By Batzel J.J., Timischl-Teschl S., Kappel F.
This paper considers a version of the human cardiovascular-respiratory controlsystem with one and shipping delays within the nation equations describing the respiratorysystem. The effectiveness of the keep watch over of the air flow cost V˙A is motivated by way of suchtransport delays simply because blood gases needs to be transported a actual distance from the lungs to the sensory websites the place those gases are measured. the fast time period cardiovascular regulate method doesn't contain such delivery delays even supposing delays do come up in different contexts reminiscent of the baroreflex loop (see ) for instance. This baroreflex hold up isn't thought of right here. The interplay among middle cost, blood strain, cardiac output, and blood vessel resistance is kind of advanced and given the constrained wisdom to be had of this interplay, we are going to version the cardiovascular keep watch over mechanism through an optimum keep watch over derived from keep watch over conception. This keep watch over could be stabilizing and is an inexpensive strategy in response to mathematical issues in addition to being additional influenced by way of the statement that many physiologists cite optimization as a possible impression within the evolution of organic platforms (see, e.g., Kenner  or Swan ). during this paper we adapt a version, formerly thought of (Timischl  and Timischl et al. ), to incorporate the results of 1 and shipping delays.We will first enforce an optimum keep watch over for the mixed cardiovascular-respiratory version with one nation house delay.We will then contemplate the results of a moment hold up within the kingdom area by means of modeling the respiration keep an eye on through an empirical formulation with hold up whereas the the advanced relationships within the cardiovascular keep an eye on will nonetheless be modeled by means of optimum keep an eye on. This moment shipping hold up linked to the sensory procedure of the breathing keep watch over performs a big position in breathing balance. As an software of this version we are going to think of congestive middle failure the place this shipping hold up is greater than basic and the transition from the quiet wakeful country to level four (NREM) sleep. The version can be utilized to check the interplay among cardiovascular and breathing functionality in quite a few occasions in addition to to contemplate the impression of optimum functionality in physiological keep an eye on process functionality.
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Additional info for A cardiovascular-respiratory control system model including state delay with application to congestive heart failure in humans
W. B. Saunders Company, Philadelphia, 1986 18. : Cycle length of periodic breathing in patients with and without heart failure. Am. J. Respir. Crit. Care. Med. 154 (2 pt. 1), 376–381 (1996) 19. : Effects of exercise training on left ventricular function and peripheral resistance in patients with chronic heart failure: A randomized trial. Jama 283 (23), 3095–3101 (2000) 20. : Pathogenesis of Cheyne-Stokes respiration in patients with congestive heart failure: relationship to arterial P CO2 . J. Batzel et al.
649–690 51. : Periodic breathing in heart failure patients: testing the hypothesis of instability of the chemoreflex loop. J. Appl. Physiol. 89 (6), 2147–2157 (2000) 52. : Kreislauf und Schlaf. In: H. , 1997 53. : Cheyne-Stokes respiration during sleep in congestive heart failure. Chest 111 (2), 467–473 (1997) 54. : General and regional circulatory responses to change in blood pH and carbon dioxide tension. J. Clin. Invest. 40, 31–43 (1961) 55. : Human Cardiovascular Control. Oxford University Press, 1993 56.
Med. Biol. Eng. Comp. 32 (1), 3–11 (1994) 67. : Respiratory control during exercise. P. S. G. R. ) Handbook of Physiology, Section 3: The Respiratory System, Volume II, Control of Breathing, Part 2, Am. Phys. Soc. Bethesda, Maryland, 1986 Appendix We assume the following: PAO2 = PaO2 , PACO2 = PaCO2 , PBO2 = PBvO2 , PBCO2 = PBvCO2 , PTO2 = PT vO2 , PTCO2 = PT vCO2 , where v = mixed venous blood, T is tissue compartment. Further we assume: – the alveoli and pulmonary capillaries are single well-mixed spaces; – constant temperature, pressure and humidity are maintained in the gas compartment; – gas exchange is by diffusion; ventilatory dead space is incorporated via the optimal control V˙A for the optimal case and control gains Gc and Gp for the empirical case (see text); – the delay in the respiratory controller signal to effector muscles is zero; – delay in the baroreceptor signal to the controller and from controller to effector muscles is zero; – metabolic rates and other parameters are constant in a given state; Cardiovascular-respiratory control system 335 – pH effects on dissociation laws and other factors are ignored or incorporated into parameters; – acid/base buffering, material transfer across the blood brain barrier, and tissue buffering effects are ignored; – no inter-cardiac shunting occurs; – intrathoracic pressure is ignored for this average flow model; – unidirectional non-pulsatile blood flow through the heart is assumed; hence, blood flow and blood pressure have to be interpreted as mean values over the length of a pulse; – fixed blood volume V0 is assumed.
A cardiovascular-respiratory control system model including state delay with application to congestive heart failure in humans by Batzel J.J., Timischl-Teschl S., Kappel F.