Evaluation of the Biocompatibility of Poly (ortho ester), Copolymer of ε-caprolactone/D,L-lactide and the Composite of Copolymer of ε-caprolactone/D,L-lactide and Tricalciumphosphate as Bone Filling Material

The purpose of this series of studies was to evaluate the biocompatibility of poly (ortho) ester (POE), copolymer of ε-caprolactone and D,L-lactide [P (ε-CL/DL-LA)] and the composite of P(ε-CL/DL-LA) and tricalciumphosphate (TCP) as bone filling material in bone defects. Tissue reactions and resorption times of two solid POE-implants (POE 140 and POE 46) with different methods of sterilization (gamma- and ethylene oxide sterilization), P(ε-CL/DL-LA)(40/60 w/w) in paste form and 50/50 w/w composite of 40/60 w/w P(ε-CL/DL-LA) and TCP and 27/73 w/w composite of 60/40 w/w P(ε-CL/DL-LA) and TCP were examined in experimental animals. The follow-up times were from one week to 52 weeks. The bone samples were evaluated histologically and the soft tissue samples histologically, immunohistochemically and electronmicroscopically. The results showed that the resorption time of gamma sterilized POE 140 was eight weeks and ethylene oxide sterilized POE 140 13 weeks in bone. The resorption time of POE 46 was more than 24 weeks. The gamma sterilized rods started to erode from the surface faster than ethylene oxide sterilized rods for both POEs. Inflammation in bone was from slight to moderate with POE 140 and moderate with POE 46. No highly fluorescent layer of tenascin or fibronectin was found in the soft tissue. Bone healing at the sites of implantation was slower than at control sites with the copolymer in small bone defects. The resorption time for the copolymer was over one year. Inflammation in bone was mostly moderate. Bone healing at the sites of implantation was also slower than at the control sites with the composite in small and large mandibular bone defects. Bone formation had ceased at both sites by the end of follow-up in large mandibular bone defects. The ultrastructure of the connective tissue was normal during the period of observation. It can be concluded that the method of sterilization influenced the resorption time of both POEs. Gamma sterilized POE 140 could have been suitable material for filling small bone defects, whereas the degradation times of solid EO-sterilized POE 140 and POE 46 were too slow to be considered as bone filling material. Solid material is difficult to contour, which can be considered as a disadvantage. The composites were excellent to handle, but the degradation time of the polymer and the composites were too slow. Therefore, the copolymer and the composite can not be recommended as bone filling material.

Reduced visual function and its association with physical functioning in the Finnish adult population : Prevalence, causes, and need for eye care services

