: Mathematical modelling of alcohol metabolism in liver: mechanism and preventive of hepatopathy Kenta ISHIMOTO1, Yoshiki KOI

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(2013), 1863: 29-37 Issue Date 2013-11 URL http://hdl.handle.

1 肝臓におけるアルコール代謝の数理モデリング : 肝障害 Titleの発生メカニズムとその予防策 ( 数学と生命現象の関連性の探究 : 新しいモデリングの数理 ) Author(s) 石本, 健太 ; 小泉, 吉輝 ; 鈴木, 理 Citation 数理解析研究所講究録 (2013), 1863: Issue Date URL Right Type Departmental Bulletin Paper Textversion publisher Kyoto University

2 : Mathematical modelling of alcohol metabolism in liver: mechanism and preventive of hepatopathy Kenta ISHIMOTO1, Yoshiki KOIZUMI2, Osamu SUZUKI Research Institute for Mathematical Sciences, Kyoto University, Kyoto JAPAN. 2 School of Medicine, College of Medical, Pharmaceutical and Health Sciences, Kanazawa University, Kanazawa, Ishikawa JAPAN. 3College of Humanities and Sciences, Nihon University, Tokyo JAPAN 1ishimoto@kurims.kyoto-u.ac.jp, 2koizumi.yoshi@gmail. com, 3 osuzuki@chs.nihon-u.ac.jp. 1 $[1]_{0}$ [2] [3] [4] 3 $[5]_{0}$ $[2]_{0}$

3 30 [6] $\oint$ $arrow$ $arrow$ 1: $n_{1 }n_{2}$ ADH 1 ALDH 2 $k_{1 }k_{2}$ $P$ $t$ $f(t)$ $n_{1}$ $n_{2}$ $\frac{dn_{1}}{dt}=f(t)-k_{1}pn_{1}$ (1) $\frac{d\iota_{2}}{d}=k_{1}pn_{1}-k_{2}pn_{2}$ (2) (1) (2) 1 2 $f(t)$ 2 $f(t)=a(t/\tau)\exp(-t/\tau)$ (3)

4 $\tau$ $\tau$ $\infty$ 31 (3) $A$ (3) $t=0$ $A/e$ ( 2 ) $\tau$ ( 2 ) $A$ ( 2 ) $ $ $(h\rangle$ 2: $f(t)$ $1Q(A=2.72$ $r=0.5)$ $10Q(A=27.2$ $\tau=0.5)$ $3Q(A=2.72{}_{ }T=1.5)$ $f(t)$ $n_{1}$ ( 3 ) [6]. $f(t)$ $t$ $0$ $\int_{0}^{\infty}f(t)dt=a\tau$ $Q$ $A=e\sim 2.72,$ $\tau=0.5$ $\int$ $f(t)dt$ $1Q$ $Q=(e/2)$ $1Q$ 1 $20g$ $[7]$ 5 1 $(500m1)$ 2 $1Q$ ( 1 ) $3Q$ ( $-\prime\triangleright$ $)$ 3 $1OQ$ ( 10 ) 0 $c$ $P$

5 32 $\frac{dp}{dt}=rp(1-p)-cpn_{2}$ (4) (4) $r$ (1)-(4) 2 $-2$ 1.5 [6][8]. (2) $\frac{h_{2}}{ck}=k_{1}b\iota_{[}-\frac{k_{2}}{1-\epsilon(t)}h_{2}$ (5) (5) $\epsilon(t)$ [9]. $\epsilon(t)=\frac{n_{d}(t)^{2}}{n_{d}(t)^{2}+k^{2}}$ (6) (6) $t$ $n_{d}(t)$ $K$ 1/2 $n_{d}(t)$ $n_{d}(t)=a_{d}(t-t_{0})\exp[-(t-t_{0})/\tau_{d}]\theta(t-t_{0})$ $A_{d}$ $\tau_{d}$ $t_{0}$ $\theta(t-t_{0})$ $n_{d}(t)$ $t_{0}$ 2 (1), (3) $\cdot(6)$ 3 3 $-1$ (1)-(4) 3 [6] $[2]_{0}$ $k_{2}$ $k_{1}$ 100 $c$ $r$ 100 $r$ $c$

6 33 A: B: 3: $A)$ $(1Q: A=2.72, \tau=0.5)$ $B $ $(10Q:A=27.2.\tau=0.5){}_{ }C)$ $(8Q:A=2.72, \tau=4.0)$ : $D)$ ; ; ; $(k_{1}=1, k_{2}=100, r=0.1, c=10)$ 3 $A,D$ 6 $8Q$ ( 8 ) 24 ( $3B$ ) ( 3 $D)$ $10Q$ ( 10 ) $0$ ( $3C,D$ ) 3 $-2$ $P=0$ $f=0$ $P=0$ $n_{1 }^{*}n_{2}^{*}$ $n_{1 }n_{2}$ $\delta n_{1 }\delta n_{2 }\delta P$ : $n_{1}=n_{1}+\delta n_{1}*$ (7) $n_{2}=n_{2}+\delta n_{2}*$ (8)

