Two-phase flow and pool boiling heat transfer in microgravity

Researches on two-phase flow and pool boiling heat transfer in microgravity, which included groundbased tests, flight experiments, and theoretical analyses, were conducted in the National Microgravity Laboratory/CAS. A semi-theoretical Weber number model was proposed to predict the slug-to-annular flow transition of two-phase gas–liquid flows in microgravity, while the influence of the initial bubble size on the bubble-to-slug flow transition was investigated numerically using the Monte Carlo method. Two-phase flow pattern maps in microgravity were obtained in the experiments both aboard the Russian space station Mir and aboard IL-76 reduced gravity airplane. Mini-scale modeling was also used to simulate the behavior of microgravity two-phase flow on the ground. Pressure drops of two-phase flow in microgravity were also measured experimentally and correlated successfully based on its characteristics. Two space experiments on pool boiling phenomena in microgravity were performed aboard the Chinese recoverable satellites. Steady pool boiling of R113 on a thin wire with a temperature-controlled heating method was studied aboard RS-22, while quasi-steady pool boiling of FC-72 on a plate was studied aboard SJ-8. Ground-based experiments were also performed both in normal gravity and in short-term microgravity in the drop tower Beijing. Only slight enhancement of heat transfer was observed in the wire case, while enhancement in low heat flux and deterioration in high heat flux were observed in the plate case. Lateral motions of vapor bubbles were observed before their departure in microgravity. The relationship between bubble behavior and heat transfer on plate was analyzed. A semi-theoretical model was also proposed for predicting the bubble departure diameter during pool boiling on wires. The results obtained here are intended to become a powerful aid for further investigation in the present discipline and development of two-phase systems for space applications.

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

New space-time trellis codes for two-antenna quasi-static channels

New space-time trellis codes with four- and eight-level phase-shift keying (PSK) and 16-phase quadrature amplitude modulation (QAM) for two transmit antennas in slow-fading channels are presented in this paper. Unlike most of the codes that are reported in the literature, the proposed codes are specifically designed to minimize the frame error probability from a union-bound perspective. The performance of the proposed codes with various memory orders and receive antennas is evaluated by simulation. It is shown that the proposed codes outperform previously known codes in all studied cases.

Initial phase modelling in numerical explosion applied to process safety

The utilisation of computational fluid dynamics (CFD) in process safety has increased significantly in recent years. The modelling of accidental explosion via CFD has in many cases replaced the classical Multi Energy and Brake Strehlow methods. The benefits obtained with CFD modelling can be diminished if proper modelling of the initial phase of explosion is neglected. In the early stages of an explosion, the flame propagates in a quasi-laminar regime. Proper modelling of the initial laminar phase is a key aspect in order to predict the peak pressure and the time to peak pressure. The present work suggests a modelling approach for the initial laminar phase in explosion scenarios. Findings are compared with experimental data for two classical explosion test cases which resemble the common features in chemical process areas (confinement and congestion). A detailed analysis of the threshold for the transition from laminar to turbulent regime is also carried out. The modelling is implemented in a fully 3D Navier-Stokes compressible formulation. Combustion is treated using a laminar flamelet approach based on the Bray, Moss and Libby (BML) formulation. A novel modified porosity approach developed for the unstructured solver is also considered. Results agree satisfactorily with experiments and the modelling is found to be robust. © 2013 The Institution of Chemical Engineers.

Quasi-thermo dynamic analysis of MOVPE growth of GaxAlyIn1-x-yN

A quasi-thermodynamic model of metalorganic vapor phase epitaxy (MOVPE) growth of GaxAlyIn1-x-yN alloys has been proposed. In view of the complex growth behavior of GaxAlyIn1-x-yN, we focus our attention on the galliumrich quaternary alloys that are lattice matched to GaN, In0.15Ga0.85N or Al0.15Ga0.85N, which are widely used in the GaN-based optoelectronic devices. The relationship between GaAlInN alloy composition and input molar ratio of group III metalorganic compounds at various growth conditions has been calculated. The influence of growth temperature, nitrogen fraction in the carrier gas, input partial pressure of group III metalorganics, reactor pressure, V/III ratio and the decomposition rate of ammonia on the composition of deposited alloys are studied systematically. Based on these calculated results, we can find out the appropriate growth conditions for the MOVPE growth of GaxAlyIn1-x-yN alloy lattice matched to GaN, In0.15Ga0.85N or Al0.15Ga0.85N. (C) 2002 Elsevier Science B.V. All rights reserved.

