# Quantifying the Growth of Glioblastoma Tumors Using Multimodal MRI Brain Images

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## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Information

#### 2.2. Preprocessing and Image Segmentation

#### 2.3. Quantification of the Tumor Growth Prediction

#### 2.4. Bayesian Regression of the Eventual Volume for Other Radiomic Features

#### 2.5. Handling the Heterogeneity among Oncogenes

## 3. Results

#### 3.1. Simulation Study

#### 3.2. Real Data Analysis: Canonical Measurement Metrics

#### 3.3. Real Data Analysis: Prediction of the Eventual Volume of GBM

#### 3.4. Real Data Analysis: Outcome of the Bayesian Regression Model

## 4. Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

GBM | Glioblastoma Multiforme |

ROIs | Regions of Interest |

ET | GD-Enhancing Tumor |

TC | Tumor core |

WT | Whole Tumor |

ED | Edema |

NET | Non-Enhancing Tumor |

## Appendix A. Background behind Deriving the Model

## Appendix B. The Probability Model

**Lemma**

**A1**.

## Appendix C. Finding the Likelihood Function

## Appendix D. Choice of Prior and Posterior

## Appendix E. Canonical Measurement Metrics—Correlation Plots

**Figure A1.**Correlation between volume and spatial features of brain for the region ET. * p < 0.05, ** p < 0.01, *** p < 0.001.

**Figure A2.**Correlation between volume and spatial features of brain for the region NET. * p < 0.05, ** p < 0.01, *** p < 0.001.

**Figure A3.**Correlation between volume and spatial features of brain for the region TC. * p < 0.05, ** p < 0.01, *** p < 0.001.

**Figure A4.**Correlation between volume and spatial features of brain for the region WT. * p < 0.05, ** p < 0.01, *** p < 0.001.

**Figure A5.**Correlation between volume and histology features of brain for the region ET. * p < 0.05, *** p < 0.001.

**Figure A6.**Correlation between volume and histology features of brain for the region NET. * p < 0.05, ** p < 0.01.

**Figure A7.**Correlation between histology and spatial features of brain for the region ET. * p < 0.05, ** p < 0.01, *** p < 0.001.

**Figure A8.**Correlation between histology and spatial features of brain for the region NET. * p < 0.05, ** p < 0.01, *** p < 0.001.

