Logarithmic Regression Equation Research Articles

PREDICTION OF MAXIMAL OXYGEN CONSUMPTION FROM SUBMAXIMAL GAS EXCHANGE DATA IN PATIENTS WITH HEART FAILURE

Maximal oxygen consumption (VO2) is a strong predictor of mortality in patients with heart failure and is used to stratify patients for cardiac transplantation. However, many patients with heart failure do not achieve maximal exercise, and the endpoint of exercise frequently varies among those who achieve maximal exercise. PURPOSE: The purpose of this study was to determine if submaximal exercise gas exchange data can predict maximal VO2. METHODS: Fifty consecutive patients' exercise tests were reviewed which had respiratory exchange ratio (RER) greater than 1.10. Maximal exercise data were averaged with the 30 second time interval and graphed against the RER. Logarithmic, linear, exponential, and power regression lines were fitted to the maximal data. Peak VO2 was predicted with submaximal gas exchange by omitting all data where RER > 0.98. Regression equations were recalculated and predicted VO2 was determined by inserting RER = 1.10 into the new equations. For reference purposes, maximal data were compared to a rolling time average and predicted values were compared to VO2 obtained by regression of the patient's achieved peak RER. Additionally, the effect of variable peak exercise endpoints upon maximal VO2 was evaluated by inserting values of RER = 1.00, 1.10, 1.20, and 1.30 into the equations. RESULTS: Using only submaximal exercise data, the logarithmic regression equation most accurately predicted peak VO2. The reference VO2 was 16.99 ± 3.99 ml/kg/min and the VO2 extrapolated to the actual RER achieved was: 16.97 ± 3.76, 17.78 ± 4.06, 18.92 ± 4.79, 20.46 ± 5.70 ml/kg/min for logarithmic, linear, power, and exponential respectively. Logarithmic regression analysis predicted maximal VO2 the best. The absolute bias between reference VO2 and logarithmic predicted VO2 was 1.59 ± 1.36 ml/kg/min. When the endpoint of peak exercise was unknown, the logarithmic predicted VO2 at a values of RER = 1.0, 1.1, 1.2, and 1.3 were: 14.24 ± 2.97, 16.22 ± 3.50, 18.14 ± 4.06, and 19.81 ± 4.59 ml/kg/min respectively. The mean increment in VO2 between 1.00 and 1.10 was 1.98 ± 0.73, between 1.10 and 1.20 was 1.80 ± 0.67, and 1.20 and 1.30 was 1.65 ± 0.61 ml/kg/min. CONCLUSION: The use of logarithmic regression analysis can be used to predict maximal VO2 in patients with congestive heart failure. Peak VO2 was typically predicted from limited submaximal data to within 1.5 ml/kg/min, while an exercise test that is considered maximal typically had more than twice as much error depending upon the endpoint RER.

Comparison of Five Methods for Estimating Leaf Area Index of Open-Grown Deciduous Trees

We compared the accuracy of five methods used to estimate leaf area index (LAI) of eight open-grown deciduous trees, including six white mulberries (Moms alba) and two black cherries (Prunus serotina var. rufula). The methods included the use of four instruments (AccuPAR Ceptometer, CI-100 Plant Canopy Analyzer, image processing with the AgVision System, LI-COR LAI-2000 Plant Canopy Analyzer) and the application of a logarithmic regression equation. The image processing method demonstrated the highest probability of accurately estimating LAI (P = 0.99). However, all methods showed bias toward returning LAI estimates that did not increase as actual LAI increased when the mulberry tree data were examined separately from the cherry data. Additional research is necessary to determine whether this bias is real or merely a function of the limited sample size.

