A topological model of biofeedback based on catecholamine interactions
© Basak et al; licensee BioMed Central Ltd. 2005
Received: 21 October 2004
Accepted: 21 March 2005
Published: 21 March 2005
The present paper describes a topological model of biofeedback. This model incorporates input from a sensory organ and a transduction phase mediated through catecholamine production in the feedback path. The transduction phase comprises both conservative and dissipative systems, from which the appropriate output is combined in a closed loop.
The model has been simulated in MATLAB 6.0 R12 in order to facilitate a comprehensive understanding of the complex biofeedback phenomena concomitant with the transduction phases associated with migraine and with psychosomatic diseases involving digestive disorders.
The complexity of the biological system influences the transduction phase and nature of the system response, which is consequent on the activation of smooth muscles by sympathetic and parasympathetic stimulation.
The paper describes a comprehensive model of a biofeedback system; it adopts a new approach to modeling. Using artificial neural networks (ANN) it is not easy to obtain a dynamic response that reflects dependence on hormone production. Therefore, the authors have endeavoured to design an approach that focuses on the internal state of the subject consequent on biofeedback stimulation.
Records of the measurements of the SCR
Per unit value
SCR rise time
Half recovery time
Before we focus on the design of the biofeedback system, some important terminology needs to be discussed: Topological model, Transduction Phase, Unity biofeedback, Homeostasis, Homeostat, Residual Homeostatic output level, Feedback Control systems, Catecholamine Interactions, Conscious and subconscious parts of the brain and Dissipative & Conservative system.
A topological model originates from a root and spreads in tree-like branches. It affords a complete description of the interactions among the different parts of the system considered. The transduction phase of a subject reflects physiological changes caused by hormone release consequent on stimulation. This phase is characteristic of an individual subject [2–7]. For example, the transduction phase of a psychosomatic patient is sometimes reflected during a journey in a high-speed vehicle, when the physiological outcome can adversely affect his mental condition, associated with headache and vomiting.
Unity biofeedback means that the homeostatic output is directly fed to the brain without going through the transduction phase, which incorporates conservative and dissipative systems. Homeostasis is the set of processes by which constant or 'static' conditions are maintained within the internal environment of a subject [6, 7, 11]; a homeostat is a controller involved in maintaining homeostasis.
In this paper the residual homeostatic output level, ΔV, has a particular value for each successive response. It can be correlated with the GSR . The residual homeostatic output arises as a result of sustained catecholamine action, which often persists for minutes or hours; control is prolonged, not just instantaneous activation or inhibition . The residual homeostatic output indicated by the GSR response signifies that sweating persists even after the withdrawal of the biofeedback stimulus .
Mammals are endowed with a vast network of feedback control systems with controllers (homeostats) without which survival would be difficult . In this control system a particular neuro-hormone exerts a negative feedback effect, preventing over-secretion of other hormones associated with over-activity of the muscles, unless there is specific disorder in the system .
Catecholamine interactions are very important in biofeedback systems. Catecholamines are excitatory or inhibitory neurotransmitters or hormonal agents. The catecholamine neuro-hormones are epinephrine, norepinephrine, dopamine and serotonin. Epinephrine and norepinephrine function as excitatory hormones. Serotonin functions as an inhibitory hormone, and dopamine is excitatory in some areas and inhibitory in others. Stimulation of sympathetic nerves in the adrenal medullae causes large quantities of epinephrine and norepinephrine to be released into the circulating blood, which carries them to all tissues of the body. Norepinephrine increases the total peripheral resistance and thus elevates the arterial pressure; epinephrine raises the arterial pressure to lesser extent but increases the cardiac output more. Epinephrine has a 5 to 10 times greater metabolic effect than norepinephrine .
The adrenergic receptors include α and β receptors. The α-receptors control such physiological activities as vasoconstriction, iris dilatation, intestinal relaxation, intestinal sphincter contraction, pilomotor contraction and bladder sphincter contraction; β-receptors control (e.g.) vasodilatation, cardio-acceleration, increased myocardial strength, intestinal relaxation, uterus relaxation, bronchodilatation, calorigenesis, glycogenesis, lipolysis and bladder wall relaxation. It is therefore evident that both α and β receptors have inhibitory and excitatory functions . Blood pressure transduction phases are associated with activation of α and β receptors [4–6].
