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Computational models for fluid exchange between microcirculation and tissue interstitium
1. | MOX, Department of Mathematics "Francesco Brioschi", Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy |
2. | Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 3700 O'Hara Street, Pittsburgh, PA 15261, United States |
References:
[1] |
L. T. Baxter and R. K. Jain, Transport of fluid and macromolecules in tumors. i. role of interstitial pressure and convection, Microvascular Research, 37 (1989), 77-104.
doi: 10.1016/0026-2862(89)90074-5. |
[2] |
L. T. Baxter and R. K. Jain, Transport of fluid and macromolecules in tumors ii. role of heterogeneous perfusion and lymphatics, Microvascular Research, 40 (1990), 246-263.
doi: 10.1016/0026-2862(90)90023-K. |
[3] |
L. T. Baxter and R. K. Jain, Transport of fluid and macromolecules in tumors. iii. role of binding and metabolism, Microvascular Research, 41 (1991), 5-23. |
[4] |
L. T. Baxter and R. K. Jain, Transport of fluid and macromolecules in tumors: Iv. a microscopic model of the perivascular distribution, Microvascular Research, 41 (1991), 252-272.
doi: 10.1016/0026-2862(91)90026-8. |
[5] |
T. R. Blake and J. F. Gross, Analysis of coupled intra- and extraluminal flows for single and multiple capillaries, Mathematical Biosciences, 59 (1982), 173-206.
doi: 10.1016/0025-5564(82)90022-0. |
[6] |
S. Canic, D. Lamponi, A. Mikelić and J. Tambaca, Self-consistent effective equations modeling blood flow in medium-to-large compliant arteries, Multiscale Modeling and Simulation, 3 (2005), 559-596.
doi: 10.1137/030602605. |
[7] |
P. Carmeliet and R. K. Jain, Angiogenesis in cancer and other diseases, Nature, 407 (2000), 249-257. |
[8] |
S. J. Chapman, R. J. Shipley and R. Jawad, Multiscale modeling of fluid transport in tumors, Bulletin of Mathematical Biology, 70 (2008), 2334-2357.
doi: 10.1007/s11538-008-9349-7. |
[9] |
C. D'Angelo, Multiscale Modeling of Metabolism and Transport Phenomena in Living Tissues, Ph.D thesis, 2007. |
[10] |
C. D'Angelo, Finite element approximation of elliptic problems with dirac measure terms in weighted spaces: Applications to one- and three-dimensional coupled problems, SIAM Journal on Numerical Analysis, 50 (2012), 194-215.
doi: 10.1137/100813853. |
[11] |
C. D'Angelo and A. Quarteroni, On the coupling of 1D and 3D diffusion-reaction equations. Application to tissue perfusion problems, Math. Models Methods Appl. Sci., 18 (2008), 1481-1504.
doi: 10.1142/S0218202508003108. |
[12] |
A. Farina, A. Fasano and J. Mizerski, A new model for blood flow in fenestrated capillaries with application to ultrafiltration in kidney glomeruli, Submitted. |
[13] |
D. A. Fedosov, G. E. Karniadakis and B. Caswell, Steady shear rheometry of dissipative particle dynamics models of polymer fluids in reverse poiseuille flow, Journal of Chemical Physics, 132 (2010).
doi: 10.1063/1.3366658. |
[14] |
M. Ferrari, Frontiers in cancer nanomedicine: Directing mass transport through biological barriers, Trends in Biotechnology, 28 (2010), 181-188.
doi: 10.1016/j.tibtech.2009.12.007. |
[15] |
G. J. Fleischman, T. W. Secomb and J. F. Gross, The interaction of extravascular pressure fields and fluid exchange in capillary networks, Mathematical Biosciences, 82 (1986), 141-151.
doi: 10.1016/0025-5564(86)90134-3. |
[16] |
G. J. Flieschman, T. W. Secomb and J. F. Gross, Effect of extravascular pressure gradients on capillary fluid exchange, Mathematical Biosciences, 81 (1986), 145-164.
doi: 10.1016/0025-5564(86)90114-8. |
[17] |
L. Formaggia, D. Lamponi and A. Quarteroni, One-dimensional models for blood flow in arteries, Journal of Engineering Mathematics, 47 (2003), 251-276.
doi: 10.1023/B:ENGI.0000007980.01347.29. |
[18] |
L. Formaggia, A. Quarteroni and A. Veneziani, Multiscale models of the vascular system, in Cardiovascular Mathematics, MS&A. Model. Simul. Appl., 1, Springer Italia, Milan, 2009, 395-446.
