An Equation for the Prediction of Oxygen Consumption in a Brazilian Population

Background: The equations predicting maximal oxygen uptake (VO2max or peak) presently in use in cardiopulmonary exercise testing (CPET) softwares in Brazil have not been adequately validated. These equations are very important for the diagnostic capacity of this method. Objective: Build and validate a Brazilian Equation (BE) for prediction of VO2peak in comparison to the equation cited by Jones (JE) and the Wasserman algorithm (WA). Methods: Treadmill evaluation was performed on 3119 individuals with CPET (breath by breath). The construction group (CG) of the equation consisted of 2495 healthy participants. The other 624 individuals were allocated to the external validation group (EVG). At the BE (derived from a multivariate regression model), age, gender, body mass index (BMI) and physical activity level were considered. The same equation was also tested in the EVG. Dispersion graphs and Bland-Altman analyses were built. Results: In the CG, the mean age was 42.6 years, 51.5% were male, the average BMI was 27.2, and the physical activity distribution level was: 51.3% sedentary, 44.4% active and 4.3% athletes. An optimal correlation between the BE and the CPET measured VO2peak was observed (0.807). On the other hand, difference came up between the average VO2peak expected by the JE and WA and the CPET measured VO2peak, as well as the one gotten from the BE (p = 0.001). Conclusion: BE presents VO2peak values close to those directly measured by CPET, while Jones and Wasserman differ significantly from the real VO2peak.

Methodology for spatialization of intense rainfall equation parameters

The aim of this study was to generate maps of intense rainfall equation parameters using interpolated maximum intense rainfall data. The study area comprised Espírito Santo State, Brazil. A total of 59 intense rainfall equations were used to interpolate maximum intense rainfall, with a 1 x 1 km spatial resolution. Maximum intense rainfall was interpolated considering recurrence of 2; 5; 10; 20; 50 and 100 years, and duration of 10; 20; 30; 40; 50; 60; 120; 240; 360; 420; 660; 720; 900; 1,140; 1,380 and 1,440 minutes, resulting in 96 maps of maximum intense rainfall. The used interpolators were inverse distance weighting and ordinary kriging, for which significance level (p-value) and coefficient of determination (R²) were evaluated for the cross-validation data, choosing the method that presented better R² to generate maps. Finally, maps of maximum intense precipitation were used to estimate, cell by cell, the intense rainfall equation parameters. In comparison with literature data, the mean percentage error of estimated intense rainfall equations was 13.8%. Maps of spatialized parameters, obtained in this study, are of simple use; once they are georeferenced, they may be imported into any geographic information system to be used for a specific area of interest.

Use of the Wasserman equation in optimization of the duration of the power ramp in a cardiopulmonary exercise test: a study of Brazilian men

This study aimed to analyze the agreement between measurements of unloaded oxygen uptake and peak oxygen uptake based on equations proposed by Wasserman and on real measurements directly obtained with the ergospirometry system. We performed an incremental cardiopulmonary exercise test (CPET), which was applied to two groups of sedentary male subjects: one apparently healthy group (HG, n=12) and the other had stable coronary artery disease (n=16). The mean age in the HG was 47±4 years and that in the coronary artery disease group (CG) was 57±8 years. Both groups performed CPET on a cycle ergometer with a ramp-type protocol at an intensity that was calculated according to the Wasserman equation. In the HG, there was no significant difference between measurements predicted by the formula and real measurements obtained in CPET in the unloaded condition. However, at peak effort, a significant difference was observed between oxygen uptake (V˙O2)peak(predicted)and V˙O2peak(real)(nonparametric Wilcoxon test). In the CG, there was a significant difference of 116.26 mL/min between the predicted values by the formula and the real values obtained in the unloaded condition. A significant difference in peak effort was found, where V˙O2peak(real)was 40% lower than V˙O2peak(predicted)(nonparametric Wilcoxon test). There was no agreement between the real and predicted measurements as analyzed by Lin’s coefficient or the Bland and Altman model. The Wasserman formula does not appear to be appropriate for prediction of functional capacity of volunteers. Therefore, this formula cannot precisely predict the increase in power in incremental CPET on a cycle ergometer.

