Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Blood flow modeling reveals improved collateral artery performance during the regenerative period in mammalian hearts

Nature Cardiovascular Research volume 1, pages 775–790 (2022)Cite this article

Subjects

Abstract

Collateral arteries bridge opposing artery branches, forming a natural bypass that can deliver blood flow downstream of an occlusion. Inducing coronary collateral arteries could treat cardiac ischemia, but more knowledge on their developmental mechanisms and functional capabilities is required. Here we used whole-organ imaging and three-dimensional computational fluid dynamics modeling to define spatial architecture and predict blood flow through collaterals in neonate and adult mouse hearts. Neonate collaterals were more numerous, larger in diameter and more effective at restoring blood flow. Decreased blood flow restoration in adults arose because during postnatal growth coronary arteries expanded by adding branches rather than increasing diameters, altering pressure distributions. In humans, adult hearts with total coronary occlusions averaged 2 large collaterals, with predicted moderate function, while normal fetal hearts showed over 40 collaterals, likely too small to be functionally relevant. Thus, we quantify the functional impact of collateral arteries during heart regeneration and repair—a critical step toward realizing their therapeutic potential.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Whole-organ imaging of coronary arteries at cellular resolution.
Fig. 2: Increased collateral arteries in neonate versus adult hearts after injury.
Fig. 3: Building a physiologically representative 3D model of mouse coronary arteries.
Fig. 4: Collateral arteries are predicted to perform better in neonate hearts.
Fig. 5: Evaluating collateral placement and the tradeoff between collateral number and size.
Fig. 6: Investigating hemodynamic differences between neonate and adult.
Fig. 7: Main branch coronary artery diameters remain constant while branching increases throughout postnatal development.
Fig. 8: Collateral arteries in adult and fetal human hearts.

Similar content being viewed by others

Data availability

All images used for collateral analysis are available in the Stanford Digital Repository (https://doi.org/10.25740/qk058jq2233). Images and meshes of the adult (https://www.vascularmodel.com/share.html?MTA2Tlk2Tg__) and neonate (https://www.vascularmodel.com/share.html?MTA1Tlk3Tg__) used for computational modeling are accessible in the vascular modeling repository (https://www.vascularmodel.com).

Code availability

The code used for flow simulations can be found on the SimVascular GitHub (https://simvascular.github.io/). Custom code for Strahler ordering and volume perfusion using publicly available modules, such as the vascular toolkit, can be found on GitHub (https://github.com/StanfordCBCL/Collateral).

References

  1. Go, A. S. et al. Heart disease and stroke statistics—2014 update: a report from the American Heart Association. Circulation 129, e28–e292 (2014).

    Article  PubMed  CAS  Google Scholar 

  2. Zimarino, M., D’andreamatteo, M., Waksman, R., Epstein, S. E. & De Caterina, R. The dynamics of the coronary collateral circulation. Nat. Rev. Cardiol. 11, 191–197 (2014).

    Article  PubMed  Google Scholar 

  3. Meier, P. et al. The impact of the coronary collateral circulation on outcomes in patients with acute coronary syndromes: results from the ACUITY trial. Heart 100, 647–651 (2014).

    Article  PubMed  Google Scholar 

  4. Yang, F. et al. Genetic engineering of human stem cells for enhanced angiogenesis using biodegradable polymeric nanoparticles. Proc. Natl Acad. Sci. USA 107, 3317–3322 (2010).

    Article  CAS  PubMed  Google Scholar 

  5. Red-Horse, K. & Das, S. New research is shining light on how collateral arteries form in the heart: a future therapeutic direction? Curr. Cardiol. Rep. 23, 30 (2021).

    Article  PubMed  Google Scholar 

  6. Maxwell, M. P., Hearse, D. J. & Yellon, D. M. Species variation in the coronary collateral circulation during regional myocardial ischaemia: a critical determinant of the rate of evolution and extent of myocardial infarction. Cardiovascular Res. 21, 737–746 (1987).

