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Drinks

Calculation of Total Dose or number of Standard Drinks Based on Drinking Scenario

𝐷 = 𝑉 × 𝐶 × ρ × m

where:

D = dose (g)

V = volume (oz. or mL.)

C = concentration (mL/100 mL)

ρ = density of ethanol (0.789 g/mL)(constant)

m = metric conversion (29.6 mL/oz if using oz.)

Time

Widmark’s Formula

Time of Incident
Absorption

Elimination Rate

𝐴𝐶 = D / Vd x w

where:
AC = alcohol concentration (g/L)

D = dose (g)
Vd = volume of distribution (L/kg)

w = weight (kg)

Assuming Reliability: Minumum Number of Drinks

Cross-examination of the Accused or Rebuttal of Defence Evidence: How Many Drinks?

Prosecutors use these equations to rebut the evidence of an accused as to drinking scenario

Human Bodies in Canada Don't Absorb & Eliminate Alcohol According to a Scientific Model

Distribution in Body

Volume of Distribution (Vd)

Fixed Vd Approach based on Sex at Birth

Individualized Vd Approach

Range of Values

TBW = total body water (L)

a = age (years)

h = height (cm)

w = weight (kg)

Vdmale = TBW /w x 0.825

±𝑉𝑑 𝑚𝑎𝑙𝑒 = 𝑉𝑑 ± (𝑉𝑑 × 9.86%)

Vdfemale = TBW / w x 0.838

±𝑉𝑑𝑓𝑒𝑚𝑎𝑙𝑒 = 𝑉𝑑 ± (𝑉𝑑 × 15.00%)

Thinking Backwards

Adjusting for an Unabsorbed or Post-incident Drink

Prosecutors use these equations to prove AC at time of Incident

Experts use them to explore "Last Drink" scenarios

Equations and Problems

List of Equations from ANSI/ASB Best Practice Recommendations 2024

Automatic Scenarios

This Calculator is designed to permit lawyers to explore possible defences or prepare for cross-examinations. Don't use it to decide whether or not to drink and drive. It is dangerous to use these calculations to determine the ability to drive a vehicle or operate machinery after consuming alcohol. If you do so you assume full risk of legal prosecution, injury, illness, or death to yourself and others.

NaN means "Not a Number". If you receive that message, the equation or calculation may be irrelevant to your inquiry or there may be an omission in your input data.

## Drinking Scenario

##### Drink #1

Dose calculation in g

Scenario Summary

##### Drink #2

Dose calculation in g

##### Drink #3

Dose calculation in g

Total Dose calculation in g and number of standard drinks.

Eq 7 Orig Dose

## Subject's Body

Height Conversion 0 cm.

Weight Conversion 0 kg.

Notes:

1. The calculation uses Sex at Birth not gender.

2. Did you select a Unit of Height (inches or cm.) and a Unit of Weight (lbs. or kg.) ?

3. Do the height and weight conversions make sense?

Body Summary

## Fixed Vd Approach Based on Sex at Birth

If a fixed Vd range based on sex is used, 0.00 to 0.00 L/kg should be used.

## Individualized Vd Approach Based on Sex at Birth, Age, Height, and Weight (3 steps):Calculate TBWCalculate VdRange of Values 1. Calculate TBW TBW = total body water (L)

TBW is 0 L

Values Check for TBW calculation: TBWconstant is 0.0, ageconstant is 0.0, age is 0, heightconstant is 0.0, heightconversion is 0, weightconstant is 0, weightconversion is 0.

𝑇𝐵𝑊 (𝑚𝑎𝑙𝑒) = 2.447 − (0.09516 × 𝑎) + (0.1074 × ℎ) + (0.3362 × 𝑤) Equation (1a)

TBW = TBWconstant - (ageconstant × 𝑎ge) + (heightconstant × ℎeightconversion) + (weigtconstant × 𝑤eightconversion)

𝑇𝐵𝑊 (𝑓𝑒𝑚𝑎𝑙𝑒) = −2.097 + (0.1069 × ℎ) + (0.2466 × 𝑤) Equation (1b)

𝑇𝐵𝑊 = TBWconstant + (ageconstant (i.e. 0) x age) + (heightconstant × ℎeightconversion) + (weightconstant × 𝑤eightconversion)

TBW = TBWconstant + (ageconstant × 𝑎ge) + (heightconstant × ℎeightconversion) + (weigtconstant × 𝑤eightconversion)

Note the - or + after the TBW constant depends on sex at birth so the sign is switched in ageconstant for males, in order to consolidate the two TBW formulas into one, for both sexes at birth.

## 2.  Calculate Individualized VdVd = volume of distribution (L/kg)

Vd is 0 L/kg

𝑉𝑑 (𝑚𝑎𝑙𝑒) = TBW / (w x 0.825) Equation (2a)

𝑉𝑑 (𝑓𝑒𝑚𝑎𝑙𝑒) = TBW / (w x 0.838)  Equation (2b)

## 3.  Range of Values for Individualized Vd

Range is 0 to 0 L/kg

𝑉𝑑 (𝑚𝑎𝑙𝑒) = 𝑉𝑑 ± (𝑉𝑑 × 9.86%) Equation (3a)

𝑉𝑑 (𝑓𝑒𝑚𝑎𝑙𝑒) = 𝑉𝑑 ± (𝑉𝑑 × 15.00%) Equation (3b)

TBW
Indiv Vd
+/- % CV
Widmark

# Equation 4 and the Widmark Equation Start at Time 0

AC (Fixed Vd) Range is 0 to 0

AC (Individualized Vd) Range is 0 to 0

Units

Notes:

1. Have you entered volume and concentration in the purple Drinks section? Have you entered age, sex, height, and weight in the brown Body section above?

