Biomedical Engineering Reference
In-Depth Information
be modeled by continuum or molecular methods alone (e.g., too small or too large),
multiscale methods can be implemented. Multiscale methods involve the use of infor-
mation at various scales, which requires mathematics and computation to simulate a
physical or biological system at more tha one scale [
1
]. These methods are mainly
divided into two types of approaches: hierarchical and concurrent. The hierarchical
approach to multiscale modeling directly uses the information at small length scales
and inputs it into larger length scales via an averaging process. The more popular
concurrent multiscale methods, in contrast, utilize information at differing scales
simultaneously.
Multiscale modeling techniques have relevant uses in many fields of study such
as engineering and biology. Materials science has benefited from multiscale methods
in the realm of solid mechanics. Studying fluid flow effects in microfluidic devices
requires analysis at two or more spatial and temporal scales with coupled chemistry,
electrochemistry, and fluid motion [
1
].
For decades, advances in biology had little to do with contribution from sophisti-
cated mathematical modeling. Biology was mainly based on observation and experi-
mentation and it was not possible to simulate large complex systems. However, now
in the age of computers and seemingly endless computational capabilities, there is
an avenue for collaboration among biologists, mathematicians, and computational
scientists to establish relevant models based on experiments. No longer are there
strict limitations in tools and resources to examine life at many scales, which rep-
resents the difficulty in modeling biology. It is well known that biological systems
are complicated to mathematically model because they involve many interrelated
processes across many scales [
2
]. Each scale level in a biological system, both tem-
poral and spatial, contains information from levels either above or before [
3
]. The
general hierarchy of scales in biological systems follows the order of atom, mole-
cule, macromolecule, organelle, cell, tissue, organ, individual, to population. These
complex scales have also been broken up into specific fields of study (i.e., molecular
biology, cellular biology, organism studies, and population studies).
In the field of cancer research, the ultimate goal of mathematical modeling and
simulation is to aid in development of personalized therapies thereby decreasing
patient suffering while increasing treatment effectiveness [
4
]. Mathematical and com-
putational models, therefore, are needed to quantify the links between 3D tumors
and migration, invasion, proliferation, and microscale cellular and environmental
characteristics [
4
]. This task is best accomplished using multiscale methods.
11.2 Multiscale Computational Methods and Challenges
Multiscale methods are specially geared to develop models that are capable of link-
ing molecular, cellular, and tissue continuum scales. The common approach taken
in constructing a mathematical model is to begin with a simple model. This model
will preserve enough biology to be meaningful, but will include less parameters [
3
]
as to not over complicate the modeling process. The advantage of this approach
is that the model can be applied to understand many different biological systems.
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