SciELO - Scientific Electronic Library Online

 
vol.40 número1Retos en la formulación magistral oftálmicaQuimioterapia al final de la vida: análisis de la práctica clínica en pacientes adultos onco-hematológicos con cáncer índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google

Compartir


Farmacia Hospitalaria

versión On-line ISSN 2171-8695versión impresa ISSN 1130-6343

Farm Hosp. vol.40 no.1 Toledo ene./feb. 2016

https://dx.doi.org/10.7399/fh.2016.40.1.8859 

ORIGINALES

 

Analysis of the concordance between the estimated values of creatinine clearance using the Cockcroft-Gault equation and the real value determined in patients from the Hospital Clínica Bíblica

Análisis de la concordancia entre los valores estimados de aclaramiento de creatinina utilizando la fórmula de Cockcroft-Gault y el valor real determinado en pacientes del Hospital Clínica Bíblica

 

 

José Miguel Chaverri-Fernández1, Esteban Zavaleta-Monestel2, José Pablo Díaz-Madriz3, Angie Ortiz-Ureña4, Mónica Ramírez-Hernández5 and Karina Trejos-Morales5

1Department of Pharmacology, Toxicology, and Drug Dependence of the School of Pharmacy, Universidad de Costa Rica. Clinical Pharmacist, Hospital Clínica Bíblica, San José.
2Head of Pharmacy at the Hospital Clínica Bíblica, San José.
3Clinical Pharmacist. Hospital Clínica Bíblica, San José.
4Department of Pharmacology, Toxicology and Drug Dependence of the School of Pharmacy, Universidad de Costa Rica.
5Intern Students. University of Medical Sciences UCIMED-Hospital Clínica Bíblica. Costa Rica.

Correspondence

 

 


ABSTRACT

Objective: to analyze the effect of the modifications in the Cockcroft-Gault equation for creatinine clearance rate determination (CrCl) and its concordance with the real value determined from 24-hours urine collection in a sample of Latin American patients hospitalized in San José de Costa Rica.
Method: an observational, retrospective study, with patients submitted to a 24-hour urine collection test, and who met the inclusion criteria. The real and estimated values of creatinine clearance were determined, and their concordance was measured by applying the Intraclass Correlation Coefficient; a descriptive analysis of data was also conducted.
Results: there were 507 subjects (61% men); their age was described (ME = 60 years SD = 17 years), as well as their height (ME = 1.66 m SD = 0.09 m), current weight (ME =75 kg SD = 15 kg), body mass index (ME = 27.3 kg/m2 SD = 4.76 kg/m2) and endogenous creatinine clearance rates (ME = 69.72 ml/min SD = 33 ml/min). The best concordance with the equation was obtained with current weight values and serum creatinine without rounding.
Conclusions: the application of the Cockcroft-Gault equation that matches more closely the real value is the one that uses current weight and does not round creatinine values below 1 mg/dL. It is suggested to conduct a prospective analysis, determining other variables that could affect CrCI real measures, and to replicate this methodology in specific populations.

Key words: Renal clearance; Creatinine; Clinical Pharmacy Unit; Pharmacokinetics.


RESUMEN

Objetivo: analizar el efecto de las modificaciones en la fórmula de Cockcroft-Gault en la medición del aclaramiento de creatinina (CrCl) y su concordancia con el valor real calculado con la orina de 24 horas en una muestra de pacientes latinoamericanos hospitalizados en San José de Costa Rica.
Método: estudio observacional, retrospectivo, con pacientes en quienes se midió la creatinina sérica en orina de 24 horas y que cumplieran los criterios de inclusión. Se determinaron los valores de aclaramiento de creatinina reales y calculados, y se estableció la concordancia entre estos, aplicando la prueba del Coeficiente de Correlación Intraclase; se realizó un análisis descriptivo de los datos.
Resultados: un total de 507 pacientes (61% hombres), de los cuales se describió la edad (*ME = 60 años**DE = 17 años), estatura (*ME = 1,66 metros**DE = 0,09 metros), peso actual (*ME = 75 kg **DE = 15 kg), índice de masa corporal (*ME = 27,3 Kg/m2**DE = 4,76 Kg/m2), y valores de aclaramiento endógeno (*ME = 69,72 ml/min **DE = 33 ml/min). Se obtuvo la mejor concordancia para la fórmula con valores de peso actual y creatinina sérica sin redondeo.
Conclusiones: la aplicación de la fórmula de Cockcroft-Gault que mejor concuerda con el valor real es aquella que utiliza el peso actual y no redondea valores de creatinina inferiores a 1 mg/dL. Se sugiere realizar un análisis prospectivo, determinando otras variables que podrían afectar a la medición real del CrCl, y replicar la metodología en poblaciones específicas.

