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Bioengineering
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Mathematical and Computational Modeling of Cancer Progression
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Mathematical and Computational Modeling of Cancer Progression

A special issue of Bioengineering (ISSN 2306-5354). This special issue belongs to the section "Biomedical Engineering and Biomaterials".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 12540

Special Issue Editors

Dr. Leili Shahriyari

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA
Interests: mathematical biology; bioinformatics; mechanistic modeling
Dr. Pasquale De Luca

E-Mail Website
Guest Editor
1. International PhD Programme/UNESCO Chair “Environment, Resources and Sustainable Development”, Department of Science and Technology, Parthenope University of Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
2. Department of Science and Technology, Parthenope University of Naples, Centro Direzionale Isola C4, 80143 Naples, Italy
Interests: deep learning; mathematical; cancer

Special Issue Information

Dear Colleagues,

We invite submissions of manuscripts to this Special Issue, ‘Mathematical and Computational Modeling of Cancer Progression,’ which aims to showcase cutting-edge research highlighting the intersection of mathematics, computational biology, and oncology, with the goal of advancing our understanding of the intricate processes driving cancer progression.

Cancer progression is a multifaceted phenomenon involving intricate interactions between genetic, molecular, and cellular components. Mathematical and computational models offer powerful tools to dissect these complexities, aiding in the identification of critical biomarkers, treatment optimization, and therapeutic development. We encourage submissions that address, but are not limited to, the following topics:

  • Spatial and temporal modeling of tumor growth;
  • Patient-specific modeling and treatment strategies;
  • Computational approaches for tumor microenvironment analysis;
  • Modeling metastasis and therapeutic resistance;
  • Multi-scale modeling in cancer biology;
  • Integration of omics data in cancer modeling;
  • Impact of heterogeneity on disease progression;
  • Machine learning and AI applications in mechanistic modeling of cancer.

Dr. Leili Shahriyari
Dr. Pasquale De Luca
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Bioengineering is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • computational oncology
  • cancer progression
  • cancer treatments
  • mechanistic modeling of cancer
  • integration of machine learning and mechanistic modeling

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (6 papers)

