Measurement of the influence of the physical environment on adverse health outcomes: technical report from the Canadian Study of Health and Aging

A paucity of information exists to characterize the relationship between the health status of elderly people and their physical environment. The Canadian Study of Health and Aging (CSHA) is a multicenter study of the distribution of dementia among community-dwelling and institutionalized Canadians aged 65 years and older. The study also provides the opportunity to examine issues such as the physical environment which may be related to the health of elderly people. Six items were used to assess the cleanliness, neatness, and maintenance of the inside and outside of the homes of 8,134 community-dwelling individuals. Data were also obtained to evaluate cognition, physical health, and functional capacity. Five years after the original survey, information pertaining to subsequent institutionalization and/or mortality was obtained. A significant relationship was found between classification of physical environment and the outcomes of institutionalization and mortality. The likelihood of both adverse outcomes was notably higher for individuals living in a "less than ideally maintained environment" compared to an "ideally maintained environment." Limitations of the six items used to assess the physical environment and ways in which to improve the sensitivity of the items, consequently avoiding measurement bias, are discussed.

High resolution comparative genomic hybridisation in clinical cytogenetics

High resolution comparative genomic hybridisation (HR-CGH) is a diagnostic tool in our clinical cytogenetics laboratory. The present survey reports the results of 253 clinical cases in which 47 abnormalities were detected. Among 144 dysmorphic and mentally retarded subjects with a normal conventional karyotype, 15 (10%) had small deletions or duplications, of which 11 were interstitial. In addition, a case of mosaic trisomy 9 was detected. Among 25 dysmorphic and mentally retarded subjects carrying apparently balanced de novo translocations, four had deletions at translocation breakpoints and two had deletions elsewhere in the genome. Seventeen of 19 complex rearrangements were clarified by HR-CGH. A small supernumerary marker chromosome occurring with low frequency and the breakpoint of a mosaic r(18) case could not be clarified. Three of 19 other abnormalities could not be confirmed by HR-CGH. One was a Williams syndrome deletion and two were DiGeorge syndrome deletions, which were apparently below the resolution of HR-CGH. However, we were able to confirm Angelman and Prader-Willi syndrome deletions, which are about 3-5 Mb. We conclude that HR-CGH should be used for the evaluation of (1) dysmorphic and mentally retarded subjects where normal karyotyping has failed to show abnormalities, (2) dysmorphic and mentally retarded subjects carrying apparently balanced de novo translocations, (3) apparently balanced de novo translocations detected prenatally, and (4) for clarification of complex structural rearrangements.

[Detection of submicroscopic chromosome abnormalities by comparative genomic hybridization]

INTRODUCTION

The purpose was to detect chromosome abnormalities in dysmorphic and mentally retarded individuals with normal karyotypes by means of comparative genomic hybridisation (CGH).

MATERIAL AND METHODS

One hundred and forty-four individuals with normal karyotype underwent CGH analysis with a new detection technique where fixed limits are replaced by dynamic standard reference intervals. This method provides improved resolution and thereby detects minor chromosome abnormalities.

RESULTS

Fifteen minor abnormalities (10%) and one trisomy 9 mosaic were found. Eleven were interstitial deletions or duplications, which cannot be detected by screening with other cytogenetic techniques. Three were terminal deletions or duplications and one was a terminal unbalanced translocation.

DISCUSSION

CGH analysis with dynamic standard reference intervals is a new objective and quantitative method, which is suitable for screening for small chromosome abnormalities that can not be detected by conventional chromosome analysis. The method is recommended for use in the investigation of dysmorphic and mentally retarded individuals, in whom abnormalities are not found by ordinary karyotyping.

Comparative genomic hybridization reveals non-random chromosomal aberrations in early preinvasive cervical lesions

We performed CGH analysis on 34 cervical lesions, which included 8 cases of koilocytosis, 6 mild dysplasias and 20 moderate dysplasias. Chromosome aberrations were detected in 11 cases of which 9 were moderate dysplasias. A total of 55 chromosome arms were involved. The most frequent aberrations were losses of 5p and Xq, each of which was present in 5/34 cases. Gain of 3q was detected in two moderate dysplasias. This aberration is the most frequent copy number change in advanced-stage cervical carcinoma. A considerable number of the aberrations found in the preinvasive cases of this study are frequently present in invasive cervical tumors. The presence of apparently non-random chromosome aberrations in early preinvasive cervical lesions has not previously been described.

