Biokmod: A Mathematica toolbox for solving system of differential equations, fitting coefficients, convolution, and more, with application for modeling Linear and Nonlinear Biokinetic Systems.   It included the current ICRP biokinetic models. It can be applied in pharmacokinetic, internal dosimetry,  bioassay evaluations,  nuclear medicine and more. This toolbox consist in Mathematica packages and tutorials . It can be downloaded here:BIOKMOD 5.4 (New, Mathematica 10 or later is required) or download the previous version here: BIOKMOD 5.3

Biokmod Summary

If you wish to be informed when Biokmod is updated or if you find some error, send a e-mail to the author Guillermo Sánchez (guillermo(at) writing in the subject: Subcribe Biokmod . Any comment will be wellcome.

BIOKMODWEB is a web application (you only need a webrowser) including some of the feactures of BIOKMOD. 

Click here: BIOKMODWEB (note: it is a new URL:


Compartmental Modeling. Constant rate transfers

Compartmental Modeling. Variable rate transfers

Estimation of unknown unknown intaken using a kind of bioassay (new ICRP 130/134/137 biokinectic model are used)

Estimation of an unknown intaken using two kind of bioassay (new ICRP 130/134/137 biokinectic model are used)

SEIO2023   F 18



Sánchez-León Guillermo.; López M.A.; Moraleda M.; Rodríguez-Díaz Juan M.: ”Bioassays in workers exposed to long time random intakes” Radiation and Applied Radiation and Isotopes (180) 2022. ( )


Lopez-Fidalgo J. G. Sanchez. ”Optimal bioassay time allocations for multiple accidental chronic intakes of radioactive particles“ Stochastic Environmental Research and Risk Assessment. March 2019, Volume 33, Issue 3, pp 905–914 |.


Juan M. Rodríguez-Díaz; G. Sánchez León: “Optimal designs for multiresponse models with double covariance structure” Chemometrics and Intelligent Laboratory Systems. Volume 189, 15 June 2019, Pages 1-7 (


Juan M. Rodríguez‑Díaz ; G. Sánchez León; “Efficient parameter estimation in multiresponse models measuring radioactivity retention” Radiation and Environmental Biophysics May 2019, Volume 58, Issue 2, pp 167–182. (


Juan M. Rodríguez-Díaz; Sánchez León G:”Design optimality for models defined by a system of ordinary differential equations” Biometrical Journal 56 (5), pag 886–900, September 2014 (Download=>)


G. Sánchez León ; J. M. Rodríguez-Díaz. Optimal design and mathematical model applied to establish bioassay programs”: Radiation Protection Dosimetry. doi:10.1093/rpd/ncl499. 2007. ISSN/ISBN: ISSN 1742-3406 (Download=>)


Sanchez-Leon G; Fitting bioassay data and performing uncertainty analysis with BIOKMOD. Health Physics. 92(1):64-72. 2007.


Lopez-Fidalgo J Rodriguez-Díaz J.M.,Sánchez León G; G., Santos-Martín M.T. Optimal designs for compartmental models with correlated observations” Journal of Applied Statistic. 32, 2006 ISSN/ISBN: 0266-4763 (Download=>)


Sánchez León G; Biokmod: A Mathematica toolbox for modeling Biokinetic Systems”. Mathematica in Education and Research: 10 (2) 2005. ISSN/ISBN: 1096-3324 (Download=>)


Lopez-Fidalgo J; Sánchez G; Statistical Criteria to Establish Bioassay Programs. Health Physics.. 89 (4). 2005. ISSN/ISBN: 0017-9078(Download=>)






Sánchez-León, G; “Simulación de la distribución de sustancias radiactivas en el organismo” ( del ciclo “Más Temáticas” del Departamento de Matemáticas de la Universidad de Salamanca.   2019-10-4.

Sanchez-Leon G;. Modelización biocinética y dosimetría interna. Aplicaciones con Biokmod. Seminario CIEMAT. Madrid 2015

Sanchez-Leon G;.  MODELIZACIÓN DE LA DISTRIBUCIÓN DE ISÓTOPOS RADIACTIVOS Y FÁRMACOS EN EL ORGANISMO.Universidad Católica de Santiago de Chile. 7 de junio de 2016

Sanchez-Leon G;.  BIOKMOD y BIOKMODWED. Aplicación a la modelización biocinética y farmacocinética. BIOSTATNET. Santiago de Compostela. 20-21 de enero de 2017



Sanchez-Leon G; Mathematica Beyond Mathematics: The Wolfram Language in the Real World. 2nd Edition. Chapman and Hall/CRC. 2023.


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