The Acetaminophen Toxicity Equations: “Solutions” for Acetaminophen Toxicity Based on the Rumack-Matthew Nomogram

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co-opted into advocacy for the patient; such representatives may
protest that presently or in the future there may be a serious or
even life-threatening illness, the treatment of which may be
compromised by a limit-setting approach. This provides the
staff with an opportunity to advise the patient that he may
indeed jeopardize his future health and care by present excesses.
The management plan should be included in the patient’s
record. Coordination with other agencies is important and may
require only a telephone call or a brief conversation with those
who accompany the patient. These tools may assist emergency
staffs in containing these difficult patients, while enabling them
to live without chaos and to minimize occurrences of acting out.
James L. Elmore, MD
Coastal Empire Community Mental Health Center
Beaufort, SC
doi:10.1016/j.annemergmed.2004.11.034
The Acetaminophen Toxicity Equations:
‘‘Solutions’’ for Acetaminophen Toxicity
Based on the Rumack-Matthew Nomogram
To the Editor:
Acetaminophen, alone and with opiates and other
coingestants, is the most frequently implicated agent reported
in exposures to the American Association of Poison Control
Centers Toxic Exposure Surveillance System.
1
Although
initially reported in the United Kingdom, an increase in the
frequency of acetaminophen overdose was recognized in the
United States in the mid-1970s, leading to the National
Multi-Clinic Open Trial of N-acetylcysteine.
2,3
The Rumack-Matthew nomogram for acetaminophen
toxicity (Figure 1), first published in 1975 and referred to as
the ‘‘200 line,’’ was derived from acetaminophen levels from
untreated patients; the ‘‘200 line’’ predicted outcome by
dividing patients who did and who did not develop an
aspartate aminotransferase level of 1,000 IU/L or greater in
relationship to their first acetaminophen level.
4
The ‘‘150
line’’ was developed as the study design line in the multiclinic
N-acetylcysteine trial and was published in 1981
2
; the ‘‘150
line’’ remains the lower treatment line for considering
N-acetylcysteine therapy. An outcome nomogram demonstrat-
ing the results of treated patients and using the ‘‘200 and
150 lines’’ has been published to further improve clinical
prediction and decisionmaking and to validate the
nomogram lines.
5
The Rumack-Matthew nomogram can easily be defined
mathematically, even though the nomogram lines are plotted
on a semilogarithmic graph and describe nonlinear relation-
ships. The equations representing the lines of the nomogram
can then enable the determination of the potential toxic level
of acetaminophen for any time after ingestion.
The general equation for a line, using 2 points P
1
=(x1, y1)
and P
2
=(x2, y2) is: yy1¼mðxx1Þwhere the slope,
m¼y2y1
x2x1
For the nomogram ‘‘200 line’’ (probable toxicity), we can
consider the y-axis to be represented linearly by the Log
10
of
the acetaminophen level (log A
tox
,mg/mL) and the x-axis to
be represented by time (t, hr). If we use the original data points
that generated the ‘‘200 line,’’ that is, Point P
1
=(log 200,
4 hr) and Point P
2
=(log 50, 12 hr), the equation becomes:
logAtox log200 ¼log50 log200
12 4ðt4Þ
Solving the numeric portions and isolating the unknown
variable yields:
logAtox 2:30103 ¼ð0:075257Þðt4Þ
logAtox ¼ð0:075257tÞþð4Þð0:075257Þ
þ2:30103 ¼ð0:075257tÞþ2:602058
Finding the antilog of each side of the equation and
simplifying:
10ðlogAtox Þ¼10ð2:6020580:075257tÞ
Atox ¼ÿ102:602058ð100:075257 Þt
The equation for the ‘‘200 line’’ then becomes:
Atox ¼400:00ð0:840897Þt400ð0:84Þt
The equation for the ‘‘150 line’’ for N-acetylcysteine
treatment for known time of acetaminophen ingestion is simply
a 25% reduction:
ANAC ¼300ð0:840897Þt
ANAC ¼300ð0:84Þt
where A
NAC
is the acetaminophen level in mg/mL above which
treatment with N-acetylcysteine may be warranted, and
tis time in hours elapsed from ingestion to acetaminophen
measurement.