## References

- Marini, B.L.; Benitez, L.L.; Zureick, A.H.; Salloum, R.; Gauthier, A.C.; Brown, J.; Wu, Y.M.; Robinson, D.R.; Kumar, C.; Lonigro, R.; et al. Blood-brain barrier–adapted precision medicine therapy for pediatric brain tumors. Transl. Res.
**2017**, 188, 27.e1–27.e14. [Google Scholar] [CrossRef] [PubMed] - Stallard, S.; Savelieff, M.G.; Wierzbicki, K.; Mullan, B.; Miklja, Z.; Bruzek, A.; Garcia, T.; Siada, R.; Anderson, B.; Singer, B.H.; et al. CSF H3F3A K27M circulating tumor DNA copy number quantifies tumor growth and in vitro treatment response. Acta Neuropathol. Commun.
**2018**, 6, 80. [Google Scholar] [CrossRef] [PubMed] - Vermeulen, P.; Gasparini, G.; Fox, S.; Toi, M.; Martin, L.; McCulloch, P.; Pezzella, F.; Viale, G.; Weidner, N.; Harris, A.; et al. Quantification of angiogenesis in solid human tumours: An international consensus on the methodology and criteria of evaluation. Eur. J. Cancer
**1996**, 32, 2474–2484. [Google Scholar] [CrossRef] [PubMed] - Vermeulen, P.; Gasparini, G.; Fox, S.; Colpaert, C.; Marson, L.; Gion, M.; Beliën, J.; De Waal, R.; Van Marck, E.; Magnani, E.; et al. Second international consensus on the methodology and criteria of evaluation of angiogenesis quantification in solid human tumours. Eur. J. Cancer
**2002**, 38, 1564–1579. [Google Scholar] [CrossRef] [PubMed] - Linzey, J.R.; Marini, B.L.; Pasternak, A.; Smith, C.; Miklja, Z.; Zhao, L.; Kumar-Sinha, C.; Paul, A.; Harris, N.; Robertson, P.L.; et al. Development of the CNS TAP tool for the selection of precision medicine therapies in neuro-oncology. J. Neuro-Oncol.
**2018**, 137, 155–169. [Google Scholar] [CrossRef] [PubMed] - Hieber, S.E.; Bikis, C.; Khimchenko, A.; Schweighauser, G.; Hench, J.; Chicherova, N.; Schulz, G.; Müller, B. Tomographic brain imaging with nucleolar detail and automatic cell counting. Sci. Rep.
**2016**, 6, 32156. [Google Scholar] [CrossRef] [Green Version] - Heuvelmans, M.A.; Vliegenthart, R.; de Koning, H.J.; Groen, H.J.; van Putten, M.J.; Yousaf-Khan, U.; Weenink, C.; Nackaerts, K.; de Jong, P.A.; Oudkerk, M. Quantification of growth patterns of screen-detected lung cancers: The NELSON study. Lung Cancer
**2017**, 108, 48–54. [Google Scholar] [CrossRef] [Green Version] - Kipps, C.; Hodges, J.; Fryer, T.; Nestor, P. Combined magnetic resonance imaging and positron emission tomography brain imaging in behavioural variant frontotemporal degeneration: Refining the clinical phenotype. Brain
**2009**, 132, 2566–2578. [Google Scholar] [CrossRef] [Green Version] - Studholme, C.; Hill, D.L.; Hawkes, D.J. Automated three-dimensional registration of magnetic resonance and positron emission tomography brain images by multiresolution optimization of voxel similarity measures. Med. Phys.
**1997**, 24, 25–35. [Google Scholar] [CrossRef] [Green Version] - Chaddad, A.; Kucharczyk, M.J.; Daniel, P.; Sabri, S.; Jean-Claude, B.J.; Niazi, T.; Abdulkarim, B. Radiomics in glioblastoma: Current status and challenges facing clinical implementation. Front. Oncol.
**2019**, 9, 374. [Google Scholar] [CrossRef] [Green Version] - Chen, J.; Han, P.; Dahiya, S. Glioblastoma: Changing concepts in the WHO CNS5 classification. Indian J. Pathol. Microbiol.
**2022**, 65, 24. [Google Scholar] - Ohgaki, H.; Kleihues, P. Epidemiology and etiology of gliomas. Acta Neuropathol.
**2005**, 109, 93–108. [Google Scholar] [CrossRef] [PubMed] - Appin, C.L.; Brat, D.J. Biomarker-driven diagnosis of diffuse gliomas. Mol. Asp. Med.
**2015**, 45, 87–96. [Google Scholar] [CrossRef] [PubMed] - Kabat, G.C.; Etgen, A.M.; Rohan, T.E. Do Steroid Hormones Play a Role in the Etiology of Glioma? Steroid Hormones and Glioma. Cancer Epidemiol. Biomarkers Prev.
**2010**, 19, 2421–2427. [Google Scholar] [CrossRef] [Green Version] - Wang, J.; Yao, L.; Zhao, S.; Zhang, X.; Yin, J.; Zhang, Y.; Chen, X.; Gao, M.; Ling, E.A.; Hao, A.; et al. Granulocyte-colony stimulating factor promotes proliferation, migration and invasion in glioma cells. Cancer Biol. Ther.
**2012**, 13, 389–400. [Google Scholar] [CrossRef] [Green Version] - Dolacek, T.; Propp, J.; Stroup, N. CBTRUS statistical report: Primary brain and central nervous system tumors diagnosed in the United States in 2006–2010. Neuro-Oncology
**2012**, 14, v1-49. [Google Scholar] [CrossRef] [Green Version] - Yuan, J.X.; Bafakih, F.F.; Mandell, J.W.; Horton, B.J.; Munson, J.M. Quantitative analysis of the cellular microenvironment of glioblastoma to develop predictive statistical models of overall survival. J. Neuropathol. Exp. Neurol.
**2016**, 75, 1110–1123. [Google Scholar] [CrossRef] [Green Version] - Urbańska, K.; Sokołowska, J.; Szmidt, M.; Sysa, P. Glioblastoma multiforme—An overview. Contemp. Oncol. Onkol.
**2014**, 18, 307–312. [Google Scholar] - Karcher, S.; Steiner, H.H.; Ahmadi, R.; Zoubaa, S.; Vasvari, G.; Bauer, H.; Unterberg, A.; Herold-Mende, C. Different angiogenic phenotypes in primary and secondary glioblastomas. Int. J. Cancer
**2006**, 118, 2182–2189. [Google Scholar] [CrossRef] - Rockne, R.; Rockhill, J.; Mrugala, M.; Spence, A.; Kalet, I.; Hendrickson, K.; Lai, A.; Cloughesy, T.; Alvord, E.; Swanson, K. Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: A mathematical modeling approach. Phys. Med. Biol.
**2010**, 55, 3271. [Google Scholar] [CrossRef] [Green Version] - Stensjøen, A.L.; Solheim, O.; Kvistad, K.A.; Håberg, A.K.; Salvesen, Ø.; Berntsen, E.M. Growth dynamics of untreated glioblastomas in vivo. Neuro-Oncology
**2015**, 17, 1402–1411. [Google Scholar] [CrossRef] [Green Version] - Kong, D.S.; Kim, J.; Ryu, G.; You, H.J.; Sung, J.K.; Han, Y.H.; Shin, H.M.; Lee, I.H.; Kim, S.T.; Park, C.K.; et al. Quantitative radiomic profiling of glioblastoma represents transcriptomic expression. Oncotarget
**2018**, 9, 6336. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kickingereder, P.; Burth, S.; Wick, A.; Götz, M.; Eidel, O.; Schlemmer, H.P.; Maier-Hein, K.H.; Wick, W.; Bendszus, M.; Radbruch, A.; et al. Radiomic profiling of glioblastoma: Identifying an imaging predictor of patient survival with improved performance over established clinical and radiologic risk models. Radiology
**2016**, 280, 880–889. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, B.; Tian, J.; Dong, D.; Gu, D.; Dong, Y.; Zhang, L.; Lian, Z.; Liu, J.; Luo, X.; Pei, S.; et al. Radiomics Features of Multiparametric MRI as Novel Prognostic Factors in Advanced Nasopharyngeal CarcinomaPretreatment Radiomics for Nasopharyngeal Carcinoma. Clin. Cancer Res.
**2017**, 23, 4259–4269. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rathore, S.; Akbari, H.; Rozycki, M.; Abdullah, K.G.; Nasrallah, M.P.; Binder, Z.A.; Davuluri, R.V.; Lustig, R.A.; Dahmane, N.; Bilello, M.; et al. Radiomic MRI signature reveals three distinct subtypes of glioblastoma with different clinical and molecular characteristics, offering prognostic value beyond IDH1. Sci. Rep.
**2018**, 8, 5087. [Google Scholar] [CrossRef] [Green Version] - Wang, S.; Martinez-Lage, M.; Sakai, Y.; Chawla, S.; Kim, S.; Alonso-Basanta, M.; Lustig, R.; Brem, S.; Mohan, S.; Wolf, R.; et al. Differentiating tumor progression from pseudoprogression in patients with glioblastomas using diffusion tensor imaging and dynamic susceptibility contrast MRI. Am. J. Neuroradiol.
**2016**, 37, 28–36. [Google Scholar] [CrossRef] [Green Version] - Liu, Y.; Xu, X.; Yin, L.; Zhang, X.; Li, L.; Lu, H. Relationship between glioblastoma heterogeneity and survival time: An MR imaging texture analysis. Am. J. Neuroradiol.
**2017**, 38, 1695–1701. [Google Scholar] [CrossRef] [Green Version] - Chow, D.; Chang, P.; Weinberg, B.D.; Bota, D.A.; Grinband, J.; Filippi, C.G. Imaging Genetic Heterogeneity in Glioblastoma and Other Glial Tumors: Review of Current Methods and Future Directions. AJR. Am. J. Roentgenol.
**2018**, 210, 30–38. [Google Scholar] [CrossRef] - Mazurowski, M.A.; Clark, K.; Czarnek, N.M.; Shamsesfandabadi, P.; Peters, K.B.; Saha, A. Radiogenomics of lower-grade glioma: Algorithmically-assessed tumor shape is associated with tumor genomic subtypes and patient outcomes in a multi-institutional study with The Cancer Genome Atlas data. J. Neuro-Oncol.
**2017**, 133, 27–35. [Google Scholar] [CrossRef] - Liang, S.; Zhang, R.; Liang, D.; Song, T.; Ai, T.; Xia, C.; Xia, L.; Wang, Y. Multimodal 3D DenseNet for IDH genotype prediction in gliomas. Genes
**2018**, 9, 382. [Google Scholar] [CrossRef] [Green Version] - Eichinger, P.; Alberts, E.; Delbridge, C.; Trebeschi, S.; Valentinitsch, A.; Bette, S.; Huber, T.; Gempt, J.; Meyer, B.; Schlegel, J.; et al. Diffusion tensor image features predict IDH genotype in newly diagnosed WHO grade II/III gliomas. Sci. Rep.
**2017**, 7, 13396. [Google Scholar] [CrossRef] [Green Version] - Delfanti, R.L.; Piccioni, D.E.; Handwerker, J.; Bahrami, N.; Krishnan, A.; Karunamuni, R.; Hattangadi-Gluth, J.A.; Seibert, T.M.; Srikant, A.; Jones, K.A.; et al. Imaging correlates for the 2016 update on WHO classification of grade II/III gliomas: Implications for IDH, 1p/19q and ATRX status. J. Neuro-Oncol.
**2017**, 135, 601–609. [Google Scholar] [CrossRef] [Green Version] - Hong, E.K.; Choi, S.H.; Shin, D.J.; Jo, S.W.; Yoo, R.E.; Kang, K.M.; Yun, T.J.; Kim, J.H.; Sohn, C.H.; Park, S.H.; et al. Radiogenomics correlation between MR imaging features and major genetic profiles in glioblastoma. Eur. Radiol.
**2018**, 28, 4350–4361. [Google Scholar] [CrossRef] [PubMed] - Scherer, H. Cerebral astrocytomas and their derivatives. Am. J. Cancer
**1940**, 40, 159–198. [Google Scholar] - Kros, J.M.; van Run, P.R.; Alers, J.C.; Avezaat, C.J.; Luider, T.M.; van Dekken, H. Spatial variability of genomic aberrations in a large glioblastoma resection specimen. Acta Neuropathol.
**2001**, 102, 103–109. [Google Scholar] [CrossRef] [PubMed] - Woodworth, G.F.; McGirt, M.J.; Samdani, A.; Garonzik, I.; Olivi, A.; Weingart, J.D. Frameless image-guided stereotactic brain biopsy procedure: Diagnostic yield, surgical morbidity, and comparison with the frame-based technique. J. Neurosurg.
**2006**, 104, 233–237. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Steinmetz, M.P.; Barnett, G.H.; Kim, B.S.; Chidel, M.A.; Suh, J.H. Metastatic seeding of the stereotactic biopsy tract in glioblastoma multiforme: Case report and review of the literature. J. Neuro-Oncol.
**2001**, 55, 167–171. [Google Scholar] [CrossRef] - Perrin, R.G.; Bernstein, M. Iatrogenic seeding of anaplastic astrocytoma following stereotactic biopsy. J. Neuro-Oncol.
**1998**, 36, 243–246. [Google Scholar] [CrossRef] - Zinn, P.O.; Singh, S.K.; Kotrotsou, A.; Hassan, I.; Thomas, G.; Luedi, M.M.; Elakkad, A.; Elshafeey, N.; Idris, T.; Mosley, J.; et al. A Coclinical Radiogenomic Validation Study: Conserved Magnetic Resonance Radiomic Appearance of Periostin-Expressing Glioblastoma in Patients and Xenograft ModelsValidation of Radiomics and Radiogenomics. Clin. Cancer Res.
**2018**, 24, 6288–6299. [Google Scholar] [CrossRef] [Green Version] - Bakas, S.; Akbari, H.; Sotiras, A.; Bilello, M.; Rozycki, M.; Kirby, J.S.; Freymann, J.B.; Farahani, K.; Davatzikos, C. Advancing the cancer genome atlas glioma MRI collections with expert segmentation labels and radiomic features. Sci. Data
**2017**, 4, 170117. [Google Scholar] [CrossRef] [Green Version] - Lu, C.F.; Hsu, F.T.; Hsieh, K.L.C.; Kao, Y.C.J.; Cheng, S.J.; Hsu, J.B.K.; Tsai, P.H.; Chen, R.J.; Huang, C.C.; Yen, Y.; et al. Machine Learning—Based Radiomics for Molecular Subtyping of GliomasMachine Learning for Molecular Subtyping of Gliomas. Clin. Cancer Res.
**2018**, 24, 4429–4436. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chaddad, A.; Desrosiers, C.; Hassan, L.; Tanougast, C. A quantitative study of shape descriptors from glioblastoma multiforme phenotypes for predicting survival outcome. Br. J. Radiol.
**2016**, 89, 20160575. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jenkinson, M.; Smith, S. A global optimisation method for robust affine registration of brain images. Med. Image Anal.
**2001**, 5, 143–156. [Google Scholar] [CrossRef] - Jenkinson, M.; Bannister, P.; Brady, M.; Smith, S. Improved optimization for the robust and accurate linear registration and motion correction of brain images. Neuroimage
**2002**, 17, 825–841. [Google Scholar] [CrossRef] [PubMed] - Smith, S.M.; Jenkinson, M.; Woolrich, M.W.; Beckmann, C.F.; Behrens, T.E.; Johansen-Berg, H.; Bannister, P.R.; De Luca, M.; Drobnjak, I.; Flitney, D.E.; et al. Advances in functional and structural MR image analysis and implementation as FSL. Neuroimage
**2004**, 23, S208–S219. [Google Scholar] [CrossRef] [Green Version] - Woolrich, M.W.; Jbabdi, S.; Patenaude, B.; Chappell, M.; Makni, S.; Behrens, T.; Beckmann, C.; Jenkinson, M.; Smith, S.M. Bayesian analysis of neuroimaging data in FSL. Neuroimage
**2009**, 45, S173–S186. [Google Scholar] [CrossRef] - Jenkinson, M.; Beckmann, C.F.; Behrens, T.E.; Woolrich, M.W.; Smith, S.M. Fsl. Neuroimage
**2012**, 62, 782–790. [Google Scholar] [CrossRef] [Green Version] - Dessai, V.S.; Arakeri, M.P.; Reddy, G.R.M. A parallel segmentation of brain tumor from magnetic resonance images. In Proceedings of the 2012 Third International Conference on Computing, Communication and Networking Technologies (ICCCNT’12), Bangalore, India, 3–7 January 2012; pp. 1–6. [Google Scholar]
- Max, J. Quantizing for minimum distortion. IRE Trans. Inf. Theory
**1960**, 6, 7–12. [Google Scholar] [CrossRef] - Lloyd, S. Least squares quantization in PCM. IEEE Trans. Inf. Theory
**1982**, 28, 129–137. [Google Scholar] [CrossRef] [Green Version] - Li, Q.; Griffiths, J.G. Least squares ellipsoid specific fitting. In Proceedings of the Geometric Modeling and Processing, Beijing, China, 13–15 April 2004; pp. 335–340. [Google Scholar]
- Thibault, G.; Fertil, B.; Navarro, C.; Pereira, S.; Cau, P.; Levy, N.; Sequeira, J.; Mari, J.L. Shape and texture indexes application to cell nuclei classification. Int. J. Pattern Recognit. Artif. Intell.
**2013**, 27, 1357002. [Google Scholar] [CrossRef] - Macyszyn, L.; Akbari, H.; Pisapia, J.M.; Da, X.; Attiah, M.; Pigrish, V.; Bi, Y.; Pal, S.; Davuluri, R.V.; Roccograndi, L.; et al. Imaging patterns predict patient survival and molecular subtype in glioblastoma via machine learning techniques. Neuro-Oncology
**2015**, 18, 417–425. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Collewet, G.; Strzelecki, M.; Mariette, F. Influence of MRI acquisition protocols and image intensity normalization methods on texture classification. Magn. Reson. Imaging
**2004**, 22, 81–91. [Google Scholar] [CrossRef] [PubMed] - Haralick, R.M.; Shanmugam, K.; Dinstein, I.H. Textural features for image classification. IEEE Trans. Syst. Man. Cybern.
**1973**, SMC-3, 610–621. [Google Scholar] [CrossRef] [Green Version] - Galloway, M.M. Texture analysis using gray level run lengths. Comput. Graph. Image Process.
**1975**, 4, 172–179. [Google Scholar] [CrossRef] - Chu, A.; Sehgal, C.M.; Greenleaf, J.F. Use of gray value distribution of run lengths for texture analysis. Pattern Recognit. Lett.
**1990**, 11, 415–419. [Google Scholar] [CrossRef] - Dasarathy, B.V.; Holder, E.B. Image characterizations based on joint gray level—Run length distributions. Pattern Recognit. Lett.
**1991**, 12, 497–502. [Google Scholar] [CrossRef] - Tang, X. Texture information in run-length matrices. IEEE Trans. Image Process.
**1998**, 7, 1602–1609. [Google Scholar] [CrossRef] [Green Version] - Thibault, G. Indices de Forme et de Texture: De la 2D vers la 3D: Application au Classement de Noyaux de Cellules. Ph.D. Thesis, Aix-Marseille 2, Marseille, France, 2009. [Google Scholar]
- Amadasun, M.; King, R. Textural features corresponding to textural properties. IEEE Trans. Syst. Man Cybern.