Peptic disease and Helicobacter pylori are highly prevalent in patients with the indeterminate form of chagas’ disease: report of 21 cases

Given that chagasic patients in the indeterminate form of this disease, can have abnormal motility of the digestive tract and immunologic abnormalities, we decided to assess the frequency of peptic disease and Helicobacter pylori (Hp) infection in these individuals. Twenty-one individuals, 13 males and 8 females, mean age 37.6 ± 11.1 years, were examined. Biopsies of the duodenum, antrum, lesser and greater gastric curvature and esophagus were performed. The endoscopic findings were of chronic gastritis in 20 (95.2%) patients, duodenal ulcer in 3 (14.3%), gastric and duodenal ulcer in 3 (14.3%), gastric ulcer alone in 1 (4.8%), esophagitis in 5 (23.8%), and duodenitis in 5 (23.8%). The diagnosis of infection by the Hp was done by the urease test and histologic examination. Hp infection was found in 20 (95.2%) individuals: in 20 out of them in the antrum, in 17 in the lesser curvature, and in 17 in the greater curvature. Hp was not found in the esophagus and duodenum. The only individual with no evidence of infection by Hp was also the only one with normal endoscopic and histologic examinations. The histologic examinations confirmed the diagnoses of gastric ulcer as peptic, chronic gastritis in 20 patients, duodenitis in 14, and esophagitis in 9. In this series the patients had a high frequency of peptic disease, which was closely associated with Hp infection

Evolutive behavior towards cardiomyopathy of treated (nifurtimox or benznidazole) and untreated chronic chagasic patients

The aim of this work was to compare the evolution of chronic chagasic untreated patients (UTPs) with that of benznidazole or nifurtimox-treated patients (TPs). A longitudinal study from a low endemic area (Santa Fe city, Argentina) was performed during an average period of 14 years. Serological and parasitological analyses with clinical exams, ECG and X-chest ray were carried out. At the onset, 19/198 infected patients showed chagasic cardiomyopathy (CrChM) while 179 were asymptomatic. In this latter group the frequency of CrChM during the follow-up was lower in TPs compared with UTPs (3.2% vs 7%). Within the CrChM group, 2/5 TPs showed aggravated myopathy whereas this happened in 9/14 UTPs. Comparing the clinical evolution of all patients, 5.9% of TPs and 13% of UTPs had unfavourable evolution, but the difference is not statistically relevant. Serological titers were assessed by IIF. Titers equal to or lower than 1/64 were obtained in 86% of the TPs, but only in 38% of UTPs. The differences were statistically significant (geometric mean: 49.36 vs. 98.2). Antiparasitic assessment of the drugs (xenodiagnosis) proved to be effective. The low sensitivity in chronic chagasic patients must be born in mind. Despite treated patients showed a better clinical evolution and lower antibody levels than untreated ones, it is necessary to carry on doing research in order to improve therapeutic guidelines, according to the risk/benefit equation and based on scientific and ethical principles.

Trypanocide treatment among adults with chronic Chagas disease living in Santa Fe city (Argentina), over a mean follow-up of 21 years: parasitological, serological and clinical evolution

The efficacy of treatment with nifurtimox and/or benznidazole among adults with chronic Chagas disease with no previous electrocardiographic disturbances was evaluated over a mean follow-up of 21 years, by means of conventional serology, xenodiagnosis, clinical examination, electrocardiograms and chest X-ray. One hundred and eleven patients, between 17 and 46 years old, were studied: 54 underwent treatment (nifurtimox 27, benznidazole 27) and 57 remained untreated (control group). Xenodiagnosis was performed on 65% of them: 36/38 of the treated and 9/34 of the untreated patients had previous positive xenodiagnosis. Post-treatment, 133 xenodiagnoses were performed on 41 patients, all resulting negative. In the control group, 29 xenodiagnoses were performed on 14 patients; 2 resulted positive. Sera stored during the follow-up were simultaneously analyzed through conventional serology tests (IHA; DA-2ME; IIF). The serological evolution in the treated group was: a) 37% underwent negative seroconversion (nifurtimox 11, benznidazole 9); b) 27.8% decreased titers (nifurtimox 9, benznidazole 6), 9 showed inconclusive final serology (nifurtimox 7, benznidazole 2); c) 35.2% remained positive with constant titers (nifurtimox 7; benznidazole 12). The control group conserved the initial antibody levels during the follow-up. In the clinical evolution, 2/54 (3.7%) of the treated and 9/57 (15.8%) of the untreated patients showed electrocardiographic disturbances attributable to Chagas myocardiopathy, with a statistically relevant difference (p<0.05). Treatment caused deparasitation in at least 37% of the chronically infected adults and a protective effect on their clinical evolution.

