4,324 research outputs found
The influence of toxicity constraints in models of chemotherapeutic protocol escalation
The prospect of exploiting mathematical and computational models to gain insight into the influence of scheduling on cancer chemotherapeutic effectiveness is increasingly being considered. However, the question of whether such models are robust to the inclusion of additional tumour biology is relatively unexplored. In this paper, we consider a common strategy for improving protocol scheduling that has foundations in mathematical modelling, namely the concept of dose densification, whereby rest phases between drug administrations are reduced. To maintain a manageable scope in our studies, we focus on a single cell cycle phase-specific agent with uncomplicated pharmacokinetics, as motivated by 5-Fluorouracil-based adjuvant treatments of liver micrometastases. In particular, we explore predictions of the effectiveness of dose densification and other escalations of the protocol scheduling when the influence of toxicity constraints, cell cycle phase specificity and the evolution of drug resistance are all represented within the modelling. For our specific focus, we observe that the cell cycle and toxicity should not simply be neglected in modelling studies. Our explorations also reveal the prediction that dose densification is often, but not universally, effective. Furthermore, adjustments in the duration of drug administrations are predicted to be important, especially when dose densification in isolation does not yield improvements in protocol outcomes
Clinical solutions: not always what they seem?
Brenner and colleagues, in their article published in Critical Care, showed elevated levels of the reactive carbonyl species (RCS) methylglyoxal (MG) in the circulation of patients with septic shock. We commend the authors’ bravery in launching this molecule into a field well-populated with biomarkers and where clinical diagnosis persists as the ‘gold standard’
A mass action model of a fibroblast growth factor signaling pathway and its simplification
We consider a kinetic law of mass action model for Fibroblast Growth Factor (FGF) signaling, focusing on the induction of the RAS-MAP kinase pathway via GRB2 binding. Our biologically simple model suffers a combinatorial explosion in the number of differential equations required to simulate the system. In addition to numerically solving the full model, we show that it can be accurately simplified. This requires combining matched asymptotics, the quasi-steady state hypothesis, and the fact subsets of the equations decouple asymptotically. Both the full and simplified models reproduce the qualitative dynamics observed experimentally and in previous stochastic models. The simplified model also elucidates both the qualitative features of GRB2 binding and the complex relationship between SHP2 levels, the rate SHP2 induces dephosphorylation and levels of bound GRB2. In addition to providing insight into the important and redundant features of FGF signaling, such work further highlights the usefulness of numerous simplification techniques in the study of mass action models of signal transduction, as also illustrated recently by Borisov and co-workers (Borisov et al. in Biophys. J. 89, 951–66, 2005, Biosystems 83, 152–66, 2006; Kiyatkin et al. in J. Biol. Chem. 281, 19925–9938, 2006). These developments will facilitate the construction of tractable models of FGF signaling, incorporating further biological realism, such as spatial effects or realistic binding stoichiometries, despite a more severe combinatorial explosion associated with the latter
A solute gradient in the tear meniscus I. A hypothesis to explain Marx's line
Marx's line is a line of mucosal staining behind the mucocutaneous junction. It can be demonstrated throughout life in all normal lids by staining with lissamine green and related dyes. Of all the body orifices, only the mucosae of the eye and mouth are directly exposed to the atmosphere. In this paper, we suggest that for the eye, this exposure leads to the formation of Marx's line. The tear meniscus thins progressively toward its apex, where it is pinned at the mucocutaneous junction of the lid. It also thins toward the black line, which segregates the meniscus from the tear film after the blink. We predict that, because of the geometry of the tear meniscus, evaporation generates a solute gradient across the meniscus profile in the anteroposterior plane, which peaks at the meniscus apices at the end of the interblink. One outcome would be to amplify the level of tear molarity at these sites so that they reach hyperosmolar proportions. Preliminary mathematical modeling suggests that dilution of this effect by advection and diffusion of solute away from the meniscus apex at the mucocutaneous junction will be restricted by spatial constraints, the presence of tear and surface mucins at this site, and limited fluid flow. We conclude that evaporative water loss from the tear meniscus may result in a physiological zone of hyperosmolar and related stresses to the occlusal conjunctiva, directly behind the mucocutaneous junction. We hypothesize that this stimulates a high epithelial cell turnover at this site, incomplete epithelial maturation, and a failure to express key molecules such as MUC 16 and galectin-3, which, with the tight junctions between surface epithelial cells, are necessary to seal the ocular surface and prevent penetration of dyes and other molecules into the epithelium. This is proposed as the basis for Marx's line. In Part II of this paper (also published in this issue of The Ocular Surface), we address additional pathophysiological consequences of this mechanism, affecting lid margins
