Generation of nonlinear internal waves by flow over topography: Rotational effects.

We use the forced Ostrovsky equation to investigate the generation of internal waves excited by a constant background current flowing over localized topography in the presence of background rotation. As is now well known in the absence of background rotation, the evolution scenarios fall into three cases, namely subcritical, transcritical, and supercritical. Here an analysis of the linearized response divides the waves into steady and unsteady waves. In all three cases, steady waves occur downstream but no steady waves can occur upstream, while unsteady waves can arise upstream only when there is a negative minimum of the group velocity. The regions occupied by the steady and unsteady waves are determined by their respective group velocities. When the background current is increased, the wave number of the steady waves decreases. In addition, the concavity (canyon or sill), the topographic width, and the relative strength of the rotation play an important role in the generation mechanism. Nonlinear effects modulate the wave amplitude and lead to the emergence of coherent wave packets. All these findings are confirmed by numerical simulations.

A coupled "AB" system: Rogue waves and modulation instabilities.

Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.

Modified reduced Ostrovsky equation: integrability and breaking.

The modified reduced Ostrovsky equation is a reduction of the modified Korteweg-de Vries equation, in which the usual linear dispersive term with a third-order derivative is replaced by a linear nonlocal integral term, representing the effect of background rotation. Here we study the case when the cubic nonlinear term has the same polarity as the rotation term. This equation is integrable provided certain slope constraints are satisfied. We demonstrate, through theoretical analysis and numerical simulations, that when this constraint is not satisfied at the initial time, wave breaking inevitably occurs.

On strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations.

In the weakly nonlinear limit, oceanic internal solitary waves for a single linear long wave mode are described by the KdV equation, extended to the Ostrovsky equation in the presence of background rotation. In this paper we consider the scenario when two different linear long wave modes have nearly coincident phase speeds and show that the appropriate model is a system of two coupled Ostrovsky equations. These are systematically derived for a density-stratified ocean. Some preliminary numerical simulations are reported which show that, in the generic case, initial solitary-like waves are destroyed and replaced by two coupled nonlinear wave packets, being the counterpart of the same phenomenon in the single Ostrovsky equation.

Nonlinear wave evolution equation for critical layers.

Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solutions when a nonlinear transformation converts the equation to a form equivalent to a steady Korteweg-de Vries equation. This enables the explicit construction of the steady solitary wave solutions.

Undular bore theory for the Gardner equation.

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations.

A phase II study of sunitinib in patients with recurrent epithelial ovarian and primary peritoneal carcinoma: an NCIC Clinical Trials Group Study.

PURPOSE: Sunitinib is a multitargeted receptor tyrosine kinase inhibitor. We conducted a two-stage phase II study to evaluate the objective response rate of oral sunitinib in recurrent epithelial ovarian cancer. PATIENTS AND METHODS: Eligibility required measurable disease and one or two prior chemotherapies, at least one platinum based. Platinum-sensitive or -resistant disease was allowed. Initial dose schedule was sunitinib 50 mg daily, 4 of 6 weeks. Observation of fluid accumulations during off-treatment periods resulted in adoption of continuous 37.5 mg daily dosing in the second stage of accrual. RESULTS: Of 30 eligible patients, most had serous histology (67%), were platinum sensitive (73%) and had two prior chemotherapies (60%). One partial response (3.3%) and three CA125 responses (10%) were observed, all in platinum-sensitive patients using intermittent dosing. Sixteen (53%) had stable disease. Five had >30% decrease in measurable disease. Overall median progression-free survival was 4.1 months. Common adverse events included fatigue, gastrointestinal symptoms, hand-foot syndrome and hypertension. No gastrointestinal perforation occurred. CONCLUSIONS: Single-agent sunitinib has modest activity in recurrent platinum-sensitive ovarian cancer, but only at the 50 mg intermittent dose schedule, suggesting that dose and schedule may be vital considerations in further evaluation of sunitinib in this cancer setting.

Advanced ovarian cancer: phase III randomized study of sequential cisplatin-topotecan and carboplatin-paclitaxel vs carboplatin-paclitaxel.