**1989**, 19, 1264–1274. [Google Scholar] [CrossRef] - Bilello, M.; Akbari, H.; Da, X.; Pisapia, J.M.; Mohan, S.; Wolf, R.L.; O’Rourke, D.M.; Martinez-Lage, M.; Davatzikos, C. Population-based MRI atlases of spatial distribution are specific to patient and tumor characteristics in glioblastoma. NeuroImage Clin.
**2016**, 12, 34–40. [Google Scholar] [CrossRef] [Green Version] - Hogea, C.; Biros, G.; Abraham, F.; Davatzikos, C. A robust framework for soft tissue simulations with application to modeling brain tumor mass effect in 3D MR images. Phys. Med. Biol.
**2007**, 52, 6893. [Google Scholar] [CrossRef] - Hogea, C.; Davatzikos, C.; Biros, G. Brain—Tumor interaction biophysical models for medical image registration. SIAM J. Sci. Comput.
**2008**, 30, 3050–3072. [Google Scholar] [CrossRef] [Green Version] - Hogea, C.; Davatzikos, C.; Biros, G. An image-driven parameter estimation problem for a reaction—Diffusion glioma growth model with mass effects. J. Math. Biol.
**2008**, 56, 793–825. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Binder, Z.; Bakas, S.; Wileyto, E.; Akbari, H.; Rathore, S.; Rozycki, M.; Morrissette, J.; Martinez-Lage, M.; Dahmane, N.; Davatzikos, C.; et al. Extracellular EGFR289 activating mutations confer poorer survival and exhibit radiographic signature of enhanced motility in primary glioblastoma. Neuro-Oncology
**2016**, 18, vi105–vi106. [Google Scholar] [CrossRef] [Green Version] - Rathore, S.; Akbari, H.; Rozycki, M.; Bakas, S.; Davatzikos, C. NIMG-20. Imaging Pattern Analysis Reveals Three Distinct Phenotypic Subtypes of gbm with Different Survival Rates; Oxford University Press: Oxford, MI, USA, 2016. [Google Scholar]
- Assefa, D.; Keller, H.; Ménard, C.; Laperriere, N.; Ferrari, R.J.; Yeung, I. Robust texture features for response monitoring of glioblastoma multiforme on-weighted and-FLAIR MR images: A preliminary investigation in terms of identification and segmentation. Med. Phys.
**2010**, 37, 1722–1736. [Google Scholar] [CrossRef] - Aerts, H.J.; Velazquez, E.R.; Leijenaar, R.T.; Parmar, C.; Grossmann, P.; Carvalho, S.; Bussink, J.; Monshouwer, R.; Haibe-Kains, B.; Rietveld, D.; et al. Decoding tumour phenotype by noninvasive imaging using a quantitative radiomics approach. Nat. Commun.
**2014**, 5, 4006. [Google Scholar] [CrossRef] [Green Version] - Bakas, S.; Akbari, H.; Sotiras, A.; Bilello, M.; Rozycki, M.; Kirby, J.; Freymann, J.; Farahani, K.; Davatzikos, C. Segmentation labels and radiomic features for the pre-operative scans of the TCGA-GBM collection. Cancer Imaging Arch.
**2017**, 286. [Google Scholar] [CrossRef] - Ansari, A.; Jedidi, K.; Jagpal, S. A hierarchical Bayesian methodology for treating heterogeneity in structural equation models. Mark. Sci.
**2000**, 19, 328–347. [Google Scholar] [CrossRef] [Green Version] - Sharkey, P.; Torrats-Espinosa, G.; Takyar, D. Community and the crime decline: The causal effect of local nonprofits on violent crime. Am. Sociol. Rev.
**2017**, 82, 1214–1240. [Google Scholar] [CrossRef] [Green Version] - Wooditch, A.; Johnson, N.J.; Solymosi, R.; Medina Ariza, J.; Langton, S. Bivariate Correlation. In A Beginner’s Guide to Statistics for Criminology and Criminal Justice Using R; Springer: Berlin/Heidelberg, Germany, 2021; pp. 227–244. [Google Scholar]
- Feller, W. An Introduction to Probability Theory and Its Applications; John Wiley & Sons: Hoboken, NJ, USA, 1950; Volume 1. [Google Scholar]
- Armocida, D.; Pesce, A.; Di Giammarco, F.; Frati, A.; Salvati, M.; Santoro, A. Histological, molecular, clinical and outcomes characteristics of Multiple Lesion Glioblastoma. A retrospective monocentric study and review of literature. Neurocirugia
