Skip to main content

pyNS: An Open-Source Framework for 0D Haemodynamic Modelling

Annals of Biomedical Engineering volume 43, pages 1461–1473 (2015)Cite this article

Abstract

A number of computational approaches have been proposed for the simulation of haemodynamics and vascular wall dynamics in complex vascular networks. Among them, 0D pulse wave propagation methods allow to efficiently model flow and pressure distributions and wall displacements throughout vascular networks at low computational costs. Although several techniques are documented in literature, the availability of open-source computational tools is still limited. We here present python Network Solver, a modular solver framework for 0D problems released under a BSD license as part of the archToolkit (http://archtk.github.com). As an application, we describe patient-specific models of the systemic circulation and detailed upper extremity for use in the prediction of maturation after surgical creation of vascular access for haemodialysis.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

43,34 €

Price includes VAT (Finland)
Tax calculation will be finalised during checkout.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

References

  1. Antiga, L., M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. Steinman. An image-based modeling framework for patient-specific computational hemodynamics. Med. Biol. Eng. Comput. 46(11):1097–1112, 2008. cited By (since 1996) 41.

  2. Azer, K., and C. Peskin. A one-dimensional model of blood flow in arteries with friction and convection based on the womersley velocity profile. Cardiovasc. Eng. 7(2):51–73, 2007.

    PubMed  Article  Google Scholar 

  3. Bessems, D., C. Giannopapa, M. Rutten, and F. van de Vosse. Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels. J. Biomech. 41(2):284–291, 2008.

    PubMed  Article  Google Scholar 

  4. Bessems, D., M. Rutten, and F. Van De Vosse. A wave propagation model of blood flow in large vessels using an approximate velocity profile function. J. Fluid Mech. 580:145–168, 2007.

    Article  Google Scholar 

  5. Botti, L., and D. A. Di Pietro. A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure. J. Comput. Phys. 230:572–585, 2011.

    CAS  Article  Google Scholar 

  6. Botti, L., K. Van Canneyt, R. Kaminsky, T. Claessens, R. N. Planken, P. Verdonck, A. Remuzzi, and L. Antiga. Numerical evaluation and experimental validation of pressure drops across a patient-specific model of vascular access for hemodialysis. Cardiovasc. Eng. Technol. 4(4):485–499, 2013.

    Article  Google Scholar 

  7. Caroli, A., S. Manini, L. Antiga, K. Passera, B. Ene-Iordache, S. Rota, G. Remuzzi, A. Bode, J. Leermakers, F. N. van de Vosse, et al. Validation of a patient-specific hemodynamic computational model for surgical planning of vascular access in hemodialysis patients. Kidney Int. 84(6):1237–1245, 2013.

    PubMed  Article  Google Scholar 

  8. Cebral, J., M. Castro, C. Putman, and N. Alperin. Flow-area relationship in internal carotid and vertebral arteries. Physiol. Meas. 29(5):585, 2008.

    CAS  PubMed Central  PubMed  Article  Google Scholar 

  9. Deane, C. R., and H. S. Markus. Colour velocity flow measurement: in vitro validation and application to human carotid arteries. Ultrasound Med. Biol. 23(3):447–452, 1997.

    CAS  PubMed  Article  Google Scholar 

  10. Hendrikse, J., A. F. van Raamt, Y. van der Graaf, W. P. Mali, and J. van der Grond. Distribution of cerebral blood flow in the circle of willis1. Radiology 235(1):184–189, 2005.

    PubMed  Article  Google Scholar 

  11. Huberts, W. Personalized Computational Modeling of Vascular Access Creation. PhD thesis, Biomedical Engineering Department, Maastricht University Medical Center, 2012.

  12. Huberts, W., A. Bode, W. Kroon, R. Planken, J. Tordoir, F. van de Vosse, and E. Bosboom. A pulse wave propagation model to support decision-making in vascular access planning in the clinic. Med. Eng. Phys. 34(2):233–248, 2012.

    CAS  PubMed  Article  Google Scholar 

  13. Huberts, W., E. Bosboom, and F. van de Vosse. A lumped model for blood flow and pressure in the systemic arteries based on an approximate velocity profile function. Math. Biosci. Eng. 6(1):27, 2009.

    PubMed  Article  Google Scholar 

  14. Huberts, W., C. de Jonge, W. van der Linden, M. Inda, J. Tordoir, F. van de Vosse, and E. Bosboom. A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part a: identification of most influential model parameters. Med. Eng. Phys. 35(6):810–826, 2013.

    CAS  PubMed  Article  Google Scholar 

  15. Huberts, W., C. de Jonge, W. van der Linden, M. Inda, K. Passera, J. Tordoir, F. van de Vosse, and E. Bosboom. A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part b: identification of possible generic model parameters. Med. Eng. Phys. 35(6):827–837, 2013.

    CAS  PubMed  Article  Google Scholar 

  16. Hughes, T., and J. Lubliner. On the one-dimensional theory of blood flow in the large vessels. Math. Biosci. 18(6–7):161–170, 1973.

    Article  Google Scholar 

  17. Jager, G. Electrical Model of the Human Systemic Arterial Tree. PhD thesis, Utrecht, RijksUniversity, 1965.

  18. Manini, S., K. Passera, W. Huberts, L. Botti, L. Antiga, and A. Remuzzi. Computational model for simulation of vascular adaptation following vascular access surgery in haemodialysis patients. Comput. Methods Biomech. Biomed. Eng. 17(12):1358–1367, 2014.