    Article  CAS  Google Scholar 

  7. Das, S. et al. A unique collateral artery development program promotes neonatal heart regeneration. Cell 176, 1128–1142 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Zhang, H. & Faber, J. E. De novo collateral formation following acute myocardial infarction: dependence on CCR2+ bone marrow cells. J. Mol. Cell. Cardiol. 87, 4–16 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. He, L. et al. Genetic lineage tracing discloses arteriogenesis as the main mechanism for collateral growth in the mouse heart. Cardiovasc. Res. 109, 419–430 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Lucitti, J. L. et al. Variants of Rab GTPase-effector binding protein-2 cause variation in the collateral circulation and severity of stroke. Stroke 47, 3022–3031 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  11. Traupe, T., Gloekler, S., De Marchi, S. F., Werner, G. S. & Seiler, C. Assessment of the human coronary collateral circulation. Circulation.122, 1210–1220 (2010).

    Article  PubMed  Google Scholar 

  12. Rios Coronado, P. E. & Red-Horse, K. Enhancing cardiovascular research with whole-organ imaging. Curr. Opin. Hematol. 28, 214–220 (2021).

    Article  CAS  PubMed  Google Scholar 

  13. Les, A. S. et al. Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics. Ann. Biomed. Eng. 38, 1288–1313 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  14. Seo, J., Ramachandra, A. B., Boyd, J., Marsden, A. L. & Kahn, A. M. Computational evaluation of venous graft geometries in coronary artery bypass surgery. Semin. Thorac. Cardiovasc. Surg. 34, 521–532 (2021).

    Article  PubMed  Google Scholar 

  15. Min, J. K. et al. Diagnostic accuracy of fractional flow reserve from anatomic CT angiography. JAMA 308, 1237–1245 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Zhao, S. et al. Patient-specific computational simulation of coronary artery bifurcation stenting. Sci. Rep. 11, 16486 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Shad, R. et al. Patient-specific computational fluid dynamics reveal localized flow patterns predictive of post-left ventricular assist device aortic incompetence. Circ. Heart Fail. 14, e008034 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  18. Su, B. et al. Numerical investigation of blood flow in three-dimensional porcine left anterior descending artery with various stenoses. Comput. Biol. Med. 47, 130–138 (2014).

    Article  PubMed  Google Scholar 

  19. Lindsey, S. E. et al. Growth and hemodynamics after early embryonic aortic arch occlusion. Biomech. Model. Mechanobiol. 14, 735–751 (2015).

    Article  PubMed  Google Scholar 

  20. Vedula, V. et al. A method to quantify mechanobiologic forces during zebrafish cardiac development using 4D light-sheet imaging and computational modeling. PLoS Comput. Biol. 13, e1005828 (2017).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  21. Suo, J. et al. Hemodynamic shear stresses in mouse aortas: implications for atherogenesis. Arterioscler. Thromb. Vasc. Biol. 27, 346–351 (2007).

    Article  CAS  PubMed  Google Scholar 

  22. Shannon, A. T. & Mirbod, P. Three-dimensional flow patterns in the feto-placental vasculature system of the mouse placenta. Microvasc. Res. 111, 88–95 (2017).

    Article  PubMed  Google Scholar 

  23. Bernabeu, M. O. et al. Computer simulations reveal complex distribution of haemodynamic forces in a mouse retina model of angiogenesis. J. R. Soc. Interface 11, 20140543 (2014).

  24. Greve, J. M. et al. Allometric scaling of wall shear stress from mice to humans: quantification using cine phase-contrast MRI and computational fluid dynamics. Am. J. Physiol. 291, 1700–1708 (2006).

    Google Scholar 

  25. Feintuch, A. et al. Hemodynamics in the mouse aortic arch as assessed by MRI, ultrasound and numerical modeling. Am. J. Physiol. 292, 884–892 (2007).

    Google Scholar 

  26. Acuna, A. et al. Computational fluid dynamics of vascular disease in animal models. J. Biomech. Eng. 140, 0808011 (2018).

    Article  PubMed Central  Google Scholar 

  27. Renier, N. et al. IDISCO: a simple, rapid method to immunolabel large tissue samples for volume imaging. Cell. 159, 896–910 (2014).

    Article  CAS  PubMed  Google Scholar 

  28. Renier, N. et al. Mapping of brain activity by automated volume analysis of immediate early genes. Cell 165, 1789–1802 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Pan, C. et al. Shrinkage-mediated imaging of entire organs and organisms using uDISCO. Nat. Methods 13, 859–867 (2016).

