The well-being model: a new drug interaction model for positive and negative effects

BACKGROUND: Drugs are routinely combined in anesthesia and pain management to obtain an enhancement of the desired effects. However, a parallel enhancement of the undesired effects might take place as well, resulting in a limited therapeutic usefulness. Therefore, when addressing the question of optimal drug combinations, side effects must be taken into account. METHODS: By extension of a previously published interaction model, the authors propose a method to study drug interactions considering also their side effects. A general outcome parameter identified as patient's well-being is defined by superposition of positive and negative effects. Well-being response surfaces are computed and analyzed for varying drugs pharmacodynamics and interaction types. In particular, the existence of multiple maxima and of optimal drug combinations is investigated for the combination of two drugs. RESULTS: Both drug pharmacodynamics and interaction type affect the well-being surface and the deriving optimal combinations. The effect of the interaction parameters can be explained in terms of synergy and antagonism and remains unchanged for varying pharmacodynamics. For all simulations performed for the combination of two drugs, the presence of more than one maximum was never observed. CONCLUSIONS: The model is consistent with clinical knowledge and supports previously published experimental results on optimal drug combinations. This new framework improves understanding of the characteristics of drug combinations used in clinical practice and can be used in clinical research to identify optimal drug dosing.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions.

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.