Quasi-thermodynamic analysis of MOVPE of AlGaN

A quasi-thermodynamic analysis of the MOVPE growth of AlxGa1-xN alloy using TMGa, TMA1 and ammonia has been proposed. The effect of varying growth conditions (growth temperature, reactor pressure, input V/III ratio, hydrogen pressure fraction in the carrier gas and the decomposed fraction of ammonia) on the distribution coefficient of Al has been calculated. In the case of AlxGa1-xN, preferential incorporation of Al is predicted. The calculated relationship between input vapour and deposited solid composition has been compared with data in the literature. A good agreement between the calculated and the experimental composition shows that our improved model is suitable for applying to the AlxGa1-xN alloy grown by MOVPE. (C) 2000 Elsevier Science B.V. All rights reserved.

Ultra-broadband optical parametric chirped-pulse amplification by matching of both group-velocity and pulse-front

Ultra-broadband optical parametric chirped-pulse amplification is analyzed based the compensation of phase-mismatch, which is achieved by matching of both group-velocity and pulse-front between signal and idler by the combination of the noncollinear-phase-match and pulse-front-tilt. The results show exactly matching of both group-velocity and pulse-front is the important criterion for constructing an UBOPCPA. Its general model is developed, in which the group velocities, noncollinear angles. spatial walk-off angles, linear angular spectral dispersion coefficients and pulse-front tilted angles are suitably linked to each other. Finally, specific numerical calculations and simulations are presented for beta-barium borate OPCPA with type-1 noncollinear angularly dispersed geometry. (C) 2005 Elsevier B.V. All rights reserved.

Phase separation and crystallization in a melt-spun Ti45Zr35Ni17Cu3 alloy

Structure and crystallization behavior of amorphous and quasicrystalline Ti45Zr35Ni17Cu3 alloy have been studied. DSC trace of the amorphous alloy obtained during continuous heating to 1300 K shows distinctly an exothermic peak and two endothermic peaks.

Extended application of edge-to-edge matching model to HCP/HCP (alpha-Mg/MgZn2) system in magnesium alloys

In the present work, the edge-to-edge matching model has been introduced to predict the orientation relationships (OR) between the MgZn2 phase which has hexagonal close packed (HCP) structure and the HCP a-Mg matrix. Based on the crystal structures and lattice parameters only, the model has predicted the two most preferred ORs and they are: (1) [1 1 2 3](alpha-Mg) vertical bar vertical bar]1 1 2 3](alpha-Mg), (0 0 0 1)(alpha-Mg) 0.27 degrees from (0 0 0 1)(MgZn2), (1 0 1 1)(alpha-Mg) 26.18 degrees from (1 1 2 2)(MgZn2), (2) [1 0 1 0](alpha-Mg),vertical bar vertical bar[1 1 2 0](MgZn2), (0 0 0 1)(alpha-Mg) vertical bar vertical bar(0 0 0 1)(MgZn2), (1 0 1 1)(alpha-Mg) 3.28 degrees from ( 1 1 2 2)(MgZn2). Four experimental ORs have been reported in the alpha-Mg/MgZn2 system, and the most frequently reported one is ideally the OR (2). The other three experimental ORs are near versions of the OR (2). The habit plane of the OR (2) has been predicted and it agrees well with the experimental results.

A novel epitaxy of isotactic polypropylene (alpha phase) on PTFE and organic substrates

Isotactic polypropylene in its a modification (alpha iPP) crystallises epitaxially on polytetrafluoroethylene (PTFE) and several hemiacids or salts of substituted benzoic acids via a novel contact plane, namely (110): so far, the only known contact plane involved in alpha iPP homo- and hetero-epitaxies was (010). In spite of its complicated architecture (alternation of antichiral helices with different azimuthal settings), the (110)(alpha iPP) contact plane displays well defined, if not prominent, rows of methyl side chains parallel to the crystallographic (112) direction (at 57 degrees to the c-axis) and approximate to 5.5 Angstrom apart. The matching contact planes of the substrates display linear gratings made of rows of e.g. chlorine atoms or PTFE chains with similar approximate to 5.5 Angstrom inter-row or interchain distances. Various morphologies are observed in iPP thin films crystallised at different cooling rates in the presence of PTFE; they can be analysed in terms of a succession and interplay of successive epitaxies: initial alpha iPP/PTFE heteroepitaxy, followed by alpha iPP/alpha iPP and gamma iPP/alpha iPP homoepitaxies. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.