doi: 10.1007/978-88-470-1152-6_11. |
[19] |
A. Harris, G. Guidoboni, J. C. Arciero, A. Amireskandari, L. A. Tobe and B. A. Siesky, Ocular hemodynamics and glaucoma: The role of mathematical modeling, European Journal of Ophthalmology, 23 (2013), 139-146.
doi: 10.5301/ejo.5000255. |
[20] |
K. O. Hicks, F. B. Pruijn, T. W. Secomb, M. P. Hay, R. Hsu, J. M. Brown, W. A. Denny, M. W. Dewhirst and W. R. Wilson, Use of three-dimensional tissue cultures to model extravascular transport and predict in vivo activity of hypoxia-targeted anticancer drugs, Journal of the National Cancer Institute, 98 (2006), 1118-1128.
doi: 10.1093/jnci/djj306. |
[21] |
S. S. Hossain, Y. Zhang, X. Liang, F. Hussain, M. Ferrari, T. J. Hughes and P. Decuzzi, In silico vascular modeling for personalized nanoparticle delivery, Nanomedicine, 8 (2013), 343-357. |
[22] |
M. Intaglietta, N. R. Silverman and W. R. Tompkins, Capillary flow velocity measurements in vivo and in situ by television methods, Microvascular Research, 10 (1975), 165-179.
doi: 10.1016/0026-2862(75)90004-7. |
[23] |
R. K. Jain, Transport of molecules, particles, and cells in solid tumors, Annual Review of Biomedical Engineering, (1999), 241-263.
doi: 10.1146/annurev.bioeng.1.1.241. |
[24] |
R. K. Jain, R. T. Tong and L. L. Munn, Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: Insights from a mathematical model, Cancer Research, 67 (2007), 2729-2735.
doi: 10.1158/0008-5472.CAN-06-4102. |
[25] |
J. Lee and T. C. Skalak, Microvascular Mechanics: Hemodynamics of Systemic and Pulmonary Microcirculation, Springer-Verlag, 1989. |
[26] |
H. Lei, D. A. Fedosov, B. Caswell and G. E. Karniadakis, Blood flow in small tubes: Quantifying the transition to the non-continuum regime, Journal of Fluid Mechanics, 722 (2013), 214-239.
doi: 10.1017/jfm.2013.91. |
[27] |
J. R. Less, T. C. Skalak, E. M. Sevick and R. K. Jain, Microvascular architecture in a mammary carcinoma: Branching patterns and vessel dimensions, Cancer Research, 51 (1991), 265-273. |
[28] |
W. K. Liu, Y. Liu, D. Farrell, L. Zhang, X. S. Wang, Y. Fukui, N. Patankar, Y. Zhang, C. Bajaj, J. Lee, J. Hong, X. Chen and H. Hsu, Immersed finite element method and its applications to biological systems, Comput. Methods Appl. Mech. Engrg., 195 (2006), 1722-1749.
doi: 10.1016/j.cma.2005.05.049. |
[29] |
Y. Liu and W. K. Liu, Rheology of red blood cell aggregation by computer simulation, Journal of Computational Physics, 220 (2006), 139-154.
doi: 10.1016/j.jcp.2006.05.010. |
[30] |
Y. Liu, L. Zhang, X. Wang and W. K. Liu, Coupling of navier-stokes equations with protein molecular dynamics and its application to hemodynamics, International Journal for Numerical Methods in Fluids, 46 (2004), 1237-1252.
doi: 10.1002/fld.798. |
[31] |
J. Peiró and A. Veneziani, Reduced models of the cardiovascular system, in Cardiovascular Mathematics, MS&A. Model. Simul. Appl., 1, Springer Italia, Milan, 2009, 347-394.
doi: 10.1007/978-88-470-1152-6_10. |
[32] |
Y. Renard and J. Pommier, Getfem++: A generic finite element library in c++, version 4.2 (2012), http://download.gna.org/getfem/html/homepage/. |
[33] |
A. M. Robertson and A. Sequeira, A director theory approach for modeling blood flow in the arterial system: An alternative to classical id models, Mathematical Models and Methods in Applied Sciences, 15 (2005), 871-906.
doi: 10.1142/S0218202505000601. |
[34] |
A. M. Robertson, A. Sequeira and R. G. Owens, Rheological models for blood. In Cardiovascular Mathematics, MS&A. Model. Simul. Appl., 1, Springer Italia, Milan, 2009, 211-241.
doi: 10.1007/978-88-470-1152-6_6. |
[35] |
T. W. Secomb, A. R. Pries, P. Gaehtgens and J. F. Gross, Theoretical and experimental analysis of hematocrit distribution in microcirculatory networks, in Microvascular Mechanics (eds. J.-S. Lee and T. C. Skalak), Springer, New York, 1989, 39-49.
