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. Author manuscript; available in PMC: 2012 Nov 1.
Published in final edited form as: Ann Biomed Eng. 2011 Aug 2;39(11):2669–2682. doi: 10.1007/s10439-011-0363-9
Symbol (units) Classification Definition
Kσθc CMM: Bounded Gain parameter governing circumferential-stress mediated
rate of production of collagen. See Eq. (1)
Kσθm CMM: Bounded Gain parameter governing circumferential-stress mediated
rate of production of smooth muscle. See Eq. (1)
Kτwc CMM: Bounded Gain parameter governing shear-stress mediated rate of
production of collagen. See Eq. (1)
Kτwm CMM: Bounded Gain parameter governing shear-stress mediated rate of
production of smooth muscle. See Eq. (1)
MMP-10 (pg) ABM: Bounded Baseline mass of MMP-1
MMP-1%A (%) ABM: Bounded Percent of MMP-1 that is active
C0 (pg) ABM: Bounded Baseline mass of collagen
CTGF ABM: Bounded Rate parameter governing TBFb mediated rate of
production of collagen (pg of collagen per pg of TGFb)
Mp ABM: Bounded Rate parameter governing PDGF mediated SMC
proliferation rate (pg of SMC per pg of PDGF)
M0 (pg) ABM: Bounded Baseline SMC proliferation rate (pg)
Ma1 ABM: Bounded Apoptosis chance for SMC (1)
Ma2 ABM: Bounded Baseline apoptosis chance for SMC (2)
PDGFσθ(pg/kPa) ABM: Bounded Rate parameter governing hoop stress mediated rate of
production of PDGF (pg of PDGF per kPa of stress)
PDGF0 (pg) ABM: Bounded Baseline mass of PDGF
TGFβσθ (pg) ABM: Bounded Rate parameter governing hoop stress mediated rate of
production of TGFb (pg of TGFb per kPa of stress)
TGFβ0 (pg) ABM: Bounded Baseline mass of TGFb
Ghe CMM: Observed Homeostatic stretch when elastin is deposited
Ghc CMM: Observed Homeostatic stretch when collagen is deposited
Ghm CMM: Observed Homeostatic stretch when SMC is deposited
Ce (kPa) CMM: Calculated Neo-Hookean material parameter for the stored energy of
elastin
c1c(kPa) CMM: Calculated Fung-type exponential material parameter for the stored
energy of collagen (1)
c1m(kPa) CMM: Calculated Fung-type exponential material parameter for the stored
energy of SMC (1)
c2c CMM: Observed Fung-type exponential material parameter for the stored
energy of collagen (2)
c2m CMM: Observed Fung-type exponential material parameter for the stored
energy of SMC (2)
Tm(kPa) CMM: Observed Maximum stress generated by SMC
λM CMM: Observed Circumferential stretch where active stress is maximum
λ0 CMM: Observed Circumferential stretch where active stress is zero
CB CMM: Observed Material parameter for the ratio of constrictor
concentration to dilator concentration
CS CMM: Observed Scaling parameter for shear stress induced change in
constrictor concentration scaling factor
ϕc(0) CMM: Observed Initial mass fraction of collagen in the arterial wall
ϕe(0) CMM: Observed Initial mass fraction of elastin in the arterial wall
ϕm(0) CMM: Observed Initial mass fraction of SMC in the arterial wall
Khm(days1) CMM: Observed Half-life of SMC
Khc(days1) CMM: Observed Half-life of collagen
NO0 (pg) ABM: Observed Baseline mass of NO
NOτw ABM: Observed Rate parameter governing shear stress mediated rate of
production of NO (pg of NO per kPa of stress)
δPDGF (pg)
αPDGF
κPDGF(kPa−1)
nPDGF
MPDGF
ABM: Observed Parameters of the sigmoid function:
PDGF = M (δ + α(1 – e−kxn))


Maximum rate of PDGF production
δET–1 (pg)
αET–1
κET–1 (kPa−1
nET–1
MET–1
ABM: Observed Parameters of the sigmoid function:
ET1 = M (δ + α(1 – e−kxn))


Maximum rate of ET-1 production
δMMP–2 (pg)
αMMP–2
κMMP–2 (kPa−1)
nMMP–2
MMMP–2
AMMP–2 (%)
ABM: Observed Parameters of the sigmoid function:
MMP2 = A (M (δ +α(1 – e−kxn)))


Maximum rate of MMP-2 production
Percent of MMP-2 Active
DMMP–2 ABM: Observed Degradation rate of MMP-2
δMMP–9 (pg)
αMMP–9
κMMP–9 (KPa−1
nMMP–9
MMMP–9
AMMP–9 (%)
ABM: Observed Parameters of the sigmoid function:
MMP9 = A (M (δ +α(1 – e−kxn)))


Maximum rate of MMP-9 production
Percent of MMP-9 Active
DMMP–9 ABM: Observed Degradation rate of MMP-9
DMMP–1 ABM: Observed Degradation rate of MMP-1

Note: Parameters within the ABM or CMM are classified as observed, bounded, or calculated. Observed parameters were either cited elsewhere or obtained via direct measurements or fits to experimental data. Bounded parameters are less well known, but are expected to fall within specified range. Lastly, calculated parameters include those that are needed to satisfy equilibrium under homeostatic conditions.

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