Relationship between plasma creatinine concentration and glomerular filtration in preterm newborn infants

Fluid management and dosage regimens of drugs in preterm infants should be based on the glomerular filtration rate. The current methods to determine glomerular flitration rate are invasive, time-consuming, and expensive. In contrast, creatinine clearance can be easy obtained and quickly determined. The purpose of this study was to compare plasma creatinine on the third and seventh day of life in preterm newborn infants, to evaluate the influence of maternal creatinine, and to demonstrate creatinine clearance can be used as a reliable indicator of glomerular filtration rate. We developed a prospective study (1994) including 40 preterm newborns (gestational age < 37 weeks), average = 34 weeks; birth weight (average) = 1840 g, in the first week of life. Inclusion criteria consisted of: absence of renal and urinary tract anomalies; O2 saturation 3 92%; adequate urine output (>1ml/kg/hr); normal blood pressure; absence of infections and no sympathomimetic amines in use. A blood sample was collected to determine plasma creatinine (enzymatic method) on the third and seventh day of life and creatinine clearance (CrCl) was obtained using the following equation: , k = 0.33 in preterm infant All plasma creatinine determinations showed normal values [third day: 0.78 mg/dl ± 0.24 (mean ± SD)and seventh day: 0.67 mg/dl ± 0.31 - (p>0.05)]. Also all creatinine clearance at third and seventh day of life were normal [third day: 19.5 ml/min ± 5.2 (mean ± SD) and seventh day: 23.8 ml/min ± 7.3 - (p>0,05)]. All preterm infants developed adequate renal function for their respective gestational age. In summary, our results indicate that, for clinical practice, the creatinine clearance, using newborn length, can be used to estimate glomerular filtration rate in preterm newborn infants.

A determinação dos números de indivíduos mínimos necessários na experimentação genética

