Acoustics of Cubic Bubbles: Six Coupled Oscillators.

We introduce cubic bubbles that are pinned to 3D printed millimetric frames immersed in water. Cubic bubbles are more stable over time and space than standard spherical bubbles, while still allowing large oscillations of their faces. We find that each face can be described as a harmonic oscillator coupled to the other ones. These resonators are coupled by the gas inside the cube but also by acoustic interactions in the liquid. We provide an analytical model and 3D numerical simulations predicting the resonance with very good agreement. Acoustically, cubic bubbles prove to be good monopole subwavelength emitters, with nonemissive secondary surface modes.

A multi-wave elastic metamaterial based on degenerate local resonances.

In this letter, an experimental and numerical study of the influence of symmetric resonators on Lamb waves that propagate in a thin metallic plate is reported. The resonators consist of a set of small, closely packed rods that pass through the plate from side to side to create a locally resonant metamaterial. Adjusting the symmetry of these rods creates degenerate flexural resonances that can be tuned to couple only with a given Lamb mode that is either symmetric (S0) or anti-symmetric (A0). This approach offers promising perspectives in the development of metamaterials for elastic waves that involve non-scalar interactions.

On band gap predictions for multiresonant metamaterials on plates.

Recently wide frequency band gaps were observed in an experimental realization of a multiresonant metamaterial for Lamb waves propagating in thin plates. The band gaps rose from hybridization between the flexural plate (A0 Lamb waves) and longitudinal resonances in rods attached perpendicularly. Shortly thereafter a theory based on considering a one-dimensional periodic array of rods and the scattering matrix for a single rod successfully described the observations. This letter presents an alternative simpler theory, arguably accurate at high rod density, that treats the full two-dimensional array of rods and makes no assumption of periodicity. This theory also fits the measurements.

Directional cloaking of flexural waves in a plate with a locally resonant metamaterial.

This paper deals with the numerical design of a directional invisibility cloak for backward scattered elastic waves propagating in a thin plate (A0 Lamb waves). The directional cloak is based on a set of resonating beams that are attached perpendicular to the plate and are arranged at a sub-wavelength scale in ten concentric rings. The exotic effective properties of this locally resonant metamaterial ensure coexistence of bandgaps and directional cloaking for certain beam configurations over a large frequency band. The best directional cloaking was obtained when the resonators' length decreases from the central to the outermost ring. In this case, flexural waves experience a vanishing index of refraction when they cross the outer layers, leading to a frequency bandgap that protects the central part of the cloak. Numerical simulation shows that there is no back-scattering in these configurations. These results might have applications in the design of seismic-wave protection devices.

Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves.

We demonstrate the experimental realization of a multiresonant metamaterial for Lamb waves, i.e., elastic waves propagating in plates. The metamaterial effect comes from the resonances of long aluminum rods that are attached to an aluminum plate. Using time-dependent measurements, we experimentally prove that this metamaterial exhibits wide band gaps as well as sub- and suprawavelength modes for both a periodic and a random arrangement of the resonators. The dispersion curve inside the metamaterial is predicted through hybridizations between flexural and compressional resonances in the rods and slow and fast Lamb modes in the plate. We finally underline how the various degrees of freedom of such system paves the way to the design of metamaterials for the control of Lamb waves in unprecedented ways.

Sub-wavelength energy trapping of elastic waves in a metamaterial.

Deep sub-wavelength focusing has been demonstrated for locally resonant metamaterials using electromagnetic and acoustic waves. The elastic equivalents of such objects are made of sub-wavelength resonating beams fixed to a two-dimensional plate, as presented here. Independent of a random or regular arrangement of the resonators, the metamaterial shows large bandgaps that are independent of the incident wave direction. Numerical simulations demonstrate that the insertion of a defect in the layout, as a shorter resonator, creates strong amplification of the wave-field on the defect. This energy trapping, which is localized on a spatial scale that is much smaller than the wavelength in the two-dimensional plate, leads to a >1 factor in terms of the local density of energy.

Adjuvant docetaxel, doxorubicin, and cyclophosphamide in node-positive breast cancer: 10-year follow-up of the phase 3 randomised BCIRG 001 trial.

