TOPOLOGICAL ASYMPTOTIC ANALYSIS FOR A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS

International audienceTopological asymptotic expansions for quasilinear elliptic equations have not been studied yet. Such questions arise from the need to apply topological asymptotic methods in shape optimization to nonlinear elasticity equations as in imaging to detect sets with codimensions ≥ 2 (e.g. points in 2D or segments in 3D). Our main contribution is to provide topological asymptotic expansions for a class of quasilinear elliptic equations, perturbed in non-empty subdomains. The obtained topological gradient can be split into a classical linear term and a new term which accounts for the non linearity of the equation. With respect to topological asymptotic analysis, moving from linear equations onto quasilinear ones requires to heavily revise the implemented methods and tools. By comparison with the steps carried out to obtain such expansions with the Laplace equation, the core issue for a quasilinear equation lies in the ability to defi ne the variation of the direct state at scale 1 in R^N . Accordingly we build dedicated weighted quotient Sobolev spaces, which semi-norms encompass both the L^p norm and the L^2 norm of the gradient in R^N. Then we consider an appropriate class of quasilinear elliptic equations, to ensure that the problem de ning the direct state at scale 1 enjoys a combined p and 2 ellipticity property. The needed asymptotic behavior of the solution of the nonlinear interface problem in R^N is then proven. An appropriate duality scheme is set up between the direct and adjoint states at each stage of approximation

Développements asymptotiques topologiques pour une classe d'équations elliptiques quasilinéaires. Estimations et développements asymptotiques de p-capacités de condensateurs. Le cas anisotrope du segment

La Partie I présente l obtention du développement asymptotique topologique pour une classe d équations elliptiques quasilinéaires. Un point central réside dans la possibilité de définir la variation de l état direct à l échelle 1 dans R^N. Après avoir défini un cadre fonctionnel approprié faisant intervenir les normes L^p et L^2, et avoir justifié la classe d équations considérée, la méthode se poursuit par l étude du comportement asymptotique de la solution du problème d interface non linéaire dans R^N et par une mise en dualité appropriée des états direct et adjoint aux différentes étapes d approximation.La Partie II traite d estimations et de développements asymptotiques de p-capacités de condensateurs, dont l obstacle est d intérieur vide et de codimension > ou = 2. Après les résultats préliminaires, les condensateurs équidistants permettent de donner deux illustrations de l anisotropie engendrée par un segment dans l équation de p-Laplace, puis d établir une minoration de la p-capacité N-dimensionnelle d un segment, qui fait intervenir les p-capacités d un point, respectivement en dimensions N et (N-1). Les condensateurs elliptiques permettent d établir que le gradient topologique de la 2-capacité n est pas un outil approprié pour distinguer les courbes des obstacles d intérieur non vide en 2DPart I deals with obtaining topological asymptotic expansions for a class of quasilinear elliptic equations. A key point lies in the ability to define the variation of the direct state at scale 1 in R^N. After setting up an appropriate functional framework involving both the L^p and the L^2 norms, and then justifying the chosen class of equations, the approach goes on with the study of the asymptotic behavior of the solution of the nonlinear interface problem in R^N and by setting up an adequate duality scheme between the direct and adjoint states at each step of approximation. Part II deals with estimates and asymptotic expansions of condenser p-capacities and focuses on obstacles with empty interiors and with codimensions > ou = 2. After preliminary results, equidistant condensers are introduced to point out the anisotropy caused by a segment in the p-Laplace equation, and to provide a lower bound to the N-dimensional condenser p-capacity of a segment, by means of the N-dimensional and of the (N-1)-dimensional condenser p-capacities of apoint. Introducing elliptical condensers, it turns out that the topological gradient of the 2-capacity is not an appropriate tool to separate curves and obstacles with nonempty interior in 2DTOULOUSE-INSA-Bib. electronique (315559905) / SudocSudocFranceF

Mechanical testing and comparison of porcine tissue, silicones and 3D-printed materials for cardiovascular phantoms