Six-hour versus 12-hour protocols for AMI: CK-MB in conjunction with myoglobin

The objective was to test the hypothesis that a protocol using myoglobin and creatine kinase-MB (CK-MB) can rapidly and safely exclude myocardial infarction (MI). The study used a prospective, convenience cohort of ED patients with clinically suspected myocardial ischemia. Myoglobin was measured on presentation, 2 and 6 hours later; CK-MB was measured on presentation, 6, 12, and 18 hours later. Of 519 patients, 76 (15%) had MIs, all of whom "ruled in" within 12 hours using a combination of myoglobin and CK-MB, for a sensitivity of 100% (95% CI, 95% to 100%), specificity of 92% (95% CI, 89% to 94%), LR (+) of 12 (95% CI, 9 to 16), and an LR (-) of 0.03 (95% CI, 0.0 to 0.05). Of the 76 patients with MIs, 73 ruled in with a 6 hour protocol, also using a combination of CK-MB and myoglobin, for a sensitivity of 96% (95% CI, 89% to 99%), specificity of 92% (95% CI, 89% to 94%), LR (+) of 11 (95% CI, 8 to 16), and an LR (-) of 0.04 (95% CI, 0.01 to 0.12). Our results support the hypothesis that, using an abbreviated protocol with CK-MB and myoglobin, MI can be reliably ruled out in ED patients with suspected ischemia.

Risk factors in habitats of the tick Ixodes ricinus influencing human exposure to Ehrlichia phagocytophila bacteria

Ixodes ricinus L. (Acari: Ixodida) were sampled during 1996-99 in southern Scotland, on vegetation using cloth drags, on humans by removal from clothing and on roe deer (Capreolus capreolus L.) by searching legs of culled deer. Developmental microclimate was recorded by automatic recorders and questing microclimate by portable instruments during tick collections. Ticks and deer were examined for infection with Ehrlichia phagocytophila bacteria (Rickettsiales) using microscopy and polymerase chain reaction. This pathogen causes tick-borne fever of sheep in Europe and human granulocytic ehrlichiosis in North America, but in Europe human clinical ehrlichiosis due to E. phagocytophila has not been recorded despite serological evidence of exposure. Among three types of habitat, coniferous woodland was most infested with questing ticks (560 ticks/km of drag; mean numbers collected on long trousers: 24.3 larvae, 13.5 nymphs and 0.8 adult ticks/km walked), deciduous woodland had slightly lower infestation (426 ticks/km drag) and upland sheep pasture had much lower infestation (220 ticks/km drag). Of the three main vegetation types, bracken was least infested (360 ticks/km drag), ericas most (430 ticks/km drag) and grassland had intermediate infestation density (413 ticks/km drag). Questing and developmental microclimates were poor predictors of exposure within these habitats, except lower infestation of pastures was attributed to greater illumination there. Collectors who walked a total of 300 km through all habitats (taking 360 h in all seasons), wearing cotton trousers hanging outside rubber boots, were bitten by only four nymphs and 11 larvae of I. ricinus (but no adult ticks). There was a negative correlation between densities of deer and ticks collected, although presence of deer remains a major indicator of exposure. The proportion of infected ticks was fairly uniform at four sites studied. Overall prevalence of E. phagocytophila in I. ricinus was 3.3% in nymphs (40/1203) but only approximately 1.5% in adults of both sexes (although males do not bite). It was estimated that nymphs of I. ricinus gave 4.4% probability of one infected bite/person/year (for occupational exposure during this research) due to presence in all seasons and habitats, their human biting rate of 0.011 nymphs/h or 0.013 nymphs/km and widespread infection with E. phagocytophila. The frequency distribution of intensity of infection in ticks was approximately normal (mean 98 morulae/nymph infected), thus there is a high risk of receiving a high dose from any one infected tick bite.

Electrostatic correction of the chromatic and of the spherical aberration of charged-particle lenses (part I)

A feasible electrostatic corrector (ECO) is outlined and the principle of the electrostatic correction is elucidated by means of a light-optical analogue. The ECO compensates for the chromatic and the spherical aberration of charged-particle lenses and reduces the resolution limit of a special LVSEM (low-voltage scanning electron microscope) from 6 nm to 1.4 nm. The geometry of the electrodes of the corrector is optimized with respect to the chromatic correction, the maximum strength of the electric field, and the residual higher-order aberrations which limit the resolution. In addition the stability criteria of the electric power supplies are discussed in detail.

