Biomedical Engineering Reference
In-Depth Information
Chapter 9
Multiscale Modeling of Arterial Adaptations:
Incorporating Molecular Mechanisms Within
Continuum Biomechanical Models
Jay D. Humphrey
Abstract
Continuum level biomechanical models of arterial adaptations are prov-
ing themselves vital both for understanding better the progression of disease and
for improving the design of clinical interventions. Although these models are most
appropriate to the clinical scale of observation, the underlying mechanisms respon-
sible for such remodeling occur at the molecular scale. The goal of this chapter is
to review a validated continuum level model of arterial adaptations and to suggest
a straightforward approach to incorporate molecular level information within such
models. In particular, it is shown that continuum mixture models reveal naturally
a means to incorporate molecular information within fundamental constitutive re-
lations within the continuum theory. There is, therefore, significant motivation to
continue to formulate molecular level models that are necessary to inform models
at scales that address the Physiome.
9.1 Introduction
The past four decades have brought forth tremendous advances in the continuum
biomechanics of arteries (Humphrey,
2002
). Nevertheless, three conspicuous short-
comings have persisted. First, most constitutive relations and stress analyses have
focused on conditions at a single instant, not how the arterial properties and stress
fields evolve due to normal development or in response to perturbed loads, disease,
injury, or clinical treatment. Second, biomechanical analyses have been based on
the assumption that arteries are materially uniform rather than consisting of many
different constituents that turnover at different rates and to different extents while
collectively defining the whole. Third, continuum biomechanical models have em-
ployed phenomenological constitutive relations that have not directly accounted for
the many classes of molecules that control arterial adaptations, including vasoac-
tive, mitogenic, proteolytic, and inflammatory molecules. The primary goal herein
is to encourage a new direction in arterial research whereby one develops multiscale
J.D. Humphrey (
)
Department of Biomedical Engineering, Yale University, New Haven, CT 06520, USA
e-mail:
jay.humphrey@yale.edu
