Modeling Intoxication

APM 115: Mathematical Modeling

Benjamin Paris, Alessio Fikre, Luke Martocchio, Tamas Tolerian

March 9, 2021
Abstract
This paper proposes a single compartment model to study the evolution of blood alcohol content (BAC) in
humans. The model has 2 components: one modeling the rate of alcohol intake as a constant function and the
other modeling the elimination of alcohol as a function of current BAC. We explore the model sensitivity to the
Michaelis constant and maximum alcohol clearance rate. Finally, the model is applied to study real-life drinking
scenarios to explore safer, more sustainable drinking behavior. Our results suggest safe drinking approaches, as
well as ways to maintain an optimal buzz and estimate time-to-sobriety.

Introduction
According to a 2019 study conducted by the National Survey on Drug Use and Health, about 50% of the
US adult population reported consuming alcohol at least once in the past month1 . Understanding precisely
how our bodies process alcohol and how it affects us over time can promote safer drinking habits. This might
include estimating blood alcohol content (BAC) based on the number of drinks consumed, or determining the
time to sobriety to avoid drunk driving, among other sources of danger.
Alcohol is absorbed into the body’s water volume over time, and processed per unit of water volume by
enzymatic action2,3 . This implies that the level of intoxication that a subject experiences depends not only on
the intake, but also the total amount of body water they have. In particular, this is often correlated with factors
such as height, weight, and physical build; women also tend to have more fat and a smaller blood volume, and
because alcohol is not able to enter fat cells because of fat’s poor solubility, sex is also an aspect that affects
the evolution of BAC4,5 . Other factors are the amount of food in the stomach, that changes the proportion of
alcohol that is digested, as well as previous exposure to alcohol, usage of certain drugs, and the type of drink
consumed.6 We will model alcohol absorption in one’s body over time as a process depending only on the
amount of alcohol consumed and the subject’s gender, height, and weight.
While the model of alcohol absorption is usually modeled simply, the model of elimination of alcohol is
a little complicated. At low levels of BAC, the elimination rate of alcohol slows down7 . Thus, Cederbaum
argues that the rate of elimination follows Michaelis-Menten Kinetics, which models enzyme-substrate clear-
ing processes8 . Michaelis-Menten Kinetics may not capture certain aspects of the unique enzyme kinetics of
alcohol—for example, the fact that a very small amount of alcohol is absorbed in the stomach lining through
alcohol dehydrogenase (ADH)—but they reflect the fact that, on the whole, at low substrate concentrations, an
enzyme-substrate pair is more prone to reversal, whereas at high concentrations, chemical equilibrium mandates
that enzyme-substrate pairs form at a higher rate. As substrate concentration increases, this rate tends toward
the maximum velocity of the reaction. This model of alcohol absorption and clearance can be used to show how
different drinking patterns effect BAC, and how to manage BAC based on different biological and behavioral
factors.

Model Description
Alcohol Absorption
We first model the effect of alcohol consumption on BAC. We assume that the rate of alcohol consumption
D(t) is independent of the current BAC level and only depends on time. We therefore model drinking most
simply as a piecewise linear function where the drinking period starts at t = 0 and ends at t = tend , after which
there is no more consumption. The equation is
(
a
t ≤ tend
D(t) = tend
0 tend ≤ t

where a is the total amount of alcohol consumed measured in grams. This model assumes that alcohol is
consumed at a constant rate over time.
1
 According to the Widmark and Wagner Models of alcohol absorption, the grams/100mL/hr rate of alcohol
absorption into the body is simply this rate D(t) divided by the water volume of the body in units of 100
milliliters V = r · W · 10 (as r · W gives the value in liters), for W one’s weight and r a constant which gives
the water density of a person based on height H and weight W for each gender. The following equations define
r: for males, W (0.3161 − 0.004821W + 0.004632H), and for females, W (0.3122 − 0.006446W + 0.004466H)9 .
Thus, we assume that alcohol is absorbed into each unit of the body’s water-volume instantaneously as it is
consumed: alcohol absorption is modeled, in BAC per unit time, as
D(t) D(t)
=
V r · W · 10

Alcohol Elimination
To model the elimination of alcohol from the body, our team decided to use the Wagner model as described
by Heck10 . In this model, the elimination of alcohol from the body at high concentrations tends toward a
maximum rate of enzymatic action, vmax ; meanwhile, the constant km defines the value of BAC for which the
speed of the enzymatic reaction is half of vmax /V :
dBAC vmax BAC
∝−
dt V (km + BAC)
Unlike consumption, which is linear in time, this differential equation depends on one’s current BAC . Since
vmax is the maximum rate of overall enzymatic action, it is this rate which the process tends toward at higher
concentrations.