High resolution comparative genomic hybridisation analysis reveals imbalances in dyschromosomal patients with normal or apparently balanced conventional karyotypes

A sensitive technique is needed for screening whole genome imbalances in dyschromosomal patients when G-banding shows normal karyotypes or apparently balanced translocations. In this study we performed highly sensitive comparative genomic hybridisation analysis on a number of such cases and revealed chromosomal imbalances in all.

Evidence from multiple gene sequences indicates that termites evolved from wood-feeding cockroaches

Despite more than half a century of research, the evolutionary origin of termites remains unresolved [1] [2] [3]. A clear picture of termite ancestry is crucial for understanding how these insects evolved eusociality, particularly because they lack the haplodiploid genetic system associated with eusocial evolution in bees, ants, wasps and thrips [4] [5]. Termites, together with cockroaches and praying mantids, constitute the order Dictyoptera, which has been the focus of numerous conflicting phylogenetic studies in recent decades [6] [7] [8] [9] [10] [11] [12]. With the aim of settling the debate over the sister-group of termites, we have determined the sequences of genes encoding 18S ribosomal RNA, mitochondrial cytochrome oxidase subunit II (COII) and endogenous endo-beta-1, 4-glucanase (EG) from a diverse range of dictyopterans. Maximum parsimony and likelihood analyses of these sequences revealed strong support for a clade consisting of termites and subsocial, wood-feeding cockroaches of the genus Cryptocercus. This clade is nested within a larger cockroach clade, implicating wood-feeding cockroaches as an evolutionary intermediate between primitive non-social taxa and eusocial termites.

A bovine model for detecting high intensity transient signals originating from mechanical heart valves

In patients with mechanical heart valves (MHVs), transcranial Doppler methods commonly detect high intensity transient signals (HITS) representing microemboli. These microemboli, which are presumably gaseous, may cause stroke and cognitive deterioration. A bovine model was therefore developed for studying the relationship between mitral MHV induced HITS and potential etiogenic factors. We placed an 18 mm, 4 MHz Doppler probe in the brachiocephalic artery to detect MHV induced microbubbles at baseline (rest) and under 9 other conditions. To elucidate the gas composition (CO2 or N2) of the microbubbles, we administered 1%, 3%, and 5% CO2, and 100% O2. To determine effect of the heart rate, we paced the heart at 120, 160, and 180 bpm. To alter the myocardial contractility, we gave dobutamine and esmolol. Two independent, blinded observers counted the HITS from recorded doppler spectra. HITS were defined by an initial unidirectional spectral deviation, a signal power of >8 dB relative to the background power, and lack of a cyclic appearance. The electrocardiogram, aortic and LV pressures, and LV dP/dt were obtained telemetrically. The calves were studied 4 to 6, 8 to 10, and 12 to 14 weeks postoperatively, after which the animals were sacrificed at an approximate 4 month study duration, and a postmortem evaluation of the heart and the main viscera was performed. In all, 27 HITS recordings were made in 10 calves. Myocardial contractility was the only factor to significantly affect HITS frequency; the heart rate and blood gas concentrations had minimal effect on HITS frequency. Our bovine model will be useful for assessing valve designs, as well as the mechanism of HITS, the composition of the microemboli, and their possible pathophysiologic effects on the kidneys and brain.

Direct identification and quantitation of prednisone in the presence of overlapping hydrocortisone by liquid chromatography with electrospray and atmospheric-pressure chemical-ionisation mass spectrometry

The paper describes the application of liquid chromatography interfaced to a triple quadrupole mass spectrometer utilising the multiple reaction monitoring (MRM) mode. The technique was shown to provide detection limits lower than 0.01% for the analysis of prednisone in the presence of hydrocortisone. Prednisone was mixed in concentrations from 0.500 to 0.0005 ppm (corresponding to 1% to 0.001% of the hydrocortisone concentration). These solutions were assayed using MRM observing the product ion transitions of 359.2-->147.1 and 359.2-->171.2 and was shown to be capable of detecting co-eluting impurities at concentrations of less than 0.001% of the major component. The assay of prednisone was shown to be linear over the range 0.500-0.0005 ppm with a correlation coefficient of 0.999 and a precision of 6.9% at the concentration of 0.005 ppm. The analysis was carried out using both atmospheric pressure chemical ionisation (APCI) and electrospray ionisation (ESI) as an interface. However, for these compounds APCI provided significantly more sensitive data compared to ESI.