Mode doubling and tripling in reaction-diffusion patterns on growing domains: A piece-wise linear model
Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates a sequence of quasi-steady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steady-state patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steady-state solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasi-steady patterns in the sequence. We also highlight a novel sequence behaviour, mode-tripling, which is a consequence of a symmetry in the reaction term of the reaction-diffusion system
Fluid mechanics of nodal flow due to embryonic primary cilia
Breaking of left–right symmetry is crucial in vertebrate development. The role of cilia-driven flow has been the subject of many recent publications, but the underlying mechanisms remain controversial. At approximately 8 days post-fertilization, after the establishment of the dorsal–ventral and anterior–posterior axes, a depressed structure is found on the ventral side of mouse embryos, termed the ventral node. Within the node, ‘whirling’ primary cilia, tilted towards the posterior, drive a flow implicated in the initial left–right signalling asymmetry. However, the underlying fluid mechanics have not been fully and correctly explained until recently and accurate characterization is required in determining how the flow triggers the downstream signalling cascades. Using the approximation of resistive force theory, we show how the flow is produced and calculate the optimal configuration to cause maximum flow, showing excellent agreement with in vitro measurements and numerical simulation, and paralleling recent analogue experiments. By calculating numerical solutions of the slender body theory equations, we present time-dependent physically based fluid dynamics simulations of particle pathlines in flows generated by large arrays of beating cilia, showing the far-field radial streamlines predicted by the theory
Mathematical modelling of cilia driven transport of biological fluids
Cilia-driven flow occurs in the airway surface liquid, in the female and male reproductive tracts and enables symmetry-breaking in the embryonic node. Viscoelastic rheology is found in healthy states in some systems, whereas in others may characterise disease, motivating the development of mathematical models that take this effect into account. We derive the fundamental solution for linear viscoelastic flow, which is subsequently used as a basis for slender-body theory. Our numerical algorithm allows efficient computation of three-dimensional time-dependent flow, bending moments, power and particle transport. We apply the model to the large-amplitude motion of a single cilium in a linear Maxwell liquid. A relatively short relaxation time of just 0.032 times the beat period significantly reduces forces, bending moments, power and particle transport, the last variable exhibiting exponential decay with relaxation time. A test particle is propelled approximately one-fifth as quickly along the direction of cilia beating for scaled relaxation time 0.032 as in the Newtonian case, and mean volume flow is abolished, emphasizing the sensitivity of cilia function to fluid rheology. These results may have implications for flow in the airways, where the transition from Newtonian to viscoelastic rheology in the peri-ciliary fluid may reduce clearance
A solute gradient in the tear meniscus II. implications for lid margin disease, including meibomian gland dysfunction
We have hypothesized previously that evaporation from the tears generates a solute gradient across the tear meniscus, which delivers hyperosmolar stress to the mucocutaneous junction (MCJ) of the lid margin. This is proposed as the basis for Marx's line, a line of staining with topically applied dyes that lies directly behind the MCJ. In this article, we consider the implications of this hypothesis for progressive damage to the lid margin as an age-related phenomenon, its amplification in dry eye states, and its possible role in the etiology of meibomian gland dysfunction (MGD). It is suggested that a hyperosmolar or related stimulus, acting behind the MCJ over a lifetime, promotes the anterior migration of the MCJ, which is a feature of the aging lid margin. This mechanism would be amplified in dry eye states, not only by reason of increased tear molarity at the meniscus apex but also by raising the concentration of inflammatory peptides at this site. This could explain the increased width and irregularity of Marx's line in dry eye. While the presence of stem cells at the lid margin may equip this region to respond to such stress, their depletion could be the basis of irreversible lid margin damage. It is further proposed, given the proximity of the MCJ to the meibomian gland orifices, that the solute gradient mechanism could play a role in the initiation of MGD by delivering hyperosmolar and inflammatory stresses to the terminal ducts and orifices of the glands. By the same token, the presence of a zone of increased epithelial permeability in this region may provide a back door route for the delivery of drugs in the treatment of MGD
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