Minimal clinically meaningful differences for the eortc QLQ-C30 and eortc QLQ-Bn20 scales in brain cancer patients

Objective: The aim of this study was to determine the smallest changes in health-related quality of life (HRQOL) scores in the European Organization for Research and Treatment of Cancer quality of life questionnaire (EORTC QLQ-C30) and the EORTC Brain Cancer Module (QLQ-BN20), which could be considered as clinically meaningful in brain cancer patients. Methods: World Health Organization (WHO) performance status (PS) and the Mini Mental State Examination (MMSE) were used as clinical anchors to determine minimal clinically important differences (MCID) in HRQOL change scores (range 0 - 100) in the EORTC QLQ-C30 and QLQ-BN20. Anchor-based MCID estimates less than 0.2SD (small effect) were not recommended for interpretation. Other selected distribution-based methods were also used for comparison purposes. Results: Based on WHO PS, our findings support the following whole number estimates of the MCID for improvement and deterioration respectively: physical functioning (6, 9), role functioning (14, 12), cognitive functioning (8, 8), global health status (7, 4*), fatigue (12, 9) and motor dysfunction (4*, 5). Anchoring with MMSE, cognitive functioning MCID estimates for improvement and deterioration were (11, 2*) and those for communication deficit were (9, 7). The estimates with asterisks were less that the set 0.2 SD threshold and are therefore not recommended for interpretation. Our MCID estimates therefore range from 5-14. Conclusion: These estimates can help clinicians to evaluate changes in HRQOL over time and, in conjunction with other measures of efficacy, help to assess the value of a health care intervention or to compare treatments. Furthermore, the estimates can be useful in determining sample sizes in the design of future clinical trials.

Substance use and suicidal conduct: a study of adolescents hospitalized for suicide attempt and ideation.

AIM: To study the prevalence of psychoactive substance use disorder (PSUD) among suicidal adolescents, psychoactive substance intoxication at the moment of the attempt, and the association between PSUD at baseline and either occurrence of suicide or repetition of suicide attempt(s). METHODS: 186 adolescents aged 16 to 21 y hospitalized for suicide attempt or overwhelming suicidal ideation were included (T0); 148 of them were traced again for evaluations after 6 mo (T1) and/or 18 mo (T2). DSM-IV diagnoses were assessed each time using the Mini International Neuropsychiatric Interview. RESULTS: At T0, 39.2% of the subjects were found to have a PSUD. Among them, a significantly higher proportion was intoxicated at the time of the attempt than those without PSUD (44.3% vs 25.4%). Among the 148 adolescents who could be traced at either T1 or T2, two died from suicide and 30 repeated suicide attempts once or more times. A marginally significant association was found between death by suicide/repetition of suicide attempt and alcohol abuse/dependence at baseline (OR=3.3, 95% CI 0.7-15.0; OR=2.6, 95% CI 0.7-9.3). More than one suicide attempt before admission to hospital at T0 (OR=3.2, 95% CI 1.1-10.0) and age over 19 y at T0 (OR=3.2, 95% CI 1.1-9.2) were independently associated with the likelihood of death by suicide or repetition of suicide attempt. CONCLUSION: Among adolescents hospitalized for suicide attempt or overwhelming suicidal ideation, the risk of death or repetition of attempt is high and is associated with previous suicide attempts--especially among older adolescents--and also marginally associated with PSUD; these adolescents should be carefully evaluated for such risks and followed up once discharged from the hospital.

Assessing depression outcome in patients with moderate dementia: sensitivity of the HoNOS65+ scale.

To date, there is no widely accepted clinical scale to monitor the evolution of depressive symptoms in demented patients. We assessed the sensitivity to treatment of a validated French version of the Health of the Nation Outcome Scale (HoNOS) 65+ compared to five routinely used scales. Thirty elderly inpatients with ICD-10 diagnosis of dementia and depression were evaluated at admission and discharge using paired t-test. Using the Brief Psychiatric Rating Scale (BPRS) "depressive mood" item as gold standard, a receiver operating characteristic curve (ROC) analysis assessed the validity of HoNOS65+F "depressive symptoms" item score changes. Unlike Geriatric Depression Scale, Mini Mental State Examination and Activities of Daily Living scores, BPRS scores decreased and Global Assessment Functioning Scale score increased significantly from admission to discharge. Amongst HoNOS65+F items, "behavioural disturbance", "depressive symptoms", "activities of daily life" and "drug management" items showed highly significant changes between the first and last day of hospitalization. The ROC analysis revealed that changes in the HoNOS65+F "depressive symptoms" item correctly classified 93% of the cases with good sensitivity (0.95) and specificity (0.88) values. These data suggest that the HoNOS65+F "depressive symptoms" item may provide a valid assessment of the evolution of depressive symptoms in demented patients.

