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Biochemomechanics of Cerebral Vasospasm and its Resolution: I. A New Hypothesis and Theoretical Framework

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Abstract

The etiology, and hence most effective treatment, of cerebral vasospasm remains unknown, thus this devastating sequela to subarachnoid hemorrhage continues to be responsible for significant morbidity and mortality. Based on abundant and diverse clinical and laboratory observations, we hypothesize that vasospasm and its subsequent resolution result from a short-term chemo-dominated turnover of cells and matrix in evolving vasoconstricted states that produces a narrowed lumen and thicker wall, which is stiffer and largely unresponsive to exogenous vasodilators, and a subsequent mechano-dominated turnover of cells and matrix in evolving vasodilated states that restores the vessel toward normal. There is, however, a pressing need for a mathematical model of arterial growth and remodeling that can guide the design and interpretation of experiments to test this and competing hypotheses. Toward this end, we present a new biochemomechanical framework that couples a 2-D model of the evolving geometry, structure, and properties of the affected arterial wall, a 1-D model of the blood flow within the affected segment, and a 0-D model of the biochemical insult to the segment. We submit that such a framework can capture salient features of the time-course of vasospasm and its potential resolution, as illustrated numerically in part II of this paper.

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References

  1. Alastruey, J., K. H. Parker, J. Peiro, 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. (in press)

  2. Baek S., Rajagopal K. R., Humphrey J. D. (2006) A theoretical model of enlarging intracranial fusiform aneurysms. ASME J. Biomech. Eng. 128:142–149

    Article  CAS  Google Scholar 

  3. Baek, S., A. Valentin, and J. D. Humphrey. Biomechanics of cerebral vasospasm and its resolution: II. Constitutive relations and model simulations. Ann. Biomed. Eng. doi: 10.1007/s10439-007-9322-x

  4. Bakker E. N. T .P, Buus C. L., VanBavel E., Mulvaney M. J. (2004) Activation of resistance arteries with endothelin-1: from vasoconstriction to functional adaptation and remodeling. J. Vasc. Res. 41:174–182

    Article  PubMed  CAS  Google Scholar 

  5. Bayer I. M., Adamson S. L., Langille B. L. (1999) Atrophic remodeling of the artery-cuffed artery. Arterioscler. Thromb. Vasc. Biol. 19:1499–1505

    PubMed  CAS  Google Scholar 

  6. Bermek H., Peng K. C., Angelova K., Ergul A., Puett D. (1996) Endothelin degradation by vascular smooth muscle cells. Reg. Peptides 66:155–162

    Article  CAS  Google Scholar 

  7. Borel C. O., McKee A., Parra A., Haglund M. M., Solan A., Prabhakar V., Sheng H., Warner D. S., Niklason L. E. (2003) Possible role for vascular cell proliferation in cerebral vasospasm after subarachnoid hemorrhage. Stroke 34:427–433

    Article  PubMed  CAS  Google Scholar 

  8. Butler W. E., Peterson J. W., Zervas N. T., Morgan K. G. (1996) Intracellular calcium, myosin light chain phosphorylation, and contractile force in experimental cerebral vasospasm. Neurosurgery 38:781–788

    Article  Google Scholar 

  9. Cebral J. R., Castro M. A., Soto O., Lohner R., Alperin N. (2003) Blood flow models of the circle of Willis from magnetic resonance data. J. Eng. Math. 47:369–386

    Article  Google Scholar 

  10. Clerin V., Nichol J. W., Petko M., Myung R. J., Gaynor J. W., Gooch K. J. (2003) Tissue engineering of arteries by directed remodeling of intact arterial segments. Tissue Eng. 9:461–472

    Article  PubMed  Google Scholar 

  11. Davies P. F. (1995) Flow-mediated endothelial mechanotransduction. Physiol. Rev. 75(3):519–560

    PubMed  CAS  Google Scholar 

  12. Dietrich H. H., Dacey R. G. (2000) Molecular keys to the problems of cerebral vasospasm. Neurosurgery 46:517–530

    Article  PubMed  CAS  Google Scholar 

  13. Dumont A. S., Dumont R. J., Chow M. M., Lin C.-L., Calisaneller T., Ley K. F., Kassell N. F., Lee K. S. (2003) Cerebral vasospasm after subarachnoid hemorrhage: putative role of inflammation. Neurosurgery 53:123–135

    Article  PubMed  Google Scholar 

  14. Dzau V. J., Gibbons G. H. (1993) Vascular remodeling: mechanisms and implications. J. Cardiovasc. Pharmacol. 21 (Suppl):S1–S5

