Peripheral resistance modeling

Relatively few data are available on the response of ANP to endotoxemia or septic shock. In an ovine model, a 13-fold increase in blood ANP concentration has been found 2 hours after endotoxin administration in a dose of 1.5 pg/kg body weight (LI7). The ANP level remained elevated during the first 6 hours and was associated with marked diuresis and natriuresis and with decreased cardiac output and increased peripheral resistence (LI7). In human studies, a significantly higher ANP blood level was observed in ARDS (E4) and in patients with acute respiratory failure associated with sepsis (M30). In a longitudinal study, we found that plasma ANP levels were increased in patients with sepsis, but the ANP levels showed no relation to the severity of disease or to the presence of shock (B8). 

The same ventricle may be coupled to a pathological arterial system, for example, one with doubled peripheral resistance R. As expected, increased peripheral resistance raises arterial pulse pressure (to 140/95 mmHg) and impedes the ventricle s ability to eject blood (Figure 8.6). The ejection fraction decreases to 50% in this experiment. Other experiments, such as altered arterial stiffness, may be performed. The model s flexibility allows description of heart pathology as well as changes in blood vessels. This one equation (Equation 8.8) with one set of measured parameters is able to describe the wide range of hemodynamics observed experimentally [11],... 

In addition to baroreceptors, chemoreceptors may also mediate a strong CV response, especially when systemic arterial pressure falls below 80 mmHg [Guyton et al., 1972 see also Dampney, 1994]. This reflex, through the CNS, increases cardiac activity and peripheral resistance. Strangely, few models include this effect, although Slate and Sheppard [ 1982] may have inadvertently included it in their simplified black box model. 

The renin-angiotensin reflex is mediated hormonally through the kidneys. When pressure falls below normal, renin is secreted into the blood stream by the kidneys, which then causes the release of free angiotensin. Angiotensin causes marked vasoconstriction and thus increases peripheral resistance and arterial pressure. This reflex is often included in models because it plays an important role in many forms of hypertension and heart failure. 

Once calculated, the drug effect can be used to modify the parameters in the CV model, much hfee the neural and humoral reflexes. Resistances, comphances (including the unstressed volumes) of each segment, neural and humoral feedback gains, heart rate, and contractility are all typically modified by drugs. For example, sodium nitroprusside causes vasodilation and blood pooling therefore it would be made to primarily increase the compliance and unstressed volume of the veins, as well as to decrease arteriolar (peripheral) resistance [Greenway, 1982 Yu et ai, 1990]. 

Although our knowledge of pulse propagation in the arterial system is extensive, it has been useful to approximate the relationship between pressure and flow in a single artery or vascular bed. Such approximations have been referred to as reduced arterial system models of which the three element Windkessel is the most widely employed [Westerhof et al., 1971 Noordergraaf, 1978]. This Windkessel model is modified here to study the effects of peripheral resistance. 

In this chapter, the dynamics of autoregulation are incorporated into the modified Windkessel model. The frequency response of this autoregulating Windkessel is then predicted and compared with that of the standard three element model. The time response is also determined and discussed relative to the experimental observations in the literature. The stability of the model is also examined with respect to very low frequency oscillation in peripheral resistance. 

There are two dynamic effects that must be accounted for to accurately model the physiological control mechanism. First, the change in peripheral resistance is delayed. This represents a delay from the time that the flow changes to when the vascular smooth muscle activity actually initiates the process of correcting the flow. This time delay in the change of peripheral resistance is denoted tq. To account for this effect, the change in peripheral resistance determined from the steady value was written as ARs(t — tq). 

FIGURE 14.2 Input impedance magnitude (a) and phase (b) frequency spectrum obtained from the model. The oscillating curve represents active autoregulation. The smooth curve is the standard three-element Windkessel with constant peripheral resistance. 

FIGURE 14.3 Flow step response of the model for steady levels of flow. The time responses of pressure and peripheral resistance are shown. 