The cerebral cortex, which includes the conscious part of the brain, never functions alone but always in association with lower centres of the nervous system. In fact, the lower brain centres (or subconscious part of the brain) initiate wakefulness in the cerebral cortex . The subconscious part of the brain performs vegetative functions; notably, the hypothalamus controls sympathetic and parasympathetic stimulation . The sweat glands secrete large quantities of sweat when the sympathetic nerves are stimulated; they are controlled primarily by centers in hypothalamus that are usually considered to be parasympathetic centers . Therefore, sweating could be called a parasympathetic function, although it is controlled by nerve fibres that are anatomically distributed through the sympathetic nervous system . The sympathetic innervation of sweat glands results from a developmental change in transmitter phenotype (from catecholaminergic to cholinergic), making parasympathetic stimulation also possible .
In biofeedback systems, the subject undergoes different transduction phases. Depending on the nature of transduction phase a system can be classified as dissipative or conservative. A dissipative system diverges from its original state during biofeedback; it may undergo successive stages during which the response decreases exponentially, with the characteristic features of a normal physiological system. A conservative system, in contrast, has an output characterised by exponentially rising phases due to sustained levels of catecholamines.
Nowadays, biofeedback has important clinical applications in at least the following areas. Headache is a psychophysiological disorder associated with disturbances in the homeostatic relationship between mind and body. The classical psychosomatic disorders are included in this category, e.g. peptic ulcer, bronchial asthma, migraine and essential hypertension. In classical migraine (in which the sufferer is sensitive to light and sound stimuli) there are neurological symptoms such as homonymous hemianopia, paresthesias, aphasia and hemiparesis, which precede the unilateral headache (tension headache) and are reflected in the subject's muscle activity . Biofeedback is useful for migraine treatment. Stimulation or inhibition of specific adrenergic receptors, mediated through catecholamines, often help relieve the pain, inducing a feeling of drowsiness by a process associated with the smelling of ripe mango or fresh lemon .
The digestive system as a whole is governed by innumerable control mechanisms at the cell and tissue levels, whereby a pathway can be activated as needed or inhibited as products accumulate . For example, acetylcholine is an excitatory cholinergic transmitter for smooth muscle fibers in some organs, but an inhibitory transmitter for smooth muscle in others. When acetylcholine excites a muscle fiber, norepinephrine ordinarily inhibits it. Conversely, when acetylcholine inhibits a fiber, norepinephrine usually excites it . Cholinergic (muscarinic) receptors are involved in the parasympathetic activity. Muscarinic receptors are age dependent; their frequency decreases with increasing age. Moreover, the fall of blood pressure and pulse rate during parasympathetic stimulation (discussed later) is due to the combined effects of adrenergic and muscarinic receptors .
Adrenergic and cholinergic receptors in the autonomic nervous system play opposite roles. De-activation of the sympathetic innervation (which operates via adrenergic receptors) is followed by enhancement of the cholinergic receptors involved in parasympathetic stimulation in smooth muscle. Conversely, noradrenergic enhancement is diminished as cholinergic neurotransmission becomes established .
In the model discussed in this paper, the stimulation of adrenergic receptors diminishes concomitantly with blood pressure and pulse-rate (a dissipative system). This diminishing of the adrenergic receptor effect enhances cholinergic receptor activity automatically in the control of smooth muscle function. Similarly, in a conservative system, adrenergic receptor stimulation is enhanced concomitantly with the blood pressure and the pulse rate. This increasing effect of the adrenergic receptors will diminish the effects of cholinergic receptors automatically in the control of smooth muscle activity. Thus, cholinergic receptors automatically operate in conjunction with adrenergic receptors in the autonomic nervous system control of mammalian smooth muscle.
The following extended account of the model focuses on the state of the subject (dissipative or conservative). Biofeedback can be fatal due to cardiac failure for subjects in an exhausted state, unless attention is given.
In the paper, emphasis is placed on catecholamine stimulation and a temporal pattern of responses is obtained. It has been established that catecholamine secretion is not only of short duration but also persists for long periods (minutes or even hours) . To take account of this, the authors have designed 1st order and 2nd order systems. In the 1st order system the response decays without oscillation during a short catecholamine secretion phase, whereas the 2nd order system represents a prolonged period marked with oscillation, concomitant with adrenergic stimulation leading to vasoconstriction and vasodilatation.