BACKGROUND: Topotecan has single-agent activity in recurrent ovarian cancer. It was evaluated in a novel combination compared with standard frontline therapy. METHODS: Women aged 75 years or younger with newly diagnosed stage IIB or greater ovarian cancer, Eastern Cooperative Oncology Group Performance Status of 1 or less, were stratified by type of primary surgery and residual disease, treatment center, and age; then randomly assigned to one of the two 21-day intravenous regimens. Patients in arm 1 (n = 409) were administered four cycles of cisplatin 50 mg/m(2) on day 1 and topotecan 0.75 mg/m(2) on days 1-5, then four cycles of paclitaxel 175 mg/m(2) over 3 hours on day 1 followed by carboplatin (area under the curve = 5) on day 1. Patients in arm 2 (n = 410) were given paclitaxel plus carboplatin as in arm 1 for eight cycles. We compared progression-free survival (PFS), overall survival, and cancer antigen-125 normalization rates in the two treatment arms. A stratified log-rank test was used to assess the primary endpoint, PFS. All statistical tests were two-sided. RESULTS: A total of 819 patients were randomly assigned. At baseline, the median age of the patients was 57 years (range = 28-78); 81% had received debulking surgery, and of these, 55% had less than 1 cm residual disease; 66% of patients were stage III and 388 (47.4%) patients had measurable disease. After a median follow-up of 43 months, 650 patients had disease progression or died without documented progression and 406 had died. Patients in arm 1 had more hematological toxicity and hospitalizations than patients in arm 2; PFS was 14.6 months in arm 1 vs 16.2 months in arm 2 (hazard ratio = 1.10, 95% confidence interval = 0.94 to 1.28, P = .25). Among patients with elevated baseline cancer antigen-125, fewer in arm 1 than in arm 2 had levels return to normal by 3 months after random assignment (51.6% vs 63.3%, P = .007) CONCLUSIONS: Topotecan and cisplatin, followed by carboplatin and paclitaxel, were more toxic than carboplatin and paclitaxel alone, but without improved efficacy. Carboplatin plus paclitaxel remains the standard of care for advanced epithelial ovarian cancer.

A phase II study of erlotinib (OSI-774) given in combination with carboplatin in patients with recurrent epithelial ovarian cancer (NCIC CTG IND.149).

OBJECTIVES: Approximately 50% of ovarian cancers have elevated levels of epidermal growth factor receptor (EGFR) which correlates with a poor prognosis. Preclinical evidence suggests that EGFR tyrosine kinase inhibitors (TKIs), such as erlotinib (OSI-774), may potentiate the anti-tumour effects of cytotoxic agents, including carboplatin. Blocking EGFR could thus potentially reverse drug resistance. The primary objective of the study was to assess the response rate to the addition of erlotinib in patients with recurrent ovarian cancer who were receiving carboplatin. METHODS: Patients enrolled on this study had either local or advanced recurrent ovarian cancer with measurable disease. They may have had up to 2 prior chemotherapy regimens, one of which must have contained platinum, and they must have responded to prior platinum therapy. Patients were stratified by platinum sensitivity and were treated with erlotinib 150 mg daily on a continuous dosing schedule, and carboplatin at an AUC of 5 every 21 days. RESULTS: Fifty patients with recurrent ovarian cancer entered the study, 33 in the platinum-sensitive arm and 17 in the platinum-resistant arm. Of patients evaluable for response, there were 14 partial responses (PR) of 30 evaluable for response (57% objective response rate (ORR)) in the platinum-sensitive arm, and 1 PR of 14 evaluable for response (7% ORR) in the platinum-resistant arm. CONCLUSIONS: The combination of erlotinib and carboplatin was active in patients with platinum-sensitive disease, but not in platinum-resistant disease. The toxicities seen were those expected with carboplatin and erlotinib.

Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity.

The initial-value problem for box-like initial disturbances is studied within the framework of an extended Korteweg-de Vries equation with both quadratic and cubic nonlinear terms, also known as the Gardner equation, for the case when the cubic nonlinear coefficient has the same sign as the linear dispersion coefficient. The discrete spectrum of the associated scattering problem is found, which is used to describe the asymptotic solution of the initial-value problem. It is found that while initial disturbances of the same sign as the quadratic nonlinear coefficient result in generation of only solitons, the case of the opposite polarity of the initial disturbance has a variety of possible outcomes. In this case solitons of different polarities as well as breathers may occur. The bifurcation point when two eigenvalues corresponding to solitons merge to the eigenvalues associated with breathers is considered in more detail. Direct numerical simulations show that breathers and soliton pairs of different polarities can appear from a simple box-like initial disturbance.

Value of targeting at-risk populations at outreach venues: findings from a local sauna.

An assessment of the need to increase access to an outreach venue, the local sauna in Walsall, UK, frequented only by men who have sex with men, was undertaken. A case-notes review of the clients who attended the monthly outreach sessions at the sauna in the year 2007 was performed. Among the 287 men seen at the 12 outreach sessions, 37% had a sexually transmitted infection (STI). Of those tested positive, 88% had never had a previous STI. Twenty-one men had syphilis and a further six tested positive for HIV. Hepatitis B vaccination was completed for 41% of the clients seen. Those who tested positive for an STI said they would not have attended a conventional setting but accepted screening at the sauna. This confirmed the need to increase access at this outreach venue, and further funding has now been provided to have outreach sessions twice a month.

