Expression and function of angiotensins in the regulation of intraocular pressure - an experimental study

Glaucoma is a multifactorial long-term ocular neuropathy associated with progressive loss of the visual field, retinal nerve fiber structural abnormalities and optic disc changes. Like arterial hypertension it is usually a symptomless disease, but if left untreated leads to visual disability and eventual blindness. All therapies currently used aim to lower intraocular pressure (IOP) in order to minimize cell death. Drugs with new mechanisms of action could protect glaucomatous eyes against blindness. Renin-angiotensin system (RAS) is known to regulate systemic blood pressure and compounds acting on it are in wide clinical use in the treatment of hypertension and heart failure but not yet in ophthalmological use. There are only few previous studies concerning intraocular RAS, though evidence is accumulating that drugs antagonizing RAS can also lower IOP, the only treatable risk factor in glaucoma. The main aim of this experimental study was to clarify the expression of the renin-angiotensin system in the eye tissues and to test its potential oculohypotensive effects and mechanisms. In addition, the possible relationship between the development of hypertension and IOP was evaluated in animal models. In conclusion, a novel angiotensin receptor type (Mas), as well as ACE2 enzyme- producing agonists for Mas, were described for the first time in the eye structures participating in the regulation of IOP. In addition, a Mas receptor agonist significantly reduced even normal IOP. The effect was abolished by a specific receptor antagonist. Intraocular, local RAS would thus to be involved in the regulation of IOP, probably even more in pathological conditions such as glaucoma though there was no unambiguous relationship between arterial and ocular hypertension. The findings suggest the potential as antiglaucomatous drugs of agents which increase ACE2 activity and the formation of angiotensin (1-7), or activate Mas receptors.

The function of Bmps and Runx2 in normal tooth development and in the pathogenesis of cleidocranial dysplasia

The development of many embryonic organs is regulated by reciprocal and sequential epithelial-mesenchymal interactions. These interactions are mediated by conserved signaling pathways that are reiteratively used. Cleidocranial dysplasia (CCD) is a congenital syndrome where both bone and tooth development is affected. The syndrome is characterized by short stature, abnormal clavicles, general bone dysplasia, and supernumerary teeth. CCD is caused by mutations in RUNX2, a transcription factor that is a key regulator of osteoblast differentiation and bone formation. The first aim of this study was to analyse the expression of a family of key signal molecules, Bone morphogenetic protein (Bmp) at different stages of tooth development. Bmps have a variety of functions and they were originally discovered as signals inducing ectopic bone formation. We performed a comparative in situ hybridisation analysis of the mRNA expression of Bmp2-7 from initiation of tooth development to differentiation of dental hard tissues. The expression patterns indicated that the Bmps signal between the epithelial and mesenchymal tissues during initiation and morphogenesis of tooth development, as well as during the differentiation of odontoblasts and ameloblasts. Furthermore, they are also part of the signalling networks whereby the enamel knot regulates the patterning of tooth cusps. The second aim was to study the role of Runx2 during tooth development and thereby to gain better understanding of the pathogenesis of the tooth phenotype in CCD. We analysed the tooth phenotype of Runx2 knockout mice and examined the patterns and regulation of Runx2 gene expression.. The teeth of wild-type and Runx2 mutant mice were compared by several methods including in situ hybridisation, tissue culture, bead implantation experiments, and epithelial-mesenchymal recombination studies. Phenotypic analysis of Runx2 -/- mutant tooth development showed that teeth failed to advance beyond the bud stage. Runx2 expression was restricted to dental mesenchyme between the bud and early bell stages of tooth development and it was regulated by epithelial signals, in particular Fgfs. We searched for downstream targets of Runx2 by comparative in situ hybridisation analysis. The expression of Fgf3 was downregulated in the mesenchyme of Runx2 -/- teeth. Shh expression was absent from the enamel knot in the lower molars of Runx2 -/- and reduced in the upper molars. In conclusion, these studies showed that Runx2 regulates key epithelial-mesenchymal interactions that control advancing tooth morphogenesis and histodifferentiation of the epithelial enamel organ. In addition, in the upper molars of Runx2 mutants extra buddings occured at the palatal side of the tooth bud. We suggest that Runx2 acts as an inhibitor of successional tooth formation by preventing advancing development of the buds. Accordingly, we propose that RUNX2 haploinsuffiency in humans causes incomplete inhibition of successional tooth formation and as a result supernumerary teeth.

