Characterizing the Flow and Interaction of Microbubbles in a 2D Capillary Network for Targeted Drug Delivery: A Simulation Study
,
Abstract
Purpose: Microbubble ultrasound contrast agents inside the bloodstream enhance the ultrasound signals of the vascular bed. In addition, microbubbles can be used for treatment. The present study assesses how air bubbles flow in a microchannel 2D capillary network. The evaluated network mimics part of a capillary system by comprising multiple bifurcations.
Materials and Methods: We designed the capillary network based on the tree pattern employed in quantitative studies per Murray’s minimum work rule and the cardiovascular network to simulate the hemodynamics of the vessels. The maximum width of the main channels in the capillary network is 1085 µm. The capillary network designed by AutoCAD software was transferred to Comsol software. We also ran fluid-structure interaction simulations in a microchannel capillary network, assuming that capillary walls were incompressible and isotropic, physiological boundary conditions were met, and non-Newtonian blood behavior occurred. After these simulations, we investigated Microbubbles’ (MBs’) capacity for targeted drug delivery through the capillary network. Specifically, we distributed four particles with 1 to 5 µm diameters and assessed the resultant performance.
Results: The greatest capillary network wall displacement is 0.225 µm. Meanwhile, the maximum velocity was 5.59 mm/s, and the minimum and maximum pressure values were 303.13 Pa and 0.42 Pa. Finally, the MB-MB interaction force exceeded the Brownian and gravitational forces. Therefore, it can be concluded that the MB-MB interaction force is crucial for MB-based targeted drug delivery. The kinetic energy of microbubbles increases while passing through the capillary bed. By increasing the amount of kinetic energy of microbubbles, the probability of adhesion to the capillary wall decreases. As the diameter of microbubbles increases, their energy increases.
Conclusion: The kinetic energy of microbubbles in the same conditions is the highest value related to Sonovue and then related to Optison, Micromarker, and Definity, respectively. The highest percentage of passing through the capillary network belongs to the Sonovue with a diameter of 2.5 µm and the lowest percentage of passing through the capillary network belongs to the Definity with a diameter of 1.1 µm.
1. Papadopoulou, V., et al., A critical review of physiological bubble formation in hyperbaric decompression. Advances in colloid and interface science, 2013. 191: p. 22-30.
2. Karlsson, L.L., et al., Venous gas emboli and exhaled nitric oxide with simulated and actual extravehicular activity. Respiratory physiology & neurobiology, 2009. 169: p. S59-S62.
3. Foster, P.P. and B.D. Butler, Decompression to altitude: assumptions, experimental evidence, and future directions. Journal of Applied Physiology, 2009. 106(2): p. 678-690.
4. Deklunder, G., et al., Microemboli in cerebral circulation and alteration of cognitive abilities in patients with mechanical prosthetic heart valves. Stroke, 1998. 29(9): p. 1821-1826.
5. Milo, S., et al., Mitral mechanical heart valves: in vitro studies of their closure, vortex and microbubble formation with possible medical implications. European journal of cardio-thoracic surgery, 2003. 24(3): p. 364-370.
6. Borger, M.A., et al., Neuropsychologic impairment after coronary bypass surgery: effect of gaseous microemboli during perfusionist interventions. The Journal of Thoracic and Cardiovascular Surgery, 2001. 121(4): p. 743-749.
7. Abu-Omar, Y., et al., Solid and gaseous cerebral microembolization during off-pump, on-pump, and open cardiac surgery procedures. The Journal of thoracic and cardiovascular surgery, 2004. 127(6): p. 1759-1765.
8. Bischel, M.D., B.G. Scoles, and J.G. Mohler, Evidence for pulmonary microembolization during hemodialysis. Chest, 1975. 67(3): p. 335-337.
9. Samuel, S., et al., In vivo microscopy of targeted vessel occlusion employing acoustic droplet vaporization. Microcirculation, 2012. 19(6): p. 501-509.
10. Muth, C.M. and E.S. Shank, Gas embolism. New England Journal of Medicine, 2000. 342(7): p. 476-482.
11. Chou, W.-L., et al., Recent advances in applications of droplet microfluidics. Micromachines, 2015. 6(9): p. 1249-1271.
12. Eshpuniyani, B., J.B. Fowlkes, and J.L. Bull, A boundary element model of microbubble sticking and sliding in the microcirculation. International journal of heat and mass transfer, 2008. 51(23-24): p. 5700-5711.
