# Quantification of Tumor Hypoxia through Unsupervised Modelling of Consumption and Supply Hypoxia MR Imaging in Breast Cancer

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Cohort

#### 2.2. Molecular Hypoxia Reference Standard

#### 2.3. MRI Examination

#### 2.4. Image Analysis

#### 2.5. Validation Cohort

#### 2.6. Statistical Analysis

## 3. Results

#### 3.1. Molecular Hypoxia Score

#### 3.2. Individual IVIM Parameters and Buffa Hypoxia Score

#### 3.3. CSH Imaging in Breast Cancer

#### 3.4. Validation in a Prostate Cohort

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Overview of the steps involved in calculating hypoxia from DWI images. IVIM; Intra voxel incoherent motion.

**Figure 2.**Examples of $ADC$ and ${f}_{p}$ maps in two patients. One with a high molecular hypoxia score ($H{S}_{mol}$) (

**A**) and one with a low $H{S}_{mol}$ (

**B**). The median $ADC$ and ${f}_{p}$ for all tumors with a low $H{S}_{mol}$ are shown against the tumors with a high $H{S}_{mol}$ in (

**C**).

**Figure 3.**The distribution of $ADC$ and ${f}_{p}$ for all voxels in the 3D breast tumor volumes, together with the corresponding distributions from the prostate cohort from Hompland et al. [7]. Median $ADC$ and ${f}_{p}$ in the breast cancer tumors were $1.06\times {10}^{-3}$ mm${}^{2}$/s and $0.12$ respectively, compared to $0.7\times {10}^{-3}$ mm${}^{2}$/s and $0.13$ in prostate cancer [7].

**Figure 4.**Two different linear decision boundaries (LDB) in a breast cancer patient (

**A**). Boundary 1 (upper row) is the same LDB as Hompland et al. found to be optimal in prostate cancer. Boundary 2 (lower row) is the LDB that gives the best results in the breast cancer cohort. The difference in calculated hypoxic fraction between more hypoxic and less hypoxic tumors, using the same two LDBs shown in A (

**B**). Mann-Whitney p-values calculated using a range of different decision boundaries (

**C**).

**Figure 5.**CSH hypoxia maps of the same two patients as shown in Figure 2; one patient with a high molecular hypoxia score $H{S}_{mol}=0.33$ (

**left**), and one with a low molecular hypoxia score $H{S}_{mol}=-0.23$ (

**right**).

**Figure 6.**Three different ways of estimating hypoxia in breast cancer using the CSH method. $H{F}_{LDB,1}$ is hypoxic fraction, calculated using the same model, with the same model-parameters as Hompland et al. used in prostate cancer. $H{F}_{LDB,2}$ is hypoxic fraction calculated using the Hompland model, but with adapted model parameters, and median $H{S}_{Euclidean}$ is the median hypoxia score, calculated by Equation (5). Area under the reciever operateor characteristic curves for all three approaches are shown to the right.

**Figure 7.**Mann-Whitney p-value (blue) for hypoxia stratification thresholds ranging from $H{S}_{mol}=-0.4$ to $H{S}_{mol}=0.6$. The resulting fractions of patient stratified as hypoxic for the thresholds are displayed in red.

**Figure 8.**The Mann-Whitney p-values from comparisons of the hypoxic fraction (HF), as calculated using a range of linear decision boundaries, with the molecular hypoxia score ($H{S}_{mol}$) (

**A**). The region surrounded by the black, dotted line is indicating the model coefficients (${f}_{p,0}$ and $AD{C}_{0}$) that gives the strongest correlation to $H{S}_{mol}$ ($p<0.005$). The difference in HF calculated using the novel, unsupervised method and linear decision boundary models (

**B**) is minimal for values of ${f}_{p,0}$ and $AD{C}_{0}$ that are largely overlapping those that gives the best decision boundary.

**Figure 9.**Hypoxic fractions in prostate cancer calculated using the original linear decision boundary($H{F}_{LDB}$) from Hompland et al., and the hypoxic fraction calculated using the unsupervised (Euclidean) method ($H{F}_{Euclidean}$) (

**A**). Area under the reciever operating characteristic curve for the two methods (

**B**).

Characteristic | All N (%) | More Hypoxic * | Less Hypoxic * | Adjusted p |
---|---|---|---|---|

Patients | 69 | 34 | 45 | |

Age (years) | ||||

Mean | 49.3 | 50.3 | 48.3 | 1.00 (MW) |

Median | 49 | 50 | 48 | |

Range | 30–70 | 39–64 | 30-70 | |

Clinical tumor stage | 0.67 (ANOVA) | |||

T2 | 21 (30.4) | 8 (23.5) | 13 (37.1) | |

T3 | 44 (63.8) | 25 (73.5) | 19 (54.3) | |

T4 | 4 (5.8) | 1 (2.9) | 3 (8.6) | |

Tumor volume (mean cm${}^{3}$) | 21.4 | 22.9 | 19.9 | 0.70 (MW) |

Lymph node status ** | 1.00 (ANOVA) | |||

cN0 | 35 (50.7) | 18 (52.9) | 17 (48.6) | |

cN1 | 6 (8.7) | 2 (5.9) | 4 (11.4) | |

pN1 | 28 (40.6) | 14 (41.2) | 14 (40.0) | |

Type | 0.02 (Fisher exact) | |||

IDC | 55 (79.7) | 22 (64.7) | 33 (94.3) | |

ILC | 14 (20.3) | 12 (35.3) | 2 (5.7) | |

Grade | 0.12 (ANOVA) | |||

1 | 5 (7.2) | 3 (8.8) | 2 (5.7) | |

2 | 50 (72.5) | 28 (82.4) | 22 (62.9) | |

3 | 13 (18.8) | 2 (5.9) | 11 (31.4) | |

N/A | 1 (1.4) | 1 (2.9) | 0 (0.0) | |

ER status | 0.63 (ANOVA) | |||

Positive | 58 (84.1) | 33 (97.1) | 25 (71.4) | |

Negative | 11 (15.9) | 1 (2.1) | 10 (28.6) |

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## Share and Cite

**MDPI and ACS Style**

Mo, T.; Brandal, S.H.B.; Köhn-Luque, A.; Engebraaten, O.; Kristensen, V.N.; Fleischer, T.; Hompland, T.; Seierstad, T.
Quantification of Tumor Hypoxia through Unsupervised Modelling of Consumption and Supply Hypoxia MR Imaging in Breast Cancer. *Cancers* **2022**, *14*, 1326.
https://doi.org/10.3390/cancers14051326

**AMA Style**

Mo T, Brandal SHB, Köhn-Luque A, Engebraaten O, Kristensen VN, Fleischer T, Hompland T, Seierstad T.
Quantification of Tumor Hypoxia through Unsupervised Modelling of Consumption and Supply Hypoxia MR Imaging in Breast Cancer. *Cancers*. 2022; 14(5):1326.
https://doi.org/10.3390/cancers14051326

**Chicago/Turabian Style**

Mo, Torgeir, Siri Helene Bertelsen Brandal, Alvaro Köhn-Luque, Olav Engebraaten, Vessela N. Kristensen, Thomas Fleischer, Tord Hompland, and Therese Seierstad.
2022. "Quantification of Tumor Hypoxia through Unsupervised Modelling of Consumption and Supply Hypoxia MR Imaging in Breast Cancer" *Cancers* 14, no. 5: 1326.
https://doi.org/10.3390/cancers14051326