The main object of the present paper consists in giving formulas and methods which enable us to determine the minimum number of repetitions or of individuals necessary to garantee some extent the success of an experiment. The theoretical basis of all processes consists essentially in the following. Knowing the frequency of the desired p and of the non desired ovents q we may calculate the frequency of all possi- ble combinations, to be expected in n repetitions, by expanding the binomium (p-+q)n. Determining which of these combinations we want to avoid we calculate their total frequency, selecting the value of the exponent n of the binomium in such a way that this total frequency is equal or smaller than the accepted limit of precision n/pª{ 1/n1 (q/p)n + 1/(n-1)| (q/p)n-1 + 1/ 2!(n-2)| (q/p)n-2 + 1/3(n-3) (q/p)n-3... < Plim - -(1b) There does not exist an absolute limit of precision since its value depends not only upon psychological factors in our judgement, but is at the same sime a function of the number of repetitions For this reasen y have proposed (1,56) two relative values, one equal to 1-5n as the lowest value of probability and the other equal to 1-10n as the highest value of improbability, leaving between them what may be called the "region of doubt However these formulas cannot be applied in our case since this number n is just the unknown quantity. Thus we have to use, instead of the more exact values of these two formulas, the conventional limits of P.lim equal to 0,05 (Precision 5%), equal to 0,01 (Precision 1%, and to 0,001 (Precision P, 1%). The binominal formula as explained above (cf. formula 1, pg. 85), however is of rather limited applicability owing to the excessive calculus necessary, and we have thus to procure approximations as substitutes. We may use, without loss of precision, the following approximations: a) The normal or Gaussean distribution when the expected frequency p has any value between 0,1 and 0,9, and when n is at least superior to ten. b) The Poisson distribution when the expected frequecy p is smaller than 0,1. Tables V to VII show for some special cases that these approximations are very satisfactory. The praticai solution of the following problems, stated in the introduction can now be given: A) What is the minimum number of repititions necessary in order to avoid that any one of a treatments, varieties etc. may be accidentally always the best, on the best and second best, or the first, second, and third best or finally one of the n beat treatments, varieties etc. Using the first term of the binomium, we have the following equation for n: n = log Riim / log (m:) = log Riim / log.m - log a --------------(5) B) What is the minimun number of individuals necessary in 01der that a ceratin type, expected with the frequency p, may appaer at least in one, two, three or a=m+1 individuals. 1) For p between 0,1 and 0,9 and using the Gaussean approximation we have: on - ó. p (1-p) n - a -1.m b= δ. 1-p /p e c = m/p } -------------------(7) n = b + b² + 4 c/ 2 n´ = 1/p n cor = n + n' ---------- (8) We have to use the correction n' when p has a value between 0,25 and 0,75. The greek letters delta represents in the present esse the unilateral limits of the Gaussean distribution for the three conventional limits of precision : 1,64; 2,33; and 3,09 respectively. h we are only interested in having at least one individual, and m becomes equal to zero, the formula reduces to : c= m/p o para a = 1 a = { b + b²}² = b² = δ2 1- p /p }-----------------(9) n = 1/p n (cor) = n + n´ 2) If p is smaller than 0,1 we may use table 1 in order to find the mean m of a Poisson distribution and determine. n = m: p C) Which is the minimun number of individuals necessary for distinguishing two frequencies p1 and p2? 1) When pl and p2 are values between 0,1 and 0,9 we have: n = { δ p1 ( 1-pi) + p2) / p2 (1 - p2) n= 1/p1-p2 }------------ (13) n (cor) We have again to use the unilateral limits of the Gaussean distribution. The correction n' should be used if at least one of the valors pl or p2 has a value between 0,25 and 0,75. A more complicated formula may be used in cases where whe want to increase the precision : n (p1 - p2) δ { p1 (1- p2 ) / n= m δ = δ p1 ( 1 - p1) + p2 ( 1 - p2) c= m / p1 - p2 n = { b2 + 4 4 c }2 }--------- (14) n = 1/ p1 - p2 2) When both pl and p2 are smaller than 0,1 we determine the quocient (pl-r-p2) and procure the corresponding number m2 of a Poisson distribution in table 2. The value n is found by the equation : n = mg /p2 ------------- (15) D) What is the minimun number necessary for distinguishing three or more frequencies, p2 p1 p3. If the frequecies pl p2 p3 are values between 0,1 e 0,9 we have to solve the individual equations and sue the higest value of n thus determined : n 1.2 = {δ p1 (1 - p1) / p1 - p2 }² = Fiim n 1.2 = { δ p1 ( 1 - p1) + p1 ( 1 - p1) }² } -- (16) Delta represents now the bilateral limits of the : Gaussean distrioution : 1,96-2,58-3,29. 2) No table was prepared for the relatively rare cases of a comparison of threes or more frequencies below 0,1 and in such cases extremely high numbers would be required. E) A process is given which serves to solve two problemr of informatory nature : a) if a special type appears in n individuals with a frequency p(obs), what may be the corresponding ideal value of p(esp), or; b) if we study samples of n in diviuals and expect a certain type with a frequency p(esp) what may be the extreme limits of p(obs) in individual farmlies ? I.) If we are dealing with values between 0,1 and 0,9 we may use table 3. To solve the first question we select the respective horizontal line for p(obs) and determine which column corresponds to our value of n and find the respective value of p(esp) by interpolating between columns. In order to solve the second problem we start with the respective column for p(esp) and find the horizontal line for the given value of n either diretly or by approximation and by interpolation. 2) For frequencies smaller than 0,1 we have to use table 4 and transform the fractions p(esp) and p(obs) in numbers of Poisson series by multiplication with n. Tn order to solve the first broblem, we verify in which line the lower Poisson limit is equal to m(obs) and transform the corresponding value of m into frequecy p(esp) by dividing through n. The observed frequency may thus be a chance deviate of any value between 0,0... and the values given by dividing the value of m in the table by n. In the second case we transform first the expectation p(esp) into a value of m and procure in the horizontal line, corresponding to m(esp) the extreme values om m which than must be transformed, by dividing through n into values of p(obs). F) Partial and progressive tests may be recomended in all cases where there is lack of material or where the loss of time is less importent than the cost of large scale experiments since in many cases the minimun number necessary to garantee the results within the limits of precision is rather large. One should not forget that the minimun number really represents at the same time a maximun number, necessary only if one takes into consideration essentially the disfavorable variations, but smaller numbers may frequently already satisfactory results. For instance, by definition, we know that a frequecy of p means that we expect one individual in every total o(f1-p). If there were no chance variations, this number (1- p) will be suficient. and if there were favorable variations a smaller number still may yield one individual of the desired type. r.nus trusting to luck, one may start the experiment with numbers, smaller than the minimun calculated according to the formulas given above, and increase the total untill the desired result is obtained and this may well b ebefore the "minimum number" is reached. Some concrete examples of this partial or progressive procedure are given from our genetical experiments with maize.