Abus sexuel, psychopathologie et réponses psycho-endocriniennes au stress

Résumé : Des événements traumatiques précoces peuvent favoriser le développement ultérieur de psychopathologies telles que les troubles anxieux ou dépressifs. Dans quelle mesure ces événements influencent-ils la réaction d'un sujet à un stress aigu ? Objectif : comparer la prévalence de troubles psychiatriques et déterminer la différence de réaction au stress à l'âge adulte de femmes ayant ou non subi un traumatisme de type abus sexuel dans leur enfance. Participants : 46 femmes âgées de 22 à 48 ans recrutées entre juin 2004 et juillet 2006 réparties en 2 groupes (groupe contrôle de 16 sujets, groupe traumatisé de 30 sujets). L'étude se déroule dans l'Unité de recherche du SUPEA, rue du Bugnon 25A, 1005 Lausanne. Mesures : hormone adrenocorticotropiqué (ACTI-I), cortisol plasmatique et salivaire, fréquence cardiaque au cours du TSST (test psychosocial de stress standardisé), réponses aux questionnaires standardisés VAS (visual analog scale) et MDBF (Mehrdimensionale Befindlichkeitsfragebogen), MINI (mini international neuropsychiatric interview), ETI (early trauma inventory). Les différences de cóncentration d'ACTH et de cortisol, du rythme cardiaque, et des réponses aux questionnaires VAS et MDBF entre des groupes contrôle et abus ont été analysés (ANOVA, ANalysis Of VAriance). Lorsque les résultats montraient une grande hétérogénéité, nous .avons également appliqué les tests de Mann-Whitney et de Kruskal-Wallis: Résultats principaux : les personnes abusées dans leur enfance souffrent à l'âge adulte plus fréquemment de troubles psychiatriques selon les critères du MINI DSM-IV. Ces personnes réagissent fortement au stress, mais seules leurs réponses subjectives montrent des différences significatives par rapport à un groupe de contrôle.

Oxygen-sensing reporter strain of Pseudomonas fluorescens for monitoring the distribution of low-oxygen habitats in soil.

The root-colonizing bacterium Pseudomonas fluorescens CHA0 was used to construct an oxygen-responsive biosensor. An anaerobically inducible promoter of Pseudomonas aeruginosa, which depends on the FNR (fumarate and nitrate reductase regulation)-like transcriptional regulator ANR (anaerobic regulation of arginine deiminase and nitrate reductase pathways), was fused to the structural lacZ gene of Escherichia coli. By inserting the reporter fusion into the chromosomal attTn7 site of P. fluorescens CHA0 by using a mini-Tn7 transposon, the reporter strain, CHA900, was obtained. Grown in glutamate-yeast extract medium in an oxystat at defined oxygen levels, the biosensor CHA900 responded to a decrease in oxygen concentration from 210 x 10(2) Pa to 2 x 10(2) Pa of O(2) by a nearly 100-fold increase in beta-galactosidase activity. Half-maximal induction of the reporter occurred at about 5 x 10(2) Pa. This dose response closely resembles that found for E. coli promoters which are activated by the FNR protein. In a carbon-free buffer or in bulk soil, the biosensor CHA900 still responded to a decrease in oxygen concentration, although here induction was about 10 times lower and the low oxygen response was gradually lost within 3 days. Introduced into a barley-soil microcosm, the biosensor could report decreasing oxygen concentrations in the rhizosphere for a 6-day period. When the water content in the microcosm was raised from 60% to 85% of field capacity, expression of the reporter gene was elevated about twofold above a basal level after 2 days of incubation, suggesting that a water content of 85% caused mild anoxia. Increased compaction of the soil was shown to have a faster and more dramatic effect on the expression of the oxygen reporter than soil water content alone, indicating that factors other than the water-filled pore space influenced the oxygen status of the soil. These experiments illustrate the utility of the biosensor for detecting low oxygen concentrations in the rhizosphere and other soil habitats.