Effects of myocardial contractility on microemboli production by mechanical heart valves in a bovine model

Microemboli caused by mechanical heart valves have the potential to cause cerebrovascular events. We investigated the effects of myocardial contractility and heart rate on microemboli production in association with conventional and experimental mechanical heart valves implanted in the mitral position in a bovine model. In 10 calves, the mitral valves were replaced with mechanical valves. Doppler recordings were analyzed for high-intensity transient signals, which are ultrasound reflections from circulating microemboli. The animals were studied at rest, during pacing at 160 bpm, after dobutamine infusion, and after esmolol infusion. The incidence of high intensity transient signals was expressed as signal frequency (signals per hour) and as signal rate (signals per 100 heart cycles). With a 68% increase in the heart rate, signal frequency increased by 135%, but signal rate increased by only 41 %. With a 144% increase in myocardial contractility, signal rate increased by 264 %. With a 31 % decrease in contractility, signal rate decreased by 62 %. We conclude that microemboli production by mechanical heart valves varies with myocardial contractility and heart rate. The fact that contractility affects the incidence of high-intensity transient signals suggests that the microemboli are gaseous in nature, that their production is pressure driven, and that cavitation is a possible cause. It is likely that mechanical heart valve design is responsible for the quantity of microemboli production.

The emerging clinical potential of cardiovascular gene therapy

Despite considerable progress, pharmacological therapies have not provided a complete solution for common cardiovascular problems, including recurrent thrombosis, restenosis, and vein graft deterioration. Optimal drug dosage, reproducing plasma concentrations achieved in animal studies establishing proof-of-principle, would often be too toxic to administer, especially when given over prolonged periods of time. Local gene therapy aims at overexpressing proteins that: (1) regulate the cell cycle of VSMC; (2) inhibit VSMC migration; (3) endow the endothelium with its vasoprotective properties; and (4) stimulate growth of endothelium and angiogenesis. Alternatively, some approaches tend to suppress gene expression of proteins believed to promote VSMC proliferation and migration. In sharp contrast to drug treatments, local gene therapy limits expression of the beneficial agent to the injured vascular site, and there, it can extend the presence of this agent to weeks and, with some gene vectors, to many months. The clinical potential of this approach has led to the initiation of trials that currently evaluate gene therapy approaches to the attenuation of peripheral and myocardial ischaemia and the prevention of vein graft disease.

Deletions below 10 megabasepairs are detected in comparative genomic hybridization by standard reference intervals

Comparative genomic hybridization (CGH) is a widely used technique for studying chromosomal imbalances. The sensitivity of the technique is, however, relatively low. Deletions down to a size of 10-12 Mbp have been detected by the use of fixed diagnostic thresholds. In this study, we applied standard reference intervals as detection criteria on a number of deletions in the range of 3 Mbp to 14-18 Mbp. All deletions were detected. Thus, detection by standard reference intervals confers a considerably higher sensitivity to CGH analysis compared to fixed diagnostic thresholds. Genes Chromosomes Cancer 25:410-413, 1999.

Comparative genomic hybridization reveals a recurrent pattern of chromosomal aberrations in severe dysplasia/carcinoma in situ of the cervix and in advanced-stage cervical carcinoma

We analyzed 17 cases of dysplasia/carcinoma in situ (CIS) of the cervix and 29 advanced-stage cervical squamous cell carcinomas by comparative genomic hybridization (CGH). A comparable recurrent pattern of aberrations was detected in both preinvasive and invasive cases, although the total number of aberrations was much higher in the latter category. The most consistent chromosomal gain was mapped to chromosome arm 3q in 35% of preinvasive cases and in 72% of invasive cases. Chromosome aberrations were detected in 13/17 preinvasive cases with a total of 61 involved chromosome arms. In the invasive cases, frequent gains also occurred on 1q (45%), 8q (41%), 15q (41%), 5p (34%), and Xq (34%), and frequent losses were mapped to chromosome arms 3p (52%), 11q (48%), 13q (38%), 6q (38%), and 4p (34%). A recurrent pattern of aberrations has not previously been described in preinvasive lesions of the cervix. Our finding is surprising considering that only few preinvasive lesions are expected to progress to invasive cancer.

