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The structure of the neural network is related to the anesthetic potency of inhalation anesthetics
International Congress Series 1283 (2005) 306 – 307
www.ics-elsevier.com
The structure of the neural network is related to the anesthetic potency of inhalation anesthetics Yoshiroh Kaminoh a,*, Chikara Tashiro a, Hiroshi Kamaya b, Issaku Ueda b a
Department of Anesthesiology, Hyogo College of Medicine, 1-1 Mukogawa-cho, Nishinomiya City, Hyogo, 663-8501, Japan b Department of Anesthesiology, University of Utah, Salt Lake City, Utah, USA
Abstract. Apparent anesthetic potency is built upon the balance between the redundancy and the vulnerability of Multi-Unit and Multi-Path System. D 2005 Published by Elsevier B.V. Keywords: Inhalation anesthetics; MAC; Potency; Age dependency; Spinal cord; Mathematical model
Introduction: We [1] proposed Multi-Unit and Multi-Path System (MUMPS) as a mathematical model of neural network related to MAC. To explain the steep dose– response curve, a large number of conduction units and conduction pathways are required. The MUMPS model predicted that the apparent anesthetic potency changed depending on the structure of neural network. In the current presentation, we analyzed the effect of the structure of neural network on the age dependency of MAC, and the different MAC in the preferentially anesthetized brain and spinal cord. Model and method: We assumed that a signal transmission between A and B occurs through m conduction pathways and n conduction units in each pathway (Fig. 1). Body movement in response to noxious stimuli is prevented when at least one conduction unit of all pathways is blocked by anesthetics. We hypothesized that the anesthetic potency on each conduction unit was constant, and calculated MAC by changing the number of conduction pathways (m) and conduction units (n). For the age dependency of MAC, the MAC of sevoflurane at different age groups [2–4] was compared with the theoretical values. For the MAC of preferentially * Corresponding author. Tel.: +81 798 45 6392; fax: +81 798 45 6393. E-mail address: [email protected] (Y. Kaminoh). 0531-5131/ D 2005 Published by Elsevier B.V. doi:10.1016/j.ics.2005.06.075
Y. Kaminoh et al. / International Congress Series 1283 (2005) 306–307
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Fig. 1. (Left): Multi-Unit and Multi-Path System (MUMPS). (Right): The in vivo results and the theoretical values of relative MAC and MAC95 / MAC. The circles show the relation between the relative MAC (rMAC) and MAC95 / MAC of in vivo results, and the line shows the theoretical values of MUMPS. The rMAC values of in vivo results and MUMPS were 1, when age was 4.31 years, and when m = 107 and n = 103, respectively. The age effects on rMAC were calculated by changing m, keeping n constant. Theoretical values of MUMPS are comparable with the in vivo results of sevoflurane.
anesthetized brain and spinal cord, isoflurane MAC in goat [5,6] was compared with the theoretical values. Results and discussion: The number of conduction pathway relates to the security of network and can be called bredundancy parameter.Q The number of conduction unit relates to the weakness of network, and can be called bvulnerability parameter.Q The decrease of MAC by aging was explained by the reduction of redundancy parameter (Fig. 1). The increase of MAC in brain was explained by the reduction of vulnerability parameter, and the decrease of MAC in spinal cord was explained mainly by the reduction of redundancy parameter (Table 1). We concluded that the apparent anesthetic potency was built upon the balance between the redundancy and the vulnerability of MUMPS. References [1] [2] [3] [4] [5] [6]
Y. Kaminoh, et al., J. Anesth. 18 (2004) 94 – 99. T. Katoh, K. Ikeda, Br. J. Anaesth. 58 (1992) 139 – 141. T. Katoh, K. Ikeda, Anesthesiology 66 (1987) 301 – 303. R. Nakajima, Y. Nakajima, K. Ikeda, Br. J. Anaesth. 70 (1993) 273 – 275. J.F. Antognini, K. Schwartz, Anesthesiology 79 (1993) 1244 – 1249. J.F. Antognini, N.D. Kien, Anesth. Analg. 81 (81) (1995) 69 – 72.