13. Müller, K., D.A. Fedosov, and G. Gompper, Understanding particle margination in blood flow–a step toward optimized drug delivery systems. Medical engineering & physics, 2016. 38(1): p. 2-10.
14. Korin, N., et al., Shear-activated nanotherapeutics for drug targeting to obstructed blood vessels. Science, 2012. 337(6095): p. 738-742.
15. Asgharian, B., W. Hofmann, and R. Bergmann, Particle deposition in a multiple-path model of the human lung. Aerosol Science & Technology, 2001. 34(4): p. 332-339.
16. Liu, Y., S. Shah, and J. Tan, Computational modeling of nanoparticle targeted drug delivery. Reviews in Nanoscience and Nanotechnology, 2012. 1(1): p. 66-83.
17. Forouzandehmehr, M. and A. Shamloo, Margination and adhesion of micro-and nanoparticles in the coronary circulation: a step towards optimised drug carrier design. Biomechanics and modeling in mechanobiology, 2018. 17(1): p. 205-221.
18. Mayer, C.R., et al., Ultrasound targeted microbubble destruction for drug and gene delivery. Expert opinion on drug delivery, 2008. 5(10): p. 1121-1138.
19. Unger, E., et al., Cardiovascular drug delivery with ultrasound and microbubbles. Advanced drug delivery reviews, 2014. 72: p. 110-126.
20. Klibanov, A.L., Microbubble contrast agents: targeted ultrasound imaging and ultrasound-assisted drug-delivery applications. Investigative radiology, 2006. 41(3): p. 354-362.
21. Bull, J.L., The application of microbubbles for targeted drug delivery. Expert opinion on drug delivery, 2007. 4(5): p. 475-493.
22. Fang, J.-Y., et al., A study of the formulation design of acoustically active lipospheres as carriers for drug delivery. European Journal of Pharmaceutics and Biopharmaceutics, 2007. 67(1): p. 67-75.
23. May, D.J., J.S. Allen, and K.W. Ferrara, Dynamics and fragmentation of thick-shelled microbubbles. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2002. 49(10): p. 1400-1410.
24. Laing, S.T. and D.D. McPherson, Cardiovascular therapeutic uses of targeted ultrasound contrast agents. Cardiovascular research, 2009. 83(4): p. 626-635.
25. Postema, M., et al., Nitric oxide delivery by ultrasonic cracking: some limitations. Ultrasonics, 2006. 44: p. e109-e113.
26. R Muzykantov, V., R. Radhakrishnan, and D. M Eckmann, Dynamic factors controlling targeting nanocarriers to vascular endothelium. Current drug metabolism, 2012. 13(1): p. 70-81.
27. Shurche, S., Simulation of Capillary Hemodynamics and Comparison with Experimental Results of Microphantom Perfusion Weighted Imaging. Journal of Biomedical Physics & Engineering, 2020. 10(3): p. 291.
28. Shurche, S. and M.Y. Sooteh, Computational simulations of nanoparticle transport in a three-dimensional capillary network. Nanomedicine Journal, 2019. 6(4): p. 291-300.
29. Murray, C.D., The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proceedings of the National Academy of Sciences, 1926. 12(3): p. 207-214.
30. Rossitti, S. and J. Löfgren, Vascular dimensions of the cerebral arteries follow the principle of minimum work. Stroke, 1993. 24(3): p. 371-377.
31. Emerson, D.R., et al., Biomimetic design of microfluidic manifolds based on a generalised Murray's law. Lab on a Chip, 2006. 6(3): p. 447-454.
32. Pawlik, G., A. Rackl, and R.J. Bing, Quantitative capillary topography and blood flow in the cerebral cortex of cats: an in vivo microscopic study. Brain research, 1981. 208(1): p. 35-58.
33. Cassot, F., et al., A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex. Microcirculation, 2006. 13(1): p. 1-18.
34. Simsek, F.G. and Y.W. Kwon, Investigation of material modeling in fluid–structure interaction analysis of an idealized three-layered abdominal aorta: aneurysm initiation and fully developed aneurysms. Journal of biological physics, 2015. 41(2): p. 173-201.
35. Raghavan, M. and D.A. Vorp, Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. Journal of biomechanics, 2000. 33(4): p. 475-482.
36. Colwell, J.A., M. Lopes-Virella, and P.V. Halushka, Pathogenesis of atherosclerosis in diabetes mellitus. Diabetes care, 1981. 4(1): p. 121-133.
