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Karunakaran V, Dadgar S, Paidi SK, Mordi AF, Lowe WA, Mim UM, Ivers JD, Rodriguez Troncoso JI, McPeake JA, Fernandes A, Tripathi SD, Barman I, Rajaram N. Investigating In Vivo Tumor Biomolecular Changes Following Radiation Therapy Using Raman Spectroscopy. ACS OMEGA 2024; 9:43025-43033. [PMID: 39464461 PMCID: PMC11500151 DOI: 10.1021/acsomega.4c06096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/02/2024] [Revised: 09/25/2024] [Accepted: 09/30/2024] [Indexed: 10/29/2024]
Abstract
Treatment resistance is a major bottleneck in the success of cancer therapy. Early identification of the treatment response or lack thereof in patients can enable an earlier switch to alternative treatment strategies that can enhance response rates. Here, Raman spectroscopy was applied to monitor early tumor biomolecular changes in sensitive (UM-SCC-22B) and resistant (UM-SCC-47) head and neck tumor xenografts for the first time in in vivo murine tumor models in response to radiation therapy. We used a validated multivariate curve resolution-alternating least-squares (MCR-ALS) model to resolve complex multicomponent Raman spectra into individual pure spectra and their respective contributions. We observed a significant radiation-induced increase in the contributions of lipid-like species (p = 0.0291) in the radiation-sensitive UM-SCC-22B tumors at 48 h following radiation compared to the nonradiated baseline (prior to commencing treatment). We also observed an increase in the contribution of collagen-like species in the radiation-resistant UM-SCC-47 tumors at 24 h following radiation compared to the nonradiated baseline (p = 0.0125). In addition to the in vivo analysis, we performed ex vivo confocal Raman microscopic imaging of frozen sections derived from the same tumors. A comparison of all control and treated tumors revealed similar trends in the contributions of lipid-like and collagen-like species in both in vivo and ex vivo measurements; however, when evaluated as a function of time, longitudinal trends in the scores of collagen-like and lipid-like components were not consistent between the two data sets, likely due to sample numbers and differences in sampling depth at which information is obtained. Nevertheless, this study demonstrates the potential of fiber-based Raman spectroscopy for identifying early tumor microenvironmental changes in response to clinical doses of radiation therapy.
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Affiliation(s)
- Varsha Karunakaran
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Sina Dadgar
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Santosh K. Paidi
- Department
of Mechanical Engineering, Johns Hopkins
University, Baltimore, Maryland 21218, United States
| | - April F. Mordi
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Whitney A. Lowe
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Umme Marium Mim
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Jesse D. Ivers
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Joel I. Rodriguez Troncoso
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Jared A. McPeake
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Alric Fernandes
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Sanidhya D. Tripathi
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
| | - Ishan Barman
- Department
of Mechanical Engineering, Johns Hopkins
University, Baltimore, Maryland 21218, United States
| | - Narasimhan Rajaram
- Department
of Biomedical Engineering, University of
Arkansas, Fayetteville, Arkansas 72701, United States
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Li J, Wang X, Min S, Xia J, Li J. Raman spectroscopy combined with convolutional neural network for the sub-types classification of breast cancer and critical feature visualization. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2024; 255:108361. [PMID: 39116820 DOI: 10.1016/j.cmpb.2024.108361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2024] [Revised: 07/14/2024] [Accepted: 07/29/2024] [Indexed: 08/10/2024]
Abstract
PROBLEMS Raman spectroscopy has emerged as an effective technique that can be used for noninvasive breast cancer analysis. However, the current Raman prediction models fail to cover all the molecular sub-types of breast cancer, and lack the visualization of the model. AIMS Using Raman spectroscopy combined with convolutional neural network (CNN) to construct a prediction model for the existing known molecular sub-types of breast cancer, and selected critical peaks through visualization strategies, so as to achieve the purpose of mining specific biomarker information. METHODS Optimizing network parameters with the help of sparrow search algorithm (SSA) for the multiple parameters in the CNN to improve the prediction performance of the model. To avoid the contingency of the results, multiple sets of data were generated through Monte Carlo sampling and used to train the model, thereby improving the credibility of the results. Based on the accurate prediction of the model, the spectral regions that contributed to the classification were visualized using Gradient-weighted Class Activation Mapping (Grad-CAM), achieving the goal of visualizing characteristic peaks. RESULTS Compared with other algorithms, optimized CNN could obtain the highest accuracy and lowest standard error. And there was no significant difference between using full spectra and fingerprint regions (within 2 %), indicating that the fingerprint region provided the most contribution in classifying sub-types. Based on the classification results from the fingerprint region, the model performances about various sub-types were as follows: CNN (95.34 %±2.18 %)>SVM(94.90 %±1.88 %)>PLS-DA(94.52 %±2.22 %)> KNN (80.00 %±5.27 %). The critical features visualized by Grad-CAM could match well with IHC information, allowing for a more distinct differentiation of sub-types in their spatial positions. CONCLUSION Raman spectroscopy combined with CNN could achieve accurate and rapid identification of breast cancer molecular sub-types. Proposed visualization strategy could be proved from biochemistry information and spatial location, demonstrated that the strategy might be used for the mining of biomarkers in future.
