Original
Research Article
A Mathematical Analysis of Intravitreal Drug
Transport
R
Avtar, D Tandon
Department of Mathematics,
Harcourt Butler Technological Institute,
Kanpur 208002, India
E-mail:
deepti_hbti@yahoo.co.in
Tropical
Journal of Pharmaceutical Research, March
2008; 7(1):
867-877
Abstract
Purpose: The aim of
our present work is the development of a
quasi steady-state model for the
distribution of intravitreally injected
drugs and investigation of the effects of
various model parameters on the drug
distribution in normal and diseased eyes.
Method:
A simple
mathematical model for the intravitreal
transport of drugs was developed using
Fick’s law of diffusion, Darcy’s law of
convective flow, and Michaelis–Menten
kinetics of metabolism. A Crank-Nicolson
finite difference scheme of the equation
describing the drug transport in the
vitreous body was written, in which the
radial and axial diffusive terms and
convective terms of the equation were
approximated by central differences, while
the temporal terms were approximated by
average of forward and backward time
differences. A system of linear algebraic
equations obtained from the Crank Nicolson
finite difference scheme was solved by line
Jacobi iterative scheme in which successive
improved approximate results are obtained.
Result:
The
model predicts that an increase in
the metabolic (consumption) rate and drug
release rate constant reduces the
concentration of intravitreally injected
drug at the centre of retina and along
centreline of vitreous body. A significant
increase in the drug concentration at the
centre of retina and along the centreline of
the vitreous body in the eye afflicted with
glaucoma and retinal detachment is observed
and the decay rate of drug concentration in
these pathological states is higher than
that in the normal eyes.
Conclusion: The vitreous
outflow as observed in the glaucomatous
and/- or rhegmatogenous eyes may contribute
to the transport of intravitreally injected
drug in the vitreous body. The drug
concentration in the vitreous body and at
the centre of retina in such diseased eyes
is higher than that in the normal eyes and
the decay rate of drug concentration is
significantly enhanced.
Keywords:
Convective-diffusive transport, intravitreal injection,
line-Jacobi iterative technique, release rate. |