Modeling Nicotine Arterial–Venous Differences to Predict Arterial Concentrations and Input Based on Venous Measurements: Application to Smokeless Tobacco and Nicotine Gum

Abstract

Significant arterio-venous differences in nicotine concentrations have been observed during and after cigarette smoking, nicotine nasal spray, and intravenous nicotine administration. In this paper we describe a novel mathematical method for estimating arterial blood levels from venous blood level data. The model allows to quantify: (i) the influence of the microcirculation in the hands and forearm on the distribution of nicotine, and (ii) the influence of disregarding the venous to arterial circulation in the estimate of systemic inputs. We also (iii) propose a general method to predict arterial concentrations and inputs given venous data. The basic model we adopt is based on the relationship C_v = T * C_a, where C_v and C_a are the concentration in the venous and arterial site, respectively, T is the arterio-venous transfer function and * indicates convolution. We use empirical data to estimate T. We then compare estimates of systemic inputs to the venous site obtained taking into account the transfer function or, as usually done, disregarding it. The relationship we use to compare estimated inputs are: C_v = T * k_a * A (where K_a is the arterial disposition function and A the systemic input), and C_v = K_v * A (where K_v is the venous disposition function), respectively. Finally, the estimated transfer function allows to estimate (average) C_a or A given arbitrary venous data. (i) Our analysis suggests that a bi-exponential T is needed to describe observed arterial–venous differences. The estimated transfer function indicates that no elimination of nicotine is involved in the forearm. (ii) Disregarding T, as usually done, erroneously obtains too complex venous input functions (because these input functions incorporate T). (iii) Disregarding T erroneously estimates significantly higher total inputs. (iv) Using the proposed model and previously published venous nicotine level data we predict substantial arterial–venous differences in blood nicotine levels for smokeless tobacco and nicotine gum. The use of disposition functions obtained from venous data may lead to erroneous estimation of the rates of entry into the circulation and systemic bioavailability for many drugs.