Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Watanabe, Sansuke M.; Blanco, Pablo J.; Feijóo, Raúl A.

doi:10.1051/m2an/2012053

Watanabe, Sansuke M. ; Blanco, Pablo J. ; Feijóo, Raúl A.

ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 961-985.

Résumé

A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model comprises 108 arterial segments, with 64 main arteries and 44 perforator arteries, with lumen radii ranging from 0.24 cm - axillary artery- to 0.018 cm - perforator arteries. The modeling of blood flow in deformable vessels is governed by a well-known set of hyperbolic partial differential equations that accounts for mass and momentum conservation and a constitutive equation for the arterial wall. The variational formulation used to solve the problem and the related numerical approach are described. The model rendered consistent pressure and flow rate outputs when compared with patient records already published in the literature. In addition, an application to dimensionally-heterogeneous modeling is presented in which the developed arterial network is employed as an underlying model for a three-dimensional geometry of a branching point to be embedded in order to perform local analyses.

EuDML MR Zbl | 1 citation dans Numdam

DOI : 10.1051/m2an/2012053

Classification : 76Z05, 92C10, 92C30
Mots-clés : hemodynamics, anatomical model, vascular territories, numerical simulation

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Watanabe, Sansuke M.; Blanco, Pablo J.; Feijóo, Raúl A. Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm. ESAIM: Mathematical Modelling and Numerical Analysis , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 961-985. doi : 10.1051/m2an/2012053. https://www.numdam.org/articles/10.1051/m2an/2012053/

Bibliographie
Cité par

[1] J. Alastruey, A.W. Khir, K.S. Matthys, P. Segers, S.J. Sherwin, P.R. Verdonck, K.H. Parker and J. Peiró, Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements. J. Biomech. 44 (2011) 2250-8.

[2] J. Alastruey, K.H. Parker, J. Peiró, S.M. Byrd and S.J. Sherwin, Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J. Biomech. 40 (2007) 1794-805.

[3] B.H. Amundsen, U. Wisloff, J. Helgerud, J. Hoff and S.A. Slordahl, Ultrasound recorded axillary artery blood flow during elbow-flexion exercise. Medicine and science in sports and exercise 34 (2002) 1288-93.

[4] A.P. Avolio, Multi-branched model of the human arterial system. Medical Biolog. Engrg. Comp. 18 (1980) 709-18.

[5] O. Bilge, Y. Pinar, M.A. Ozer and F. Gövsa, A morphometric study on the superficial palmar arch of the hand. Surg. Radiol. Anat.: SRA 28 (2006) 343-50.

[6] P.J. Blanco and R.A. Feijóo, The role of the variational formulation in the dimensionally-heterogeneous modelling of the human cardiovascular system, in Modeling of Physiological Flows, edited by H. Ambrosi, A. Quarteroni and G. Rozza. Springer, Italy (2012) 251-288.

[7] P.J. Blanco, R.A. Feijóo and S.A. Urquiza, A unified variational approach for coupling 3D-1D models and its blood flow applications. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4391-4410. | MR | Zbl

[8] P.J. Blanco, J.S. Leiva, R.A. Feijóo and G.S. Buscaglia, Black-box decomposition approach for computational hemodynamics: One-dimensional models. Comput. Methods Appl. Mech. Engrg. 200 138 (2011) 9-1405. | MR | Zbl

[9] P.J. Blanco, M.R. Pivello, S.A. Urquiza and R.A. Feijóo, On the potentialities of 3D-1D coupled models in hemodynamics simulations. J. Biomech. 42 (2009) 919-930.

