16.8 Conclusions and Future Work In this paper we studied a linear mechano-hydraulic model of brain dynamics. We discussed its derivation, parameter values, and behavior. This simplified model allows us to study the separate effects of a hydraulic system, which was inspired by the Marmarou and Ursino-Lodi models of CSF dynamics, and a mechanical system, that predicts brain mechanics using a Kelvin-Voigt model. This allows us to directly incorporate recent research about the mechanics of the brain to further improve models of ICP dynamics. We also investigated the stability of the steady-state solution and found it to be stable for all of the physically-meaningful regions of the parameter space that were tested. The model suggests that we will need to consider two time scales to be able to study fast and slow behaviors. In the future, we intend to study the necessary conditions for the equilibrium point to lose stability, as is the case when patients suffer from Lundberg A-Waves. This will involve expanding the model to include nonlinear effects and statedependence of the model parameters. References 1. Suarez, J.I.: Critical Care Neurology and Neurosurgery. Springer, New York (2004) 2. Wakeland, W., Goldstein, B.: A review of physiological simulation models of intracranial pressure dynamics. Comput. Biol. Med. 38(9), 1024–1041 (2008) 3. Ursino, M., Lodi, C.A.: A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics. J. Appl. Phycol. 82(4), 1256–1269 (1997) 4. Marmarou, A., Shulman, K., Rosende, R.M.: A nonlinear analysis of the cerebrospinal fluid system and intracranial pressure dynamics. J. Neurosurg. 48(3), 332–344 (1978) 5. Hasan, M.M., Drapaca, C.S.: A poroelastic-viscoelastic limit for modeling brain biomechanics. In: MRS Proceedings, vol. 1753, pp. mrsf14–1753. Cambridge University Press, Cambridge (2015) 6. Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomech. Model. Mechanobiol. 1(2), 151–164 (2002) 7. Goldsmith, W.: The state of head injury biomechanics: past, present, and future: Part 1 Crit. Rev. Biomed. Eng. 29(5&6), 441–600 (2001) 8. Cutler, R.W.P., Page, L, Galicich, J., Watters, G.V.: Formation and absorption of cerebrospinal fluid in man. Brain 91(4), 707–720 (1968) 9. Attwell, D., Buchan, A.M., Charpak, S., Lauritzen, M., MacVicar, B.A. Newman, E.A.: Glial and neuronal control of brain blood flow. Nature 468(7321), 232–243 (2010) 10. Tanaka, M., Sugawara, M., Ogasawara, Y., Izumi, T., Niki, K., Kajiya, F.: Intermittent, moderate-intensity aerobic exercise for only eight weeks reduces arterial stiffness: evaluation by measurement of stiffness parameter and pressure–strain elastic modulus by use of ultrasonic echo tracking. J. Med. Ultrason. 40(2), 119–124 (2013) 11. Kruse, S.A., Rose, G.H., Glaser, K.J., Manduca, A., Felmlee, J.P., Jack, C.R., Ehman, R.L.: Magnetic resonance elastography of the brain. Neuroimage 39(1), 231–237 (2008) 12. Jordan, D.W., Smith, P.: Nonlinear Ordinary Differential Equations, 4th edn. Oxford University Press, Oxford (2007) 118 D. Evans et al.
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