Polydimethylsiloxane tissue-mimicking phantoms with tunable optical properties

Abstract

Significance: The polymer, polydimethylsiloxane (PDMS), has been increasingly used to make tissue simulating phantoms due to its excellent processability, durability, flexibility, and limited tunability of optical, mechanical, and thermal properties. We report on a robust technique to fabricate PDMS-based tissue-mimicking phantoms where the broad range of scattering and absorption properties are independently adjustable in the visible- to near-infrared wavelength range from 500 to 850 nm. We also report on an analysis method to concisely quantify the phantoms' broadband characteristics with four parameters.

Aim: We report on techniques to manufacture and characterize solid tissue-mimicking phantoms of PDMS polymers. Tunability of the absorption (μa ( λ ) ) and reduced scattering coefficient spectra (μs'(λ)) in the wavelength range of 500 to 850 nm is demonstrated by adjusting the concentrations of light absorbing carbon black powder (CBP) and light scattering titanium dioxide powder (TDP) added into the PDMS base material.

Approach: The μa ( λ ) and μs'(λ) of the phantoms were obtained through measurements with a broadband integrating sphere system and by applying an inverse adding doubling algorithm. Analyses of μa ( λ ) and μs'(λ) of the phantoms, by fitting them to linear and power law functions, respectively, demonstrate that independent control of μa ( λ ) and μs'(λ) is possible by systematically varying the concentrations of CBP and TDP.

Results: Our technique quantifies the phantoms with four simple fitting parameters enabling a concise tabulation of their broadband optical properties as well as comparisons to the optical properties of biological tissues. We demonstrate that, to a limited extent, the scattering properties of our phantoms mimic those of human tissues of various types. A possible way to overcome this limitation is demonstrated with phantoms that incorporate polystyrene microbead scatterers.

Conclusions: Our manufacturing and analysis techniques may further promote the application of PDMS-based tissue-mimicking phantoms and may enable robust quality control and quality checks of the phantoms.

Keywords: absorption coefficient spectrum; integrating sphere; polydimethylsiloxane; scattering coefficient spectrum; tissue-mimicking phantom.

Fig. 1

A step-by-step phantom fabrication procedure.

Fig. 2

PDMS phantoms. (a) A set of PDMS samples with various concentration combinations of TDP and CBP. The diameter of each sample is 87.0 mm. (b) A 3D plot of the mass ratio percentages of TDP (cyan) and CBP (gray) with respect to PDMS, respectively, for the samples shown in (a). The numbers shown are actual mass ratio percentages of the additives in each sample.

Fig. 3

Optical properties of the phantoms. (a) Absorption and (b) scattering coefficients of the phantoms with both TDP and CBP at various concentration combinations across the wavelength range of 500 to 850 nm. The numbers labeling each curve are the concentrations (% w/w) of TDP and CBP, respectively. (c), (d) The coefficient of variation of the absorption and scattering coefficients of each sample. The curve for each sample is plotted using the same color scheme as in (a) and (b). (e) Absorption and (f) reduced scattering coefficients at 700 nm versus the concentration of CBP and TDP, respectively, demonstrating that both coefficients depend linearly on the concentration of the corresponding additive. Note that high CODs confirm excellent linear fit for both cases. Other details of the fitting results are listed as well. The inset of (e) shows the absorption coefficient at low absorber concentration. In (a), (b), (e), and (f), the plotted uncertainties [shaded areas in (a) and (b) and the bars in (e) and (f)] for the coverage factor $k=1$ are calculated as described in Sec. 2.

Fig. 4

Analyses of the absorption and reduced scattering spectra. (a) An absorption coefficient spectrum ${\mu }_a(\lambda )$ for a phantom containing scattering TDP and absorbing CBP with concentrations of 0.1% and 0.0055% (w/w), respectively, and fit to a wavelength-dependent linear function, ${\mu }_a(\lambda )=c·\lambda +d$. The gray area represents an uncertainty bound ($k=1$) of experimental data. (b), (c) Plots of the fitted parameters $(a,b,c,d)$ versus CBP concentration. (d) A reduced scattering coefficient ${\mu }_s^{\prime }(\lambda )$ for the same sample as in (a) and fit to a wavelength-dependent power law function, ${\mu }_s^{\prime }(\lambda )=a{(\lambda /500)}^{-b}$. The gray area represents an uncertainty bound ($k=1$) of the experimental data. (e), (f) Fit parameters ($a$, $b$, $c$, and $d$) versus TDP concentration (e) and (f). In (b) and (e), linear fits to the parameters $d$ and $a$, respectively, are shown along with slopes and CODs of the linear fits.

Fig. 5

Comparison of the optical properties of phantoms versus human tissue. A plot of $b$ versus $a$ for human tissues and PDMS phantoms, where the parameters $a$ and $b$ are defined in Eq. (2). The $a$ and $b$ parameters for tissues are taken from Jacques (Ref. 1). The inset shows the same parameters for PDMS phantoms with CBP and TDP (round dots) and three PDMS phantoms with varying concentrations of TDP and PS beads (“x” marks). The vertical bars represent uncertainty bounds ($k=1$), although in most cases the plotted uncertainty is smaller than the point size.