# Method for Quantitative Broadband Diffuse Optical Spectroscopy of Tumor-Like Inclusions

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## Abstract

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## Featured Application

**This work describes a new hybrid diffuse optical imaging (DOI) method that extracts broadband optical properties of deep tumor-like inhomogeneities with a simple handheld probe more accurately than the conventional topographic DOI methods. This method is applicable to human breast tumor diagnosis as it can be used to characterize breast lesions by revealing enhanced optical information.**

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hyperspectral Hybrid Frequency-Domain (FD) and Continuous-Wave (CW) Diffuse Optical Imaging DOI

#### 2.2. Simulation Overview

#### 2.3. Tissue-Simulating Phantom Validation

#### 2.3.1. Phantom Composition

#### 2.3.2. Phantom Measurements

## 3. Results

#### 3.1. Simulated Results of Hybrid DOI Method

#### 3.2. Simulated Results of Topographic DOI Method

#### 3.3. Phantom Experimental Results

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Hybrid frequency-domain (FD)- and CW-DOT (Continuous Wave-Diffuse Optical Tomography) method (

**a**) overview and (

**b**) example.

**Figure 3.**Simulated heterogeneous system. Blue circles and red crosses identify sources and detectors, respectively. The gray ellipsoid is the heterogeneity, which was varied in depth.

**Figure 5.**(

**a**) DOS (Diffuse Optical Spectroscopic) handheld imaging probe geometry. (

**b**) Rectangular grid measurement pattern on phantom (7 cm × 7 cm).

**Figure 6.**Ground truth (row 1) versus simulated recovery (row 2) in ${\mu}_{a}$ (650 nm) at different tumor depths (columns).

**Figure 7.**Spatially interpolated topographic DOI recovered absorption at 650 nm with region of interest (ROI) selection for tumor and normal regions.

**Figure 8.**Bar plot representation of ground truth (gray), hybrid DOI, and conventional topographic DOI simulated recovery in ${\mu}_{a}$ at 650 nm for (

**a**) tumor and (

**b**) normal tissue and ${\mu}_{\mathrm{s}}{}^{\prime}$ at 650 nm for (

**c**) tumor and (

**d**) normal tissue.

**Figure 9.**Hyperspectral normal (row 1) and tumor ${\mu}_{a}$ (row 2) at wavelengths 650 nm to 1000 nm at different tumor depths (columns).

**Figure 10.**Hyperspectral normal (row 1) and tumor ${\mu}_{\mathrm{s}}{}^{\prime}$ (row 2) at wavelengths 650 nm to 1000 nm at different tumor depths (columns).

**Figure 11.**Hyperspectral substrate (row 1) and inclusion ${\mu}_{a}$ (row 2) at wavelengths 650 nm to 1000 nm for phantoms A and B.

**Figure 12.**Hyperspectral substrate (row 1) and inclusion ${\mu}_{s}{}^{\prime}$ (row 2) at wavelengths 650 nm to 1000 nm for phantoms A and B.

**Table 1.**Normal versus tumor parameters used for simulations [37].

Parameters | Normal | Tumor |
---|---|---|

Absorbing Chromophores | ||

HbO (µM) | 8.6 | 17.5 |

HHb (µM) | 6.3 | 9.8 |

H_{2}O (%) | 21.8 | 31.3 |

Lipids (%) | 80.6 | 66.3 |

NGB (g/L) | -- | 0.05 |

Scattering Parameters | ||

Scattering amplitude (a) (mm^{−1}) | 2.29 | 3.11 |

Scattering power (b) | 1.2 | 1.5 |

**Table 2.**Difference and percent difference of recovered ${\mu}_{a}$ and ${\mu}_{\mathrm{s}}{}^{\prime}$ from true ${\mu}_{a}$ and ${\mu}_{\mathrm{s}}{}^{\prime}$ at 650 nm.

Depths (mm) | Tumor | |||||||

Hybrid DOI | Topographic DOI | |||||||

$\mathbf{Difference}\mathbf{from}\mathbf{True}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | % Difference of mean from true (%) | Difference from True$\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | % Difference of Mean from True (%) | |||||

${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | |

0 | 4.4 × 10^{−4} ± 6.3 × 10^{−5} | −0.25 ± 7.9 × 10^{−3} | 4.4 | −12.0 | −2.3 × 10^{−3} ± 1.6 × 10^{−5} | −0.08 ± 2.6 × 10^{−3} | −22.6 | −3.9 |

5 | 8.9 × 10^{−4} ± 1.5 × 10^{−4} | −0.49 ± 0.02 | 8.9 | −23.5 | −2.8 × 10^{−3} ± 2.3 × 10^{−5} | −0.32 ± 2.4 × 10^{−3} | −28.0 | −15.3 |