    PubMed  CAS  Google Scholar 

  15. Ferrandez A., David T., Brown M. D. (2002) Numerical models of auto-regulation and blood flow in the cerebral circulation. Comput. Meth. Biomech. Biomed. Eng. 5:7–20

    Article  CAS  Google Scholar 

  16. Gao E., Young W. L., Pile-Spellman J., Ornstein E., Ma Q. (1998) Mathematical considerations for modeling cerebral blood flow autoregulation to systemic arterial pressure. Am. J. Physiol. 274: H1023–H1031

    PubMed  CAS  Google Scholar 

  17. Gleason R. L., Taber L. A., Humphrey J. D. (2004) A 2-D model of flow-induced alterations in the geometry, structure and properties of carotid arteries. ASME J. Biomech. Eng. 126:371–381

    Article  CAS  Google Scholar 

  18. Gleason R. L., Humphrey J. D. (2004) A mixture model of arterial growth and remodeling in hypertension: Altered muscle tone and tissue turnover. J. Vasc. Res. 41:352–363

    Article  PubMed  CAS  Google Scholar 

  19. Grasso G. (2004) An overview of new pharmacological treatments for cerebrovascular dysfunction after experimental subarachnoid hemorrhage. Brain Res. Dev. 44:49–63

    Article  CAS  Google Scholar 

  20. Handa Y., Hayashi M., Takeuchi H., Kubota T., Kobayashi H., Kawano H., Time course of the impairment of cerebral autoregulation during chronic cerebral vasospasm after subarachnoid hemorrhage in primates. J. Neurosurg. 78:112–119, 1993

    PubMed  CAS  Google Scholar 

  21. Hu J. J, Fossum T. W., Miller M. W., Xu H., Liu S., Humphrey J. D. (2007) Biomechanical behavior of the porcine basilar artery in hypertension. Ann. Biomed. Eng. 35:19–29

    Article  PubMed  CAS  Google Scholar 

  22. Hu, J. J., S. Baek, and J. D. Humphrey. Stress–strain behavior of the passive basilar artery in normotension and hypertension. J. Biomech. (in press).

  23. Humphrey J. D. (2002) Cardiovascular Solid Mechanics: Cells, Tissues, and Organs. Springer-Verlag, NY

    Google Scholar 

  24. Humphrey J. D., Rajagopal K. R. (2003) A constrained mixture model for arterial adaptations to a sustained step change in blood flow. Biomech. Model Mechanobiol. 2:109–126

    Article  PubMed  CAS  Google Scholar 

  25. Humphrey J. D., Na S. (2002) Elastodynamics and arterial wall stress. Ann. Biomed. Eng. 30:509–523

    Article  PubMed  CAS  Google Scholar 

  26. Humphrey J. D., Wilson E. (2003) A potential role of smooth muscle tone in early hypertension: a theoretical study. J. Biomech. 36:1595–1601

    Article  PubMed  Google Scholar 

  27. Humphrey J. D., Delange S. L. (2004) An Introduction to Biomechanics: Solids and Fluids, Analysis and Design. Springer-Verlag, NY

    Google Scholar 

  28. Kapp J. P., Neill W. R., Neill C. L., Hodges L. R., Smith R. R. (1982) The three phases of vasospasm. Surg. Neurol. 18:40–45

    Article  PubMed  CAS  Google Scholar 

  29. Kassell N. F., Helm G., Simmons N., Phillips C. D., Cail W. S. (1992) Treatment of cerebral vasospasm with intra-arterial papaverine. J. Neurosurg. 77:848–852

    PubMed  CAS  Google Scholar 

  30. Khanin M. A., Semenov V. V. (1989) A mathematical model of the kinetics of blood coagulation. J. Theor. Biol. 136:127–134

    Article  PubMed  CAS  Google Scholar 

  31. Kim P., Sundt T. M., Vanhoutte P. M. (1989) Alterations of mechanical properties in canine basilar arteries after subarachnoid hemorrhage. J. Neurosurg. 71:430–436

    PubMed  CAS  Google Scholar 

  32. Langille B. L., Bendeck M. P., Keeley F. W. (1989) Adaptations of carotid arteries of young and mature rabbits to reduced carotid blood flow. Am. J. Physiol. 256:H931-H939