ELECTROCHEMICAL DETECTION OF COBALT IN HAIR FOLLOWING ON-COLUMN DERIVATIZATION WITH 1-(2-PYRIDYLAZO)-2-NAPHTHOL-6-SULFONIC ACID AND REVERSED-PHASE LIQUID-CHROMATOGRAPHY

A method for the specific determination of cobalt based on reversed-phase liquid chromatography with amperometric detection via on-column complex formation has been developed. A water-soluble chelating agent, 1-(2-pyridylazo)-2-naphthol-6-sulphonic acid (PAN-6S), is added to the mobile phase and aqueous cobalt solutions are injected directly into the column to form in situ the cobalt-PAN-6S chelate, which is then separated from other metal PAN-6S chelates and subjected to reductive amperometric detection at a moderate potential of -0.3 V. Because the procedure eliminates the interference of oxygen and depresses the electrochemical reduction of the mobile phase-containing ligand PAN-6S, by virtue of the quasi:reversible electrode process of the cobalt-PAN-6S complex, a low detection limit of 0.06 ng can be readily obtained. Interference effects were examined for sixteen common metal species, and at a 5- to 8000-fold excess by mass no obvious interference was observed. The feasibility of the method as an approach to the specific analysis of cobalt in a hair sample has been demonstrated.

The impact of nurse-directed protocolised-weaning from mechanical ventilation on nursing practice: A quasi-experimental study

Background:
Internationally, nurse-directed protocolised-weaning has been evaluated by measuring its impact on patient outcomes. The impact on nurses’ views and perceptions has been largely ignored.

Aim:
To determine the change in intensive care nurses’ perceptions, satisfaction, knowledge and attitudes following the introduction of nurse-directed weaning. Additionally, views were obtained on how useful protocolised-weaning was to practice.

Methods:
The sample comprised nurses working in general intensive care units in three university-affiliated hospitals. Nurse-directed protocolised-weaning was implemented in one unit (intervention group); two ICUs continued with usual doctor-led practice (control group). Nurses’ perceptions, satisfaction, knowledge and attitudes were measured by self-completed questionnaires before (Phase I) and after the implementation of nurse-directed weaning (Phase II) in all units.

Results:
Response rates were 79% (n=140n=140) for Phase 1 and 62% (n=132n=132) for Phase II. Regression-based analyses showed that changes from Phase I to Phase II were not significantly different between the intervention and control groups. Sixty-nine nurses responded to both Phase I and II questionnaires. In the intervention group, these nurses scored their mean perceived level of knowledge higher in Phase II (6.39 vs 7.17, p=0.01p=0.01). In the control group, role perception (4.41 vs 4.22, p=0.01p=0.01) was lower and, perceived knowledge (6.03 vs 6.63, p=0.04p=0.04), awareness of weaning plans (6.09 vs 7.06, p=0.01p=0.01) and satisfaction with communication (5.28 vs 6.19, p=0.01p=0.01) were higher in Phase II. The intervention group found protocolised weaning useful in their practice (75%): this was scored significantly higher by junior and senior nurses than middle grade nurses (p=0.02p=0.02).

Conclusion

We conclude that nurse-directed protocolised-weaning had no effect on nurses’ views and perceptions due to the high level of satisfaction which encouraged nurses’ participation in weaning throughout. Control group changes are attributed to a ‘reactive effect’ from being study participants. Weaning protocols provide a uniform method of weaning practice and are particularly beneficial in providing safe guidance for junior staff.

Quasi-classical model of non-destructive wavepacket manipulation by intense ultrashort nonresonant laser pulses