[10] P.J. Blanco, P.R. Trenhago, L.G. Fernandes and R.A. Feijóo, On the integration of the baroreflex control mechanism in a heterogeneous model of the cardiovascular system. Int. J. Numer. Methods Biomed. Engng. 28 (2012) 412-433. | MR

[11] P.J. Blanco, S.A. Urquiza and R.A. Feijóo, Assessing the influence of heart rate in local hemodynamics through coupled 3D-1D-0D models. Int. J. Numer. Methods Biomed. Engng. 26 (2010) 890-903. | Zbl

[12] P.J. Blanco, S.M. Watanabe and R.A. Feijóo, Identification of vascular territory resistances in one-dimensional hemodynamics simulations. J. Biomech. 45 (2012) 2066-2073.

[13] V. Casoli, E. Kostopoulos, P. Pélissier, P. Caix, D. Martin and J. Baudet, The middle collateral artery: anatomic basis for the extreme lateral arm flap. Surg. Radiol. Anat.: SRA 26 (2004) 172-7.

[14] S. Chen, D. Xu, M. Tang, H. Ding, W. Sheng and T. Peng, Measurement and analysis of the perforator arteries in upper extremity for the flap design. Surg. Radiol. Anat.: SRA 31 687-93 (2009).

[15] H. Claassen, O. Schmitt, D. Werner, W. Schareck, J.C. Kröger and A. Wree, Superficial arm arteries revisited: Brother and sister with absent radial pulse. Annals of anatomy = Anatomischer Anzeiger: official organ of the Anatomische Gesellschaft 192 (2010) 151-5.

[16] W. Dauber, Pocket Atlas of Human Anatomy by Feneis. Thieme, 5th edition (2007).

[17] T.A. Denton, L. Trento, M. Cohen, R.M. Kass, C. Blanche, S. Raissi, W. Cheng, G.P. Fontana and A. Trento, Radial artery harvesting for coronary bypass operations: neurologic complications and their potential mechanisms. The Journal of thoracic and cardiovascular surgery 121 (2001) 951-6.

[18] F. Duparc, J.M. Muller and P. Fréger, Arterial blood supply of the proximal humeral epiphysis. Surg. Radiol. Anat.: SRA 23 (2001) 185-90.

[19] V.P.S. Fazan, C.T. Borges, J.H. Da Silva, A.G. Caetano and O.A.R. Filho, Superficial palmar arch: an arterial diameter study. J. Anat. 204 (2004) 307-11.

[20] L. Formaggia, D. Lamponi and A. Quarteroni, One-dimensional models for blood flow in arteries. J. Engrg Math. 47 (2003) 251-276. | MR | Zbl

[21] L. Formaggia, A. Moura and F. Nobile, On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. ESAIM: M2AN 41 (2007) 743-769. | Numdam | MR | Zbl

[22] L. Formaggia, F. Nobile, A. Quarteroni and A. Veneziani, Computing and Visualization in Science Regular article Multiscale modelling of the circulatory system: a preliminary analysis. 83 (1999) 75-83. | Zbl

[23] M. Haerle, F. Tonagel and H.E. Schaller, Collateral arterial pathways in the forearm. Surg. Radiol. Anat.: SRA 26 (2004) 208-11.

[24] K.R.S. Holzbaur, W.M. Murray, G.E. Gold and S.L. Delp, Upper limb muscle volumes in adult subjects. J. Biomech. (2007) 742-749.

[25] T.J.R. Hughes and J. Lubliner, On the one-dimensional theory of blood flow in the larger vessels. Math. Biosci. 18 (1973) 161-170. | Zbl

[26] H.J. Kim, I.E. Vignon-Clementel, C.A. Figueroa, J.F. Ladisa, K.E. Jansen, J.A. Feinstein and C.A. Taylor, On coupling a lumped parameter heart model and a three-dimensional finite element aorta model 37 (2009) 2153-2169.

[27] K. Knobloch, S. Tomaszek, A. Lichtenberg, M. Karck and A. Haverich, Long-term palmar microcirculation after radial artery harvesting: an observational study. The Annal. Thorac. Surg. 81 (2006) 1700-7.