**2021**, 32, 114–123. [Google Scholar] [CrossRef] - Showalter, T.N.; Andrel, J.; Andrews, D.W.; Curran, W.J., Jr.; Daskalakis, C.; Werner-Wasik, M. Multifocal glioblastoma multiforme: Prognostic factors and patterns of progression. Int. J. Radiat. Oncol. Biol. Phys.
**2007**, 69, 820–824. [Google Scholar] [CrossRef] - LeCun, Y.; Bengio, Y.; Hinton, G. Deep learning. Nature
**2015**, 521, 436–444. [Google Scholar] [CrossRef] [PubMed] - Holland, E.C. Glioblastoma multiforme: The terminator. Proc. Natl. Acad. Sci. USA
**2000**, 97, 6242–6244. [Google Scholar] [CrossRef] - Felsher, D.W.; Bishop, J.M. Reversible tumorigenesis by MYC in hematopoietic lineages. Mol. Cell
**1999**, 4, 199–207. [Google Scholar] [CrossRef] - Pelengaris, S.; Littlewood, T.; Khan, M.; Elia, G.; Evan, G. Reversible activation of c-Myc in skin: Induction of a complex neoplastic phenotype by a single oncogenic lesion. Mol. Cell
**1999**, 3, 565–577. [Google Scholar] [CrossRef] [PubMed] - Chin, L.; Tam, A.; Pomerantz, J.; Wong, M.; Holash, J.; Bardeesy, N.; Shen, Q.; O’Hagan, R.; Pantginis, J.; Zhou, H.; et al. Essential role for oncogenic Ras in tumour maintenance. Nature
**1999**, 400, 468–472. [Google Scholar] [CrossRef] [PubMed] - Bilgel, M.; Jedynak, B.; Wong, D.F.; Resnick, S.M.; Prince, J.L. Temporal trajectory and progression score estimation from voxelwise longitudinal imaging measures: Application to amyloid imaging. In Information Processing in Medical Imaging, Proceedings of the 24th International Conference, IPMI 2015, Sabhal Mor Ostaig, Isle of Skye, UK, 28 June– 3 July 2015; Proceedings 24; Springer: Berlin/Heidelberg, Germany, 2015; pp. 424–436. [Google Scholar]
- Li, D.; Iddi, S.; Thompson, W.K.; Donohue, M.C.; Initiative, A.D.N. Bayesian latent time joint mixed effect models for multicohort longitudinal data. Stat. Methods Med Res.
**2019**, 28, 835–845. [Google Scholar] [CrossRef] - Abi Nader, C.; Ayache, N.; Frisoni, G.B.; Robert, P.; Lorenzi, M.; Initiative, A.D.N. Simulating the outcome of amyloid treatments in Alzheimer’s disease from imaging and clinical data. Brain Commun.
**2021**, 3, fcab091. [Google Scholar] [CrossRef] [PubMed] - Marinescu, R.V.; Eshaghi, A.; Alexander, D.C.; Golland, P. BrainPainter: A software for the visualisation of brain structures, biomarkers and associated pathological processes. In Multimodal Brain Image Analysis and Mathematical Foundations of Computational Anatomy, Proceedings of the 4th International Workshop, MBIA 2019, and 7th International Workshop, MFCA 2019, Held in Conjunction with MICCAI 2019, Shenzhen, China, 17 October 2019; Proceedings 4; Springer: Berlin/Heidelberg, Germany, 2019; pp. 112–120. [Google Scholar]
- Burnham, S.C.; Fandos, N.; Fowler, C.; Pérez-Grijalba, V.; Dore, V.; Doecke, J.D.; Shishegar, R.; Cox, T.; Fripp, J.; Rowe, C.; et al. Longitudinal evaluation of the natural history of amyloid-β in plasma and brain. Brain Commun.
**2020**, 2, fcaa041. [Google Scholar] [CrossRef] [Green Version] - Gromeier, M.; Lachmann, S.; Rosenfeld, M.R.; Gutin, P.H.; Wimmer, E. Intergeneric poliovirus recombinants for the treatment of malignant glioma. Proc. Natl. Acad. Sci. USA
**2000**, 97, 6803–6808. [Google Scholar] [CrossRef] - Mitchell, D.A.; Fecci, P.E.; Sampson, J.H. Immunotherapy of malignant brain tumors. Immunol. Rev.
**2008**, 222, 70–100. [Google Scholar] [CrossRef] [Green Version] - Tomaszewski, W.; Sanchez-Perez, L.; Gajewski, T.F.; Sampson, J.H. Brain tumor microenvironment and host state: Implications for immunotherapy. Clin. Cancer Res.
**2019**, 25, 4202–4210. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hotchkiss, K.M.; Sampson, J.H. Temozolomide treatment outcomes and immunotherapy efficacy in brain tumor. J. Neuro-Oncol.
**2021**, 151, 55–62. [Google Scholar] [CrossRef] - Kim, S.S.; Harford, J.B.; Pirollo, K.F.; Chang, E.H. Effective treatment of glioblastoma requires crossing the blood–brain barrier and targeting tumors including cancer stem cells: The promise of nanomedicine. Biochem. Biophys. Res. Commun.
**2015**, 468, 485–489. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lin, K.W.; Liao, A.; Qutub, A.A. Simulation predicts IGFBP2-HIF1α interaction drives glioblastoma growth. PLoS Comput. Biol.
**2015**, 11, e1004169. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ozdemir-Kaynak, E.; Qutub, A.A.; Yesil-Celiktas, O. Advances in glioblastoma multiforme treatment: New models for nanoparticle therapy. Front. Physiol.
**2018**, 9, 170. [Google Scholar] [CrossRef] [Green Version] - Chow, R.D.; Guzman, C.D.; Wang, G.; Schmidt, F.; Youngblood, M.W.; Ye, L.; Errami, Y.; Dong, M.B.; Martinez, M.A.; Zhang, S.; et al. AAV-mediated direct in vivo CRISPR screen identifies functional suppressors in glioblastoma. Nat. Neurosci.
**2017**, 20, 1329–1341. [Google Scholar] [CrossRef] [Green Version] - Decarvalho, A.C.; Kim, H.; Poisson, L.M.; Winn, M.E.; Mueller, C.; Cherba, D.; Koeman, J.; Seth, S.; Protopopov, A.; Felicella, M.; et al. Discordant inheritance of chromosomal and extrachromosomal DNA elements contributes to dynamic disease evolution in glioblastoma. Nat. Genet.
**2018**, 50, 708–717. [Google Scholar] [CrossRef] - Robertson, F.L.; Marqués-Torrejón, M.A.; Morrison, G.M.; Pollard, S.M. Experimental models and tools to tackle glioblastoma. Dis. Model. Mech.
**2019**, 12, dmm040386. [Google Scholar] [CrossRef] [Green Version] - McNutt, T.R.; Benedict, S.H.; Low, D.A.; Moore, K.; Shpitser, I.; Jiang, W.; Lakshminarayanan, P.; Cheng, Z.; Han, P.; Hui, X.; et al. Using big data analytics to advance precision radiation oncology. Int. J. Radiat. Oncol. Biol. Phys.
**2018**, 101, 285–291. [Google Scholar] [CrossRef]