We can find an analytical solution of the alcohol clearance equation by the following system:
Z Z
km + BAC 1
dBAC = − dt
vmax BAC V
km BAC t
ln(BAC) + =− +C
vmax vmax V
This equation cannot be solved for BAC, but we can find the inverse of the analytical solution:
V
BAC−1 (t) = [km (ln(BAC0 ) − ln(BAC)) + (BAC0 − BAC)]
vmax
where BAC0 = BAC(0) is the initial condition, representing the starting BAC in the subject.

Full Model Equation

Thus, with both the consumption and elimination of alcohol modeled, we can write the full model:

dBAC D(t) vmax BAC

= −
dt V (km + BAC)V

BAC = blood alcohol concentration, measured in grams per 100ml

t = time, measured in hours
D(t) = rate of alcohol intake, measured in grams per hour
V = total body water, measured in 100ml
vmax = the maximum velocity of the Michaelis-Menten reaction, measured in grams per hour
km = Michaelis constant, measured in grams per 100ml

Sensitivity of Alcohol Clearance

Figure 1 included below shows the sensitivity of the solution to the parameters km and vmax , given the
initial conditions BAC(0) = 0.01 and BAC(0) = 0.05, respectively. The range of these parameters come from
Jones, who gives empirical ranges for km of 2 to 10mg/100mL, or 0.002 to 0.01 in our preferred units, and
10 to 35mg/100mL/hr for vmax , or 5.5 to 19.3 in our units.∗ The behavior of parameters is also as expected,
with higher levels of vmax —a constant which specifies the maximum rate of the Michaelis-Menten reaction—
associated with steeper declines in BAC. The value of km should be interpreted as the level of BAC at which
the velocity of the enzyme reactive is half of vmax /V , the maximum velocity per unit volume.11 On Figure 1
it is apparent that higher values of km are associated with a more curved rate of alcohol elimination that lags
behind the lower values of km , for which the curve stays at the (steeper) vmax linear phase for longer. The
2 not have great effect when BAC >>> k
different initial BAC values reflect the fact that km does m
 Figure 1: Left: Sensitivity to km Right: Sensitivity to vmax

Stability Analysis
dBAC
Let us now examine the stability of the system, by finding the fixed points through setting dt = 0:

D(t) vmax BAC∗

0= −
V V (km + BAC∗ )
which we can solve for BAC∗
D(t)km
BAC∗ =
vmax − D(t)
This equation confirms initial expectations that when D(t) = 0, BAC∗ = 0 is the only fixed point, being in
line with previous expectations. Let us also examine the stability of this fixed point to confirm that is according
to expectations. To do so, we will assume that D(t) = a0 , where a0 ≥ 0 such that the derivative does not depend
on t. This assumption is satisfied in our assumption of the form of the D(t) we made above, and thus applies
for the consumption and elimination periods as well. Let  be a small disturbance such that  = BAC − BAC∗ .
Further, let f (BAC) = dBAC
dt Then, we can use a Taylor approximation to write:

d vmax km vmax − a0
≈ f 0 (BAC∗ ) = − 0 = −
dt V (km + v a km
max−a0 )
V
0
The above quantity is negative whenever vmax > a meaning that the fixed point is stable, and otherwise
it is unstable. This has a convenient interpretation: whenever the rate of intake is greater than or equal to
vmax , the maximum rate of elimination, the level of BAC goes out of control and keeps on increasing without a
boundary. In this scenario, we also see from the equation of the fixed point that BAC ∗ < 0. This interpretation
does not make biological sense, but it is still non-problematic for the model because the negative fixed point is
unstable, so the BAC will never reach negative values according to the model.

Analysis & Discussion

This section will analyze the behavior of the model as the individual agent’s profile parameters and drinking
behavior vary. This section will also incorporate discussion to comment on why the behavior of the model
with respect to different parameter combinations makes sense. In order to conduct our analysis, we make
assumptions about the appropriate values of the constants. We take the unit of a standard drink to contain
14 grams of alcohol. For the constants of the Michaelis-Menten kinetics we use vmax = 10.2 and km = 0.0045.
These are kept constant throughout the analysis, and we will vary the variables weight, height, gender, length
of drinking, and number of standard drinks consumed. Our analysis in this section will refer to two ’standard’
agents for whom the following weight and height parameter combinations apply.

