Biomedical Engineering Reference
In-Depth Information
12.3.3 Perspectives
The 4DIB approach has some important drawbacks and limitations. It requires a
large data set of images, which is not always available, even if some problem-
specific workarounds can be devised to overcome this problem, as presented in Sect.
12.3.2.1. Moreover, this approach does not provide information on solid mechanics
of the walls and it is therefore suitable when the focus of the study is on the flow
features alone. However, this DA methodology splits the pipeline into a phase ded-
icated to the “offline” retrieval of the wall motion from images and a phase for the
computation of the dynamics of the fluid alone, which has important computational
advantages with respect to full FSI simulations. Furthermore, this approach could
guarantee a reasonable reliability to patient-specific simulations of blood flow when
the vascular motion is determined by external components that could not readily be
included in a wall model, or more in general, when individual mechanical parameters
for a single patient are not available.
Many open problems deserve to be addressed. As we have mentioned, a complete
analysis of the accuracy of the registration process and how the registration errors
affect the computation of fluid dynamics still needs to be carried out. In this context,
it is particularly relevant the correlation of the numerical procedure with the noise
affecting the image acquisition and segmentation. The effects of noise/errors in the
recovery of the vessel wall motion affect indeed the boundary data for the flow sim-
ulation and eventually the estimation of WSS (or other post-processing quantities).
A detailed error analysis is therefore in order.
Using the terminology in [76] this DA procedure can be considered as a
frame-
to-frame pseudo-observational approach
. More mathematically advanced methods
advocated in [76] which entail an integrated variational assimilation of data and
images similar to the ones introduced in Sect. 12.2 could be considered as a future
development.
12.4 Variational parameter estimation
Since mathematical and numerical models are earning more relevance in medical
applications and are used as patient-specific tools, a precise estimation of individual
physical parameters featured by the equations is needed. Moreover, by themselves,
some parameters can play the role of landmarks of pathologies. This is for instance
the case of the stiffness of soft tissues in detecting breast cancer. Significant changes
of the stiffness of the tissue can identify the presence of tumors. On the other hand,
a small value of the compliance of the tissue could be an indicator of atherosclerosis
or hypertension, while an increase of the stiffness of the left ventricle wall is a clear
marker of
diastolic dysfunction
, which can lead to an increase of the end diastolic left
ventricle pressure and, possibly, to heart failure (see e.g. [1, 77]). This has motivated
sophisticated image-based diagnostic approaches, such as the
elastography
(see e.g.
[78, 79, 80, 81]).
Either for a direct diagnostic purpose or for an individual-based evaluation to
be used in numerical simulations, a precise estimation of biological parameters
in