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Research

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22 pages, 14156 KiB  
Article
Plasticity of Expression of Stem Cell and EMT Markers in Breast Cancer Cells in 2D and 3D Culture Depend on the Spatial Parameters of Cell Growth; Mathematical Modeling of Mechanical Stress in Cell Culture in Relation to ECM Stiffness
by Małgorzata Szostakowska-Rodzoś, Mateusz Chmielarczyk, Weronika Zacharska, Anna Fabisiewicz, Agata Kurzyk, Izabella Myśliwy, Zofia Kozaryna, Eligiusz Postek and Ewa A. Grzybowska
Bioengineering 2025, 12(2), 147; https://doi.org/10.3390/bioengineering12020147 - 4 Feb 2025
Viewed by 930
Abstract
The majority of the current cancer research is based on two-dimensional cell cultures and animal models. These methods have limitations, including different expressions of key factors involved in carcinogenesis and metastasis, depending on culture conditions. Addressing these differences is crucial in obtaining physiologically [...] Read more.
The majority of the current cancer research is based on two-dimensional cell cultures and animal models. These methods have limitations, including different expressions of key factors involved in carcinogenesis and metastasis, depending on culture conditions. Addressing these differences is crucial in obtaining physiologically relevant models. In this manuscript we analyzed the plasticity of the expression of stem cell and epithelial/mesenchymal markers in breast cancer cells, depending on culture conditions. Significant differences in marker expression were observed in different growth models not only between 2D and 3D conditions but also between two different 3D models. Differences observed in the levels of adherent junction protein E-cadherin in two different 3D models suggest that spatial parameters of cell growth and physical stress in the culture may affect the expression of junction proteins. To provide an explanation of this phenomenon on the grounds of mechanobiology, these parameters were analyzed using a mathematical model of the 3D bioprinted cell culture. The finite element mechanical model generated in this study includes an extracellular matrix and a group of regularly placed cells. The single-cell model comprises an idealized cytoskeleton, cortex, cytoplasm, and nucleus. The analysis of the model revealed that the stress generated by external pressure is transferred between the cells, generating specific stress fields, depending on growth conditions. We have analyzed and compared stress fields in two different growth conditions, each corresponding to a different elasticity of extracellular matrix. We have demonstrated that soft matrix conditions produce more stress than a stiff matrix in the single cell as well as in cellular spheroids. The observed differences can explain the plasticity of E-cadherin expression in response to mechanical stress. These results should contribute to a better understanding of the differences between various growth models. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling of Cancer Progression)
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9 pages, 2205 KiB  
Article
Intratumoral Chemotherapy: The Effects of Drug Concentration and Dose Apportioning on Tumor Cell Injury
by Jacob S. Warner, C. Matthew Kinsey, Jason H. T. Bates and Vitor Mori
Bioengineering 2024, 11(8), 809; https://doi.org/10.3390/bioengineering11080809 - 9 Aug 2024
Viewed by 1821
Abstract
The addition of intravenous (i.v.) chemotherapy to i.v. immunotherapy for patients with lung cancer results in improved overall survival but is limited by synergistic side effects and an unknown, highly variable final cytotoxic dose within the tumor. The synergy between i.v. chemo- and [...] Read more.
The addition of intravenous (i.v.) chemotherapy to i.v. immunotherapy for patients with lung cancer results in improved overall survival but is limited by synergistic side effects and an unknown, highly variable final cytotoxic dose within the tumor. The synergy between i.v. chemo- and immunotherapies is hypothesized to occur as a result of cell injury caused by chemotherapy, a mechanism demonstrated to drive antigen presentation within the tumor microenvironment. Intratumoral delivery of chemotherapy may thus be optimized to maximize tumor cell injury. To assess the balance between the damage versus the death of tumor cells, we developed a computational model of intratumoral dynamics within a lung cancer tumor for three different chemotherapy agents following direct injection as a function of location and number of injection sites. We based the model on the morphology of a lung tumor obtained from a thoracic CT scan. We found no meaningful difference in the extent of tumor cell damage between a centrally injected versus peripherally injected agent, but there were significant differences between a single injection versus when the total dose was apportioned between multiple injection sites. Importantly, we also found that the standard chemotherapeutic concentrations used for intravenous administration were effective at causing cell death but were too high to generate significant cell injury. This suggests that to induce maximal tumor cell injury, the optimal concentration should be several orders of magnitude lower than those typically used for intravenous therapy. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling of Cancer Progression)
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11 pages, 2149 KiB  
Article
Constructing a Clinical Patient Similarity Network of Gastric Cancer
by Rukui Zhang, Zhaorui Liu, Chaoyu Zhu, Hui Cai, Kai Yin, Fan Zhong and Lei Liu
Bioengineering 2024, 11(8), 808; https://doi.org/10.3390/bioengineering11080808 - 9 Aug 2024
Viewed by 1499
Abstract
Objectives: Clinical molecular genetic testing and molecular imaging dramatically increase the quantity of clinical data. Combined with the extensive application of electronic health records, a medical data ecosystem is forming, which calls for big-data-based medicine models. We tried to use big data analytics [...] Read more.
Objectives: Clinical molecular genetic testing and molecular imaging dramatically increase the quantity of clinical data. Combined with the extensive application of electronic health records, a medical data ecosystem is forming, which calls for big-data-based medicine models. We tried to use big data analytics to search for similar patients in a cancer cohort, showing how to apply artificial intelligence (AI) algorithms to clinical data processing to obtain clinically significant results, with the ultimate goal of improving healthcare management. Methods: In order to overcome the weaknesses of most data processing algorithms that rely on expert labeling and annotation, we uniformly adopted one-hot encoding for all types of clinical data, calculating the Euclidean distance to measure patient similarity and subgrouping via an unsupervised learning model. Overall survival (OS) was investigated to assess the clinical validity and clinical relevance of the model. Results: We took gastric cancers (GCs) as an example to build a high-dimensional clinical patient similarity network (cPSN). When performing the survival analysis, we found that Cluster_2 had the longest survival rates, while Cluster_5 had the worst prognosis among all the subgroups. As patients in the same subgroup share some clinical characteristics, the clinical feature analysis found that Cluster_2 harbored more lower distal GCs than upper proximal GCs, shedding light on the debates. Conclusion: Overall, we constructed a cancer-specific cPSN with excellent interpretability and clinical significance, which would recapitulate patient similarity in the real-world. The constructed cPSN model is scalable, generalizable, and performs well for various data types. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling of Cancer Progression)
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23 pages, 2398 KiB  
Article
Lightweight Low-Rank Adaptation Vision Transformer Framework for Cervical Cancer Detection and Cervix Type Classification
by Zhenchen Hong, Jingwei Xiong, Han Yang and Yu K. Mo
Bioengineering 2024, 11(5), 468; https://doi.org/10.3390/bioengineering11050468 - 8 May 2024
Cited by 4 | Viewed by 3060
Abstract
Cervical cancer is a major health concern worldwide, highlighting the urgent need for better early detection methods to improve outcomes for patients. In this study, we present a novel digital pathology classification approach that combines Low-Rank Adaptation (LoRA) with the Vision Transformer (ViT) [...] Read more.
Cervical cancer is a major health concern worldwide, highlighting the urgent need for better early detection methods to improve outcomes for patients. In this study, we present a novel digital pathology classification approach that combines Low-Rank Adaptation (LoRA) with the Vision Transformer (ViT) model. This method is aimed at making cervix type classification more efficient through a deep learning classifier that does not require as much data. The key innovation is the use of LoRA, which allows for the effective training of the model with smaller datasets, making the most of the ability of ViT to represent visual information. This approach performs better than traditional Convolutional Neural Network (CNN) models, including Residual Networks (ResNets), especially when it comes to performance and the ability to generalize in situations where data are limited. Through thorough experiments and analysis on various dataset sizes, we found that our more streamlined classifier is highly accurate in spotting various cervical anomalies across several cases. This work advances the development of sophisticated computer-aided diagnostic systems, facilitating more rapid and accurate detection of cervical cancer, thereby significantly enhancing patient care outcomes. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling of Cancer Progression)
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14 pages, 2518 KiB  
Article
Modeling the Synergistic Impact of Yttrium 90 Radioembolization and Immune Checkpoint Inhibitors on Hepatocellular Carcinoma
by Minah Kang, Yerim Shin, Yeseul Kim, Sangseok Ha and Wonmo Sung
Bioengineering 2024, 11(2), 106; https://doi.org/10.3390/bioengineering11020106 - 23 Jan 2024
Cited by 2 | Viewed by 2215
Abstract
The impact of yttrium 90 radioembolization (Y90-RE) in combination with immune checkpoint inhibitors (ICIs) has recently gained attention. However, it is unclear how sequencing and dosage affect therapeutic efficacy. The purpose of this study was to develop a mathematical model to simulate the [...] Read more.
The impact of yttrium 90 radioembolization (Y90-RE) in combination with immune checkpoint inhibitors (ICIs) has recently gained attention. However, it is unclear how sequencing and dosage affect therapeutic efficacy. The purpose of this study was to develop a mathematical model to simulate the synergistic effects of Y90-RE and ICI combination therapy and find the optimal treatment sequences and dosages. We generated a hypothetical patient cohort and conducted simulations to apply different treatments to the same patient. The compartment of models is described with ordinary differential equations (ODEs), which represent targeted tumors, non-targeted tumors, and lymphocytes. We considered Y90-RE as a local treatment and ICIs as a systemic treatment. The model simulations show that Y90-RE and ICIs administered simultaneously yield greater benefits than subsequent sequential therapy. In addition, applying Y90-RE before ICIs has more benefits than applying ICIs before Y90-RE. Moreover, we also observed that the median PFS increased up to 31~36 months, and the DM rates at 3 years decreased up to 36~48% as the dosage of the two drugs increased (p < 0.05). The proposed model predicts a significant benefit of Y90-RE with ICIs from the results of the reduced irradiated tumor burden and the associated immune activation and suppression. Our model is expected to help optimize complex strategies and predict the efficacy of clinical trials for HCC patients. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling of Cancer Progression)
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Review