A Study on Some Biological Characteristics of Capoeta tinca (Heckel, 1843) Living in the Kirmir Stream of Sakarya River (Ankara, Türkiye)

This research was carried out in Kirmir Çayi a branch of Sakarya River (Western Anatolia) in between the dates of March, 1993 and February, 1994 period. Totally 461 specimens, taken from five different localities, during this period. Age composition, length and weight distribution increasing of length, weight percentages, length - weight relationships, condition factor and logarithmic regression equation were estimated, according to sexual position of Capoeta tinca (Heckel, 1843). The age composition of this species, ranges from I to VII. In the age group three, individuals were considered to be dominant. 54% of the individuals were males and the rest were females. The length distribution ranges from 71.1 mm. to 281.2 mm. where as for the weight distribution, it changes from 7.2 g. to 344.2 g. In the age groups of I, V, VI and VII, males were found to be taller considerably. However, females were observed to be heavier in the age groups of I, V, VI, VII. The condition factor of females were estimated to be higher in the ages of I, II, V, VI, VII.

Fishing in Denmark during the Ertebølle periodxs

AbstractFishing in Denmark during the Ertebølle period is discussed on the basis of almost 100000 identified fishbones from 14 coastal and two inland settlements. Forty‐one fish species were identified from coastal materials, 15 from inland ones. The frequency distribution of total body length of the numerically most important fish species was estimated from bone measurements, using logarithmic regression equations. Otoliths were analysed in order to provide an estimate of season of catch. The main conclusion of the study is that fishing was predominantly conducted by means of stationary fish traps with which uncritical samples of the local fish faunas were taken. Regional differences in the spectrum of species and their relative frequencies are shown to exist. Examples of connections between the coast and inland are given.

Micromorphological index for the evaluation of soil evolution in central Spain

Micromorphological indices for the evaluation of the degree of soil evolution are established on the basis of micromorphological properties. The indices are applied to a chronosequence of soils formed on fluvial terraces. The indices, which reflect microstructural properties, characteristics of fine material and groundmass birefringence, illuvial clay pedofeatures and the prevalence of illuvial clays, all increased steadily with soil age. Soil/age dispersion plots fit linear, power and logarithmic regression equations, with high correlation coefficients and levels of significance. Carbonate indices showed similar trends, although with much greater dispersions. Indices for organic matter, hydromorphy and mineralogical alterations showed clear tendencies to increase in younger soils. The change in the index values with soil age did not support the appearance of a steady state at any time.

Uptake of Nitrogen and Phosphate, and Water Purification by Water Hyacinth Eichhornia Crassipes (Mart.) Solms

Water hyacinth (Eichhornia crassipes (Mart.) Solms) grows very vigorously and has a high content of nutrients. Cultivation experiments were conducted on water hyacinth to check whether it is worth using for water purification and to obtain guiding principles for the practical use of water hyacinth grown in natural water channels or ponds. The average dry weight, nitrogen and phosphate content in the biomass were 5.0%, 2.5% and 0.57%, respectively. The growth rate of the water hyacinth was higher from May to June than in other seasons. The logarithmic regression equation between the growth rate (Y) and solar radiation (X) was expressed by Ln (Y) = 0.0042X-4.92 with a coefficient of correlation of 0.768. The relationship between the concentration of nutrients in water (X) and in water hyacinth (Y) is expressed by Y = Cmax.X/(Ks+X). The relationship between the relative growth rate and the concentration of nutrients was also expressed by the same type of equation. The relationship between a harvesting interval and the total yield of the water hyacinth within a given period was expressed by a mathematical model. It was made clear from the model that the shorter the harvesting interval was, the more the total yield of the crop increased.

Laboratory studies of properties of the stone masonry in the Old Aswan Dam

The paper describes the results of mechanical and physical tests carried out on the masonry of the Old Aswan Dam for later assessment of its seismic stability and structural integrity. Mechanical tests were performed on 150 mm diameter cores obtained from various stages of construction of the dam. Tests indicate that the masonry in the first heightening exhibits higher strength characteristics than the masonry in the rest of the dam. Noticeably lower strength properties of the masonry in the second heightening were due to a higher water/cement ratio. The weakest link in the masonry of all three stages of construction from the point of view of its mechanical performance was the granite-mortar interfacial region. Analyses of test results show that the modulus of elasticity and the splitting tensile strength of the masonry may be expressed as a function of the compressive strength using the power regression equation and the logarithmic regression equation, respectively. The split cylinder test provides a more reliable measure of the tensile strength of the stone masonry than the direct tension test. In general, a wide scatter of test results in relation to the mean value appeared to be an inherent characteristic of this type of masonry. Variations were more pronounced in the case of the Poisson’s ratio test and in all instances when fracture at the horizontal mortar-stone interface was a primary mode of failure.

