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Mathematical Model of Blood Flow in an Anatomically DetailedArterial Network of the Arm

Published online by Cambridge University Press:  13 June 2013

Sansuke M. Watanabe ,
Pablo J. Blanco  and
Raúl A. Feijóo
Sansuke M. Watanabe
Affiliation:
Universidade Federal Rural de Pernambuco, Unidade Acadêmica de Garanhuns, Garanhuns, Brazil.. [email protected] Laboratório Nacional de Computação Científica, LNCC, Petrópolis, Brazil.; [email protected]; [email protected]; [email protected] Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica, INCT-MACC, Petrópolis, Brazil.
Pablo J. Blanco
Affiliation:
Laboratório Nacional de Computação Científica, LNCC, Petrópolis, Brazil.; [email protected]; [email protected]; [email protected] Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica, INCT-MACC, Petrópolis, Brazil.
Raúl A. Feijóo
Affiliation:
Laboratório Nacional de Computação Científica, LNCC, Petrópolis, Brazil.; [email protected]; [email protected]; [email protected] Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica, INCT-MACC, Petrópolis, Brazil.
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Abstract

A distributed-parameter (one-dimensional) anatomically detailed model for the arterialnetwork of the arm is developed in order to carry out hemodynamics simulations. This workfocuses on the specific aspects related to the model set-up. In this regard, stringentanatomical and physiological considerations have been pursued in order to construct thearterial topology and to provide a systematic estimation of the involved parameters. Themodel 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 – perforatorarteries. The modeling of blood flow in deformable vessels is governed by a well-known setof hyperbolic partial differential equations that accounts for mass and momentumconservation and a constitutive equation for the arterial wall. The variationalformulation used to solve the problem and the related numerical approach are described.The model rendered consistent pressure and flow rate outputs when compared with patientrecords already published in the literature. In addition, an application todimensionally-heterogeneous modeling is presented in which the developed arterial networkis employed as an underlying model for a three-dimensional geometry of a branching pointto be embedded in order to perform local analyses.

Keywords

Hemodynamicsanatomical modelvascular territoriesnumerical simulation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 4: Direct and inverse modeling of the cardiovascular and respiratory systems , July 2013 , pp. 961 - 985
Copyright
© EDP Sciences, SMAI, 2013