7 34 $P=\delta P$ (9) 2 $\frac{d}{dt}\delta P=(r-cn_{2}*\mu P$ (10). $r$ $P=0$ $n_{2}<-c$ (11) $n_{2}^{*}$ $r/c$ $f(t)=f=$ const. $>0$ $P^{*}\in(0,1)$ $P^{\cdot}(1-P^{*})= \frac{cf}{rk_{2}}$ (12) $F \leq\frac{rk_{2}}{4c}$ (13) $F$ (13) $P=0$ $P$ $P^{*}$ (13) 2 $(0<P_{1}^{*}<1/2<P_{2}^{*}<$ 1 $)$ $\frac{d}{c\#}(\begin{array}{l}\delta\iota_{1}\delta\iota_{2}\delta P\end{array})=(\begin{array}{lll}-k_{1}P 0 -k_{1}n]k_{1}p^{*} -k_{2}p^{*} 00 -cp^{*} r(1-2p.)-cn_{2}\end{array}) (\begin{array}{l}\ _{1}\ _{2}\delta P\end{array})$ (14) $(x+k_{1}p^{*}xx+k_{2}pxx+rp)-rk_{1}k_{2}p^{2}(1-p)=0$ (15) (15) $a_{0}x^{3}+a_{1}x^{2}+a_{2}x+a_{3}=0$ $a_{0 }a_{1 }a_{2 }a_{3 }$ $(a_{1}a_{2}-a_{0}a_{3})$ $a_{1}a_{2}-a_{0}a_{3}=[(k_{1}+k_{2} Xk_{1}+rXk_{2}+\gamma)+\frac{1-P^{*}}{P^{*}}k_{1}k_{2}r]P^{*3}>0$ (16)

8 35 $P^{*}> \frac{1}{2}$ (17) $P_{1 }^{*}P_{2}^{*}$ $P_{1}^{*}$ $P_{2}^{*}$ (13) $P=0$ $r/c$ $k_{2}$ (17) $P=1/2$ $F$ 3 $-3$ (1), (3) $-(8)$ 4 $\tau$d $\tau$ $\tau_{d}=1.0$ $K=1.0$ 2 $A_{d}=e\sim 2.72$ $f(t)$ 3 $B$ ( $8Q$ : 8 ) A: B:5 4: $A)$ $\{$ to $=0\}$ $B)5$ $(to=5)$ $C\rangle 10$ (ro 10) : $=$ (0-100%) : : $D)$ : : :5 :10 $(k_{j}=1,k_{\underline{\backslash }}=100,r=0.1,c=10, \tau=4.0,.4=2.72,k=1.0,\tau_{d}=1.0,a_{d}=2.72)$

9 $4A,D$ 5 ( 4A- $C$ ) ( 4 $D$ ) 4 2 ADH 2 36

10 37 [1]. News&Reports Vol.15 No.2, 2009 [2]. $\backslash$ Jpn Alcohol&Drug Dependence, 46(1), , $J$ 2011 [3]. Jones.A. $W$., Evidence-based survey of elimination rates of ethanol from blood with applications in forensic casework. Forensic Science International, Vol.200, 1-20, 2010 [4]. Levitt, M. $D$. and Levitt, D.G. Use of a two-compartment model to assess the pharmacokinetics of human ethanol metabolism. Alcholism: Clinical and Experimental Research, Vol.22(8), $1680\cdot 1988$, 1998 [5] , 2009 [6]. $HP$ : html [7]. [8]. $60$ $HP$ : [9]. DeLean, A., Munson, P. $J$. and Rodbard, D. Simultaneous analysis of families of sigmoidal curves application to bioassay, radioligand assay, and physiological $HP$ : dose-response curves. Am. J. Physiol. Endocrinol. Metab., $235:E97$, 1978

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~ ご再 ~ Title 經濟法令 Author(s) Citation 經濟論叢 (1925), 20(5): 925-942 Issue Date 1925-05-01 URL http://dx.doi.org/10.14989/128271 Right Type Departmental Bulletin Paper Textversion publisher Kyoto University ~ ご再

: Mathematical modelling of alcohol metabolism in liver: mechanism and preventive of hepatopathy Kenta ISHIMOTO1, Yoshiki KOI

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