37. Sarnak, M.J., et al., Anemia as a risk factor for cardiovascular disease in The Atherosclerosis Risk in Communities (ARIC) study. Journal of the American College of Cardiology, 2002. 40(1): p. 27-33.
38. Pries, A.R., D. Neuhaus, and P. Gaehtgens, Blood viscosity in tube flow: dependence on diameter and hematocrit. American Journal of Physiology-Heart and Circulatory Physiology, 1992. 263(6): p. H1770-H1778.
39. Kwon, O., et al., Effect of blood viscosity on oxygen transport in residual stenosed artery following angioplasty. Journal of Biomechanical Engineering, 2008. 130(1).
40. Gori, F. and A. Boghi, Two new differential equations of turbulent dissipation rate and apparent viscosity for non-newtonian fluids. International communications in heat and mass transfer, 2011. 38(6): p. 696-703.
41. Gavrilov, A.A. and V.Y. Rudyak, Reynolds-averaged modeling of turbulent flows of power-law fluids. Journal of Non-Newtonian Fluid Mechanics, 2016. 227: p. 45-55.
42. Gavrilov, A. and V.Y. Rudyak, Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes. Fluid Dynamics, 2017. 52(3): p. 363-374.
43. Shamloo, A., et al., In silico study of patient-specific magnetic drug targeting for a coronary LAD atherosclerotic plaque. International Journal of Pharmaceutics, 2019. 559: p. 113-129.
44. Kobari, M., et al., Blood flow velocity in the pial arteries of cats, with particular reference to the vessel diameter. Journal of Cerebral Blood Flow & Metabolism, 1984. 4(1): p. 110-114.
45. Helfield, B.L. and D.E. Goertz, Nonlinear resonance behavior and linear shell estimates for Definity™ and MicroMarker™ assessed with acoustic microbubble spectroscopy. The Journal of the Acoustical Society of America, 2013. 133(2): p. 1158-1168.
46. Qin, S., C.F. Caskey, and K.W. Ferrara, Ultrasound contrast microbubbles in imaging and therapy: physical principles and engineering. Physics in medicine & biology, 2009. 54(6): p. R27.
47. Guan, J. and T.J. Matula, Using light scattering to measure the response of individual ultrasound contrast microbubbles subjected to pulsed ultrasound in vitro. The Journal of the Acoustical Society of America, 2004. 116(5): p. 2832-2842.
48. Marmottant, P., et al., A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture. The Journal of the Acoustical Society of America, 2005. 118(6): p. 3499-3505.
49. Borden, M.A. and K.-H. Song, Reverse engineering the ultrasound contrast agent. Advances in colloid and interface science, 2018. 262: p. 39-49.
50. van Rooij, T., Ultrasound contrast agents for imaging and therapy. 2017.
51. Kirby, B.J., Micro-and nanoscale fluid mechanics: transport in microfluidic devices. 2010: Cambridge university press.
52. Turton, R. and O. Levenspiel, A short note on the drag correlation for spheres. Powder technology, 1986. 47(1): p. 83-86.
53. Saffman, P.G., The lift on a small sphere in a slow shear flow. Journal of fluid mechanics, 1965. 22(2): p. 385-400.
54. Furlani, E., Magnetophoretic separation of blood cells at the microscale. Journal of Physics D: Applied Physics, 2007. 40(5): p. 1313.
55. Jorgensen, W.L. and J. Tirado-Rives, The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin. Journal of the American Chemical Society, 1988. 110(6): p. 1657-1666.
56. Ascher, U.M. and L.R. Petzold, Computer methods for ordinary differential equations and differential-algebraic equations. Vol. 61. 1998: Siam.
57. Curtiss, C.F. and J.O. Hirschfelder, Integration of stiff equations. Proceedings of the National Academy of Sciences, 1952. 38(3): p. 235-243.
58. Chung, J. and G. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. 1993.
59. Ivanov, K., M. Kalinina, and Y.I. Levkovich, Blood flow velocity in capillaries of brain and muscles and its physiological significance. Microvascular research, 1981. 22(2): p. 143-155.
60. Shore, A.C., Capillaroscopy and the measurement of capillary pressure. British journal of clinical pharmacology, 2000. 50(6): p. 501-513.
61. Fong, S.W., E. Klaseboer, and B.C. Khoo, Interaction of microbubbles with high intensity pulsed ultrasound. The Journal of the Acoustical Society of America, 2008. 123(3): p. 1784-1793.