    Article  CAS  PubMed  Google Scholar 

  30. Feng, Y. et al. Bifurcation asymmetry of small coronary arteries in juvenile and adult mice. Front. Physiol. 9, 519 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  31. Arshadi, C., Günther, U., Eddison, M., Harrington, K. I. S. & Ferreira, T. A. SNT: a unifying toolbox for quantification of neuronal anatomy. Nat. Methods 18, 374–377 (2021).

    Article  CAS  PubMed  Google Scholar 

  32. Longair, M. H., Baker, D. A. & Armstrong, J. D. Simple Neurite Tracer: open source software for reconstruction, visualization and analysis of neuronal processes. Bioinformatics 27, 2453–2454 (2011).

    Article  CAS  PubMed  Google Scholar 

  33. Updegrove, A. et al. SimVascular: an open source pipeline for cardiovascular simulation. Ann. Biomed. Eng. 45, 525–541 (2017).

    Article  PubMed  Google Scholar 

  34. Le, V. P. & Wagenseil, J. E. Echocardiographic characterization of postnatal development in mice with reduced arterial elasticity. Cardiovasc. Eng. Technol. 3, 424–438 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  35. Huo, Y., Guo, X. & Kassab, G. S. The flow field along the entire length of mouse aorta and primary branches. Ann. Biomed. Eng. 36, 685–699 (2008).

    Article  PubMed  Google Scholar 

  36. Vignon-Clementel, I. E., Figueroa, C. A., Jansen, K. E. & Taylor, C. A. Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries. Comput. Methods Biomech. Biomed. Engin. 13, 625–640 (2010).

    Article  CAS  PubMed  Google Scholar 

  37. Kim, H. J. et al. Patient-specific modeling of blood flow and pressure in human coronary arteries. Ann Biomed Eng. 38, 3195–3209 (2010).

    Article  CAS  PubMed  Google Scholar 

  38. Tran, J. S., Schiavazzi, D. E., Ramachandra, A. B., Kahn, A. M. & Marsden, A. L. Automated tuning for parameter identification and uncertainty quantification in multi-scale coronary simulations. Comput. Fluids 142, 128–138 (2017).

    Article  PubMed  Google Scholar 

  39. Huang, Y., Guo, X. & Kassab, G. S. Axial nonuniformity of geometric and mechanical properties of mouse aorta is increased during postnatal growth. Am. J. Physiol. 290, 657–664 (2006).

    Article  CAS  Google Scholar 

  40. Seiler, C., Fleisch, M., Garachemani, A. & Meier, B. Coronary collateral quantitation in patients with coronary artery disease using intravascular flow velocity or pressure measurements. J. Am. Coll. Cardiol. 32, 1272–1279 (1998).

    Article  CAS  PubMed  Google Scholar 

  41. Stoner, J. D., Angelos, M. G. & Clanton, T. L. Myocardial contractile function during postischemic low-flow reperfusion: critical thresholds of NADH and O2 delivery. Am. J. Physiol. Heart Circ. Physiol. 286, H375–H380 (2004).

    Article  CAS  PubMed  Google Scholar 

  42. Huang, W., Yen, R. T., McLaurine, M. & Bledsoe, G. Morphometry of the human pulmonary vasculature. J. Appl. Physiol. 81, 2123–2133 (1996).

    Article  CAS  PubMed  Google Scholar 

  43. Kassab, G. S., Rider, C. A., Tang, N. J. & Fung, Y. C. B. Morphometry of pig coronary arterial trees. Am. J. Physiol. 265, H350–H365 (1993).

    CAS  PubMed  Google Scholar 

  44. Fleeter, C. M., Geraci, G., Schiavazzi, D. E., Kahn, A. M. & Marsden, A. L. Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics. Comput. Methods Appl. Mech. Eng. 365, 113030 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  45. Pfaller, M. R., Pham, J., Verma, A., Pegolotti, L., Wilson, N. M., Parker, D. W., Yang, W. and Marsden, A. L. Automated generation of 0D and 1D reduced-order models of patient-specific blood flow. Int. J. Numer. Method. Biomed. Eng. Preprint at https://arxiv.org/abs/2111.04878 (2022).

  46. Wustmann, K., Zbinden, S., Windecker, S., Meier, B. & Seiler, C. Is there functional collateral flow during vascular occlusion in angiographically normal coronary arteries? Circulation 107, 2213–2220 (2003).