A phase III randomized trial of BAY 12-9566 (tanomastat) as maintenance therapy in patients with advanced ovarian cancer responsive to primary surgery and paclitaxel/platinum containing chemotherapy: a National Cancer Institute of Canada Clinical Trials Group Study.

OBJECTIVE: BAY 12-9566 (tanomastat) is a biphenyl matrix metalloprotease inhibitor (MMPI) with antiangiogenic and antimetastatic properties in vivo. The objective of the study was to determine whether the addition of BAY 12-9566 after optimal response to chemotherapy could improve time to progression (TTP). PATIENTS AND METHODS: Patients enrolled in the study had received 6-9 cycles of platinum/paclitaxel containing chemotherapy for stage III or IV ovarian carcinoma, with a response of no evidence of disease, or complete or partial response with residual disease < 2 cm. Patients were then randomized to BAY 12-9566 800 mg p.o. b.i.d. or placebo. The primary endpoint was progression-free survival (PFS); secondary endpoints were quality of life, toxicity, changes in CA 125 levels, response, and overall survival (OS). The total planned sample size was 730. RESULTS: The study was closed after 243 patients had been randomized because of Bayer's decision to close all ongoing trials due to negative results from other phase III trials in pancreatic and small cell lung cancer. The final analysis was performed in August 2000 after the requisite number of events for the first planned interim analysis had occurred; 54% of patients had progressed and 18% had died. PATIENT CHARACTERISTICS: performance status was ECOG 0/1/2 in 65/33/2%; median age 57 years; 79% of patients were FIGO stage III; 41% were optimally debulked; 76% had serous histology, and 67% had > or = grade 3 histology. Toxicity was generally grade 1 or 2 in severity, with the most common (BAY 12-9566 vs. placebo) being nausea (26% vs. 13%), fatigue (24% vs. 12%), diarrhea (14% vs. 10%), rash (12% vs. 7%), grade 3/4 thrombocytopenia (3% vs. 1%), and grade 3/4 anemia (5% vs. 1%). Median time to progression (TTP) was 10.4 months (8.5-11.5) for BAY 12-9566 and 9.2 months (7.2-13.9) for placebo (P = 0.67). Median overall survival (OS) was 13.9 months (12.9-infinity) for BAY 12-9566 and 11.9 months (10.5-16.5) for placebo (P = 0.53). CONCLUSION: We conclude that BAY 12-9566 was generally well tolerated and at the time of the final analysis, there was no evidence of an impact of BAY 12-9566 on PFS or OS.

Analytic model for a weakly dissipative shallow-water undular bore.

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by viscosity. This is derived in Riemann variables using a modified finite-gap integration technique for the Ablowitz-Kaup-Newell-Segur (AKNS) scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.

A cancer research (UK) randomized phase II study of idoxifene in patients with locally advanced/metastatic breast cancer resistant to tamoxifen.

Idoxifene is a novel selective oestrogen receptor modulator (SERM) which had greater binding affinity for the oestrogen receptor (ER) and reduced agonist activity compared with tamoxifen in preclinical studies. In a randomized phase II trial in 56 postmenopausal patients with progressive locally advanced/metastatic breast cancer we assessed whether idoxifene showed evidence of activity compared with an increased 40 mg/day dose of tamoxifen in patients who had previously demonstrated resistance to the standard 20 mg/day dose of tamoxifen. Of 47 patients eligible for response (25 idoxifene, 22 tamoxifen), two partial responses and two disease stabilizations (SD) for >6 months were seen with idoxifene (overall clinical benefit rate 16%, 95% CI 4.5-36.1%). The median duration of clinical benefit was 9.8 months. In contrast, no objective responses were seen with the increased 40 mg/day dose of tamoxifen, although two patients had SD for 7 and 14 months (clinical benefit rate 9%, 95% CI 1.1-29.2%). Idoxifene was well tolerated and the reported possible drug-related toxicities were similar in frequency to those with tamoxifen (hot flushes 13% vs 15%, mild nausea 20% vs 15%). Endocrine and lipid analysis in both groups showed a similar significant fall in serum follicle-stimulating hormone and luteinizing hormone after 4 weeks, together with a significant rise in sex hormone binding globulin levels and 11% reduction in serum cholesterol levels. In conclusion, while idoxifene was associated with only modest evidence of clinical activity in patients with tamoxifen-resistant breast cancer, its toxicity profile and effects on endocrine/lipid parameters were similar to those of tamoxifen.

