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Laboratory of Mathematical Modeling of Physiological Processes

Joanna Stachowska-Piętka, PhD - Head of Lab.
Prof. Jacek Waniewski, PhD, DSc
Prof. Leon Bobrowski, PhD, DSc
Małgorzata Dębowska, PhD
Jan Poleszczuk, PhD
Mauro Pietribiasi, MSc
Leszek Pstraś, MSc
Zofia Rudnicka, MSc
Grzegorz Wojdyga, MSc

Current Research Activities

  • The analysis of dialysis adequacy indices carried out previously for urea and creatinine (standard markers of dialysis efficiency) has now been extended to other solutes such as phosphates and calcium. A significant differences were found between the kinetics of phosphates and standard markers within the weekly cycle of hemodialysis. Clinical data (including solutes concentrations in blood and dialysate, measurements on body water distribution) allow to estimate the effectiveness of dialysis, the validation of kinetic models and are the basis for physiological interpretation of models parameters (M. Dębowska, J. Poleszczuk and J. Waniewski in collaboration with Karolinska Institutet, Stockholm, Sweden, and Medical University of Lublin).
  • Treatment outcomes and clinical problems often depend, in a complex way, on many interacting factors of various types. An example of such a relationship is chronic kidney disease (CKD) with related complications such as diabetes mellitus, inflammation, protein energy wasting, cardiovascular disease. Anthropometric, demographic, diet, blood biomarkers, genotype (single nucleotide polymorphism, SNP) and other data as well as physiological parameters obtained from mathematical models are analyzed in patients in various stages of CKD including those treated by hemodialysis or peritoneal dialysis. Extensive statistical analysis and various bioinformatics methods are applied to determine factors associated with treatment outcomes and clinical complications (M. Dębowska, M. Pietribiasi, J. Stachowska-Piętka, J. Poleszczuk and J. Waniewski in collaboration with Laboratory of Biostatistics IBBE PAS, Karolinska Institutet, Stockholm, Sweden and Hospital de Especialidades, Centro Medico Nacional Siglo XXI, Mexico City, Mexico).
  • One method used for the treatment of end stage renal disease is peritoneal dialysis that uses peritoneal cavity to remove the end products of metabolism and excess water. In peritoneal dialysis the tissue surrounding peritoneal cavity (including lymphatic and blood vessels) constructs a complex system for fluid and solute transport. In a phenomenological approach this complex system is considered as semi-permeable membrane and enabling estimation of the basic transport parameters. Phenomenological models, as classical membrane model and three-pore model are used in clinical trials and experiments in order to find the parameters that characterize transport properties of peritoneal system as well as the effectiveness of the therapy. Various aspects of water and solute transports are analyzed based on clinical and experimental data using phenomenological approach and statistical methods (J.Stachowska-Piętka, J. Poleszczuk, M. Dębowska, J. Waniewski in collaboration with University of Warsaw, Karolinska Institutet, Stockholm, Sweden, University of Gothenburg, Sweden, Hospital de Especialidades, Centro Medico Nacional Siglo XXI, Mexico City, Mexico, Keele University, UK,  Hospital Universitari,  Barcelona, Spain)
  • To characterize patients’ response to the fast removal of water during hemodialysis - the mathematical models that describe water shift between body compartment are developing. The main areas of interests are the kinetic of serum proteins (e.g. albumin), and the main solutes of plasma as sodium, potassium and chloride. (M. Pietribiasi, J. Waniewski, in collaboration with Karolinska Institutet, Stockholm, Sweden, and Medical University of Lublin).
  • Around 30% patients on haemodialysis experience highly undesired hypotensive episodes during the dialysis sessions. In order to study this phenomenon, a mathematical model of the cardiovascular response to haemodialysis is being developed. The model will describe the mechanisms of water and solute transport between different body compartments and the mechanisms of blood pressure regulation responding to blood volume changes during haemodialysis (L. Pstraś, J. Waniewski).