doi: 10.1007/978-1-4612-3674-0_4. |
[36] |
T. W. Secomb, Microvascular Network Structures, http://www.physiology.arizona.edu/people/secomb. |
[37] |
T. W. Secomb, R. Hsu, R. D. Braun, J. R. Ross, J. F. Gross and M. W. Dewhirst, Theoretical simulation of oxygen transport to tumors by three-dimensional networks of microvessels, Advances in Experimental Medicine and Biology, 454 (1998), 629-634.
doi: 10.1007/978-1-4615-4863-8_74. |
[38] |
T. W. Secomb, R. Hsu, E. Y. H. Park and M. W. Dewhirst, Green's function methods for analysis of oxygen delivery to tissue by microvascular networks, Annals of Biomedical Engineering, 32 (2004), 1519-1529.
doi: 10.1114/B:ABME.0000049036.08817.44. |
[39] |
R. J. Shipley and S. J. Chapman, Multiscale modelling of fluid and drug transport in vascular tumours, Bulletin of Mathematical Biology, 72 (2010), 1464-1491.
doi: 10.1007/s11538-010-9504-9. |
[40] |
M. Soltani and P. Chen, Numerical modeling of fluid flow in solid tumors, PLoS ONE, (2011).
doi: 10.1371/journal.pone.0020344. |
[41] |
Q. Sun and G. X. Wu, Coupled finite difference and boundary element methods for fluid flow through a vessel with multibranches in tumours, International Journal for Numerical Methods in Biomedical Engineering, 29 (2013), 309-331.
doi: 10.1002/cnm.2502. |
[42] |
C. J. Van Duijn, A. Mikelić, I. S. Pop and C. Rosier, Effective dispersion equations for reactive flows with dominant pclet and damkohler numbers, Advances in Chemical Engineering, 34 (2008), 1-45. |
[43] |
G. Vilanova, I. Colominas and H. Gomez, Capillary networks in tumor angiogenesis: From discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis, International Journal for Numerical Methods in Biomedical Engineering, 29 (2013), 1015-1037.
doi: 10.1002/cnm.2552. |
[44] |
L. Zhang, A. Gerstenberger, X. Wang and W. K. Liu, Immersed finite element method, Comput. Methods Appl. Mech. Engrg., 193 (2004), 2051-2067.
doi: 10.1016/j.cma.2003.12.044. |
show all references
References:
[1] |
L. T. Baxter and R. K. Jain, Transport of fluid and macromolecules in tumors. i. role of interstitial pressure and convection, Microvascular Research, 37 (1989), 77-104.
doi: 10.1016/0026-2862(89)90074-5. |
[2] |
L. T. Baxter and R. K. Jain, Transport of fluid and macromolecules in tumors ii. role of heterogeneous perfusion and lymphatics, Microvascular Research, 40 (1990), 246-263.
doi: 10.1016/0026-2862(90)90023-K. |
[3] |
L. T. Baxter and R. K. Jain, Transport of fluid and macromolecules in tumors. iii. role of binding and metabolism, Microvascular Research, 41 (1991), 5-23. |
[4] |
L. T. Baxter and R. K. Jain, Transport of fluid and macromolecules in tumors: Iv. a microscopic model of the perivascular distribution, Microvascular Research, 41 (1991), 252-272.
doi: 10.1016/0026-2862(91)90026-8. |
[5] |
T. R. Blake and J. F. Gross, Analysis of coupled intra- and extraluminal flows for single and multiple capillaries, Mathematical Biosciences, 59 (1982), 173-206.
doi: 10.1016/0025-5564(82)90022-0. |
[6] |
S. Canic, D. Lamponi, A. Mikelić and J. Tambaca, Self-consistent effective equations modeling blood flow in medium-to-large compliant arteries, Multiscale Modeling and Simulation, 3 (2005), 559-596.
doi: 10.1137/030602605. |
[7] |
P. Carmeliet and R. K. Jain, Angiogenesis in cancer and other diseases, Nature, 407 (2000), 249-257. |
[8] |
S. J. Chapman, R. J. Shipley and R. Jawad, Multiscale modeling of fluid transport in tumors, Bulletin of Mathematical Biology, 70 (2008), 2334-2357.
doi: 10.1007/s11538-008-9349-7. |
[9] |
C. D'Angelo, Multiscale Modeling of Metabolism and Transport Phenomena in Living Tissues, Ph.D thesis, 2007. |
[10] |
C. D'Angelo, Finite element approximation of elliptic problems with dirac measure terms in weighted spaces: Applications to one- and three-dimensional coupled problems, SIAM Journal on Numerical Analysis, 50 (2012), 194-215.