The purpose of this study was to estimate the prevalence and distribution of reduced visual acuity, major chronic eye diseases, and subsequent need for eye care services in the Finnish adult population comprising persons aged 30 years and older. In addition, we analyzed the effect of decreased vision on functioning and need for assistance using the World Health Organization’s (WHO) International Classification of Functioning, Disability, and Health (ICF) as a framework. The study was based on the Health 2000 health examination survey, a nationally representative population-based comprehensive survey of health and functional capacity carried out in 2000 to 2001 in Finland. The study sample representing the Finnish population aged 30 years and older was drawn by a two-stage stratified cluster sampling. The Health 2000 survey included a home interview and a comprehensive health examination conducted at a nearby screening center. If the invited participants did not attend, an abridged examination was conducted at home or in an institution. Based on our finding in participants, the great majority (96%) of Finnish adults had at least moderate visual acuity (VA ≥ 0.5) with current refraction correction, if any. However, in the age group 75–84 years the prevalence decreased to 81%, and after 85 years to 46%. In the population aged 30 years and older, the prevalence of habitual visual impairment (VA ≤ 0.25) was 1.6%, and 0.5% were blind (VA < 0.1). The prevalence of visual impairment increased significantly with age (p < 0.001), and after the age of 65 years the increase was sharp. Visual impairment was equally common for both sexes (OR 1.20, 95% CI 0.82 – 1.74). Based on self-reported and/or register-based data, the estimated total prevalences of cataract, glaucoma, age-related maculopathy (ARM), and diabetic retinopathy (DR) in the study population were 10%, 5%, 4%, and 1%, respectively. The prevalence of all of these chronic eye diseases increased with age (p < 0.001). Cataract and glaucoma were more common in women than in men (OR 1.55, 95% CI 1.26 – 1.91 and OR 1.57, 95% CI 1.24 – 1.98, respectively). The most prevalent eye diseases in people with visual impairment (VA ≤ 0.25) were ARM (37%), unoperated cataract (27%), glaucoma (22%), and DR (7%). One-half (58%) of visually impaired people had had a vision examination during the past five years, and 79% had received some vision rehabilitation services, mainly in the form of spectacles (70%). Only one-third (31%) had received formal low vision rehabilitation (i.e., fitting of low vision aids, receiving patient education, training for orientation and mobility, training for activities of daily living (ADL), or consultation with a social worker). People with low vision (VA 0.1 – 0.25) were less likely to have received formal low vision rehabilitation, magnifying glasses, or other low vision aids than blind people (VA < 0.1). Furthermore, low cognitive capacity and living in an institution were associated with limited use of vision rehabilitation services. Of the visually impaired living in the community, 71% reported a need for assistance and 24% had an unmet need for assistance in everyday activities. Prevalence of ADL, instrumental activities of daily living (IADL), and mobility increased with decreasing VA (p < 0.001). Visually impaired persons (VA ≤ 0.25) were four times more likely to have ADL disabilities than those with good VA (VA ≥ 0.8) after adjustment for sociodemographic and behavioral factors and chronic conditions (OR 4.36, 95% CI 2.44 – 7.78). Limitations in IADL and measured mobility were five times as likely (OR 4.82, 95% CI 2.38 – 9.76 and OR 5.37, 95% CI 2.44 – 7.78, respectively) and self-reported mobility limitations were three times as likely (OR 3.07, 95% CI 1.67 – 9.63) as in persons with good VA. The high prevalence of age-related eye diseases and subsequent visual impairment in the fastest growing segment of the population will result in a substantial increase in the demand for eye care services in the future. Many of the visually impaired, especially older persons with decreased cognitive capacity or living in an institution, have not had a recent vision examination and lack adequate low vision rehabilitation. This highlights the need for regular evaluation of visual function in the elderly and an active dissemination of information about rehabilitation services. Decreased VA is strongly associated with functional limitations, and even a slight decrease in VA was found to be associated with limited functioning. Thus, continuous efforts are needed to identify and treat eye diseases to maintain patients’ quality of life and to alleviate the social and economic burden of serious eye diseases.

In-situ one-step hydrothermal synthesis of a lead germanate-graphene composite as a novel anode material for lithium-ion batteries

Lead germanate-graphene nanosheets (PbGeO3-GNS) composites have been prepared by an efficient one-step, in-situ hydrothermal method and were used as anode materials for Li-ion batteries (LIBs). The PbGeO3 nanowires, around 100–200 nm in diameter, are highly encapsulated in a graphene matrix. The lithiation and de-lithiation reaction mechanisms of the PbGeO3 anode during the charge-discharge processes have been investigated by X-ray diffraction and electrochemical characterization. Compared with pure PbGeO3 anode, dramatic improvements in the electrochemical performance of the composite anodes have been obtained. In the voltage window of 0.01–1.50 V, the composite anode with 20 wt.% GNS delivers a discharge capacity of 607 mAh g−1 at 100 mA g−1 after 50 cycles. Even at a high current density of 1600 mA g−1, a capacity of 406 mAh g−1 can be achieved. Therefore, the PbGeO3-GNS composite can be considered as a potential anode material for lithium ion batteries.