The effect of internal audit function quality and internal audit contribution to external audit on audit fees

Corporate governance mandates and listing rules identify internal audit functions (IAF) as a central internal control mechanism. External audits are expected to assess the quality of IAF before placing reliance on its work. We provide evidence on the effect of IAF quality and IAF contribution to external audit on audit fees. Using data from a matched survey of both external and internal audits, we extend prior research which is based mainly on internal audits' assessment and conducted predominantly in highly developed markets. We find a positive relationship between IAF quality and audit fees as well as a reduction in audit fees as a result of external auditors' reliance on IAF. The interaction between IAF quality and IAF contribution to external audit suggests that high quality IAF induces greater external auditor reliance on internal auditors' work and thus result in lower external audit fees.

Functional imaging of peripheral vision and dorsal stream function in the human cerebral cortex

Visual information processing in brain proceeds in both serial and parallel fashion throughout various functionally distinct hierarchically organised cortical areas. Feedforward signals from retina and hierarchically lower cortical levels are the major activators of visual neurons, but top-down and feedback signals from higher level cortical areas have a modulating effect on neural processing. My work concentrates on visual encoding in hierarchically low level cortical visual areas in human brain and examines neural processing especially in cortical representation of visual field periphery. I use magnetoencephalography and functional magnetic resonance imaging to measure neuromagnetic and hemodynamic responses during visual stimulation and oculomotor and cognitive tasks from healthy volunteers. My thesis comprises six publications. Visual cortex forms a great challenge for modeling of neuromagnetic sources. My work shows that a priori information of source locations are needed for modeling of neuromagnetic sources in visual cortex. In addition, my work examines other potential confounding factors in vision studies such as light scatter inside the eye which may result in erroneous responses in cortex outside the representation of stimulated region, and eye movements and attention. I mapped cortical representations of peripheral visual field and identified a putative human homologue of functional area V6 of the macaque in the posterior bank of parieto-occipital sulcus. My work shows that human V6 activates during eye-movements and that it responds to visual motion at short latencies. These findings suggest that human V6, like its monkey homologue, is related to fast processing of visual stimuli and visually guided movements. I demonstrate that peripheral vision is functionally related to eye-movements and connected to rapid stream of functional areas that process visual motion. In addition, my work shows two different forms of top-down modulation of neural processing in the hierachically lowest cortical levels; one that is related to dorsal stream activation and may reflect motor processing or resetting signals that prepare visual cortex for change in the environment and another local signal enhancement at the attended region that reflects local feed-back signal and may perceptionally increase the stimulus saliency.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

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.

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.

Carotid Stenosis, Endarterectomy, and the Brain : Brain microcirculation, diffusion, and cognitive function before and after carotid endarterectomy in patients with a high-grade carotid stenosis

