ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

around 100µm (halfway through the entire fascicle) in order to generate 3D images of
the location of the cells within the collagen fibres. Strain was then applied at 0.5%
increments, at a rate of 8%/min -1 , with z stacks taken at each increment, up to a strain of
5%.
4. IMAGE REGISTRATION PROCESS
Image registration is a process of aligning the images from a same scene with each
other. Recently this method is employed as a tool to study the behaviour of the
biological systems by detecting and tracking any changes in the systems [7]. These
changes can be in the form of translation, deformation, appearing or disappearing of
objects in the images. In the present research, the interest is in measuring translations of
the objects (sampling points) in the images which can be used to calculate local strain
distribution in the systems. A function which describes the displacement of the points
in reference image to match the corresponding points in the registered image, is called
mapping function.
In the present research, the Sheffield Image Registration Toolkit (ShIRT) has been used
[8,9]. In ShIRT the mapping function is defined in terms of degrees of freedom at
discrete points (nodes), and interpolated across the domain using shape functions.
The operation of the registration algorithm determines the values of the nodal
displacements between pairs of images by minimising a cost function, J(a) that
describes the difference between the images
J(a)
1
(f
2
t
1 t
m(a)) (f m(a)) λa Ca
2
The first term on the right hand side is the squared intensity difference between the
‘fixed’ image f and the ‘moved’ image m after the latter has been mapped by the
parameters a. Presence of different mapping parameter with which images registered
together necessitate the introduction of a constraint term. The second term on the right
hand side is a constraint term. The default form of the constraint in ShIRT is the square
of the Laplacian of the mapping parameters. These two terms generally work against
each other, minimising the first term often requires mapping that is not smooth,
especially with noisy data, whilst minimising the constraint term results in an imperfect
registration. The parameter λ controls the relative importance of these two terms
To perform image registration with ShIRT, microscopic images of fascicle with cell
nuclei marked in green are used. A sample 2D image (cross section) of fascicle taken
with 10X objective lens is shown in Figure 2. During application of global strain to
fascicle a section of first image (image at 0% global strain) will move out of field of
view due to limitation on the lens size. Therefore common areas in the images (before
and after global straining) are selected for registration purpose. Note that in the present
paper, symbols ‘x’,’y’ and ‘z’ represent the direction of applied force, the transverse
direction in planes parallel to the lens and the direction through the depth of fascicle,
respectively.
(1)