62. de Saint Victor, M.-A., Investigating magnetically targeted microbubbles for ultrasound-enhanced thrombolysis. 2016, University of Oxford.
63. Shamloo, A., F. Manuchehrfar, and H. Rafii-Tabar, A viscoelastic model for axonal microtubule rupture. Journal of biomechanics, 2015. 48(7): p. 1241-1247.
64. Shamloo, A., et al., Targeted drug delivery of microbubble to arrest abdominal aortic aneurysm development: a simulation study towards optimized microbubble design. Scientific reports, 2020. 10(1): p. 1-17.
65. Bento, D., et al., Bubbles moving in blood flow in a microchannel network: The effect on the local hematocrit. Micromachines, 2020. 11(4): p. 344.
2. Karlsson, L.L., et al., Venous gas emboli and exhaled nitric oxide with simulated and actual extravehicular activity. Respiratory physiology & neurobiology, 2009. 169: p. S59-S62.
3. Foster, P.P. and B.D. Butler, Decompression to altitude: assumptions, experimental evidence, and future directions. Journal of Applied Physiology, 2009. 106(2): p. 678-690.
4. Deklunder, G., et al., Microemboli in cerebral circulation and alteration of cognitive abilities in patients with mechanical prosthetic heart valves. Stroke, 1998. 29(9): p. 1821-1826.
5. Milo, S., et al., Mitral mechanical heart valves: in vitro studies of their closure, vortex and microbubble formation with possible medical implications. European journal of cardio-thoracic surgery, 2003. 24(3): p. 364-370.
6. Borger, M.A., et al., Neuropsychologic impairment after coronary bypass surgery: effect of gaseous microemboli during perfusionist interventions. The Journal of Thoracic and Cardiovascular Surgery, 2001. 121(4): p. 743-749.
7. Abu-Omar, Y., et al., Solid and gaseous cerebral microembolization during off-pump, on-pump, and open cardiac surgery procedures. The Journal of thoracic and cardiovascular surgery, 2004. 127(6): p. 1759-1765.
8. Bischel, M.D., B.G. Scoles, and J.G. Mohler, Evidence for pulmonary microembolization during hemodialysis. Chest, 1975. 67(3): p. 335-337.
9. Samuel, S., et al., In vivo microscopy of targeted vessel occlusion employing acoustic droplet vaporization. Microcirculation, 2012. 19(6): p. 501-509.
10. Muth, C.M. and E.S. Shank, Gas embolism. New England Journal of Medicine, 2000. 342(7): p. 476-482.
11. Chou, W.-L., et al., Recent advances in applications of droplet microfluidics. Micromachines, 2015. 6(9): p. 1249-1271.
12. Eshpuniyani, B., J.B. Fowlkes, and J.L. Bull, A boundary element model of microbubble sticking and sliding in the microcirculation. International journal of heat and mass transfer, 2008. 51(23-24): p. 5700-5711.
13. Müller, K., D.A. Fedosov, and G. Gompper, Understanding particle margination in blood flow–a step toward optimized drug delivery systems. Medical engineering & physics, 2016. 38(1): p. 2-10.
14. Korin, N., et al., Shear-activated nanotherapeutics for drug targeting to obstructed blood vessels. Science, 2012. 337(6095): p. 738-742.
15. Asgharian, B., W. Hofmann, and R. Bergmann, Particle deposition in a multiple-path model of the human lung. Aerosol Science & Technology, 2001. 34(4): p. 332-339.
16. Liu, Y., S. Shah, and J. Tan, Computational modeling of nanoparticle targeted drug delivery. Reviews in Nanoscience and Nanotechnology, 2012. 1(1): p. 66-83.
17. Forouzandehmehr, M. and A. Shamloo, Margination and adhesion of micro-and nanoparticles in the coronary circulation: a step towards optimised drug carrier design. Biomechanics and modeling in mechanobiology, 2018. 17(1): p. 205-221.
18. Mayer, C.R., et al., Ultrasound targeted microbubble destruction for drug and gene delivery. Expert opinion on drug delivery, 2008. 5(10): p. 1121-1138.
19. Unger, E., et al., Cardiovascular drug delivery with ultrasound and microbubbles. Advanced drug delivery reviews, 2014. 72: p. 110-126.
20. Klibanov, A.L., Microbubble contrast agents: targeted ultrasound imaging and ultrasound-assisted drug-delivery applications. Investigative radiology, 2006. 41(3): p. 354-362.
