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There are many diseases that manifest in the posterior segment of the eye. These include age-related macular degeneration (AMD), retinal vein occlusion, and diabetic retinopathy and maculopathy. Together they account for the majority of blind registrations in the developed world.\cite{Bunce2010} Many of these diseases are treated with regular injections of drugs into the vitreous cavity, with the inconvenience of regular clinic review, cost of injection, discomfort, and small but repeated risks of complications.\cite{Edelhauser2010} Given the many downsides of regular intravitreal injections, the drug industry is actively investigating novel methods of delivering drugs to the posterior segment, including sustained release intravitreal devices,\cite{Callanan2008} transscleral drug delivery,\cite{Ambati2002, Ambati2000a, Ambati2000b} topical drug delivery (eye drops),\cite{Tanito2011} oral \cite{McLaughlin2013} and others such as iontophoresis.\cite{Molokhia2009}
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, (Lucentis\textregistered, 48~kDa), aflibercept
(Eylea, (Eylea\textregistered, 97~kDa), and bevacizumab
(Avastin, (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}
...
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
an effect to 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} For example, Ambati et al.\ reported that the globular protein albumin, with a MW of 69~kDa and $R_h$ of 3.62~nm, had approximately twice the scleral permeability of a linear dextran of 40~kDa and $R_h$ of 4.5~nm.\cite{Ambati2000a} 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
NMR 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 R_h^W (\text{\AA}) = 4.75\cdot N^{0.29} \label{eq:Wilkins}
\end{equation}
and Dill
\textit{et al.} \cite{Dill2011}
\begin{equation}
R_h R_h^D (\text{\AA}) = 1.45\cdot(2.24\cdot N^{0.392}) = 3.248\cdot N^{0.392} \label{eq:Dill}
\end{equation}
%\subsection{Radius measurement from anisotropy}
It is also possible to measure the hydrodynamic radius of a molecule by time-resolved fluorescence anisotropy measurements, which can help determine molecular
size, volume, mobility, rigidity, shape, and the molecule's surrounding environment.\cite{Lakowicz2006} The sample solution is excited with a pulse of polarised light, and the fluorescence is collected in parallel and perpendicular polarisation directions as a function of time. The anisotropy $r(t)$ of a molecule undergoing rotational diffusion in the solution can be obtained from the measured intensities $I_\parallel$ and $I_\perp$ by
\begin{equation}
r(t)= \frac{I(t)_\parallel-GI(t)_\perp}{I(t)_\parallel+2GI(t)_\perp} \label{eq:anisotropy}
\end{equation}
where $G$ is a correction factor that compensates for different transmission and detection efficiencies in the parallel and the perpendicular directions. If the sample solution contains spherical molecules of homogeneous size, the anisotropy
decay follows a single-exponential function
\begin{equation}
r(t) =
A\cdot r_0\cdot e^{-\frac{t}{\phi}} \label{eq:1expfit}
\end{equation}
where
$A$ $r_0$ is a constant and $\phi$ is the rotational correlation time. If the rotating unit is not spherical, a more complex model is required.
$\phi$ can thus be obtained by fitting eq~\ref{eq:1expfit} (or the more complex model) to the experimental anisotropy decay. $\phi$ is related to the volume $V$, and thus the effective radius, of the rotating molecule by
the Stokes-Einstein-Debye equation \cite{VanHolde1998}
\begin{equation}
\phi = \frac{\eta V}{kT} \label{eq:SED}
\end{equation}
where $\eta$ is the solvent
viscosity coefficient, viscosity, $k$ is the Boltzmann constant and $T$ is the absolute temperature.
Although time-resolved anisotropy measurements are a well established tool in molecular biology, only a few studies report applications in ophthalmology.\cite{McLaughlin2013,
Danysh2010, Srikantha2012} Danysh2010} In this study the
diffusion coefficients and subsequently the effective hydrodynamic radii of three important posterior segment drugs -- ranibizumab, aflibercept and bevacizumab -- were measured
by $\mu$s time-resolved fluorescene anisotropy and compared to radii calculated from the MW. A well-characterised protein bovine serum albumin (BSA) of comparable size (66.5~kDa) with known radius \cite{Axelsson1978} was also measured to validate the results.