1. Standard Male: Height: 175 centimeters, Weight: 70 kilograms

2. Standard Female: Height: 160 centimeters, Weight: 60 kilograms

One may consider varying the number of drinks consumed and the drinking period duration for the standard
female, as well as applying different weights and heights for female agents more generally. Each of these plots
holds all other parameters constant to facilitate observation.

3
 0.175
BAC vs. Time for Varying Number of Drinks BAC vs. Time for Varying Drinking Period Duration
2 drinks 1 hours
3 drinks 0.08 2 hours
0.150 4 drinks 3 hours
5 drinks 4 hours
6 drinks 5 hours
0.125
0.06

BAC (g/100mL)

BAC (g/100mL)
0.100

0.075 0.04

0.050
0.02
0.025

0.000 0.00
0 2 4 6 8 10 12 0 2 4 6 8 10 12
t (hours) t (hours)
BAC vs. Time for Varying Weight BAC vs. Time for Varying Height
0.08 40 kg 140 cm
50 kg 0.07 150 cm
0.07 60 kg 160 cm
70 kg 170 cm
80 kg 0.06 180 cm
0.06
0.05
BAC (g/100mL)

BAC (g/100mL)
0.05
0.04
0.04

0.03 0.03

0.02 0.02

0.01 0.01

0.00 0.00
0 2 4 6 8 10 12 0 2 4 6 8 10 12
t (hours) t (hours)

Figure 2: Top row: Standard female weight & height fixed Bottom row: 3 drinks in 2 hours fixed

Figure 2 represents parameter sensitivity to the core inputs of the model. The top left graph demonstrates
that the number of drinks drastically affects the BAC reached in a fixed 2-hour period of time. Specifically, in
this same period, if the standard female consumes 6 drinks (reaching about 0.16%) versus 2 drinks (reaching
about 0.03%), the individual will experience roughly a difference of 0.13% BAC. The top right graph considers
changes in the alcohol consumption period, which by definition encompasses the notion of the rate of consump-
tion of 2 drinks. Here, observations include that if the standard female consumes 2 drinks in 1 hour, then she
will reach a BAC above 0.08%, the legal BAC driving limit in the United States. Instead, if the agent were to
elongate her consumption period, the BAC curve would begin to flatten; when consuming 2 drinks in a 5 hour
period, the standard female will not reach a BAC level above 0.02%. It is evident that varying both the number
of drinks and the length of the consumption period yield significant differences in the BAC level achieved. As
expected, it can be said that this model is moderately sensitive to these parameters.
The bottom row of plots in Figure 2 demonstrate differences in BAC level reached when varying weight and
height. When varying solely weight for females at a height of 160 cm, the greater the weight of the individual,
the lower the BAC level achieved. Interestingly, the difference between the maximum BACs reached when
comparing a female at a weight of 40kg to that of 80kg is roughly a 0.02%. This is strikingly low as this is
comparing two females that are identical except for the fact that one individual weighs twice as much as the
other. When varying solely height for a female weighing 60 kg, we find that the taller the individual, the lower
the BAC level achieved. Given the different heights considered, the range of BAC levels is once again relatively
low as compared to the top row plots of Figure 2. A female with height of 140 cm and another female with
a height of 180 cm attain maximum BACs less than 0.02% apart. These results when varying the height and
weight parameters suggest that the model is less sensitive to changes in profile parameters and more responsive
to changes in the number of drinks and the duration of the consumption period.

Pulsing Model Extension

In order to more accurately apply our model to real-life drinking behavior, we decided to extend the model
by introducing the option to have break periods in between the consumption of individual drinks. To make our
model more realistic and accurate in its calculation of blood alcohol content over the course of one’s drinking
period, we adjusted our model to account for each individual drink consumed as its own discrete step function
with specified start and end time. This update allows us to visualize the more realistic ’pulsing’ behavior of
BAC vs. time over the course of one’s consumption of alcohol. BAC increases during discrete drinking events
and then begins to decrease as alcohol is eliminated from the body during breaks in consumption.