Carotid atherosclerotic disease is a major cause of stroke, but it may remain clinically asymptomatic. The factors that turn the asymptomatic plaque into a symptomatic one are not fully understood, neither are the subtle effects that a high-grade carotid stenosis may have on the brain. The purpose of this study was to evaluate brain microcirculation, diffusion, and cognitive performance in patients with a high-grade stenosis in carotid artery, clinically either symptomatic or asymptomatic, undergoing carotid endarterectomy (CEA). We wanted to find out whether the stenoses are associated with diffusion or perfusion abnormalities of the brain or variation in the cognitive functioning of the patients, and to what extent the potential findings are affected by CEA, and compare the clinically symptomatic and asymptomatic subjects as well as strictly healthy controls. Coagulation and fibrinolytic parameters were compared with the rate microembolic signals (MES) in transcranial Doppler (TCD) and the macroscopic appearance of stenosing plaques in surgery. Patients (n=92) underwent CEA within the study. Blood samples pertaining to coagulation and fibrinolysis were collected before CEA, and the subjects underwent repeated TCD monitoring for MES. A subpopulation (n= 46) underwent MR imaging and repeated neuropsychological examination (preoperative, as well 4 and 100 days after CEA). In MRI, the average apparent diffusion coefficients were higher in the ipsilateral white matter (WM), and altough the interhemispheric difference was abolished by CEA, the levels remained higher than in controls. Symptomatic stenoses were associated with more sluggish perfusion especially in WM, and lower pulsatility of flow in TCD. All patients had poorer cognitive performance than healthy controls. Cognitive functions improved as expected by learning effect despite transient postoperative worsening in a few subjects. Improvement was greater in patients with deepest hypoperfusion, primarily in executive functions. Symptomatic stenoses were associated with higher hematocrit and tissue plasminogen activator antigen levels, as well as higher rate of MES and ulcerated plaques, and better postoperative improvement of vasoreactivity and pulsatility. In light of the findings, carotid stenosis is associated with differences in brain diffusion, perfusion, and cognition. The effect on diffusion in the ipsilateral WM, partially reversible by CEA, may be associated with WM degeneration. Asymptomatic and symptomatic subpopulations differ from each other in terms of hemodynamic adaptation and in their vascular physiological response to removal of stenosis. Although CEA may be associated with a transient cognitive decline, a true improvement of cognitive performance by CEA is possible in patients with the most pronounced perfusion deficits. Mediators of fibrinolysis and unfavourable hemorheology may contribute to the development of a symptomatic disease in patients with a high-grade stenosis.

Testicular function in adolescent boys with Klinefelter syndrome

Klinefelter syndrome (KS) is the most frequent karyotype disorder of male reproductive function. Since its original clinical description in 1942 and the identification of its chromosomal basis 47,XXY in 1959, the typical KS phenotype has become well recognized, but the mechanisms behind the testicular degeneration process have remained unrevealed. This prospective study was undertaken to increase knowledge about testicular function in adolescent KS boys. It comprised a longitudinal follow-up of growth, pubertal development, and serum reproductive hormone levels in 14 prepubertal and pubertal KS boys. Each boy had a testicular biopsy that was analyzed with histomorphometric and immunohistochemical methods. The KS boys had sufficient testosterone levels to allow normal onset and progression of puberty. Their serum testosterone levels remained within the low-normal range throughout puberty, but from midpuberty onwards, findings like a leveling-off in testosterone and insulin-like factor 3 (INSL3) concentrations, high gonadotropin levels, and exaggerated responses to gonadotropin-releasing hormone stimulation suggest diminished testosterone secretion. We also showed that the Leydig cell differentiation marker INSL3 may serve as a novel marker for onset and normal progression of puberty in boys. In the KS boys the number of germ cells was already markedly lower at the onset of puberty. The pubertal activation of the pituitary-testicular axis accelerated germ cell depletion, and germ cell differentiation was at least partly blocked at the spermatogonium or early primary spermatocyte stages. The presence of germ cells correlated with serum reproductive hormone levels. The immature Sertoli cells were incapable of transforming to the adult type, and during puberty the degeneration of Sertoli cells increased markedly. The older KS boys displayed an evident Leydig cell hyperplasia, as well as fibrosis and hyalinization of the interstitium and peritubular connective tissue. Altered immunoexpression of the androgen receptor (AR) suggested that in KS boys during puberty a relative androgen deficiency develops at testicular level. The impact of genetic features of the supernumerary X chromosome on the KS phenotype was also studied. The present study suggests that parental origin of the supernumerary X chromosome and the length of the CAG repeat of the AR gene influence pubertal development and testicular degeneration. The current study characterized by several means the testicular degeneration process in the testes of adolescent KS boys and confirmed that this process accelerates at the onset of puberty. Although serum reproductive hormone levels indicated no hypogonadism during early puberty, the histological analyses showed an already markedly reduced fertility potential in prepubertal KS boys. Genetic features of the X chromosome affect the KS phenotype.