[28] C.A.D. Leguy, E.M.H. Bosboom, A.S.Z. Belloum, A.P.G. Hoeks and F.N. Van De Vosse, Global sensitivity analysis of a wave propagation model for arm arteries. Medical Engrg. Phys. 33 (2011) 1008-16.

[29] J.S. Leiva, P.J. Blanco and G.C. Buscaglia, Partitioned analysis for dimensionally-heterogeneous hydraulic networks. SIAM Multiscale Model. Simulat. 9 (2011) 872-903. | MR | Zbl

[30] R.C. Mahabir, J.S. Williamson, N.J. Carr and D.J. Courtemanche, Vascular Resistance in Human Muscle Flaps. Annal. Plast. Surg. 47 (2001) 148-152.

[31] K.L. Moore, A.F. Dalley and A.M.R. Agur, Clinically Oriented Anatomy. Wolters Kluwer, 6th edition (2010).

[32] S.F. Morris, M. Tang, K. Almutari, C. Geddes and D. Yang, The anatomic basis of perforator flaps. Clinics in plastic surgery 37 (2010) 553-70.

[33] F.H. Netter, Atlas of Human Anatomy. Elsevier, 5th edition (2011).

[34] M.S. Olufsen, Structured tree outflow condition for blood flow in larger systemic arteries. Amer. J. Phys. 276 (1999) H257-68.

[35] S. Omokawa, Y. Tanaka, J. Ryu and V.L. Kish, The anatomical basis for reverse first to fifth dorsal metacarpal arterial flaps. J. Hand Surgery (Edinburgh, Scotland) 30 (2005) 40-4.

[36] M.F. O'Rourke and W.W. Nichols, McDonald's Blood Flow in Arteries - Theoretical, Experimental and Clinical Principles. Arnold, 4th edition (1998).

[37] C.D. Prevel, H.S. Matloub, Z. Ye, J.R. Sanger and N.J. Yousif, The extrinsic blood supply of the ulnar nerve at the elbow: an anatomic study. The J. Hand Surgery 18 (1993) 433-8.

[38] P. Reymond, F. Merenda, F. Perren, D. Rüfenacht and N. Stergiopulos, Validation of a one-dimensional model of the systemic arterial tree. Amer. J. Physiol. Heart circulatory Physiol. 297 (2009) H208-22.

[39] A.G. Royse, G.S. Chang, D.M. Nicholas and C.F. Royse, No late ulnar artery atheroma after radial artery harvest for coronary artery bypass surgery. The Annal. Thoracic Surgery 85 (2008) 891-4.

[40] M. Sauerbier and F. Unglaub, Perforator flaps in the upper extremity. Clinics in plastic Surg. 37 (2010) 667-76.

[41] I. Schafhalterzoppoth and A. Gray, The Musculocutaneous Nerve: Ultrasound Appearance for Peripheral Nerve Block. Regional Anesthesia and Pain Medicine 30 (2005) 385-390.

[42] T.F. Sherman, On Connecting Large Vessels to Small The Meaning of Murray's Law. J. General Physiol. (1981).

[43] N. Stergiopulos, D.F. Young and T.R. Rogge, Computer simulation of arterial flow with applications to arterial and aortic stenoses. J. Biomech. 25 (1992) 1477-1488.

[44] G. Taylor, The angiosomes of the body and their supply to perforator flaps. Clin. Plast. Surg. 30 (2003) 331-342.

[45] S. Trager, M. Pignataro, J. Anderson and J.M. Kleinert, Color flow Doppler: imaging the upper extremity. J. Hand Surg. 18 (1993) 621-5.

[46] S.A. Urquiza, P.J. Blanco, M.J. Vénere and R.A. Feijóo, Multidimensional modelling for the carotid artery blood flow. Comput. Methods Appl. Mech. Engrg. 195 (2006) 4002-4017. | MR | Zbl

[47] G. Walther, S. Nottin, M. Dauzat and P. Obert, Femoral and axillary ultrasound blood flow during exercise: a methodological study. Med. Sci. Sports Exerc. 38 (2006) 1353.

