Evaluating intra-articular drug delivery for the treatment of osteoarthritis in a rat model.

Osteoarthritis (OA) is a degenerative joint disease that can result in joint pain, loss of joint function, and deleterious effects on activity levels and lifestyle habits. Current therapies for OA are largely aimed at symptomatic relief and may have limited effects on the underlying cascade of joint degradation. Local drug delivery strategies may provide for the development of more successful OA treatment outcomes that have potential to reduce local joint inflammation, reduce joint destruction, offer pain relief, and restore patient activity levels and joint function. As increasing interest turns toward intra-articular drug delivery routes, parallel interest has emerged in evaluating drug biodistribution, safety, and efficacy in preclinical models. Rodent models provide major advantages for the development of drug delivery strategies, chiefly because of lower cost, successful replication of human OA-like characteristics, rapid disease development, and small joint volumes that enable use of lower total drug amounts during protocol development. These models, however, also offer the potential to investigate the therapeutic effects of local drug therapy on animal behavior, including pain sensitivity thresholds and locomotion characteristics. Herein, we describe a translational paradigm for the evaluation of an intra-articular drug delivery strategy in a rat OA model. This model, a rat interleukin-1beta overexpression model, offers the ability to evaluate anti-interleukin-1 therapeutics for drug biodistribution, activity, and safety as well as the therapeutic relief of disease symptoms. Once the action against interleukin-1 is confirmed in vivo, the newly developed anti-inflammatory drug can be evaluated for evidence of disease-modifying effects in more complex preclinical models.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.