mathematical modelling

/Tag:mathematical modelling

A Compartment Model to Calculate Time dependent Applied Chemical Compounds in the Anterior Compartments of the Rabbit Eye

Heike Pospisil and Hermann-Georg HolzhütterRE

Hitherto, none of the existing in vitro methods has been convincingly demonstrated to be suitable as a replacement for the Draize rabbit eye irritation test. We examine the hypothesis that one reason for this is that insufficient consideration has been given to the differences in the effective concentrations at which chemicals operate in vitro and in vivo. When a chemical is applied topically to the eye, the strength of the observed irritation that it elicits depends both on its toxic potential toward cells or tissues, and its effective oncentration in the tissues of the eye. Most of the existing in vitro methods are based on isolated cells or tissues, and thus may be useful in assessing the cytotoxic potentials of chemicals. However, a reliable approach to assessing the effective concentrations of chemicals within the various tissues of the eye is lacking. A simplified compartment model is presented for calculating the time-dependent, intra-ocular concentration profiles of topically applied chemicals. The model encompasses the outer surface of the eye, three distinct segments of the cornea (subdivided into the epithelium, stroma and endothelium) and the conjunctiva. Transport through the membranes of these compartments is described as passive diffusion. For the transport coefficients, rate equations are established that contain, as free parameters, the molecular size and the partition coefficient of the chemical, as well as some intrinsic membrane parameters, such as thickness, viscosity and pore density. Numerical values for the unknown membrane parameters were estimated by fitting the theoretical rate equations to measured permeability coefficients. The compartment model was applied to an independent set of 52 test chemicals compiled from the European Commission/UK Home Office validation study. The calculated passage times (required to let 95% of the chemical reach the posterior eye tissues) varied between 0.33 minutes and 50.6 minutes, and are generally much shorter than the typical duration of observed impairments in the cornea or conjunctiva. This finding suggests that short-term contacts of the eye tissues with a chemical are sufficient to elicit long-term eye irritation. An example is given, showing how the conventional approach of using in vitro endpoints as predictors of eye irritation can be improved significantly by incorporating into the prediction the calculated intra-ocular concentration of a chemical.
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Comment – A Critical Review of Anaesthetised Animal Models and Alternatives for Military Research, Testing and Training, with a Focus on Blast Damage, Haemorrhage and Resuscitation

Robert D. Combes

Military research, testing, and surgical and resuscitation training, are aimed at mitigating the consequences of warfare and terrorism to armed forces and civilians. Traumatisation and tissue damage due to explosions, and acute loss of blood due to haemorrhage, remain crucial, potentially preventable, causes of battlefield casualties and mortalities. There is also the additional threat from inhalation of chemical and aerosolised biological weapons. The use of anaesthetised animal models, and their respective replacement alternatives, for military purposes — particularly for blast injury, haemorrhaging and resuscitation training — is critically reviewed. Scientific problems with the animal models include the use of crude, uncontrolled and non-standardised methods for traumatisation, an inability to model all key trauma mechanisms, and complex modulating effects of general anaesthesia on target organ physiology. Such effects depend on the anaesthetic and influence the cardiovascular system, respiration, breathing, cerebral haemodynamics, neuroprotection, and the integrity of the blood–brain barrier. Some anaesthetics also bind to the NMDA brain receptor with possible differential consequences in control and anaesthetised animals. There is also some evidence for gender-specific effects. Despite the fact that these issues are widely known, there is little published information on their potential, at best, to complicate data interpretation and, at worst, to invalidate animal models. There is also a paucity of detail on the anaesthesiology used in studies, and this can hinder correct data evaluation. Welfare issues relate mainly to the possibility of acute pain as a side-effect of traumatisation in recovered animals. Moreover, there is the increased potential for animals to suffer when anaesthesia is temporary, and the procedures invasive. These dilemmas can be addressed, however, as a diverse range of replacement approaches exist, including computer and mathematical dynamic modelling of the human body, cadavers, interactive human patient simulators for training, in vitro techniques involving organotypic cultures of target organs, and epidemiological and clinical studies. While the first four of these have long proven useful for developing protective measures and predicting the consequences of trauma, and although many phenomena and their sequelae arising from different forms of trauma in vivo can be induced and reproduced in vitro, non-animal approaches require further development, and their validation and use need to be coordinated and harmonised. Recommendations to these ends are proposed, and the scientific and welfare problems associated with animal models are addressed, with the future focus being on the use of batteries of complementary replacement methods deployed in integrated strategies, and on greater transparency and scientific cooperation.

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