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Affiliation(s)
- Juan Li
- School of Pharmaceutical Sciences and Institute of Materia Medica & Xinjiang Key Laboratory of Biological Resources and Genetic Engineering, College of Life Science and Technology, Xinjiang University, Urumqi, 830017, China
| | - Xiaoting Wang
- School of Pharmaceutical Sciences and Institute of Materia Medica & Xinjiang Key Laboratory of Biological Resources and Genetic Engineering, College of Life Science and Technology, Xinjiang University, Urumqi, 830017, China
| | - Shungeng Min
- College of science, China agriculture university, Beijing, 100094, China
| | - Jingjing Xia
- School of Pharmaceutical Sciences and Institute of Materia Medica & Xinjiang Key Laboratory of Biological Resources and Genetic Engineering, College of Life Science and Technology, Xinjiang University, Urumqi, 830017, China.
| | - Jinyao Li
- School of Pharmaceutical Sciences and Institute of Materia Medica & Xinjiang Key Laboratory of Biological Resources and Genetic Engineering, College of Life Science and Technology, Xinjiang University, Urumqi, 830017, China
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Zhang Y, Li Z, Li Z, Wang H, Regmi D, Zhang J, Feng J, Yao S, Xu J. Employing Raman Spectroscopy and Machine Learning for the Identification of Breast Cancer. Biol Proced Online 2024; 26:28. [PMID: 39266953 PMCID: PMC11396685 DOI: 10.1186/s12575-024-00255-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2024] [Accepted: 09/04/2024] [Indexed: 09/14/2024] Open
Abstract
BACKGROUND Breast cancer poses a significant health risk to women worldwide, with approximately 30% being diagnosed annually in the United States. The identification of cancerous mammary tissues from non-cancerous ones during surgery is crucial for the complete removal of tumors. RESULTS Our study innovatively utilized machine learning techniques (Random Forest (RF), Support Vector Machine (SVM), and Convolutional Neural Network (CNN)) alongside Raman spectroscopy to streamline and hasten the differentiation of normal and late-stage cancerous mammary tissues in mice. The classification accuracy rates achieved by these models were 94.47% for RF, 96.76% for SVM, and 97.58% for CNN, respectively. To our best knowledge, this study was the first effort in comparing the effectiveness of these three machine-learning techniques in classifying breast cancer tissues based on their Raman spectra. Moreover, we innovatively identified specific spectral peaks that contribute to the molecular characteristics of the murine cancerous and non-cancerous tissues. CONCLUSIONS Consequently, our integrated approach of machine learning and Raman spectroscopy presents a non-invasive, swift diagnostic tool for breast cancer, offering promising applications in intraoperative settings.
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Affiliation(s)
- Ya Zhang
- Division of Electrical and Computer Engineering, College of Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Zheng Li
- Division of Electrical and Computer Engineering, College of Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Zhongqiang Li
- Division of Electrical and Computer Engineering, College of Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Huaizhi Wang
- Division of Electrical and Computer Engineering, College of Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Dinkar Regmi
- Division of Electrical and Computer Engineering, College of Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Jian Zhang
- Division of Computer Science & Engineering, College of Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Jiming Feng
- Department of Comparative Biomedical Science, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Shaomian Yao
- Department of Comparative Biomedical Science, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA, 70803, USA
| | - Jian Xu
- Division of Electrical and Computer Engineering, College of Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA.