Background: Cardiovascular phantoms for patient education, pre-operative planning, surgical training, haemodynamic simulation, and device testing may help improve patient care. However, currently used materials may have different mechanical properties compared to biological tissue. Methods/Aim: The aim of this study was to investigate the mechanical properties of 3D-printing and silicone materials in comparison to biological cardiovascular tissues. Uniaxial cyclic tension testing was performed using dumbbell samples from porcine tissue (aorta, pulmonary artery, right and left ventricle). Flexible testing materials included 15 silicone (mixtures) and three 3D-printing materials. The modulus of elasticity was calculated for different deformation ranges. Results: The modulus of elasticity (0%–60%) for the aorta ranged from 0.16 to 0.18 N/mm^2, for the pulmonary artery from 0.07 to 0.09 N/mm^2, and for the right ventricle as well as the left ventricle short-axis from 0.1 to 0.16 N/mm^2. For silicones the range of modulus of elasticity was 0.02–1.16 N/mm^2, and for the 3D-printed materials from 0.85 to 1.02 N/mm^2. The stress-strain curves of all tissues showed a non-linear behaviour in the cyclic tensile testing, with a distinct toe region, followed by exponential strain hardening behaviour towards the peak elongation. The vessel samples showed a more linear behaviour comparted to myocardial samples. The silicones and 3D printing materials exhibited near-linearity at higher strain ranges, with a decrease in stiffness following the initial deformation. All samples showed a deviation between the loading and unloading curves (hysteresis), and a reduction in peak force over the first few cycles (adaptation effect) at constant deformation. Conclusion: The modulus of elasticity of silicone mixtures is more in agreement to porcine cardiovascular tissues than 3D-printed materials. All synthetic materials showed an almost linear behaviour in the mechanical testing compared to the non-linear behaviour of the biological tissues, probably due to fibre recruitment mechanism in the latter

"If it is left, it becomes easy for me to get tested": use of oral self-tests and community health workers to maximize the potential of home-based HIV testing among adolescents in Lesoth

Home-based HIV testing fails to reach high coverage among adolescents and young adults (AYA), mainly because they are often absent during the day of home-based testing. ADORE (ADolescent ORal tEsting) is a mixed-method nested study among AYA in rural Lesotho, measuring the effect of home-based secondary distribution of oral HIV self-tests (HIVST) on coverage, as well as exploring how AYA perceive this HIV self-testing model.; ADORE study was nested in a cluster-randomized trial. In intervention village-clusters, oral HIVST were left for household members who were absent or declined testing during a testing campaign. One present household member was trained on HIVST use. Distributed HIVST were followed up by village health workers (VHW). In control clusters no self-tests were distributed. The quantitative outcome was testing coverage among AYA (age 12 to 24) within 120 days, defined as a confirmed HIV test result or known status, using adjusted random-effects logistic regression on the intention-to-treat population. Qualitatively, we conducted in-depth interviews among both AYA who used and did not use the distributed HIVST.; From July 2018 to December 2018, 49 and 57 villages with 1471 and 1620 consenting households and 1236 and 1445 AYA in the control and intervention arm, respectively, were enrolled. On the day of the home-visit, a testing coverage of 37% (461/1236) and 41% (596/1445) in the control and the intervention arm, respectively, were achieved. During the 120 days follow-up period, an additional 23 and 490 AYA in control and intervention clusters, respectively, knew their status. This resulted in a testing coverage of 484/1236 (39%) in the control versus 1086/1445 (75%) in the intervention arm (aOR 8.80 [95% CI 5.81 to 13.32]; p < 0.001). 21 interviews were performed. Personal assistance after the secondary distribution emerged as a key theme and VHWs were generally seen as a trusted cadre.; Secondary distribution of HIVST for AYA absent or refusing to test during home-based testing in Lesotho resulted in an absolute 36% increase in coverage. Distribution should, however, go along with clear instructions on the use of the HIVST and a possibility to easily access more personal support