Varying Number of Drinks Analysis

In considering the pulsing model, Figure 3 explores the effect of varying the number of drinks consumed on
predicted BAC percentage for both the standard male and the standard female. In this case, we consider the
4
case of a uniform drinking schedule, in which the agent takes 30 minutes to consume a drink and then takes a
15 minute break before starting their next drink.
BAC vs. Time for Standard Male (30m on 15m off) BAC vs. Time for Standard Female (30m on 15m off)
1 drinks 1 drinks
0.14 2 drinks 0.14 2 drinks
3 drinks 3 drinks
4 drinks 4 drinks
0.12 5 drinks 0.12 5 drinks
6 drinks 6 drinks
0.10 7 drinks 0.10 7 drinks
BAC (g/100mL)

BAC (g/100mL)
0.08 0.08

0.06 0.06

0.04 0.04

0.02 0.02

0.00 0.00
0 2 4 6 8 10 12 0 2 4 6 8 10 12
t (hours) t (hours)

Figure 3: Left: Standard Female Right: Standard Male

Overarching trends for the male and female are consistent between the pulsing and non-pulsing models:
as you increase the number of drinks consumed, the BAC of the individual increases. Beyond this simple
observation, there are more intriguing results. It is evident that the BAC curves for any number of drinks all
follow the same form, and are in fact perfectly overlaid. We observe that the BAC of the standard male who is
drinking a total of 3 drinks has the same exact BAC at the end of 3 drinks as the standard male who has had
3 drinks but will continue to drink a total of 6 drinks. Thus, as one would expect, the future consumption of
alcohol has no bearing on previous BAC levels.
Another observation one might make is that the standard female generally surpasses the legal limit of 0.08
% with fewer drinks than does the standard male. In considering why this may be the case, the plot on the
right-hand side demonstrates that the same unit of alcohol consumed by the female results in a steeper increase
in BAC. Given the drinking behavior of 30 minutes on and 15 minutes off, the female in this scenario will reach
a higher BAC for every drink than does the standard male.

Different Consumption Behaviors Analysis

Central to the pulsing model is the drinking behavior defined by the number of drinks, the length of the
period of drinking each unit of alcohol, and the waiting (break) period between drinks. These 3 parameters
are considered simultaneously in Figure 4 below. Figure 4 explores 4 different drinking behaviors, which may
be categorized into an aggressive consumption schedule (top row) and a conservative consumption schedule
(bottom row). As previously discussed, the agent follows the same uniform drinking pattern, and the number
of drinks simply describes how many times the pattern of an increase in BAC during consumption followed by
a decrease in BAC during a break period iterates. As such, the number of local maxima in our plots of BAC
vs. time equals the number of drinks consumed by the agent. In the aggressive drinking schedules presented in
which the standard female is consuming a unit of alcohol every 30 minutes, it is evident that the maximum BAC
level achieved will increase for every additional drink consumed in both the cases of 30-minute and 45-minute
breaks. This suggests that finishing a drink every 30 minutes and then taking a break 30 or 45-minute break
is a relatively aggressive drinking strategy for the standard female.
On the other hand, the presented results from the conservative consumption schedules suggest that a
standard female consuming each unit of alcohol in 45 minutes before taking a 45 minute break would achieve
a relatively stable BAC level over time. Furthermore, a drinking behavior of 45 minutes on followed by a
60-minute break leads to a decreasing BAC level over time. These results suggest that drinking a single unit
of alcohol in 45 minutes followed by a break of at lest 45 minutes is a sustainable schedule to either remain at
a specific level of intoxication or to have one’s BAC level decrease down to a safer level.

Discussion: Optimal Buzz

The notion of choosing a drinking behavior in accordance with one’s desired BAC is particularly applicable
to the idea of the optimal buzz. For this discussion, the optimal buzz is considered to be 0.05%. Without being
overly concerned with the question of how one may reach the optimal buzz of about 0.05%, this discussion may
turn to the more difficult question of how one may maintain the optimal buzz. Figure 4 addresses this question
directly and offers a solution for the standard female. The bottom left plot demonstrates the standard female
who achieves a ’stable’ BAC level that remains between a buffer ranging from 0.04% and 0.06%. As such, for
5
 BAC vs. Time for Standard Female (30m on 30m off) BAC vs. Time for Standard Female (30m on 45m off)
0.14 1 drinks 0.14 1 drinks
2 drinks 2 drinks
3 drinks 3 drinks
0.12 4 drinks 0.12 4 drinks
5 drinks 5 drinks
6 drinks 6 drinks
0.10 0.10
BAC (g/100mL)

BAC (g/100mL)
0.08 0.08

0.06 0.06

0.04 0.04

0.02 0.02

0.00 0.00
0 2 4 6 8 10 12 0 2 4 6 8 10 12
t (hours) t (hours)
BAC vs. Time for Standard Female (45m on 45m off) BAC vs. Time for Standard Female (45m on 60m off)
0.14 1 drinks 0.14 1 drinks
2 drinks 2 drinks
3 drinks 3 drinks
0.12 4 drinks 0.12 4 drinks
5 drinks 5 drinks
6 drinks 6 drinks
0.10 0.10
BAC (g/100mL)