Here, input stimulus to the biofeedback system is a step function while the homeostatic output response is exponential. The input stimulus may be optical (e.g. flash of light), auditory (e.g. tone), tactile (e.g. a blow to the Achilles tendon), or a direct electrical stimulation of some part of the nervous system. Any sinusoidal or ramp input can be simplified by expressing it as a function of step inputs. For this reason the input is taken as a step. In this particular model, the output responses are of two types: exponential rise and exponential decay. Exponential rise signifies that the system is unable to withstand the biofeedback stimulus, depending on the responses of homeostat. Exponential decay signifies a normal homeostatic response. The homeostatic responses are regulated mainly by the functioning of the kidney and heart in tandem.
Methods and Results
In respect of the homeostatic output level in GSR, the constants a1, a2, a3 relate to the peak value; a2, a4 represent residual output level. K1, K3, K5 respectively indicate the slopes, i.e. the inverses of the respective time constants of the successive rising phases of the GSR; and K2, K4, K6 respectively represent the inverses of the e time constants of the successive decaying phases. These constants are selected so as to represent the GSR attributable to activation of sweat glands concomitant with stimulation through catecholamine [9, 13]. The hormonal stimulation helps elicit physiological responses that obey an exponential law with rising and decaying phases.
In all these cases we see that the residual homeostatic output level increases for each successive response .
Tp(Φd) = Φd0 ± ∂(ψd)/∂t and Tp(Φc) = Φc0 ± ∫(ψc)dt
where Φd0 and Φc0 are the initial states of the dissipative and conservative system respectively, ψd is the time dependent 1st order dissipative system and ψc is the time dependent 1st order conservative system. Here, the transduction phase signifies the state of the internal environment of the subject . It reflects the topological asymmetry of cellular organization, which shows a relaxation jump associated with hydrophobic linkages among polar heads .
Depending on the state of the subject, homeostasis is perturbed in a conservative system. This is the first order system transduction phase where the value of a is taken as 2 and the output appears as
Here peak amplitude = 0.101 p.u and settling time = 17 s
From Fig.16 we see that the exponentially decaying output phase indicates that the subject returns to the original state within a time frame depending on the duration of the catecholamine signal. When the 2nd order transduction phase is incorporated into the biofeedback loop, the block diagram representation of the system is shown below.
Here peak amplitude = 0.129 p.u and settling time = 19 s. Fig. 18 illustrates the fluctuations of parameters such as blood pressure and pulse rate, which persist for a certain period of time concomitant with the sustained catecholamine signal.
Keeping the value of b fixed at 1 and by putting a = 0.5 we obtain the output response shown in Fig. 19.
Figs. 19, 20, 21, 22 model states with different values of 'a'. With decreasing 'a' values, the settling time increases with the increase of oscillations. This is true for a subject with sustained biofeedback.
Figs. 23, 24 represent a subject with a permanent disorder; the biofeedback stimuli cause the disorder to be manifest. By putting a = 0 we can have the output response. Here we clearly see that sustained oscillations amplify in a conservative transduction phase due to the prolonged period of catecholamine activation.
The features of both dissipative and conservative systems are represented in this comprehensive model, which is based on catecholamine activation. The transduction phase of the 2nd order system in biofeedback can act as either a dissipative or a conservative system depending on the system dissipation factor (which is related to catecholamine production). For a dissipative system the catecholamine signal is of shorter duration, whereas for a conservative system it survives for a longer period. Biofeedback can sometimes produce complex responses in biological systems depending on how sustained the catecholamine signal is; these complexities are represented by the present model. In the context of this paper, the envelopes of the exponentially rising and decaying phases also represent the stimulation of adrenergic receptors in monotonic phase concomitant with the catecholamine production. Adrenergic and cholinergic receptors have opposing roles in the autonomic nervous system. Downregulation of sympathetic innervation via adrenergic receptor is followed by enhancement of the cholinergic receptors involved in parasympathetic stimulation in smooth muscle. Conversely, noradrenergic enhancement is diminished as cholinergic neurotransmission becomes established. Thus it may be concluded that cholinergic receptors automatically participate, along with adrenergic receptors, in the autonomic nervous system control of mammalian smooth muscle function.
In this paper a new conceptual approach has been taken to modeling dynamic responses in biofeedback that depend on hormone activity, by introducing homeostats and transduction phases in the feedback path.
The authors are grateful to the authorities of Jadavpur University and to Prof. T. K. Ghoshal, ex-head of the Electrical Engineering Department. Professor T. K. Basak is particularly indebted for inspiration received from his late wife, Mala Basak who is in the heavenly abode of Shree Shree Ramakrishna Paramhansa.
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