**Figure 1.**Tumor segmentation steps for one randomly selected subject, including the mMRI image (

**left**), the tumor mask image (

**middle**), and the highlighted tumor region in the mMRI image (

**right**).

**Figure 2.**Estimated probability derived from proposed growth model and the corresponding 95% confidence intervals.

**Figure 3.**Correlation between volume and spatial features of brain for tumor region “Edema”. * p < 0.05, ** p < 0.01, *** p < 0.001.

**Figure 4.**Correlation between volume and histology features of brain for tumor region “Edema”. * p < 0.05, ** p < 0.01, *** p < 0.001.

**Figure 5.**Probability that no cancer cells would remain undetected was high when we could find the eventual volume of cancer cells expected to proliferate from the tumor.

**Figure 6.**Correlation between histology and spatial features of brain for tumor region “Edema”. * p < 0.05, ** p < 0.01, *** p < 0.001.

**Figure 7.**Probability that no cancer cells would remain undetected increased from the previous case when we ran a regression of the predicted eventual volume on the different radiomic features of the tumor.

Radiomic Features | Parameters | Mean | Standard Deviation |
---|---|---|---|

Volume | Whole Tumor | 107,999.84 | 52,700.74 |

Edema | 62,139.61 | 35,360.39 | |

Tumor Core | 45,560.24 | 31,424.16 | |

Non-enhancing Tumor | 15,578.29 | 17,475.42 | |

GD-Enhancing Tumor | 29,981.94 | 22,104.20 | |

Spatial Parameters | Spatial Frontal | 25.64 | 35.69 |

Spatial Temporal | 42.39 | 38.89 | |

Spatial Occipital | 4.22 | 14.13 | |

Spatial Insula | 2.95 | 5.76 | |

Spatial Fornix | 1.19 | 3.04 | |

Spatial Parietal | 18.34 | 29.50 | |

Spatial Brain Stem | 0.25 | 0.71 | |

Histology Parameters | Occipital Cortex | 0.375 | 0.8097 |

Temporal Cortex | 0.146 | 0.3546 | |

Basal Ganglia | 0.681 | 1.508 | |

Morphology | Eccentricity | 0.68 | 0.09 |

Solidity | 0.40 | 0.14 | |

Survival Length (in years) | 1.5 | 1.4 |

**Table 2.**Posterior mean values and the corresponding probabilities up to a given fixed time point obtained from the simulated data. Note: The time point did not play any role in this simulation.