21. Bull, J.L., The application of microbubbles for targeted drug delivery. Expert opinion on drug delivery, 2007. 4(5): p. 475-493.
22. Fang, J.-Y., et al., A study of the formulation design of acoustically active lipospheres as carriers for drug delivery. European Journal of Pharmaceutics and Biopharmaceutics, 2007. 67(1): p. 67-75.
23. May, D.J., J.S. Allen, and K.W. Ferrara, Dynamics and fragmentation of thick-shelled microbubbles. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2002. 49(10): p. 1400-1410.
24. Laing, S.T. and D.D. McPherson, Cardiovascular therapeutic uses of targeted ultrasound contrast agents. Cardiovascular research, 2009. 83(4): p. 626-635.
25. Postema, M., et al., Nitric oxide delivery by ultrasonic cracking: some limitations. Ultrasonics, 2006. 44: p. e109-e113.
26. R Muzykantov, V., R. Radhakrishnan, and D. M Eckmann, Dynamic factors controlling targeting nanocarriers to vascular endothelium. Current drug metabolism, 2012. 13(1): p. 70-81.
27. Shurche, S., Simulation of Capillary Hemodynamics and Comparison with Experimental Results of Microphantom Perfusion Weighted Imaging. Journal of Biomedical Physics & Engineering, 2020. 10(3): p. 291.
28. Shurche, S. and M.Y. Sooteh, Computational simulations of nanoparticle transport in a three-dimensional capillary network. Nanomedicine Journal, 2019. 6(4): p. 291-300.
29. Murray, C.D., The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proceedings of the National Academy of Sciences, 1926. 12(3): p. 207-214.
30. Rossitti, S. and J. Löfgren, Vascular dimensions of the cerebral arteries follow the principle of minimum work. Stroke, 1993. 24(3): p. 371-377.
31. Emerson, D.R., et al., Biomimetic design of microfluidic manifolds based on a generalised Murray's law. Lab on a Chip, 2006. 6(3): p. 447-454.
32. Pawlik, G., A. Rackl, and R.J. Bing, Quantitative capillary topography and blood flow in the cerebral cortex of cats: an in vivo microscopic study. Brain research, 1981. 208(1): p. 35-58.
33. Cassot, F., et al., A novel three-dimensional computer-assisted method for a quantitative study of microvascular networks of the human cerebral cortex. Microcirculation, 2006. 13(1): p. 1-18.
34. Simsek, F.G. and Y.W. Kwon, Investigation of material modeling in fluid–structure interaction analysis of an idealized three-layered abdominal aorta: aneurysm initiation and fully developed aneurysms. Journal of biological physics, 2015. 41(2): p. 173-201.
35. Raghavan, M. and D.A. Vorp, Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. Journal of biomechanics, 2000. 33(4): p. 475-482.
36. Colwell, J.A., M. Lopes-Virella, and P.V. Halushka, Pathogenesis of atherosclerosis in diabetes mellitus. Diabetes care, 1981. 4(1): p. 121-133.
37. Sarnak, M.J., et al., Anemia as a risk factor for cardiovascular disease in The Atherosclerosis Risk in Communities (ARIC) study. Journal of the American College of Cardiology, 2002. 40(1): p. 27-33.
38. Pries, A.R., D. Neuhaus, and P. Gaehtgens, Blood viscosity in tube flow: dependence on diameter and hematocrit. American Journal of Physiology-Heart and Circulatory Physiology, 1992. 263(6): p. H1770-H1778.
39. Kwon, O., et al., Effect of blood viscosity on oxygen transport in residual stenosed artery following angioplasty. Journal of Biomechanical Engineering, 2008. 130(1).
40. Gori, F. and A. Boghi, Two new differential equations of turbulent dissipation rate and apparent viscosity for non-newtonian fluids. International communications in heat and mass transfer, 2011. 38(6): p. 696-703.
41. Gavrilov, A.A. and V.Y. Rudyak, Reynolds-averaged modeling of turbulent flows of power-law fluids. Journal of Non-Newtonian Fluid Mechanics, 2016. 227: p. 45-55.
42. Gavrilov, A. and V.Y. Rudyak, Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes. Fluid Dynamics, 2017. 52(3): p. 363-374.
43. Shamloo, A., et al., In silico study of patient-specific magnetic drug targeting for a coronary LAD atherosclerotic plaque. International Journal of Pharmaceutics, 2019. 559: p. 113-129.