    Article  PubMed  Google Scholar 

  47. Meier, P. et al. The collateral circulation of the heart. BMC Med. 11, 143 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  48. Reiner, L., Molnar, J., Jimenez, F. A. & Freudenthal, R. R. Interarterial coronary anastomoses in neonates. Arch. Pathol. 71, 103–112 (1961).

    CAS  PubMed  Google Scholar 

  49. Bloor, C. M., Keefe, J. F. & Browne, M. J. Intercoronary anastomoses in congenital heart disease. Circulation 33, 227–231 (1966).

    Article  CAS  PubMed  Google Scholar 

  50. Kolesová, H., Bartoš, M., Hsieh, W. C., Olejníčková, V. & Sedmera, D. Novel approaches to study coronary vasculature development in mice. Dev. Dyn. 247, 1018–1027 (2018).

    Article  PubMed  CAS  Google Scholar 

  51. Kirst, C. et al. Mapping the fine-scale organization and plasticity of the brain vasculature. Cell 180, 780–795 (2020).

    Article  CAS  PubMed  Google Scholar 

  52. Mittal, N. et al. Analysis of blood flow in the entire coronary arterial tree. Am. J. Physiol. 289, 439–446 (2005).

    Google Scholar 

  53. Huo, Y. et al. Growth, ageing and scaling laws of coronary arterial trees. J. R. Soc. Interface 12, 20150830 (2015).

  54. Hutchins, G. M., Miner, M. M. & Bulkley, B. H. Tortuosity as an index of the age and diameter increase of coronary collateral vessels in patients after acute myocardial infarction. Am. J. Cardiol. 41, 210–215 (1978).

    Article  CAS  PubMed  Google Scholar 

  55. Chilian, W. M., Eastham, C. L. & Marcus, M. L. Microvascular distribution of coronary vascular resistance in beating left ventricle. Am. J. Physiol. 251, H779–H788 (1986).

    CAS  PubMed  Google Scholar 

  56. Nellis, S. H., Liedtke, A. J. & Whitesell, L. Small coronary vessel pressure and diameter in an intact beating rabbit heart using fixed-position and free-motion techniques. Circ. Res. 49, 342–353 (1981).

    Article  CAS  PubMed  Google Scholar 

  57. Gould, K. L., Lipscomb, K. & Calvert, C. Compensatory changes of the distal coronary vascular bed during progressive coronary constriction. Circulation 51, 1085–1094 (1975).

    Article  CAS  PubMed  Google Scholar 

  58. Dick, G. M., Namani, R., Patel, B. & Kassab, G. S. Role of coronary myogenic response in pressure-flow autoregulation in Swine: a meta-analysis with coronary flow modeling. Front. Physiol. 9, 580 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  59. Shalman, E., Rosenfeld, M., Dgany, E. & Einav, S. Numerical modeling of the flow in stenosed coronary artery. The relationship between main hemodynamic parameters. Comput. Biol. Med. 32, 329–344 (2002).

    Article  CAS  PubMed  Google Scholar 

  60. Malkasian, S., Hubbard, L., Dertli, B., Kwon, J. & Molloi, S. Quantification of vessel-specific coronary perfusion territories using minimum-cost path assignment and computed tomography angiography: Validation in a swine model. J. Cardiovasc. Comput. Tomogr. 12, 425–435 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  61. Van Doormaal, M. A. et al. Haemodynamics in the mouse aortic arch computed from MRI-derived velocities at the aortic root. J. R. Soc. Interface 9, 2834–2844 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  62. Hartley, C. J., Reddy, A. K., Michael, L. H., Entman, M. L. & Taffet, G. E. Coronary flow reserve as an index of cardiac function in mice with cardiovascular abnormalities. in 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society 1094–1097 https://doi.org/10.1109/IEMBS.2009.5332488 (IEEE, 2009).

  63. Sankaran, S. et al. Patient-specific multiscale modeling of blood flow for coronary artery bypass graft surgery. Ann. Biomed. Eng. 40, 2228–2242 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  64. Fåhræus, R. & Lindqvist, T. The viscosity of the blood in narrow capillary tubes. Am. J. Physiol. 96, 562–568 (1931).

    Article  Google Scholar 

  65. Dong, M. et al. Image-based scaling laws for somatic growth and pulmonary artery morphometry from infancy to adulthood. Am. J. Physiol. 319, H432–H442 (2020).

    Article  CAS  Google Scholar 

  66. Raftrey, B. et al. Dach1 extends artery networks and protects against cardiac injury. Circ. Res. 129, 702–716 (2021).

