Mária ĎURIŠOVÁ, PhD, DSc (Math/Phys)
Department of Pharmacology of Inflammation
Institute of Experimental Pharmacology and Toxicology,
Slovak Academy of Sciences
Slovak Republic, 841 04 Bratislava, Dúbravská cesta 9
Phone/Fax: +4212 5477 5928

The ideas presented at this www site were developed in conjunction with author’s current activities related to COST Action BM0701, and to the European Network of Excellence - Virtual Physiological Human (VPH NoE), under 7th Framework Program for Research and Technological Development of the EU.  These ideas were influenced by author’s previous activities related to COST Actions B15, B22, and B25, and to the European Biosimulation Network of Excellence - a new tool in drug development (BioSim), under 6th Framework Program for Research and Technological Development of the EU.


The undergoing physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much more complicated to be soluble. P.A.M. Dirac (1902-1984,  an English   theoretical physicist).
     In this age, which believes that there is a short cut to everything, the greatest lesson to be learned is that the most difficult way is, in the long run, the easiest. H. Miller (1891-1980, an American novelist).


There are the following highly significant differences in terminology used in biomedicine (e.g. pharmacokinetics, physiology) and terminology used at this www site: 1) The difference between the physiological nature of information conveyed by physiological systems and the functional nature of information conveyed by the systems used at this www site; 2) The difference in the use of the term „dynamic“:  In biomedicine, the term „dynamic“ is commonly used in expressions describing drug actions. At this www site, the term „dynamic“ is  used to indicate   that a system or process changes over time. The terminology differences may trigger misunderstanding for visitors not familiar with the theory of dynamic systems (1-40). Therefore, visitors interested are referred to (2-40). The studies cited here attempted to link the theory of dynamic systems to biomedicine.
Using tools from the dynamic system theory, a drug effect, disposition, dissolution, bioavailability, and many other dynamic processes developing over a period of time (41), can be investigated with the aid of dynamic systems, see e.g.  (2-40). 
An introduction to the general concept of the use of dynamic systems for effective biomedical investigations can be done in a simple fashion using the theoretical example presented below:













The following two assumptions are used: 1) a same drug dose is administered intravenously either by a single bolus, or by a short-term infusion, or by multiple bolus doses, schematically illustrated in the column headed “INPUTS”; 2) physiological properties of the body do not change  during the experiment. The resulting plasma concentration-time profiles of the drug are schematically illustrated in the column headed “OUTPUTS”. If traditional pharmacokinetic modeling methods are used to analyze the data, significantly different models are obtained, due to significantly drug concentration-time profiles. On the contrary, if methods based on the theory of dynamic systems are used, a same model is obtained by taking into account either the single bolus dose, or short-time infusion, or multiple bolus doses. The reason for this is that, the latter model is dependent only on physiological properties of the body and on physicochemical properties of the drug administered, and is not depended on the mode of drug administration.  This very unique property of the latter model suggests that the model is worth to be used in many ways.  For example, to adjust drug dosing aimed at achieving and then maintaining required drug concentration-profiles, as exemplified by continuous infusions of Factor VIII k hemophilia A patients (28).
The principal difference between traditional pharmacokinetic modeling methods and modeling methods that use tools from  the theory of dynamic systems is that the former methods are based on modeling plasma (or blood) concentration-time profiles of drugs, however  the latter methods are based on modeling relationships between drug administrations and resulting plasma (or blood) concentration-time profiles of drugs, see e.g. (2-40).
Software named CTDB has been developed according to the theory of dynamic systems (9). This software has been developed to meet needs of biomedical researchers in the area of mathematical modeling. A demo version of CTDB can be downloaded here:  CTDB


Although the understanding of fundamental principles of modeling methods which use tools from the theory of dynamic systems requires necessary theoretical background knowledge and abstract ways of thinking, potential rewards compensate initial inconveniences. Advances in user sophistication, coupled with the demonstrable benefit, will be important for the enduring success of methods considered in biomedicine. Therefore, the primary concern of this www site is to draw attention of medical scientists, clinicians, and medical students, to mathematically elegant modeling methods based on the dynamic system theory and designed for building mathematical models of various dynamic processes in biomedicine.



  1. Ljung, L.  System identification – theory for the user. 2nd ed. PTR Prentice Hall, Upper Saddle River, 1999, New York, The United States.

