Estimating the dose
The estimation of dose is often helpful to confirm other pieces of evidence or to indicate the possibility of an accidental or suicidal death. As indicated previously, many assumptions need to be made if any realistic calculation is to be performed. Of particular importance is the knowledge whether a single dose has occurred or multiple doses, the overall health of the person and the time elapsed since the last dose. Measurement of a blood concentration may not always allow the differentiation of multiple therapeutic doses from large accidental or suicidal doses. Thus, long-half-life drugs, such as thioridazine, may show a marked overlap in blood concentrations following multiple doses with those seen in fatal poisonings. In the same way that drug and metabolite concentrations can be linked to time, they can also be related to dose regimens. Thus, steady state drug: metabolite concentration ratios are sometimes used to check drug compliance. Also, since the extent of drug metabolism tends to decrease with increasing dose, the ratio of unchanged drug to metabolite will increase with increasing dose. Examination of the relative concentrations of parent drug and its major metabolite(s) in blood, or in other tissues as necessary, can provide useful information on the likely size of the dose administered. Thus, an amitriptyline: nortriptyline concentration ratio of less than 2 is consistent with steady-state drug concentrations following administration of therapeutic doses, while a ratio greater than 2 is more consistent with the ingestion of larger, potentially toxic doses.
When a drug is extensively metabolised, large acute doses can result in metabolic profiles significantly different from those seen after therapeutic doses. Thus, following administration of normal single doses of phenylbutazone, the ratio of the blood concentrations of its major metabolites oxyphenbutazone and 3 hydroxy phenylbutazone may be as high as 10: 1. In overdose, the pattern of metabolism can be reversed, giving ratios as low as 1:5.
Similarly, the metabolic profile of diazepam in urine changes dramatically with dose, and the ratio of nordiazepam: oxazepam concentrations may provide useful information regarding the relative size of an ingested dose of the drug. When doses are low, demethylation of diazepam appears to be more important than hydroxyl ation, while hydroxylation becomes more important at higher doses. Once tissue drug concentrations or drug: metabolite concentration ratios have established whether an overdose was administered, the actual amount of drug ingested may be estimated. Ideally, the dose should be determined by measuring the total amount of drug remaining in the body (including any unabsorbed drug in the gastrointestinal tract), adding to this the amount that has been metabolised and/or excreted. For obvious reasons, this is rarely possible. A compromise is usually made by estimating the minimum amount of drug ingested. This can be attempted in a number of ways. Analytical results may be compared with previously recorded data in fatal cases for which drug doses are known. The next best method is the direct comparison of peripheral blood concentrations with clinical data, i.e. blood concentrations following the administration of therapeutic doses. Finally, drug doses can be estimated using pharmacokinetic data. The half-life of the drug (t1/2) and a reasonable estimate of the time elapsed between administration and sampling (t), together with the blood concentration at the time of sampling (Ct), allow the calculation of a theoretical drug concentration at time zero (C0), which for intravenous administration is ln C0=ln Ct+0.693t/t1/2.
This concentration can be used to estimate the dose if the volume of distribution of the drug (Vd) is known (see section on volume of distribution), or it may be compared with clinical data as described above.
This pharmacokinetic approach probably gives a better estimate of the actual dose administered since it takes some account of the amount of drug eliminated. However, pharmacokinetic equations should be interpreted with great caution, especially if relatively accurate survival times are not available and if the kinetic characteristics of the drug following administration of large acute doses are significantly different from those observed following therapeutic doses. In reality, elimination rates of drugs following over dose are invariably slower than with normal doses due to saturation of normal metabolic and excretory mechanisms, or even drug-induced reduction in physiological state. If these formulae are applied, the use of a range of likely pharmacokinetic parameters to estimate a possible range of doses is advised, rather than relying on a point estimate. Some of these problems can be overcome in a clinical situation if sufficient samples are available to characterise the terminal elimination kinetics of a drug taken in overdose. Such an approach is not possible with postmortem samples and considerably more care needs to be taken when estimating the dose.