Long-term follow-up confirms a survival advantage of the paclitaxel-cisplatin regimen over the cyclophosphamide-cisplatin combination in advanced ovarian cancer.

Two independent and consecutive randomized clinical trials, conducted by the American Gynecological Oncology Group and by an European-Canadian Intergroup, have shown superiority, in clinical response rate, progression-free survival, and overall survival, of a cisplatin-paclitaxel regimen over cisplatin-cyclophosphamide given as first-line chemotherapy for women with advanced epithelial ovarian cancer. The results of these studies, published with a median follow-up of about 3 years, have been updated with a 6.5-year follow-up: In each case, an 11% absolute gain in survival favoring the paclitaxel arm is shown; this advantage remains both statistically and clinically significant and supports a role for paclitaxel in frontline chemotherapy for advanced ovarian cancer.

Effectiveness of letters to Cape Breton women who have not had a recent Pap smear.

Nova Scotia, and especially Cape Breton, has high cervical cancer incidence and mortality rates. Letters were sent to 15,691 unscreened and 6,995 under-screened women from Cape Breton Island encouraging them to obtain a Pap test. Controls were 61,510 unscreened women and 32,996 under- screened women in mainland Nova Scotia who were not sent letters. For this cohort study, the provincial Health Card Number database and Provincial Cytology Registry were linked. Having a Pap smear was associated with having received a letter (OR = 1.64), having been previously under-screened rather than unscreened (OR = 1.85), with youth and with higher income (OR = 1.13). After receiving a letter, women in Aboriginal, Mixed Black, Acadian, and rural communities had smear rates similar to those of other women. Being previously unscreened, rather than under-screened, was associated with higher rates of abnormalities (OR = 1.62), indicating greater need for early detection and treatment to prevent invasive cancer. While one-time letters to women improved the Pap smear screening rates, multiple, continuous interventions are needed to make a more substantive improvement in these rates.

Generation of undular bores in the shelves of slowly-varying solitary waves.

We study the long-time evolution of the trailing shelves that form behind solitary waves moving through an inhomogeneous medium, within the framework of the variable-coefficient Korteweg-de Vries equation. We show that the nonlinear evolution of the shelf leads typically to the generation of an undular bore and an expansion fan, which form apart but start to overlap and nonlinearly interact after a certain time interval. The interaction zone expands with time and asymptotically as time goes to infinity occupies the whole perturbed region. Its oscillatory structure strongly depends on the sign of the inhomogeneity gradient of the variable background medium. We describe the nonlinear evolution of the shelves in terms of exact solutions to the KdV-Whitham equations with natural boundary conditions for the Riemann invariants. These analytic solutions, in particular, describe the generation of small "secondary" solitary waves in the trailing shelves, a process observed earlier in various numerical simulations. (c) 2002 American Institute of Physics.

Epoetin alfa in cancer patients: evidence-based guidelines.

Anemia is a common cause of cancer-related fatigue. A systematic review of the literature was performed to establish guidelines on the use of epoetin alfa for the treatment of anemia. The evidence in support of these guidelines was selected, reviewed, and summarized by the members of the Canadian Cancer and Anemia Guidelines Development Group. The effects of epoetin alfa on quality of life (QOL) in patients with cancer were examined in 5 randomized, placebo-controlled trials and 2 large, open-label, nonrandomized, community-based studies. The effects of epoetin alfa on red blood cell transfusion requirements were examined in 19 randomized controlled trials (RCTs) with 21 comparisons. All trials compared epoetin alfa to a suitable control group, examined specified outcome measures that could be analyzed, and studied patients with cancer who were receiving chemotherapy. Trials involving patients with hematologic malignancies originating in the bone marrow were excluded. Outcome measures included 1) quality of life (QOL) (as measured by scales including the Linear Analogue Self-Assessment [LASA] and the Functional Assessment of Cancer Therapy [FACT] subscales), and 2) transfusion requirements (as measured by the proportion of patients requiring transfusion and amount of transfusion). The analysis confirmed that epoetin alfa produced statistically significant and clinically relevant improvements in QOL in patients with cancer. The overall relative risk ratio for transfusion among patients receiving epoetin alfa was calculated to be 0.60 (95% Cl, 0.53-0.69; P < 0.00001), representing a 40% reduction in the proportion of patients requiring transfusion. These results support recommendations for the use of epoetin alfa in patients with cancer-related anemia.