[48] J.J. Wang and K.H. Parker, Wave propagation in a model of the arterial circulation. J. Biomech. 37 (2004) 457-70.

[49] G. Wavreille, J. Bricout, S. Mouliade, S. Lemoine, G. Prodhomme, P. Khanchandani, C. Chantelot and C. Fontaine, Anatomical bases of the free posterior brachial fascial flap. Surg. Radiol. Anat.: SRA 32 (2010) 393-9.

[50] G. Wavreille, C. Dos Remedios, C. Chantelot, M. Limousin and C. Fontaine, Anatomic bases of vascularized elbow joint harvesting to achieve vascularized allograft. Surg. Radiol. Anat.: SRA 28 (2006) 498-510.

[51] F.H. Zhang, S.G. Topp, W.J. Zhang, H.P. Zheng and F. Zhang, Anatomic study of distally based pedicle compound flaps with nutrient vessels of the cutaneous nerves and superficial veins of the forearm. Microsurgery 26 (2006) 373-385.

Dalmaso, Caterina; Fossan, Fredrik Eikeland; Bråten, Anders Tjellaug; Müller, Lucas Omar Uncertainty Quantification and Sensitivity Analysis for Non‐invasive Model‐Based Instantaneous Wave‐Free Ratio Prediction, International Journal for Numerical Methods in Biomedical Engineering, Volume 41 (2025) no. 1 | DOI:10.1002/cnm.3898
Blanco, Pablo J.; Müller, Lucas O. One‐Dimensional Blood Flow Modeling in the Cardiovascular System. From the Conventional Physiological Setting to Real‐Life Hemodynamics, International Journal for Numerical Methods in Biomedical Engineering, Volume 41 (2025) no. 3 | DOI:10.1002/cnm.70020
Cowley, James; Kyeremeh, Justicia; Stewart, Grant D.; Luo, Xichun; Shu, Wenmiao; Kazakidi, Asimina Near Real-Time Estimation of Blood Loss and Flow–Pressure Redistribution during Unilateral Nephrectomy, Fluids, Volume 9 (2024) no. 9, p. 214 | DOI:10.3390/fluids9090214
Krivovichev, Gerasim V. The splitting-based semi-implicit finite-difference schemes for simulation of blood flow in arteries, Computers Fluids, Volume 266 (2023), p. 106049 | DOI:10.1016/j.compfluid.2023.106049
Rao, V. Sree Hari; Radhika, T. S. L. The Dynamics of the Flow of Blood in the Human Circulatory System, Differential Equations and Dynamical Systems, Volume 31 (2023) no. 3, p. 673 | DOI:10.1007/s12591-022-00617-8
Cowley, James; Luo, Xichun; Stewart, Grant D.; Shu, Wenmiao; Kazakidi, Asimina A Mathematical Model of Blood Loss during Renal Resection, Fluids, Volume 8 (2023) no. 12, p. 316 | DOI:10.3390/fluids8120316
Argus, Finbar; Zhao, Debbie; Babarenda Gamage, Thiranja P.; Nash, Martyn P.; Maso Talou, Gonzalo D. Automated model calibration with parallel MCMC: Applications for a cardiovascular system model, Frontiers in Physiology, Volume 13 (2022) | DOI:10.3389/fphys.2022.1018134
Heusinkveld, Maarten H. G.; Holtackers, Robert J.; Adriaans, Bouke P.; Op’t Roodt, Jos; Arts, Theo; Delhaas, Tammo; Reesink, Koen D.; Huberts, Wouter Complementing sparse vascular imaging data by physiological adaptation rules, Journal of Applied Physiology, Volume 130 (2021) no. 3, p. 571 | DOI:10.1152/japplphysiol.00250.2019
Shahidi, Niloofar; Pan, Michael; Safaei, Soroush; Tran, Kenneth; Crampin, Edmund J.; Nickerson, David P.; Beard, Daniel A. Hierarchical semantic composition of biosimulation models using bond graphs, PLOS Computational Biology, Volume 17 (2021) no. 5, p. e1008859 | DOI:10.1371/journal.pcbi.1008859