Corpus Christianorum Series Apocryphorum. Une collection au profil original, portée par un projet de recherche collectif

(Résumé de l'ouvrage) In 1953 the first fascicle of the first volume of the Corpus Christianorum was published. Now, fifty years later, this series has established itself as one of the great scientific enterprises in the field of patristic and medieval studies. We offer this birthday-present to ourselves, our old and new collaborators and our friends as a celebration of what has been achieved, as a survey of where we currently stand and as an insight into our future. The book opens with an essay on fifty years of the Corpus Christianorum. It tells the story of how the enterprise started as an ambitious yet limited project and how it developed into what it is today: a conglomerate of many different research projects located in different places all over the world. The second part presents a florilegium of patristic and medieval texts, all of which have been edited in the series, some only recently, others long ago. The selection has been made by a group of scholars representing the variety of interests reflected in the subseries of the Corpus Christianorum. At the end of the volume an Onomasticon has been added. It gives a complete survey of all the text-editions published to date. This "mini-clavis" will make it easier to find one's way in the library of the Corpus Christianorum.

Validation of an adapted falls efficacy scale in older rehabilitation patients.

OBJECTIVE: To determine the psychometric properties of an adapted version of the Falls Efficacy Scale (FES) in older rehabilitation patients. DESIGN: Cross-sectional survey. SETTING: Postacute rehabilitation facility in Switzerland. PARTICIPANTS: Seventy elderly persons aged 65 years and older receiving postacute, inpatient rehabilitation. INTERVENTIONS: Not applicable. MAIN OUTCOME MEASURES: FES questions asked about subject's confidence (range, 0 [none]-10 [full]) in performing 12 activities of daily living (ADLs) without falling. Construct validity was assessed using correlation with measures of physical (basic ADLs [BADLs]), cognitive (Mini-Mental State Examination [MMSE]), affective (15-item Geriatric Depression Scale [GDS]), and mobility (Performance Oriented Mobility Assessment [POMA]) performance. Predictive validity was assessed using the length of rehabilitation stay as the outcome. To determine test-retest reliability, FES administration was repeated in a random subsample (n=20) within 72 hours. RESULTS: FES scores ranged from 10 to 120 (mean, 88.7+/-26.5). Internal consistency was optimal (Cronbach alpha=.90), and item-to-total correlations were all significant, ranging from .56 (toilet use) to .82 (reaching into closets). Test-retest reliability was high (intraclass correlation coefficient, .97; 95% confidence interval, .95-.99; P<.001). Subjects reporting a fall in the previous year had lower FES scores than nonfallers (85.0+/-25.2 vs 94.4+/-27.9, P=.054). The FES correlated with POMA (Spearman rho=.40, P<.001), MMSE (rho=.37, P=.001), BADL (rho=.43, P<.001), and GDS (rho=-.53, P<.001) scores. These relationships remained significant in multivariable analysis for BADLs and GDS, confirming FES construct validity. There was a significant inverse relationship between FES score and the length of rehabilitation stay, independent of sociodemographic, functional, cognitive, and fall status. CONCLUSIONS: This adapted FES is reliable and valid in older patients undergoing postacute rehabilitation. The independent association between poor falls efficacy and increased length of stay has not been previously described and needs further investigations.

Calbindin-immunoreactive sensory neurons in dissociated dorsal root ganglion cell cultures of chick embryo: role of culture conditions.

