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A learning model of autonomic function in biofeedback
International Congress Series 1301 (2007) 119 – 122
www.ics-elsevier.com
A learning model of autonomic function in biofeedback Chiaki Nishimura a,⁎, Li-Qun Wang b , Aki Nagase a , Kazuko Terada a , Yoshifumi Miyamoto c , Hisayuki Tsukuma a , Masuo Muro a b
a Toho University School of Medicine, Japan Research Center for Advanced Technologies, Tokyo Denki University, Japan c Department of Mechanical Engineering, Osaka Sangyo University, Japan
Abstract. Biofeedback is an acquisition technique of self-regulation ability of an autonomic function, of which we are normally unaware, through a series of training aided by an additional outer feedback pathway. We proposed a mathematical model of biofeedback in which a learning system on the conscious level learns characteristics of a subconscious regulation system corresponding to the biological function. When the learning converges, the learning system itself becomes an inverse system of the regulation system. Then, if a regulation command is put to the learning system on the conscious level, it drives the regulation system strictly following the command without the outer feedback pathway, which enables voluntary control of the biological function. © 2007 Elsevier B.V. All rights reserved. Keywords: Biofeedback; Learning; Mathematical model; Autonomic function; Self-regulation
1. Introduction Biofeedback is an acquisition technique of self-regulation ability of an autonomic function, of which we are normally unaware. It is characterized by (1) addition of an outer informational pathway to feedback inner physiological condition to a sense such as vision ⁎ Corresponding author. 5-21-16 Omori-Nishi, Ota-ku, Tokyo 143-8540, Japan. Tel.: +81 3 3762 4151; fax: +81 3 5493 5419. E-mail address: [email protected] (C. Nishimura). 0531-5131/ © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2006.12.001
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Fig. 1. Scheme of biofeedback.
and audition, (2) mental training on the level of consciousness referring the information from the sense, and (3) eventual acquisition of ability to voluntarily control the autonomic condition without the aid of the outer pathway. A biofeedback device provides the outer pathway by detecting current condition of the autonomic function and feeding its information back to a subject in an appropriate way (Fig. 1). Starting with trial-and-error, the subject trains oneself so that the physiological condition can be controlled referring the information from the sense. In most cases, as the training proceeds, the subject learns to voluntarily control the autonomic function and finally acquires ability to control it without the aid of the outer feedback pathway or the biofeedback device. Although biofeedback has been widely applied to treatment of psychosomatic disorder and proved to be effective, only psychological models based on operant conditioning have been proposed [1] and its neural basis is still unclear. In order to understand the underlying neural mechanism of biofeedback, mathematical modelling would be useful. In the present paper the authors proposed a mathematical model of biofeedback. 2. Modelling The mathematical model is shown in Figs. 2 and 3. The inner condition of an autonomic function chosen as the target of biofeedback is controlled in a module consisting of a
Fig. 2. Block diagram of the biofeedback model in learning mode. LS: Learning System, FC: Feedback Controller, BFN: Biological Function. IFB: Inner Feedback Pathway, ICS: Internal Control Signal, and OFB: Outer Feedback Pathway. x(s), y(s), z(s), and u(s): Laplace transform of each signal (see Table 1).
C. Nishimura et al. / International Congress Series 1301 (2007) 119–122
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Fig. 3. Block diagram of the biofeedback model in voluntary control mode. LS: Learning System, FC: Feedback Controller, BFN: Biological Function IFB: Inner Feedback Pathway, ICS: Internal Control Signal, and VCS: Voluntary Control Signal. x(s), y(s), z(s), and u(s): Laplace transform of each signal (see Table 1).
