Biomedical Engineering Reference
In-Depth Information
Fig. 7.1
A schematic
representation of regional
stress-strain trajectory loop.
Stress-strain area (SSA) is the
specific area in the
stress-strain (SS) diagram
surrounded by the
end-systolic SS line, the
end-diastolic SS line and the
systolic segment of the SS
trajectory for contraction
(Delhaas et al.,
1994
)
the intracellular environment induced by the diffusion obstacles can be changed due
to pathological conditions, such as ischemia or ischemia-reperfusion damage (Kay
et al.,
1997
; Boudina et al.,
2002
). The kinetics of actomyosin ATPase, a main con-
sumer of ATP in the cardiomyocytes (Suga,
1990
), is also influenced by intracellular
compartmentation as evidenced by strong coupling between creatine kinase and ac-
tomyosin (Ventura-Clapier et al.,
1987
). Studies of intracellular compartmentation
has benefited from the development of several mathematical models that allowed
us to analyze intracellular diffusion using a 2D (Vendelin et al.,
2004
)or3D(Ra-
may and Vendelin,
2009
) description of the intracellular environment and suggest
the possible intracellular structures that can lead to compartmentalization of the
cell (Ramay and Vendelin,
2009
). However, this analysis so far has been limited to
relaxed cardiomyocytes or fibers with the models taking into account only the en-
dogenous ATPase activity at low calcium concentrations (Saks et al.,
2003
; Vendelin
et al.,
2004
; Ramay and Vendelin,
2009
; Sepp et al.,
2010
). To study intracellular
energy fluxes and how they are changed depending on the contraction of the heart,
the development of actomyosin models that are able to link ATPase activity of the
muscle and mechanical performance are vital. Using such models, the changes in
energy transfer pathways induced by variation in workload as demonstrated by
31
P-
NMR inversion and saturation transfer experiments (Vendelin et al.,
2010
) can be
analyzed using mechanistic models.
As an important link between mechanical contraction and ATPase activity of ac-
tomyosin, a linear relationship between pressure-volume area (PVA) and oxygen
consumption of the heart during a single beat has been established experimentally
(Suga,
1990
). On a fiber level, the linear relationship between an analog of PVA—
stress-strain area (SSA, see Fig.
7.1
)—and oxygen consumption has been estab-
lished (Hisano and Cooper,
1987
).
There are several published models that link mechanical contraction and ATPase
activity of actomyosin (Cooke and Pate,
1985
; Taylor et al.,
1993a
,
b
; Landesberg
and Sideman,
2000
; Vendelin et al.,
2000
; Månsson,
2010
;Tranetal.,
2010
). Several
of these models are based on a Huxley description of the contraction and achieve
thermodynamic consistency by applying Hill formalism (Hill,
1974
; Eisenberg et
al.,
1980
). That formalism involves describing the spatial dimension of cross-bridge
placing and for that partial differential equations (PDE) were used. Solving PDEs is
usually considered to be computationally expensive and for that many cross-bridge