doi: 10.1137/100813853. |
[11] |
C. D'Angelo and A. Quarteroni, On the coupling of 1D and 3D diffusion-reaction equations. Application to tissue perfusion problems, Math. Models Methods Appl. Sci., 18 (2008), 1481-1504.
doi: 10.1142/S0218202508003108. |
[12] |
A. Farina, A. Fasano and J. Mizerski, A new model for blood flow in fenestrated capillaries with application to ultrafiltration in kidney glomeruli, Submitted. |
[13] |
D. A. Fedosov, G. E. Karniadakis and B. Caswell, Steady shear rheometry of dissipative particle dynamics models of polymer fluids in reverse poiseuille flow, Journal of Chemical Physics, 132 (2010).
doi: 10.1063/1.3366658. |
[14] |
M. Ferrari, Frontiers in cancer nanomedicine: Directing mass transport through biological barriers, Trends in Biotechnology, 28 (2010), 181-188.
doi: 10.1016/j.tibtech.2009.12.007. |
[15] |
G. J. Fleischman, T. W. Secomb and J. F. Gross, The interaction of extravascular pressure fields and fluid exchange in capillary networks, Mathematical Biosciences, 82 (1986), 141-151.
doi: 10.1016/0025-5564(86)90134-3. |
[16] |
G. J. Flieschman, T. W. Secomb and J. F. Gross, Effect of extravascular pressure gradients on capillary fluid exchange, Mathematical Biosciences, 81 (1986), 145-164.
doi: 10.1016/0025-5564(86)90114-8. |
[17] |
L. Formaggia, D. Lamponi and A. Quarteroni, One-dimensional models for blood flow in arteries, Journal of Engineering Mathematics, 47 (2003), 251-276.
doi: 10.1023/B:ENGI.0000007980.01347.29. |
[18] |
L. Formaggia, A. Quarteroni and A. Veneziani, Multiscale models of the vascular system, in Cardiovascular Mathematics, MS&A. Model. Simul. Appl., 1, Springer Italia, Milan, 2009, 395-446.
doi: 10.1007/978-88-470-1152-6_11. |
[19] |
A. Harris, G. Guidoboni, J. C. Arciero, A. Amireskandari, L. A. Tobe and B. A. Siesky, Ocular hemodynamics and glaucoma: The role of mathematical modeling, European Journal of Ophthalmology, 23 (2013), 139-146.
doi: 10.5301/ejo.5000255. |
[20] |
K. O. Hicks, F. B. Pruijn, T. W. Secomb, M. P. Hay, R. Hsu, J. M. Brown, W. A. Denny, M. W. Dewhirst and W. R. Wilson, Use of three-dimensional tissue cultures to model extravascular transport and predict in vivo activity of hypoxia-targeted anticancer drugs, Journal of the National Cancer Institute, 98 (2006), 1118-1128.
doi: 10.1093/jnci/djj306. |
[21] |
S. S. Hossain, Y. Zhang, X. Liang, F. Hussain, M. Ferrari, T. J. Hughes and P. Decuzzi, In silico vascular modeling for personalized nanoparticle delivery, Nanomedicine, 8 (2013), 343-357. |
[22] |
M. Intaglietta, N. R. Silverman and W. R. Tompkins, Capillary flow velocity measurements in vivo and in situ by television methods, Microvascular Research, 10 (1975), 165-179.
doi: 10.1016/0026-2862(75)90004-7. |
[23] |
R. K. Jain, Transport of molecules, particles, and cells in solid tumors, Annual Review of Biomedical Engineering, (1999), 241-263.
doi: 10.1146/annurev.bioeng.1.1.241. |
[24] |
R. K. Jain, R. T. Tong and L. L. Munn, Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: Insights from a mathematical model, Cancer Research, 67 (2007), 2729-2735.
doi: 10.1158/0008-5472.CAN-06-4102. |
[25] |
J. Lee and T. C. Skalak, Microvascular Mechanics: Hemodynamics of Systemic and Pulmonary Microcirculation, Springer-Verlag, 1989. |
[26] |
H. Lei, D. A. Fedosov, B. Caswell and G. E. Karniadakis, Blood flow in small tubes: Quantifying the transition to the non-continuum regime, Journal of Fluid Mechanics, 722 (2013), 214-239.