Palabras clave: Aclaramiento renal; Creatinina; Servicio de Farmacia Clínica; Farmacocinética.


Abreviations:
*ME: Media
**DE: Desviación Estándar.
*ME: Mean
**SD: Standard Deviation.

 

Introduction

Clinical assessment of renal function is essential for the evaluation and treatment of patients, as it allows to determine the likelihood of conducting invasive procedures for diagnosis or treatment, as well as to detect, assess and monitor the renal disease, both chronic and acute; it also allows to approximate the dosing of medications to be used in an effective and safe manner, in the case of products being excreted by the kidneys in a rate above 60%1-4. The reason is that the majority of manufacturers of medications with high renal excretion recommend to adjust the dose based on creatinine clearance, in order to reduce any potential toxicities or the appearance of side effects, besides changes in the volume of medication distribution and its binding to plasmatic proteins. However, the final effect will depend ultimately on the metabolic processes suffered by each medication5,6.

One of the best renal function predictors is the Glomerular Filtration Rate (GFR); its normal range varies between 90 and 120 mL/min, and it is reduced at a 10ml/ min rate per each 10 years after the age of 40. Its measurement in clinical practice is not easy; direct measurement techniques can be used, or different methods for an approximate measurement through equations using parameters such as serum creatinine, age, ethnicity, gender and height, among others1,2,7,8.

The majority of direct techniques require urine collection during 24 hours, collection of blood samples, or the use of gamma cameras. The clearance of inulin (a polysaccharide which filters freely at glomerular level) is a parameter used to assess GFR. Other methods use the measurement of urea, aminohippuric acid, iotalamate and creatinine with simultaneous administration of cimetidine, and radioactive isotopes, due to the characteristics of filtration experienced by all of them at renal level9-12.

Under these circumstances, around eight equations have been created in order to estimate the glomerular filtration rate; the most widely used and accepted in clinical practice are the Modification of Diet in Renal Disease (MDRD) and the Cockcroft-Gault equation9,13,14. However, these won't always provide a clear idea of GFR in all patients, specifically in those with advanced age and/or major weight variations15,16. Originally, the MDRD equation required six variables, which included serum creatinine, albumin, urea nitrogen, gender, age and ethnicity. This was later simplified into four variables, excluding albumin and urea nitrogen. This is the most widely used equation in order to stratify patients according to their renal function4,15,17.

In order to apply the Cockcroft-Gault (C-G) equation, it is required to have the values of weight and age of patients, as well as their gender, and the creatinine concentration in serum, usually obtained through collection of a blood sample. This is because creatinine is an organic compound obtained after creatine degradation (a muscular metabolic product), which is used as a renal function indicator because kidneys will filter it and at the same time excrete it, thus allowing to calculate creatinine clearance (CrCl)10; Clearance is calculated as follows: CrCl = 140 - age (years) x weight (kg) / 72 x serum creatinine (SCr), and all this must be multiplied by 0.85 in the case of a woman. This equation was designed for a person with 72 kg of weight and 1.73m2 of body area 7, and it has been the most widely used in clinical practice due to its ease of use, efficacy, speed, low cost and confirmed validity in order to suggest changes in medication dosing18.

However, there is ambiguity and controversy regarding the variables used in the C-G equation, because it has not been determined if the equation must use current weight, ideal weight, or omit the weight; moreover, it is widely known that any major variations in the muscular mass of the patient could have a noticeable impact on the serum creatinine value and the final estimated CrCl value. It is suggested that, in patients with low SCr, the value must be rounded to 0.8-1 mg/dl, which could generate underestimations in measurement19.