10 | 3.5 × 10^{−4} ± 1.9 × 10^{−4} | −1.3 ± 0.02 | 3.5 | −62.0 | −3.5 × 10^{−3} ± 2.1 × 10^{−5} | −0.38 ± 1.9 × 10^{−3} | −35.2 | −18.2 |

Normal | ||||||||

Hybrid DOI | Topographic DOI | |||||||

$\mathbf{Difference}\mathbf{from}\mathbf{true}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | % Difference of mean from true (%) | Difference from true$\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | % Difference of mean from true (%) | |||||

${\mu}_{a}$ | ${\mu}_{s}{}^{\mathbf{\prime}}$ | ${\mu}_{a}$ | ${\mu}_{s}{}^{\mathbf{\prime}}$ | ${\mu}_{a}$ | ${\mu}_{s}{}^{\mathbf{\prime}}$ | ${\mu}_{a}$ | ${\mu}_{s}{}^{\mathbf{\prime}}$ | |

0 | 1.3 × 10^{−4} ± 5.7 × 10^{−6} | −0.05 ± 1.0 × 10^{−3} | 2.1 | −3.1 | −2.8 × 10^{−4} ± 1.6 × 10^{−5} | 0.07 ± 2.3 × 10^{−3} | −4.5 | 4.2 |

5 | 1.2 × 10^{−4} ± 3.5 × 10^{−6} | −0.05 ± 1.2 × 10^{−3} | 1.9 | −3.0 | −2.9 × 10^{−4} ± 2.2 × 10^{−5} | 0.07 ± 3.5 × 10^{−3} | −4.5 | 4.3 |

10 | 1.1 × 10^{−4} ± 1.2 × 10^{−5} | −0.05 ± 1.5 × 10^{−3} | 1.7 | −2.9 | −2.9 × 10^{−4} ± 1.1 × 10^{−5} | 0.07 ± 1.1 × 10^{−3} | −4.7 | 4.4 |

**Table 3.**Mean difference and mean percentage difference of recovered (${\mu}_{a}$, ${\mu}_{\mathrm{s}}{}^{\prime}$) from true (${\mu}_{a}$, ${\mu}_{\mathrm{s}}{}^{\prime}$) over all wavelengths.

Depths (mm) | Tumor | |||||||

Hybrid DOI | Topographic DOI | |||||||

$\mathbf{Mean}\mathbf{Difference}\mathbf{from}\mathbf{True}\mathbf{Over}\mathbf{all}\mathbf{Wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% Change from True Over all Wavelengths (%) | $\mathbf{Mean}\mathbf{Difference}\mathbf{from}\mathbf{True}\mathbf{Over}\mathbf{all}\mathbf{Wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% Change from True Over all Wavelengths (%) | |||||

${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | |

0 | 3.9 × 10^{−4} | 0.13 | 3.87 | 7.86 | 2.2 × 10^{−3} | 0.03 | 22.35 | 1.78 |

5 | 7.2 × 10^{−4} | 0.25 | 7.49 | 15.34 | 2.6 × 10^{−3} | 0.16 | 26.52 | 10.38 |

10 | 1.2 × 10^{−3} | 0.75 | 8.39 | 47.86 | 3.2 × 10^{−3} | 0.21 | 32.26 | 13.04 |

Normal | ||||||||

Hybrid DOI | Topographic DOI | |||||||

$\mathbf{Mean}\mathbf{difference}\mathbf{from}\mathbf{true}\mathbf{over}\mathbf{all}\mathbf{wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% change from true over all wavelengths (%) | $\mathbf{Mean}\mathbf{difference}\mathbf{from}\mathbf{true}\mathbf{over}\mathbf{all}\mathbf{wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% change from true over all wavelengths (%) | |||||

${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | |

0 | 1.1 × 10^{−4} | 0.03 | 1.64 | 1.9 | 1.9 × 10^{−4} | 0.04 | 3.65 | 3.14 |

5 | 1.0 × 10^{−4} | 0.02 | 1.50 | 1.76 | 2.1 × 10^{−4} | 0.04 | 3.89 | 3.30 |

10 | 1.0 × 10^{−4} | 0.02 | 1.35 | 1.64 | 2.2 × 10^{−4} | 0.04 | 4.10 | 3.37 |

**Table 4.**Mean difference and mean percentage change of recovered (${\mu}_{a}$, ${\mu}_{\mathrm{s}}{}^{\prime}$) from true (${\mu}_{a}$, ${\mu}_{\mathrm{s}}{}^{\prime}$) over all wavelengths for phantom A.