    Article  Google Scholar 

  19. Marchandise, E., M. Willemet, and V. Lacroix. A numerical hemodynamic tool for predictive vascular surgery. Med. Eng. Phys. 31(1):131–144, 2009.

    PubMed  Article  Google Scholar 

  20. Mulder, G., A. Bogaerds, P. Rongen, and F. van de Vosse. The influence of contrast agent injection on physiological flow in the circle of willis. Med. Eng. Phys. 33(2):195–203, 2011.

    CAS  PubMed  Article  Google Scholar 

  21. Passera, K., S. Manini, L. Antiga, and A. Remuzzi. Patient-specific model of arterial circulation for surgical planning of vascular access. J. Vasc. Access 14(2):180–192, 2012.

    PubMed  Article  Google Scholar 

  22. Planken, R., X. Keuter, A. Hoeks, J. Kooman, F. Van Der Sande, A. Kessels, T. Leiner, and J. Tordoir. Diameter measurements of the forearm cephalic vein prior to vascular access creation in end-stage renal disease patients: graduated pressure cuff versus tourniquet vessel dilatation. Nephrol. Dial. Transplant. 21(3):802, 2006.

    PubMed  Article  Google Scholar 

  23. Planken, R., X. Keuter, A. Kessels, A. Hoeks, T. Leiner, and J. Tordoir. Forearm cephalic vein cross-sectional area changes at incremental congestion pressures: towards a standardized and reproducible vein mapping protocol. J. Vasc. Surg. 44(2):353–358, 2006.

    PubMed  Article  Google Scholar 

  24. Reymond, P., F. Merenda, F. Perren, D. Rufenacht, and N. Stergiopulos. Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 297(1):H208, 2009.

    CAS  PubMed  Article  Google Scholar 

  25. Segers, P., N. Stergiopulos, P. Verdonck, and R. Verhoeven. Assessment of distributed arterial network models. Med. Biol. Eng. Comput. 35(6):729–736, 1997.

    CAS  PubMed  Article  Google Scholar 

  26. Sherwin, S., L. Formaggia, J. Peiro, and V. Franke. Computational modelling of 1d blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system. Int. J. Numer. Methods Fluids 43(6–7):673–700, 2003.

    Article  Google Scholar 

  27. Steele, B., J. Wan, J. Ku, T. Hughes, and C. Taylor. In vivo validation of a one-dimensional finite-element method for predicting blood flow in cardiovascular bypass grafts. IEEE Trans. Biomed. Eng. 50(6):649–656, 2003.

    PubMed  Article  Google Scholar 

  28. Stergiopulos, N., B. Westerhof, and N. Westerhof. Total arterial inertance as the fourth element of the windkessel model. Am. J. Physiol. Heart Circ. Physiol. 276(1):H81, 1999.

    CAS  Google Scholar 

  29. Tanaka, H., N. Fujita, T. Enoki, K. Matsumoto, Y. Watanabe, K. Murase, and H. Nakamura. Relationship between variations in the circle of willis and flow rates in internal carotid and basilar arteries determined by means of magnetic resonance imaging with semiautomated lumen segmentation: reference data from 125 healthy volunteers. Am. J. Neuroradiol. 27(8):1770–1775, 2006.

    CAS  PubMed  Google Scholar 

  30. Westerhof, N., F. Bosman, C. De Vries, and A. Noordergraaf. Analog studies of the human systemic arterial tree. J. Biomech. 2(2):121–134, 1969.

    CAS  PubMed  Article  Google Scholar 

  31. Westerhof, N., G. Elzinga, and P. Sipkema. An artificial arterial system for pumping hearts. J. Appl. Physiol. 31(5):776, 1971.

    CAS  PubMed  Google Scholar 

  32. Wolters, B., M. Emmer, M. Rutten, G. Schurink, and F. Van De Vosse. Assessment of endoleak significance after endovascular repair of abdominal aortic aneurysms: a lumped parameter model. Med. Eng. Phys. 29(10):1106–1118, 2007.

    CAS  PubMed  Article  Google Scholar 

Download references

Acknowledgments

The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7-ICT-2007-2: Project ARCH n. 224390). Partners of the ARCH Consortium are: IRCCS Mario Negri Institute, Bergamo (IT); Academisch Ziekenhuis Maastricht (NL); Philips Medical Systems, Eindhoven (NL); Philips Research, Eindhoven (NL); Esaote Europe BV, Maastricht (NL); Ghent University (BE); Sheffield University (UK); Lubljana Medical University (SL).

Author information

Affiliations

  1. Orobix Srl, Bergamo, Italy

    Simone Manini & Luca Antiga

  2. Biomedical Engineering Department, IRCCS Mario Negri Institute for Pharmacological Research, Milan, Italy

    Andrea Remuzzi

  3. Industrial Engineering Department, University of Bergamo, Bergamo, Italy

    Lorenzo Botti & Andrea Remuzzi

Authors
  1. Simone Manini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luca Antiga
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lorenzo Botti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrea Remuzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Simone Manini.

Additional information

Associate Editor Diego Gallo oversaw the review of this article.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Manini, S., Antiga, L., Botti, L. et al. pyNS: An Open-Source Framework for 0D Haemodynamic Modelling. Ann Biomed Eng 43, 1461–1473 (2015). https://doi.org/10.1007/s10439-014-1234-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-014-1234-y

Keywords

  • 0D modeling
  • Vascular access
  • Haemodialysis
  • Blood flow adaptation
  • Wall shear stress