    PubMed  CAS  Google Scholar 

  33. Langille B. L. (1996) Arterial remodeling: relation to hemodynamics. Can. J. Physiol. Pharmacol. 74(7):834–841

    Article  PubMed  CAS  Google Scholar 

  34. Lee R. M. K. W. (1995) Morphology of cerebral arteries. Pharmac Ther 66:149–173

    Article  CAS  Google Scholar 

  35. Levy B. I. (1999) Tedgui. Biology of the Arterial Wall. Kluwer Academic Press, Dordrecht

    Google Scholar 

  36. Lodi C. A., Ursino M. (1999) Hemodynamic effect of cerebral vasospasm in humans: a modeling study. Ann. Biomed. Eng. 27:257–273

    Article  PubMed  CAS  Google Scholar 

  37. Macdonald R. L. (2001) Pathophysiology and molecular genetics of vasospasm. Acta Neurochir. 77:7–11

    CAS  Google Scholar 

  38. Macdonald R. L, Weir B. (2001) Cerebral Vasospasm. Academic Press, San Diego

    Google Scholar 

  39. Martinez-Lemus, L. A., Hill M. A., Bolz S. S., Pohl U., Meininger G. A. (2004) Acute mechanoadaptation of vascular smooth muscle cells in response to continuous arteriolar vasoconstriction: implications for functional remodeling. FASEB J 18:708–710

    PubMed  CAS  Google Scholar 

  40. Mayberg M. R., Okada T., Bark D. H. (1990) Morphologic changes in cerebral arteries after subarachnoid . Neurosurg. Clinics N Am. 1:417–432

    CAS  Google Scholar 

  41. Mayberg M. R, Okada T., Bark D. H. (1990) The significance of morphological changes in cerebral arteries after subarachnoid hemorrhage. J Neurosurg 72:626–633

    PubMed  CAS  Google Scholar 

  42. McGirt M. J, Lynch J. R., Blessing R., Warner D. S., Friedman A. H., Laskowitz D. T. (2002) Serum von Willebrand factor, matrix metalloproteinase-9, and vascular endothelial growth factor levels predict the onset of cerebral vasospasm after aneurysmal subarachnoid hemorrhage. Neurosurgery 51:1128–1135

    Article  PubMed  Google Scholar 

  43. Milnor, W. R. Cardiovascular Physiology. Oxford University Press, 1990

  44. Moore S., David T., Chase J. G., Arnold J., Fink J. (2005) 3D models of blood flow in the cerebral vasculature. J Biomech 39:1454–1463

    Article  PubMed  Google Scholar 

  45. Nagasawa S., Handa H., Okumura A., Naruo Y., Okamoto S., Moritake K., Hayashi K. (1980) Mechanical properties of human cerebral arteries: part 2. Vasospasm. Surg. Neurol. 14:285–290

    PubMed  CAS  Google Scholar 

  46. Nagasawa S., Handa H., Naruo Y., Moritake K., Hayashi K. (1982) Experimental cerebral vasospasm arterial wall mechanics and connective tissue composition. Stroke 13:595–600

    PubMed  CAS  Google Scholar 

  47. Nagasawa, Handa H., Naruo Y., Watanabe H., Moritake K., Hayashi K. (1983) Experimental cerebral vasospasm. Part 2. Contractility of spastic arterial wall. Stroke 14:579–584

    PubMed  CAS  Google Scholar 

  48. Olufsen M. S., Peskin C. S., Kim W. Y., Pedersen E. M., Nadim A., Larsen J. (2000) Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions. Ann. Biomed. Eng. 28:1281–1299

    Article  PubMed  CAS  Google Scholar 

  49. Olfusen M. S., Nadim A., Lipsitz L. A. (2002) Dynamics of cerebral blood flow regulation explained using a lumped parameter model. Am. J. Physiol. 282:R611–R622

    Google Scholar 

  50. Oskouian Jr. R. J., Martin N. A., Lee J. H., Glenn T. C., Guthrie D., Gonzalez N. R., Afari A., Vinuela F. (2002) Multimodal quantitation of the effects of endovascular therapy for vasospasm on cerebral blood flow, transcranial doppler ultrasonographic velocities, and cerebral artery diameters. Neurosurgery 51:30–41

    Article  PubMed  Google Scholar 

  51. Potter M. C., Wiggert D. C. (1991) Mechanics of Fluids. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  52. Price J. M., Davis D. L., Knauss E. B. (1981) Length-dependent sensitivity in vascular smooth muscle. Am. J. Physiol. 241:H557–H563

    PubMed  CAS  Google Scholar 

  53. Pluta R. M. (2005) Delayed cerebral vasospasm and nitric oxide: Review, new hypothesis, and proposed treatment. Pharmacol. Therapeut. 105:23–56