BACKGROUND: We compared standard adjuvant anthracycline chemotherapy with anthracycline-taxane combination chemotherapy in women with operable node-positive breast cancer. Here we report the final, 10-year follow-up analysis of disease-free survival, overall survival, and long-term safety. METHODS: BCIRG 001 was an open label, phase 3, multicentre trial in which 1491 patients aged 18-70 years with node-positive, early breast cancer and a Karnofsky score of 80% or more were randomly assigned to adjuvant treatment with docetaxel, doxorubicin, and cyclophosphamide (TAC) or fluorouracil, doxorubicin, and cyclophosphamide (FAC) every 3 weeks for six cycles. Randomisation was stratified according to institution and number of involved axillary lymph nodes per patient (one to three vs four or more). Disease-free survival was the primary endpoint and was defined as the interval between randomisation and breast cancer relapse, second primary cancer, or death, whichever occurred first. Efficacy analyses were based on the intention-to-treat principle. BCIRG 001 is registered with ClinicalTrials.gov, number NCT00688740. FINDINGS: Enrolement took place between June 11, 1997 and June 3, 1999; 745 patients were assigned to receive TAC and 746 patients were assigned to receive FAC. After a median follow-up of 124 months (IQR 90-126), disease-free survival was 62% (95% CI 58-65) for patients in the TAC group and 55% (51-59) for patients in the FAC group (hazard ratio [HR] 0·80, 95% CI 0·68-0·93; log-rank p=0·0043). 10-year overall survival was 76% (95% CI 72-79) for patients in the TAC group and 69% (65-72) for patients in the FAC group (HR 0·74, 0·61-0·90; log-rank p=0·0020). TAC improved disease-free survival relative to FAC irrespective of nodal, hormone receptor, and HER2 status, although not all differences were significant in these subgroup analyses. Grade 3-4 heart failure occurred in 26 (3%) patients in the TAC group and 17 (2%) patients in the FAC group, and caused death in two patients in the TAC group and four patients in the FAC group. A substantial decrease in left ventricular ejection fraction (defined as a relative decrease from baseline of 20% or more) was seen in 58 (17%) patients who received TAC and 41 (15%) patients who received FAC. Six patients who received TAC developed leukaemia or myelodysplasia, as did three patients who received FAC. INTERPRETATION: Our results provide evidence that the initial therapeutic outcomes seen at the 5-year follow-up with a docetaxel-containing adjuvant regimen are maintained at 10 years. However, a substantial percentage of patients had a decrease in left ventricular ejection fraction, probably caused by anthracycline therapy, which warrants further investigation. FUNDING: Sanofi.

Motesanib, or open-label bevacizumab, in combination with paclitaxel, as first-line treatment for HER2-negative locally recurrent or metastatic breast cancer: a phase 2, randomised, double-blind, placebo-controlled study.

BACKGROUND: Vascular endothelial growth factor (VEGF) has a crucial role in angiogenesis, and is a valid target in metastatic breast cancer. Motesanib is an investigational oral inhibitor of VEGF receptors. We aimed to determine whether treatment with motesanib plus paclitaxel is better than placebo plus paclitaxel in patients with HER2-negative locally recurrent or metastatic breast cancer. METHODS: Between Dec 1, 2006, and July 4, 2008, patients with untreated HER2-negative metastatic breast cancer were randomly assigned (using a randomisation list created by personnel not associated with the study) in a 1:1:1 ratio to paclitaxel (90 mg/m(2) on days 1, 8, and 15 every 3 weeks) plus either masked motesanib 125 mg orally once per day (n=91), masked placebo orally once per day (n=94), or open-label bevacizumab 10 mg/kg intravenously on days 1 and 15 of each 28-day cycle (n=97), after stratification according to adjuvant or neoadjuvant chemotherapy (taxane-containing regimens vs other regimens vs none), number of metastatic sites (<3 vs ≥3), and hormone receptor status (positive vs negative). Placebo was provided as a replica of motesanib 25 mg tablets. The primary endpoint was objective response rate (ORR) based on the population as assigned to treatment. This trial is registered with ClinicalTrials.gov, number NCT00356681. FINDINGS: ORRs for the motesanib group and the placebo group did not differ significantly (49%vs 41%; absolute difference 8% [95% CI -6 to 22]; p=0.31). The ORR in the bevacizumab group (52%) was similar to that in the motesanib group. The most common grade 3 or higher adverse events included diarrhoea (18 of 92 patients in the motesanib group, none of 89 patients in the placebo group, and four of 96 patients in the bevacizumab group), fatigue (11, eight, and six), hypertension (11, one, and seven), and peripheral sensory neuropathy (ten, seven, and 19). More patients in the motesanib group had serious adverse events than did those in the placebo or bevacizumab groups (34, 26, and 21 patients, respectively); the most common of these in the motesanib group were gastrointestinal in nature. INTERPRETATION: Data from this trial do not support the further investigation of motesanib at this dose and schedule in this population. FUNDING: Amgen.

Negative index metamaterial through multi-wave interactions: numerical proof of the concept of low-frequency Lamb-wave multiplexing.

We study numerically the potential of a multimodal elastic metamaterial to filter and guide Lamb waves in a plate. Using a sub-wavelength array of elongated beams attached to the plate, and combining the coupling effects of the longitudinal and flexural motion of these resonators, we create narrow transmission bands at the flexural resonances of the beams inside the wide frequency bandgap induced by their longitudinal resonance. The diameter of the beams becomes the tuning parameter for selection of the flexural leakage frequency, without affecting the main bandgap. Finally, by combination of the monopolar and dipolar scattering effects associated with the coupled beam and plate system, we create a frequency-based multiplexer waveguide in a locally resonant metamaterial.