Immunoreactivity to calbindin D-28k, a vitamin D-dependent calcium-binding protein, is expressed by neuronal subpopulations of dorsal root ganglia (DRG) in the chick embryo. To determine whether the expression of this phenotypic characteristic is maintained in vitro and controlled by environmental factors, dissociated DRG cell cultures were performed under various conditions. Subpopulations of DRG cells cultured at embryonic day 10 displayed calbindin-immunoreactive cell bodies and neurites in both neuron-enriched or mixed DRG cell cultures. The number of calbindin-immunoreactive ganglion cells increased up to 7-10 days of culture independently of the changes occurring in the whole neuronal population. The presence of non-neuronal cells, which promotes the maturation of the sensory neurons, tended to reduce the percentage of calbindin-immunoreactive cell bodies. Addition of horse serum enhanced both the number of calbindin-positive neurons and the intensity of the immunostaining, but does not prevent the decline of the subpopulation of calbindin-immunoreactive neurons during the second week of culture; on the contrary, the addition of muscular extract to cultures at 10 days maintained the number of calbindin-expressing neurons. While calbindin-immunoreactive cell bodies grown in culture were small- or medium-sized, no correlation was found between cell size and immunostaining density. At the ultrastructural level, the calbindin immunoreaction was distributed throughout the neuroplasm. These results indicate that the expression of calbindin by sensory neurons grown in vitro may be modulated by horse serum-contained factors or interaction with non-neuronal cells. As distinct from horse serum, muscular extract is able to maintain the expression of calbindin by a subpopulation of DRG cells.

Antecedents, psychiatric characteristics and follow-up of adolescents hospitalized for suicide attempt of overwhelming suicidal ideation.

To evaluate the socio-demographic as well as the health and psychiatric profiles of adolescents hospitalised for suicide attempt or overwhelming suicide ideation and to assess repetition of suicide attempt over a period of 18 months. Between April 2000 and September 2001, all patients aged 16 to 21 years admitted to the University Hospitals of Geneva and Lausanne for suicide attempt or ideation were included in the study. At this time (T0) semi-structured face to face interviews were conducted to identify socio-demographic data, mental health and antecedents regarding suicidal conducts. Current psychiatric status was assessed with the MINI (Mini International Neuropsychiatric Instrument). At T1 and T2, reassessments included psychiatric status (MINI) as well as lifestyles, socio-professional situation and suicidal behaviours. At T0, 269 subjects met the study criteria, among whom 83 subjects (56 girls and 27 boys) left the hospital too quickly to be involved or refused to participate in the study (final sample at T0: 149 girls; 37 boys). The participation rate at T1 and T2 was respectively 66% and 62% of the original sample. The percentage of adolescents meeting the criteria for psychiatric diagnoses (91%) was high: affective disorder (78%); anxiety disorder (64%); substance use disorder (39%); eating disorder (9%); psychotic disorder (11%); antisocial personality (7%) with most subjects (85%) having more than one disorder. Around 90% of the subjects interviewed at T1, and/or T2, had received follow-up care after their hospitalisation, either by a primary care physician or a psychotherapist or both. Two subjects died of violent death and 18% made a further suicide attempt. Most adolescents hospitalised for suicidal episodes suffer from psychiatric problems which should be addressed by a careful psychiatric assessment, followed up if needed by a structured after care plan.

Amoebae as a tool to isolate new bacterial species, to discover new virulence factors and to study the host-pathogen interactions.

Amoebae are unicellular protozoan present worldwide in several environments mainly feeding on bacteria. Some of them, the amoebae-resistant bacteria (ARBs), have evolved mechanisms to survive and replicate inside amoebal species. These mainly include legionella, mycobacteria and Chlamydia-related bacteria. Amoebae can provide a replicative niche, can act as reservoir for bacteria whereas the cystic form can protect the internalized bacteria. Moreover, the amoebae represent a Trojan horse for ARBs to infect animals. The long interaction between amoebae and bacteria has likely selected for bacterial virulence traits leading to the adaptation towards an intracellular lifestyle, and some ARBs have acquired the ability to infect mammals. This review intends to highlight the important uses of amoebae in several fields in microbiology by describing the main tools developed using amoebal cells. First, amoebae such as Acanthamoeba are used to isolate and discover new intracellular bacterial species by two main techniques: the amoebal co-culture and the amoebal enrichment. In the second part, taking Waddlia chondrophila as example, we summarize some important recent applications of amoebae to discover new bacterial virulence factors, in particular thanks to the amoebal plaque assay. Finally, the genetically tractable Dictyostelium discoideum is used as a model organism to study host-pathogen interactions, in particular with the development of several approaches to manipulate its genome that allowed the creation of a wide range of mutated strains largely shared within the Dictyostelium community.