2. NaN means "Not a Number".

3. Vd ranges above 1.0 L/kg or a negative Vd number indicate an error.

4. If you forget to enter weight your BAC results will be absurdly high.

5. If you forget to enter sex at birth your BAC results will be absurdly low.

6. Adjust units to g/L, g/dL, or mg/100mL below. Default is g/dL or g/210L.

7. Adjust for absorption % and elimination below using the slider inputs.

Scenario Summary

Body Summary

Vd Summary

Widmark and Time Summary

## The Effects of Time

#### (similar to Equation 8)

𝐴𝐶 = D / Vd x w

where:
AC = alcohol concentration (g/L)

D = dose (g)
Vd = volume of distribution (L/kg)

w = weight (kg)

At your first interview with the new client, you should establish a starting point in time, Time 0, when:

1. the client started drinking,

2. and hopefully the client had a BAC of 0 when they started drinking,

3. and hopefully the client has some restaurant/bar receipts, or some other independent way of establishing that Time 0 through a witness, mobile phone record, or parking receipt.

For purposes of Equation 4, "Widmark's Formula", start by assuming that all of the Drinks were absorbed instantaneously into the subject Body at Time 0 with no elimination. You probably already know that absorption of the Drinks by the subject Body does not happen instantaneously, and the drinking scenario obviously happens over time. However, to estimate BAC (what the Equation calls "AC") at a later time you need to start somewhere. Specifically, you need to account for all of the Drinks being in the subject Body, use the basic Widmark Formula  and then adjust. In reality, the AC concentration rises rapidly after consumption during the absorptive phase (some elimination is also taking place) and falls slowly during the post-absorptive phase (elimination only). In between those two phases, there is a plateau phase when the AC bounces up and down somewhat because both absorption and elimination are competing at the same time. The time of the incident is critical and as we know, the prosecutor sometimes has difficulty establishing that time. At the time of the incident, the subject Body may have been in the absorptive phase, the plateau phase, or in the post-absorptive elimination only phase.

I highly suggest that you join the DUIDLA and subscribe to Counterpoint Journal, if you have not already done so. Use their continuing education programs and videos to learn about absorption and elimination.

I have done my best to make this calculator user-friendly for both Criminal Lawyers Association members in Canada and DUIDLA members in the United States and Canada. Please indicate whether you wish to use the original Widmark formula units g/L, the US units g/dL, or the Canadian units mg/100mL for purposes of Equation 4. If you decide to use Retrograde Extrapolation Equations 9 or 10 (green section), or Equations 5 or 6 calculations (orange section), please be consistent in using US or Canadian units.

Methodology for Defence lawyers who receive confidential information from the client:

1. Calculate AC at Time 0 using the Widmark formula Equation 4.

2. Adjust below for incomplete absorption by %.

3. Adjust below (this red section) for elimination of alcohol for various rates between .010 to .025 g/dL per hour or 10 to 25 mg/100mls per hour.

Methodology for Experts who receive a Request for Opinion from Crown/state or Defence including a reliable  Evidentiary Breath Test or Blood Draw (and lawyers examining or cross-examining them):

1. Use the green section of this site to calculate an Adjusted AC for unabsorbed alcohol, "Last Drink" defence, or post-incident drinking

2. Input AC under Retrograde Extrapolation and apply .010 to .025 g/dL per hour, if necessary, using Equation 9. Elapsed time between incident and breath test/blood draw can be input as 0 if necessary.

3. Calculate the theoretical Max AC associated with the unabsorbed alcohol, Last Drink, or post-incident drink using Equations 7 and 8 for this Body.

Methodology for Experts who receive a Request for Opinion from Crown/state including an expected statement from the Accused as to drinking scenario and a known AC from an Evidentiary Breath Test or Blood Draw (and lawyers examining or cross-examining them):

1. Use the orange section of this site to calculate "How Many Drinks" are associated with this AC for this Body.

2. Calculate the minimum Dose required to generate this AC in this body using Equation 5.

3. Calculate using Equation 6, the minimum number of drinks of the type mentioned by the Accused in their statement or expected evidence.

Methodology Using Examples from the Best Practices Annex as Precedents:

1. Review the Best Practices document and Choose a Precedent illustrative example from the Annex.

2. Use the dropdown list which resets defaults in this calculator to match an illustrative example.

3. Alternatively use Manual entry to copy over relevant data.

3. Input data into this calculator, for your own case using Manual entry or adjusting the precedent default values, respecting the subject body, respecting retrograde extrapolation and/or adjustments to AC, or a calculation of "How Many drinks?".

Steps to a review by a Defence lawyer using confidential information from the Accused:

AC (Fixed Vd) at Time 0

AC (Individualized Vd) at Time 0

Possible Error Messages: NaN means "Not a Number". "Infinity"is not a good AC calculation. Vd ranges above 1.0 L/kg or a negative Vd number indicate an error. If you receive one of these errors please check to make sure you have entered at least one drink in the Drinks section and all the inputs in the Body section.

#### Adjust for Incomplete Absorption (Use the Slider to Adjust Percentage Absorption)

100 Percent Absorbed

#### Before Elimination but After Any Absorption Adjustment 🧽

AC (Fixed Vd) Range is 0 to 0

AC (Individualized Vd) Range is 0 to 0

.010 g/dL/hour

Elimination 0

#### After Elimination 🚽

AC (Fixed Vd) Range is 0 to 0

AC (Individualized Vd) Range is 0 to 0

Units

# Thinking Backwards and then Adjusting

Assume for purposes of this Green section that the evidentiary breath test or blood draw has resulted in a reliable analysis of the alcohol concentration (or AC) of the accused at the time of the breath test or blood draw. I recognize that assuming reliability of these tests for a forensic purpose is a huge assumption, but unfortunately deemed reliability rather than scientific reliability, seems to be the law in Canada.

Connecting the AC at the time of the breath test or blood draw to the AC at the time of the incident is the subject of Equations 9 and 10. Equation 9 is applicable if the subject is post-absorptive and there was no post-incident drinking. Equation 10 reduces the Equation 9 AC estimate, in the event that there is a "Last Drink" defence, there was post-incident drinking, or the subject's body was still absorbing the alcohol at the time of the evidentiary breath test or blood draw. In order to use Equation 10 one must first input and analyze data respecting the "Last Drink", the post-incident drink, or a drink not yet absorbed, using Equations  7 (to calculate Dose in g) and, using Equation 8, a range of AC (use the maximum of the range) that theoretically could have been the result of the "Last Drink", the post-incident drink, or the drink not yet absorbed.

