Biomedical Engineering Reference
In-Depth Information
11.2.3 optical Properties of collagen Gels
SHG signal intensity depends upon the square of the incident laser intensity, the square of local collagen
concentration, and, due to SHG coherence, on the spatial organization and scattering properties of the
generating collagen dipole arrays [10-12,14,16]. SHG intensity,
I
SHG
, may be expressed as
I
= 16
π ω
(
2
/
n n c
2
2
2
)
κ
S
2
d
2
I
2
,
SHG
ω
ω
ω
eff
ω
(11.2)
where ω is the fundamental (laser frequency),
n
ω
is the refractive index at the fundamental frequency,
n
2
ω
is the refractive index at the second-harmonic frequency,
c
is the speed of light, κ is a function of
particle size,
S
2
ω
is the second-harmonic backscattering coefficient (SHG scattering cross-section),
d
ef
is
the effective second-order nonlinear susceptibility, and
I
ω
is the laser intensity within the focal region
[14,16,82,83].
The SHG signal from collagen gels arises from a coherent/quasi-coherent component due to direct
detection of the generated signal and an incoherent component due to the detection of multiply-scat-
tered signal. SHG signal depends, therefore, on collagen gel-scattering properties that influence the
incoherent component as well as fibril size, aggregation, and orientation that influence the coherent
signal component [84]. Collagen possesses a high refractive index (
n
~ 1.5) [14], and thus scatters a
significant amount of light in an aqueous environment (
n
= 1.33). Single-photon scattering by collagen
occurs according to Mie theory, in which collagen fibrils smaller than the wavelength of incident light
tend to scatter equally in the forward and backward direction. Collagen fibers and close-packed fibrils
that approach and exceed the wavelength of scattered light possess increasing scattering cross-sections,
and are predominantly forward scattering [14]. Similarly, SHG from a point source smaller than λ
2ω
/10
(or about 40 nm) radiates more homogenously, whereas SHG from a cluster of harmonophores larger
than λ
2ω
~ 400 nm, the second-harmonic wavelength, produces almost entirely forward-generated sec-
ond harmonic [10,14,84]. Theoretical and experimental work suggest that collagen fibril aggregates can
generate significant backward-generated second-harmonic signal due to relaxed phase-matching condi-
tions imparted by interfibrillar spacing roughly equal to the coherence length in the backward direction
[85]. Hence, SHG is primarily forward generated by large fibers and fibril bundles >λ
2ω
, but significant
backward-generated SHG may result from small fibrils <<λ
2ω
with spacing on the order of the back-
ward coherence length, which for collagen SHG is < 7 μm [85]. At a typical LSM optical resolution of
~450 nm, collagen fibers and fibril aggregates at least two pixels wide will be 900 nm > λ
2ω
, resulting
in primarily forward SHG. Smaller fibrils, however, may produce up to 25% backward-generated SHG,
augmenting signal detection in the epidirection [84,85].
Turbidity of a collagen gel solution has been shown to vary linearly with collagen concentration for
low concentrations of collagen (<4 mg/mL) [56]. Not surprisingly, due to the reliance of SHG signal on
backscattering events, a linear dependence of SHG on acellular collagen gel concentration has also been
reported [14]. Thus, it is clear that the bulk optical properties of nonlinear scattering signals from a
collagen-rich tissue depend on collagen concentration, microstructure, and fiber size [86].
11.2.4 image Processing
Generally speaking, quantitative information from SHG images can result from analysis of signal lev-
els or from analysis of image textural and spatial features. To the extent that second-harmonic image
parameters are sensitive to collagen fiber and network structure (e.g., fiber, orientation, or network
anisotropy), the parameters may be used as indices that track microstructure-mechanics relationships.
The interpretation of some quantitative image parameters is unambiguous. For example, the diame-
ter of collagen fibers or network pores measured manually or algorithmically from SHG images is a
direct assessment of fiber and network structure. The mean SHG signal, on the other hand, is a func-
tion of fiber shape, orientation, image area fraction, bulk gel collagen content, and bulk gel scattering