BaZr0.8Y0.2O3--NiO composite anodic powders for proton-conducting SOFCs prepared by a combustion method

BaZr0.8Y0.2O3- (BZY)-NiO composite powders with different BZY-NiO weight ratios were prepared by a combustion method as anodes for proton-conducting solid oxide fuel cells (SOFCs). After heating to 1100C for 6 h, the composite powders were made of a well-dispersed mixture of two phases, BZY and NiO. Chemical stability tests showed that the BZY-NiO anodic powders had good stability against CO2, whereas comparative tests under the same conditions showed degradation for BaCe0.7Zr 0.1Y0.2O3--NiO, which is at present the most used anode material for proton-conducting SOFCs. Area specific resistance (ASR) measurements for BZY-NiO anodes showed that their electrochemical performance depended on the BZY-NiO weight ratio. The best performance was obtained for the anode containing 50 wt BZY and 50 wt NiO, which showed the smallest ASR values in the whole testing temperature range (0.37 cm2 at 600C). The 50 wt BZY and 50 wt NiO anode prepared by combustion also showed superior performance than that of the BZY-NiO anode conventionally made by a mechanical mixing route, as well as that of Pt.

A rare P2X7 variant Arg307Gln with absent pore formation function protects against neuroinflammation in multiple sclerosis

Multiple sclerosis (MS) is a chronic relapsing-remitting inflammatory disease of the central nervous system characterized by oligodendrocyte damage, demyelination and neuronal death. Genetic association studies have shown a 2-fold or greater prevalence of the HLA-DRB1*1501 allele in the MS population compared with normal Caucasians. In discovery cohorts of Australasian patients with MS (total 2941 patients and 3008 controls), we examined the associations of 12 functional polymorphisms of P2X7, a microglial/macrophage receptor with proinflammatory effects when activated by extracellular adenosine triphosphate (ATP). In discovery cohorts, rs28360457, coding for Arg307Gln was associated with MS and combined analysis showed a 2-fold lower minor allele frequency compared with controls (1.11% for MS and 2.15% for controls, P = 0.0000071). Replication analysis of four independent European MS case–control cohorts (total 2140 cases and 2634 controls) confirmed this association [odds ratio (OR) = 0.69, P = 0.026]. A meta-analysis of all Australasian and European cohorts indicated that Arg307Gln confers a 1.8-fold protective effect on MS risk (OR = 0.57, P = 0.0000024). Fresh human monocytes heterozygous for Arg307Gln have >85% loss of ‘pore’ function of the P2X7 receptor measured by ATP-induced ethidium uptake. Analysis shows Arg307Gln always occurred with 270His suggesting a single 307Gln–270His haplotype that confers dominant negative effects on P2X7 function and protection against MS. Modeling based on the homologous zP2X4 receptor showed Arg307 is located in a region rich in basic residues located only 12 Å from the ligand binding site. Our data show the protective effect against MS of a rare genetic variant of P2RX7 with heterozygotes showing near absent proinflammatory ‘pore’ function.

High-strength bulk Al-based bimodal ultrafine eutectic composite with enhanced plasticity

An in situ bulk ultrafine bimodal eutectic Al-Cu-Si composite was synthesized by solidification. This heterostructured composite with microstructural length scale hierarchy in the eutectic microstructure, which combines an ultrafine-scale binary cellular eutectic (alpha-Al + Al2Cu) and a nanometer-sized anomalous ternary eutectic (alpha-Al + Al2Cu + Si), exhibits high fracture strength (1.1 +/- 0.1 GPa) and large compressive plastic strain (11 +/- 2%) at room temperature. The improved compressive plasticity of the bimodal-nanoeutectic composite originates from homogeneous and uniform distribution of inhomogeneous plastic deformation (localized shear bands), together with strong interaction between shear bands in the spatially heterogeneous structure.