There are studies comparing the creatinine clearance measured in 24 hours (24-hour urine) with the clearance estimation using the Cockcroft-Gault equation, modifying the different variables used in the equation (weight and SCr). In some cases, it has been suggested that the best way to calculate the creatinine clearance by using the C-F equation could be to omit the weight or to use the adjusted weight if the patient is obese19, while other study suggests that current weight must be used for persons with low weight20. In their review published in 2013, Brown and colleagues point out that, in the case of weight, the ideal weight and the current weight should be used respectively as lower and upper limits (total weight); all authors reach the conclusion that the real value of serum creatinine should be used without rounding19-21. There is currently no information about the Latin American population suggesting how to act and which variables to use for CrCl estimation through the C-G equation, which would improve dose adjustment and the adequate timepoints according to these patients' reality.

The current research project is intended to analyze the variations in CrCl estimated through the C-G equation in a sample of Latin American patients hospitalized at the Hospital Clínica Bíblica in San José, Costa Rica, from January, 2010 to November, 2014 (taking into account modifications in the weight and serum creatinine variables), looking for the closest concordance with the creatinine clearance measured during 24 hours (real reported CrCl). Determining the equation with the best concordance with the real value of CrCl will provide a better idea of GFR and renal function; moreover, it will be a guide in order to suggest dose adjustments in those medications which require them. To this aim, the hypothesis put forward was that ideal weight and serum creatinine without rounding are the ideal descriptors to be used for estimating the creatinine clearance by using the Cockcroft-Gault equation.

 

Methodology

The current observational retrospective study included all those Latin American patients who underwent a 24-hour urine test at the Hospital Clínica Bíblica during the period from January, 2010 to November, 2014. Data for this population were obtained through consultations at the Integrated Hospital Management System of the Hospital Clínica Bíblica (IHMS); those used for the analysis present a normal behaviour as assessed through the Kolmogorov-Smirnov Test.

The data of patients who met the following inclusion criteria were collected and included:

- 18 years of age or more.

- Weight value as reported in the file.

- Serum creatinine value as reported by the lab.

- Endogenous clearance value as reported by the lab.

The sub-population to be worked upon was applied the following exclusion criteria:

- Endogenous creatinine clearances reported by the lab with values of 140 mL/min or higher.

The respective calculations of serum CrCl were conducted through the C-G equation, applying modifications in the calculation for the weight variable (with real weight, ideal weight, and no weight), and serum creatinine (rounded and without rounding). Then the concordance of said methods of calculation regarding the real value (24 h. CrCl) was determined, by applying the Intraclass Correlation Coefficient (ICC) Test, through the SPSS V.19 software, and with a pre-established 95% Confidence Interval. This test was selected based on its validity to determine between a series of measurements obtained through different methods (instruments or electronic equipment) that or those series which match more closely the real value in analysis.22 Additionally, a descriptive analysis of the population used was also conducted.

The Clinical Research Management of the Hospital Clínica Bíblica agreed to the conduction of this study. The adequate ethical management and confidentiality of data of the patients included in the study was guaranteed. No personal details of those patients selected were used or known.

 

Results

The current study analyzed 507 patients in total: 311 men (61%) and 196 women (39%), with an age range between 18 and 103 years, Mean (ME) = 60 years, Standard Deviation (SD) =17 years. The height of the participants (used for the estimation of the ideal weight) ranged between 1.41 and 1.90 metres, ME= 1.66 metres, SD= 0.09 metres. Regarding weight, there was a range between 42 and 124 kilos, ME=75 kilos, SD: 15 kilos. The Body Mass Index (BMI) ranged between 15.9 Kg/m2 and 44.6 Kg/m2, ME= 27.2Kg/m2 SD= 4.7 Kg/m2. Table 1 shows additional details about the characteristics of the study population.

 

 

When conducting the analysis of variables, it was found that the values of serum creatinine reported by the lab ranged between 0.45 and 8.90 mg/dl, ME=1.47 mg/dl SD=1.17mg/dl. The presence of protein in urine was reported in 85% of patients. The reported value of serum creatinine was rounded to 1 mg/dl for 18% of patients, as it was below 0.8 mg/dL, a equation modification previously mentioned. Regarding the volume of urine collected in 24 hours, a ME= 2211 ml, SD=935 ml was obtained.

