The study investigated the effect of the angular position of the head on the blood flow in the jugular vein of giraffes. The vein considered is elastic and collapsible such that its cross-sectional area is not uniform. Transmural pressure causes the blood to move along the vein. Mathematical equations describing the flow were developed, and the vein was considered to be inclined at an angle φ to the horizontal. A finite-difference scheme was used to solve the equations of motion for the flow. The results are presented via relevant tables and plots. Our findings show that a change in the position of the head causes variation in the external pressure, which in turn causes variation in the cross-sectional area of the vein. Moreover, a drop (or increase) in the inertial pressure of the blood may cause the vein to collapse (or distend), which again triggers a change in the pressure.
References
[1]
Ashraf, M.Z. (2018) Mathematical Modelling to Simulate Biological Fluid Flow in a Collapsible Tube. American Journal of Mechanics and Applications, 6.
[2]
Hargens, A.R., Millard, R.W., Pettersson, K. and Johansen, K. (1987) Gravitational Haemodynamics and Oedema Prevention in the Giraffe. Nature, 329, 59-60. https://doi.org/10.1038/329059a0
[3]
Müller, L.O. and Toro, E.F. (2014) Enhanced Global Mathematical Model for Studying Cerebral Venous Blood Flow. Journal of Biomechanics, 47, 3361-3372. https://doi.org/10.1016/j.jbiomech.2014.08.005
[4]
Shapiro, A.H. (1977) Steady Flow in Collapsible Tubes. Journal of Biomechanical Engineering, 99, 126-147. https://doi.org/10.1115/1.3426281
[5]
Pedley, T.J. and Luo, X.Y. (1998) Modelling Flow and Oscillations in Collapsible Tubes. Theoretical and Computational Fluid Dynamics, 10, 277-294. https://doi.org/10.1007/s001620050064
[6]
Kozlovsky, P., Zaretsky, U., Jaffa, A.J. and Elad, D. (2014) General Tube Law for Collapsible Thin and Thick-Wall Tubes. Journal of Biomechanics, 47, 2378-2384.
[7]
Pedley, T.J., Pihler-Puzovic, D. and Puzovic, P. (2015) Flow and Oscillations in Collapsible Tubes: Physiological Applications and Low-Dimensional Models. Technical Report.
[8]
Goetz, R.H., Warren, J.V., Gauer, O.H., Patterson, J.L., Doyle, J.T., Keen, E.N., McGregor, M., Tiller, L.M., Smith, M. and Mance, E. (1960) Circulation of the Giraffe. Circulation Research, 8, 1049-1058. https://doi.org/10.1161/01.RES.8.5.1049
[9]
Heil, M. and Hazel, A.L. (2011) Fluid-Structure Interaction in Internal Physiological Flows. Annual Review of Fluid Mechanics, 43, 141-162.
[10]
Hicks, J.W. and Badeer, H.S. (1992) Gravity and the Circulation: “Open” vs. “Closed” Systems. The American Journal of Physiology, 262, R725-R732. https://doi.org/10.1152/ajpregu.1992.262.5.R725
[11]
Nahar, S., Dubey, B.N. and Windhab, E.J. (2019) Influence of Flowing Fluid Property through an Elastic Tube on Various Deformations along the Tube Length. Physics of Fluids, 31, Article ID: 101905. https://doi.org/10.1063/1.5123182
[12]
Gadda, G., Taibi, A., Sisini, F., Gambaccini, M., Zamboni, P. and Ursino, M. (2015) A New Hemodynamic Model for the Study of Cerebral Venous Outflow. American Journal of Physiology-Heart and Circulatory Physiology, 308, H217-H231.
[13]
Badeer, H.S. (1985) Elementary Hemodynamic Principles Based on Modified Bernoulli’s Equation. The Physiologist, 28, 41-46.
[14]
Low, H.T. and Chew, Y.T. (1991) Pressure/Flow Relationships in Collapsible Tubes; Effects of Upstream Pressure Fluctuations. Medical & Biological Engineering & Computing, 29, 217-221.
[15]
Pedley, T.J., Brook, B.S. and Seym, R.S. (1996) Blood Pressure and Flow Rate in the Giraffe Jugular Vein. Technical Report.
[16]
Pontrelli, G. (2000) Blood Flow through a Circular Pipe with an Impulsive Pressure Gradient. Mathematical Models and Methods in Applied Sciences, 10, 187-202. https://doi.org/10.1142/S0218202500000124