Sample No. | Posterior Mean Volume | Probability | ||
---|---|---|---|---|

Estimate | 95% C.I. | Estimate | 95% C.I. | |

43 | 1038 | [1037.924, 1038.076] | 0.5625000 | [0.2944, 0.8306] |

51 | 1346 | [1345.911, 1346.089] | 0.6400000 | [0.4286, 0.8514] |

8 | 3528 | [3527.910, 3528.090] | 0.6944444 | [0.4643, 0.9125] |

65 | 5008 | [5007.907, 5008.093] | 0.7901235 | [0.6155, 0.9245] |

101 | 6224 | [6223.896, 6224.104] | 0.8264463 | [0.7092, 0.9408] |

96 | 6559 | [6558.842, 6559.158] | 0.8622449 | [0.8119, 0.9436] |

12 | 8587 | [8586.837, 8587.163] | 0.9070295 | [0.8732, 0.9570] |

38 | 8990 | [8989.836, 8990.164] | 0.9420415 | [0.9271, 0.9647] |

17 | 9001 | [9000.813, 9001.187] | 0.9674819 | [0.9430, 0.9771] |

74 | 9101 | [9100.723, 9101.277] | 0.9760488 | [0.9579, 0.9990] |

ROIs | Spatial Features | Histology Features | ||||
---|---|---|---|---|---|---|

F-Stat. | p-Val. | ${\mathbf{\rho}}_{\mathbf{vol},\mathbf{spatial}}$ | F-Stat. | p-Val. | ${\mathbf{\rho}}_{\mathbf{vol},\mathbf{histology}}$ | |

ED | 0.8814 | 0.2104 | 0.3445 | 0.8540 | 0.0381 | 0.3826 |

ET | 0.8601 | 0.1083 | 0.3746 | 0.8676 | 0.0076 | 0.3638 |

NET | 0.7899 | 0.0074 | 0.4584 | 0.8822 | 0.0154 | 0.3432 |

TC | 0.7805 | 0.0012 | 0.4685 | - | - | - |

WT | 0.7820 | 0.0052 | 0.4669 | - | - | - |

**Table 4.**Eventual volume of cancer cells (predicted based on the model) and the corresponding probabilities that no cancer cell would remain undetected up to the survival time of the tumor obtained from the actual data for a sample of subjects.

Eventual Volume (In Nearest Cubic mm) | Probability That No Cancer Cells Remain Undetected | Tumor Subregion | ||
---|---|---|---|---|

Estimate | 95% C.I. | Estimate | 95% C.I. | |

9525 | [9433.78, 9616.22] | 0.9937805 | [0.9934967, 0.9940643] | ET |

68,592 | [68,500.78, 68,683.33] | 0.9961458 | [0.9958620, 0.9964296] | ET |

5899 | [5807.78, 5990.22] | 0.9556447 | [0.9553609, 0.9559285] | ET |

31,614 | [31,522.78, 31,705.22] | 0.9907852 | [0.9905014, 0.9910690] | NET |

7338 | [7246.78, 7429.22] | 0.8806554 | [0.8803716, 0.8809392] | NET |

17,679 | [17,587.78, 17,770.22] | 0.9778719 | [0.9775881, 0.9781557] | NET |

34,935 | [34,843.78, 35,026.22] | 0.9738203 | [0.9735365, 0.9741041] | ED |

70,998 | [70,906.78, 71,089.22] | 0.9777224 | [0.9774386, 0.9780062] | ED |

83,517 | [83,425.78, 83,608.22] | 0.9890068 | [0.9887230, 0.9892906] | ED |

117,105 | [117,013.78, 117,196.22] | 0.9839206 | [0.9836368, 0.9842044] | TC |

86,271 | [86,179.78, 86,362.22] | 0.9632160 | [0.9629322, 0.9634998] | TC |

37,513 | [37,421.78, 37,604.22] | 0.9502363 | [0.9499525, 0.9505201] | TC |

279,108 | [278,136.78, 281,916.22] | 0.9618206 | [0.9536135, 0.9871034] | WT |

196,472 | [183,412.78, 203,120.22] | 0.9931245 | [0.9910266, 0.9954483] | WT |

138,532 | [113,574.78, 158,964.22] | 0.9802536 | [0.9795436, 0.9871256] | WT |

**Table 5.**Cross-validation results obtained using R-squared, Akaike Information Criterion (AIC), and an unsupervised learning tool. Note: “Cross Validation” has been abbreviated here as C.V.

ROIs | R-Squared | AIC | C.V. Error | |||
---|---|---|---|---|---|---|

GLM | Bayesian | GLM | Bayesian | GLM | Bayesian | |

ED | 0.7936 | 0.8341 | 212.56 | 179.69 | 0.3637 | 0.2931 |

ET | 0.8924 | 0.9018 | 265.23 | 259.86 | 0.7750 | 0.7236 |

NET | 0.8825 | 0.9341 | 338.53 | 338.38 | 2.1869 | 1.1805 |

TC | 0.5301 | 0.5305 | 301.25 | 251.61 | 0.7304 | 0.7293 |

WT | 0.9176 | 0.9372 | 190.46 | 187.35 | 0.3634 | 0.3130 |

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**MDPI and ACS Style**

Das, A.; Ding, S.; Liu, R.; Huang, C.
Quantifying the Growth of Glioblastoma Tumors Using Multimodal MRI Brain Images. *Cancers* **2023**, *15*, 3614.
https://doi.org/10.3390/cancers15143614

**AMA Style**

Das A, Ding S, Liu R, Huang C.
Quantifying the Growth of Glioblastoma Tumors Using Multimodal MRI Brain Images. *Cancers*. 2023; 15(14):3614.
https://doi.org/10.3390/cancers15143614

**Chicago/Turabian Style**

Das, Anisha, Shengxian Ding, Rongjie Liu, and Chao Huang.
2023. "Quantifying the Growth of Glioblastoma Tumors Using Multimodal MRI Brain Images" *Cancers* 15, no. 14: 3614.
https://doi.org/10.3390/cancers15143614