Evidence for follicle-stimulating hormone mediation in the hemiorchidectomy-induced compensatory increase in the function of the remaining testis of the adult male bonnet monkey (Macaca radiata)

Hemiorchidectomy (HO) in the adult male bonnet monkey results in a selective increase in circulating concentrations of FSH and testosterone, and this is accompanied by compensatory increase in sperm production by the remaining testis. We investigated the possible role of increased FSH concentration that occurs after HO in the compensatory increase in the activity of the remaining testis. Of eight adult male bonnet monkeys that underwent HO, four received i.v. injections every other day for 30 days of a well-characterized ovine FSH antiserum (a/s) that cross-reacts with monkey FSH. The remaining four males received normal monkey serum (NMS) as control treatment in a protocol similar to that employed for ais-treated males. Blood samples were collected between 2100 and 2200 h before and 1/2, 1, 3, 5, 7, 14, 22, and 29 days after HO. Testicular weight, number of 3 beta-hydroxy steroid dehydrogenase-positive (3 beta-HSD+) cells, and DNA flow cytometric analysis of germ cell populations were obtained for testes collected before and at the termination of NMS or ais treatment. In NMS-treated males, circulating serum FSH concentrations progressively increased to reach a maximal level by Day 7 after HO (1.95 +/- 0.3 vs. 5.6 +/- 0.7 ng/ml on Days -1 and 7, respectively). Within 30 min of ais injection, FSH antibodies were detected in circulation, and the antibody level was maintained at a constant level between Day 7 and end of treatment (exhibiting 50-60% binding to I-125-hFSH). Although circulating mean nocturnal serum testosterone concentration showed an initial decrease, it rose gradually to pre-HO concentrations by Day 7 in NMS-treated males. In contrast, nocturnal mat serum testosterone concentrations in a/s-treated males remained lower than in NMS-treated controls (p < 0.05) up to Day 22 and thereafter only marginally increased. Testicular weights increased (p < 0.05) over the pre-HO weight in NMS- but not in ais-treated males. After HO, the number of 3 beta-HSD+ cells (Leydig cells) was markedly increased but was significantly (p < 0.05) higher in NMS-treated males compared to a/s-treated males. A significant (p < 0.05) reduction in the primary spermatocyte population of germ cells was observed in ais-treated compared to NMS-treated males. These results suggest that the increased FSH occurring after HO could be intimately involved in increasing the compensatory functional activity of the remaining testis in the male bonnet monkey.

Thermal instability in a three-dimensional rigid container with prescribed heat flux at lower boundary

The Bénard–Marangoni convection is studied in a three-dimensional container with thermally insulated lateral walls and prescribed heat flux at lower boundary. The upper surface of the incompressible, viscous fluid is assumed to be flat with temperature dependent surface tension. A Galerkin–Tau method with odd and even trial functions satisfying all the essential boundary conditions except the natural boundary conditions at the free surface has been used to solve the problem. The critical Marangoni and Rayleigh numbers are determined for the onset of steady convection as a function of aspect ratios x0 and y0 for the cases of Bénard–Marangoni, pure Marangoni and pure Bénard convections. It is observed that critical parameters are decreasing with an increase in aspect ratios. The flow structures corresponding to the values of the critical parameters are presented in all the cases. It is observed that the critical parameters are higher for case with heat flux prescribed than those corresponding to the case with prescribed temperature. The critical Marangoni number for pure Marangoni convection is higher than critical Rayleigh number corresponding to pure Bénard convection for a given aspect ratio whereas the reverse was observed for two-dimensional infinite layer.