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References

Alastruey, J., Khir, A.W., Matthys, K.S., Segers, P., Sherwin, S.J., Verdonck, P.R., Parker, K.H. and Peiró, J., 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. Google Scholar
Alastruey, J., Parker, K.H., Peiró, J., Byrd, S.M. and Sherwin, S.J., Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J. Biomech. 40 (2007) 1794–805. Google ScholarPubMed
Amundsen, B.H., Wisloff, U., Helgerud, J., Hoff, J. and Slordahl, S.A., Ultrasound recorded axillary artery blood flow during elbow-flexion exercise. Medicine and science in sports and exercise 34 (2002) 1288–93. Google ScholarPubMed
Avolio, A.P., Multi-branched model of the human arterial system. Medical Biolog. Engrg. Comp. 18 (1980) 709–18. Google ScholarPubMed
Bilge, O., Pinar, Y., Ozer, M.A. and Gövsa, F., A morphometric study on the superficial palmar arch of the hand. Surg. Radiol. Anat.: SRA 28 (2006) 343–50. Google ScholarPubMed
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.
Blanco, P.J., Feijóo, R.A. and Urquiza, S.A., A unified variational approach for coupling 3D–1D models and its blood flow applications. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4391–4410. Google Scholar
Blanco, P.J., Leiva, J.S., Feijóo, R.A. and Buscaglia, G.S., Black-box decomposition approach for computational hemodynamics: One-dimensional models. Comput. Methods Appl. Mech. Engrg. 200 138 (2011) 9–1405. Google Scholar
Blanco, P.J., Pivello, M.R., Urquiza, S.A. and Feijóo, R.A., On the potentialities of 3D–1D coupled models in hemodynamics simulations. J. Biomech. 42 (2009) 919–930. Google ScholarPubMed
Blanco, P.J., Trenhago, P.R., Fernandes, L.G. and Feijóo, R.A., 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. Google Scholar
Blanco, P.J., Urquiza, S.A. and Feijóo, R.A., 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. Google Scholar
Blanco, P.J., Watanabe, S.M. and Feijóo, R.A., Identification of vascular territory resistances in one-dimensional hemodynamics simulations. J. Biomech. 45 (2012) 2066–2073. Google ScholarPubMed
Casoli, V., Kostopoulos, E., Pélissier, P., Caix, P., Martin, D. and Baudet, J., The middle collateral artery: anatomic basis for the extreme lateral arm flap. Surg. Radiol. Anat.: SRA 26 (2004) 172–7. Google ScholarPubMed
Chen, S., Xu, D., Tang, M., Ding, H., Sheng, W. and Peng, T., Measurement and analysis of the perforator arteries in upper extremity for the flap design. Surg. Radiol. Anat.: SRA 31 687–93 (2009). Google ScholarPubMed
Claassen, H., Schmitt, O., Werner, D., Schareck, W., Kröger, J.C. and Wree, A., 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. Google ScholarPubMed
W. Dauber, Pocket Atlas of Human Anatomy by Feneis. Thieme, 5th edition (2007).
Denton, T.A., Trento, L., Cohen, M., Kass, R.M., Blanche, C., Raissi, S., Cheng, W., Fontana, G.P. and Trento, A., Radial artery harvesting for coronary bypass operations: neurologic complications and their potential mechanisms. The Journal of thoracic and cardiovascular surgery 121 (2001) 951–6. Google ScholarPubMed
Duparc, F., Muller, J.M. and Fréger, P., Arterial blood supply of the proximal humeral epiphysis. Surg. Radiol. Anat.: SRA 23 (2001) 185–90. Google ScholarPubMed
Fazan, V.P.S., Borges, C.T., Da Silva, J.H., Caetano, A.G. and Filho, O.A.R., Superficial palmar arch: an arterial diameter study. J. Anat. 204 (2004) 307–11. Google ScholarPubMed
Formaggia, L., Lamponi, D. and Quarteroni, A., One-dimensional models for blood flow in arteries. J. Engrg Math. 47 (2003) 251–276. Google Scholar
Formaggia, L., Moura, A. and Nobile, F., On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. ESAIM: M2AN 41 (2007) 743–769. Google Scholar
Formaggia, L., Nobile, F., Quarteroni, A. and Veneziani, A., Computing and Visualization in Science Regular article Multiscale modelling of the circulatory system: a preliminary analysis. 83 (1999) 75–83. Google Scholar
Haerle, M., Tonagel, F. and Schaller, H.E., Collateral arterial pathways in the forearm. Surg. Radiol. Anat.: SRA 26 (2004) 208–11. Google ScholarPubMed
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.
Hughes, T.J.R. and Lubliner, J., On the one-dimensional theory of blood flow in the larger vessels. Math. Biosci. 18 (1973) 161–170. Google Scholar
Kim, H.J., Vignon-Clementel, I.E., Figueroa, C.A., LaDisa, J.F., Jansen, K.E., Feinstein, J.A. and Taylor, C.A., On coupling a lumped parameter heart model and a three-dimensional finite element aorta model 37 (2009) 2153–2169. Google Scholar