Cardiac function before and after treatment for various types of loading conditions and in myocardial restriction : A prospective study on pediatric patients with two- and three-dimensional echocardiography and measurement of serum natriuretic peptides

Background: The incidence of all forms of congenital heart defects is 0.75%. For patients with congenital heart defects, life-expectancy has improved with new treatment modalities. Structural heart defects may require surgical or catheter treatment which may be corrective or palliative. Even those with corrective therapy need regular follow-up due to residual lesions, late sequelae, and possible complications after interventions. Aims: The aim of this thesis was to evaluate cardiac function before and after treatment for volume overload of the right ventricle (RV) caused by atrial septal defect (ASD), volume overload of the left ventricle (LV) caused by patent ductus arteriosus (PDA), and pressure overload of the LV caused by coarctation of the aorta (CoA), and to evaluate cardiac function in patients with Mulibrey nanism. Methods: In Study I, of the 24 children with ASD, 7 underwent surgical correction and 17 percutaneous occlusion of ASD. Study II had 33 patients with PDA undergoing percutaneous occlusion. In Study III, 28 patients with CoA underwent either surgical correction or percutaneous balloon dilatation of CoA. Study IV comprised 26 children with Mulibrey nanism. A total of 76 healthy voluntary children were examined as a control group. In each study, controls were matched to patients. All patients and controls underwent clinical cardiovascular examinations, two-dimensional (2D) and three-dimensional (3D) echocardiographic examinations, and blood sampling for measurement of natriuretic peptides prior to the intervention and twice or three times thereafter. Control children were examined once by 2D and 3D echocardiography. M-mode echocardiography was performed from the parasternal long axis view directed by 2D echocardiography. The left atrium-to-aorta (LA/Ao) ratio was calculated as an index of LA size. The end-diastolic and end-systolic dimensions of LV as well as the end-diastolic thicknesses of the interventricular septum and LV posterior wall were measured. LV volumes, and the fractional shortening (FS) and ejection fraction (EF) as indices of contractility were then calculated, and the z scores of LV dimensions determined. Diastolic function of LV was estimated from the mitral inflow signal obtained by Doppler echocardiography. In three-dimensional echocardiography, time-volume curves were used to determine end-diastolic and end-systolic volumes, stroke volume, and EF. Diastolic and systolic function of LV was estimated from the calculated first derivatives of these curves. Results: (I): In all children with ASD, during the one-year follow-up, the z score of the RV end-diastolic diameter decreased and that of LV increased. However, dilatation of RV did not resolve entirely during the follow-up in either treatment group. In addition, the size of LV increased more slowly in the surgical subgroup but reached control levels in both groups. Concentrations of natriuretic peptides in patients treated percutaneously increased during the first month after ASD closure and normalized thereafter, but in patients treated surgically, they remained higher than in controls. (II): In the PDA group, at baseline, the end-diastolic diameter of LV measured over 2SD in 5 of 33 patients. The median N-terminal pro-brain natriuretic peptide (proBNP) concentration before closure measured 72 ng/l in the control group and 141 ng/l in the PDA group (P = 0.001) and 6 months after closure measured 78.5 ng/l (P = NS). Patients differed from control subjects in indices of LV diastolic and systolic function at baseline, but by the end of follow-up, all these differences had disappeared. Even in the subgroup of patients with normal-sized LV at baseline, the LV end-diastolic volume decreased significantly during follow-up. (III): Before repair, the size and wall thickness of LV were higher in patients with CoA than in controls. Systolic blood pressure measured a median 123 mm Hg in patients before repair (P < 0.001) and 103 mm Hg one year thereafter, and 101 mm Hg in controls. The diameter of the coarctation segment measured a median 3.0 mm at baseline, and 7.9 at the 12-month (P = 0.006) follow-up. Thicknesses of the interventricular septum and posterior wall of the LV decreased after repair but increased to the initial level one year thereafter. The velocity time integrals of mitral inflow increased, but no changes were evident in LV dimensions or contractility. During follow-up, serum levels of natriuretic peptides decreased correlating with diastolic and systolic indices of LV function in 2D and 3D echocardiography. (IV): In 2D echocardiography, the interventricular septum and LV posterior wall were thicker, and velocity time integrals of mitral inflow shorter in patients with Mulibrey nanism than in controls. In 3D echocardiography, LV end-diastolic volume measured a median 51.9 (range 33.3 to 73.4) ml/m² in patients and 59.7 (range 37.6 to 87.6) ml/m² in controls (P = 0.040), and serum levels of ANPN and proBNP a median 0.54 (range 0.04 to 4.7) nmol/l and 289 (range 18 to 9170) ng/l, in patients and 0.28 (range 0.09 to 0.72) nmol/l (P < 0.001) and 54 (range 26 to 139) ng/l (P < 0.001) in controls. They correlated with several indices of diastolic LV function. Conclusions (I): During the one-year follow-up after the ASD closure, RV size decreased but did not normalize in all patients. The size of the LV normalized after ASD closure but the increase in LV size was slower in patients treated surgically than in those treated with the percutaneous technique. Serum levels of ANPN and proBNP were elevated prior to ASD closure but decreased thereafter to control levels in patients treated with the percutaneous technique but not in those treated surgically. (II): Changes in LV volume and function caused by PDA disappeared by 6 months after percutaneous closure. Even the children with normal-sized LV benefited from the procedure. (III): After repair of CoA, the RV size and the velocity time integrals of mitral inflow increased, and serum levels of natriuretic peptides decreased. Patients need close follow-up, despite cessation of LV pressure overload, since LV hypertrophy persisted even in normotensive patients with normal growth of the coarctation segment. (IV): In children with Mulibrey nanism, the LV wall was hypertrophied, with myocardial restriction and impairment of LV function. Significant correlations appeared between indices of LV function, size of the left atrium, and levels of natriuretic peptides, indicating that measurement of serum levels of natriuretic peptides can be used in the clinical follow-up of this patient group despite its dependence on loading conditions.