doi: 10.1017/jfm.2013.91. |
[27] |
J. R. Less, T. C. Skalak, E. M. Sevick and R. K. Jain, Microvascular architecture in a mammary carcinoma: Branching patterns and vessel dimensions, Cancer Research, 51 (1991), 265-273. |
[28] |
W. K. Liu, Y. Liu, D. Farrell, L. Zhang, X. S. Wang, Y. Fukui, N. Patankar, Y. Zhang, C. Bajaj, J. Lee, J. Hong, X. Chen and H. Hsu, Immersed finite element method and its applications to biological systems, Comput. Methods Appl. Mech. Engrg., 195 (2006), 1722-1749.
doi: 10.1016/j.cma.2005.05.049. |
[29] |
Y. Liu and W. K. Liu, Rheology of red blood cell aggregation by computer simulation, Journal of Computational Physics, 220 (2006), 139-154.
doi: 10.1016/j.jcp.2006.05.010. |
[30] |
Y. Liu, L. Zhang, X. Wang and W. K. Liu, Coupling of navier-stokes equations with protein molecular dynamics and its application to hemodynamics, International Journal for Numerical Methods in Fluids, 46 (2004), 1237-1252.
doi: 10.1002/fld.798. |
[31] |
J. Peiró and A. Veneziani, Reduced models of the cardiovascular system, in Cardiovascular Mathematics, MS&A. Model. Simul. Appl., 1, Springer Italia, Milan, 2009, 347-394.
doi: 10.1007/978-88-470-1152-6_10. |
[32] |
Y. Renard and J. Pommier, Getfem++: A generic finite element library in c++, version 4.2 (2012), http://download.gna.org/getfem/html/homepage/. |
[33] |
A. M. Robertson and A. Sequeira, A director theory approach for modeling blood flow in the arterial system: An alternative to classical id models, Mathematical Models and Methods in Applied Sciences, 15 (2005), 871-906.
doi: 10.1142/S0218202505000601. |
[34] |
A. M. Robertson, A. Sequeira and R. G. Owens, Rheological models for blood. In Cardiovascular Mathematics, MS&A. Model. Simul. Appl., 1, Springer Italia, Milan, 2009, 211-241.
doi: 10.1007/978-88-470-1152-6_6. |
[35] |
T. W. Secomb, A. R. Pries, P. Gaehtgens and J. F. Gross, Theoretical and experimental analysis of hematocrit distribution in microcirculatory networks, in Microvascular Mechanics (eds. J.-S. Lee and T. C. Skalak), Springer, New York, 1989, 39-49.
doi: 10.1007/978-1-4612-3674-0_4. |
[36] |
T. W. Secomb, Microvascular Network Structures, http://www.physiology.arizona.edu/people/secomb. |
[37] |
T. W. Secomb, R. Hsu, R. D. Braun, J. R. Ross, J. F. Gross and M. W. Dewhirst, Theoretical simulation of oxygen transport to tumors by three-dimensional networks of microvessels, Advances in Experimental Medicine and Biology, 454 (1998), 629-634.
doi: 10.1007/978-1-4615-4863-8_74. |
[38] |
T. W. Secomb, R. Hsu, E. Y. H. Park and M. W. Dewhirst, Green's function methods for analysis of oxygen delivery to tissue by microvascular networks, Annals of Biomedical Engineering, 32 (2004), 1519-1529.
doi: 10.1114/B:ABME.0000049036.08817.44. |
[39] |
R. J. Shipley and S. J. Chapman, Multiscale modelling of fluid and drug transport in vascular tumours, Bulletin of Mathematical Biology, 72 (2010), 1464-1491.
doi: 10.1007/s11538-010-9504-9. |
[40] |
M. Soltani and P. Chen, Numerical modeling of fluid flow in solid tumors, PLoS ONE, (2011).
doi: 10.1371/journal.pone.0020344. |
[41] |
Q. Sun and G. X. Wu, Coupled finite difference and boundary element methods for fluid flow through a vessel with multibranches in tumours, International Journal for Numerical Methods in Biomedical Engineering, 29 (2013), 309-331.
doi: 10.1002/cnm.2502. |
[42] |
C. J. Van Duijn, A. Mikelić, I. S. Pop and C. Rosier, Effective dispersion equations for reactive flows with dominant pclet and damkohler numbers, Advances in Chemical Engineering, 34 (2008), 1-45. |
[43] |
G. Vilanova, I. Colominas and H. Gomez, Capillary networks in tumor angiogenesis: From discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis, International Journal for Numerical Methods in Biomedical Engineering, 29 (2013), 1015-1037.
doi: 10.1002/cnm.2552. |
[44] |
L. Zhang, A. Gerstenberger, X. Wang and W. K. Liu, Immersed finite element method, Comput. Methods Appl. Mech. Engrg., 193 (2004), 2051-2067.
doi: 10.1016/j.cma.2003.12.044. |
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