Engagement in care, viral suppression, drug resistance and reasons for non-engagement after home-based same-day ART initiation in Lesotho: a two-year follow-up of the CASCADE trial

The CASCADE trial showed that compared to usual care (UC), offering same-day (SD) ART during home-based HIV testing improved engagement in care and viral suppression 12 months after diagnosis. However, open questions remain regarding long-term outcomes and the risk of propagating drug resistance.; After completion of the primary endpoint at 12 months, participants not in care in both arms were traced and encouraged to access care. At 24 months, the following outcomes were assessed in both arms: Engagement in care, viral suppression, and reasons for non-engagement. Furthermore, we explored among SD arm non-linkers the acquisition of drug resistance mutations (DRMs).; At 24 months, 64% (88/137) in the SD vs 59% (81/137) in the UC arm were in care (absolute difference 5%; 95%CI -6-16; p=0.38) and 57% (78/137) vs 54% (74/137) had documented viral suppression (3%; -9-15; p=0.28). Among 36 participants alive and not in care at 24 months with ascertained status, the majority rejected contact with the health system or were unwilling to take ART. Among eight interviewed SD arm non-linkers, six had not initiated ART upon enrolment and no acquired DRMs were detected. Two had taken the initial 30-day ART supply and acquired DRMs.; SD ART resulted in higher rates of engagement in care and viral suppression at 12 but not 24 months. Levelling off between both arms was driven by linkage beyond 12 months in the UC arm. We did not observe compensatory long-term disengagement in the SD arm. These long-term results endorse SD ART initiation policies

Community-based models of care for management of type 2 diabetes mellitus among non-pregnant adults in sub-Saharan Africa: a scoping review protocol

Background:; The burden of type 2 diabetes mellitus (T2DM) is increasing in low- and middle-income countries, including sub-Sahara Africa (SSA). However, awareness of and access to T2DM diagnosis and care remain low in SSA, leading to delayed treatment, early morbidity, and mortality. Particularly in rural settings with long distances to health care facilities, community-based care models may contribute to increased timely diagnosis and care. This scoping review aims to summarize and categorize existing models of community-based care for T2DM among non-pregnant adults in SSA, and to synthesize the evidence on acceptance, clinical outcomes, and engagement in care.; Method and analysis:; This review will follow the framework suggested by Arskey and O'Malley, which has been further refined by Levac; et al.; and the Joanna Briggs Institute. Electronic searches will be performed in Medline, Embase, Cumulative Index to Nursing and Allied Health Literature (CINAHL) and Scopus, supplemented with backward and forward citation searches. We will include cohort studies, randomized trials and case-control studies that report cases of non-pregnant individuals diagnosed with T2DM in SSA who receive a substantial part of care in the community. Our outcomes of interest will be model acceptability, blood sugar control, end organ damage, and patient engagement in care. A narrative analysis will be conducted, and comparisons made between community-based and facility-based models, where within-study comparison is reported.; Conclusion:; Care for T2DM has become a global health priority. Community-based care may be an important add-on approach especially in populations with poor access to health care facilities. This review will inform policy makers and program implementers on different community-based models for care of T2DM in SSA, and critically appraise their acceptability and clinical outcomes. It will further identify evidence gaps and future research priorities in community-based T2DM care

Switch to second-line versus continued first-line antiretroviral therapy for patients with low-level HIV-1 viremia: an open-label randomized controlled trial in Lesotho

