Abstract
This work deals with forced oscillations of fluid flows generated by infusive pump connected to a human ventricular artery. Response curves are obtained and the nonlinearity is investigated for various geometrical conditions, excitation amplitudes, and periodic conditions. The nonlinearity related to the energy losses has been taken into considerations. An overall model for the study of an isothermal fluid flow across a highly incompressible medium is proposed. The main difficulty being that the infusion fluid flow results from a pressure prescribed over the venous artery involving impact boundary conditions. The proposed solution has been constructed by taking into account the interactions between all the solid and fluid components directly in mass balance and energy conservation equations. Applications of nonsmooth time transformations and introducing a unified physical basis for analyses of infusive fluid flow with essentially nonharmonic, and discontinuous time shapes revealed explicit links between impact dynamics and hyperbolic (complex) algebras analogously to the link between harmonic oscillations and conventional complex analyses. This study also deals with the coupling condition between the barrel fluid region and venous instantaneous states. This appears as prime importance for a global model of infusion processes.
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References
Strogatz, H.S.: Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering. Colorado Westview Press, Denver (2000)
Kasprowicz, M., Czosnyka, M., Czosnyka, Z., Momjian, S., Smielewski, P., Juniewicz, H., Pickard, J.D.: Hysteresis of the cerebrospinal pressure-volume curve in hydrocephalus. Acta Neurochir. Suppl. 86, 529–532 (2003)
Dos Santos, A.P., Guimaraes, R.C., de Carvalho, E.M., Gastaldi, A.C.: Mechanical behaviors of flutter vrp1, shaker, and acapella devices. Respir. Care 58, 298–304 (2013)
Southwell, R., Gough, F.: The free transverse vibration of airscrew blade, British A.R.C. Reports and Memoranda, 766 (1921)
Putter, S., Manor, H.: Natural frequencies of radial rotating beams. J. Sound Vib. 56, 175–185 (1978)
Wright, A.D., Smith, C.E., Thresher, R.W., Wang, J.L.C.: Vibration modes of centrifugally stiffened beams. J. Appl. Mech. 49, 197–201 (1982)
Trzaska, Z.: Straightforward method for studies of periodic non-harmonic states of linear systems. Arch Electr. Eng. 53, 191–215 (2004)
Trzaska, Z.: Efficient approach to determine the steady-state energy in networks with periodic discontinuous excitations. Int. J. EEE 44, 378–392 (2007)
Trzaska, Z.: Dynamical processes in sequential-bipolar pulse sources supplying nonlinear loads. Electr. Rev. 12–18 (2014)
Masci, P., Ayoub, A., Curzon, P., Lee, I., Sokolsky, O., Thimbleby, H.: Model-based development of the Generic PCA infusion pump user interface prototype in PVS. Proceedings of Safecomp 2013, 32nd International Conference of Computer Safety, Reliability and Security, LAAS-CNRS, Toulouse, France, September 24–27 (2013)
Campos, J.C., Harrison, M.: Modelling and analyzing the interactive behaviour of an infusion pump. J. Electron. Commun. EASST 45, 1–16 (2011)
Medicines and Healthcare products Regulatory Agency. Devices in practice: a guide for health and social care professionals, http://www.mhra.gov.uk/Publications/Safetyguidance/Otherdevicesafetyguidance/CON007423 (2008)
Medicines and Healthcare products Regulatory Agency. Reporting adverse incidents and disseminating medical device alerts. DB 2010(01), 1, 1–8, (2010)
Bolton, M.L., Bass, E.J.: Formally verifying human–automation interaction as part of a system model: limitations and tradeoffs. Innov. Syst. Softw. Eng. 6, 219–231 (2010)
Zhang, P., Wang, S., Yu, C., Zhang, M.: Design of occlusion pressure testing system for infusion pump. J. Biomed. Sci. Eng. 2, 431–434 (2009)