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Ya N, Zhang D, Wang Y, Zheng Y, Yang M, Wu H, Oudeng G. Recent advances of biocompatible optical nanobiosensors in liquid biopsy: towards early non-invasive diagnosis. NANOSCALE 2024; 16:13784-13801. [PMID: 38979555 DOI: 10.1039/d4nr01719f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
Liquid biopsy is a non-invasive diagnostic method that can reduce the risk of complications and offers exceptional benefits in the dynamic monitoring and acquisition of heterogeneous cell population information. Optical nanomaterials with excellent light absorption, luminescence, and photoelectrochemical properties have accelerated the development of liquid biopsy technologies. Owing to the unique size effect of optical nanomaterials, their improved optical properties enable them to exhibit good sensitivity and specificity for mitigating signal interference from various molecules in body fluids. Nanomaterials with biocompatible and optical sensing properties play a crucial role in advancing the maturity and diversification of liquid biopsy technologies. This article offers a comprehensive review of recent advanced liquid biopsy technologies that utilize novel biocompatible optical nanomaterials, including fluorescence, colorimetric, photoelectrochemical, and Raman broad-spectrum-based biosensors. We focused on liquid biopsy for the most significant early biomarkers in clinical medicine, and specifically reviewed reports on the effectiveness of optical nanosensing technology in the detection of real patient samples, which may provide basic evidence for the transition of optical nanosensing technology from engineering design to clinical practice. Furthermore, we introduced the integration of optical nanosensing-based liquid biopsy with modern devices, such as smartphones, to demonstrate the potential of the technology in portable clinical diagnosis.
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Affiliation(s)
- Na Ya
- Pediatric Research Institute, Shenzhen Children's Hospital, Shenzhen, Guangdong, P.R. China
- Department of Biomedical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, P.R. China
| | - Dangui Zhang
- Pediatric Research Institute, Shenzhen Children's Hospital, Shenzhen, Guangdong, P.R. China
- Research Center of Translational Medicine, Second Affiliated Hospital of Shantou University Medical College, Shantou, Guangdong, P.R. China
| | - Yan Wang
- Department of Biomedical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, P.R. China
| | - Yi Zheng
- Department of Biomedical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, P.R. China
| | - Mo Yang
- Department of Biomedical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, P.R. China
| | - Hao Wu
- Department of Orthopedics, The Eighth Affiliated Hospital, Sun Yat-Sen University, Shenzhen, Guangdong, P.R. China
| | - Gerile Oudeng
- Pediatric Research Institute, Shenzhen Children's Hospital, Shenzhen, Guangdong, P.R. China
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Wiebe M, Milligan K, Brewer J, Fuentes AM, Ali-Adeeb R, Brolo AG, Lum JJ, Andrews JL, Haston C, Jirasek A. Metabolic profiling of murine radiation-induced lung injury with Raman spectroscopy and comparative machine learning. Analyst 2024; 149:2864-2876. [PMID: 38619825 DOI: 10.1039/d4an00152d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/16/2024]
Abstract
Radiation-induced lung injury (RILI) is a dose-limiting toxicity for cancer patients receiving thoracic radiotherapy. As such, it is important to characterize metabolic associations with the early and late stages of RILI, namely pneumonitis and pulmonary fibrosis. Recently, Raman spectroscopy has shown utility for the differentiation of pneumonitic and fibrotic tissue states in a mouse model; however, the specific metabolite-disease associations remain relatively unexplored from a Raman perspective. This work harnesses Raman spectroscopy and supervised machine learning to investigate metabolic associations with radiation pneumonitis and pulmonary fibrosis in a mouse model. To this end, Raman spectra were collected from lung tissues of irradiated/non-irradiated C3H/HeJ and C57BL/6J mice and labelled as normal, pneumonitis, or fibrosis, based on histological assessment. Spectra were decomposed into metabolic scores via group and basis restricted non-negative matrix factorization, classified with random forest (GBR-NMF-RF), and metabolites predictive of RILI were identified. To provide comparative context, spectra were decomposed and classified via principal component analysis with random forest (PCA-RF), and full spectra were classified with a convolutional neural network (CNN), as well as logistic regression (LR). Through leave-one-mouse-out cross-validation, we observed that GBR-NMF-RF was comparable to other methods by measure of accuracy and log-loss (p > 0.10 by Mann-Whitney U test), and no methodology was dominant across all classification tasks by measure of area under the receiver operating characteristic curve. Moreover, GBR-NMF-RF results were directly interpretable and identified collagen and specific collagen precursors as top fibrosis predictors, while metabolites with immune and inflammatory functions, such as serine and histidine, were top pneumonitis predictors. Further support for GBR-NMF-RF and the identified metabolite associations with RILI was found as CNN interpretation heatmaps revealed spectral regions consistent with these metabolites.