Any calculation of the theoretical maximum AC for the drink should consider both Fixed Vd and Individualized Vd.

Retrograde Extrapolation (if subject post-absorptive at time of incident)

Equation (9)

𝐴𝐶inc = where:

ACinc = ACtest + (𝛽 x T)

where:

𝐴𝐶inc = estimated alcohol concentration at the time of the incident (g/dL)

ACtest = measured alcohol concentration (g/dL)
𝛽 = elimination rate (0.010-0.025 g/dL/hour)
T = time between incident and time of breath test/blood draw (hours)

AC at time of incident is 0 to 0

Units

If the drinking scenario indicates unabsorbed alcohol at the time of the incident, or there is evidence of post incident alcohol consumption, the next step is to subtract the impact of those drinks from the estimated post absorptive alcohol range of concentrations.

Equation (10)

Adjusted ACinc = ACinc – ACdrink(s) where:

Adjusted ACinc = estimated AC at time of the incident, accounting for potentially unabsorbed alcohol or post incident alcohol consumption

ACinc = estimated AC at time of the incident if subject were in post absorptive state (calculated from Equation 9)

ACdrink(s) = maximum AC contribution from drink(s) (calculated from Equation 8)

​​

Warning: This subtraction can result in lots of errors so it is ripe for cross-examination. Watch for errors in your own calculation and in calculations made by experts:

1. Incomplete information or data entry as to sex at birth, age, height, and weight. Fixed Vd calculations require data entry of weight, weight units, and sex at birth. Individualized Vd calculations additionally require data entry of age, height, and height units.

2. Errors related to data entry of ounces v. mLs, inches v. cm.

3. Errors or confusion of decimals among g/L, g/dL, and mg/100mL.

To manually subtract an unabsorbed drink or a post incident drink using Equations 7, 8, 9, and 10, enter the unabsorbed or post incident adjustment drink volume and concentration under Equation 7 and 8 below , enter subject sex at birth, (age, height - if you are calculating individualized Vd), and weight in the Body section of this page, select the Unit of Alcohol Concentration (US or Canada units) in the green section above, read the two ranges of adjustment below, and subtract the following from the Retrograde Extrapolation Equation 9 AC range calculation. Warning: It very easy to err in making this calculation. Read the data entry summaries below to make sure they match your unabsorbed drink or post incident drink scenario only. Individualized Vd calculations will not work properly unless you have entered all Body fields including age and height.

Did you select a "Unit of Alcohol Concentration for Retrograde Extrapolation" (green section) above to ensure that results are stated correctly in g/dL or mg/100mL?

Did you enter data for this person's body in the Body (brown) section above?

Eq 7 Post Dose

## Maximum Theoretical AC That Could Be Reached From A Known Drink Equations 7 and 8

Use Equations 7 and 8 to calculate a Maximum Theoretical AC that could be reached in this Body from a known Drink, of a known Volume, Unit of Measurement, and alcohol concentration.

You can use Equations 7 and 8 calculation of maximum theoretical AC (whether Fixed Vd or Individualized Vd) with Equation 10 to subtract from the Equation 9 Retrograde Extrapolation Analysis (or presumed reliable evidentiary breath or blood test)  to adjust for a "Last Drink Defence", post-incident drink, or incomplete absorption.

You can also use Equations 7 and 8, to answer the "Question: Is the stated drinking history consistent with the alcohol concentration (AC) result?", by considering, for example, "What is maximum AC that could be reached from 2 pints of Brand X beer?" Prosecutors and Crowns often will use this type of calculation to rebut defence evidence and support cross-examination of the accused. State or Crown experts may say that they are using this approach to "Support/refute drinking history".

## AC Drink(s): Using Equations 7 and 8, what is the maximum theoretical AC that could be reached from:  An Unabsorbed Drink or Post-Incident Drink or any Specific Alleged Drink

Widmark unit and ACunit

ACdrinks calculation of dose

Eq 8 Max AC

ACdrink(s) (Fixed Vd) Range is 0 to 0

ACdrink(s) (Individualized Vd) Range is 0 to 0

Units

Body Summary

## Use these Equations to Destroy the Evidence of the Accused as to Drinking Scenario: Theoretical Minimum Number of Drinks

Equation 5 Minimum dose (in g) of alcohol to achieve a particular alcohol concentration in the body of this Accused.
Equation 6 Minimum number of “drinks” to achieve that dose when the Accused has given evidence of a type of beverage with a known concentration.

THIS CALCULATOR WILL NOT WORK PROPERLY UNLESS YOU HAVE SPECIFIED US g/dL OR CANADIAN mg/100 mL UNITS IN THE RETROGRADE EXTRAPOLATION GREEN SECTION ABOVE

Units of AC for Equations 5 and 6 are the same as Equations 9 (and 10) "Unit of Alcohol Concentration for Retrograde Extrapolation"

Equation 5 summary

Body Summary

Vd Summary

(Equation 5 2024) Calculation of Minimum Dose of Alcohol to Produce a Concentration

(5) 𝐷 (in g) =𝐴𝐶 × 𝑉𝑑 × 𝑤 × 10 dL/L (in US)

where:
D = dose (g)
AC = alcohol concentration (g/dL)

Vd= volume of distribution (L/kg)

w= weight (kg)

Use of this equation requires input of an alcohol concentration determined by blood draw or breath test as well as input of data (to calculate Vd) as to sex at birth, age, height in inchesor cm and weight in lbs. or kg.

Use the inputs in the "Body" section of this page to calculate both fixed Vd ranges and individualized Vd ranges.