The endogenous clearance values measured in 24 hours reported by the lab ranged between 2.6 and 139.6 ml/min, ME= 69.72 ml/min SD=33 ml/min. The rest of the maximum, minimum, average, and SD values of the estimated clearances are detailed in table 2.

 

 

The Intraclass Correlation Coefficient Test was applied in order to analyze the concordance between the values obtained through 24-hour urine test and the values obtained by applying the C-G equation, with the above mentioned modifications. The best statistical concordance was shown by CrCl using current weight and SCr without rounding: 0.827 (0.798-0.853) CI95%; on the other hand, the lowest concordance was obtained with the CrCl using ideal weight and rounded SCr.

In the case of obese patients as defined by their Body Mass Index (BMI above 30 kg/m2), the best correlation is also obtained when the current weight and creatinine without rounding are used: 0.87 (0.83-0.91) CI95%. This was not calculated for low-weight patients, because these only represent 1% of the sample. Table 3 shows more details regarding the rest of the results obtained after applying this test.

 

 

Discussion

Cockcroft-Gault equation is the most widely used formula in clinical practice, due to its ease of use, efficacy, speed and low cost, for renal function assessment. It is also the most widely validated equation to suggest changes in medication dosing10. Different adjustments in the variables used have been suggested for its clinical implementation; thus, variations in weight were applied in the current study, using current weight, ideal weight, and omitting the weight value in the equation. Variations in serum creatinine values were also applied, which consisted in rounding to the 1 mg/dL value in those cases in which the reported value was lower4.

When conducting the creatinine clearance estimation by using the Cockcroft-Gault equation in a Latin American population (Costa Rica), the result obtained was that the equation applied which has the closest concordance with the values obtained through 24-hour assessment is the one which uses the current weight of the patient and does not round creatinine values below 1 mg/dL; the difference in the level of concordance of this equation is very low regarding the case where no weight and no rounded Cr are used. A similar result, and with a good intraclass correlation, is obtained in the case of the specific analysis of obese patients only (BMI above 30 kg/m2), without the mediation of a correction factor in the equation, as suggested by other authors19-21.

The majority of the research articles similar to the current study show that there is concordance when using serum creatinine without variation, because rounding does not improve the predicted clearance; therefore, it would be expected that the behaviour of the Latin American population should coincide with the one found in other latitudes4,19,21,22. On the other hand, this research has not reached the same conclusions regarding weight as other similar research studies; for example, Winter, Gurh and Bergh21 suggest the use of current weight in low-weight patients, of ideal weight in normal weight patients, and to add a 0.4 correction factor to their current weight in the case of obese patients. It is suggested that these strategies will result in less biased and more accurate values.

Other researchers, such as Wilhelm and Kale-Pradhan19, have concluded that the C-G equation is closer to the real creatinine clearance value when weight is removed from the equation, and they point out at the addition of a 0.3-0.4 correction factor upon weight in the case of obese patients.

The differences obtained in the present study regarding other similar studies could be explained by the variability in the studied subjects, and the ethnic differences in the subjects of other research studies. It must also be taken into account that, even though there is a low proportion of patients over 80-year-old (less than 10%), this was not excluded, and there is controversy regarding the reliability of the C-G equation in this specific population2,19,23,24.

Regarding weight, 74% of patients in the current study had a weight close to the ideal (patients with normal weight and/or BMI overweight between 18.5 and 30 kg/m2); and as was previously mentioned for obese patients defined by their Body Mass Index (BMI > 30kg/ m2), the best correlation is also obtained when using the current weight variable and the creatinine without rounding 0.87 (0.83-0.91) CI95%. This is a very good correlation, and it does not require en additional common correction factor in each case, a piece of data different to what has been reported in literature19,20.

Another aspect worth mentioning is that it was not possible to know the conditions, special characteristics, or concomitant treatments of the sample selected, which could have an impact on the endogenous value of creatinine clearance. Due to the fact that this was a retrospective data analysis, it was difficult to collect this information, as well as to conduct the correct segmentation and minimization of those biases associated with these variables or characteristics, an aspect which had been taken into account by other similar research studies13,14,15,25. Even so, the number of patients analyzed suggests that the results obtained can have a good statistical potency, which would allow an extrapolation of results to the local population.