A quasi-classical model (QCM) of nuclear wavepacket generation, modification and imaging by three intense ultrafast near-infrared laser pulses has been developed. Intensities in excess of 10(13) W cm(-2) are studied, the laser radiation is non-resonant and pulse durations are in the few-cycle regime, hence significantly removed from the conditions typical of coherent control and femtochemistry. The 1s sigma ground state of the D-2 precursor is projected onto the available electronic states in D-2(+) (1s sigma(g) ground and 2p sigma(u) dissociative) and D+ + D+ (Coulomb explosion) by tunnel ionization by an ultrashort 'pump' pulse, and relative populations are found numerically. A generalized non-adiabatic treatment allows the dependence of the initial vibrational population distribution on laser intensity to be calculated. The wavepacket is approximated as a classical ensemble of particles moving on the 1s sigma(g) potential energy surface (PES), and hence follow trajectories of different amplitudes and frequencies depending on the initial vibrational state. The 'control' pulse introduces a time-dependent polarization of the molecular orbital, causing the PES to be modified according to the dynamic Stark effect and the transition dipole. The trajectories adjust in amplitude, frequency and phase-offset as work is done on or by the resulting force; comparing the perturbed and unperturbed trajectories allows the final vibrational state populations and phases to be determined. The action of the 'probe' pulse is represented by a discrete internuclear boundary, such that elements of the ensemble at a larger internuclear separation are assumed to be photodissociated. The vibrational populations predicted by the QCM are compared to recent quantum simulations (Niederhausen and Thumm 2008 Phys. Rev. A 77 013404), and a remarkable agreement has been found. The applicability of this model to femtosecond and attosecond time-scale experiments is discussed and the relation to established femtochemistry and coherent control techniques are explored.

Efficacy and safety of radium-223 dichloride in patients with castration-resistant prostate cancer and symptomatic bone metastases, with or without previous docetaxel use: A prespecified subgroup analysis from the randomised, double-blind, phase 3 ALSYMPCA trial

Background: Primary results from the phase 3 ALSYMPCA trial showed that radium-223 dichloride (radium-223), a targeted α-emitter, improved overall survival compared with placebo and was well tolerated in patients with castration-resistant prostate cancer and symptomatic bone metastases. We did a prespecified subgroup analysis from ALSYMPCA to assess the effect of previous docetaxel use on the efficacy and safety of radium-223. 

Methods: In the phase 3, randomised, double-blind ALSYMPCA trial, patients with symptomatic castration-resistant prostate cancer, at least two symptomatic bone metastases, no known visceral metastases, and who were receiving best standard of care were randomly assigned (2:1) via an interactive voice response system to receive six injections of radium-223 (50 kBq/kg intravenously) or matching placebo, with one injection given every 4 weeks. Patients had either received previous docetaxel treatment or were unsuitable for or declined docetaxel; previous docetaxel use (yes or no) was a trial stratification factor. We investigated the effect of previous docetaxel use on radium-223 treatment for the primary endpoint of overall survival, the main secondary efficacy endpoints, and safety. Efficacy analyses were done for the intention-to-treat population; safety analyses were done for the safety population. The trial has been completed and is registered with ClinicalTrials.gov, number NCT00699751. 

Findings: Randomisation took place between June 12, 2008, and Feb 1, 2011. 526 (57%) of 921 randomly assigned patients had received previous docetaxel treatment (352 in the radium-223 group and 174 in the placebo group) and 395 (43%) had not (262 in the radium-223 group and 133 in the placebo group). Radium-223 prolonged median overall survival compared with placebo, irrespective of previous docetaxel use (previous docetaxel use, hazard ratio [HR] 0·70, 95% CI 0·56-0·88; p=0·002; no previous docetaxel use, HR 0·69, 0·52-0·92; p=0·01). The benefit of radium-223 compared with placebo was seen in both docetaxel subgroups for most main secondary efficacy endpoints; risk for time to time to first symptomatic skeletal event was reduced with radium-223 versus placebo in patients with previous docetaxel use, but the difference was not significant in those with no previous docetaxel use. 322 (62%) of 518 patients previously treated with docetaxel had grade 3-4 adverse events, compared with 205 (54%) of 383 patients without docetaxel. Patients who had previously been treated with docetaxel had a higher incidence of grade 3-4 thrombocytopenia with radium-223 than with placebo (31 [9%] of 347 patients vs five [3%] of 171 patients), whereas the incidence was similar between treatment groups among patients with no previous docetaxel use (seven [3%] of 253 patients vs one [1%] of 130 patients). The incidences of grade 3-4 anaemia and neutropenia were similar between the radium-223 and placebo groups within both docetaxel subgroups. 

Interpretation: Radium-223 is effective and well tolerated in patients with castration-resistant prostate cancer and symptomatic bone metastases, irrespective of previous docetaxel use. 

Funding: Algeta ASA and Bayer HealthCare Pharmaceuticals.