Liisa Hirvonen edited Introduction.tex  over 8 years ago

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Topical drug delivery has many potential advantages, including self-administration, reduced cost, sustained drug levels, potentially fewer clinic visits, and the elimination of the risks associated with eye injections. Whilst desirable, topical drug delivery to the posterior segment is greatly impeded by the external ocular barriers to diffusion. This is compounded by the fact that many of the drugs used to treat posterior segment disease have a high molecular weight (MW), including ranibizumab (Lucentis\textregistered, 48~kDa), aflibercept (Eylea\textregistered, 97~kDa), and bevacizumab (Avastin\textregistered, 150~kDa).  Drug size and shape will influence how intravitreal drugs cross the vitreous, and retina, to reach diseased macular and choroidal tissue. Studies have shown a slower movement of tritiated water in normal rabbit vitreous compared with rabbit vitreous that has undergone a depolymerisation reaction with hyaluronidase. This suggests that the structural components of vitreous impose a diffusional barrier to the transport of even small molecules.\cite{Foulds1985} Gisladottir et al.\ showed that dexamethasone diffuses 4-5 times faster in saline than it does in porcine vitreous humor, and concluded that the diffusion of large molecules was impeded by the fibrillar structure of the vitreous.\cite{Gisladottir2009}  %\subsection{Radius calculation from MW}  Many factors, such as the molecular size and shape, will influence how intravitreal drugs cross the vitreous, and retina, to reach diseased macular and choroidal tissue.\cite{Foulds1985, Gisladottir2009, Srikantha2012}  It is well known that increasing MW reduces the speed of diffusion across biological tissue,\cite{Maurice1977, Pitkanen2005, Geroski2001} and other studies have shown that the molecular radius is a better predictor of tissue penetration than MW.\cite{Ambati2002, Ambati2000a, Geroski2001, Bohrer1984, Ohlson2001, Venturoli2005} It is possible to estimate the radius of a protein from the MW. Erickson uses the fact that all proteins have approximately the same density, 1.37 g/cm$^3$, to calculate the protein volume from the MW.\cite{Erickson2009} Assuming a smooth spherical shape, this yields a minimum possible radius \begin{equation}  R_{min} \text{(nm)} = 0.066 \cdot \text{MW}^{1/3} \label{eq:Erickson}  \end{equation}  However, proteins have a rough surface, are often not perfectly spherical, and the ionic charge has affects the diffusion of a molecule in solution. The hydrodynamic radius $R_h$, defined as the radius of a hard sphere that diffuses at the same rate as that solute, takes these effects into account. The hydrodynamic radius is important in predicting transretinal penetration.\cite{Jackson2003, Ambati2000a} Small-angle scattering studies using X-rays (SAXS) or neutrons (SANS) \cite{Svergun_2013} as well as dynamic light scattering (DLS) \cite{Pecora_1985, Hong_2009} and nuclear magnetic resonance (NMR) techniques \cite{Wilkins1999} have been used for measuring $R_h$. Global analysis of hundreds of proteins has led to the definition of empirical relationships between $R_h$ and the number of amino acids $N$, related to the MW by \(N = \frac{\text{MW}}{110 \text{ Da}}\). Such formulas have been defined, for example, by Wilkins \textit{et al.} \cite{Wilkins1999}  \begin{equation}  R_h^W (\text{\AA}) = 4.75\cdot N^{0.29} \label{eq:Wilkins}