Influence of sectility speed on the relationship between sensory and instrumental evaluation of edible fat firmness

For three samples of butter and margarine each the dependence of sample temperature and the applied sectility speed on instrumentally determined wire sectility forces is described in terms of semilogarithmic and double logarithmic regression equations, respectively. The mean cutting speed in sensory firmness assessments was found to be 976 mm·min−1. A close agreement of sensory and instrumental firmness evaluations of butter and margarine was observed only at instrumentally applied sectility speeds approaching the cutting speed used in sensory experiments.

Maturation of a transient outward potassium current in mouse fetal hypothalamic neurons in culture

The whole-cell voltage clamp technique was used to record potassium currents in mouse fetal hypothalamic neurons developing in culture medium from days 1 to 17. The neurons were derived from fetuses of IOPS/OF1 mice on the 14th day of gestation. The mature neurons (>six days in culture) showed both a transient potassium current and a non-inactivating delayed rectifier potassium current. These were identified pharmacologically by using the potassium channel blockers tetraethyl ammonium chloride and 4-aminopyridine, and on the basis of their kinetics and voltage sensitivities. The delayed rectifier potassium current had a threshold of −20 mV, a slow time-course of activation, and was sustained during the voltage pulse. The 4-aminopyridine-sensitive current was transient, and was activated from a holding potential more negative (−80 mV) than that required for evoking the delayed rectifier potassium current (−40 mV). The delayed rectifier potassium current was detectable from day 1 onwards, while the transient potassium current showed a distinct developmental trend. The time-constant of inactivation became faster with age in culture. The half steady-state inactivation potential showed a shift towards less negative membrane potentials with age, and the relationship was best described by a logarithmic regression equation. The developmental trend of the transient potassium current may relate functionally to the progressive morphological changes, and the appearance of synaptic connections during ontogenesis.

Static compliance in subjects with intact lungs.

The static compliance was determined in 55 subjects with healthy lungs. Average values are within 2.696 liters/kPa (age between 20 and 30 years) and 1.794 liters/kPa (age between 71 and 80 years). Static compliance was shown to be exclusively related to age (p less than 0.001). Broca index, sex, cigarette smoking and intrathoracic gas volume did not influence static compliance. The relation can best be described by a logarithmic regression equation.

Determination of ejection fraction from contrast echocardiography using videodensitometry in an in vitro model.

To examine whether ejection fraction can be estimated by videodensitometric analysis of contrast washout from a chamber, a model was constructed consisting of a 60-ml syringe and a modified Harvard respirator. Ejection fraction could be adjusted mechanically. Echocardiographic images were recorded on videotape and analyzed on an offline computerized analysis system. To calibrate the relationship between target concentration and videodensity on our sector scanner-videodensity analysis system, we used a phantom with constant attenuation and eight cones with known, varying relative scatterer concentration. The time-gain-compensation curve was kept constant on the ultrasound instrument and videodensity was measured from videotapes by an offline computer system. In the image of each cone, a 10 X 70 pixel operator-designated region of interest was chosen, and mean videodensity/pixel (256 level gray scale) was calculated. A logarithmic relation was found between scatterer concentration and videodensity. This excellent log relationship existed at all three gain levels studied: at 40% of maximum gain, r = .96; at 50% gain, r = .99; and at 60% gain, r = .99 (all p less than .001). Boluses of .5 ml sonicated Hypaque were then injected into the chamber and the contrast washout was recorded at ejection fractions of 20, 30, 40, 50, 60, and 70%. Bolus delivery and complete contrast mixing was attained except at ejection fraction 20%. Using the first two to four stroke videodensity decay the ejection fraction was calculated by estimating microbubble concentration decline using the logarithmic regression equation between videodensity and scatter concentration obtained during calibration.(ABSTRACT TRUNCATED AT 250 WORDS)

A Comparison of Detransformed Logarithmic Regressions and Power Function Regressions

A comparison of detransformed logarithmic regressions and power function regressions is illustrated with regressions of sediment concentration in a Swedish river. Quite different parameters were obtained when power function equations were developed from log-transformed data compared with development from the original data. This is a consequence of different model assumptions. Power function regressions are calculated from an additive model. While detransformed logarithmic regressions represent a multiplicative model. Detransformed logarithmic regression equations are biased with respect to the original data. Some of the bias can be reduced by a correction factor.