See ANSI/ASB 2024

Using Equation 5, calculate with a fixed Vd range: AC x Vd L/kg (minimum and maximum) x w kg x 10 (dL/L in US) = Dose in g

Using Equation 5 calculate with an individualized Vd range: AC x Vd L/kg (minimum and maximum) x w kg x 10 (dL/L in US) = Dose in g

​​

Dose in g can them be converted into the minimum number of "drinks" when the concentration is known. Use Equation 6.

(Equation 6 2024) Dose in g converted into the minimum number of "drinks" when the concentration is known.

V = D / (C x p x m)

where:

V = Volume in oz.

D = Dose in g.

C = Beverage concentration mL/100mL

p = Density of ethanol 0.789 g/mL

m = metric conversion 29.6 ml/oz.

Use of this equation requires prior calculation of Dose and data input of Concentration of the "drinks". In the US a "standard drink" is a beverage containing 14 grams of ethyl alcohol:

12 US oz, 5% beer

5 US oz, 12% wine

1.5 US oz, 80 proof liquor (40%)

See ANSI/ASB 2024

Using Equation 6, calculate V in US oz. with a fixed Vd range: Dose 0 g / (Concentration of the Beverage .000 ethyl alcohol x p .789 g/mL x metric conversion in US) = Volume measured in the following size units or glasses.

Using Equation 6 calculate V in US oz. with an individualized Vd range: Dose 0 g / (Concentration of the Beverage .000 ethyl alcohol x p .789 g/mL x metric conversion in US) = Volume measured in the following size units or glasses.

Equation Summary Array

Glass Volume Conversion

Warning: Use of equations 5 and 6 can result in lots of errors so they are ripe for cross-examination and rebuttal evidence. They assume the evidentiary breath test result or blood draw result is reliable. It may not be. Watch for errors in your own calculation and in calculations made by experts:

1. Incomplete information or data entry as to sex at birth, age, height, and weight. Fixed Vd calculations require data entry of weight, weight units, and sex at birth. Individualized Vd calculations additionally require data entry of age, height, and height units.

2. Errors related to data entry of ounces v. mLs, inches v. cm.

3. Errors or confusion of decimals among g/L, g/dL or g/210L, and mg/100mL.

Eq 5 Min Dose
Eq 6 # Drinks

# Equations and Problems

List of Equations in ANSI/ASB Best Practice Recommendation 122, 1st Ed. 2024:

(Equation 1 2024) Calculate Total Body Water (TBW) from Watson, et al :

(1a) 𝑇𝐵𝑊 (𝑚𝑎𝑙𝑒) = 2.447 − (0.09516 × 𝑎) + (0.1074 × h) + (0.3362 × 𝑤)

(1b) 𝑇𝐵𝑊 (𝑓𝑒𝑚𝑎𝑙𝑒) = −2.097 + (0.1069 × h) + (0.2466 × 𝑤)

Use of this equation requires input of data as to sex at birth, age, height in inches or cm, and weight in lbs. or kg.

See ANSI/ASB 2024 footnote 31

(Equation 2 2024) Calculate the individualized Volume of Distribution (Vd) from Maskell, et al:

(2a) 𝑉𝑑 (𝑚𝑎𝑙𝑒) = TBW / (w x 0.825)

(2b) 𝑉𝑑 (𝑓𝑒𝑚𝑎𝑙𝑒) = TBW / (w x 0.838)

Use of this equation requires input of data as to sex at birth, age, height in inches or cm, and weight in lbs. or kg.

See ANSI/ASB 2024 footnotes 16, 19

) Apply the ± %CV from Maskell, Cooper:
(3a) 𝑉𝑑 (𝑚𝑎𝑙𝑒) = 𝑉𝑑 ± (𝑉𝑑 × 9.86%)

(3b) 𝑉𝑑 (𝑓𝑒𝑚𝑎𝑙𝑒) = 𝑉𝑑 ± (𝑉𝑑 × 15.00%)

Use of this equation requires input of data as to sex at birth, age, height in inches or cm, and weight in lbs. or kg.

(Equation 4 2024) Widmark’s Formula:

𝐴𝐶 = D / Vd x w

(Equation 5 2024) Calculation of Minimum Dose of Alcohol to Produce a Concentration

(5) 𝐷 (in g) =𝐴𝐶 × 𝑉𝑑 × 𝑤 × 10 dL/L (in US)

where:
D = dose (g)
AC = alcohol concentration (g/dL)

Vd= volume of distribution (L/kg)

w= weight (kg)

Use of this equation requires input of an alcohol concentration determined by blood draw or breath test as well as input of data (to calculate Vd) as to sex at birth, age, height in inchesor cm and weight in lbs. or kg.

Use the inputs in the "Body" section of this page to calculate both fixed Vd ranges and individualized Vd ranges.

See ANSI/ASB 2024

Dose in g can them be converted into the minimum number of "drinks" when the concentration is known. See Equation 6.

(Equation 6 2024) Dose in g converted into the minimum number of "drinks" when the concentration is known.

V = D / (C x p x m)

where:

V = Volume in oz.

D = Dose in g.

C = Beverage concentration mL/100mL

p = Density of ethanol 0.789 g/mL

m = metric conversion 29.6 ml/oz.

Use of this equation requires prior calculation of Dose and data input of Concentration of the "drinks". In the US a "standard drink" is a beverage containing 14 grams of ethyl alcohol:

12 US oz, 5% beer

5 US oz, 12% wine

1.5 US oz, 80 proof liquor (40%)

See ANSI/ASB 2024

(Equation 7 2024) Dose of alcohol from a drink

𝐷= 𝑉 ×𝐶 × ρ × 𝑚

where:

V = Volume in oz.

D = Dose in g.

C = Beverage concentration mL/100mL

p = Density of ethanol 0.789 g/mL

m = metric conversion 29.6 ml/oz.