BAC (g/100mL)
0.08 0.08

0.06 0.06

0.04 0.04

0.02 0.02

0.00 0.00
0 2 4 6 8 10 12 0 2 4 6 8 10 12
t (hours) t (hours)

Figure 4: Top: Aggressive Consumption Bottom: Conservative Consumption

the standard female, once achieving the optimal buzz of about 0.05%, the model suggests that one method of
sustaining the optimal buzz would be consuming a unit of alcohol every 45 minutes, followed by taking a 45
minute break, and then repeating this process indefinitely for however many drinks the individual desires.

Rate of Decrease of BAC Analysis

Finally, this analysis will address the model behavior with respect to varying initial, non-zero BAC levels
while not incorporating the consumption of any additional drinks. The implications of these observations
directly relate to the notion of the time it takes one to achieve sobriety after beginning at a certain level of
intoxication.
BAC vs. Time for Standard Female BAC vs. Time for Standard Male
y0=0.025 y0=0.025
y0=0.05 y0=0.05
0.14 y0=0.075 0.14 y0=0.075
y0=0.1 y0=0.1
y0=0.125 y0=0.125
y0=0.15 y0=0.15
0.12 0.12

0.10 0.10
BAC (g/100mL)

BAC (g/100mL)

0.08 0.08

0.06 0.06

0.04 0.04

0.02 0.02

0.00 0.00
0 2 4 6 8 10 12 0 2 4 6 8 10 12
t (hours) t (hours)

Figure 5: Left: Standard Female Right: Standard Male

When excluding any further consumption of alcohol, the model describes for the discharge rate or the rate
of alcohol elimination for the individual being considered. As demonstrated in the two plots in Figure 5, the
curves follow an expected behavior in that the rate of change of the BAC level with respect to time for both
genders and for any number of drinks is negative. But it is striking that the rate of decrease of the BAC level
for each individual profile is mostly linear until BAC approaches 0.0%. Furthermore, the rate of decrease is
nearly identical for the varying initial conditions of this system. For example, whether the standard female
starts at a BAC of 0.1% or 0.05% does affect the rate at which the BAC decreases significantly in any way.

6
Discussion: Time to Sobriety
A natural extension and real-life application of this model would be in calculating the amount of time
it would take individuals of varying sex, weight, and height to achieve sobriety given an initial BAC. This
information may be particularly useful for an individual who has consumed a significant volume of alcohol and
may desire to drive a motor-vehicle the following morning, and would like to do so knowing that it is safe
and legal. Because our model incorporates alcohol discharge using a functional form such that BAC only gets
arbitrarily close to 0.0% as one sobers up while never achieving the actual value, we decided to define complete
sobriety as the point at which one’s BAC is below a tolerance level of 0.001%. The following tables present the
times it would take to achieve a BAC below our specified tolerance level based on different initial BACs and
weight of the agents (for both males and females of average height). We see from observing these results that
males (who are on average heavier and taller, and thus usually carry more water value than females) take longer
to sober up than women. Referring to our model’s functional form, we conclude that these results make sense
because the rate of alcohol discharge is inversely proportional to the water volume of the individual agent.

Table 1: Female Time to Sobriety (in hrs) Table 2: Male Time to Sobriety (in hrs)

40kg 50kg 60kg 70kg 80kg 50kg 60kg 70kg 80kg 90kg
0.025% 1.17 1.33 1.45 1.53 1.55 0.025% 1.63 1.85 2.03 2.17 2.28
0.050% 2.01 2.30 2.51 2.64 2.67 0.050% 2.82 3.20 3.51 3.75 3.94
0.075% 2.82 3.23 3.52 3.70 3.75 0.075% 3.96 4.48 4.92 5.27 5.53
0.100% 3.62 4.14 4.51 4.73 4.80 0.100% 5.07 5.74 6.30 6.75 7.08
0.125% 4.40 5.04 5.49 5.76 5.85 0.125% 6.17 6.99 7.67 8.21 8.62
0.150% 5.18 5.93 6.46 6.78 6.88 0.150% 7.26 8.22 9.02 9.66 10.14