Table 1 Minimum alveolar concentration of isoflurane on goat, and calculated values
m n MACCAL MACEXP
Whole body
Brain
Spinal cord
1.0 107 1.0 102 1.3% 1.3 F 0.2%
1.0 107 4.9 101 2.9% 2.9 F 0.7%
1.4 102 5.1 101 0.80% 0.8 F 0.1%
MACCAL were calculated values from Eq. (4) in our previous report [1]. MACEXP were the experimental values on goat [5,6].
www.ics-elsevier.com
The structure of the neural network is related to the anesthetic potency of inhalation anesthetics Yoshiroh Kaminoh a,*, Chikara Tashiro a, Hiroshi Kamaya b, Issaku Ueda b a
Department of Anesthesiology, Hyogo College of Medicine, 1-1 Mukogawa-cho, Nishinomiya City, Hyogo, 663-8501, Japan b Department of Anesthesiology, University of Utah, Salt Lake City, Utah, USA
Abstract. Apparent anesthetic potency is built upon the balance between the redundancy and the vulnerability of Multi-Unit and Multi-Path System. D 2005 Published by Elsevier B.V. Keywords: Inhalation anesthetics; MAC; Potency; Age dependency; Spinal cord; Mathematical model
Introduction: We [1] proposed Multi-Unit and Multi-Path System (MUMPS) as a mathematical model of neural network related to MAC. To explain the steep dose– response curve, a large number of conduction units and conduction pathways are required. The MUMPS model predicted that the apparent anesthetic potency changed depending on the structure of neural network. In the current presentation, we analyzed the effect of the structure of neural network on the age dependency of MAC, and the different MAC in the preferentially anesthetized brain and spinal cord. Model and method: We assumed that a signal transmission between A and B occurs through m conduction pathways and n conduction units in each pathway (Fig. 1). Body movement in response to noxious stimuli is prevented when at least one conduction unit of all pathways is blocked by anesthetics. We hypothesized that the anesthetic potency on each conduction unit was constant, and calculated MAC by changing the number of conduction pathways (m) and conduction units (n). For the age dependency of MAC, the MAC of sevoflurane at different age groups [2–4] was compared with the theoretical values. For the MAC of preferentially * Corresponding author. Tel.: +81 798 45 6392; fax: +81 798 45 6393. E-mail address: [email protected] (Y. Kaminoh). 0531-5131/ D 2005 Published by Elsevier B.V. doi:10.1016/j.ics.2005.06.075
Y. Kaminoh et al. / International Congress Series 1283 (2005) 306–307
307
Fig. 1. (Left): Multi-Unit and Multi-Path System (MUMPS). (Right): The in vivo results and the theoretical values of relative MAC and MAC95 / MAC. The circles show the relation between the relative MAC (rMAC) and MAC95 / MAC of in vivo results, and the line shows the theoretical values of MUMPS. The rMAC values of in vivo results and MUMPS were 1, when age was 4.31 years, and when m = 107 and n = 103, respectively. The age effects on rMAC were calculated by changing m, keeping n constant. Theoretical values of MUMPS are comparable with the in vivo results of sevoflurane.
anesthetized brain and spinal cord, isoflurane MAC in goat [5,6] was compared with the theoretical values. Results and discussion: The number of conduction pathway relates to the security of network and can be called bredundancy parameter.Q The number of conduction unit relates to the weakness of network, and can be called bvulnerability parameter.Q The decrease of MAC by aging was explained by the reduction of redundancy parameter (Fig. 1). The increase of MAC in brain was explained by the reduction of vulnerability parameter, and the decrease of MAC in spinal cord was explained mainly by the reduction of redundancy parameter (Table 1). We concluded that the apparent anesthetic potency was built upon the balance between the redundancy and the vulnerability of MUMPS. References [1] [2] [3] [4] [5] [6]
Y. Kaminoh, et al., J. Anesth. 18 (2004) 94 – 99. T. Katoh, K. Ikeda, Br. J. Anaesth. 58 (1992) 139 – 141. T. Katoh, K. Ikeda, Anesthesiology 66 (1987) 301 – 303. R. Nakajima, Y. Nakajima, K. Ikeda, Br. J. Anaesth. 70 (1993) 273 – 275. J.F. Antognini, K. Schwartz, Anesthesiology 79 (1993) 1244 – 1249. J.F. Antognini, N.D. Kien, Anesth. Analg. 81 (81) (1995) 69 – 72.
Table 1 Minimum alveolar concentration of isoflurane on goat, and calculated values
m n MACCAL MACEXP
Whole body
Brain
Spinal cord
1.0 107 1.0 102 1.3% 1.3 F 0.2%
1.0 107 4.9 101 2.9% 2.9 F 0.7%
1.4 102 5.1 101 0.80% 0.8 F 0.1%
MACCAL were calculated values from Eq. (4) in our previous report [1]. MACEXP were the experimental values on goat [5,6].