  2. Works of the author
    Invited lectures

  3. Dedík, L. System approach for modeling in vitro/in vivo drug absorption, 6th European Congress of Pharmaceutical  Sciences, EUFEPS, 2000, Budapest, Hungary.
  4. Dedík, L. New mathematical approaches in pharmacokinetic studies during phase I and II. 5th Congress of the European Association for Clinical Pharmacology and Therapeutics, 2001, Odense, Denmark.
  5. Dedík, L., Chládek, J. Mathematical modeling of metabolite formation. Symposium COST B15. 51st Meeting of Czech and Slovak Pharmacological Society,  2001, Hradec Králové,  Czech Republic.
  6. Ďurišová, M., Dedík, L., Macheras, P., Mircioiu, C., Modeling of enterohepatic recirculation, 5th Xenobiotic Metabolism and Toxicology Workshop of Balkan Countries, 2002,  Constanta, Romania.
  7. Dedík, L.  In silico-man analysis of the fate of biologically active substances after i.v. and p.o. administration considered from the point of view of human individual identifiable parameters. 56th Meeting of Czech and Slovak Pharmacological Society and COST B25 Meeting, 2006, Bratislava, Slovak Republic
  8. Monograph and contributions in books

  9. Dedík, L., Ďurišová, M. System Approach in Technical, Environmental, and Bio-Medical Studies. Publishing House of Slovak University of Technology, 1999, Bratislava, Slovak Republic.
  10. Dedík,  L.,  Ďurišová, M.   Combination   of modeling  in frequency and time domain  in surrogate endpoint evaluations. In: Proceedings of 3rd MATHMOD, IMACS Symposium on Mathematical Modeling, Vienna.   University of Technology, 563-566,  2000, Vienna, Austria.
  11. Dedík L., Ďurišová M. Advanced system-approach based methods for modeling biomedical systems. In: Lecture Series on Computer and Computational Series I. International Conference of Computational Methods in Science and Engineering. 246-251, 2004, Athens, (Simos, T.E. (ed.)), Brill Academic Publishers, Acton, 2004,  Australia.
  12. Ďurišová, M.,  Dedík, L., Tvrdoňová, M. New computational approach to mathematical modeling in pharmacological research. In: Trends in pharmacological research. 101-110, 2008, Bratislava, Slovak Republic. (view article PDF)
  13. Refereed papers

