TRU Mathematics 20−1 （1984）
STATISTI（AL ANALYSIS OF THE PHASE I
IN THE．］（INETICS OF THE：ETHANOI． INFUSION
．Motosaburo MASUYAMA
（Rece ived Apri1 2 S， 1984）
At the end of the second paper−on this line ［2］， I have． raised two
questlons：
lo Why the Mi（血aelis−Menten scheme does not hold in the phase I I I， and
20 why almost all predicted values in the phase I by the original authors
［4］ are underestirnated ？
Mソ answer to the first question was given in my third paper ［3］， in which
I noticed the existence of a negative feedback in this phase．
Then it is curioUs to assume the Michaeli5−Ment〔≧n s（圭eme ill the first
phase． It is rather natural to assume a negative feedback in the phase I too．
We assume now that
〔1） dC／dt＝Ji−∂／「ft−Ot／
holds in the phase I， where J and J denote the constant sし4）ply rate and a
P・・itive c・n・t・nt re・pectiv・ly・b・th・nit・b・i・g［mσ／r梱剛・CtφgタZ／i・
the concentration of ethanol in blood at the moment t（hr）．We set O ＝0．
O
Then the solution is given by
〔・） ・t・イ…11／2・・ち
whi。h i， q。。drati。 i。 tl／2． H。nce．・e app・y・he regressi・n・q・・ti・n・f the
form ．
1／2
〔3） 0カ＝α・・n＄t・nt≠「2」t」
≠lt
to obtain Table 1， where ア and d stand for the correlation coefficient between
the observed and the estimated values and the mean of squared deviat ion
r吻。bser。。d−th。 e。吻。鋤2 re。pecti。。1y．〆・nd・d’are th・・e・bt・ined
from the original paper． The estimated♂ is not equal to A in the phase I I I
［3］， but it is close to the constant r一αノ in the phase I I． What is happening
in this transitional phase during a quarter hour ’∼
125
126
M．MASUYAMA
Subj． ヱ
αoon．stαnt−0．014
工
♂
r
rt
d
d、，
0．ヱ45
0．042
0．98・7
0．982
0．0013
0．OO31
2
一〇．006
0．150
0．028
0．999
0．995
0．000ヱ
0．00ヱ1
3
0．002
0．253
0．027
0．999
0．996
0．000ヱ
0．0025
4
一〇．014
0．092 ＞
0．104
0．998
0．980
0．0002
0．0022
5
一〇．011
0，302
0．003
0．995
0．996
0．0005
0．0011
6 、
一〇．014
0．260
0．021
0．998
0．996
0．OOO3
0．OO14
Table 1
New estimates in Tabユe 2 do not show any systematic deviations．
0
t
0．083
0．25
0．5
0．75
ヱ
ヱ．5
2
θst
obs
一〇．0140．O
0．08ヱ 0．077
0．167 0．15
0．263 0．21
0．345 0．36
0．42ヱ 0．50
0．558 0．54
0．686 0．67
est
一〇．006
0．074
obs
0．0
0．062
0．ヱ49 0．15
0．235 0．23
0．310 0．32
0．379 0．39
0．506 0．49
0．626 0．63
est
obs
0．002 0．0
0．090
0．1810．18
0．293 0．31
0．393 0．39
0・488 0．47
0．666 0．67
0．832 0．84
e＄t
obs
一〇．0ヱ40．0
0．ヱ25 0．10
0．238 0．23
0．355 0．37
0．45ヱ 0．47
0．535 0．52
0．684 0．69
1ノ．816 0．81
θst
obs
一〇．01ヱ0．0
0．036 0．031
0．ヱ02 0．085
0．ヱ94 0．19
0．281 0．26
0．367 0．40
0．535 0．57
0．70ヱ 0．67
es亡
obs
一〇．024 0．0
0．067 0．046
0．153 0．14
0．26ヱ 0．26
0．358 0．39
0．450 0．46
0．626 0．60
0．795 0．80
Table 2
エnvi・w。f these th・ee crit・ri・w・卿Wth・t th。 n。g。ti。。 feedback。。d。l
fit・b・tter t・th・bb・erv・ti・・th・n th・Mi。haeli、．M。。t。n m。d。1．一
127
PHASE I IN T田三 KINETICS OF E「lltlANOL
If errors in measurement are sufficiently s皿a11， it is useful to app1＞’
the foiTnula 〔2） to determine the moment t
such that the infus ion must end
O
at the given va1…fthe c・ncentrati・n・t t・av・id・・ert・i・ill・ffect・・
H。w・ver， i・thi・case the st・ndard d・vi・ti・n9・f estim・tes are f・i・1y larg・．
See Table 3．
Subj．
i＝1
2
3
mean
4占 D〃0
ヱ／2
r2の
0．289 ± 0．126
0．235 ± 0．033
0．233 ± 0．035
0．457 ± 0．052
0．076 ± 0．079
0・204 ± 0．063
0◆249 ± 0．］24
f
O．ヱ45 ± 0．084
0．ヱ50 ± 0．022
0．253 ± 0．023
0．092 ± 0．035
0．302 ± 0．053
0◆260 ± 0・042
0．200 ± 0．083
ρrr2の1／2。∫ノ．．。．88、
Table 3
Remark． If we assume the equation
〔4） d°t／dt 一 r−♂・ノrエt−・t／
instead°f the equati°n〔1）i・・h…x・・md・r・h・i・i・i・…ndi・i…。一・，
the second term on the right becomes O／0，0therwise its e）qplicit solution is
91ven elementa「ily by th・t・…f・㎜ti・nヱーCt／t・
REFERENCES
［1］
［2］
［3］
［4］
Masuya皿a， M．〔1984）：The almost−one para皿eter hypothesis on the metabolic
tumover，
Tfi∼〃∼』たztアzematics， 20−1， 1−4．
Ma
剣Z。：㍑4よ。畠：：1霊，灘？1i跳’㌶：th・v’・wp・’…f
Masuyama， M．（1984〕：Statistical analysis of the phase III in the
metabolism of ethano1， ibid．，105−110．
W’
汚h：・：1’｛kl1：！二・ll9°呈㌶：1・匡゜：；：：霊’＝蹴ll’18：’n・
DEPARTMENT OF APPLIED MATHEMATICS
SCIENCE UNIVERSITY OF TOKYO