See ANSI/ASB 2024

(Equation 8 2024) Theoretical maximum alcohol concentration from a given drink(s), Widmark formula with 100% absorption and no elimination

𝐴𝐶 = D / Vd x w x 10 dL/L in US [note the similarity to Equation 4]

where:
AC = alcohol concentration (g/L)

D = dose (g)
Vd = volume of distribution (L/kg)

w = weight (kg)

See ANSI/ASB 2024

𝐴𝐶inc = where:

ACinc = ACtest + (𝛽 x T)

where:

𝐴𝐶inc = estimated alcohol concentration at the time of the incident (g/dL)

ACtest = measured alcohol concentration (g/dL)
𝛽 = elimination rate (0.010-0.025 g/dL/hour)
T = time between incident and time of breath test/blood draw (in hours)

(Equation 10 2024) Adjustment to Retrograde Extrapolation for Unabsorbed Alcohol or Post-incident Alcohol Consumption

Adjusted ACinc = ACinc – ACdrink(s) where:

Adjusted ACinc = estimated AC at time of the incident, accounting for potentially unabsorbed alcohol or post incident alcohol consumption

ACinc = estimated AC at time of the incident if subject were in post absorptive state (calculated from Equation 9)

ACdrink(s) = maximum AC contribution from drink(s) (calculated from Equation 8)

See ANSI/ASB 2024

Learn by Doing

[Note: It appears, from the perspective of this author, that the following examples are designed to help Crowns and other Prosecutors prove their cases or discredit the evidence of an accused person. They are not designed to help accused persons, defence lawyers, and their experts prove, what in Canada, we used to call a Carter defence (evidence of the accused as to drinking scenario, combined with a toxicological opinion, as to BAC contradicting the approved instrument result). Defence lawyers need, however, to learn/experiment with/apply the following Crown/Prosecutor examples, to find weaknesses in expert assumptions/methodologies and statutory presumptions.

Within a defence lawyer's office you will frequently need to assess the veracity of your client's story and the disclosure/discovery you have received, in order to determine whether or not you should be retaining an expert and to develop possible lines of defence. Use these tools.]

List of illustrative examples to apply the recommendations contained within ANSI/ASB Best Practice Recommendation 122, 1st Ed. 2024

A.1 Support/refute drinking history

History: A male subject was pulled over for suspected impaired driving. He had an evidential breath test result of 0.19 g/210 L. He stated he had been at a local bar for the last 3 hours and only had 2 pints of Brand X beer. He ate chicken wings and french fries.

Question: Is the stated drinking history consistent with the alcohol concentration (AC) result?

2 approaches:

• by calculating the minimum number of drinks needed to attain a certain AC

• by calculating the maximum AC attainable from a drinking history

A.1.1 What is the minimum number of drinks needed to reach a 0.19 g/210 L alcohol concentration?

A.1.2 What is maximum AC that could be reached from 2 pints of Brand X beer?

A.2 Retrograde extrapolation, subject is post absorptive

History: A woman was drinking wine at an out-of-town wedding. She left the wedding at 6:00 pm and had a five-hour drive home. At approximately 9:00 pm she crossed over the center line and crashed into an oncoming vehicle. She was injured and transported to the hospital; a blood kit was collected at 11:45 pm. The result of the blood test was 0.068 g/dL. There were no alcoholic beverages in the vehicle. She stated she had not had anything to drink since leaving the wedding.

Question: Was she above the 0.08 legal limit at the time of the crash?

A.3 Retrograde extrapolation, subject is not post absorptive

History: A female subject was drinking at a bar. She stopped drinking around 10:00 pm. When she was ready to leave, she paid her tab and got one last shot of tequila. She drank it and immediately left the bar at ~11:00 pm. She crashed her car while trying to leave the parking lot. Her blood was drawn at 12:30 am and was a 0.082 g/dL. Her defense is that she was below 0.08 g/dL at the time of the crash.

Question: Could the subject’s AC have been under 0.08 g/dL at the time of the crash?

A.4 Post Incident Consumption

History: A man drove his vehicle through his garage door at ~6:00 pm. A neighbor witnessed the crash and called the police. When the police arrived at the home, the subject greeted them with a partially consumed bottle of vodka in his hand (80 proof, 750 mL), and he appeared to be intoxicated. He was arrested for suspected DUI and had a breath test result of 0.215 g/210 L. The defendant claimed he had not been drinking prior to the crash, and that his AC was from the vodka consumption after the crash. He claimed it was a new bottle; approximately one-third was missing.

Question: Could the consumption of ~1/3 bottle of vodka account for the measured AC?

A.5 Minimal Case History Available

History: Subject is a 160 lbs female. Crash at 1:00 am, blood draw at 3:00 am, AC 0.075 g/dL. No drinking history available.

Question: What was her AC at the time of the crash?

To learn how these Equations work, you can use this calculator, to apply the case histories above, and check to see if you get the same results as are shown in the Annex A to the Best Practices document. For learning purposes, use this calculator in one of two ways:

1. Manually enter each type of case history data into the appropriate section of this calculator.

2. Use the automatic reset dropdown menu at the bottom of this calculator (under construction) to change all defaults in the calculator to match those in the Best Practices examples. This action deletes all defaults, including any previous manual entry of data, and replaces them with the data from the example.

#### Automatic Entry to match the History in each Best Practices example (under construction)(warning: erases some manually input data):

By selecting an item in the above dropdown list of Best Practices Annex examples, you have automatically loaded into this calculator, all the input data from the "history" and "assumptions" in the particular example. Please check the data details below to make sure they match the particular example. The calculations below should match those in the Annex to the Best Practices document. If they don't, please alert the author of this site.

Once you have studied the Best Practices Annex example, consider whether you can apply their calculation methodology to one of your own cases, by adding, amending, or inputting data that fit your own scenario, manually into the relevant sections of this calculator above. The types of data input are colour-coded to help you find the right section into which you can input your own data.

If you are using the Best Practices methodology of a particular Example as your precedent, you will likely be entering your own data into the brown Body section, the green Equation 7, 8, 9, 10 section, and perhaps the orange Equation 5 and 6 section.

If you are a defence lawyer and you wish to quickly calculate/estimate your client's BAC based on their drinking scenario given to you in your office, you will brobably be using the purple Drinks section, the brown Body section, and the Red Widmark and Time (absorption, elimination) sections.