A lei de Mitscherlich aplicada a experimentos de adubação com vinhaça

The author studies, with the aid of Mitscherlich's law, two experiments of sugar cane fertilization with vinasse. The first one, carried out in Piracicaba, State of S. Paulo, by ARRUDA, gave the following yields. No vinasse 47.0 tons/ha. 76.0 tons/ha. 250 c.m./ha. of vinasse 75.0 do. 112.0 do. 500 do. 90.0 do. 112.0 do. 1000 do. 98.0 do. 107.0 do. Data without NPK were appropriate for the fitting of the law, the equation of which was found to be: y = 100.8 [1 - 10 -0.00132 (x + 206) ], where y is measured in metric tons/hectare, and x in cubic meters/hectare. The optimum amount of vinasse to be used is given by the formula x* = 117.2 + 1 log w u , ______ ____ 0.00132 250 t being u the response to the standard dressing of 250 cubic meters/hectare of vinasse, w the price per ton of sugar cane, and t the price per cubic meter for the transportation of vinasse. In Pernambuco, a 3(4) NPK vinasse experiment gave the following mean yields: No vinasse 41.0 tons/hectare 250 cm./ha. of vinasse 108.3 do. 500 do. 134.3 do. The equation obtained was now y = 150.7 [1 - 10 -000165 (x + 84)], being the most profitable level of vinasse x* = 115.2 + 1 log w u , _______ ____ 0.00165 250 t One should notice the close agreement of the coefficients c (0.00132 in S. Paulo and 0.00165 in Pernambuco). Given the prices of Cr$ 20.00 per cubic meter for the transportation of vinasse (in trucks) and Cr$ 250.00 per ton of sugar cane (uncut, in the fields) the most profitable dressings are: 236 c.m./ha. of vinasse in S. Paulo, and 434 c.m./ha. in Pernambuco.

Estudo sôbre as temperaturas médias em Campinas

This paper deals with the study by orthogonal polynomials of trends in the mean annual and mean monthly temperatures (in degrees Centigrade) in Campinas (State of São Paulo, Brasil), from 1890 up to 1956. Only 4 months were studied (January, April, July and October) taken as typical of their respective season. For the annual averages both linear and quadratic components were significant, the regression equation being y = 19.95 - 0.0219 x + 0.00057 x², where y is the temperature (in degrees Centigrade) and x is the number of years after 1889. Thus 1890 corresponds to x = 1, 1891, to x = 2, etc. The equation shows a minimum for the year 1908, with a calculated mean y = 19.74. The expected means by the regression equation are given below. Anual temperature means for Campinas (SP, Brasil) calculated by the regression equation Year Annual mean (Degrees Centigrade) 1890 19.93 1900 10.78 1908 19.74 (minimum) 1010 19.75 1920 19.82 1930 20.01 1940 20.32 1950 20.74 1956 21.05 The mean for 67 years was 20.08°C with standard error of the mean 0.08°G. For January the regression equation was y = 23.08 - 0.0661 x + 0.00122 x², with a minimum of 22.19°C for 1916. The average for 67 years was 22.70°C, with standard error 0.12°C. For April no component of regression was significant. The average was 20.42°C, with standard error 0.13°C. For July the regression equation was of first degree, y = 16.01 + 0.0140X. The average for 67 years was 16.49°C, with standard error of the mean 0.14°C. Finally, for October the regression equation was y = 20.55 - 0.0362x + 0.00078x², with a minimum of 20.13°C for 1912. The average was 20.52°C, with standard error of the mean equal to 0.14°C.

Seroepidemioplogy of schistosomiasis mansoni

In population surveys in wich the Schistosoma mansoni intensity of infection is low, or in localities where the schistosomiasis control program had success the parasitologic methods lack in sensitivity. Despite of some limitations the immunological methods are useful to provide valuable information in such field conditions. Thus, the prevalaence of schistosomiasis in untreated population can be determined by the detection of IgG or IgM antibodies, as well as the incidence by the IgA antibodies , employing mainly immunofluorescence (IF) and immunoenzymatic (ELISA), and in some extent hemagglutination (HA) or even skin test. The true prevalence and incidence of schistosomiasis can be estimated using a probabilistic model equation, since knowing before-hand the sensitivity and specificity of emploved test. The sensitivity and the specificity of serologic test become higher in low aged group, under 14. The geometric mean IF titers also gives a positive correlation with the intensity of infection. Presently there are need of serologic tests wich are economic and pratical in soroepidemiologic inquires, requiring no specialized personnel to collect population blood or serum and also easily interpret the test results. The reagents for such tests are desired to be stable and reproducible. Moreover, it is expected that the tests can distinguish an ative infection.