    Article  CAS  PubMed  Google Scholar 

  67. Yardeni, T., Eckhaus, M., Morris, H. D., Huizing, M. & Hoogstraten-Miller, S. Retro-orbital injections in mice. Lab Anim. 40, 155–160 (2011).

    Article  Google Scholar 

  68. Cunningham, F. G. et al. Abortion. in Williams Obstetrics, 25e (McGraw-Hill Education, 2018).

  69. Cunningham, F. G. et al. Prenatal care. in Williams Obstetrics, 25e (McGraw-Hill Education, 2018).

Download references

Acknowledgements

We thank A. Olson and M. Howard for technical support of light-sheet imaging and H. Wang for advice on surgical procedures. S.A. is supported by the BioX Bowes Fellowship. P.E.R.C. is supported by the NIGMS of the NIH (T32GM007276) and NSF-GRFP (DGE-1656518). M.L.D. is supported by the NSF-GRFP (DGE-1656518). D.B. is supported by the Department of Defense CMDRP in Congenital Heart Disease (W81XWH-16-1-0727). K.N. is supported by the NIH/NHLBL (R01HL141712; R01HL146754) and reports unrestricted institutional research support from Siemens Healthineers, Bayer, HeartFlow Inc., Novartis unrelated to this work, consulting for Siemens Medical Solutions USA and equity in Lumen Therapeutics. A.L.M. is supported by NIH (R01EB018302) and NSF Award (1663671). K.R.H. is supported by the NIH/NHLBL (R01-HL128503) and is an HHMI Investigator.

Author information

Author notes

  1. These authors contributed equally: Suhaas Anbazhakan, Pamela E. Rios Coronado.

Authors and Affiliations

  1. Department of Bioengineering, Stanford University, Stanford, CA, USA

    Suhaas Anbazhakan, Melody L. Dong, Martin R. Pfaller & Alison L. Marsden

  2. Department of Biology, Stanford University, Stanford, CA, USA

    Pamela E. Rios Coronado, Ana Natalia L. Sy-Quia, Lek Wei Seow, Aubrey M. Hands, Zhainib A. Amir, Brian C. Raftrey, Christopher K. Cook, Gaetano D’Amato, Xiaochen Fan, Ian M. Williams, Sawan K. Jha & Kristy Red Horse

  3. Department of Pediatrics, Stanford University School of Medicine, Stanford, CA, USA

    Mingming Zhao, Martin R. Pfaller, Daniel Bernstein, Anca M. Pașca & Alison L. Marsden

  4. Stanford Cardiovascular Institute, Stanford University School of Medicine, Stanford, CA, USA

    Mingming Zhao, Daniel Bernstein, Alison L. Marsden & Kristy Red Horse

  5. Departments of Cardiovascular Medicine and Radiology, School of Medicine, Stanford University, Stanford, CA, USA

    Koen Nieman

  6. Institute for Stem Cell Biology and Regenerative Medicine, Stanford University School of Medicine, Stanford, CA, USA

    Kristy Red Horse

  7. Howard Hughes Medical Institute, Stanford, CA, USA

    Kristy Red Horse

Authors
  1. Suhaas Anbazhakan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pamela E. Rios Coronado
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ana Natalia L. Sy-Quia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lek Wei Seow
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Aubrey M. Hands
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mingming Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Melody L. Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Martin R. Pfaller
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Zhainib A. Amir
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Brian C. Raftrey
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Christopher K. Cook
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Gaetano D’Amato
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Xiaochen Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Ian M. Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. Sawan K. Jha
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. Daniel Bernstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. Koen Nieman
    View author publications

    You can also search for this author in PubMed Google Scholar

  18. Anca M. Pașca
    View author publications

    You can also search for this author in PubMed Google Scholar

  19. Alison L. Marsden
    View author publications

    You can also search for this author in PubMed Google Scholar

  20. Kristy Red Horse
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.A., P.E.R.C., A.L.M. and K.R.H. conceived and designed the project. S.A., P.E.R.C., A.N.L.S.-Q., C.K.C., G.D., X.F., I.M.W. and S.K.J. performed experiments. S.A., P.E.R.C., A.N.L.S.-Q., L.W.S., A.M.H. and Z.A.A. analyzed data. S.A. performed fluid simulations. P.E.R.C., B.C.R., M.Z. and D.B. performed mouse cardiac injury studies. K.N. and A.M.P. contributed human adult and fetal samples, respectively. S.A., M.L.D. and M.R.P. provided analysis tools. S.A. and P.E.R.C. prepared the figures. S.A., P.E.R.C., A.L.M. and K.R.H. wrote the article.