The validity of the equations can be demonstrated by
substituting the original times from which the equations were
derived (t=4 hr and t=12 hr). Using the more precise equation
for the ‘‘200 line,’’ using 0.840897 to the power of t, yields
200.00 mg/mL and 50.00 mg/mL, respectively, whereas the
approximated equation using 0.84 gives values of 199.15 mg/
mL and 49.36 mg/mL. This difference is clinically insignificant,
given the usual approximations of the time of ingestion and
draw time of the acetaminophen level.
Finally, when ingestion time is uncertain but an approximate
range of times is known, the equation can be solved for time
Correspondence
Volume 45, no. 5 : May 2005 Annals of Emergency Medicine 563

tin terms of acetaminophen level Ato determine the earliest
time that an acute ingestion could have been taken without
likely toxicity, given a measured level of acetaminophen:
t¼32:9155 13:2878ðlog AÞ
t¼33 13:3ðlog AÞ
where Ais measured acetaminophen level in mg/mL and
tis time interval in hours, within which acetaminophen level
is likely to be nontoxic.
The simplified versions of these 2 equations are relatively
easy to memorize and can be solved on any calculator with
‘‘x^y’’ (x to the y power) and ‘‘log’’[log-base 10] keys. Such
a calculator is available on any computer running under the
Windows (Microsoft Corporation, Redmond, WA) operating
system (Figure 2). In addition, the precise forms of the
equations can be used within a computer spreadsheet or can be
programmed into a handheld personal digital assistant. The
equations can also be incorporated within a hospital’s in-
formatics system in such a way that customized treatment
guidelines could be reported to the clinician in conjunction with
the acetaminophen laboratory results. However, as with the
Rummack-Matthew nomogram, these equations should not
substitute for judicious consultation
with a regional poison control center.
Steven J. White, MD
Departments of Emergency Medicine and Pediatrics
Vanderbilt University Medical Center
Nashville, TN
Barry H. Rumack, MD
Rocky Mountain Poison and Drug Center
University of Colorado School of Medicine
Denver, CO
doi:10.1016/j.annemergmed.2004.11.033
1. Watson WA, Litovitz TL, Rodgers GC, et al. 2002 Annual Report
of the American Association of Poison Control Centers Toxic
Exposure Surveillance System. Am J Emerg Med. 2003;21:
353-421.
2. Rumack BH, Peterson RC, Koch GC, et al. Acetaminophen overdose:
662 cases with oral acetylcysteine therapy. Arch Intern Med. 1981;
141:380-385.
3. Smilkstein MJ, Knapp GL, Kulig KW, et al. Efficacy of oral
N-acetylcysteine in the treatment of acetaminophen overdose.
Analysis of the national multicenter study (1976 to 1985). N Engl
J Med. 1988;319:1557-1562.
4. Rumack BH, Matthew H. Acetaminophen poisoning and toxicity.
Pediatrics. 1975;55:871-876.
5. Rumack BH. Acetaminophen hepatic toxicity: the first 35 years.
Clin Toxicol. 2002;40:3-20.
Clinical Policy on Pediatric Procedural Sedation
To the Editor:
I applaud Mace et al
1
for the ‘‘Clinical Policy: Evidence-
Based Approach to Pharmacologic Agents Used in Pediatric
Sedation and Analgesia in the Emergency Department,’’
published in the October 2004 issue of Annals. However,
in addition to identifying potential agents for emergency
department (ED) pediatric sedation, I believe it is equally
important to note those drugs that should not be considered
for this procedure. For example, chloral hydrate, diphenhydra-
mine, meperidine, and the ‘‘DPT cocktail’’ (demerol-phener-
gan-thorazine) have been used for decades for pediatric
sedation, despite their adverse risk profiles and absence of
supporting data.
2-5
Although many emergency physicians
choose better regimens (such as those described in the clinical
policy), these less-desirable agents of habit are still used in many
Figure 1. Rumack-Matthew nomogram. Modified from Rumack
BH, Peterson RC, Koch GC, et al. Acetaminophen overdose:
662 cases with oral acetylcysteine therapy. Arch Intern Med.
1981;141:380-385.
2
Figure 2. Sample calculation using Windows operating system
calculator (scientific view) for known ingestion with level drawn
at 7 hours and 20 minutes after acute ingestion.
Correspondence
564 Annals of Emergency Medicine Volume 45, no. 5 : May 2005