Current World Health Organization (WHO) antiretroviral therapy (ART) guidelines define virologic failure as two consecutive viral load (VL) measurements ≥1,000 copies/mL, triggering empiric switch to next-line ART. This trial assessed if patients with sustained low-level HIV-1 viremia on first-line ART benefit from a switch to second-line treatment.; This multicenter, parallel-group, open-label, superiority, randomized controlled trial enrolled patients on first-line ART containing non-nucleoside reverse transcriptase inhibitors (NNRTI) with two consecutive VLs ≥100 copies/mL, with the second VL between 100-999 copies/mL, from eight clinics in Lesotho. Consenting participants were randomly assigned (1:1), stratified by facility, demographic group, and baseline VL, to either switch to second-line ART (switch group) or continued first-line ART (control group; WHO guidelines). The primary endpoint was viral suppression (<50 copies/mL) at 36 weeks. Analyses were by intention to treat, using logistic regression models, adjusted for demographic group and baseline VL. Between August 1, 2017, and August 7, 2019, 137 individuals were screened, of whom 80 were eligible and randomly assigned to switch (n = 40) or control group (n = 40). The majority of participants were female (54 [68%]) with a median age of 42 y (interquartile range [IQR] 35-51), taking tenofovir disoproxil fumarate/lamivudine/efavirenz (49 [61%]) and on ART for a median of 5.9 y (IQR 3.3-8.6). At 36 weeks, 22/40 (55%) participants in the switch versus 10/40 (25%) in the control group achieved viral suppression (adjusted difference 29%, 95% CI 8%-50%, p = 0.009). The switch group had significantly higher probability of viral suppression across different VL thresholds (<20, <100, <200, <400, and <600 copies/mL) but not for <1,000 copies/mL. Thirty-four (85%) participants in switch group and 21 (53%) in control group experienced at least one adverse event (AE) (p = 0.002). No hospitalization or death or other serious adverse events were observed. Study limitations include a follow-up period too short to observe differences in clinical outcomes, missing values in CD4 cell counts due to national stockout of reagents during the study, and limited generalizability of findings to other than NNRTI-based first-line ART regimens.; In this study, switching to second-line ART among patients with sustained low-level HIV-1 viremia resulted in a higher proportion of participants with viral suppression. These results endorse lowering the threshold for virologic failure in future WHO guidelines.; The trial is registered at ClinicalTrials.gov, NCT03088241

SESOTHO trial ("Switch Either near Suppression Or THOusand") - switch to second-line versus WHO-guided standard of care for unsuppressed patients on first-line ART with viremia below 1000 copies/mL: protocol of a multicenter, parallel-group, open-label, randomized clinical trial in Lesotho, Southern Africa

The World Health Organization (WHO) recommends viral load (VL) measurement as the preferred monitoring strategy for HIV-infected individuals on antiretroviral therapy (ART) in resource-limited settings. The new WHO guidelines 2016 continue to define virologic failure as two consecutive VL ≥1000 copies/mL (at least 3 months apart) despite good adherence, triggering switch to second-line therapy. However, the threshold of 1000 copies/mL for defining virologic failure is based on low-quality evidence. Observational studies have shown that individuals with low-level viremia (measurable but below 1000 copies/mL) are at increased risk for accumulation of resistance mutations and subsequent virologic failure. The SESOTHO trial assesses a lower threshold for switch to second-line ART in patients with sustained unsuppressed VL.; In this multicenter, parallel-group, open-label, randomized controlled trial conducted in Lesotho, patients on first-line ART with two consecutive unsuppressed VL measurements ≥100 copies/mL, where the second VL is between 100 and 999 copies/mL, will either be switched to second-line ART immediately (intervention group) or not be switched (standard of care, according to WHO guidelines). The primary endpoint is viral resuppression (VL &lt; 50 copies/mL) 9 months after randomization. We will enrol 80 patients, giving us 90% power to detect a difference of 35% in viral resuppression between the groups (assuming two-sided 5% alpha error). For our primary analysis, we will use a modified intention-to-treat set, with those lost to care, death, or crossed over considered failure to resuppress, and using logistic regression models adjusted for the prespecified stratification variables.; The SESOTHO trial challenges the current WHO guidelines, assessing an alternative, lower VL threshold for patients with unsuppressed VL on first-line ART. This trial will provide data to inform future WHO guidelines on VL thresholds to recommend switch to second-line ART.; ClinicalTrials.gov ( NCT03088241 ), registered May 05, 2017

