Technical Note

Simplified Estimation of Widmark "r" Values by the Method of Forrest

Alan D Barbour
Central Valley Toxicology, 1521 Tollhouse Road, Suite J, Clovis, California 93611, USA
Science & Justice 2001; 41(1): 53-54
Received 17 July 2000; accepted 27 September 2000

Introduction

The mathematical method propounded by Professor Dr EMP Widmark [1, 2] for estimation of blood alcohol levels from consumption and vice versa has proven robust and continues in general use after the passage of more than seventy years, despite the development of other, arguably more exact, approaches such as that of Watson [3].

Widmark's "reduced body mass," or "r" value represents that proportion of the body available for the distribution of alcohol, and is an important part of the calculation. The average "r" values reported by Widmark (male average 0.68, standard deviation 0.085; female average 0.55, standard deviation 0.055) are often used as defaults, but they are open to question on several grounds:

It is an inconvenient fact that the specific Widmark "r" value for an individual can be known with certainty only by experiment, and furthermore that it can change with the passage of time. It is possible, however, to make a reasonable estimate of the "r" value at the time of interest; several methods have been proposed for this. Notable among such methods is that of Forrest [6], which is based upon the Body Mass Index (BMI; weight divided by height squared).

The procedure set out in Forrest's paper for the calculation is rather onerous if done by hand, and the BASIC computer program offered by the author is no longer available (Forrest ARW, personal communication). The tables below were calculated by Forrest's method and are offered here as a simplification; the uncertainties in interpolated numbers are negligible.

While the values in the tables below are applicable to a wide range of body types, like all other methods of estimation they will fail for extreme body types, such as the highly muscular (e.g., bodybuilders), the emaciated, those in an advanced stage of pregnancy, and those suffering from morbid obesity. This has been partly dealt with by limiting the range of BMI over which the tables are calculated. Even for normal individuals there is some inherent mathematical uncertainty in the estimates, but a critical evaluation of its magnitude is beyond the scope of this technical note.

Table: Widmark "r" Values by the Method of Forrest [6]

Males, Body Mass Index 15-30

Wt lbs 99 110 121 132 143 154 165 176 187 198 209 220 231 242 253    
Wt kg 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115    
  0.78 0.75 0.72 0.69 0.67                     150 4'11"
  0.79 0.77 0.74 0.71 0.69 0.66                   155 5'1"
  0.80 0.78 0.76 0.73 0.71 0.69 0.66                 160 5'3"
  0.82 0.80 0.77 0.75 0.73 0.71 0.68 0.66               165 5'5"
  0.83 0.81 0.79 0.77 0.75 0.72 0.70 0.68 0.66             170 5'7"
    0.82 0.80 0.78 0.76 0.74 0.72 0.70 0.68 0.66           175 5'9"
    0.83 0.81 0.79 0.77 0.76 0.74 0.72 0.70 0.68 0.66         180 5'11"
      0.82 0.81 0.79 0.77 0.75 0.73 0.72 0.70 0.68 0.66       185 6'1"
      0.83 0.82 0.80 0.78 0.77 0.75 0.73 0.72 0.70 0.68 0.67     190 6'3"
        0.83 0.81 0.79 0.78 0.76 0.75 0.73 0.71 0.70 0.68 0.67   195 6'5"
        0.84 0.82 0.81 0.79 0.78 0.76 0.74 0.73 0.71 0.70 0.68 0.67 200 6'7"
          0.83 0.82 0.80 0.79 0.77 0.76 0.74 0.73 0.71 0.70 0.69 205 6'9"
                                Ht cm Ht ft,in

Females, Body Mass Index 15-30

Wt lbs 99 110 121 132 143 154 165 176 187 198 209 220 231 242 253    
Wt kg 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115    
  0.69 0.66 0.63 0.61 0.58                     150 4'11"
  0.70 0.68 0.65 0.63 0.60 0.57                   155 5'1"
  0.72 0.69 0.67 0.65 0.62 0.60 0.57                 160 5'3"
  0.73 0.71 0.69 0.66 0.64 0.62 0.59 0.57               165 5'5"
  0.74 0.72 0.70 0.68 0.66 0.64 0.61 0.59 0.57             170 5'7"
    0.73 0.71 0.69 0.67 0.65 0.63 0.61 0.59 0.57           175 5'9"
    0.74 0.73 0.71 0.69 0.67 0.65 0.63 0.61 0.59 0.57         180 5'11"
      0.74 0.72 0.70 0.68 0.66 0.65 0.63 0.61 0.59 0.57       185 6'1"
      0.75 0.73 0.71 0.70 0.68 0.66 0.64 0.63 0.61 0.59 0.58     190 6'3"
        0.74 0.72 0.71 0.69 0.68 0.66 0.64 0.63 0.61 0.59 0.58   195 6'5"
        0.75 0.73 0.72 0.70 0.69 0.67 0.66 0.64 0.63 0.61 0.60 0.58 200 6'7"
          0.74 0.73 0.71 0.70 0.69 0.67 0.66 0.64 0.63 0.61 0.60 205 6'9"
                                Ht cm Ht ft,in

BASIC and QBASIC versions of computer programs for the calculation of Widmark "r" values by Forrest's method are available from the author by E-mail to abarbour@lightspeed.net.

Acknowledgements

The author would like to thank Professor ARW Forrest, Robert Abrams and Dr James Garriott for reviewing this note and for discussion of the issues involved; Naomi Barbour for writing the BASIC program; and Dr Martin Senftleben for writing the QBASIC program.

References

  1. Widmark EMP. Die theoretischen Grundlagen und die praktische Verwendbarkeit der gerichtlich-medizinischen Alkoholbestimmung. Berlin: Urban & Schwarzenberg, 1932.
  2. Widmark EMP. Principles and Applications of Mediocolegal Alcohol Determination. English translation of the 1932 German edition with permission of Urban & Schwarzenberg. Davis: Biomedical Publications, 1981.
  3. Watson PE, Total Body Water and Blood Alcohol Levels: Updating the Fundamentals. In: Crow KE and Batt RD eds. Human Metabolism of Alcohol. Boca Raton: CRC Press, 1989.
  4. Garriott JC ed. Medicolegal Aspects of Alcohol Determinations in Biological Specimens. Littleton: PSG Publishing Company, 1988.
  5. Cowan JM et al. Determination of Volume of Distribution for Ethanol in Male and Female Subjects. Journal of Analytical Toxicology 1996; 20:287-290.
  6. Forrest ARW. The Estimation of Widmark's Factor. Journal of the Forensic Science Society 1986; 26: 249-252.