Biomedical Engineering Reference
In-Depth Information
changes in collagen fiber concentrations (Figure 11.11, SHG versus simulation). For example, SHG signal
intensity is a linear function of collagen concentration (Figure 11.11a, solid line,
m
= 6.8 a.u./mg/mL,
R
2
= 0.78), which is corroborated by the linear relationship between image intensity and concentration
in the simulated images (Figure 11.11a, dashed line,
m
= 6.9 a.u./mg/mL,
R
2
= 1.0).
SHG signal area fraction increases quickly to a plateau near 100% by ~60 mg/mL (Figure 11.11b, solid
markers), and depends upon collagen concentration in a logarithmic fashion (
R
2
= 0.66 for the linear fit
of ln(1-
area fraction
) versus
concentration
). This relationship is confirmed by the simulated signal area
fraction (Figure 11.11b, open markers), which reaches a plateau near 100% by ~100 mg/mL (
R
2
= 0.99 for
the linear fit of ln(1-
area fraction
) versus
concentration
). SHG signal intensity is not instrument indepen-
dent and therefore, without calibration, has little microstructural information to provide, other than the
expected linearity of the signal intensity with collagen concentration. SHG signal area fraction is more
robust to instrument parameters, and suggests that in this experiment, cellularized gels containing
~60 mg/mL collagen contain very few “pores” or void regions with cross-sections larger than a single
pixel (in this study, ~0.2 μm
2
). Therefore, an image analysis algorithm to extract pore information or
image area fraction of the signal will be unhelpful to characterize the range of collagen microstructures
over all gel contraction levels, and other robust image parameters should be sought.
The image parameters such as skewness and speckle contrast (SC) are gain independent and are
thus more robust parameters to potentially characterize the structural features that impact bulk
mechanics. In contrast to the linear intensity and log area fraction dependences, we find that the skew-
ness of the image pixel histograms relates to collagen concentration in SHG images (Figure 11.11c)
with a power-law dependence (SHG, exponent
n
= −0.6,
R
2
= 0.90; simulation,
n
= −0.5,
R
2
= 0.99).
The SC of SHG images (Figure 11.11d, solid markers) and texture simulation images (Figure 11.11d,
(a)
(b)
2000
100
1000
50
Simulation
Simulation
SHG AF
SHG mean
0
0
0 100
Collagen concentration (mg/mL)
200
300
0
100
200
300
Collagen concentration (mg/mL)
(d)
(c)
9
4
Simulation
SHG SC
6
2
Simulation
SHG skew
3
0
0
0 100
Collagen concentration (mg/mL)
200
300
0
100
200
300
Collagen concentration (mg/mL)
FIgurE 11.11
(a) Mean image intensity versus collagen concentration for SHG and texture simulation images.
(b) SHG signal image area fraction versus collagen concentration for SHG and texture simulation images. (c) Mean
image skewness versus collagen concentration for SHG and texture simulation images. (d) Mean speckle contrast
versus collagen concentration for SHG and texture simulation images. SHG values are filled circles; simulation
values are open circles. The data points from SHG data represent an average of five images per gel.
R
2
coefficients
for the linear best fits (a), logarithmic fits (b), and power-law fits (c,d) are given in the text. (Reprinted from
Acta
Biomater,
6, Raub, C. B. et al., Predicting bulk mechanical properties of cellularized collagen gels using multipho-
ton microscopy, 4657-4665. Copyright 2010, with permission from Elsevier.)
