ABSTRACT
In general, the ophthalmologists evaluate tortuosity of retinal blood vessels using subjective estimates, for example, optometric scales [1]. But objective estimates also exist.
For such estimates, it is generally assumed that blood vessel is a planar curve that does not intersect itself. It can be dened parametrically. In computer memory, it can be stored discretely (nite number of points). For every point of a continuous curve (and most of the points of discrete curve), it is possible to calculate curvature. The curvature of a parametric curve can be calculated from derivatives of coordinates by the following formula:
k x y y x
x y =
′ ′′ ′ ′′
′ + ′
−
( ) ./2 2 3 2 (20.1)
One of the most simple methods to estimate the tortuosity of the curve using curvature is the ratio between the integral of module or square of curvature and curve’s length L [2]:
τ1 1
= ∫L k t t t
| ( )| .d (20.2)
A possible modication of this method uses the curvatures of edges of the vessel instead of the center line. That takes into account the fact that tortuosity is calculated not for the idealized lines, but for objects that have width [3]. Later, this modication has been generalized [4]:
CONTENTS
20.1 Related Work ...................................................................................................................... 395 20.2 Biomechanical Modeling of Blood Vessel Using the Finite Element Method .......... 397 20.3 Experimental Validation of Blood Vessel Model ........................................................... 398 References .....................................................................................................................................405