Effects of flooding and temperature on Aedes albifasciatus development time and larval density in two rain pools at Buenos Aires University City

Aedes albifasciatus is a floodwater mosquito that breeds in temporary waters. This semi-domestic species, widely distributed in Argentina, is a competent vector of the western equine encephalitis. The present study was carried out in two rain pools of the city of Buenos Aires, from April 1998 through March 1999. Samples were taken twice a week during the cold season and daily during the warmer months, starting from October. Immature mosquitoes were collected with a dipper, being the number of dippers proportional to the flooded area. The estimated rainfall thresholds to initiate cohorts of Ae. albifasciatus were: 16-17 mm in the fall-winter period, 25 mm in the spring, and 30 mm in the summer. The development time of the different cohorts and the mean air temperature of their respective periods were estimated in all seasons, ranging from six days (at 24ºC) to 32 days (at 13ºC). The equation that best expresses the relationship between development time and mean air temperature is dt =166,27.e-0,1435.T (R²=0,92). Significantly shorter development times were recorded for larvae of the first three stages as compared to the fourth larval stage and pupae.

Cristallochemical characterization of synthetic Zn-substituted maghemites (g-Fe2-xZn xO3)

Maghemite (g-Fe2O3) is the most usually found ferrimagnetic oxide in red basalt-derived soils. The variable degrees of ionic substitution of Fe3+ for different metals (e.g. Ti4+, Al3+, Mg2+, Zn2+, and Mn2+) and non-metals in the maghemite structure influence some cristallochemical features of this iron oxide. In this study, synthetic Zn-substituted maghemites were prepared by co-precipitation in alkaline aqueous media of FeSO4.7H2O with increasing amounts of ZnSO4.7H2O to obtain the following sequence of Fe3+ for Zn2+ substitutions: 0.0, 0.025, 0.05, 0.10, 0.15, 0.20, and 0.30 mol mol-1. The objective of this work was to evaluate the cristallochemical alterations of synthetic Zn-substituted maghemites. The dark black synthetic precipitated material was heated to 250 °C during 4 h forming a brownish maghemite that was characterized by chemical analysis as well as X ray diffraction (XRD), specific surface area and mass-specific magnetic susceptibility. The isomorphic substitution levels observed were of 0.0013, 0.0297, 0.0590, 0.1145, 0.1764, 0.2292 and 0.3404 mol mol-1, with the formation of a series of maghemites from Fe2Zn0O3 to Fe(1.49)Zn(0.770)O3 . The increase in Fe3+ for Zn2+ substitution, [Zn mol mol-1] increased the dimension a0 of the cubic unit cells of the studied maghemites according to the regression equation: a0 = 0.8343 + 0.02591Zn (R² = 0.98). On the other hand, the mean crystallite dimension and mass-specific magnetic susceptibility of the studied maghemites decreased with increasing isomorphic substitution.

Method to estimate soil macroporosity and microporosity based on sand content and bulk density

Macroporosity is often used in the determination of soil compaction. Reduced macroporosity can lead to poor drainage, low root aeration and soil degradation. The aim of this study was to develop and test different models to estimate macro and microporosity efficiently, using multiple regression. Ten soils were selected within a large range of textures: sand (Sa) 0.07-0.84; silt 0.03-0.24; clay 0.13-0.78 kg kg-1 and subjected to three compaction levels (three bulk densities, BD). Two models with similar accuracy were selected, with a mean error of about 0.02 m³ m-3 (2 %). The model y = a + b.BD + c.Sa, named model 2, was selected for its simplicity to estimate Macro (Ma), Micro (Mi) or total porosity (TP): Ma = 0.693 - 0.465 BD + 0.212 Sa; Mi = 0.337 + 0.120 BD - 0.294 Sa; TP = 1.030 - 0.345 BD 0.082 Sa; porosity values were expressed in m³ m-3; BD in kg dm-3; and Sa in kg kg-1. The model was tested with 76 datum set of several other authors. An error of about 0.04 m³ m-3 (4 %) was observed. Simulations of variations in BD as a function of Sa are presented for Ma = 0 and Ma = 0.10 (10 %). The macroporosity equation was remodeled to obtain other compaction indexes: a) to simulate maximum bulk density (MBD) as a function of Sa (Equation 11), in agreement with literature data; b) to simulate relative bulk density (RBD) as a function of BD and Sa (Equation 13); c) another model to simulate RBD as a function of Ma and Sa (Equation 16), confirming the independence of this variable in relation to Sa for a fixed value of macroporosity and, also, proving the hypothesis of Hakansson & Lipiec that RBD = 0.87 corresponds approximately to 10 % macroporosity (Ma = 0.10 m³ m-3).