  14. Dedík, L., Ďurišová, M. General moments in linear pharmacokinetic models. Clin. Res. Regul. Affairs 13, 1996, 199-210.
  15. Dedík, L., Ďurišová, M.  Application of frequency method in pharmacokinetics - a mini review. Anal. Pharmacol. 1, 2000, 59-64 (an invited study for an inauguration issue of the journal).
  16. Ďurišová, M., Dedík, L. New mathematical methods in pharmacokinetic modeling. Basic Clin. Pharmacol. Toxicol. 96, 2005, 335-342. (an invited review)  (view review PDF)
  17. Ďurišová,  M.,  Dedík,  L.  Comparative study  of  human  pentacaine  pharmacokinetics in  time and frequency domain. Methods Find.  Exp. Clin. Parmacol. 16, 1994, 219-232.       (view article abstract)
  18. Dedík, L., Ďurišová,  M. Frequency response method in  pharmacokinetics.  J. Pharmacokinet. Biopharm.  22,   1994, 293-307.  (view article PDF)
  19. Ďurišová,  M.,  Dedík,  L., Balan, M. Building a structured  model of  a complex pharmacokinetic system  with time delays. Bull.  Math. Biol. 57,   1995, 787-808.  (view article PDF)
  20. Dedík, L., Ďurišová,  M. CXT - a programme for analysis of  linear dynamic  systems in the frequency  domain. Int. J. Biomed.  Comput.  39,  1995, 231-241. (view article PDF)
  21. Dedík, L., Ďurišová,  M. New general  formulas for estimation of mean residence time and its variance.   Pharmazie, 52,  1997, 404-405.
  22. Dedík, L., Ďurišová,  M. CXT-MAIN: A software package for  determination of the analytical form of the pharmacokinetic system weighting function.  Comput. Methods Programs Biomed.  51, 1996, 183-192. (view article PDF)
  23. Ďurišová,  M.,  Dedík,  L.  Determination of analytical form  of system  weighting function.  Methods  Find. Exp. Clin. Pharmacol. 18, 1996, 407-412. (view article  abstract)
  24. Ďurišová,  M., Dedík,  L. Modeling in frequency domain used for assessment of  in vivo dissolution profile.  Pharm. Res. 14, 1997, 860-864. (view article PDF)
  25. Ďurišová,  M.,  Dedík,  L.   Bátorová, A., Sakalová, A., Hedera, J.  Pharmacokinetics of  Factor VIII  in hemophilia A  patients assessed by frequency response method. Methods  Find. Exp. Clin. Pharmacol. 20,  1998, 217-226. (view article abstract)
  26. Dedík, L., Ďurišová,  M. Srikusalanukul, W.,  Mc Culagh, P. Model of lymphocyte migration in merino ewes under physiological conditions. Physiol. Res. 48, 1999, 525-528. (view article PDF)
  27. Wimmer, G., Dedík, L.,  Michal, M., Mudríková, A., Ďurišová, M. Numerical simulations of stochastic circulatory models, Bull.  Math. Biol. 61, 1999, 365-377. (view article PDF)
  28. Dedík, L., Ďurišová,  M., Bátorová, A. Weighting function used for adjustment of multiple-bolus drug dosing. Methods  Find. Exp. Clin. Pharmacol. 22, 2000, 543-549. (view article abstract)
  29. Dedík, L., Ďurišová, M.  Modeling drug absorption from enteric-coated granules. Methods Find.  Exp. Clin. Pharmacol. 23, 2001, 213-217. (view article abstract)
  30. Dedík, L., Ďurišová, M.  System-approach methods for modeling and  testing  similarity of  in vitro  dissolutions of  drug dosage formulations. Compt. Methods Programs Biomed.  69, 2002, 49-55.  (view article PDF)
  31. Dedík, L., Ďurišová, M. System approach to modeling metabolite formation from parent drug: A  working example with methotrexate. Methods  Find. Exp. Clin. Pharmacol. 24,  2002, 481-486. (view article abstract)
  32. Ďurišová, M., Dedík, L. A system-approach method for the adjustment of time-varying continuous drug infusion in individual patients. A simulation study. J. Pharmacokinet. Pharmacodyn. 29, 2002, 427-444. (view article PDF)
  33. Dedík, L., Ďurišová, M., Svrček, V.,  Vojtko, R.,   Kristová, V.,  Kriška. M. Computer-based methods for measurement, recording, and modeling vessel responses  in vitro: A pilot study with noradrenaline. Methods  Find. Exp. Clin. Pharmacol.  25,   2003, 441-445. (view article abstract)
  34. Dedík, L., Ďurišová,M.,  Penesová, A. Circulatory model for glucose – insulin  interaction after intravenous administration of glucose  to healthy volunteers.  Klin. Farmakol. Farm. 17,  2003,  132-138. (view article PDF)
  35. Dedík, L., Ďurišová, M., Penesová, A. Model for evaluation of data from oral glucose tolerance test. Klin. Farmakol.  Farm. 17,  2003,    139-144. (view article PDF)
  36. Dedík, L., Ďurišová, M., Bruley, D.F. Modeling behavior of protein C during and after subcutaneous administration. Adv.  Exper. Med.  Biol. 566,   2005,  389-395.
  37. Dedík, L.,  Ďurišová, M., Penesová, A., Miklovičová, D., Tvrdoňová, M. Estimation of influence of gastric emptying on shape of glucose concentration-time profile measured in  oral glucose tolerance test.   Diabetes Res. Clin. Pract.  77,  2007, 377-384. (view article PDF)
  38. Ďurišová, M., Dedík, L., Kristová, V., Vojtko, R. Mathematical model indicates nonlinearity of noradrenaline effect on rat renal artery. Physiol.  Res. 2008, 57, 785-788. (view article PDF)
