Page 137 - Computational Modeling in Biomedical Engineering and Medical Physics

126 Computational Modeling in Biomedical Engineering and Medical Physics

here as hyperelastic, neo-Hookean (Dobre et al., 2011b; Morega et al. 2010), which yields
the strain energy density

1 2 1 2 1
21
W 5 J 2 3 I 2 I 1 C 21 1 κJJ 2 1ÞC ;
2 3 2 ð ð4:25Þ
where J 5 det(F) is the relative variation of the volume, F is the deformation gradient,
T
C 5 F F is the right Cauchy Green tensor, and I 1 5 trace(C). For the muscle, the
2=3
initial shear modulus is μ 5 719,676 Pa, I 1 5 I 1 J , and the initial bulk modulus is
κ 5 14,393,520 Pa that corresponds to the Poisson ratio ν 5 0.45 (Bangash et al.,
2007). The stress, S, is then the derivative of the strain energy density function, W,
with respect to Green-strains, E, that is, S 5 @W=@E.
The boundary conditions in this structural analysis are shown in Fig. 4.23. The
outer surface of the arm (the skin) is set “free,” and “roller” type BCs are set for
the cross-sections. The total stress solved for in the first step is used as BC (load) in the
structural analysis of the arterial walls deformations produced by the pulsatile flow.

Pressure transducers and their positioning
Piezoelectric or capacitive pressure transducers may be used to determine pressure vari-
ation by detecting oscillations in the skin and convert them into measurable electrical
quantities (Figliola and Beasley, 1994). The force transmission structure of the trans-
ducer (sometimes called artery rider) is smaller than the flattened area of the artery,
and centered over the flattened area (Eckerle, 2006; Lee and Nam, 2009). The capaci-
tive sensor consists of a pair of armatures, one fastened and one mobile, compliant to
the skin displacement. The distance between the armatures changes yielding a pressure
induced change in the electric capacity. The advantages of capacitive sensors over pie-
zoelectric sensors are increased sensitivity, simplicity, at lower costs (Webster, 2006).
Metrological properties such as sensitivity, stability, and linearity recommend these
sensors (Kumar, 2000).
The precision of the transducers readouts is highly influenced by the sensors proper
positioning with respect to the ROI. Their precise centered positioning with respect
to the artery is needed for reliable recordings (Kelly et al., 1989), and arrays of fixed
sensors might be used to best measure the radial pulse wave that indents the radial
artery (Terry et al., 1990; Kemmotsu et al., 1991a,b; Webster, 2006). One or more
sensors are placed over the artery and recognized by comparing the measured pressure
and the pressure distribution of each sensor at a diastolic interval. Several accompa-
nying, inherent factors (physiological and psychological variations, movements) may
affect the measurement accuracy and care should be devoted to reduce or eliminate
them (Lee and Nam, 2009). Standardized measurement settings are suggested to shed
the subject’s variation (Van Bortel et al., 2002).