Scenario Summary

Body Summary

Equation Summary Array

Vd Summary

Widmark and Time Summary

Problem Summary

Equation 5 Fixed Vd Minimum Dose in g for an AC Result

Equation 5 Individualized Vd Minimum Dose in g for an AC Result

Equation 6 Fixed Vd Dose converted to Volume Result

Equation 6 Individualized Vd Dose converted to Volume Result

Equation 6 Size of Drink or Units

Equation 7 Dose in g from a Drink Result

Equation 8 Fixed Vd Theoretical Max AC Result

Equation 8 Individualized Vd Theoretical Max AC Result

Unit of AC

Equation 9 Retrograde Extrapolation ACInc Range Result

Equation 10 Warning: Equation 10 Results may not be applicable and may be misleading to this scenario.

Equation 10 Fixed Vd Adjusted ACInc Range Result

Equation 10 Individualized Vd Adjusted ACInc Range Result

Unit of AC

#### I have colour coded the data input areas in this calculator:

##### A.1 Support/refute drinking history

Body:

Male sex at birth

73 inches height

230 lbs. weight

Age 32

Assume:

Evidentiary Breath Test 0.19

US units:

g/210L

Accused states:

Brand X Beer .043 concentration

Pints US 16 oz.

Quantity 2

A.1.1 What is the minimum number of drinks needed to reach a 0.19 g/210 L alcohol concentration?

[To use this calculator, you will primarily enter data and use results in the orange Crown cross-examination section, but you will also need to input data (and verify Vd calculations) in the brown Body section and clarify US or Canadian units inthe green Thinking Backwards section.]

a) Calculate with a fixed Vd range

Using Equation 6, calculate the equivalent number of drinks for that dose

b) Calculate with an individualized Vd range

Using Equation 1a, calculate the TBW

Using Equation 2a, calculate the Individualized Vd

Using Equation 3a, apply the %CV

Using Equation 6, calculate the equivalent number of drinks for that dose

A.1.2 What is maximum AC that could be reached from 2 pints of Brand X beer?

Body:

Male sex at birth

73 inches height

230 lbs. weight

Age 32

Assume:

Evidentiary Breath Test 0.19

US units :

g/210L

Accused states (Best Practices):

Brand X Beer .043 concentration

Pints US 16 oz.

Quantity 2 = 32 oz.

Using Equation 7, (Best Practices approach) calculate the dose from 2 pints of Brand X beer

​a) Calculate with a fixed Vd range

Using Equation 8 and the fixed Vd range in L/kg, calculate the maximum AC range this dose could theoretically reach

b) Calculate with an individualized Vd range

Using Equation 8 and the same Vd range as A.1.1.b calculate the maximum range of ACs this dose could theoretically reach

A.2 Retrograde extrapolation, subject is post absorptive

Body:

Female sex at birth

63 inches height

125 lbs. weight

Age 45

Assume:

Blood Test 0.068 @ 23:45

Incident @ 21:00

Elapsed Time calculation  2.75 hours

3 hours between the end of drinking and the incident

No post incident alcohol consumption

US units:

g/dL

Using Equation 9 and an elimination rate range of 0.010 - 0.025 g/dL/hour, calculate AC range at time of incident.

A.3 Retrograde extrapolation, subject is not post absorptive

Body:

Female sex at birth

68 inches height

160 lbs. weight

Age 22

Assume:

Blood Test 0.082 @ 00:30

Incident @ 23:00

Elapsed Time calculation 1.5 hours

US units:

g/dL

Accused states:

Stopped main drinking scenario 22:00

Last Drink: Tequila .40 concentration

Shot US 1.5 oz.

@23:00

Using Equation 9 and an elimination rate range of 0.010 - 0.025 g/dL/hour, calculate AC range at the time of incident, if the subject were post absorptive.

Using Equation 7 calculate the dose of alcohol from the Last Drink shot.

Using Equations 1b, 2b, and 3b, calculate an individualized Vd range.

Using Equation 8 and the individualized Vd range in L/kg, calculate the maximum AC the Last Drink shot could contribute.

Using Equation 10, adjust the AC to remove the theoretical maximum contribution the Last Drink shot could have contributed

A.4 Post Incident Consumption

Body:

Male sex at birth

70 inches height

210 lbs. weight

Age 55

Assume:

Evidentiary Breath Test 0.215

Drove through garage door @ 18:00

US units:

g/210L

Accused states:

No pre-driving alcohol

Vodka .40 concentration, 750 ml. bottle 1/3 empty

Post-driving consumption 250 ml.

Using Equation 7, calculate the dose of alcohol consumed post-driving.

Using Equations 1b, 2b, and 3b, calculate an individualized Vd range.

Using Equation 8 and the individualized Vd range  calculate the maximum AC the vodka could contribute.

A.5 Minimal Case History Available

Body:

Female sex at birth

Unknown height

160 lbs. weight

Age unknown

Assume:

Blood Test 0.075 @ 03:00

Incident @ 01:00

Elapsed Time calculation 2.0 hours

US units:

g/dL

Use “Standard” drink = 14 g of alcohol

Use fixed Vd

Using Equation 9 and an elimination rate range of 0.010 - 0.025 g/dL/hour, calculate the AC at time of incident if post absorptive.

Using Equation 8 and a fixed Vd range in L/kg, calculate the maximum AC a “standard” drink could contribute.

Using Equation 10, adjust the AC to remove the number of drinks that would have to be unabsorbed to have the subject be below the legal limit at the time of the incident (using the calculated ranges of ACinc and ACdrink(s)).

