Uniqueness in a class of Hamilton-Jacobi equations with constraints

International audienceIn this note, we discuss a class of time-dependent Hamilton-Jacobi equations depending on a function of time, this function being chosen in order to keep the maximum of the solution to the constant value 0. The main result of the note is that the full problem has a unique classical solution. The motivation is a selection-mutation model which, in the limit of small diffusion, exhibits concentration on the zero level set of the solution of the Hamilton-Jacobi equation. The uniqueness result that we prove implies strong convergence and error estimates for the selection-mutation model

Activation of plasma membrane voltage-dependent calcium-permeable channels by disruption of microtubules in carrot cells

AbstractPlasma membrane-bound voltage-dependent calcium channels may couple the perception of an initial stimulus to a regulated pathway for calcium influx. The activities of these channels have been shown to be very low and highly unstable but may be recruited by large-predepolarizing pulses, according to a process referred to as recruitment. By combining pharmacological and electrophysiological approaches, we demonstrate in the present paper that the cytoskeleton plays an important role in the regulation of the activity and stability of voltage-dependent calcium channels during whole-cell patch-clamp experiments on carrot protoplasts. Whereas drugs affecting the organization of the microfilament network have no measurable effect, the manipulation of the microtubule network elicits important changes. Thus, the addition of colchicine or oryzalin, which are known to disrupt microtubule organization, leads to a 6–10-fold increase in calcium channel activities and half-life. In contrast, stabilization of the microtubules by taxol has no effect on any of these parameters. The data obtained suggest that interactions of microtubules and voltage-dependent calcium channels by either direct or indirect mechanisms inhibit channel activities and decrease their half-life. In contrast, the disruption of the network overcomes such an inhibitory effect and allows the activation of calcium channels. It is speculated that under normal physiological conditions these protein-protein interactions may work in a reversible manner and contribute to signal transduction in higher plants

Impact of radiotherapy in the management of locally advanced extrahepatic cholangiocarcinoma

BACKGROUND: Optimal therapy for patients with unresectable locally advanced extrahepatic cholangiocarcinoma (ULAC) remains controversial. We analysed the role of radiotherapy in the management of such tumors. METHODS: We retrospectively reviewed the charts of patients treated in our institution with conformal-3D external-beam-radiotherapy (EBRT) with or without concurrent chemotherapy. RESULTS: Thirty patients were included: 24 with a primary tumor (group 1) and 6 with a local relapse (group 2). Toxicity was low. Among 25 patients assessable for EBRT response, we observed 9 complete responses, 4 partial responses, 10 stabilisations, and 2 progressions. The median follow-up was 12 months. Twenty out of 30 patients (66%) experienced a relapse, which was metastatic in 75% of cases in the whole series, 87% in group 1, 60% in group 2 (p = 0.25). Twenty-eight patients (93%) died of relapse or disease complications. Median overall survivals in the whole group and in group 1 or 2 were respectively 12, 11 and 21 months (p = 0.11). The 1-year and 3-year progression-free survivals were respectively 38% and 16% in the whole series; 31% and 11% in group 1, 67% and 33% in group 2 (p = 0.35). CONCLUSION: EBRT seems efficient to treat ULAC, with acceptable toxicity. For primary disease, the high rate of metastatic relapse suggests to limit EBRT to non-progressive patients after induction chemotherapy

Short Children with CHARGE Syndrome: Do They Benefit from Growth Hormone Therapy?

AIM: The aim of this study was to evaluate the response to recombinant growth hormone (GH) treatment in short children with CHARGE syndrome. PATIENTS: We identified 51 children (28 boys and 23 girls) in KIGS (Pfizer International Growth Database). The median chronological age was 7.6 years at the start of GH therapy and 13.2 years at the latest visit. Evaluation for GH deficiency (n = 33) was based on the following: peak GH level 7.3 μg/l and IGF-I level -2.01 standard deviation score (SDS). Sixteen subjects (9 boys) were followed longitudinally for 2 years. RESULTS: Birth length (median SDS, -0.47) and weight (-0.97) were slightly reduced. At the start of GH therapy, height was -3.6 SDS, BMI -0.7 SDS, and the GH dose was 0.26 mg/kg/week. At the latest visit after 2.7 years of GH therapy, height had increased to -2.2 SDS and BMI to -0.5 SDS. In the longitudinal group, height increased from -3.72 SDS at the start of GH therapy to -2.92 SDS after 1 year to -2.37 SDS after 2 years of therapy (start - 2 years: p < 0.05), height velocity increased from -1.69 to 2.98 to 0.95 SDS, and BMI and GH dose (mg/kg/week) remained almost unchanged. CONCLUSIONS: Our data show a positive effect of conventional doses of GH on short-term growth velocity for the longitudinal as well as for the total group, without any safety issues.This study was sponsored by Pfizer Inc.This is the author accepted manuscript. The final version is available from Karger via http://dx.doi.org/10.1159/00038201

A class of Hamilton-Jacobi equations with constraint: uniqueness and constructive approach

International audienceWe discuss a class of time-dependent Hamilton-Jacobi equations, where an unknown function of time is intended to keep the maximum of the solution to the constant value 0. Our main result is that the full problem has a unique viscosity solution, which is in fact classical. The motivation is a selection-mutation model which, in the limit of small diffusion, exhibits concentration on the zero level set of the solution of the Hamilton-Jacobi equation. Uniqueness is obtained by noticing that, as a consequence of the dynamic programming principle, the solution of the Hamilton-Jacobi equation is classical. It is then possible to write an ODE for the maximum of the solution, and treat the full problem as a nonstandard Cauchy problem

Forum Report: Issues in the Evaluation of Diagnostic Tests, Use of Historical Controls, and Merits of the Current Multicenter Collaborative Groups

This forum report contains conclusions about 3 different issues relevant to conducting clinical trials in deep mycoses. (1) Trials of diagnostic tests for deep mycoses must define the population appropriate for testing and the clinical question being asked. The unanswered question for the serum Aspergillus galactomannan assay is whether knowledge of results can change use of empirical therapy to treat febrile patients at high risk of invasive aspergillosis. (2) Use of historical controls is suboptimal but offers a pragmatic solution for studying rare mycoses; use of contemporaneous controls, matched for critical variables and evaluated by a blinded data review committee using detailed criteria, appears optimal. (3) Established groups of independent investigators, such as the European Organization for Research on Treatment of Cancer's Invasive Fungal Infections Group and National Institute of Allergy and Infectious Diseases's Bacteriology and Mycology Study Group, provide a pool of experienced investigators, defined operating rules, impartiality, and specialized expertise. Considering the enormous investment required for adequately powered efficacy trials of antifungal agents and the importance of these trials to guide clinical practice, use of collaborative groups outweighs the extra administrative time that is sometimes require

Forum Report: Issues in the Design of Trials of Drugs for the Treatment of Invasive Aspergillosis

A recent trial of drugs for invasive aspergillosis was used as a background for discussing critical features in the design of antifungal trials. The study under discussion allowed stopping either drug without classifying the patient as having treatment failure, so the trial should be understood as a comparison of 2 treatment strategies, not just 2 drugs. Although the study was a noninferiority trial, the outcome permitted a claim of superiority. Use of the category of "probable” in addition to "proven” aspergillosis permitted inclusion of patients for whom the diagnosis was less certain but who were still early enough in the disease progression to respond to therapy. Different opinions still exist about some of the criteria for the diagnosis of "probable” aspergillosis. A blinded data review committee was helpful in evaluating efficacy in this unblinded trial but had limited value in assessing toxicity. An understanding of these features of design of antifungal drug trials is important in applying the results to clinical practic