feedback controller (FC), the corresponding biological function (BFN), and an internal feedback pathway (IFB). The negative feedback loop leads the inner condition to a desired level guided by an internal control signal (ICS) on the subconscious level. Here, we hypothesize existence of a learning system (LS) on the conscious level. Its input is information on the output of the biological function supplied through an artificially added outer feedback pathway (OFB), and its output, u(s), is added to the output of the FC, z(s). By learning, LS organizes itself so that the signal z(s) tends to zero. Namely, z(s) works as an evaluation function of the learning. The information on z(s) is supposed to be supplied internally from FC. The process is referred to as “learning mode” (Fig. 2). When the learning proceeds and converges, LS runs into another mode, “voluntary control mode”, where OFB is removed and the input of LS is connected to a voluntary control signal (VCS) on the conscious level. In this mode LS no longer refers the output of FC or the output of FC, but simply sends its output signal to BFN (Fig. 3). In this mode, when VCS is applied to LS, it directly appears in y(s), which corresponds to voluntary control of the autonomic function. The detailed mechanism and behaviour will be discussed in the next section. 3. Discussion The proposed model explains the characteristics of biofeedback. Namely, addition of the informational pathway made it possible to learn the input–output relation of the target BFN Table 1 Laplace transforms of transfer functions and signals in the model Category
Item
Laplace transform
Transfer function
Learning System (LS) Feedback Controller (FC) Biological Function (BFN) Internal Control Signal (ICS) Output of BFN Output of FC Output of LS
L(s) C(s) K(s) x(s) y(s) z(s) u(s)
Signal
122
C. Nishimura et al. / International Congress Series 1301 (2007) 119–122
with z(s) being the evaluation function, and if the learning converges, the input–output characteristic of LS is the inverse characteristic of BFN. This is proved as follows. We denote the Laplace transform of each signal and each transfer function as shown in Table 1. Here, we have the following equations according to the system configuration. 8 < zðsÞ ¼CðsÞ½xðsÞ−yðsÞ yðsÞ ¼KðsÞ½zðsÞ þ uðsÞ : : uðuÞ ¼LðsÞyðsÞ: When the learning converges, z(s) tends to 0. Therefore, after convergence of the learning, substituting z(s) = 0 into the equations we get ½1−LðsÞKðsÞyðsÞ ¼ 0: This leads to LðsÞ ¼ K −1 ðsÞ; showing that the input–output characteristic of LS is equal to the inverse characteristic of BFN, namely, LS has become the inverse system of BFN at this stage. Thus, after convergence of the learning, the cascade combination of LS and BFN forms a feedforward system, and when VCS is applied to LS, the output of BFN directly follows the VCS without OFB, i.e. voluntary control has been made possible. In this manner, the model well describes the characteristics of biofeedback including the role of the outer feedback pathway in learning, method of learning, and eventual acquisition of control ability, although there is few neurological basis for it at present. Therefore, the model would involve important aspects commonly underlying learning behaviour between conscious and subconscious levels in the brain. Hereafter, mathematically detailed study on the model would be necessary. In addition, physiological investigation for its neurological relationship is also important. The authors have actually shown neurological activities in prefrontal brain area relating to a sensation of state alteration of consciousness in biofeedback using fMRI and discussed its relationship with the model [2]. 4. Conclusion A mathematical model of biofeedback in which a learning system on the conscious level learns characteristics of a subconscious regulation system corresponding to an autonomic function. When the learning converges, the learning system itself becomes an inverse system of the target regulation system. Then, if a regulation command is put to the learning system on the conscious level, it drives the regulation system strictly following the command without referring the outer feedback pathway, which enables voluntary control of the autonomic function. It would provide a theoretical basis of biofeedback. References [1] A.J. Yate, Biofeedback and the Modification of Behavior, Plenum Press, New York, 1980, pp. 393–479. [2] C. Nishimura, et al., A mathematical model of biofeedback and its relation to neural activity, IFMBE Proc. 11 (2005) 3850–3853.
www.ics-elsevier.com
A learning model of autonomic function in biofeedback Chiaki Nishimura a,⁎, Li-Qun Wang b , Aki Nagase a , Kazuko Terada a , Yoshifumi Miyamoto c , Hisayuki Tsukuma a , Masuo Muro a b
a Toho University School of Medicine, Japan Research Center for Advanced Technologies, Tokyo Denki University, Japan c Department of Mechanical Engineering, Osaka Sangyo University, Japan
Abstract. Biofeedback is an acquisition technique of self-regulation ability of an autonomic function, of which we are normally unaware, through a series of training aided by an additional outer feedback pathway. We proposed a mathematical model of biofeedback in which a learning system on the conscious level learns characteristics of a subconscious regulation system corresponding to the biological function. When the learning converges, the learning system itself becomes an inverse system of the regulation system. Then, if a regulation command is put to the learning system on the conscious level, it drives the regulation system strictly following the command without the outer feedback pathway, which enables voluntary control of the biological function. © 2007 Elsevier B.V. All rights reserved. Keywords: Biofeedback; Learning; Mathematical model; Autonomic function; Self-regulation
1. Introduction Biofeedback is an acquisition technique of self-regulation ability of an autonomic function, of which we are normally unaware. It is characterized by (1) addition of an outer informational pathway to feedback inner physiological condition to a sense such as vision ⁎ Corresponding author. 5-21-16 Omori-Nishi, Ota-ku, Tokyo 143-8540, Japan. Tel.: +81 3 3762 4151; fax: +81 3 5493 5419. E-mail address: [email protected] (C. Nishimura). 0531-5131/ © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2006.12.001
120
C. Nishimura et al. / International Congress Series 1301 (2007) 119–122
Fig. 1. Scheme of biofeedback.
and audition, (2) mental training on the level of consciousness referring the information from the sense, and (3) eventual acquisition of ability to voluntarily control the autonomic condition without the aid of the outer pathway. A biofeedback device provides the outer pathway by detecting current condition of the autonomic function and feeding its information back to a subject in an appropriate way (Fig. 1). Starting with trial-and-error, the subject trains oneself so that the physiological condition can be controlled referring the information from the sense. In most cases, as the training proceeds, the subject learns to voluntarily control the autonomic function and finally acquires ability to control it without the aid of the outer feedback pathway or the biofeedback device. Although biofeedback has been widely applied to treatment of psychosomatic disorder and proved to be effective, only psychological models based on operant conditioning have been proposed [1] and its neural basis is still unclear. In order to understand the underlying neural mechanism of biofeedback, mathematical modelling would be useful. In the present paper the authors proposed a mathematical model of biofeedback. 2. Modelling The mathematical model is shown in Figs. 2 and 3. The inner condition of an autonomic function chosen as the target of biofeedback is controlled in a module consisting of a
Fig. 2. Block diagram of the biofeedback model in learning mode. LS: Learning System, FC: Feedback Controller, BFN: Biological Function. IFB: Inner Feedback Pathway, ICS: Internal Control Signal, and OFB: Outer Feedback Pathway. x(s), y(s), z(s), and u(s): Laplace transform of each signal (see Table 1).
