We give estimates of lower bounds on the p-p total cross section based on cosmic-ray data. We find that o&& rises at least as rapidly as 88,8+0.41n (s/sp) from E-10 to 8 && 10 GeV incident energy, corresponding to 0~-60 mb at the highest energy available.In view of large experimental errors at the highest energies, a value of cr&&-48 mb can be estimated at 95% confidence level at & 104 GeV.Total particle-proton cross sections are of immense theoretical interest. Much of the excitement about the early Serphukov data arose because of the unexpected behavior of these cross sections, and a variety of models and explanations for the behavior of the cross sections have been advanced and await experimental test. ' Unfortunately, all of these models seem to suggest that the dependence of the total cross sections on energy will be logarithmic, so that it becomes difficult to test them at accelerator energies.

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A computer program has been developed to quantitatively evaluate changes in tumor growth rates of a solid tumor model (hepatoma 3924A) after a series of radiation doses from 375 R to 3750 R. The computer-derived growth curves are simulated from the volumes of the individual tumors rather than from the mean tumor volume at any specific time point after treatment. The ability to generate ata from a family of tumor growth curves permits a more precise evaluation of therapeutic effects on tumors than can beobtained with conventional methods. The quantitative determination of equivalent amounts of radiation needed to produce comparable 5-fluorouracil-induced changes in tumor growth rate has been made. The ability to determine quantitatively radiotherapeutic and chemotherapy equivalents on these solid tumor models has direct implications in regard to our effort to improve the treatment of cancer. At present no specific solid tumor or groups of solid tumors have provided al1 of the necessary information for clinical utilization in therapeutic scheduling of different forms of cancer treatment. Since solid tumors comprise the majority of human cancer, one of the primary objectives of these studies has been the establishment of a solid tumor model that could serve both as a system for devising improved therapeutic scheduling and for a better understanding of solid tumors. The rate of change of tumor volume with time is one of the basic measurements for the study of tumor growth (1-9).While Morris hepatomas have been extensively used in cancer research, no systematic study has been made of the effects of radiation on these solid tumors (10,11). This study of the effects of different x-radiation doses on tumors is part of a continuing study of the assessment of therapeutic response of different modalities of treatment in this experimental solid tumor system. Studies of the effects of radiation on cycle times, potential doubling times, cell loss factor, and the fraction of proliferating and nonproliferating cells (growth fraction) are needed along with the effects of radiation on tumor growth rates to assess treatment properly. This report is primarily concerned with the methods of evaluation of radiation-induced changes in tumor volumes and the results of different doses of radiation over a range of 375-3750 R.MATERIALS AND METHODS Female ACI rats were inoculated subcutaneously in the back with 3924A hepatoma cells by Dr. Harold Morris in Washington D.C. and shipped to this laboratory. The rats were maintained under standard laboratory conditions including commercial laboratory rat chow (Charles River Laboratories, Wilmington, Mass.) supplied ad libitum, and a 12 hr lighting schedule, the dark period beginning at 8:00 p.m.Tumor volumes, V, (mm3) were calculated from measurements of length (L), width (W), and height (H) (5). It was assumed that the tumors are approximately hemiellipsoids whose volume is lit L-W-H (1). The tumors were measured and the rats weighed daily before radiation and for 6 days afterward. The m...

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