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Affiliation(s)
- Mitchell Wiebe
- Department of Computer Science, Mathematics, Physics, and Statistics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Kirsty Milligan
- Department of Computer Science, Mathematics, Physics, and Statistics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Joan Brewer
- Department of Computer Science, Mathematics, Physics, and Statistics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Alejandra M Fuentes
- Department of Computer Science, Mathematics, Physics, and Statistics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Ramie Ali-Adeeb
- Department of Chemistry, The University of Victoria, Victoria, Canada
| | - Alexandre G Brolo
- Department of Chemistry, The University of Victoria, Victoria, Canada
| | - Julian J Lum
- Department of Biochemistry and Microbiology, University of Victoria, Victoria, Canada
- Trev and Joyce Deeley Research Centre, BC Cancer, Victoria, Canada
| | - Jeffrey L Andrews
- Department of Computer Science, Mathematics, Physics, and Statistics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Christina Haston
- Department of Computer Science, Mathematics, Physics, and Statistics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Andrew Jirasek
- Department of Computer Science, Mathematics, Physics, and Statistics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
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Cheng N, Gao Y, Ju S, Kong X, Lyu J, Hou L, Jin L, Shen B. Serum analysis based on SERS combined with 2D convolutional neural network and Gramian angular field for breast cancer screening. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2024; 312:124054. [PMID: 38382221 DOI: 10.1016/j.saa.2024.124054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Revised: 02/08/2024] [Accepted: 02/17/2024] [Indexed: 02/23/2024]
Abstract
Breast cancer is a significant cause of death among women worldwide. It is crucial to quickly and accurately diagnose breast cancer in order to reduce mortality rates. While traditional diagnostic techniques for medical imaging and pathology samples have been commonly used in breast cancer screening, they still have certain limitations. Surface-enhanced Raman spectroscopy (SERS) is a fast, highly sensitive and user-friendly method that is often combined with deep learning techniques like convolutional neural networks. This combination helps identify unique molecular spectral features, also known as "fingerprint", in biological samples such as serum. Ultimately, this approach is able to accurately screen for cancer. The Gramian angular field (GAF) algorithm can convert one-dimensional (1D) time series into two-dimensional (2D) images. These images can be used for data visualization, pattern recognition and machine learning tasks. In this study, 640 serum SERS from breast cancer patients and healthy volunteers were converted into 2D spectral images by Gramian angular field (GAF) technique. These images were then used to train and test a two-dimensional convolutional neural network-GAF (2D-CNN-GAF) model for breast cancer classification. We compared the performance of the 2D-CNN-GAF model with other methods, including one-dimensional convolutional neural network (1D-CNN), support vector machine (SVM), K-nearest neighbor (KNN) and principal component analysis-linear discriminant analysis (PCA-LDA), using various evaluation metrics such as accuracy, precision, sensitivity, F1-score, receiver operating characteristic (ROC) curve and area under curve (AUC) value. The results showed that the 2D-CNN model outperformed the traditional models, achieving an AUC value of 0.9884, an accuracy of 98.13%, sensitivity of 98.65% and specificity of 97.67% for breast cancer classification. In this study, we used conventional nano-silver sol as the SERS-enhanced substrate and a portable laser Raman spectrometer to obtain the serum SERS data. The 2D-CNN-GAF model demonstrated accurate and automatic classification of breast cancer patients and healthy volunteers. The method does not require augmentation and preprocessing of spectral data, simplifying the processing steps of spectral data. This method has great potential for accurate breast cancer screening and also provides a useful reference in more types of cancer classification and automatic screening.