C. Nishimura et al. / International Congress Series 1301 (2007) 119–122
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Fig. 3. Block diagram of the biofeedback model in voluntary control mode. LS: Learning System, FC: Feedback Controller, BFN: Biological Function IFB: Inner Feedback Pathway, ICS: Internal Control Signal, and VCS: Voluntary Control Signal. x(s), y(s), z(s), and u(s): Laplace transform of each signal (see Table 1).
feedback controller (FC), the corresponding biological function (BFN), and an internal feedback pathway (IFB). The negative feedback loop leads the inner condition to a desired level guided by an internal control signal (ICS) on the subconscious level. Here, we hypothesize existence of a learning system (LS) on the conscious level. Its input is information on the output of the biological function supplied through an artificially added outer feedback pathway (OFB), and its output, u(s), is added to the output of the FC, z(s). By learning, LS organizes itself so that the signal z(s) tends to zero. Namely, z(s) works as an evaluation function of the learning. The information on z(s) is supposed to be supplied internally from FC. The process is referred to as “learning mode” (Fig. 2). When the learning proceeds and converges, LS runs into another mode, “voluntary control mode”, where OFB is removed and the input of LS is connected to a voluntary control signal (VCS) on the conscious level. In this mode LS no longer refers the output of FC or the output of FC, but simply sends its output signal to BFN (Fig. 3). In this mode, when VCS is applied to LS, it directly appears in y(s), which corresponds to voluntary control of the autonomic function. The detailed mechanism and behaviour will be discussed in the next section. 3. Discussion The proposed model explains the characteristics of biofeedback. Namely, addition of the informational pathway made it possible to learn the input–output relation of the target BFN Table 1 Laplace transforms of transfer functions and signals in the model Category
Item
Laplace transform
Transfer function
Learning System (LS) Feedback Controller (FC) Biological Function (BFN) Internal Control Signal (ICS) Output of BFN Output of FC Output of LS
L(s) C(s) K(s) x(s) y(s) z(s) u(s)
Signal
122
C. Nishimura et al. / International Congress Series 1301 (2007) 119–122
with z(s) being the evaluation function, and if the learning converges, the input–output characteristic of LS is the inverse characteristic of BFN. This is proved as follows. We denote the Laplace transform of each signal and each transfer function as shown in Table 1. Here, we have the following equations according to the system configuration. 8 < zðsÞ ¼CðsÞ½xðsÞ−yðsÞ yðsÞ ¼KðsÞ½zðsÞ þ uðsÞ : : uðuÞ ¼LðsÞyðsÞ: When the learning converges, z(s) tends to 0. Therefore, after convergence of the learning, substituting z(s) = 0 into the equations we get ½1−LðsÞKðsÞyðsÞ ¼ 0: This leads to LðsÞ ¼ K −1 ðsÞ; showing that the input–output characteristic of LS is equal to the inverse characteristic of BFN, namely, LS has become the inverse system of BFN at this stage. Thus, after convergence of the learning, the cascade combination of LS and BFN forms a feedforward system, and when VCS is applied to LS, the output of BFN directly follows the VCS without OFB, i.e. voluntary control has been made possible. In this manner, the model well describes the characteristics of biofeedback including the role of the outer feedback pathway in learning, method of learning, and eventual acquisition of control ability, although there is few neurological basis for it at present. Therefore, the model would involve important aspects commonly underlying learning behaviour between conscious and subconscious levels in the brain. Hereafter, mathematically detailed study on the model would be necessary. In addition, physiological investigation for its neurological relationship is also important. The authors have actually shown neurological activities in prefrontal brain area relating to a sensation of state alteration of consciousness in biofeedback using fMRI and discussed its relationship with the model [2]. 4. Conclusion A mathematical model of biofeedback in which a learning system on the conscious level learns characteristics of a subconscious regulation system corresponding to an autonomic function. When the learning converges, the learning system itself becomes an inverse system of the target regulation system. Then, if a regulation command is put to the learning system on the conscious level, it drives the regulation system strictly following the command without referring the outer feedback pathway, which enables voluntary control of the autonomic function. It would provide a theoretical basis of biofeedback. References [1] A.J. Yate, Biofeedback and the Modification of Behavior, Plenum Press, New York, 1980, pp. 393–479. [2] C. Nishimura, et al., A mathematical model of biofeedback and its relation to neural activity, IFMBE Proc. 11 (2005) 3850–3853.