It can be concluded that the application of the Cockcroft-Gault equation with the best concordance with the real creatinine clearance value estimated through 24-hour urine is the one using the current weight of patients which does not round creatinine values below 1 mg/dL when these appear; however, it is suggested to conduct similar analyses in a prospective manner, determining other variables which could have an impact on the real measurement of CrCl, as well as to replicate the methodology in specific populations.

 

Bibliography

1. Levey AS, Stevens LA, Schmidt CH, Zhang YL, Castro AF, Feldman HI, et al. A new equation to estimate glomerular filtration rate. Ann Intern Med (Internet). Jun 2009 (citado 5 de Mayo 2014); 150(9):9 Disponible en: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2763564/.         [ Links ]

2. Marx GM, Blake GM, Galani E, Steer CB, Harper SE, Adamson KL, et al. Evaluation of the Cockroft-Gault, Jeliffe and Wright formulae in estimating renal function in elderly cancer patients. Ann. Oncol. 2004;15(2):291-5.         [ Links ]

3. Spruill WJ, Wade WE, Cobb HH III. Continuing the use of the Cockcroft-Gault equation for drug dosing in patients with impaired renal function. Clin Pharmacol Ther. 2009; 86(5):468-70.         [ Links ]

4. Nyman HA, Dowling TC, Hudson JQ, Peter WL, Joy MS, Nolin TD. Comparative evaluation of the Cockroft-Gault equation and the modification of diet in renal disease (MDRD) study equation for drug dosing: an opinion of the Nephrology Practice and Research Network of the American College of Clinical Pharmacy. Pharmacotherapy 2011; 31(11):1130-44.         [ Links ]

5. Graham J. Estimating renal function for drug dosing decisions. Clin Biochem Rev. (Internet). Jul 2011 (citado 5 de Mayo 2014); 32(2):81-88. Disponible en: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3100285/pdf/cbr_32_2_81.pdf.         [ Links ]

6. Drion I, Joosten H, Dikkeschei LD, Groenier KH, Bilo HJ. eGFR and creatinine clearance in relation to metabolic changes in an unselected patient population. Eur J Intern Med. 2009; 20(7): 722-7.         [ Links ]

7. Murillo-GodínezG. La fórmula de Cockcroft-Gault. Rev Med IMSS(Internet). Jul 2005 (citado 5 de Mayo 2014); 43(1): 69-70. Disponible en: http://revistamedica.imss.gob.mx/index.php?option=-com_multicategories&view=article&id=1256:la-formula-de-cockcroft-gault&Itemid=642.         [ Links ]

8. Cirillo M, Anastasio P, De SantoNG. Relationship of gender, age, and body mass index to errors in predicted kidney function. Nephrol Dial Transplant (Internet). Ene 2005 (citado 5 de Mayo 2014); 20(9): 1791-8. Disponible en: http://ndt.oxfordjournals.org/content/20/9/1791.long.         [ Links ]

9. Ali A, Asif N, Rais Z. Estimation of GFR by MDRD Formula and Its Correlation to Cockcroft-Gault Equation in Five Stages of Chronic Kidney Disease. O J Neph.(Internet). Jul 2013 (citado 5 de Mayo 2014); 3(1):37-40. Disponible en: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=29070.         [ Links ]

10. Botev R, Mallié JP, Couchoud C, Schück O, Fauvel JP, Wetzels JF, et al. Estimating glomerular filtration rate: Cockcroft-Gault and Modification of Diet in Renal Disease formulas compared to renal inulin clearance. Clin J Am Soc Nephrol. 2009; 4(5): 899-906.         [ Links ]

11. Gimeno JA, Lou LM, Molinero E, Campos B, Boned B, Sánchez-Vañó R. Concordancia entre las fórmulas de Cockcroft-Gault y del estudio MDRD para estimar la tasa de filtración glomerular en pacientes con diabetes tipo 2. Nefrología (Internet). Ago 2006 (citado 5 de Mayo 2014); 26(5):615-18. Disponible en: http://www.revistanefrologia.com/es-publicacion-nefrologia-articulo-concordancia-entre-las-formulas-cockcroft-gault-del-estudio-mdrd-estimar-X021169950602027X.         [ Links ]