Potential Shortcomings
Although our model provides useful and flexible method for calculating how any given drinking schedule
would contribute to one’s blood alcohol content over time, it relies on a number of foundational, simplifying
assumptions. Our model treats the absorption of alcohol as a process that is uniform and begins instanta-
neously. This is not the case in practice, but we made this assumption to simplify our analysis. Our staggered
consumption model does add a degree of sophistication to our representation of consumption behavior because
it allows us to model BAC vs. time for any drinking strategy; however, our modeling of each discrete drink
that is being consumed is not completely accurate because it treats each drink consumed as the addition of
another uniform step function. In addition, in our analysis, the amount of mgs of alcohol per drink must be
held constant (we chose 14g of alcohol as the standard potency per drink). Our model would be more flexible
and useful if it enabled one to model the consumption of a variety of drinks with different respective alcohol
concentrations. The type of alcohol consumed is also not taken into account in our model, while in practice,
it has been shown that drinks with CO2 are absorbed to a larger degree than something like wine). Moreover,
our model does not account for stomach contents and hydration at the time of drinking (drinking with full vs
empty stomach).

Conclusion
This model is motivated by a widespread desire to consume alcohol safely and sustainably. Different drinking
behaviors and profiles of individuals add complexity to one’s awareness of the intoxication level they may reach
when drinking. As such, we find good reason to explore several central questions that this model can help
explain. The following questions were addressed. How does the BAC of the ’standard male’ and ’standard
female’ vary over time when adjusting the volume of alcohol consumed? How can one maintain an optimal buzz
for a prolonged period of time? And how long does it take for one to reach complete sobriety when terminating
a drinking period at varying initial BAC levels? Findings related to these questions are summarized below.
The analysis on varying the quantity of alcohol consumed indicates that the driving factor in increasing BAC
is the unit of alcohol and that the standard male experiences less of an increase in BAC from the same amount
of alcohol consumed as compared to the standard female. The analysis on different consumption behaviors finds
that in sustaining an optimal buzz (0.04-0.06 % BAC), the standard female would be well-advised to consume
one drink every 45 minutes followed by 45 minutes of ’rest’. Doing this results in a stable BAC indefinitely.
The model could be used for a similar analysis for any specific individual profile. Finally, in considering how
long it may take a person to reach a 0.00% BAC, this analysis finds that all else being equal, males take longer
to reach complete sobriety as compared to females. Overall, this model explores the number of drinks, the
drinking behavior, and the time to sobriety for different profiles and enables people to make more informed
decisions when consuming alcohol.

7
Contributions
Abstract: Tamas, Alessio
Introduction: Benny, Tamas
Model Description: Benny, Alessio, Luke, Tamas
Analysis: Benny, Alessio, Luke, Tamas
Discussion: Alessio, Luke
Conclusion: Alessio, Luke
Code (Python File): Benny, Alessio, Luke, Tamas
Presentation Slides: Benny, Alessio, Luke, Tamas

Notes
1 National Institutes of Health. “Alcohol facts and statistics.” (n.d.). Retrieved March 08, 2021, from https://www.niaaa.nih.gov/publications/

and-fact-sheets/alcohol-facts-and-statistics: :text=Prevalence%20of%20Drinking%3A%20According%20to,in%20this%20age%20group%20and

2 Paton, A. (2005). Alcohol in the body. BMJ, 330(7482), 85-87. doi:10.1136/bmj.330.7482.85

3 Cederbaum, A. I. (2012). Alcohol metabolism. Clinics in Liver Disease, 16(4), 667-685. doi:10.1016/j.cld.2012.08.002

4 Paton, 2005

5 Cederbaum, 2012

6 Paton, 2005

7 Cederbaum, 2012

8 Cederbaum, 2012

9 Heck, A. J. (2007). Modelling Intake and Clearance of Alcohol in Humans. The Electronic Journal of Mathematics and

Technology, 1 (3), 232-237. Retreived March 08, 2021, from https://staff.fnwi.uva.nl/a.j.p.heck/Research/art/ICTMT82 .pdf

10 Heck, 2007

∗ Note: There are two conventions for the units associated with vmax : one is to have it be a per-unit-water-volume rate of alcohol

clearance, while the other is to have it be an overall rate of alcohol clearance. We choose the latter, and convert 10mg/100mL/hr
10mg 1g 55.2461L 10100mL
by the following: 100ml∗hr
· 1000mg
· averagemale
· 1L
= 5.52461g/hr and likewise for 35mg/100mL/hr.

11 Introduction to enzymes. (n.d.). Retrieved March 08, 2021, from http://www.worthington-biochem.com/introbiochem/substrateConc.html