# Computational Modeling of Degenerative Diseases

Mathematical models are widely employed for the study of degenerative diseases, in particular to investigate their biomechanical and mechanobiological aspects. Continuum mechanics theory provides the tools to build a system of partial differential equations and boundary conditions representing arbitrary ...

Mathematical models are widely employed for the study of degenerative diseases, in particular to investigate their biomechanical and mechanobiological aspects. Continuum mechanics theory provides the tools to build a system of partial differential equations and boundary conditions representing arbitrary mechanical systems, such as for example articular joints and arteries. Discretization methods such as the finite element method allow finding a solution to such a system, by approximating it with a system of ordinary differential or algebraic equations which can be solved by means of standard numerical algorithms.
Numerical simulation is a powerful tool to investigate degenerative and age-related changes of biological tissues, and show advantages compared to other investigative methods such as in vitro testing: in numerical models the occurrence and severity of the different degenerative changes can be easily controlled to represent a wide range of clinical scenarios, whereas in experiments they are dependent on the availability of the specimens which are usually few in numbers and often severely degenerated. The body of scientific literature describing numerical models of degenerative diseases is rapidly expanding and current papers deal with complex clinical conditions simulated by means of sophisticated multi-physics models at the macro and micro scale.
In a previous Research Topic, we collected articles about the numerical modeling of orthopedic degenerative diseases. Here, we focused on the advances in the biomechanical simulation of the degenerative changes of the intervertebral disc but also covered the modeling approaches and constitutive laws used in numerical studies of the knee ligaments.

In this current Research Topic we enlarge the scope to degenerative diseases more generally including but not limited to age-related changes in the cardiovascular system (aortic stenosis, coronary artery disease), the urinary system (incontinence disease), the cornea, and also neurodegenerative disorders. In doing so we aim to stimulate further innovation in the field more generally and attract the interest of basic scientists to these clinically relevant diseases. Papers describing multi-physics and multiscale models which go beyond the consolidated approach of pure structural of fluid dynamics simulations using commercial finite element packages are especially welcome.

Keywords: aging, mathematical modeling, degeneration, Neurodegenerative diseases, Musculoskeletal system, Cardiovascular system, aortic valve stenosis, coronary artery disease, Ocular system, cornea, urinary incontinence, Multi-physics models, Multi-scale models

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