Multiscale Computational Modeling in Vascular Biology: From Molecular Mechanisms to Tissue-Level Structure and Function - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 214

collagenases, gelatinases, stromelysins, matrilysins, and membrane-type MMPs.
ProMMPs are cleaved into active forms, which degrade ECM proteins, and their
effects are balanced by tissue inhibitors of metalloproteinases (TIMPs) that prevent
excessive proteolytic ECM degradation.
As noted in subsequent sections, MMP-2 and MMP-9 (gelatinases A and B) are
upregulated during sustained hypertension and contribute to ECM reorganization,
SMC proliferation and migration, and vascular hypertrophy in large vessels.
Increased MMP-2 levels, in particular, have been associated with impaired NO-
mediated vasorelaxation, arterial wall hypertrophy, and excessive collagen and
elastin deposition. Therapeutic MMP inhibition with doxycycline has been pro-
posed as a pharmacological strategy to attenuate SMC proliferation and hyper-
trophy during hypertension (for review see Ref. [ 15 ]) as well as the treatment of
aneurysms. MMPs can also liberate and activate matrix-bound growth factors,
such as TGF-beta [ 13 ], which may have opposing influences on SMC differenti-
ation. Thus it is important to quantitatively assess these interactions with spatial
and temporal resolution in order to resolve issues of therapeutic dose and timing.
3 Modeling Foundations and Current Models
3.1 Continuum Biomechanics and Illustrative Vascular Models
Continuum biomechanics has proven to be an important contributor to our
understanding of physiology and pathophysiology as well as to the design of
medical devices, biomaterials, and tissue engineered constructs. It is fundamental,
for example, to many analyses of vascular biology and pathophysiology that are
based on clinically available information such as blood pressure, local blood flow,
and complex geometry [ 30 ]. Continuum biomechanics is founded upon five basic
postulates: balance of mass, linear momentum, and energy as well as balance of
angular momentum and the entropy inequality. Whereas the first three types of
relations provide partial differential equations of motion, the last two provide
important restrictions on the forms of the constitutive relations (i.e., descriptors of
individual material behaviors). An underlying assumption is that one can compute
at each macroscopic point (or location) and each instant a meaningful ''continuum
average'' of properties or physical quantities of interest; a general guideline is that
the continuum assumption is reasonable if the characteristic length scale of the
microstructure is much less than the characteristic length scale of the physical
problem. For example, continuum biomechanics can be equally applicable to
studying an arterial wall (wherein diameters of collagen and elastic fibers are on
the order of lm and overall vessel diameter is on the order of mm or cm) or an
isolated cell (wherein diameters of cytoskeletal filaments are on the order of nm
and overall cell dimensions are on the order of lm).