44. Kobari, M., et al., Blood flow velocity in the pial arteries of cats, with particular reference to the vessel diameter. Journal of Cerebral Blood Flow & Metabolism, 1984. 4(1): p. 110-114.
45. Helfield, B.L. and D.E. Goertz, Nonlinear resonance behavior and linear shell estimates for Definity™ and MicroMarker™ assessed with acoustic microbubble spectroscopy. The Journal of the Acoustical Society of America, 2013. 133(2): p. 1158-1168.
46. Qin, S., C.F. Caskey, and K.W. Ferrara, Ultrasound contrast microbubbles in imaging and therapy: physical principles and engineering. Physics in medicine & biology, 2009. 54(6): p. R27.
47. Guan, J. and T.J. Matula, Using light scattering to measure the response of individual ultrasound contrast microbubbles subjected to pulsed ultrasound in vitro. The Journal of the Acoustical Society of America, 2004. 116(5): p. 2832-2842.
48. Marmottant, P., et al., A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture. The Journal of the Acoustical Society of America, 2005. 118(6): p. 3499-3505.
49. Borden, M.A. and K.-H. Song, Reverse engineering the ultrasound contrast agent. Advances in colloid and interface science, 2018. 262: p. 39-49.
50. van Rooij, T., Ultrasound contrast agents for imaging and therapy. 2017.
51. Kirby, B.J., Micro-and nanoscale fluid mechanics: transport in microfluidic devices. 2010: Cambridge university press.
52. Turton, R. and O. Levenspiel, A short note on the drag correlation for spheres. Powder technology, 1986. 47(1): p. 83-86.
53. Saffman, P.G., The lift on a small sphere in a slow shear flow. Journal of fluid mechanics, 1965. 22(2): p. 385-400.
54. Furlani, E., Magnetophoretic separation of blood cells at the microscale. Journal of Physics D: Applied Physics, 2007. 40(5): p. 1313.
55. Jorgensen, W.L. and J. Tirado-Rives, The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin. Journal of the American Chemical Society, 1988. 110(6): p. 1657-1666.
56. Ascher, U.M. and L.R. Petzold, Computer methods for ordinary differential equations and differential-algebraic equations. Vol. 61. 1998: Siam.
57. Curtiss, C.F. and J.O. Hirschfelder, Integration of stiff equations. Proceedings of the National Academy of Sciences, 1952. 38(3): p. 235-243.
58. Chung, J. and G. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. 1993.
59. Ivanov, K., M. Kalinina, and Y.I. Levkovich, Blood flow velocity in capillaries of brain and muscles and its physiological significance. Microvascular research, 1981. 22(2): p. 143-155.
60. Shore, A.C., Capillaroscopy and the measurement of capillary pressure. British journal of clinical pharmacology, 2000. 50(6): p. 501-513.
61. Fong, S.W., E. Klaseboer, and B.C. Khoo, Interaction of microbubbles with high intensity pulsed ultrasound. The Journal of the Acoustical Society of America, 2008. 123(3): p. 1784-1793.
62. de Saint Victor, M.-A., Investigating magnetically targeted microbubbles for ultrasound-enhanced thrombolysis. 2016, University of Oxford.
63. Shamloo, A., F. Manuchehrfar, and H. Rafii-Tabar, A viscoelastic model for axonal microtubule rupture. Journal of biomechanics, 2015. 48(7): p. 1241-1247.
64. Shamloo, A., et al., Targeted drug delivery of microbubble to arrest abdominal aortic aneurysm development: a simulation study towards optimized microbubble design. Scientific reports, 2020. 10(1): p. 1-17.
65. Bento, D., et al., Bubbles moving in blood flow in a microchannel network: The effect on the local hematocrit. Micromachines, 2020. 11(4): p. 344.
| Files | ||
| Issue | Vol 12 No 1 (2025) | |
| Section | Original Article(s) | |
| DOI | https://doi.org/10.18502/fbt.v12i1.17733 | |
| Keywords | ||
| Blood Flow Microbubble Microcirculation Drug Delivery | ||
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How to Cite
1.
Shurche S, Shahidani A, Bodaghi Hossein Abadi R. Characterizing the Flow and Interaction of Microbubbles in a 2D Capillary Network for Targeted Drug Delivery: A Simulation Study. Frontiers Biomed Technol. 2025;12(1):54-65.