Improved sensitivity in comparative genomic hybridization analysis of DNA heteroploid cell mixtures after pre-enrichment of subpopulations by fluorescence activated cell sorting

Cytogenetic analysis of solid tumors with comparative genomic hybridization (CGH) is hampered by the dilution of DNA from individual tumor subpopulations with DNA from other cells. We investigated to what extent this dilution effect can be alleviated using fluorescence activated cell sorting (flow sorting) of experimental DNA heteroploid cell mixtures prior to CGH. From mixtures of normal lymphocytes with triploid K-562 cells the individual components were sorted according to stemline DNA content and processed by CGH in comparison with pure K-562 samples and the original mixtures. Compared with 30 autosome copy number imbalances found in pure K-562 samples, a mixture with 32% K-562 cells showed 16 imbalances, and none were detected in mixtures with 13% or 5% K-562 cells. In contrast, 29, 22 and 23 imbalances were detected in K-562 nuclei sorted from the 32%, 13% and 5% mixtures, respectively. This indicate that CGH analysis of flow sorted DNA aneuploid subpopulations enables a specific cytogenetic analysis of the individual subclones in a DNA heteroploid cell population.

Cardioprotective actions of KC 12291. I. Inhibition of voltage-gated Na+ channels in ischemia delays myocardial Na+ overload

To characterize KC 12291 (1-(5-phenyl-1,2, 4-thiadiazol-3-yl-oxypropyl)-3-[N-methyl-N-[2-(3,4-dimethoxy phenyl) ethyl] amino] propane hydrochloride), a newly synthezised inhibitor of voltage-gated Na+ channels, the effects of the agent on Na+ current and ischemia-induced Na+ overload were investigated in isolated cardiomyocytes, atria and saline-perfused hearts. As measured by the patch clamp technique, KC 12291 (1 microM) significantly reduced peak Na+ current after activation of voltage-gated Na+ channels in rat cardiomyocytes. Partial depolarization enhanced the inhibitory effects during steady state conditions of the channel. In isolated guinea pig atria, 1 microM KC 12291 had no effect on contractility under basal conditions but effectively delayed the onset and reduced the extent of anoxic contracture. The concentration-response curve was clearly shifted to the left when atria were partially depolarized by increased extracellular K+. As measured by 23Na NMR spectroscopy in isolated perfused guinea pig hearts, intracellular Na+ rose more than four-fold in a linear fashion during 60 min of low-flow ischemia. KC 12291 (1 microM) prevented Na+ overload within the initial 12 min of ischemia; thereafter the slope of Na+ accumulation was identical to controls. Electrical excitability of hearts, evaluated by intracardial ECG, completely ceased within 15 min after the onset of ischemia. KC 12291 (1 microM) accelerated this process by more than 6 min. The data provide first evidence that KC 12291 reduces Na+ influx through voltage-gated Na+ channels during ischemia and thus delays Na+ overload by enhancing the inexcitability of the heart.

Halothane, but not isoflurane, impairs the beta-adrenergic responsiveness in rat myocardium

BACKGROUND

The aim of this study was to identify the mechanisms by which halothane and isoflurane change the myocardial beta-adrenergic signal transduction pathway.

METHODS

The authors investigated the influence of volatile anesthetics on the isometric force of contraction of rat papillary muscles. Concentration-response curves for isoproterenol and epinephrine were studied under control conditions and in the presence of halothane or isoflurane. In radioligand receptor-binding studies, the beta-adrenoceptor affinities for isoproterenol and epinephrine were investigated with and without guanosine triphosphate. In addition, the isoproterenol-induced cyclic adenosine monophosphate accumulations in viable cardiomyocytes in the absence and in the presence of halothane were determined by radioimmunoassays.

RESULTS

The half-maximal positive inotropic effect of isoproterenol was reached at a half-maximal effective concentration (EC50 value) of 68 nM (33-141 nM; n = 10). A minimum alveolar concentration of 1.3 halothane reduced the positive inotropic potency of isoproterenol (EC50 = 158 nM [118-214 nM; n = 10; P < 0.01 vs. control]), whereas isoflurane did not changed it. This observation held true when the force of contraction was stimulated with epinephrine. Halothane (1.3 minimum alveolar concentration) depressed beta-adrenoceptor high-affinity binding and beta-adrenoceptor agonist affinity in radioligand binding assays, an effect not seen with isoflurane. Halothane shifted the intracellular cyclic adenosine monophosphate response curve of isoproterenol to the right.