Substance use and suicidal conducts : a study of adolescents hospitalized for suicide attempt and ideation

RESUME Objectifs: Etudier la prévalence des troubles liés à l'utilisation de substances psychoatives parmi des adolescents suicidaires; évaluer l'influence de la prise de substances psychoactives sur le geste suicidaire; analyser l'association entre les troubles liés à l'utilisation de substances psychoactives et le risque de récidive de la conduite suicidaire. Méthode: 186 adolescents, âgés de 16 à 21 ans, hospitalisés pour tentative de suicide ou idées suicidaires envahissantes, ont été inclus. Parmi eux, 148 ont été revus pour évaluation à 6 et/ou 18 mois. Des diagnostics psychiatriques, basés sur les critères du DSM-IV, ont été posés à l'aide d'un questionnaire, le MINI (Mini International Neuropsychiatric Interview). Résultats: A l'inclusion, 39.2% des sujets avaient un trouble lié à l'utilisation de substances psychoactives. Parmi eux, une proportion significativement plus élevée était sous l'influence d'alcool ou drogue au moment de la tentative de suicide (44.3% versus 25.4%). Des 148 adolescents suivis et revus à 6 ou 18 mois, 2 sont décédés par suicide et il y a eu 30 récidives de tentative de suicide durant l'étude. Une association significative a été trouvée entre les récidives de suicide et un diagnostic d'abus/dépendance à l'alcool à l'inclusion (OR=3.3; CI 0.7-15.0; 0R=2.6, CI 0.7-9.3). Des antécédents de plusieurs tentatives de suicide (OR=3.2; CI 1.1-10.0) et un âge supérieur à 19 ans (OR=3.2; CI 1.1-9.2) à l'inclusion étaient associés à la probabilité de mort par suicide ou de récidive de tentative de suicide. Conclusion: Parmi les adolescents hospitalisés pour tentative de suicide ou idées suicidaires envahissantes, le risque de décès ou de récidive est important. Ce risque est associé, entre autres, à des antécédents suicidaires et au diagnostic de trouble lié à l'utilisation de substances psychoactives. Le risque suicidaire ainsi que la consommation de substances psychoactives devrait être évalué chez les adolescents. De plus, les sujets jugés à risque devraient être suivis systématiquement après une hospitalisation pour conduite suicidaire. ABSTRACT Aim: To study the prevalence of psychoactive substance use disorder (PSUD) among suicidal adolescents, psychoactive substance intoxication at the moment of the attempt and the association between PSUD at baseline and either occurrence of suicide or repetition of suicide attempt(s). Methods: 186 adolescents aged 16 to 21 hospitalised for suicide attempt or overwhelming suicidal ideation were included (TO); 148 of them were traced again for evaluations after 6 months and/or 18 months. DSM-IV diagnoses were assessed each time using the Mini International Neuropsychiatric Interview. Results: At TO, 39.2% of the subjects were found to have a PSUD. Among them, a significantly higher proportion was intoxicated at the time of the attempt than those without PSUD (44-.3% vs. 25.4%). Among the 148 adolescents who could be traced at either Ti or T2, two died from suicide and 30 repeated suicide attempt once or more time. A marginally significant association was found between death by suicide/repetition of suicide attempt and alcohol abuse/dependence at baseline (0R=3.3; CI 0.7-15.0; 0R=2.6, CI 0.7-9.3). More than one suicide attempt before admission to hospital at TO (OR=3.2; CI 1.1-10.0) and age over 19 at TO (0R=3.2; CI 1.1-9.2) were independently associated with the likelihood of death by suicide or repetition of suicide attempt. Conclusion: Among adolescents hospitalised for suicide attempt or overwhelming suicidal ideation, the risk of death or repetition of attempt is high and is associated with previous suicide attempts - especially among older adolescents - and also marginally associated with PSUD; these adolescents should be carefully evaluated for such risks and followed up once discharged from the hospital.

Differentiation of postmitotic neuroblasts into substance P-immunoreactive sensory neurons in dissociated cultures of chick dorsal root ganglion.