FIGURE 17.3 The coupled model of the left ventricle (LV) and the arterial system (AS). The LV is represented here by a time-varying compliance and a resistance. The AS is represented by the modified windkessel model with characteristic impedance, Zo, peripheral resistance, Rs, and compliance of the arterial system, C. C(P) denotes the case when compliance is allowed to change with blood pressure levels. 

The circulatory fluid is ejected by an electropneumatically driven ventricular pump. Downstream of the pump, an aortic valve assembly is located two different models have been built in order to offer lateral or frontal view of the prosthesis movements. Suitable stent adapters allow to test prostheses of different type and size. The aorta is a variable compliance rubber tube. Through a rigid conduit the fluid is conveyed to the laminar flow assembly which controls peripheral resistances. Aortic compliance and peripheral resistances are hydropneumatically controlled. The fluid, passing through a venous reservoir open to atmospheric pressure, reaches the left atrium. This is a rigid wall chamber in which a hydropneumatic system relates cardiac output to venous return, reproducing Frank--Starling s Law. Between atrium and ventricle there is another valve test assembly which allows to test mitral valves. 

The role of ventricular resistance in the coupling of the ventricle to its arterial load was also investigated. For this purpose, a computer simulation study was performed where the LV was represented by the above model and the arterial load by a modified Windkessel (i.e., peripheral resistance, lumped arterial compliance and a characteristic impedance). It was observed that inclusion of a ventricular resistance slightly decreased mean arterial pressure (3 to 10%) and stroke volume (3 to 7%). In contrast, the pulsatile nature of the flow was markedly altered suggesting that ventricular resistance may play an important role in minimizing the external pulsatile power and in optimally coupling the ventricle to its arterial load (Shroff et ai, 1983a). 

In order to analyze the functional coupling between the heart and the blood vessels, we will use a model in which the cardiovascular system has been reduced to its simplest components (Levy, 1979 Berne and Levy, 1981). The model consists of a pump, an elastic arterial system, a peripheral resistance (/ ), and an elastic venous system (Figure 1). The relative ease of analysis of the interactions among the components of this simplified model permits the elucidation of certain basic principles. For many purposes the model is much too simple and potentially misleading. For such purposes, more complicated models must be used, such as those developed by Grodins and his coworkers (1959,1960), Sagawa (1972), and Guyton et al. (1973). 

This suggests one use for a model such as presented here. This is to systematically investigate the sensitivity of coronary blood flow to various parameters, e.g. peripheral resistance, wall properties, geometric branching pattern, etc. Such a parametric ananalysis can be extended as the model is expanded. One possible modification to the model is to include somewhat more detail on the venous side of the coronary system. Also, as is indicated by Figure 1, it is possible to insert into the calculation multiple stenoses as well as to allow for the presence of multiple aorto-coronary bypass grafts. In the latter case, it is necessary to separately specify the wave-speed characteristics of any such grafts. 

The end result of centrally mediated sympathetic stimulation is an increase in peripheral resistance. This is reflected in elevations of both resting and stimulated vascular tone in the resistance arteries of the moderately vitamin Bg-deficient hypertensive rats. Elevated peripheral resistance is the hallmark of hypertension as seen in other models of hypertension. The increase in tone of caudal artery segmeuts from the hypertensive vitamin Bg-deficient rat is calcium depeudent. The decrease in tone following the addition to the medium of the calcium chaunel antagouist, uifed-ipine, indicates that the increased peripheral resistance resulting from increased permeability of smooth muscle plasma membraue to Ca + might be ceutral to the development of hypertension in the vitamin Bg-deficient rat. 

It is clear that the peripheral resistance decreases, while compliance increases with mammalian body size. Thus, the dynamic features of blood pressure and flow pulse transmission can be scaled through this kind of modeling. The ratio of Zq/Rs corresponds to the ratio of pulsatile energy loss due to oscillatory flow to the energy dissipated due to steady flow (to overcome R ) and has been reported to be between 5 and 10% and is an invariant for the mammalian arterial circulation [Li, 1996,2004]. 

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