Automatic
Manual

## Canada's Per Se Law: "80 Plus", "80 and above", "Over 80"

320.14 (1) Everyone commits an offence who

(b) subject to subsection (5), has, within two hours after ceasing to operate a conveyance, a blood alcohol concentration that is equal to or exceeds 80 mg of alcohol in 100 mL of blood;

320.31 (1) If samples of a person’s breath have been received into an approved instrument operated by a qualified technician, the results of the analyses of the samples are conclusive proof of the person’s blood alcohol concentration at the time when the analyses were made if the results of the analyses are the same — or, if the results of the analyses are different, the lowest of the results is conclusive proof of the person’s blood alcohol concentration at the time when the analyses were made — if

• (a) before each sample was taken, the qualified technician conducted a system blank test the result of which is not more than 10 mg of alcohol in 100 mL of blood and a system calibration check the result of which is within 10% of the target value of an alcohol standard that is certified by an analyst;

• (b) there was an interval of at least 15 minutes between the times when the samples were taken; and

• (c) the results of the analyses, rounded down to the nearest multiple of 10 mg, did not differ by more than 20 mg of alcohol in 100 mL of blood.

(3) Evidence of the following does not constitute evidence tending to show that an analysis of a sample of a person’s blood was performed improperly:

• (a) the amount of alcohol or a drug that they consumed;

• (b) the rate at which the alcohol or the drug would have been absorbed or eliminated by their body; or

• (c) a calculation based on the evidence referred to in paragraphs (a) and (b) of what their blood alcohol concentration or blood drug concentration would have been at the time the sample was taken.

Marginal note:Presumption — blood alcohol concentration

320.31 (4) For the purpose of paragraphs 320.14(1)(b) and (d), if the first of the samples of breath was taken, or the sample of blood was taken, more than two hours after the person ceased to operate the conveyance and the person’s blood alcohol concentration was equal to or exceeded 20 mg of alcohol in 100 mL of blood, the person’s blood alcohol concentration within those two hours is conclusively presumed to be the concentration established in accordance with subsection (1) or (2), as the case may be, plus an additional 5 mg of alcohol in 100 mL of blood for every interval of 30 minutes in excess of those two hours.

The above rule applies to all human bodies in Canada. An individual's actual drinking scenario, absorption percentage or rate (e.g. "Last Drink" unabsorbed alcohol), and elimination rate are irrelevant to the Canadian law related to Retrograde Extrapolation calculation in impaired driving cases. Scientific defences are irrelevant to Retrograde Extrapolation in Canada, unless there is evidence of Post-Incident drinking.

1. Count and enter the number of half-hours (minimum of 5) between the incident and the first breath test or blood draw.

2. If the number of half-hours is 0 to 4 then the Retrograde Extrapolation BAC result is the same as the lowest breath test or blood draw and this calculation is irrelevant.

3. Enter the BAC result (in truncated mg/100mls) from the lowest breath test or blood draw.

4. The minimum BAC to enter is 20.

The person's blood alcohol concentration is conclusively presumed to be 0 mg/100mls within the two hours after the incident, i.e. within the two hours after the person ceased to operate the conveyance.

Hours Conversion

## Post-Incident Drink in Canada (very much under construction)

​​

320.14 (5) No person commits an offence under paragraph (1)(b) if

• (a) they consumed alcohol after ceasing to operate the conveyance;

• (b) after ceasing to operate the conveyance, they had no reasonable expectation that they would be required to provide a sample of breath or blood; and

• (c) their alcohol consumption is consistent with their blood alcohol concentration as determined in accordance with subsection 320.31(1) or (2) and with their having had, at the time when they were operating the conveyance, a blood alcohol concentration that was less than 80 mg of alcohol in 100 mL of blood.

The following is an Excerpt from:

"Legislative Background: reforms to the Transportation Provisions of the Criminal Code (Bill C-46)"

The new formulation of the offence “operating at or over 80 within two hours of driving” would eliminate the bolus drinking defence, by changing the timeframe within which the offence can be committed. Also, it significantly limits the intervening drink defence. The bolus drinking defence arises when the driver claims to have consumed a large amount of alcohol just before or while driving. Although they admit that their BAC was “over 80” at the time of testing, they claim that the alcohol was still being absorbed and, at the time of driving, they were not “over 80”. Making this behaviour subject to criminal sanctions is consistent with the comments of the Supreme Court of Canada in R v St-Onge – Lamoureux (St-Onge). Footnote 15 The Court stated that such a defence showed “significant irresponsibility with regard to public safety.”

This formulation of the offence is used in at least 16 American states Footnote 16 and has been upheld by the courts. As one Washington court noted in upholding such a law in 1997, “[t]he [legal limit for] BAC is not some magical bright line between safely drunk and unsafely drunk, and the fact that driving with less than a [legal limit for] BAC may prove to be criminal under the two-hour rule does not mean that the rule is arbitrary or not substantially related to public safety”. Footnote 17

The formulation also limits the intervening drink defence which arises when a driver drinks after driving but before they provide a breath sample. This defence often arises where there has been a serious collision and the driver claims to have been settling their nerves. This undermines the integrity of the justice system as it rewards conduct specifically aimed at frustrating the breath testing process. The only situation in which a driver could rely on intervening consumption to avoid a conviction is captured in subsection 320.14(5).The offence is not made out if all of the following conditions are met:

• The person consumed alcohol after ceasing to operate the conveyance;

• The person had no reasonable expectation that they would be required to provide a sample of breath or blood; and,

• Their alcohol consumption is consistent with their BAC at the time the samples were taken and with their having had a BAC of less than 80 at the time of operation.

Situations in which a person would have “a reasonable expectation” that they would be required to provide a sample would be decided on a case-by-case basis by the courts. However, a person involved in a serious collision causing death, bodily harm, or major damage should reasonably expect to be required to provide a sample. This limitation is consistent with the Supreme Court comment in St-Onge where the Court indicated that, “there is good reason to suspect that post‑driving drinking (or just the claim thereof) is an act of mischief intended to thwart police investigators. All such cases, at the very least, involve a significant degree of irresponsibility and a cavalier disregard for the safety of others and the integrity of the judicial system.” Footnote 18.

Footnote 15: [2012] 3 S.C.R. 187 at paragraph 90.

Footnote 16: Per letter from Jennifer Mnookin, Professor of Law, UCLA School of Law, July 2008.