12. Zanocco JA, Nishida SK, Passos MT, Pereira AR, Silva MS, Pereira AB, et al. Race adjustment of Estimating glomerular filtration rate is not always necessary. Nephron Extra.2012; 2(1): 293-302.         [ Links ]

13. Van Denventer HE, George JA, Paikier JE, Becker PJ, Katz IJ. Estimating glomerular filtration rate in black South Africans by use of the modification of diet in renal disease and Cockroft-Gault equations. Clin Chem. 2008; 54(7): 1197-1202.         [ Links ]

14. Rodrigues Ferreira-Filho S, Caetano Cardoso C, Vieira de Castro LA, Mendes Oliveira R, Rodrigues Sá R. Comparison of Measured Creatinine Clearance and Clearances Estimated by Cockcroft-Gault and MDRD Formulas in Patients with a Single Kidney. Int J Nephrol. 2011; Article ID 626178, 4 páginas.         [ Links ]

15. Demirovic JA, Pai AB, Pai MP. Estimation of creatinine clearance in morbidly obese patients. Am J Health Syst Pharm. (Internet) Ene 2009 (citado 5 de Mayo 2014); 66(7):642-8. Disponible en: http://www.ajhp.org/content/66/7/642.         [ Links ]

16. Michels WM, Groontendorst DC, Verduijn M, Elliott EG, Dekker FW, Krediet RT. Performance of the Cockroft-Gault, MDRD and new CDK-EPI formulas in relation to GFR, age and body size. Clin J Am Soc Nephrol. (Internet) Jul 2010 (citado 5 de Mayo 2014);5(10):1003-9. Disponible en: http://cjasn.asnjournals.org/content/5/6/1003.         [ Links ]

17. Moranville MP, Jennings HR. Implications of using modification of diet in renal disease versus Cockcroft-Gault equations for renal dosing adjustments. Am J Health Syst Pharm. 2009;66(2):154-61.         [ Links ]

18. Poggio ED, Wang X, Greene T, Van Lente F, Hall PM. Performance of the Modification of Diet in Renal Disease and Cockcroft-Gault equations in the estimation of GFR in health and in chronic kidney disease. J Am Soc Nephrol. 2005; 16(2): 459-66.         [ Links ]

19. Wilhelm SM, Kale-Pradhan PB. Estimating creatinine clearance: a meta-analysis. Pharmacotherapy.2011; 31(7):658-64.         [ Links ]

20. Winter MA, Guhr KN, Berg GM. Impact of various body weights and serum creatinine concentrations on the bias and accuracy of the Cockcroft-Gault equation. Pharmacotherapy. 2012;32(7):604-12.         [ Links ]

21. Brown DL, Masselink AJ, Lalla CD. Functional range of creatinine clearance for renal drug dosing: a practical solution to the controversy of which weight to use in the Cockcroft-Gault equation. Ann Pharmacother. 2013; 47(7-8):1039-44.         [ Links ]

22. Martínez-González MA, Sánchez-Villegas A, Toledo Atucha E, Faulin Fajardo J. Procedimientos descriptivos en: Bioestadística amigable Tercera Edición. Barcelona, España: Editorial Elsevier; 2014.p 13-63.         [ Links ]

23. Dooley MJ, Singh S, Rischin D. Rounding of low serum creatinine levels and consequent impact on accuracy of bedside estimates of renal function in cancer patients. Br J Cancer. 2004; 90(5): 991-5.         [ Links ]

24. Garg AX, Papaioannou A, Ferko N, Campbell G, Clarke JA, Ray JG. Estimating the prevalence of renal insufficiency in seniors requiring long-term care. Kidney Int. 2004; 65(2):649-53.         [ Links ]

25. Pedone C, Corsonello A, Incalzi RA. Estimating renal function in older people: a comparison of three formulas. Age Ageing. 2006; 35(2): 121-6.         [ Links ]

26. Wright JG, Boddy AV, Highley M, Fenwick J, McGill A, Calvert AH. Estimation of glomerular filtration rate in cancer patients. Br J Cancer. 2001; 84(4): 452-9.         [ Links ]

 

 

Correspondence:
Correo electrónico: jose.chaverri@ucr.ac.cr
(José Miguel Chaverri Fernández).

Recibido: el 16 de febrero de 2015;
Aceptado: el 26 de agosto de 2015.

Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons