The reverse protraction factor in the induction of bone sarcomas in radium-224 patients

More than 50 bone sarcomas have occurred among a collective of about 800 patients who had been injected in Germany after World War II with large activities of radium-224 for the intended treatment of bone tuberculosis and ankylosing spondylitis.^In an earlier analysis it was concluded that, at equal mean absorbed doses in the skeleton, patients with longer exposure time had a higher incidence of bone sarcomas.^The previous analysis was based on approximations; in particular, it did not account for the varying times at risk of the individual patients.^In view of the implications of a reverse protraction factor for basic considerations in radiation protection, the need was therefore felt to reevaluate the data from the continued follow-up by more rigorous statistical methods.^A first step of the analysis demonstrates the existence of the reverse dose-rate effect in terms of a suitably constructed rank-order test.^In a second step of the analysis it is concluded that the data are consistent with a linear no-threshold dose dependence under the condition of constant exposure time, while there is a steeper than linear dependence on dose when the exposure times increase proportionally to dose.^A maximum likelihood fit of the data is then performed in terms of a proportional hazards model that includes the individual parameters, dose, treatment duration, and age at treatment.^The fit indicates proportionality of the tumor rates to mean skeletal dose with an added factor (1 + 0.18.tau), where tau is the treatment time in months.^This indicates that a protraction of the injections over 15 months instead of 5 months doubles the risk of bone sarcoma

Time and dose dependency of bone-sarcomas in patients injected with radium-224

The time course and dose dependency of the incidence of bone-sarcomas among 900 German patients treated with high doses of radium-224 is analysed in terms of a proportional hazards model with a log-normal dependency of time to tumor and a linear-quadratic dose relation. The deduced dose dependency agrees well with a previous analysis in terms of a non-parametric proportional hazards model, and confirms the temporal distribution which has been used in the Radioepidemiological Tables of NIH. However, the linear-quadratic dose-response model gives a risk estimate for low doses which is somewhat less than half that obtained under the assumption of linearity. Dedicated to Prof. W. Jacobi on the occasion of his 60th birthday Work performed under Euratom contracts BI6-D-083-D, BI6-F-111-D, U.S. Department of Energy contract DE-AC 02-76 EV-00119, the U.S. National Cancer Institut

Bone sarcoma cumulative tumor rates in patients injected with 224Ra

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An epidemiological assessment of lens opacifications that impaired vision in patients injected with radium-224

The incidence of lens opacifications that impaired vision (cataract) was analyzed among 831 patients who were injected with known dosages of 224Ra in Germany shortly after World War II. The dependence of the incidence on dosage, i.e., injected activity per unit body weight, and on time after treatment was determined. The observations are equally consistent with proportionality of the incidence of cataract to the square of dosage or with a linear dependence beyond a threshold of 0.5 MBq/kg. The possibility of a linear dependence without threshold was strongly rejected (P less than 0.001). The analysis of temporal dependences yielded a component that was correlated with the injected amount of 224Ra and a component that was uncorrelated. The former was inferred by a maximum likelihood analysis to increase approximately as the square of the time after treatment. The component unrelated to the treatment was found to increase steeply with age and to become dominant within the collective of patients between age 50 and 60. The relative magnitudes of the two components were such that a fraction of 55 to 60% of the total of 58 cataracts had to be ascribed to the dose-related incidence. Impaired vision due to cataract was diagnosed before age 54 in 25 cases. In terms of injected activity per unit body weight no dependence of the sensitivity on age was found; specifically there was no indication of a faster occurrence of the treatment-related cataracts in patients treated at older ages

Structure, Scaling and Phase Transition in the Optimal Transport Network

We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous model [J. R. Banavar {\it et al} Phys. Rev. Lett. {\bf 84}, 004745 (2000)] optimizing a power-law cost function in an abstract network. We show the currents derive from a potential, and the scaling of the conductances depends only locally on the currents. A numerical study reveals that the transition in the topology of the optimal network corresponds to a discontinuity in the slope of the power dissipation.Comment: 4 pages, 3 figure

Hierarchical Assemblies of Block-Copolymer-Based Supramolecules in Thin Films

The hierarchical assemblies of supramolecules, which consisted of polystyrene-b-poly(4- vinylpyridine) (PS-b-P4VP) with 3-pentadecylphenol (PDP) hydrogen-bonded to the 4VP, were investigated in thin films after solvent annealing in a chloroform atmosphere. The synergistic coassembly of PS-b-P4VP and PDP was utilized to generate oriented hierarchical structures in thin films. Hierarchical assemblies, including lamellae-within-lamellae and cylinders-within-lamellae, were simultaneously ordered and oriented from a few to several tens of nanometers over macroscopic length scales. The macroscopic orientation of supramolecular assembly depends on the P4VP(PDP) fraction and can be tailored by varying the PDP to P4VP ratio without interfering with the supramolecular morphologies. The lamellar and cylindrical microdomains, with a periodicity of ∼40 nm, could be oriented normal to the surface, while the assembly of comb blocks, P4VP(PDP), with a periodicity of ∼4 nm, were oriented parallel to the surface. Furthermore, using one PS-b-P4VP copolymer, thin films with different hierarchical structures, i.e., lamellae-within-lamellae and cylinders-within-lamellae, were obtained by varying the ratio of PDP to 4VP units. The concepts described in these studies can be potentially applied to other BCP-based supramolecular thin films, thus creating an avenue to functional, hierarchically ordered thin films