Biokmod: An application for solving system of differential equations, fitting coefficients, convolution, and more, with application for modeling Linear and Nonlinear Biokinetic Systems.  Some ICRP biokinetic models are included  . It can be applied in pharmacokinetic, internal dosimetry,  bioassay evaluations,  nuclear medicine and more.

There two version:

A) The classical BIOKMOD.- An Mathematica version that  consists in Mathematica packages and tutorials . It can be downloaded here: BIOKMOD 5.4. This version included the ICRP Models ICRP 66/78 (Biokmod Summary)

B) BIOKMOD web version: It is an updated version of BIOKMOD, including some current OIR Models. You only need a web browser:  Here or below.

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)



M.A. López , J. G. Sánchez-León , C. Hernández , M. Moraleda , J.M. Rodríguez-Díaz , I. Sierra, S. Sierra, D. García.  Improving the reliability of internal dosimetry for uranium workers: application of the ICRP/OIR uranium model to long-term occupational intakes. Radiation Measurements. June 2024.


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. ( )

F 18 model.- Presentation in SEIO 2023


Lopez-Fidalgo J.; Sanchez J. G. ”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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