Biomedical Engineering Reference
In-Depth Information
is valid if the phase mismatch Δ k and the index of refraction remain constant regardless of fiber orienta-
tion. In fact, collagen's birefringence of Δ n ~ 0.003 (where n along the collagen monomer's long axis > n
along the short axis) is assumed to be negligible. This seems a valid assumption since the calculation
is compared to an experimental SHG signal averaged over an ensemble of collagen fibers only roughly
aligned. Furthermore, Δ k may be assumed constant since the SHG interaction volume (roughly the
focal volume dimensions, ~200 nm lateral × 600 nm axial) is smaller than the mean fiber diameter and
length in these cases, and can be assumed to be completely filled when centered on a collagen fiber
regardless of fiber orientation. For an incident wavelength of 780 nm, Δ k ~ 0.48 μm, with a correspond-
ing coherence length of 6.5 μm, allowing efficient SHG from ~3 μm thick bundles of collagen fibrils.
In summary, second-harmonic-generating dipoles within a collagen fibril or fiber tend to align with
the fibril long axis. For linearly polarized laser light, SHG depends on the angle between the laser's
electric field polarization direction and the fibril long axis. For circularly polarized incident light, this
dependence is removed. However, SHG still depends upon the angle of the fibril long axis with respect
to the laser propagation direction, with maximal signal perpendicular and minimal signal parallel to
the propagation direction. In essence, a circularly polarized LSM with SHG capability will capture the
signal from collagen oriented within the plane of the image, but with less and less signal from collagen
oriented increasingly perpendicular to the image plane. While an image of SHG signal from a collagen
gel may thus underestimate the true collagen content, most collagen structures seem to emit detectable
SHG signal. A superimposition of SHG and TPF signals from the same region of an acellular collagen
gel typically reveals the full cross-sectional structure of the collagen network.
11.3.6 Quantification of collagen network Architecture
from Second-Harmonic images
The pores within collagen gels allow diffusion, facilitate cell migration, and affect gel mechanical proper-
ties. Collagen network pores larger than the optical resolution set for a given imaging experiment may be
quantified from SHG images. The collagen network could become so dense that 100% of image pixels con-
tain collagen SHG signal, in which case, an alternative method to determine the pore characteristics would
have to be used, but for most acellular collagen gels, the collagen network is sparse enough that pores may
be characterized from SHG images. The pore characteristics were quantified from SHG and TPF signal of
collagen gels polymerized at 4 mg/mL and pH 5.5-8.5 (Figures 11.6a and 11.6b). The average pore size and
pore area fraction tended to decrease, whereas pore number density increased with increasing polymer-
ization, pH, as the available collagen tended to form more numerous, thinner fibers at higher pH values.
Particle analysis of thresholded SHG images produced a mean pore size ±SE of 81.7 ± 3.7 mm 2 for the pH
5.5 condition, decreasing ~90% to 7.8 ± 0.4 mm 2 for the pH 8.5 condition (Figure 11.6a). As expected, the
number density of pores increased ~3.2-fold from 7.1 ± 0.2 to 23.0 ± 0.6 per 1000 mm 2 (Figure 11.6b). The
trends in pore characteristics were confirmed by particle analysis of thresholded SEM images that dem-
onstrated a similarly trending decrease in pore size and increase in pore number density with increasing
polymerization pH. From this analysis, it appears that SHG images of acellular gels yield direct informa-
tion about pore characteristics that correspond to measurements from SEM images. In case TPF images
contain additional pore information due to the orientation independence of TPF signal, pores were quanti-
fied from thresholded SHG signal alone and also from thresholded SHG and TPF signals combined. The
particle analysis method of measuring pore characteristics is fairly robust, as analysis of the combined
SHG and TPF signal-masked images showed little change in the pore measurements.
11.3.7 Determining Mechanical Relationships in Acellular Gels
from Second-Harmonic images
In two separate studies described below, an attempt was made to correlate SHG and other image param-
eters to bulk gel mechanical properties from shear and indentation tests. In the first study, varying
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