CONCLUSION

Halothane, but not isoflurane, impairs the beta-adrenergic responsiveness in rat myocardium by reducing the agonist affinity of the beta-adrenoceptors.

Detection of chromosomal gains and losses in comparative genomic hybridization analysis based on standard reference intervals

Criteria for detection of chromosome aberrations by Comparative Genomic Hybridization (CGH) are not standardized and improvement of this part of the analysis is of paramount importance to the applicability of the technique. The aim of this work was to suggest CGH detection criteria that increase the specificity and sensitivity and at the same time include chromosome regions previously excluded from CGH analysis. We analyzed 33 hybridizations with normal DNA and modified our CGH software in order to use a selection of these normal analyses as a model for interpretation of analyses of unknown samples. This approach was successfully tested on 14 samples with known aberrations.

Detection of chromosomal aberrations in seminomatous germ cell tumours using comparative genomic hybridization

Comparative genomic hybridization (CGH) was used to evaluate tissue specimens from 16 seminomas in order to elucidate the pathogenesis of germ cell tumours in males. A characteristic pattern of losses and gains within the entire genomes was detected in 94% of the seminomas by comparing the ratio profiles of the tumours with a standard of cytogenetically normal genomic DNA. Losses represented 43% of the total number of alterations often affecting chromosomes and chromosome arms 4, 5, 11, 13q, and 18q. Gains amounted to 57% and were often observed on 1q, 7, 8, 12, 14q, 15q, 21q, and 22q. Aberrations of 12p and 21q appeared most consistently. Results from CGH analysis displayed no relationship to the clinical stages of the malignancy. Some rare aberrations appeared, however, only in clinical stage II and in tumours showing relapse in the contralateral testis following orchiectomy, although the alterations were not present in all of the tumours in question. Losses of 16q13-21 and gains of 9q22.1-22.2 were demonstrated in both groups, while loss of 16p12 and gains of 6p21 and 6q23.3-24 were detected in the latter group as well. In conclusion, a specific pattern of chromosomal alterations was demonstrated in the seminomas by improved detection criteria, which increased specificity and sensitivity. The rare aberrations, which appeared only in tumours in improved detection criteria, which increased specificity and sensitivity. The rare aberrations, which appeared only in tumours in clinical stage II and relapsed tumours, may be linked to tumour progression, invasiveness, and bilateral disease.

Automatic correction of the interfering effect of unsuppressed interspersed repetitive sequences in comparative genomic hybridization analysis

Comparative genomic hybridization (CGH) is a relatively new technique whose application is increasing. The method has mostly been employed for detection of chromosome aberrations in cancers, and a large amount of data in this field is accumulating. At the same time, efforts are made to improve the technique in order to increase the sensitivity and the generation of reliable results. Based on experimental data, we have developed a computer algorithm for eliminating some of the interfering effects of unsuppressed repetitive sequences in CGH analysis, and thereby improved our CGH analysis system.

Optimization of road networks using evolutionary strategies

A road network usually has to fulfill two requirements: (i) it should as far as possible provide direct connections between nodes to avoid large detours; and (ii) the costs for road construction and maintenance, which are assumed proportional to the total length of the roads, should be low. The optimal solution is a compromise between these contradictory demands, which in our model can be weighted by a parameter. The road optimization problem belongs to the class of frustrated optimization problems. In this paper, a special class of evolutionary strategies, such as the Boltzmann and Darwin and mixed strategies, are applied to find differently optimized solutions (graphs of varying density) for the road network, depending on the degree of frustration. We show that the optimization process occurs on two different time scales. In the asymptotic limit, a fixed relation between the mean connection distance (detour) and the total length (costs) of the network exists that defines a range of possible compromises. Furthermore, we investigate the density of states, which describes the number of solutions with a certain fitness value in the stationary regime. We find that the network problem belongs to a class of optimization problems in which more effort in optimization certainly yields better solutions. An analytical approximation for the relation between effort and improvement is derived.