Knobloch, K., Tomaszek, S., Lichtenberg, A., Karck, M. and Haverich, A., Long-term palmar microcirculation after radial artery harvesting: an observational study. The Annal. Thorac. Surg. 81 (2006) 1700–7. Google ScholarPubMed
Leguy, C.A.D., Bosboom, E.M.H., Belloum, A.S.Z., Hoeks, A.P.G. and van de Vosse, F.N., Global sensitivity analysis of a wave propagation model for arm arteries. Medical Engrg. Phys. 33 (2011) 1008–16. Google ScholarPubMed
Leiva, J.S., Blanco, P.J. and Buscaglia, G.C., Partitioned analysis for dimensionally-heterogeneous hydraulic networks. SIAM Multiscale Model. Simulat. 9 (2011) 872–903. Google Scholar
Mahabir, R.C., Williamson, J.S., Carr, N.J. and Courtemanche, D.J., Vascular Resistance in Human Muscle Flaps. Annal. Plast. Surg. 47 (2001) 148–152. Google ScholarPubMed
K.L. Moore, A.F. Dalley and A.M.R. Agur, Clinically Oriented Anatomy. Wolters Kluwer, 6th edition (2010).
Morris, S.F., Tang, M., Almutari, K., Geddes, C. and Yang, D., The anatomic basis of perforator flaps. Clinics in plastic surgery 37 (2010) 553–70. Google ScholarPubMed
F.H. Netter, Atlas of Human Anatomy. Elsevier, 5th edition (2011).
Olufsen, M.S., Structured tree outflow condition for blood flow in larger systemic arteries. Amer. J. Phys. 276 (1999) H257–68. Google ScholarPubMed
Omokawa, S., Tanaka, Y., Ryu, J. and Kish, V.L., The anatomical basis for reverse first to fifth dorsal metacarpal arterial flaps. J. Hand Surgery (Edinburgh, Scotland) 30 (2005) 40–4. Google ScholarPubMed
M.F. O’Rourke and W.W. Nichols, McDonald’s Blood Flow in Arteries - Theoretical, Experimental and Clinical Principles. Arnold, 4th edition (1998).
Prevel, C.D., Matloub, H.S., Ye, Z., Sanger, J.R. and Yousif, N.J., The extrinsic blood supply of the ulnar nerve at the elbow: an anatomic study. The J. Hand Surgery 18 (1993) 433–8. Google Scholar
Reymond, P., Merenda, F., Perren, F., Rüfenacht, D. and Stergiopulos, N., Validation of a one-dimensional model of the systemic arterial tree. Amer. J. Physiol. Heart circulatory Physiol. 297 (2009) H208–22. Google ScholarPubMed
Royse, A.G., Chang, G.S., Nicholas, D.M. and Royse, C.F., No late ulnar artery atheroma after radial artery harvest for coronary artery bypass surgery. The Annal. Thoracic Surgery 85 (2008) 891–4. Google ScholarPubMed
Sauerbier, M. and Unglaub, F., Perforator flaps in the upper extremity. Clinics in plastic Surg. 37 (2010) 667–76. Google ScholarPubMed
Schafhalterzoppoth, I. and Gray, A., The Musculocutaneous Nerve: Ultrasound Appearance for Peripheral Nerve Block. Regional Anesthesia and Pain Medicine 30 (2005) 385–390. Google Scholar
T.F. Sherman, On Connecting Large Vessels to Small The Meaning of Murray’s Law. J. General Physiol. (1981).
Stergiopulos, N., Young, D.F. and Rogge, T.R., Computer simulation of arterial flow with applications to arterial and aortic stenoses. J. Biomech. 25 (1992) 1477–1488. Google ScholarPubMed
Taylor, G., The angiosomes of the body and their supply to perforator flaps. Clin. Plast. Surg. 30 (2003) 331–342. Google ScholarPubMed
Trager, S., Pignataro, M., Anderson, J. and Kleinert, J.M., Color flow Doppler: imaging the upper extremity. J. Hand Surg. 18 (1993) 621–5. Google ScholarPubMed
Urquiza, S.A., Blanco, P.J., Vénere, M.J. and Feijóo, R.A., Multidimensional modelling for the carotid artery blood flow. Comput. Methods Appl. Mech. Engrg. 195 (2006) 4002–4017. Google Scholar
Walther, G., Nottin, S., Dauzat, M. and Obert, P., Femoral and axillary ultrasound blood flow during exercise: a methodological study. Med. Sci. Sports Exerc. 38 (2006) 1353. Google ScholarPubMed
Wang, J.J. and Parker, K.H., Wave propagation in a model of the arterial circulation. J. Biomech. 37 (2004) 457–70. Google Scholar
Wavreille, G., Bricout, J., Mouliade, S., Lemoine, S., Prodhomme, G., Khanchandani, P., Chantelot, C. and Fontaine, C., Anatomical bases of the free posterior brachial fascial flap. Surg. Radiol. Anat.: SRA 32 (2010) 393–9. Google ScholarPubMed
Wavreille, G., Dos Remedios, C., Chantelot, C., Limousin, M. and Fontaine, C., Anatomic bases of vascularized elbow joint harvesting to achieve vascularized allograft. Surg. Radiol. Anat.: SRA 28 (2006) 498–510. Google ScholarPubMed
Zhang, F.H., Topp, S.G., Zhang, W.J., Zheng, H.P. and Zhang, F., 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. Google ScholarPubMed