Corresponding authors

Correspondence to Alison L. Marsden or Kristy Red Horse.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Cardiovascular Research thanks Nicola Smart, Luke Timmins, Jonathan Butcher and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Collateral formation in neonatal mice is a response of injury.

a, Maximum intensity projections of a representative, non-injured neonatal P6 heart immunolabeled with α-SMA. b, Maximum projection of traces beginning at the most proximal segment of the left coronary artery (LCA) and extended until the α-SMA signal discontinues. c, Quantification of collateral numbers in healthy and injured (4-days post MI) neonatal hearts. n = 6 uninjured, n = 9 injured hearts. Scale bars, 500 μm. Error bars are mean ± st dev: ****, p≤0.0001 by two-sided Student’s t-test.

Extended Data Fig. 2 Collateral artery assessments.

a,b, Maximum intensity projection of an entire neonate and adult heart 4-days post myocardial infarction (MI) immunolabeled with α-SMA. (a) P6 neonatal heart. (b) Adult (12-week-old) heart. c, Collateral numbers in neonate (n=9 hearts) and adult (n=6 hearts) 4 days post-MI. d–f, Evaluation of collateral patency in P6 neonatal heart 4-days post MI. (d) Schematic of staining method. (e) 3D reconstruction of α-SMA+ collaterals (purple) overlaid with α-SMA and CD31 staining. (f) MIPs of representative Z-stacks (30 μm) within e highlighting (solid purple arrow) a patent (α-SMA+ and CD31+) collateral. Scale bars: a and b 1 mm; e 500 μm. Error bars are mean ± st dev: ****, p≤0.0001 by two-sided Student’s t-test.

Extended Data Fig. 3 Investigation into parameters related to collateral artery placement.

a,b, Location of collateral bridges in relationship to infarcted tissue. (a) Schematic of categorization shown in b. b, Pie chart showing distribution of collateral location (n = 87 collaterals, n = 6 hearts). Distribution by collateral configuration type (n = 47 collaterals, n = 3 hearts). c, Distances between the aorta and collateral bridges (n = 47 collaterals, n = 3 hearts). d–f, Septal artery evaluation. (d) Distances between most distal RCA and SpA branch tips to the aorta. (e) Representative image of 3D rendered coronary artery branch tips and distances. (f) Quantification of distances in e between most distal branch tips of RCA and SpA to LCA. Right (RCA), left (LCA), and septal (SpA) coronary arteries. d–f, n = 3 hearts. Error bars are mean ± st dev: ****, p≤0.0001 by two-sided Student’s t-test.

Extended Data Fig. 4 0D surrogate model of pulsatile coronary flow.

a, Schematic of coronary lumped parameter network (LPN). b, Pressure quantities of the coronary LPN. Pa, Pressure at point a; Pb, pressure at point b; Paorta, pressure at aortic inlet; ΔPcor, pressure difference between Paorta and Pb.

Extended Data Fig. 5 Virtual coronary collateral configurations in adult and neonates.

a–e, Adult configurations: 6 collaterals, 20 μm (a); 6 collaterals, 28 μm (b); 12 collaterals, 20 μm (c); 3 collaterals, 40 μm (d); 9 collaterals, 40 μm (e). f, Pressure increases for each collateral in c with and without a 99% stenosis. g–j, Neonatal configurations: 6 collaterals, 20 μm (g); 12 collaterals, 10 μm (h); 12 collaterals, 20 μm (i); 1 collateral, 40 μm (j). Pie chart indicates number of collaterals per connection type.

Extended Data Fig. 6 Verification that collateral flows are in line with expected solutions.

a, Schematic of total collateral flow quantification. b, Total collateral flow vs. diameter of the collateral at each stenosis level. c, Total collateral flow vs. resistance of the collateral configurations 6 collaterals, 20 μm; 12 collaterals, 20 μm; 6 collaterals, 28 μm; 3 collaterals, 40 μm. Resistance was calculated based on the number, diameter, and length of the collaterals via Poiseuille’s Law.

