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

Despite the importance of taking the above criteria into account, little research has been
done to model these requirements. Therefore this research focuses on developing a
methodology to predict the stability of a guide design based on its 3D model and the 3D
model of the patient’s anatomy. Our focus in this paper is on predicting the stability of a
guide with respect to the haptic feeling of stability a user experiences.
2. METHOD
2.1 Computational model
A computational model was developed to verify the stable position of a surgical guide
during the design phase. Based on previous research from the field of fixture lay-out
optimization [13] and navigation registration [14], the relationship between the contact
surface of the guide and the patient’s anatomy is investigated.
The contact surface between guide and bone model is defined by its contact points
and the unit outward normal vector at each point. Using this information, Lin et al
developed a frame-invariant method to compare grasps and fixtures using the spatial
stiffness matrix of the contact surface [13]:
∑ [
] [ ] [
] (1)
This stiffness matrix is a positive definite matrix with a block-diagonal
structure. Its submatrices , and are used to define two new matrices that
characterize the stiffness behaviour of the contact.
The eigenvalues , and of the submatrix characterize the translational stiffness
of the contact. Similar, a matrix was defined, that characterizes the rotational
behaviour of the contact:
The eigenvalues , and of the matrix are the principal rotational stiffness
parameters of the contact. The principal rotational stiffness parameters are scaled such
that the rotational stiffness of the contact can be investigated with respect to a userdefined
target point:
(2)
( ) (3)
where is the distance of the instantaneous axis of rotation to the target point [13].
The stiffness of the contact improves if the minimal principal translational or rotational
stiffness parameter increases. We defined a translational and rotational stability
parameter based on the target registration error as defined by Ma and Ellis [14]:
√
√
(4)