Adjuvant docetaxel for node-positive breast cancer.

BACKGROUND: We compared docetaxel plus doxorubicin and cyclophosphamide (TAC) with fluorouracil plus doxorubicin and cyclophosphamide (FAC) as adjuvant chemotherapy for operable node-positive breast cancer. METHODS: We randomly assigned 1491 women with axillary node-positive breast cancer to six cycles of treatment with either TAC or FAC as adjuvant chemotherapy after surgery. The primary end point was disease-free survival. RESULTS: At a median follow-up of 55 months, the estimated rates of disease-free survival at five years were 75 percent among the 745 patients randomly assigned to receive TAC and 68 percent among the 746 randomly assigned to receive FAC, representing a 28 percent reduction in the risk of relapse (P=0.001) in the TAC group. The estimated rates of overall survival at five years were 87 percent and 81 percent, respectively. Treatment with TAC resulted in a 30 percent reduction in the risk of death (P=0.008). The incidence of grade 3 or 4 neutropenia was 65.5 percent in the TAC group and 49.3 percent in the FAC group (P<0.001); rates of febrile neutropenia were 24.7 percent and 2.5 percent, respectively (P<0.001). Grade 3 or 4 infections occurred in 3.9 percent of the patients who received TAC and 2.2 percent of those who received FAC (P=0.05); no deaths occurred as a result of infection. Two patients in each group died during treatment. Congestive heart failure and acute myeloid leukemia occurred in less than 2 percent of the patients in each group. Quality-of-life scores decreased during chemotherapy but returned to baseline levels after treatment. CONCLUSIONS: Adjuvant chemotherapy with TAC, as compared with FAC, significantly improves the rates of disease-free and overall survival among women with operable node-positive breast cancer.

Symmetry issues in the hybridization of multi-mode waves with resonators: an example with Lamb waves metamaterial.

Locally resonant metamaterials derive their effective properties from hybridization between their resonant unit cells and the incoming wave. This phenomenon is well understood in the case of plane waves that propagate in media where the unit cell respects the symmetry of the incident field. However, in many systems, several modes with orthogonal symmetries can coexist at a given frequency, while the resonant unit cells themselves can have asymmetric scattering cross-sections. In this paper we are interested in the influence of symmetry breaking on the hybridization of a wave field that includes multiple propagative modes. The A0 and S0 Lamb waves that propagate in a thin plate are good candidates for this study, as they are either anti-symmetric or symmetric. First we designed an experimental setup with an asymmetric metamaterial made of long rods glued to one side of a metallic plate. We show that the flexural resonances of the rods induce a break of the orthogonality between the A0/S0 modes of the free-plate. Finally, based on numerical simulations we show that the orthogonality is preserved in the case of a symmetric metamaterial leading to the presence of two independent polariton curves in the dispersion relation.

Breast cancer subtypes and response to docetaxel in node-positive breast cancer: use of an immunohistochemical definition in the BCIRG 001 trial.

PURPOSE: To investigate the prognostic and predictive significance of subtyping node-positive early breast cancer by immunohistochemistry in a clinical trial of a docetaxel-containing regimen. METHODS: Pathologic data from a central laboratory were available for 1,350 patients (91%) from the BCIRG 001 trial of docetaxel, doxorubicin, and cyclophosphamide (TAC) versus fluorouracil, doxorubicin, and cyclophosphamide (FAC) for operable node-positive breast cancer. Patients were classified by tumor characteristics as (1) triple negative (estrogen receptor [ER]-negative, progesterone receptor [PR]-negative, HER2/neu [HER2]-negative), (2) HER2 (HER2-positive, ER-negative, PR-negative), (3) luminal B (ER-positive and/or PR-positive and either HER2-positive and/or Ki67(high)), and (4) luminal A (ER-positive and/or PR-positive and not HER2-positive or Ki67(high)), and assessed for prognostic significance and response to adjuvant chemotherapy. RESULTS: Patients were subdivided into triple negative (14.5%), HER2 (8.5%), luminal B (61.1%), and luminal A (15.9%). Three-year disease-free survival (DFS) rates (P values with luminal B as referent) were 67% (P < .0001), 68% (P = .0008), 82% (referent luminal B), and 91% (P = .0027), respectively, with hazard ratios of 2.22, 2.12, and 0.46. Improved 3-year DFS with TAC was found in the luminal B group (P = .025) and a combined ER-positive/HER2-negative group treated with tamoxifen (P = .041), with a marginal trend in the triple negatives (P = .051) and HER2 (P = .068) subtypes. No DFS advantage was seen in the luminal A population. CONCLUSION: A simple immunopanel can divide breast cancers into biologic subtypes with strong prognostic effects. TAC significantly complements endocrine therapy in patients with luminal B subtype and, in the absence of targeted therapy, is effective in the triple-negative population.