processed and analyzed in an attempt to characterize the seismic source characteristics of these explosions and assess their relevance to the cavity decoupling evasion scenario. The results of these analyses indicate that the explosions in the water-®lled cavity were not decoupled, but rather show evidence of enhanced seismic coupling with respect to that which would be expected from tamped explosions of the same yields in salt. Theoretical ®nite dierence simulations of these tests have been conducted in which the complex, nonlinear interactions between the shock eects in both the water and surrounding salt medium have been explicitly modeled. The results of these simulations indicate that the most prominent yield dependent features of the observed seismic source functions can be largely explained by the dynamic interactions between the expanding and contracting steam bubbles generated by the explosions in water and the shock-wave re¯ections from the cavity wall. More speci®cally, it has been found that the shock-wave re¯ection from the cavity wall retards the expansion of the steam bubble in a yield dependent fashion relative to that expected in the open ocean, resulting in a smaller maximum bubble radius and a shorter bubble oscillation period.

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