Mathematical model of blood flow in an anatomically detailed arterial network of the arm

ESAIM: Mathematical Modelling and Numerical Analysis

Volumn 47, Issue 4, 2013, Pages 961-985

  Watanabe, Sansuke M ^a,b,c   Blanco, Pablo J ^b,c   Feijoó, Raúl A ^b,c  

^a UNIVERSIDADE FEDERAL RURAL DE PERNAMBUCO   (Brazil)

^b LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^c National Institute in Medicine Assisted by Scientific Computing   (Brazil)

Author keywords

Anatomical model; Hemodynamics; Numerical simulation; Vascular territories

Indexed keywords

BLOOD; BLOOD VESSELS; COMPUTER SIMULATION; DISTRIBUTED PARAMETER CONTROL SYSTEMS; HEMODYNAMICS; PERFORATORS; PHYSIOLOGICAL MODELS;

ANATOMICAL MODELING; HETEROGENEOUS MODELING; HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION; MODELING OF BLOOD FLOW; MOMENTUM CONSERVATIONS; THREE DIMENSIONAL GEOMETRY; VARIATIONAL FORMULATION; VASCULAR TERRITORIES;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 84877589274     PISSN: 28227840     EISSN: 28047214     Source Type: Journal    
DOI: 10.1051/m2an/2012053     Document Type: Article

References (51)

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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.