Viallon, Marie‐Claude Domain decomposition methods in a geometrical multiscale domain using finite volume schemes, International Journal for Numerical Methods in Fluids, Volume 92 (2020) no. 5, p. 391 | DOI:10.1002/fld.4788
Fiore, Sandro; Elia, Donatello; Blanquer, Ignacio; Brasileiro, Francisco V.; Nuzzo, Alessandra; Nassisi, Paola; Rufino, Iana A.A.; Seijmonsbergen, Arie C.; Anders, Niels S.; de O. Galvão, Carlos; de B.L. Cunha, John E.; Caballer, Miguel; Sousa-Baena, Mariane S.; Canhos, Vanderlei P.; Aloisio, Giovanni BioClimate: A Science Gateway for Climate Change and Biodiversity research in the EUBrazilCloudConnect project, Future Generation Computer Systems, Volume 94 (2019), p. 895 | DOI:10.1016/j.future.2017.11.034
van den Boom, Tim; Stevens, Raoul; Delhaas, Tammo; van de Vosse, Frans; Huberts, Wouter Zero‐dimensional lumped approach to incorporate the dynamic part of the pressure at vessel junctions in a 1D wave propagation model, International Journal for Numerical Methods in Biomedical Engineering, Volume 34 (2018) no. 9 | DOI:10.1002/cnm.3116
Sazonov, Igor; Khir, Ashraf W.; Hacham, Wisam S.; Boileau, Etienne; Carson, Jason M.; van Loon, Raoul; Ferguson, Colin; Nithiarasu, Perumal A novel method for non-invasively detecting the severity and location of aortic aneurysms, Biomechanics and Modeling in Mechanobiology, Volume 16 (2017) no. 4, p. 1225 | DOI:10.1007/s10237-017-0884-8
Quanyu, Wu; Xiaojie, Liu; Lingjiao, Pan; Weige, Tao; Chunqi, Qian SIMULATION ANALYSIS OF BLOOD FLOW IN ARTERIES OF THE HUMAN ARM, Biomedical Engineering: Applications, Basis and Communications, Volume 29 (2017) no. 04, p. 1750031 | DOI:10.4015/s1016237217500314
Carson, Jason; Van Loon, Raoul An implicit solver for 1D arterial network models, International Journal for Numerical Methods in Biomedical Engineering, Volume 33 (2017) no. 7 | DOI:10.1002/cnm.2837
Budiawan, Inge Wijayanti; Mungkasi, Sudi Finite volume numerical solution to a blood flow problem in human artery, Journal of Physics: Conference Series, Volume 795 (2017), p. 012042 | DOI:10.1088/1742-6596/795/1/012042
Obeid, Hasan; Soulat, Gilles; Mousseaux, Elie; Laurent, Stéphane; Stergiopulos, Nikos; Boutouyrie, Pierre; Segers, Patrick Numerical assessment and comparison of pulse wave velocity methods aiming at measuring aortic stiffness, Physiological Measurement, Volume 38 (2017) no. 11, p. 1953 | DOI:10.1088/1361-6579/aa905a
Korade, Ivan; Virag, Zdravko; Krizmanić, Severino A fast method for solving a linear model of one-dimensional blood flow in a viscoelastic arterial tree, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, Volume 231 (2017) no. 3, p. 203 | DOI:10.1177/0954411916688718
Brasileiro, Francisco; Vivas, Jose Luis; Farias Da Silva, Giovanni; Lezzi, Daniele; Diaz, Carlos; Badia, Rosa M.; Caballer, Miguel; Blanquer, Ignacio, 2016 30th International Conference on Advanced Information Networking and Applications Workshops (WAINA) (2016), p. 165 | DOI:10.1109/waina.2016.128