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Affiliation(s)
- Nuo Cheng
- School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China
| | - Yan Gao
- School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China; Chinese Academy of Science, Shenzhen Institutes of Advanced and Technology, Shenzhen 518000, PR China
| | - Shaowei Ju
- School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China
| | - Xiangwei Kong
- School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China
| | - Jiugong Lyu
- School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China; School of Biological Engineering, Dalian University of Technology, Dalian 116024, PR China
| | - Lijie Hou
- School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China
| | - Lihong Jin
- School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China
| | - Bingjun Shen
- School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China
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Fuentes AM, Milligan K, Wiebe M, Narayan A, Lum JJ, Brolo AG, Andrews JL, Jirasek A. Stratification of tumour cell radiation response and metabolic signatures visualization with Raman spectroscopy and explainable convolutional neural network. Analyst 2024; 149:1645-1657. [PMID: 38312026 DOI: 10.1039/d3an01797d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2024]
Abstract
Reprogramming of cellular metabolism is a driving factor of tumour progression and radiation therapy resistance. Identifying biochemical signatures associated with tumour radioresistance may assist with the development of targeted treatment strategies to improve clinical outcomes. Raman spectroscopy (RS) can monitor post-irradiation biomolecular changes and signatures of radiation response in tumour cells in a label-free manner. Convolutional Neural Networks (CNN) perform feature extraction directly from data in an end-to-end learning manner, with high classification performance. Furthermore, recently developed CNN explainability techniques help visualize the critical discriminative features captured by the model. In this work, a CNN is developed to characterize tumour response to radiotherapy based on its degree of radioresistance. The model was trained to classify Raman spectra of three human tumour cell lines as radiosensitive (LNCaP) or radioresistant (MCF7, H460) over a range of treatment doses and data collection time points. Additionally, a method based on Gradient-Weighted Class Activation Mapping (Grad-CAM) was used to determine response-specific salient Raman peaks influencing the CNN predictions. The CNN effectively classified the cell spectra, with accuracy, sensitivity, specificity, and F1 score exceeding 99.8%. Grad-CAM heatmaps of H460 and MCF7 cell spectra (radioresistant) exhibited high contributions from Raman bands tentatively assigned to glycogen, amino acids, and nucleic acids. Conversely, heatmaps of LNCaP cells (radiosensitive) revealed activations at lipid and phospholipid bands. Finally, Grad-CAM variable importance scores were derived for glycogen, asparagine, and phosphatidylcholine, and we show that their trends over cell line, dose, and acquisition time agreed with previously established models. Thus, the CNN can accurately detect biomolecular differences in the Raman spectra of tumour cells of varying radiosensitivity without requiring manual feature extraction. Finally, Grad-CAM may help identify metabolic signatures associated with the observed categories, offering the potential for automated clinical tumour radiation response characterization.
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Affiliation(s)
- Alejandra M Fuentes
- Department of Physics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Kirsty Milligan
- Department of Physics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Mitchell Wiebe
- Department of Physics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
| | - Apurva Narayan
- Department of Computer Science, Western University, London, Canada
- Department of Computer Science, The University of British Columbia Okanagan Campus, Kelowna, Canada
| | - Julian J Lum
- Department of Biochemistry and Microbiology, The University of Victoria, Victoria, Canada
- Trev and Joyce Deeley Research Centre, BC Cancer, Victoria, Canada
| | - Alexandre G Brolo
- Department of Chemistry, The University of Victoria, Victoria, Canada
| | - Jeffrey L Andrews
- Department of Statistics, The University of British Columbia Okanagan Campus, Kelowna, Canada
| | - Andrew Jirasek
- Department of Physics, The University of British Columbia Okanagan Campus, Kelowna, Canada.
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