Footnote 17: United States v. Skinner, 973 F. Supp. 975 (W.D. Wash. 1997). See also: Commonwealth v. Duda, 923 A. 2d 1138 (Pa. 2007); City of Fargo v. Stensland, 492 N.W.2d 591, 594-95 (N.D. 1992); Sereika v. State, 114 Nev. 142, 955 P.2d 175 (Nev. 1998); Bohannon v. State, 497 S. 552 (Ga. 1998); State v. Chirpich, 392 N.W.2d 34, 37 (Minn. App. 1986).

Footnote 18: St-Onge at paragraph 90 quoting R v St. Pierre, [1995] 1 SCR 791 at paragraph 106.

[Please note the Legislative Background says:

"Their alcohol consumption is consistent with their BAC at the time the samples were taken (italics added) and with their having had a BAC of less than 80 at the time of operation.(italics added)"

Comment: Section 320.31(1) says "at the time when the analyses were made" and section 320.31(2) says "at the time when the sample was taken".]

Parliament has left some room open for a Post-Incident Drink Defence in Canada. An individual's sex at birth, age, height, and weight will be relevant to a calculation by an expert of "consistent with their blood alcohol concentration" at the time of the breath tests or blood draw AND  "a blood alcohol concentration that was less than 80 mg of alcohol in 100 mL of blood" "at the time when they were operating the conveyance" Canadian lawyers can therefore make good use of the brown Body section of this calculator to study TBW, range of fixed Vd, and range of Individualized Vd.

The calculation of whether or not there is a good available defence REQUIRES an assumption that the approved instrument breath test or blood draw result was reliable as per 320.31(1) or (2). Parliament and Canadian Courts find that assumption of reliability easy to accept. I have difficulty with that assumption, even if there is prima facie compliance with section 320.31(1)(a), (b), and (c). However, to run a section 320.14(5) post-incident drinking defence, a defence lawyer must act within the confines of Canadian law and ask their expert to assume reliability of the breath test or blood draw.

For purposes of "blood concentration is consistent with" the time relevant to the expert's calculation is the time of "their blood alcohol concentration as determined in accordance with subsection 320.31(1) or (2)".   The Legislative Background describes this time as "at the time the samples were taken". In other words, the Crown or defence expert must calculate a range of possible alcohol concentrations for a given drinking scenario, including the post-incident drink(s) and a given subject body at the time of the breath tests or blood draw. The wording of the section says "consistent with". There is no statutory requirement of an exact correspondence between the expert's calculation of BAC and the breath test or blood draw. Please let me know if you find any case law to the contrary.

For purposes of "a blood alcohol concentration that was less than 80 mg of alcohol in 100 mL of blood" the time relevant to the expert's calculation is "at the time when they were operating the conveyance". That time probably doesn't correspond exactly to the time of the actus reus of the offence.  Time of actus reus in our per se law is a range of at least two hours and maybe more if retrograde extrapolation is used. What happens if the Crown doesn't prove a specific time of "operating"? Should the expert in such cases work with a range of times for the "less than 80 mg" calculation? Please let me know if you find any case law on this calculation.

Interestingly, section 320.14 makes no mention of deeming scientific consideration of incomplete absorption or range of elimination rates irrelevant to a calculation of 1. "consistent with" the breath test/blood draw or 2. the maximum effects of the Post-Incident Drink or 3. the "less than 80 mg" calculation. Perhaps the section should be construed and applied liberally and scientifically to permit consideration of full ranges of fixed and individualized Vd, absorption % possibilities, and elimination rates, along with an uncertainty calculation in the BAC itself? 320.14(5) doesn't preclude such range calculation. Maybe good science will be permitted because it is a defence and Parliament hasn't stated otherwise. Any case law?

The Maximum Theoretical AC contribution calculation in Equations 7 and 8 of the 2024 US Best Practices may help in isolating the effects, on the total "consistent with" BAC, of the post-incident drink(s). Perhaps Equation 10 in the US Best Practices could be used to separate and subtract the isolated post-incident MAX AC to show BAC at time of operating the conveyance. You will need to call an expert with respect to both BAC calculations.

Respecting "consistent with"., I expect a toxicologist will calculate Vd, calculate dose in g using the whole drinking scenario, convert to mg/100mls Time 0 using Widmark, adjust for absorption/unabsorbed alcohol/last drink, adjust for elimination 10-25 mg/100ml/hour and provide a range of BAC for that scenario that may or may not be similar to the Intoxilyzer result.

To date I have not yet found any statement of Canadian Best Practices with respect to 320.14(5) or its predecessor. If one exists or there is a published article on the subject of proper 320.14(5) methodology please let me know at biss@lawyers.ca.

​Possible methodologies:

A.1. Calculate TBW, Vd fixed and individualized ranges

A.2. Calculate dose for whole drinking scenario including post-incident drink

A.3. Using Widmark calculate a BAC at Time 0

A.4. Adjust for incomplete absorpton and range of elimination at TimeTest.

A.5. Is range of values consistent with Intoxilyzer result or blood draw?

A.6  Do A.1 to A.4 for TimeInc.

A.7  Is part of range of values at TimeInc below 80?

B.1. Calculate TBW, Vd fixed and individualized ranges

B.2. Calculate dose for whole drinking scenario including post-incident drink

B.3. Using Widmark calculate a BAC at Time 0

B.4. Adjust for incomplete absorpton and range of elimination at TimeTest.

B.5. Is range of values consistent with Intoxilyzer result or blood draw?

B.6  Using Equation 7 and 8 calculate the MAX AC that could be reached for a post-incident drink.

B.7 Using Equation 10 Subtract that MAX AC from Intoxilyzer result or blood draw.

B.7  Is low end of resulting range of values at TimeInc below 80?

C.1. Calculate TBW, Vd fixed and individualized ranges

C.2. Calculate dose for whole drinking scenario including post-incident drink

C.3. Using Widmark calculate a BAC at Time 0

C.4. Adjust for incomplete absorpton and range of elimination at TimeTest.

C.5. Is range of values consistent with Intoxilyzer result or blood draw?

C.6 Carter calculation for TimeInc.

C.7 Is low end of resulting range below 80?

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