  39. Tvrdoňová, M.,  Dedík, L.,  Mircioiu, C., Miklovičová, D., Durišová,  M. Physiologically-motivated time-delay model to account for mechanisms underlying enterohepatic circulation of piroxicam in humans. Basic Clin. Pharmacol. Toxicol.,  2009, 104, 35-42. (view article PDF)
  40. Tvrdoňová,  M., Chrenová,  J., Rausová,  Z., Miklovičová, D., Ďurišová,  M., Mircioiu, C., Dedik, L. Novel approach to bioequivalence assessment based on physiologically motivated model. Int. J. Pharm. 2009, 380, 89-95. (view article PDF)
  41. Dedík,  L., Tvrdońová, M., Ďurišová, M.,  Penesová, A., Miklovičová, D.,  M. Kozlovský, M. Computer controlled sequential simulation method: reconsidering evaluation of measurements from frequently sampled intravenous glucose tolerance test. Comput.  Methods  Programs Biomed. 2009, 95, 1-8. (view article PDF)
  42. Chrenová,J.,  Ďurišová, M., Mircioiu, C.,  Dedík, L. Effect of gastric emptying and entero-hepatic circulation on bioequivalence assessment of ranitidine, Methods  Find. Exp. Clin. Pharmacol. 32, 2010, 413-419.  (view article PDF)
  43. Ďurišová, M.  Physiologically based structure of mean residence time. The Sci World J Pharmacology, 2012 (view article PDF)
  44. Ďurišová, M. A physiological view of mean residence times. Gen. Physiol. Biophys. 33, 2014, 75–80 (view article PDF)
  45. Weiss, M., Pang, K., S. Dynamics of drug distribution. I. Role of the second and third curve moments, J. Pharmacokinet.  Biopharm.  20, 1992, 253-278.
  46. Ďurišová M. The use of methods based on the theory of dynamical systems for mathematical modeling in biomedical research, Research 2014;1:732 (view article PDF)
  47. Ďurišová M. Mathematical model of pharmacokinetic behavior of orally administered prednisolone in healthy volunteers, J Pharmaceu Pharmacol, October 2014 Vol.:2, Issue:2 (view article PDF)
  48. Ďurišová M. Another Example of a Successful Use of Computational and Modeling Tools from the Theory of Dynamic Systems in Pharmacokinetic Modeling, J Pharmaceu Pharmacol, January 2015 Vol.:3, Issue:1 (view article PDF)
  49. Ďurišová M. Three Examples Illustrating the Good Performance of an Advanced Mathematical Modeling Method Based on the Theory of Dynamic Systems in Pharmacokinetics, J Pharmaceu Pharmacol, April 2015 Vol.:3, Issue:1 (view article PDF)
  50. Ďurišová M. Further worked out examples that illustrated the successful use of an advanced mathematical modeling method based on the theoryof dynamic systems in pharmacokinetics, International Journal of Recent Scientific Research, Vol. 6, 2015 (view article PDF)
  51. Ďurišová M. Mathematical Models of the Pharmacokinetic Behavior of Cefamandole in Healthy Adult Volunteers after 10 min Intravenous Administration of Cefamadole., International Journal of Drug Development and Research Vol. 7, 2015 (view article PDF)
  52. Ďurišová M. Mathematical Models of the Pharmacokinetic Behavior of Digoxin in Five Healthy Subjects Following Rapid Intravenous Injection of 1 mg of Digoxin, Journal of Developing Drugs Vol. 4 2015 (view arcticle PDF)
  53. Ďurišová, M. Mathematical models of the pharmacokinetic behavior of clindamycin in healthy subjects after oral administration of 150 mg of clindamycin. Int J Drug Dev & Res 7, 2015, 65-68. (view arcticle PDF)
  54. Ďurišová, M. Model based description of the pharmacokinetic behavior of pentobarbital in fasted male volunteers after oral administration of 10 mg of pentobarbital. Clin Exp Pharmacol 2016 6(1) 2016, 1-4 (view arcticle PDF)
  55. Ďurišová, M. Mathematical model of the pharmacokinetic behavior of orally administered erythromycin to healthy adult male volunteers. SOJ Pharm Pharm Sci 3(1) 1-5 (view arcticle PDF)
  56. Ďurišová M. Mathematical Model of the pharmacokinetic behavior of orally administered methylprednisolone to healthy adult male volunteers, J Pharm Nano in press 2016 4(1) 1-6 (view arcticle PDF)
  57. Ďurišová M. Advanced Modeling and Computational Tools from Theory of Dynamic Systems Used in Pharmacokinetics Adv Pharm J 2016 1(1) (view arcticle PDF)
  58. Ďurišová, M. Mathematical Modeling Formation of 7-hydroxymethotrexate from Methotrexate in Patients Undergoing Treatment for Psoriasis with Methotrexate J Drug Metab Toxicol 2016 7(2) 7-2 (view arcticle PDF)
  59. Ďurišová M. Computational analysis of pharmacokinetic behavior of ampicillin. J Appl Bioanal 2016 2 (3) 84-89 (view arcticle PDF)
  60. Ďurišová M. Mathematical model of pharmacokinetic behavior of warfarin. Adv Pharm Clin Trials 2016 1(1) 1-7 (view arcticle PDF)
  61. Ďurišová M. Mathematical models of pharmacokinetic behavior of acetaminophen in rats. J Anal Pharmaceut Res 2016 3(2) 1-6 (view arcticle PDF)

To make the presented information more useful, visitors are kindly invited to send their questions, comments, suggestions, and remarks to the author  exfamadu@savba.sk

This information presented at this www site is current as February 2014. The www site will be updated when new relevant information is available.