PEBRA trial - effect of a peer-educator coordinated preference-based ART service delivery model on viral suppression among adolescents and young adults living with HIV: protocol of a cluster-randomized clinical trial in rural Lesotho

Despite tremendous progress in controlling the HIV epidemic in sub-Saharan Africa, HIV-related mortality continues to increase among adolescents and young people living with HIV (AYPLHIV). Globally, sub-Saharan Africa accounts for 85% of the AYPLHIV. Overall outcomes along the HIV care cascade are worse among AYPLHIV as compared to all other age groups due to various challenges in accessing and adhering to antiretroviral therapy (ART). New, innovative multicomponent packages of differentiated service delivery (DSD) models, are required to address the specific needs of AYPLHIV. This study aims to evaluate the feasibility and effectiveness of a multicomponent DSD model (PEBRA model) designed for AYPLHIV and coordinated by a peer-educator.; PEBRA (Peer-Educator Based Refill of ART) is a cluster randomized, open-label, superiority trial conducted at 20 health facilities in three districts of Lesotho, Southern Africa. The clusters (health facilities) are randomly assigned to either the PEBRA model or standard of care in a 1:1 ratio, stratified by district. AYPLHIV aged 15-24 years old in care and on ART at one of the clusters are eligible. In the PEBRA model, a peer-educator coordinates the antiretroviral therapy (ART) services - such as medication pick-up, SMS notifications and support options - according to the preferences of the AYPLHIV. The peer-educator delivers this personalized model using a tablet-based application called PEBRApp. The control clusters continue to offer standard of care: ART services coordinated by the nurse. The primary endpoint is viral suppression at 12 months. Secondary endpoints include self-reported adherence to ART, quality of life, satisfaction with care and engagement in care. The target sample size is 300 AYPLHIV. Statistical analyses are conducted and reported in line with CONSORT guidelines for cluster randomized trials.; The PEBRA trial will provide evidence on the feasibility and effectiveness of an inclusive, holistic and preference-based DSD model for AYPLHIV that is coordinated by a peer-educator. Many countries in SSA have an existing peer-educator program. If proven effective, the PEBRA model and PEBRApp have the potential to be scaled up to similar settings.; Clinicaltrials.gov, NCT03969030. Registered on 31 May 2019. More information: www.pebra.info

Effect and cost of two successive home visits to increase HIV testing coverage: a prospective study in Lesotho, Southern Africa

Home-based HIV testing and counselling (HB-HTC) is frequently used to increase awareness of HIV status in sub-Saharan Africa. Whereas acceptance of HB-HTC is usually high, testing coverage may remain low due to household members being absent during the home visits. This study assessed whether two consecutive visits, one during the week, one on the weekend, increase coverage.; The study was a predefined nested-study of the CASCADE-trial protocol and conducted in 62 randomly selected villages and 17 urban areas in Butha-Buthe district, Lesotho. HB-HTC teams visited each village/urban area twice: first during a weekday, followed by a weekend visit to catch-up for household members absent during the week. Primary outcome was HTC coverage after first and second visit. Coverage was defined as all individuals who knew their HIV status out of all household members (present and absent).; HB-HTC teams visited 6665 households with 18,286 household members. At first visit, 69.2 and 75.4% of household members were encountered in rural and urban households respectively (p &lt; 0.001) and acceptance for testing was 88.5% in rural and 79.5% in urban areas (p &lt; 0.001), resulting in a coverage of 61.8 and 61.5%, respectively. After catch-up visit, the HTC coverage increased to 71.9% in rural and 69.4% in urban areas. The number of first time testers was higher at the second visit (47% versus 35%, p &lt; 0.001). Direct cost per person tested and per person tested HIV positive were lower during weekdays (10.50 and 335 USD) than during weekends (20 and 1056 USD).; A catch-up visit on weekends increased the proportion of persons knowing their HIV status from 62 to 71% and reached more first-time testers. However, cost per person tested during catch-up visits was nearly twice the cost during first visit.; NCT02692027 (prospectively registered on February 21, 2016)