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A. Wittek et al.
11.4 Visibility Criterion for Modelling of Surgical Dissection
and Soft Tissue Rupture
Surgical dissection and injury-related rupture introduce discontinuities/cracks in
the body tissues and organs. In the computational biomechanics algorithms that
rely on finite element discretisation discussed in Chap. 10, surgical dissection is
simulated by subdividing the elements forming the mesh [40–44]. This requires
sophisticated re-meshing techniques to generate new elements with good aspect
ratio and map the field variables from the original to the new mesh. With an
exception of Bui et al. [44], the re-meshing is in practice limited to tetrahedral
elements that exhibit volumetric locking when applied to soft tissues and other
incompressible continua unless special countermeasures are applied (see Chap. 10).
Furthermore, error accumulation due to re-meshing tends to constrain the accuracy
of finite element method in modelling of surgical cutting/dissection [42, 45]. As the
meshless methods utilise spatial discretisation in a form of a ‘cloud’ of points/nodes,
the burden associated with re-meshing required by finite element method is to a
large extent alleviated. Therefore, meshless discretisation has been proposed by
several authors as a method of choice for modelling of continua undergoing crack
propagation and fragmentation [8, 46–52].
The specialised algorithm, created for the MTLED framework by Jin et al. [20]
at the Intelligent Systems for Medicine Laboratory at the University of Western
Australia, models the progressive surgical cutting by adding and/or splitting nodes
on the cutting path using the visibility criterion. The visibility criterion prevents
the nodes located on the opposite sides of dissection/crack from interacting with
each other (they are ‘invisible’ to each other) [3, 53]. In the algorithm by Jin et al.
[20], the surgical cut and injury-caused rupture/crack are geometrically represented
using a series of line segments with the aid of the level-set method [54, 55] to
mathematically describe the location of all the nodes and integration points in
relation to the cutting/rupture path (Fig. 11.9). The effect of cutting-/rupture-induced
discontinuity is entirely reflected in the changes of the shape and size of the nodal
influence domains (Fig. 11.10).
Quantitative evaluation through application in modelling of rupture-causing
elongation of the specimen of pia-arachnoid complex has confirmed the robustness
and accuracy of the specialised visibility criterion for modelling dissection and
rupture in MTLED framework (Fig. 11.11) [20, 58]. However, application in
modelling of dissection of 3-D continua indicated challenges associated with high
computational cost of the visibility criterion and level-set method in 3-D [59].
Therefore, we recommend visibility criterion only for modelling of dissection
and rupture of thin tissue layers such as the brain meninges. To the best of
our knowledge, despite ongoing research effort that includes application of the
methods such as the phase-field approach [60], the problem of modelling of crack
propagation in 3-D continuum subjected to large deformations and exhibiting nonlinear stress-strain relationship still awaits solution that can be regarded as accurate
(in a sense of quantitatively accurate predictions of forces and deformations),
A. Wittek et al.
11.4 Visibility Criterion for Modelling of Surgical Dissection
and Soft Tissue Rupture
Surgical dissection and injury-related rupture introduce discontinuities/cracks in
the body tissues and organs. In the computational biomechanics algorithms that
rely on finite element discretisation discussed in Chap. 10, surgical dissection is
simulated by subdividing the elements forming the mesh [40–44]. This requires
sophisticated re-meshing techniques to generate new elements with good aspect
ratio and map the field variables from the original to the new mesh. With an
exception of Bui et al. [44], the re-meshing is in practice limited to tetrahedral
elements that exhibit volumetric locking when applied to soft tissues and other
incompressible continua unless special countermeasures are applied (see Chap. 10).
Furthermore, error accumulation due to re-meshing tends to constrain the accuracy
of finite element method in modelling of surgical cutting/dissection [42, 45]. As the
meshless methods utilise spatial discretisation in a form of a ‘cloud’ of points/nodes,
the burden associated with re-meshing required by finite element method is to a
large extent alleviated. Therefore, meshless discretisation has been proposed by
several authors as a method of choice for modelling of continua undergoing crack
propagation and fragmentation [8, 46–52].
The specialised algorithm, created for the MTLED framework by Jin et al. [20]
at the Intelligent Systems for Medicine Laboratory at the University of Western
Australia, models the progressive surgical cutting by adding and/or splitting nodes
on the cutting path using the visibility criterion. The visibility criterion prevents
the nodes located on the opposite sides of dissection/crack from interacting with
each other (they are ‘invisible’ to each other) [3, 53]. In the algorithm by Jin et al.
[20], the surgical cut and injury-caused rupture/crack are geometrically represented
using a series of line segments with the aid of the level-set method [54, 55] to
mathematically describe the location of all the nodes and integration points in
relation to the cutting/rupture path (Fig. 11.9). The effect of cutting-/rupture-induced
discontinuity is entirely reflected in the changes of the shape and size of the nodal
influence domains (Fig. 11.10).
Quantitative evaluation through application in modelling of rupture-causing
elongation of the specimen of pia-arachnoid complex has confirmed the robustness
and accuracy of the specialised visibility criterion for modelling dissection and
rupture in MTLED framework (Fig. 11.11) [20, 58]. However, application in
modelling of dissection of 3-D continua indicated challenges associated with high
computational cost of the visibility criterion and level-set method in 3-D [59].
Therefore, we recommend visibility criterion only for modelling of dissection
and rupture of thin tissue layers such as the brain meninges. To the best of
our knowledge, despite ongoing research effort that includes application of the
methods such as the phase-field approach [60], the problem of modelling of crack
propagation in 3-D continuum subjected to large deformations and exhibiting nonlinear stress-strain relationship still awaits solution that can be regarded as accurate
(in a sense of quantitatively accurate predictions of forces and deformations),