Aletti, F., Hammond, R.L., Sala-Mercado, J.A., Chen, X., O’Leary, D.S., Baselli, G., Mukkamala, R.: Cardiac output is not a significant source of low frequency mean arterial pressure variability. Physiol. Meas. 34, 1207–1216 (2013)
Svensen, ChH, Rodhe, P.M., Prough, D.S.: Pharmacokinetic aspects of fluid therapy. Best Pract. Res. Clin. Anaesthesiol. 23, 213–224 (2009)
Lesniak, M.S., Clatterbuck, R.E., Rigamonti, D., Williams, M.A.: Low pressure hydrocephalus and ventriculomegaly: hysteresis, non-linear dynamics, and the benefits of CSF diversion. Br. J. Neurosurg. 16, 555–561 (2002)
Galvanetto, U., Magri, L.: On the use of the theory of dynamical systems for transient problems. Nonlinear Dyn. 74, 373–380 (2013)
Podhaisky, H., Marszalek, W.: Bifurcations and synchronization of singularly perturbed oscillators: an application case study. Nonlinear Dyn. 69, 949–959 (2012)
Pilipchuk, V.N.: Nonlinear Dynamics. Springer, New York (2008)
Bar-Meir, G.: Basics of Fluid Mechanics, Last modified: Version 0.3.4.0 March 17, (2013), www.potto.org/downloads.php
Guckenheimer, J., Holmes, E.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, Berlin (1984)
Celle, P., Drapier, S., Bergheau, J.-M.: Numerical modelling of liquid infusion into fibrous media undergoing compaction. Eur. J. Mech. A 27, 647–6612 (2008)
Walchenbach, R., Geiger, E., Thomeer, R.T., Vanneste, J.A.: The value of temporary external lumbar CSF drainage in predicting the outcome of shunting on normal pressure hydrocephalus. J. Neurol. Neurosurg. Psychiatry 72, 503–536 (2002)
Morrison, L., Agnew, J.: Oscillating devices for airway clearance in people with cystic fibrosis Cochrane Database. Syst. Rev. 21, 1–99 (2009)
Arars, K., Aldredge, R.C.: Computational analysis of catheter-tip geometries for optimizing drug infusion in arterial blood flow. Am. J. Biomed. Eng. 3, 91–98 (2013)
Marszalek, W.: Fold points and singularity induced bifurcation in inviscid transonic flow. Phys. Lett. A 376, 2032–2037 (2012)
Yaturu, S.: Insulin therapies: current and future trends at dawn. World J Diabetes 4, 1–7 (2013)
Hong, H., Rahal, M., Demosthenous, A., Bayford, R.H.: Comparison of a new integrated current source with the modified Howland circuit for EIT applications. Physiol. Meas. 30, 999–1007 (2009)
Dimitrakopoulos, E.G.: Nonsmooth analysis of the impact between successive skew bridge-segments. Nonlinear Dyn. 74, 911–928 (2013)
Pintelon, R., Louarroudi, E., Lataire, J.: Detection and quantification of the influence of time variation in frequency response function measurements using arbitrary excitations. IEEE Trans. Instrum. Meas. 61, 3387–3395 (2012)
Chen, M., Chen, C.: Improved permittivity calibration method for wideband in situ permittivity probe. IEEE Geosci. Remote Sens. Lett. 10, 323–327 (2013)
Gao, J., Sultan, H., Hu, J., Tung, W.W.: Denoising nonlinear time series by adaptive filtering and wavelet shrinkage: a comparison. IEEE Signal Process. Lett. 17, 237–40 (2010)
Xiao, H., Shao, Y., Xu, J.: Investigation into the energy dissipation of a lap joint using the one-dimensional microslip friction model. Eur. J. Mech. A 43, 1–8 (2014)
Ulrych, S.: Relativistic quantum physics with hyperbolic numbers. Phys. Lett. B 625, 313–323 (2005)
Hestenes, D., Sobczyk, G.: Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics. Kluwer, Dordrecht (1992)
Poodiack, R.D., LeClair, K.J.: Fundamental theorems of algebra for the perplexes. Coll. Math. J. 40, 322–335 (2009)
Higham, D.J., Higham, N.J.: MATLAB Guide, 2nd edn. SIAM, Cambridge University Press, Cambridge (2005)
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Trzaska, Z. Nonsmooth analysis of the pulse pressured infusion fluid flow. Nonlinear Dyn 78, 525–540 (2014). https://doi.org/10.1007/s11071-014-1458-2
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DOI: https://doi.org/10.1007/s11071-014-1458-2