1 research outputs found
Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications
Nonlocality is important in realistic mathematical models of physical and
biological systems at small-length scales. It characterizes the properties of
two individuals located in different locations. This review illustrates
different nonlocal mathematical models applied to biology and life sciences.
The major focus has been given to sources, developments, and applications of
such models. Among other things, a systematic discussion has been provided for
the conditions of pattern formations in biological systems of population
dynamics. Special attention has also been given to nonlocal interactions on
networks, network coupling and integration, including models for brain dynamics
that provide us with an important tool to better understand neurodegenerative
diseases. In addition, we have discussed nonlocal modelling approaches for
cancer stem cells and tumor cells that are widely applied in the cell migration
processes, growth, and avascular tumors in any organ. Furthermore, the
discussed nonlocal continuum models can go sufficiently smaller scales applied
to nanotechnology to build biosensors to sense biomaterial and its
concentration. Piezoelectric and other smart materials are among them, and
these devices are becoming increasingly important in the digital and physical
world that is intrinsically interconnected with biological systems.
Additionally, we have reviewed a nonlocal theory of peridynamics, which deals
with continuous and discrete media and applies to model the relationship
between fracture and healing in cortical bone, tissue growth and shrinkage, and
other areas increasingly important in biomedical and bioengineering
applications. Finally, we provided a comprehensive summary of emerging trends
and highlighted future directions in this rapidly expanding field.Comment: 71 page