Disappearance of Organochlorine Residues from Abdominal and Egg Fats of Chickens, Ontario, Canada, 1969-1982

Abdominal fats were collected from 8-week old broilers slaughtered at provincially inspected abattoirs across Ontario between 1969 and 1982. Domestically produced hen eggs were collected from either egg grading stations or producers over the same period. Composite samples were analyzed for organochlorine insecticides and industrial chemicals. Between 1979 and 1982, organophosphorus insecticides were routinely included in these analyses. Sigma DDT and PCB residues declined rapidly between 1969 and 1982 in extractable lipids of both abdominal and egg fats, while dieldrin declined less markedly over the same period. Declines in residues followed first order logarithmic regression equations. Chlordane and heptachlor epoxide were rarely observed above the detection limit of 1 microgram/kg in egg fat; however, the incidence of these residues in abdominal fat increased after 1973 following the removal of aldrin, dieldrin, and heptachlor in 1969 and the subsequent increased use of chlordane for soil insect control until 1977. Lindane residues were rarely observed above the detection limit. In 1979, when the detection limit was reduced, both alpha-BHC and lindane were identified, but at levels below 1 microgram/kg. Endosulfan, methoxychlor, and fenthion were identified on one or 2 occasions over the 13-year period.

Effect of urea fertilization on allometric relations in young Douglas-fir trees

The effect of nitrogen fertilization on allometric relations was examined for 23-year-old site class III Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) trees 2 years after urea fertilization. Logarithmic regression equations using stem diameter (centimetres) to predict tree biomass components (kilograms) were not significantly (p = 0.05) different between fertilized and control trees for total foliage, total branch, dead branch, stembark, or stemwood. New foliage and new twig components, however, were higher in fertilized trees than in control trees. Analysis of data from this and earlier studies suggests fertilization will increase leaf biomass per tree relative to control trees on sites having low nitrogen availability; however, this response will decrease with increasing nitrogen availability. Regression equations based on regional analysis of unfertilized trees yield estimates of foliage biomass for average trees on average sites. If N fertilization brings the site above average in terms of nitrogen availability then these regression equations will underestimate foliage biomass. However, on sites that are initially very nitrogen deficient, N fertilization will bring the site closer to average in terms of nitrogen availability, resulting in more accurate predictions of foliage biomass for fertilized stands than for control stands.

Organochlorine and Organophosphorus Residues in Fat of Bovine and Porcine Carcasses Marketed in Ontario, Canada from 1969 to 1981

Between 1969 and 1981, 2482 bovine and 554 porcine carcasses were sampled at provincially inspected abattoirs across Ontario. Abdominal fats were composited into 505 bovine and 122 porcine samples for analyses of organochlorine insecticides and industrial chemicals. Mean ∑DDT residues decreased from 257 μg/kg in 1969–70 to 12 μg/kg in 1981 for bovine fats and from 356 μg/kg in 1971–72 to 5 μg/kg in 1981 for porcine fats. Similar decreases in residue levels were observed for PCB. Dieldrin, with lower initial residues (i.e. 33 μg/kg in bovine fat and 12 μg/kg in porcine), decreased an order of magnitude over this same period. All decreases fitted first order logarithmic regression equations. Chloradane and heptachlor epoxide were rarely observed in bovine or porcine fat; however, the incidence in bovine fat increased after 1973 following the removal of aldrin, dieldrin and heptachlor in 1969 for soil insect control and the subsequent increased use of chlordane. Chlordane appeared at low levels (1–2 μg/kg) in bovine fat during the mid 1970s and remained detectable through 1981. Lindane residues in both bovine and porcine fat fluctuated from year to year and appeared to vary with the need to control insect pests. While present (2 to 39 μg/kg) in the early 1970s, lindane residues disappeared by mid 1970 but reappeared in fatty tissues in 1981 (3–13 μg/kg). A limited number of samples were analyzed for organophosphorus insecticides between 1973 and 1980 and residues were occasionally found. In 1981, the analyses became routine and 3.6% of bovine samples were found to contain detectable residues of fenthion; only 2 of 197 bovine samples exceeded the maximum residue levels permitted under the Food and Drug Act.