Unraveling the Intricate Organization of Mammalian Mitochondrial Presequence Translocases: Existence of Multiple Translocases for Maintenance of Mitochondrial Function

Mitochondria are indispensable organelles implicated in multiple aspects of cellular processes, including tumorigenesis. Heat shock proteins play a critical regulatory role in accurately delivering the nucleus-encoded proteins through membrane-bound presequence translocase (Tim23 complex) machinery. Although altered expression of mammalian presequence translocase components had been previously associated with malignant phenotypes, the overall organization of Tim23 complexes is still unsolved. In this report, we show the existence of three distinct Tim23 complexes, namely, B1, B2, and A, involved in the maintenance of normal mitochondrial function. Our data highlight the importance of Magmas as a regulator of translocase function and in dynamically recruiting the J-proteins DnaJC19 and DnaJC15 to individual translocases. The basic housekeeping function involves translocases B1 and B2 composed of Tim17b isoforms along with DnaJC19, whereas translocase A is nonessential and has a central role in oncogenesis. Translocase B, having a normal import rate, is essential for constitutive mitochondrial functions such as maintenance of electron transport chain complex activity, organellar morphology, iron-sulfur cluster protein biogenesis, and mitochondrial DNA. In contrast, translocase A, though dispensable for housekeeping functions with a comparatively lower import rate, plays a specific role in translocating oncoproteins lacking presequence, leading to reprogrammed mitochondrial functions and hence establishing a possible link between the TIM23 complex and tumorigenicity.

Lower bounds for testing triangle-freeness in Boolean functions

Given a Boolean function , we say a triple (x, y, x + y) is a triangle in f if . A triangle-free function contains no triangle. If f differs from every triangle-free function on at least points, then f is said to be -far from triangle-free. In this work, we analyze the query complexity of testers that, with constant probability, distinguish triangle-free functions from those -far from triangle-free. Let the canonical tester for triangle-freeness denotes the algorithm that repeatedly picks x and y uniformly and independently at random from , queries f(x), f(y) and f(x + y), and checks whether f(x) = f(y) = f(x + y) = 1. Green showed that the canonical tester rejects functions -far from triangle-free with constant probability if its query complexity is a tower of 2's whose height is polynomial in . Fox later improved the height of the tower in Green's upper bound to . A trivial lower bound of on the query complexity is immediate. In this paper, we give the first non-trivial lower bound for the number of queries needed. We show that, for every small enough , there exists an integer such that for all there exists a function depending on all n variables which is -far from being triangle-free and requires queries for the canonical tester. We also show that the query complexity of any general (possibly adaptive) one-sided tester for triangle-freeness is at least square root of the query complexity of the corresponding canonical tester. Consequently, this means that any one-sided tester for triangle-freeness must make at least queries.

Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

A lower-bound limit analysis formulation, by using two-dimensional finite elements, the three-dimensional Mohr-Coulomb yield criterion, and nonlinear optimization, has been given to deal with an axisymmetric geomechanics stability problem. The optimization was performed using an interior point method based on the logarithmic barrier function. The yield surface was smoothened (1) by removing the tip singularity at the apex of the pyramid in the meridian plane and (2) by eliminating the stress discontinuities at the corners of the yield hexagon in the pi-plane. The circumferential stress (sigma(theta)) need not be assumed. With the proposed methodology, for a circular footing, the bearing-capacity factors N-c, N-q, and N-gamma for different values of phi have been computed. For phi = 0, the variation of N-c with changes in the factor m, which accounts for a linear increase of cohesion with depth, has been evaluated. Failure patterns for a few cases have also been drawn. The results from the formulation provide a good match with the solutions available from the literature. (C) 2014 American Society of Civil Engineers.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.