    Article  CAS  Google Scholar 

  54. Rachev A., Hayashi K. (1999) Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Ann. Biomed. Eng. 27:459–468

    Article  PubMed  CAS  Google Scholar 

  55. Reilly C., Amidei C., Tolentino J., Jahromi B. S., Macdonald R. L. (2004) Clot volume and clearance rate as independent predictors of vasospasm after aneurysmal subarachnoid hemorrhage. J. Neurosurg. 101:255–261

    Article  PubMed  Google Scholar 

  56. Rodriguez E. K., Hoger A., McCulloch A. D. (1994) Stress-dependent finite growth in soft elastic tissues. J. Biomech. 27:455–467

    Article  PubMed  CAS  Google Scholar 

  57. Torbey M. T., Hauser T.-K., Bhardwaj A., Williams M. A., Ulatowski J. A., Mirski M. A., Razumovsky A. Y. (2001) Effect of age on cerebral blood flow velocity and incidence of vasospasm after aneurysmal subarachnoid hemorrhage. Stroke 32:2005–2011

    PubMed  CAS  Google Scholar 

  58. Vajkoczy P., Horn P., Bauhuf C., Munch E., Hubner U., Ing D., Thome C., Poeckler-Schoeninger C., Roth H., Schmiedek P. (2001) Effect of intra-arterial papaverine on regional cerebral blood flow in hemodynamically relevant cerebral vasospasm. Stroke 32: 498–505

    PubMed  CAS  Google Scholar 

  59. Valentin, A., and J. D. Humphrey. On time-courses of cell and matrix turnover in arterial remodeling. (submitted)

  60. Walmsley J. G., Campling M. R., Chertkow H. M. (1983) Interrelationships among wall structure, smooth muscle orientation, and contraction in human major cerebral arteries. Stroke 14:781–790

    PubMed  CAS  Google Scholar 

  61. Weaver J. P., Fisher M. (1994) Subarachnoid hemorrhage: an update of pathogenesis, diagnosis and management. J. Neurolog. Sci. 125:119–131

    Article  CAS  Google Scholar 

  62. Yamaguchi-Okada M., Nishizawa S., Koide M., Nonaka Y. (2005) Biomechanical and phenotypic changes in the vasospastic canine basilar artery after subarachnoid hemorrhage. J. Appl. Physiol. 99:2045–2052

    Article  PubMed  Google Scholar 

  63. Young D. F. (1979) Fluid mechanics of arterial stenoses. ASME J. Biomech. Eng. 101:157–175

    Google Scholar 

  64. Zarnitsina V. I., Pokhilko A. V., Ataullakhanov F. I. (1996) A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I The model description. Thrombosis Res. 84: 225–236

    Article  CAS  Google Scholar 

  65. Zhang B., Fugleholm K., Day L. B., Ye S., Weller R. O., Day I. N. M. (2003) Molecular pathogenesis of subarachnoid haemorrhage. Int. J. Biochem. Cell Biol. 35:1341–1360

    Article  PubMed  CAS  Google Scholar 

  66. Zhang Z.-D., Macdonald R. L. (2006) Contribution of the remodeling response to cerebral vasospasm. Neurol. Res. 28:713–720

    Article  PubMed  Google Scholar 

  67. Zubkov Y. N., Nikiforov B. M., Shustin V. A. (1984) Balloon catheter technique for dilatation of constricted cerebral arteries after aneurysmal SAH. Acta Neurochir.70:1–2

    Article  Google Scholar 

  68. Zuccarello M. (2001) Endothelin: the “prime suspect” in cerebral vasospasm. Acta Neurochir. 77: 61–65

    CAS  Google Scholar 

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Acknowledgments

This work was supported by NIH grants HL-80415 and HL-64372 (through the Bioengineering Research Partnership Program).

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Authors and Affiliations

  1. Department of Biomedical Engineering and M.E. DeBakey Institute, Texas A&M University, College Station, TX, USA

    J. D. Humphrey

  2. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA

    S. Baek

  3. Departments of Anesthesiology and Biomedical Engineering, Yale University, New Haven, CT, USA

    L. E. Niklason

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  1. J. D. Humphrey
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Address correspondence to J. D. Humphrey, Department of Biomedical Engineering, Texas A&M University, 337 Zachry Engineering Center, 3120 TAMU, College Station, TX 77843-3120, USA. Electronic mail: jhumphrey@tamu.edu

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Humphrey, J., Baek, S. & Niklason, L. Biochemomechanics of Cerebral Vasospasm and its Resolution: I. A New Hypothesis and Theoretical Framework. Ann Biomed Eng 35, 1485–1497 (2007). https://doi.org/10.1007/s10439-007-9321-y

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