Letter to the Editor: Inapplicability of the Logarithmic Regression Equation for the Factorial Calculation of Total Body Iron in Preschool Children

Letter to the Editor: Inapplicability of the Logarithmic Regression Equation for the Factorial Calculation of Total Body Iron in Preschool Children

Biomass and nutrient equations for mature Betulapapyrifera Marsh.

Biomass and nutrient accumulation by tree components for 66-year-old mature paper birch is presented. Logarithmic regression equations are given relating aboveground tree component biomass and contents of N, P, K, Ca, and Mg to tree diameter at breast height (dbh). Branches, bole bark, and bole wood accounted for 90–97% of the total aboveground tree biomass. Highest concentrations of most nutrients were in the foliage. For the tree of mean basal area (dbh = 15 cm), the crown components of branches and foliage constituted only 16% of the biomass but accounted for 49, 57, 53, 37, and 44%, respectively, of the N, P, K, Ca, and Mg accumulated.

Pre- and postnatal study of the carcass growth of sheep. 2. The cellular growth of adipose tissues

ABSTRACTThe diameter of adipocytes from subcutaneous, intermuscular and internal cavity fat depots of 5 pre- and 14 postnatal Romney female sheep was measured, the volume calculated, and the number per depot computed from the weight of triglyceride in the depots.The rates of increase of adipocyte volume relative to the increase in weight of total side adipose tissue, and of the fat depots and their chemical components, were calculated using linear regression analyses of the natural logarithmic transformed data. These logarithmic regression equations were used to estimate the volume of adipocytes in sheep at different stages of development. The total numbers of adipocytes at each stage of growth were estimated using linear double logarithmic regressions of adipocyte number on carcass weight.The growth of total adipose tissue and of each of the fat depots occurred mainly by an increase in the adipocyte volume, which increased over 70-fold from 120 days gestation to 5 years of age. The increase in adipocyte volume during growth occurred at similar rates in all of the fat depots and no significant differences between the volumes of adipocytes from the fat depots were found within sheep of similar carcass weight. During the same growth period the total number of adipocytes increased about 6-fold. Differences in the relative rates of growth of the fat depots were attributed to cellular multiplication rather than to cellular enlargement.

Standing crops of dominant <i>combretum</i> species at three browsing levels in the Kruger National Park

In red bushwillow veld near the Sand River in the Kruger National Park, Republic of South Africa, a determination was made of the standing crops of Combretum apiculatum and C. zeyheri at browsing levels delineated by the maximum feeding heights of impala (1,5 m), kudu (2,5 m) and giraffe (5,5 m). Using harvested sample trees, logarithmic or linear regression equations were generated which related basal diameter or stem height to biomass or percentage of total biomass at the different levels. Biomass was divided into two components: current shoots and wood plus bark. Regression forms and variables which produced the highest correlation coefficients changed with changes in species or browsing level, however, most equations were logarithmic with basal diameter as the independent variable.

An experiment on the interaction between cultivated rice and barnyard grass at different planting densities

To examine the relation between the effects of density and interaction between species, a rice and a barnyard grass strain were tested in pure and mixed (1 : 1) plantings at five different densities. In pure stands, the data for dry weight per plant and other characters gave a good fit to the logarithmic regression equation on plant density (derived from WN a = K). For the mixed plantings, a parameter showing neighbor effect was added to the equation, and its values were estimated. Rice and barnyard grass had different signs for this parameter. The trend of competition effect to increase with density was not observed. Both species tended to reduce reproductive effort at high densities, but at different rates. Rice showed logarithmically linear density responses in both size and number of stems, while barnyard grass showed it only in stem number.