Depths (mm) | Phantom A—Inclusion | |||||||

Hybrid DOI | Topographic DOI | |||||||

$\mathbf{Mean}\mathbf{Difference}\mathbf{from}\mathbf{True}\mathbf{over}\mathbf{All}\mathbf{Wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% Change from True Over all Wavelengths (%) | $\mathbf{Mean}\mathbf{Difference}\mathbf{from}\mathbf{True}\mathbf{over}\mathbf{All}\mathbf{Wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% Change from True Over all Wavelengths (%) | |||||

${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | |

2 | 4.0 × 10^{−4} | 0.03 | 3.65 | 4.99 | 3.3 × 10^{−3} | 0.03 | 25.19 | 4.89 |

7 | 1.0 × 10^{−3} | 0.09 | 8.37 | 15.34 | 5.1 × 10^{−3} | 0.03 | 38.43 | 3.52 |

Phantom A—Substrate | ||||||||

Hybrid DOI | Topographic DOI | |||||||

$\mathbf{Mean}\mathbf{difference}\mathbf{from}\mathbf{true}\mathbf{over}\mathbf{all}\mathbf{wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% change from true over all wavelengths (%) | Mean% change from true over all wavelengths (%) | ||||||

${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | |

2 | 4.6 × 10^{−5} | 0.008 | 1.01 | 0.78 | 3.31 × 10^{−5} | 0.0018 | 0.75 | 0.32 |

7 | 8.1 × 10^{−5} | 0.010 | 1.78 | 1.32 | 3.32 × 10^{−5} | 0.002 | 0.76 | 0.31 |

**Table 5.**Mean difference and mean percentage change of recovered (${\mu}_{a}$, ${\mu}_{\mathrm{s}}{}^{\prime}$) from true (${\mu}_{a}$, ${\mu}_{\mathrm{s}}{}^{\prime}$) over all wavelengths for phantom B.

Depths (mm) | Phantom B—Inclusion | |||||||

Hybrid DOI | Topographic DOI | |||||||

$\mathbf{Mean}\mathbf{Difference}\mathbf{from}\mathbf{True}\mathbf{over}\mathbf{All}\mathbf{Wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% Change from True over All Wavelengths (%) | $\mathbf{Mean}\mathbf{Difference}\mathbf{from}\mathbf{True}\mathbf{over}\mathbf{all}\mathbf{Wavelengths}\mathbf{\left(}{\mathbf{mm}}^{\mathbf{-}\mathbf{1}}\mathbf{\right)}$ | Mean% Change from True over All Wavelengths (%) | |||||

${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | |

2 | 1.8 × 10^{−3} | 0.14 | 13.89 | 13.67 | 1.8 × 10^{−3} | 0.25 | 13.88 | 24.12 |

9 | 1.5 × 10^{−3} | 0.49 | 10.64 | 51.99 | 4.3 × 10^{−3} | 0.43 | 32.05 | 43.49 |

Phantom B—Substrate | ||||||||

Hybrid DOI | Topographic DOI | |||||||

Mean% change from true over all wavelengths (%) | Mean% change from true over all wavelengths (%) | |||||||

${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | ${\mathbf{\mu}}_{\mathit{a}}$ | ${\mathbf{\mu}}_{\mathit{s}}{}^{\mathbf{\prime}}$ | |

2 | 1.8 × 10^{−4} | 0.03 | 2.62 | 5.58 | 1.7 × 10^{−5} | 0.005 | 0.22 | 0.90 |

9 | 1.9 × 10^{−4} | 0.004 | 2.64 | 0.67 | 1.66 × 10^{−5} | 0.0052 | 0.23 | 0.91 |

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**MDPI and ACS Style**

Vasudevan, S.; Forghani, F.; Campbell, C.; Bedford, S.; O’Sullivan, T.D.
Method for Quantitative Broadband Diffuse Optical Spectroscopy of Tumor-Like Inclusions. *Appl. Sci.* **2020**, *10*, 1419.
https://doi.org/10.3390/app10041419

**AMA Style**

Vasudevan S, Forghani F, Campbell C, Bedford S, O’Sullivan TD.
Method for Quantitative Broadband Diffuse Optical Spectroscopy of Tumor-Like Inclusions. *Applied Sciences*. 2020; 10(4):1419.
https://doi.org/10.3390/app10041419

**Chicago/Turabian Style**

Vasudevan, Sandhya, Farnoush Forghani, Chris Campbell, Savannah Bedford, and Thomas D. O’Sullivan.
2020. "Method for Quantitative Broadband Diffuse Optical Spectroscopy of Tumor-Like Inclusions" *Applied Sciences* 10, no. 4: 1419.
https://doi.org/10.3390/app10041419