Comput. Biol. Med. - ODE/PDE analysis of corneal curvature.

Tópicos

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Resumo

The starting point for this paper is a nonlinear, two-point boundary value ordinary differential equation (BVODE) that defines corneal curvature according to a static force balance. A numerical solution to the BVODE is computed by first converting the BVODE to a parabolic partial differential equation (PDE) by adding an initial value (t, pseudo-time) derivative to the BVODE. A numerical solution to the PDE is then computed by the method of lines (MOL) with the calculation proceeding to a sufficiently large value of t such that the derivative in t reduces to essentially zero. The PDE solution at this point is also the solution for the BVODE. This procedure is implemented in R (an open source scientific programming system) and the programming is discussed in some detail. A series approximation to the solution is derived from which an estimate for the rate of convergence is obtained. This is compared to a fitted exponential model. Also, two linear approximations are derived, one of which leads to a closed form solution. Both provide solutions very close to that obtained from the full nonlinear model. An estimate for the cornea radius of curvature is also derived. The paper concludes with a discussion of the features of the solution to the ODE/PDE system.

Resumo Limpo

start point paper nonlinear twopoint boundari valu ordinari differenti equat bvode defin corneal curvatur accord static forc balanc numer solut bvode comput first convert bvode parabol partial differenti equat pde ad initi valu t pseudotim deriv bvode numer solut pde comput method line mol calcul proceed suffici larg valu t deriv t reduc essenti zero pde solut point also solut bvode procedur implement r open sourc scientif program system program discuss detail seri approxim solut deriv estim rate converg obtain compar fit exponenti model also two linear approxim deriv one lead close form solut provid solut close obtain full nonlinear model estim cornea radius curvatur also deriv paper conclud discuss featur solut odepd system

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