Trenhago, Paulo Roberto; Fernandes, Luciano Gonçalves; Müller, Lucas Omar; Blanco, Pablo Javier; Feijóo, Raúl Antonino An integrated mathematical model of the cardiovascular and respiratory systems, International Journal for Numerical Methods in Biomedical Engineering, Volume 32 (2016) no. 1 | DOI:10.1002/cnm.2736
Müller, Lucas O.; Blanco, Pablo J.; Watanabe, Sansuke M.; Feijóo, Raúl A. A high‐order local time stepping finite volume solver for one‐dimensional blood flow simulations: application to the ADAN model, International Journal for Numerical Methods in Biomedical Engineering, Volume 32 (2016) no. 10 | DOI:10.1002/cnm.2761
Müller, Lucas O.; Leugering, Günter; Blanco, Pablo J. Consistent treatment of viscoelastic effects at junctions in one-dimensional blood flow models, Journal of Computational Physics, Volume 314 (2016), p. 167 | DOI:10.1016/j.jcp.2016.03.012
Safaei, Soroush; Bradley, Christopher P.; Suresh, Vinod; Mithraratne, Kumar; Muller, Alexandre; Ho, Harvey; Ladd, David; Hellevik, Leif R.; Omholt, Stig W.; Chase, J. Geoffrey; Müller, Lucas O.; Watanabe, Sansuke M.; Blanco, Pablo J.; de Bono, Bernard; Hunter, Peter J. Roadmap for cardiovascular circulation model, The Journal of Physiology, Volume 594 (2016) no. 23, p. 6909 | DOI:10.1113/jp272660
Perdikaris, Paris; Grinberg, Leopold; Karniadakis, George Em. An Effective Fractal-Tree Closure Model for Simulating Blood Flow in Large Arterial Networks, Annals of Biomedical Engineering, Volume 43 (2015) no. 6, p. 1432 | DOI:10.1007/s10439-014-1221-3
Viallon, Marie-Claude Error estimate for a finite volume scheme in a geometrical multi-scale domain, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 49 (2015) no. 2, p. 529 | DOI:10.1051/m2an/2014042
Kahveci, Kamil; Becker, Bryan R. A numerical model of pulsatile blood flow in compliant arteries of a truncated vascular system, International Communications in Heat and Mass Transfer, Volume 67 (2015), p. 51 | DOI:10.1016/j.icheatmasstransfer.2015.06.010
Boileau, Etienne; Nithiarasu, Perumal; Blanco, Pablo J.; Müller, Lucas O.; Fossan, Fredrik Eikeland; Hellevik, Leif Rune; Donders, Wouter P.; Huberts, Wouter; Willemet, Marie; Alastruey, Jordi A benchmark study of numerical schemes for one‐dimensional arterial blood flow modelling, International Journal for Numerical Methods in Biomedical Engineering, Volume 31 (2015) no. 10 | DOI:10.1002/cnm.2732
Romaniuk, Ryszard S.; Pieniak, Marcin; Piechna, Adam; Cieślicki, Krzysztof, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2015, Volume 9662 (2015), p. 96621S | DOI:10.1117/12.2205912
Blanco, Pablo J.; Watanabe, Sansuke M.; Dari, Enzo A.; Passos, Marco Aurélio R. F.; Feijóo, Raúl A. Blood flow distribution in an anatomically detailed arterial network model: criteria and algorithms, Biomechanics and Modeling in Mechanobiology, Volume 13 (2014) no. 6, p. 1303 | DOI:10.1007/s10237-014-0574-8
Blanco, P. J.; de Queiroz, R. A. B.; Feijóo, R. A. A computational approach to generate concurrent arterial networks in vascular territories, International Journal for Numerical Methods in Biomedical Engineering, Volume 29 (2013) no. 5, p. 601 | DOI:10.1002/cnm.2547

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