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14 pages, 661 KiB  
Review
Mathematical and Machine Learning Models of Renal Cell Carcinoma: A Review
by Dilruba Sofia, Qilu Zhou and Leili Shahriyari
Bioengineering 2023, 10(11), 1320; https://doi.org/10.3390/bioengineering10111320 - 16 Nov 2023
Cited by 4 | Viewed by 1820
Abstract
This review explores the multifaceted landscape of renal cell carcinoma (RCC) by delving into both mechanistic and machine learning models. While machine learning models leverage patients’ gene expression and clinical data through a variety of techniques to predict patients’ outcomes, mechanistic models focus [...] Read more.
This review explores the multifaceted landscape of renal cell carcinoma (RCC) by delving into both mechanistic and machine learning models. While machine learning models leverage patients’ gene expression and clinical data through a variety of techniques to predict patients’ outcomes, mechanistic models focus on investigating cells’ and molecules’ interactions within RCC tumors. These interactions are notably centered around immune cells, cytokines, tumor cells, and the development of lung metastases. The insights gained from both machine learning and mechanistic models encompass critical aspects such as signature gene identification, sensitive interactions in the tumors’ microenvironments, metastasis development in other organs, and the assessment of survival probabilities. By reviewing the models of RCC, this study aims to shed light on opportunities for the integration of machine learning and mechanistic modeling approaches for treatment optimization and the identification of specific targets, all of which are essential for enhancing patient outcomes. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling of Cancer Progression)
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