Page 30 - Advances in Biomechanics and Tissue Regeneration

24 2. BIOMECHANICS OF THE VESTIBULAR SYSTEM: A NUMERICAL SIMULATION

The main effective therapy used in the reported condition is the vestibular rehabilitation composed of particle repo-
sitioning maneuvers and habituation therapy. Despite the success rates of such therapy, there are some key details that
should be better analyzed. Therefore, due to the vestibular system conditions, a computational biomechanical
approach seems to be a suitable analysis methodology.

2.3 NUMERICAL METHODS APPLIED TO HUMAN MORPHOLOGY

The reduced dimensions of the vestibular system hinder the experimental analysis of such a system, being the com-
putational simulation an alternative approach to study the rehabilitation process.
In 1933, when the primary investigations of the vestibular system were performed, Steinhausen formulated a math-
ematical description of the SCC that considered the dynamics of the cupula endolymph system as a highly damped
torsion pendulum for the sensation of the angular motion [22].
The fluid–structure interaction simulation of the endolymph and cupula during head rotation allows the measure-
ment of the fluid interactions between the three ducts and the displacement of the cupula during the movement. This
model could be useful to understand the physiological and mechanical aspects of SCC, and it could be described as a
band-pass filter relating the displacement of the cupula to the angular velocity of the head [23]. Simulation methods for
fluid-structure interaction include the finite element method (FEM), which have been gradually developed. FEM is a
computational tool for performing mathematical analysis. It includes the use of mesh generation techniques for divid-
ing a complex problem into small elements.
Simultaneously, meshless methods have been under strong development and are continuously extending their
application field [24]. Additionally, due to the efficiency and accuracy of their discretization formulation, meshless
methods are more flexible discretization techniques and a competitive and alternative numerical method in compu-
tational mechanical analysis [25].
The meshless methods discretize the domain based on a cloud of nodes [25, 26], instead of the rigid element concept
used in FEM. In the early years, the solution of partial differential equations was the main focus of interest. However,
today, meshless methods are applied to a wide range of applications [27].
Meshless methods can be divided into many classes or even subclasses; one of the most common classifications used
is the “not-truly meshless method” or “truly meshless method” classification [27].
A meshless method is labeled “not truly” when a background mesh is required to perform the numerical integration
of the integrodifferential equations ruling the studied physical phenomenon.
On the other hand, “truly” meshless methods only require an unstructured cloud of nodes to discretize the problem
domain, because the influence domain, integration points, shape functions, and other necessary mathematical con-
structions are obtained directly from the spatial coordinates of the nodes.
Thus truly meshless methods are capable to obtain the cloud of nodes using just CAT scan or the MR images by
considering the pixels (or voxels) position. Afterward, using only the nodal spatial information, these truly meshless
methods are able to obtain directly the nodal connectivity, the integration points, and the shape functions. Further-
more, using a gray range of medical images, truly meshless methods are even capable of recognizing distinct biological
structures and then attribute to each node the corresponding material properties [27, 28].
The natural neighbor radial point interpolation method (NNRPIM) is an example of a truly meshless method, which
allows discretizing the problem domain using only a nodal cloud coming from the voxel position of the micro-CT
scan (no other information is required). Then, using the natural neighbor concept, the Voronoï diagram discretizing
the problem domain can be constructed. From the Voronoï diagram, it is possible to establish directly the nodal con-
nectivity and define the position and weight of background integration points. The NNRPIM formulation and
its extension to free vibration analysis were used in the present work, and some applications will be detailed in the
next section.
Another popular and accurate meshless method used in this work is the radial point interpolation method (RPIM).
The RPIM is an interpolator meshless method that enforces nodal connectivity using the influence-domain concept. To
solve the integrodifferential equations governing the physical phenomenon, the RPIM uses a background cloud of
integration points, constructed using integration cells and the Gauss-Legendre quadrature rule. This numerical inte-
gration process represents a significant percentage of the total computational cost of the analysis.
There are other meshless methods used in the present work that could be used to simulate biological structures, such
as the smoothed-particle hydrodynamics (SPH), which is a computational method used also for simulating fluid flows.

I. BIOMECHANICS