Key words: mathematical modelling, computer simulations, physiology, hemodialysis, peritoneal dialysis, dialysis adequacy, peritoneal transport, compartment models, kinetic modelling, diffusion, convection

External funding

  1. Project 2014/15/N/ST7/05316 “Mathematical modelling of fluid and electrolytes transport in patients on hemodialysis” founded by the National Science Centre (Poland), 2015-2017.
  2. Project 2013/11/B/ST7/01704 „Mathematical modeling of pulse-wave propagation for cardiovascular diagnostics in patients on hemodialysis” in collaboration with Medical University of Lublin, founded by the National Science Centre (Poland), 2014-2017.
  3. Project 2898/B/T02/2011/40 „ Evaluation of disturbances of calcium-phosphate management in patients on dialysis” in collaboration with Medical University of Lublin, founded by the National Science Centre (Poland), 2011-2014.
  4. Long-term Swedish - Polish research project to support the costs of collaboration between IBIB PAN and Karolinska Institutet, Divisions of Baxter Novum and Renal Medicine (Project Novum-IBBE, running).

Selected publications

  1. Debowska M, Poleszczuk J, Wojcik-Zaluska A, Ksiazek A, Zaluska W. Phosphate kinetics during weekly cycle of hemodialysis sessions: application of mathematical modeling. Artif Organs 2015; DOI: 10.1111/aor.12489.
  2. Debowska M, Wojcik-Zaluska A, Ksiazek A, Zaluska W, Waniewski J. Phosphate, urea and creatinine clearances: haemodialysis adequacy assessed by weekly monitoring. Nephrol Dial Transplant 2015; 30:129-36.
  3. Debowska M, Paniagua R, Ventura MD, Avila-Diaz M, Prado-Uribe C, Mora C, García-López E, Qureshi AR, Lindholm B, Waniewski J. Dialysis adequacy indices and body composition in male and female patients on peritoneal dialysis. Perit Dial Int 2014; 34(4):417-25.
  4. Waniewski J, Debowska M, Lindholm B. Are dialysis adequacy indices independent of solute generation rate? ASAIO Journal 2014; 60(1):90-4.
  5. Bobrowski L, Lukaszuk T, Lindholm B, Stenvinkel P, Heimburger O, Axelsson J, Bárány P, Carrero JJ, Qureshi AR, Luttropp K, Debowska M, Nordfors L, Schalling M, Waniewski J. Selection of genetic and phenotypic features associated with inflammatory status of patients on dialysis using relaxed linear separability method. PLoS One 2014; 28; 9(1).
  6. Pietribiasi M, Katzarski K, Galach M, Stachowska-Piętka J, Schneditz D, Lindholm B and Waniewski J. Kinetics of plasma refilling during hemodialysis sessions with different initial fluid status. ASAIO J 2015; DOI: 10.1097/MAT.0000000000000206.
  7. Waniewski J, Poleszczuk J, Antosiewicz S, Baczynński D, Gałach, M, Pietribiasi M and Wanńkowicz Z. Can the three pore model correctly describe peritoneal transport of protein? ASAIO J 2014; 60(5):576-81.
  8. Waniewski J, Paniagua R, Stachowska-Pietka J, Ventura MD, Avila-Diaz M, Prado-Uribe C, Mora C, Garcia-Lopez E, Lindholm B: Threefold peritoneal test of osmotic conductance, ultrafiltration efficiency, and fluid absorption. Perit Dial Int 2013;33:419-425.
  9. Stachowska-Pietka J, Waniewski J, Flessner MF, Lindholm B: Computer simulations of osmotic ultrafiltration and small-solute transport in peritoneal dialysis: A spatially distributed approach. Am J Physiol Renal Physiol 2012;302:F1331-1341.
  10. Waniewski J, Cherniha R, Stachowska-Pietka J. A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis. International Journal of Applied Mathematics and Computer Science. 2014; Vol. 24, No. 4.
  11. Pstras L, Thomaseth K, Waniewski J, Balzani I, Bellavere F: The valsalva manoeuvre: Physiology and clinical examples. Acta Physiol (Oxf) 2016;217:103-119.



Nalecz Institute of Biocybernetics and Biomedical Engineering Polish Academy of Sciences
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