Counts performed on dissociated cell cultures of E10 chick embryo dorsal root ganglia (DRG) showed after 4-6 days of culture a pronounced decline of the neuronal population in neuron-enriched cultures and a net gain in the number of ganglion cells in mixed DRG cell cultures (containing both neurons and nonneuronal cells). In the latter case, the increase in the number of neurons was found to depend on NGF and to average 119% in defined medium or 129% in horse serum-supplemented medium after 6 days of culture. The lack of [3H]thymidine incorporation into the neuronal population indicated that the newly formed ganglion cells were not generated by proliferation. On the contrary, the differentiation of postmitotic neuroblasts present in the nonneuronal cell compartment was supported by sequential microphotographs of selected fields taken every hour for 48-55 hr after 3 days of culture. Apparently nonneuronal flat dark cells exhibited morphological changes and gradually evolved into neuronal ovoid and refringent cell bodies with expanding neurites. The ultrastructural organization of these evolving cells corresponded to that of primitive or intermediate neuroblasts. The neuronal nature of these rounding up cell bodies was indeed confirmed by the progressive expression of various neuronal cell markers (150 and 200-kDa neurofilament triplets, neuron specific enolase, and D2/N-CAM). Besides a constant lack of immunoreactivity for tyrosine hydroxylase, somatostatin, parvalbumin, and calbindin-D 28K and a lack of cytoenzymatic activity for carbonic anhydrase, all the newly produced neurons expressed three main phenotypic characteristics: a small cell body, a strong immunoreactivity to MAG, and substance P. Hence, ganglion cells newly differentiated in culture would meet characteristics ascribed to small B sensory neurons and more specifically to a subpopulation of ganglion cells containing substance P-immunoreactive material.

Predisposing and precipitating factors of delirium after cardiac surgery: a prospective observational cohort study.

OBJECTIVE: To comprehensively assess pre-, intra-, and postoperative delirium risk factors as potential targets for intervention. BACKGROUND: Delirium after cardiac surgery is associated with longer intensive care unit (ICU) stay, and poorer functional and cognitive outcomes. Reports on delirium risk factors so far did not cover the full range of patients' presurgical conditions, intraoperative factors, and postoperative course. METHODS: After written informed consent, 221 consecutive patients ≥ 50 years scheduled for cardiac surgery were assessed for preoperative cognitive performance, and functional and physical status. Clinical and biochemical data were systematically recorded perioperatively. RESULTS: Of the 215 patients remaining for analysis, 31% developed delirium in the intensive care unit. Using logistic regression models, older age [73.3 (71.2-75.4) vs 68.5 (67.0-70.0); P = 0.016], higher Charlson's comorbidity index [3.0 (1.5-4.0) vs 2.0 (1.0-3.0) points; P = 0.009], lower Mini-Mental State Examination (MMSE) score (MMSE, [27 (23-29) vs 28 (27-30) points; P = 0.021], length of cardiopulmonary bypass (CPB) [CPB; 133 (112-163) vs 119 (99-143) min; P = 0.004], and systemic inflammatory response syndrome in the intensive care unit [25 (36.2%) vs 13 (8.9%); P = 0.001] were independently associated with delirium. Combining age, MMSE score, Charlson's comorbidity index, and length of CPB in a regression equation allowed for a prediction of postoperative delirium with a sensitivity of 71.19% and a specificity of 76.26% (receiver operating analysis, area under the curve: 0.791; 95% confidence interval: 0.727-0.845). CONCLUSIONS: Further research will evaluate if modification of these risk factors prevents delirium and improves outcomes.

Permanent stallion contact hastens onset of mares' cyclicity after winter anoestrus

The species Equus caballus is characterized as a seasonal polyoestrous herd mammal, providing continuous interactions between stallions and mares in feral herds throughout the year. Under domesticated conditions mares and stallions are stabled and kept separated mostly due to hygienic and safety concerns. Managing mares through the spring transitional phase until they show fertile cycles represents a high multifactorial challenge for horse breeders and veterinarians. The goal of this study was to examine the influence of a permanent stallion contact on the onset of cyclicity in anoestrous mares in the transition period.

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.