Evaluation of Vestibular Function with Visual Feedback Posturography and Motorized Head Impulse Test.

Objectives: To evaluate the applicability of visual feedback posturography (VFP) for quantification of postural control, and to characterize the horizontal angular vestibulo-ocular reflex (AVOR) by use of a novel motorized head impulse test (MHIT). Methods: In VFP, subjects standing on a platform were instructed to move their center of gravity to symmetrically placed peripheral targets as fast and accurately as possible. The active postural control movements were measured in healthy subjects (n = 23), and in patients with vestibular schwannoma (VS) before surgery (n = 49), one month (n = 17), and three months (n = 36) after surgery. In MHIT we recorded head and eye position during motorized head impulses (mean velocity of 170º/s and acceleration of 1 550º/s²) in healthy subjects (n = 22), in patients with VS before surgery (n = 38) and about four months afterwards (n = 27). The gain, asymmetry and latency in MHIT were calculated. Results: The intraclass correlation coefficient for VFP parameters during repeated tests was significant (r = 0.78-0.96; p < 0.01), although two of four VFP parameters improved slightly during five test sessions in controls. At least one VFP parameter was abnormal pre- and postoperatively in almost half the patients, and these abnormal preoperative VFP results correlated significantly with abnormal postoperative results. The mean accuracy in postural control in patients was reduced pre- and postoperatively. A significant side difference with VFP was evident in 10% of patients. In the MHIT, the normal gain was close to unity, the asymmetry in gain was within 10%, and the latency was a mean ± standard deviation 3.4 ± 6.3 milliseconds. Ipsilateral gain or asymmetry in gain was preoperatively abnormal in 71% of patients, whereas it was abnormal in every patient after surgery. Preoperative gain (mean ± 95% confidence interval) was significantly lowered to 0.83 ± 0.08 on the ipsilateral side compared to 0.98 ± 0.06 on the contralateral side. The ipsilateral postoperative mean gain of 0.53 ± 0.05 was significantly different from preoperative gain. Conclusion: The VFP is a repeatable, quantitative method to assess active postural control within individual subjects. The mean postural control in patients with VS was disturbed before and after surgery, although not severely. Side difference in postural control in the VFP was rare. The horizontal AVOR results in healthy subjects and in patients with VS, measured with MHIT, were in agreement with published data achieved using other techniques with head impulse stimuli. The MHIT is a non-invasive method which allows reliable clinical assessment of the horizontal AVOR.