Extended Data Fig. 7 Performance of neonate collaterals formed 4 days post injury.

ai-ii, Coronary vasculature with (ai) and without (aii) collaterals formed in response to injury, respectively. aiii, Perfusion territories of the left (LCA), right (RCA), and septal (SpA) coronary arteries. aiv, Pressure distribution based on CFD simulation. Red arrow indicates location of occlusion that has been virtually restored. b, Pressures at tips near real collateral (red segment) attachment sites (green circles) after injury and non-attached tips (orange circles) in the injury region. c, Pressure at every tip and only distal tips of the SpA or RCA in non-injured hearts (n=81 all RCA tips, n=67 all SpA tips, n=22 distal RCA tips, n=16 distal SpA tips, n=1 heart). d, Fold change at the connection sites of the collateral (red segment) when it is present and removed. The circle on the left is the pressure on either the RCA or SpA branch and the square on the right is the pressure on the LCA branch. e, The difference in pressure across the two connection sites with and without the collateral (n=8 connections, n=1 heart). f,g, The bar graph of percent volume-at-risk (VaR) above 30% (f), and total flow in vessels downstream of the virtual occlusion (g) within the VaR. Error bars are mean ± st dev: ****, p≤0.0001.

Extended Data Fig. 8 Streamlines of adult collaterals.

a–d, Streamlines of collateral flow for configurations: 16 collaterals, 20 μm (a) and 3 different types of 1 collateral, 40 μm b–d, Colors represent the streamlines from 1 collateral.

Extended Data Fig. 9 User segmentation variability and sensitivity analysis.

a, Radius measurements from 5 users of 16 segmentations over 3 vessels. The coefficient of variation is 16.7%. b, Sensitivity of pressure drop along the coronary tree to the radius of segmented vessels. Adult vessel radius was reduced by 20% and neonate vessel radius was increased by 20%.

Extended Data Fig. 10 Collaterals in fetal human hearts.

a, Maximum intensity projection (MIP) of GW22 fetal human heart labeled with α-SMA, ventral side. bi, ROI of ventral side (blue boxed region). Closed orange arrows point to collateral segments. bii, Traced collateral connection (green filaments) on ventral side. ci, MIP of fetal human heart, dorsal side. cii, Traced collateral connections (green filaments) on dorsal side. d–f, MIP of entire fetal human GW14.5 (d), GW18.5 (e) and GW19.5 (f) hearts, ventral side. Scale bars, a–f, 1.5 mm.

Supplementary information

Supplementary Information

Extended Data figure legends, Supplementary Tables 1 and 2 and legends and Supplementary Video 1–3 captions

Reporting Summary

Supplementary Video 1

Collateral tracing method. Representative collateral traces of P6 neonatal heart labeled with α-SMA (white), 4 d after MI. The first clip shows a subset of optical cross-sections and the collateral connections that were semi-automatically traced (magenta) from downstream of the suture (red cross). The second clip shows 3D rendering of traced collateral arteries (magenta) overlaid with the entire heart volume (gray). Next, the traced collaterals (magenta) were isolated, quantified and categorized in 3D (cyan).

Supplementary Video 2

Collateral patency assay. 3D reconstruction of entire P6 neonatal heart 4 d after MI subjected to collateral patency assay. Coronary arteries were immunolabeled with α-SMA (white) and endothelial cells were labeled in vivo (anti-CD31, orange) to assess perfusion of α-SMA+ collaterals (purple surface). Next, the video shows optical cross-sections of the volume occupied by one representative patent collateral artery (α-SMA+ and CD31+). An outline (purple dashed line) of the collateral bridge as well as an arrow (solid purple) follows the collateral bridge throughout the heart.

Supplementary Video 3

Collateral bridge. 3D rendering of one representative collateral bridge in a P6 neonatal heart 4 d after MI labeled with α-SMA (white) and podocalyxin (cyan). Next, the video shows optical cross-sections of the isolated volume and the entire path of the representative collateral bridge (red dashed line). The infarcted zone was outlined by the lack of autofluorescence signal (yellow).

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anbazhakan, S., Rios Coronado, P.E., Sy-Quia, A.N.L. et al. Blood flow modeling reveals improved collateral artery performance during the regenerative period in mammalian hearts. Nat Cardiovasc Res 1, 775–790 (2022). https://doi.org/10.1038/s44161-022-00114-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s44161-022-00114-9

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing