From the above physical definitions of stationary steady state, of the state of reference and of its stability, it is now possible to give a clear definition and description of internal homeostasis.
Definition of internal homeostasis
In open systems which are maintained constant by continuous exchanges of matter,energy and information, the resting spontaneous reference state of internal homeostasis, should no longer be viewed as a state of mechanical or thermodynamic equilibrium, but rather as a thermodynamic stationary state of nonequilibrium (Nicolis & Prigogine, 1989). Since this state is stable over time, homeostasis should be a time-independent state, and, according to Bertalanffy, a state independent from initial conditions. Mathematically homeostasis may be represented by the actual state X(t) composed of a time-independent steady state (XS) and a time-dependent state variable, x(t), as previously illustrated. The teleological meaning implicitly present in the term ‘homeostasis’ is well expressed by the physical definition of equifinality (Recordati, 1984; Bertalanffy, 1969).
In healthy conditions the distance of the steady state XS from thermodynamic equilibrium, hence its displacement along the ordinate axis, is dependent on prevailing behaviour. By assuming that XS should be zero at equilibrium and maximal at the maximum possible distance from equilibrium it follows that the more precise representation of XS is given by the metabolic rate of the living being under consideration. As a consequence, the definition of homeostasis in the frame of thermodynamics of nonequilibrium becomes strictly related to the level of energy balance and metabolic rate, as a description of a steady state at a given measurable distance from thermodynamic equilibrium. This definition will allow the linkage, through the allometric power function, of constancy and homeostasis to the mass, the biological efficiency, the entropy production and the physiological ‘eigen time’ of the biological system under consideration (Darveau et al. 2002; Gillooly et al. 2002; Toussaint et al. 2002; West et al. 2002).
At least two different spontaneous steady states of rest may be identified in humans.
First, the conscious resting state of quiet wakefulness. It may be considered a mean level around which all the internal variables rhythmically oscillate (heart rate, blood pressure, sympathetic and parasympathetic efferent activities) and fluctuate with a circadian rhythmicity (temperature) (Akselrod et al. 1981; Pagani et al. 1986; Badra et al. 2001). If these oscillations and fluctuations are bounded the reference state may be considered stable in the sense of Lyapounov. While in this state, however, the system threshold for moving away from stability is low. Either the subject may become drowsy favouring a prevalence of the parasympathetic tone and a concomitant fall in metabolic rate (Colrain et al. 1987; Fraser et al. 1989), or a sudden stimulus may elicit a sympathetic activation. Hence this state may be considered only locally and not globally stable (Nicolis & Prigogine, 1989). Secondly, the unconscious steady state of sleep, which is characterized by the lowest basal metabolic rate, temperature, rate of breathing, tidal volume, heart rate and blood pressure. In contrast to the previous state, this state is not a mean level around which the variables oscillate, but it is the lowest possible steady level to be asymptotically reached.
The decline in metabolic rate is very fast at the beginning of sleep, slowing as stage two of NREM sleep is approached and reaching the lowest possible value during phases three and four of NREM sleep. This time course results in a classic asymptotic approach to the basal metabolic baseline values (Fraser et al. 1989; Fontvieille et al. 1994; Zhang et al. 2002), as is shown in the accompanying figure for energy expenditure (Fig. 4). Similar asymptotic declines have been demonstrated for breathing rate and tidal volume (Colrain et al. 1987), temperature (Palca et al. 1986; Edwards et al. 2002), heart rate and blood pressure changes (Ohkubo et al. 2002; Sherwood et al. 2002) during sleep. Hence while the resting conscious state is stable in the sense of Lyapounov, the resting state of NREM sleep's stages three and four seem to be an asymptotically stable state, thus becoming a global attractor.
Figure 4. Example of an asymptotic approach of a state variable, the oxygen consumption, to a steady state at the beginning of sleep Data shown are from 25 min before lights out to 60 min after onset of stage two sleep for two normal subjects (I.B. and A.C.). Variable duration transition period has been plotted as quartiles and is shown in shaded portion of the graph. After lights out the oxygen consumption spontaneously and asymptotically declines towards the steady state. Other cardiovascular and respiratory variables, and temperature, show similar time-course changes. Partial representation of Fig. 3 from Fraser et al. (1989). Reproduced with permission from the authors and the publisher.
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Figure 5 schematically shows the two spontaneous resting steady states for the variable X as a function of time. These two spontaneous steady states of rest are representative of the constancy of the internal environment and of homeostasis. When in the appropriate environmental and subjective conditions healthy human beings, whatever race and culture, hence independently of inherited initial conditions, should be able to reach these stable states, thus confirming that the genome, metabolism and neurohumoral control have been progressively shaped in relation to environmental conditions (Recordati, 2002, 2003).
Figure 5. Schematic diagram of the two main spontaneous steady states of rest, quiet wakefulness and sleep, and of the unstable state of exercise in humans (top trace) and of the stable state of hibernation in eterothermic mammals (bottom trace) Each state is composed of a time-independent state (XS) and of a time-dependent state variable x(t), thus being asymptotically stable (hibernation and sleep), stable in the sense of Lyapounov (quiet wakefulness) or unstable (muscle exercise). With the exception of hibernation, all other states occur at an increasing distance from thermodynamic equilibrium. The upward and downward arrows on the right of the scheme indicate the directions of displacement of the reference states under prevailing sympathetic or parasympathetic influences. The parasympathetic drive moves the reference state towards equilibrium, favouring homeostasis and stability. Sympathetic dominance shifts the reference state away from equilibrium, simultaneously increasing metabolic rate and entropy production. The interval between sleep and exercise describes the normal range of neurohumoral control.
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Sustained muscle exercise, although an active, non-spontaneous and non-resting state, is sometimes also called a steady state. It has been included in Fig. 5, top trace, to give the idea that it is positioned fairly above the resting states, in as much as it requires sympathetic activation, vagal withdrawal and maximum metabolic rate. Although stability for open systems far away from equilibrium has not yet been defined, it probably is an unstable state (Nicolis & Prigogine, 1989). This state is under volitional control, the so-called central command (Rowell, 1993). If heart rate and cardiac output are taken as representative state variables and expressed as percent of the final response, they tend to approach the maximum exercise level asymptotically (Rowell, 1993). As soon as the central command is halted, all these variables rapidly decline towards pre-exercise levels following a progressive and asymptotic time-course change. Figure 5 schematically illustrates variables changes during and after exercise according to the classic work by Rowell (1993) which recalls the top of a relief used by Prigogine to illustrate an unstable state (Nicolis & Prigogine, 1989).
An additional stationary steady state which has been represented in Fig. 4, is that of hibernation. As in the case of sleep, this behaviour is introduced by withdrawal of sympathetic tone and progressive reinforcement of vagal tone (Recordati, 2003). As a time-dependent variable typical of this state, the body temperature of an hibernating alpine marmot is illustrated in Fig. 5, temperature asymptotically declining toward the steady level of ambient temperature (Ortmann & Heldmaier, 2000). During bouts of torpor, however, the hibernators accumulate sleep debt, and the central nervous system undergoes progressive disorganization and alterations, while visceral organs such as the liver and the kidneys halt their functionality (Buck & Barnes, 2000). These mammals should regularly arise from torpor reactivating their metabolism, to increase brain temperature to be able to sleep, and to recover and reorganize their nervous and visceral functions (Buck & Barnes, 2000).
The periods of transition from an active to a resting state (from exercise to quiet wakefulness, from this to sleep and from euthermia to torpor) are all characterized by an asymptotic decline of the variable towards the corresponding time-independent resting state and by sympathetic withdrawal and parasympathetic reinforcement. This asymptotic ‘off’ response may represent the final output of the complex interactions between autonomic nervous system, metabolism and target organ function and it has been used as a predictor of morbidity and mortality in cardiovascular function testing (Cole et al. 1999; Recordati, 2003).
The homeostatic controller
The hypothalamic centres integrating and regulating body temperature, fluid volume, composition (osmolality) and pressure, and metabolic energy exchanges, may be viewed as a complex thermodynamic controller. Within the general frame of nonequilibrium thermodynamics it appears that this neurohumoral control may start at a given distance from equilibrium, requiring metabolic rate and body temperature above a given threshold which has yet to be measured.
In homeotherms the displacement of the resting steady state XS above this level is related not only to the stability of the system's state, but also to metabolism, entropy changes and the autonomic nervous system function. In heterotherms the downward displacement toward torpor metabolic rate is largely caused by a direct temperature effect and by metabolic inhibition (Song et al. 1997).
The range between sleep and strenuous exercise, inside which all the internal variables are under ordered neurohumoral control, may be increased by both physical (Rowell, 1993) and mental training (Wallace et al. 1971). It is known that, while physical conditioning improves cardiac output and oxygen utilization (Rowell, 1993), raising their upper level, transcendental meditation may induce a wakeful hypometabolic state (Wallace et al. 1971; Recordati, 2003). Figure 5 therefore not only illustrates the two main spontaneous resting steady states which quantify the concept of the homeostasis of the internal variable, but also the normal range inside which ordered neurohumoral regulation should occur. The positioning along the ordinate axis of the two resting steady states is also the result of the sympathetic and parasympathetic interactions at the target organ level, thus becoming a measurable index of the so-called sympatho-vagal balance.
Figure 5 also illustrates that, with respect to the general nonequilibrium thermodynamic frame, the sympathetic moves towards far from equilibrium, for example by increasing gradients, while the parasympathetic moves towards equilibrium, increasing stability and favouring the steady states of rest. Amongst these two complementary and differently directed vectorial forces the main homeostatic agency is therefore the parasympathetic and not the sympathetic nervous system (Recordati, 2003). The disengagement from the external environment, which is essential to parasympathetic dominance, is addressed to favour self-protection, control and recovery and perhaps to minimize sympathetic nervous control with respect to driving influences from genome, metabolism and endocrine systems. In other words, if homeostasis is used to indicate an ‘equifinal’ spontaneous stable state of rest, an increase of the parasympathetic tone will address variables towards this state, while a sudden vagal withdrawal and a simultaneous increase in sympathetic activity will activate processes, fluxes and exchanges, which will displace the variables away from it.
Hence also from the approach proposed here it is possible to confirm the already reached conclusion that the parasympathetic division, and not the sympathetic division, is the main controller of homeostasis and stability (Recordati, 2002, 2003).
Stable states are also characterized by the minimum entropy production and maximum efficiency (Andresen et al. 2002), which is to say that during sympathetic activation which moves the system away from equilibrium, the efficiency of visceral organs probably declines, as it has been clearly demonstrated for cardiac contraction under adrenergic influences (Suga, 1990). Hence the parasympathetic drive contributes not only to stability but also to the efficiency of target organs function.