Pathological changes at the target tissue level in Sjögren's syndrome and their effect on the exocrine function of the salivary glands

Sjögren s syndrome (SS) is a common autoimmune disease affecting the lacrimal and salivary glands. SS is characterized by a considerable female predominance and a late age of onset, commonly at the time of adreno- and menopause. The levels of the androgen prohormone dehydroepiandrosterone-sulphate (DHEA-S) in the serum are lower in patients with SS than in age- and sex-matched healthy control subjects. The eventual systemic effects of low androgen levels in SS are not currently well understood. Basement membranes (BM) are specialized layers of extracellular matrix and are composed of laminin (LM) and type IV collagen matrix networks. BMs deliver messages to epithelial cells via cellular LM-receptors including integrins (Int) and Lutheran blood group antigen (Lu). The composition of BMs and distribution of LM-receptors in labial salivary glands (LSGs) of normal healthy controls and patients with SS was assessed. LMs have complex and highly regulated distribution in LSGs. LMs seem to have specific tasks in the dynamic regulation of acinar cell function. LM-111 is important for the normal acinar cell differentiation and its expression is diminished in SS. Also LM-211 and -411 seem to have some acinar specific functional tasks in LSGs. LM-311, -332 and -511 seem to have more general structure maintaining and supporting roles in LSGs and are relatively intact also in SS. Ints α3β1, α6β1, α6β4 and Lu seem to supply structural basis for the firm attachment of epithelial cells to the BM in LSGs. The expression of Ints α1β1 and α2β1 differed clearly from other LM-receptors in that they were found almost exclusively around the acini and intercalated duct cells in salivons suggesting some type of acinar cell compartment-specific or dominant function. Expression of these integrins was lower in SS compared to healthy controls suggesting that the LM-111 and -211-to-Int α1β1 and α2β1 interactions are defective in SS and are crucial to the maintenance of the acini in LSGs. DHEA/DHEA-S concentration in serum and locally in saliva of patients with SS seems to have effects on the salivary glands. These effects were first detected using the androgen-dependent CRISP-3 protein, the production and secretion of which were clearly diminished in SS. This might be due to the impaired function of the intracrine DHEA prohormone metabolizing machinery, which fails to successfully convert DHEA into its active metabolites in LSGs. The progenitor epithelial cells from the intercalated ductal area of LSGs migrate to the acinar compartment and then undergo a phenotype change into secretory acinar cells. This migration and phenotype change seem to be regulated by the LM-111-to-Int α1β1/Int α2β1 interactions. Lack of these interactions could be one factor limiting the normal remodelling process. Androgens are effective stimulators of Int α1β1 and α2β1 expression in physiologic concentrations. Addition of DHEA to the culture medium had effective stimulating effect on the Int α1β1 and α2β1 expression and its effect may be deficient in the LSGs of patients with SS.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Conservation law with the flux function discontinuous in the space variable- II - Convex-concave type fluxes and generalized entropy solutions

We deal with a single conservation law with discontinuous convex-concave type fluxes which arise while considering sign changing flux coefficients. The main difficulty is that a weak solution may not exist as the Rankine-Hugoniot condition at the interface may not be satisfied for certain choice of the initial data. We develop the concept of generalized entropy solutions for such equations by replacing the Rankine-Hugoniot condition by a generalized Rankine-Hugoniot condition. The uniqueness of solutions is shown by proving that the generalized entropy solutions form a contractive semi-group in L-1. Existence follows by showing that a Godunov type finite difference scheme converges to the generalized entropy solution. The scheme is based on solutions of the associated Riemann problem and is neither consistent nor conservative. The analysis developed here enables to treat the cases of fluxes having at most one extrema in the domain of definition completely. Numerical results reporting the performance of the scheme are presented. (C) 2006 Elsevier B.V. All rights reserved.